Seismic Guidelines January 2010

IITK-RDSO GUIDELINES ON SEISMIC DESIGN OF RAILWAY BRIDGES

Provisions with Commentary and Explanatory Examples

Indian Institute of Technology Kanpur

Research Designs and Standards Organisation Lucknow

November 2010

NATIONAL INFORMATION CENTRE OF EARTHQUAKE ENGINEERING



Developed for Indian Railways

Prepared by: Indian Institute of Technology Kanpur Kanpur

With Funding by: Research Designs and Standards Organisation Lucknow

November 2010

NATIONAL INFORMATION CENTRE OF EARTHQUAKE ENGINEERING

The material presented in this document is to help educate engineers/designers on the subject. This document has been prepared in accordance with generally recognized engineering principles and practices. While developing this material, many international codes, standards and guidelines have been referred. This document is intended for the use by individuals who are competent to evaluate the significance and limitations of its content and who will accept responsibility for the application of the material it contains. The authors, publisher and sponsors will not be responsible for any direct, accidental or consequential damages arising from the use of material content in this document.

Preparation of this document was supported by Railway Design and Standards Organisations (RDSO), Lucknow, through a project at Indian Institute of Technology Kanpur, using World Bank finances. The views and opinions expressed in this document are those of the authors and not necessarily of the RDSO, or IIT Kanpur.

The material presented in these guidelines cannot be reproduced without written permission, for which please contact: Co-ordinator, National Information Center of Earthquake Engineering, Indian Institute of Technology Kanpur, Kanpur 208 016 ([email protected]).

Copies of this publication can be requested from:

National Information Center of Earthquake Engineering Department of Civil Engineering Indian Institute of Technology Kanpur Kanpur 208 016 Email: [email protected] Website: www.nicee.org ISBN .................................

PARTICIPANTS

Prepared by:

Sudhir K. Jain, Indian Institute of Technology Kanpur

Durgesh C. Rai, Indian Institute of Technology Kanpur

O. R. Jaiswal, Visvesvaraya National Institute of Technology, Nagpur

Coordinated by:-

R. K.Goel, Director/SB-I/B&S/RDSO

Review comments from RDSO, Lucknow by:

Piyush Agarwal, the then Executive Director/B&S

Mahesh Kr. Gupta, Executive Director/B&S

R. K. Goel, Director/ SB-I, B&S

Pradip Kumar, Director/ CB-II, B&S

Anil Kalra, Director/ CB-I, B&S

Vivek Bhushan Sood, Professor/Bridge, IRICEN, Pune.

Atul Verma, ADEN/Bridge Design/SEC Railway at RDSO.

H. O. Narayan, Asstt. Design Engr., B&S

R. N. Shukla, Senior Section Engineer/Design, B&S

Sujeet Nath Gupta, Section Engineer/Design, B&S

S. S. Singh, Section Engineer/Design, B&S

Additional Review Comments by:

Debasis Roy, Indian Institute of Technology Kharagpur

S. K. Thakkar, Indian Institute of Technology Roorkee

Mahesh Tandon, Tandon Consultant, Delhi

Laxmy Parameswaran, Central Road Research Institute, Delhi

T. Viswanathan, Aarvee Associates Architects Engineers & Consultants Pvt. Ltd., Delhi

Alok Bhowmick, B & S Engineering Consultants Pvt. Ltd., Delhi

D. B. Rao, NBRDC, Hyderabad

A. K. Gupta, Professor & Head, Structural Engineering Department, MBM Engineering College, Jodhpur

K. N. Sreenivasa, L&T Railway Business Unit, Faridabad

P. K. Jain, Chief Engineer/KRCL, New Delhi

Milind Bhoot, IBG Asia, Mumbai

PREFACE

In India, there are three codes / standards for seismic design of bridges. These are: IRC 6 of Indian Road Congress, IS 1893 of Bureau of Indian Standards and existing Bridge Rules of Indian Railways. IRC 6, published by the Indian Road Congress, deals with highway bridges and its seismic loading provisions have been modified in 2006, to bring them in line with the IS 1893(Part 1):2002. Bureau of Indian Standards code, IS 1893(1984) has provisions for highway as well as railway bridges. The revised version of this code, which is to be published as IS 1893(Part 3), has not yet been finalized. Existing Bridge Rules of the Indian Railways has derived its seismic loading provisions from IS 1893 (1984). In these provisions, seismic coefficient method is used for bridges, wherein design seismic coefficient does not depend on the flexibility of the bridge. Moreover, the ductility of bridge components is not considered while calculating the design seismic loads. Similarly, there are no details about response spectrum and time history analysis. The present guidelines on seismic design of railway bridges have been developed under a project given to IIT Kanpur by the Indian Railways. The scope of these guidelines is limited to the seismic design of new railway bridges and these shall not be used for seismic evaluation of the existing railway bridges. The provisions included herein, are in line with the general provisions of IS 1893(Part 1):2002. For example, the zone map is taken from IS 1893(Part 1) and the response spectra is similar to the one used in IS 1893(Part 1). In line with the present international practice, these guidelines are written in two column format with provision on the left side and explanatory commentary on the right side. The purpose of commentary is to explain background / concept / basis of the provision. The commentary should help understand the provision better and remove any confusion, but cannot be used in lieu of the provision.

This document was developed by a team consisting of Professor Sudhir K. Jain, Professor Durgesh C. Rai (Indian Institute of Technology Kanpur) and Professor O. R. Jaiswal (Visvesvaraya National Institute of Technology, Nagpur). Effective coordination was done from RDSO side by Shri R.K.Goel, Director/SB-I/B&S/RDSO to communicate the various parts to concerned officials at RDSO & with other organizations and giving feed back to I.I.T.-Kanpur. Engineers from RDSO, Luckow have reviewed several versions of this document. Piyush Agarwal, the then Executive Director/B&S; Mahesh Kr. Gupta, Executive Director/B&S; R.K. Goel, Director/ SB-I, B&S; Pradip Kumar, Director/ CB-II, B&S; Anil Kalra, Director/ CB-I, B&S; Vivek Bhushan Sood, Professor/Bridge, IRICEN, Pune; Atul Verma, ADEN/Bridge Design/SEC Railway at RDSO; H. O. Narayan, Asstt. Design Engr., B&S; R.N. Shukla, Senior Section Engineer/Design, B&S; Sujeet Nath Gupta, Section Engineer/Design, B&S have provided valuable suggestions to improve the same. Comments and suggestions have also been received from Debasis Roy, Indian Institute of Technology Kharagpur; S K Thakkar, Indian Institute of Technology Roorkee; Mahesh Tondon, Tandon Consultant, Delhi; Laxmy Parameswaran, Central Road Research Institute, Delhi; T. Viswanathan, Aarvee Associates architects engineers & consultants Pvt. Ltd., Delhi; Alok Bhowmick, B & S Engineering Consultants Pvt. Ltd., Delhi; D.B. Rao, NBRDC, Hyderabad; A. K. Gupta, Professor & Head, Structural Engineering Department, MBM Engineering College, Jodhpur K. N. Sreenivasa, L&T Railway Business Unit, Faridabad; P. K. Jain, Chief Engineer/KRCL, New Delhi; Milind Bhoot, IBG Asia, Mumbai.

IIT Kanpur

RDSO Lucknow

CONTENTS

PART 1: Provisions and Commentary

1. Terminology ........................................................................................................................... 1

2. Symbols ............................................................................................................................. 5

3. Introduction ............................................................................................................................ 8

3.1 - General .........................................................................................................................................8 3.2 - Modifications over Existing Bridge Rules ................................................................................8 3.3 - Railway and Road Bridges ......................................................................................................10 3.4 - References.................................................................................................................................11

4. Relevant Codes/ Standards................................................................................................. 12

5. Scope ........................................................................................................................... 13

6. General concepts................................................................................................................. 14

6.1 - ......................................................................................................................................................14 6.2 - ......................................................................................................................................................14 6.3 - ......................................................................................................................................................14 6.4 - ......................................................................................................................................................15 6.5 - ......................................................................................................................................................15 6.6 - ......................................................................................................................................................15 6.7 - ......................................................................................................................................................15 6.8- Ground Motion ............................................................................................................................18 6.9 - Assumptions...............................................................................................................................18

7. Conceptual Considerations.................................................................................................. 20

8. Design Criteria ..................................................................................................................... 23

8.1 - Seismic Zone Map ....................................................................................................................23 8.2 - Importance Factor .....................................................................................................................24 8.3 - Methods of Calculating Design Seismic Force.....................................................................26 8.4 - Seismic Weight and Live Load................................................................................................29 8.5 - Combination of Seismic Components....................................................................................30 8.6 - Damping and soil Properties ...................................................................................................33 8.7 - Combination of Seismic Design Forces with Other Forces ................................................37 8.8 - Vertical Motions .........................................................................................................................39

9. Seismic Coefficient Method (Single mode Method)............................................................. 41

9.1 - Elastic Seismic Acceleration Coefficient................................................................................42 9.2 - Maximum Elastic Forces and Deformations .........................................................................46 9.3 - Design Seismic Force Resultants for Bridge Components.................................................47

10. Response Spectrum Method (Multi mode Method) ........................................................... 51

10.1 - Elastic Seismic Acceleration Coefficient in Mode k ...........................................................51 10.2 - Inertia Force due to Mass of Bridge at Node j in Mode k .................................................53 10.3 - Maximum Elastic Forces and Deformations .......................................................................55 10.4 - Design Seismic Force Resultants in Bridge Components................................................56 10.5 - Multi-directional Shaking........................................................................................................57

11. Time History Method.......................................................................................................... 58

11.1 - Modeling of Bridge..................................................................................................................58 11.2 - Analysis ....................................................................................................................................58 11.3 - Ground Motion.........................................................................................................................59 11.4 - Interpretation of Time History Analysis Results .................................................................60

12. Pushover Analysis ............................................................................................................. 62

13. Superstructure ................................................................................................................... 63

13.1- .....................................................................................................................................................63 13.2 - ....................................................................................................................................................63 13.3 - ....................................................................................................................................................63

14. Substructure ...................................................................................................................... 68

14.1 - Scour Depth .............................................................................................................................68 14.2 - Hydrodynamic Force ..............................................................................................................68 14.3 - Design Seismic Foce..............................................................................................................72 14.4 - Substructure of Continuous Girder Superstructure ...........................................................73

15. Foundations ....................................................................................................................... 74

15.1 - ....................................................................................................................................................74 15.2 - ....................................................................................................................................................74 15.3 - ....................................................................................................................................................74

16. Connections....................................................................................................................... 76

16.1 - Design Force for Connections ..............................................................................................76 16.2 - Displacements at Connections .............................................................................................77 16.3 - Minimum Seating Width Requirements ...............................................................................77

17. Special Ductile Detailing Requirements for Bridges Substructures ................................... 80

18. Special Devices ................................................................................................................. 81

18.1 - Seismic Isolation Devices......................................................................................................81 18.2 - Shock Transmission Units .....................................................................................................81

19. Bridges with Seismic Isolation ........................................................................................... 83

19.1 - General .....................................................................................................................................83 19.2 - Design Criteria.........................................................................................................................86 19.3 - Analysis Procedure.................................................................................................................87 19.4 - Requirements on Isolator Unit ..............................................................................................88 19.5 - Tests on Isolation System .....................................................................................................90 19.6 - System Adequacy ...................................................................................................................94 19.7 - Requirements for Elastomeric Bearings..............................................................................94

20. Post earthquake Operation and Inspection ....................................................................... 97

Appendix – (A) References...................................................................................................... 98

Appendix – (B) Relevant Codes and Standards ...................................................................... 99

Appendix – (C) Ductile Detailing Specifications..................................................................... 100

Appendix – (D) Zone Factors for Some Important Towns ..................................................... 107

Appendix – (E) Pushover Analysis ........................................................................................ 108

Appendix – (F) Dynamic Earth Pressure ............................................................................... 111

Appendix – (G) Simplified Procedure for Evaluation of Liquefaction Potential ...................... 115

Appendix – (H) System property modification factors............................................................ 125

Appendix – (I) Post Earthquake Operations and Inspections ................................................ 129

PART 2: Explanatory Examples

Example 1 – Railway Bridge with Simply Supported Steel Superstructure ........................... 132

Example 2 – Comparison of Design Seismic Forces for Short and Long Span Railway Bridges140

Example 3 – Calculation of Seismic Forces for Superstructure............................................. 145

Example 4 – Analysis of Superstructure for Vertical Component of Earthquake................... 154

Example 5 – Base Isolated Railway Bridge with Simply Supported Steel Superstructure .... 157

Example 6 – M- curve for a Reinforced Concrete (RC) Section .......................................... 164

Example 7 – Obtain plastic moment, MP for RC pier and the maximum seismic coefficient required for plastic hinge formation .................................................................. 168

Example 8 - Liquefaction Analysis using SPT data ............................................................... 170

Example 9 - Liquefaction Analysis using CPT data ............................................................... 172



Part 1 – Provisions and Commentary

IITK-RDSO Guidelines for Seismic Design of Railway Bridges

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1. Terminology For the purpose of these guidelines, the following terms are defined

Base

The level at which inertia forces generated in the substructure and superstructure are transferred to the foundation.

Bearing

An element often used to connect bridge girders to piers and abutments. Bearing are designed to allow or prevent rotation and translation in different directions.

Bent

The intermediate support under the superstructure. A bent may have one or more columns, or it may consist of a pier wall.

Bridge Flexibility Factor (Sa/g)

Also called Response Acceleration Coefficient (Sa/g). It is a factor to obtain the elastic acceleration spectrum depending on flexibility of the structure; it depends on natural period of vibration of the bridge.

Center of Mass

The point through which the resultant of the masses of a system acts. This point corresponds to the center of gravity of the system.

Closely-Spaced Mode

Closely-Spaced modes of a structure are those of its natural modes of vibration whose natural frequencies differ from each other by 10 percent or less of the lower frequency.

Critical Damping

The minimum damping above which free vibration motion is not oscillatory.

Damping

The effect of internal friction, imperfect elasticity of material, slipping, sliding, etc., in reducing the amplitude of vibration and is expressed as a percentage of critical damping.

Design Acceleration Spectrum

It refers to graph of maximum acceleration as a function of natural frequency or natural period of vibration of a Single Degree Of Freedom (SDOF) system, for a specified damping ratio to be used in the design of structures.

Design Horizontal Coefficient

It is a horizontal acceleration coefficient that shall be used to obtain design horizontal seismic force on structures. Refer clause 9.1 and 10.1

Design Seismic Force

The seismic force prescribed by this standard for each bridge component that shall be used in its design. It is obtained as the maximum elastic seismic force divided by the appropriate response reduction factor specified in this standard for each component. Refer clause 9.3 and 10.3.

Design Seismic Force Resultant (V)

The force resultant (namely axial force, shear force, bending moment or torsional moment) at a cross-section of the bridge due to design seismic force for shaking along a considered direction applied on the structure.

Ductility


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Ductility of a structure, or its members, is the capacity to undergo large inelastic deformations without significant loss of strength or stiffness.

Ductile Detailing

The preferred choice of location and amount of reinforcement in reinforced concrete structures to provide for adequate ductility in them. In steel structures, it is the design of members and their connections to make them adequately ductile.

Elastic Seismic Acceleration Coefficient (Ah)

A plot of horizontal acceleration value, as a fraction of acceleration due to gravity, versus natural period of vibration T that shall be used in the design of structures.

Epicenter

The geographical point on the surface of the earth vertically above the focus of the earthquake.

Focus

The point inside earth on the fault where the slip starts that causes the earthquake.

Importance Factor (I)

A factor used to obtain the design spectrum depending on the importance of the structure.

Linear Elastic Analysis

Analysis of the structure considering linear properties of the material and load-versus deformation characteristics of the different component of the structure.

Liquefaction

Liquefaction is the state in saturated cohesion less soil wherein the effective shear strength is reduced to negligible value during an earthquake due to pore pressures caused by vibrations approaching the total confining pressure. In this situation, the soil tends to behave like a fluid mass.

Magnitude

The magnitude of earthquake is a number which is a measure of energy released in an earthquake. It is defined as logarithm to the base 10 of the maximum trace amplitude, expressed in microns, which the standard short-period torsion seismometer world register due to the earthquake at an epicenteral distance of 100 km.

Maximum Considered Earthquake (MCE)

Maximum considered earthquake is the largest reasonably conceivable earthquake that appears possible along a recognized fault or within a tectonic province.

Maximum Elastic Force Resultant (Fenet)

The force resultant (namely axial force, shear force, bending moment or torsional moment) at a cross-section of the bridge due to maximum elastic seismic force for shaking along a considered direction applied on the structure.

Maximum Elastic Seismic Force (Fe)

The maximum force in the bridge component due to the expected seismic shaking in the considered seismic zone.

Modal Mass (Mk)

Modal mass of structure subjected to horizontal or vertical ground motion is a part of total seismic mass of the structure that is effective in mode k of vibration. The modal mass for a given mode has a unique value irrespective of scaling of the mode shape.

Mode Shapes Coefficient (Φjk)

The spatial pattern of vibration when the structure is vibrating in its normal mode k is called as mode


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shape of vibration of mode k. Φjk is coefficient for jth node in kth mode.

Natural Period

Natural period of a structure is its time period of undamped vibration.

(a) Fundamental Natural Period: It is the highest modal time period of vibration along the considered direction of earthquake motion.

(b) Modal Natural Period: The modal natural period of mode k is the time period of vibration in mode k.

Normal Mode

Mode of vibration at which all its masses attain maximum values of displacements and rotations simultaneously, and they also pass through equilibrium positions simultaneously.

Over strength

Strength considering all factors that may cause an increase, e.g., steel strength being higher than the specified characteristic strength, effect of strain hardening in steel with large strains, and concrete strength being higher than specified characteristic value.

P- Δ Effect

IT is the secondary effect on shears and moments of frame members due to action of the vertical loads , interacting with the lateral displacement of structure resulting from seismic forces.

Response Acceleration Coefficient (Sa/g)

It is factor denoting the design acceleration spectrum of the structure subjected to earthquake ground motion, and depends on natural period of vibration and damping of structures.

Response Reduction Factor (R)

The factor by which the actual lateral force, that would be generated if the structure were to remain elastic during the most severe shaking that is likely at that site, shall be reduced to obtain the design lateral force.

Response Spectrum

It is a representation of the maximum response of idealized single degree of freedom systems of different periods for a fixed value of damping, during that earthquake. The maximum response is plotted against the undamped natural period and for various damping values, and can be expressed in terms of maximum absolute acceleration, maximum relative velocity or maximum relative displacement.

Restrainer

A steel rod, steel cable, rubber-impregnated chain, or similar device that prevents a superstructure from becoming unseated during an earthquake.

Seismic Mass

Seismic weight divided by acceleration due to gravity.

Seismic Weight ( W )

Total dead load plus part of live load.

Skew

The angle between the centerline of the superstructure and a horizontal line perpendicular to the abutments or bents.

Soil Profile Factor

A factor used to obtain the elastic acceleration spectrum depending on the soil profile underneath the structure at the site.

Strength

The usable capacity of a structure or its members to resist the applied loads.


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Stiffness of Piers ( or bents )

The force required to produce unit deformation in the pier under a lateral load applied at its top.

Substructure

Elements such as piers, abutments, and foundations that support the superstructure.

Superstructure

The bridge elements supported by the substructure.

Zone Factor (Z)

A factor to obtain the design spectrum depending on the perceived seismic risk of the earthquake zone in which the structure is located.


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2. Symbols a Structural width in the direction of hydrodynamic pressure

A Elastic seismic acceleration coefficient

Ao Sectional area of the substructure

Ac Area of the concrete core = 2

kD4

Ag Gross area of the column cross section

Ak Elastic seismic acceleration coefficient of mode

rA As per APPENDIX C, Area of confined core concrete in the rectangular hoop

measure to its outer side dimensions

Ash Area of cross-section of circular hoop

b Structural width perpendicular to hydrodynamic pressure

B

BI

Bonded plan dimension or bonded diameter in loaded direction of rectangular

bearing or diameter of circular bearing,

Damping coefficient (Table -10)

Ce

Hydrodynamic force coefficient

Cj Fraction of missing mass for jth mode.

C1, C2, C3, C4

Pressure coefficients to estimate flow load due to stream on the substructure

Dk Diameter of core measured to the outside of the spiral or hoops

di Thickness of any layer

Ec Modulus of elasticity of concrete

EDC Energy dissipated per cycle ( Figure – 11 )

Ex, Ey Earthquake force in x-and y-direction respectively

Es Modulus of elasticity of steel

F Hydrodynamic force on substructure; (also, Horizontal force in kN applied at center of mass of superstructure for one mm horizontal deflection of bridge along considered direction of horizontal force)

Fe Inertia force due to mass of a bridge component under earthquake shaking along a

direction

Fmissing Lateral force associated with missing mass

fck Characteristic strength of concrete at 28 days in MPa.

fy Yield stress of steel

ekF Inertia force vector due to mass of bridge under earthquake shaking along a

direction in mode k

Fp Maximum Positive force

Fn Maximum Negative force


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enetF

Maximum elastic force resultants at a cross-section due to all modes considered

Fmax Maximum force

Fy Yield Force

g Acceleration due to gravity

h Longer dimension of the rectangular confining hoop measured to its outer face

Hp Height of Pier

I Importance Factor

K Bulk modulus of elastomer

Kd , Ku & Keff

Post – elastic stiffness, Elastic ( unloading ) stiffness , Effective stiffness resp.

( Clause 19.4.2 and Figure – 11 )

eiK

Smaller effective stiffness

ejK larger effective stiffness

L

Length (in meters) of the superstructure to the adjacent expansion joint or to the end of superstructure. In case of bearings under suspended spans, it is sum of the lengths of the two adjacent portions of the superstructure. In case of single span bridges, it is equal to the length of the superstructure

m Number of modes of vibration considered

jm Total mass of the jth mode

]m[ Seismic mass matrix of the bridge structure

My Moment Capacity of the column/pier section at the first yield of the reinforcing steel

OM Sum of the over strength moment capacities of the hinges resisting lateral loads

N Average SPT value of the soil profile

Ni Standard penetration resistance of layer i

kP Modal participation factor of mode k of vibration

bp Pressure due to fluid on submerged superstructures

Qd Characteristic strength

R Response Reduction Factor

321 rrr ,, Force resultants due to full design seismic force along two principal horizontal directions and along the vertical direction, respectively

S Pitch of spiral or spacing of hoops

g

Sa Bridge flexibility factor along the considered direction

k

a

g

S

Bridge flexibility factor of mode k of vibration

ti Thickness of ith layer


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1T Fundamental natural period of vibration of bridge in considered direction

kT Natural Period of Vibration of mode k

Tr Total elastomer thickness

su

Displacement at position s caused in the acting direction of inertial force when the force corresponding to the weight of the superstructure and substructure above the ground surface for seismic design is assumed to act in the acting direction of inertial force

V

Lateral Shear Force

eV

Maximum elastic force resultant at a cross-section of a bridge component

netV

Design seismic force resultant in any component of the bridge due to all modes considered

W

Seismic weight, which includes full dead load and part live load

21,, WWWb Widths of seating at bearing supports at expansion ends of girders.

eW Weight of water in a hypothetical enveloping cylinder around a substructure

Z Seismic zone factor

1 Vector consisting of unity (one) associated with translational degrees of freedom in the considered direction of shaking, and zero associated with all other degrees of freedom

Displacement at the acting position of inertial force of the superstructures when the force corresponding to 80% of the weight of the substructure above the ground surface for seismic design and all weight of the superstructure portion supported by it is assumed to act in the acting direction of inertial force (m)

P Maximum positive displacement

n Maximum negative displacement

max Maximum bearing displacement ( Figure 11)

Y yield displacement

EdF Additional vertical load due to seismic overturning effects, base on peak response under the design seismic action

Ratio of natural frequencies of modes i and j, Also equivalent damping ratio ( Sec.19.5.8)

k Mode shape vector of the bridge in mode k of vibration

jk Mode shape coefficient for jth, degree of freedom in kth mode of vibration

y Yield Curvature

Net response due to all modes considered

k Response in mode k of vibration

gmissin Maximum response of missing mass


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PROVISIONS COMMENTARY

3. Introduction C3.0 Introduction

3.1 - General The present guidelines deal with the seismic design of new railway bridges. These guidelines have been developed to reduce the damage from earthquakes. Bridges and portions thereof shall be designed and constructed, to resist the effects of design seismic force specified in these guidelines as a minimum. The intention of these guidelines is to ensure that bridges possess at least a minimum strength to withstand earthquakes. The intention is not to prevent damage to them due to the most severe shaking that they may be subjected to during their lifetime.

C3.1- General Bridges play an important role in the efficient functioning of railway transport. Reliability against the natural calamities like earthquakes is of serious concern for safety of passengers, goods, and employees. Bridges are lifeline structures and need to remain functional after the design earthquake. The designer may choose to design bridges for seismic forces larger than those specified in this code and but not less.

3.2 - Modifications over Existing Bridge Rules As compared to the seismic loading provisions of the existing Bridge Rules of Indian Railways, following important provisions and changes have been included :

C3.2- Modifications Over Existing Bridge Rules In our country, three codes/standards deal with the seismic design of bridges. These are: IS 1893 (1984), IRC 6:2000 and existing Bridge Rules of Indian Railways. Amongst these, IRC 6 (2000) is the latest one and it deals with highway bridges only. IS 1893 is under revision. The seismic loading provisions of the existing Bridge Rules are based on IS 1893(1984) and have not been revised since very long time.

a) Effect of flexibility of the bridge on the design seismic force is included with the help of time period of bridge.

a) In the present guidelines, first maximum earthquake force which will act on the bridge (also called elastic earthquake force) is obtained. Then, depending on ductility and energy dissipating capacity of different bridge component, design force is specified for different bridge component. In contrast to this, the existing Bridge Rules provisions, suggest seismic coefficient method for bridges. In this method, the seismic coefficient for different zone is specified and this coefficient is same for all types of bridges. Thus, design earthquake force does not depend on the structural dynamic characteristics of the bridges. For example, as per existing Bridge Rules, the design seismic coefficient for a bridge with pier height of 10 m and 30 m will be same, and it does not depend on the flexibility of the bridge.


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PROVISIONS COMMENTARY b) The concept of design earthquake force for elastic behavior of bridge and reduction in design earthquake using inelastic behavior by considering ductility of components is included.

b) In existing Bridge Rules, the design seismic

forces are directly specified, which is often misunderstood as the maximum expected seismic force on the bridge under design seismic shaking.

c) Seismic zones and response spectrum as per IS 1893(Part 1):2002 are used.

c) In IS 1893 (Part 1): 2002 a new seismic zone

map along with zone factors is given. As against this, for bridges, IS 1893 (1984) which has old zone map, gives seismic coefficient for each zone. The same coefficients are also used in existing Bridge Rules.

d) Combination of horizontal and vertical component of ground motion is included.

d)

e) New load combinations consistent with the present international practice are introduced.

e) In existing Bridge Rules, load combinations

are not mentioned. The Indian Railway Standard (IRS) for concrete bridge design specifies load combination, for ultimate and serviceability limit state. In these load combinations, load factors for live load and seismic loads are quite different than other international bridge codes. The IRS for steel bridge design and sub-structure and foundation, does not explicitly specify load combinations.

f) Details of the response spectrum method and time history method are given along with the pushover analysis.

f)

g) The earthquake effect on retaining walls and abutments is included. The hydrodynamic effect and method of assessment of liquefaction potential of soil is also included.

g)

h) Provisions for seismic design of bridges with seismic isolation devices are also incorporated.

h)

i) Information on the post-earthquake operation and inspection is provided

i) This information is taken from AREMA code.


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3.3 - Railway and Road Bridges Railway bridges are functionally and behaviorally different from the other bridges. Firstly, the controlled traffic environment permits better assessment of train load on the bridges. Secondly, the presence of continuous rails over the bridge spans provides restraint against longitudinal and transverse movement during earthquakes. Thirdly, the superstructure configuration of railway bridges is different than that of the other types of bridges.

C3.3 – Railway and Road Bridges In case of railway bridges, the ratio of dead load of superstructure to live load could be quite different than that for highway bridges. This ratio could also be significantly different for bridges with steel superstructure and concrete superstructure. Various differences of railway bridges and highway bridges are as follows:-

(i) Simple span structures are preferred over continuous structures for railway bridges. Many of the factors that make continuous spans attractive for highway bridges are not as advantageous for railway use. Continuous spans are also more difficult to replace in emergencies than simple spans.

(ii) The ratio of live to dead load is much higher for a railway bridge than for a similarly sized highway bridge. This can lead to serviceability issues such as fatigue and central deflection governing the designs rather than strength.

(iii) Design impact load on railway bridges is higher as compared to highway bridges.

(iv) Interruptions in service are typically much more critical for railway than for highway agencies. Therefore constructability and maintainability without disruption to traffic are crucial for railway bridges.

(v) Since the bridge supports the track structure, the combination of track and bridge movement cannot exceed the tolerances in track standards. Interaction between the track and bridge should be considered in designing and detailing.

(vi) Seismic performance of highway and railway bridges can vary significantly. Railroad bridges have performed well during seismic events.

(vii) Track structure (along with guard rail) serves as an effective restraint (and damping agent) against bridge displacements in case of railway bridges.

(viii) Railway bridge owners typically expect a longer service life from their structures than highway bridge owner expect from theirs.

(ix) Trains operate in a controlled environment, which makes type of damage permissible


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PROVISIONS COMMENTARY for railway bridges that might not be acceptable generally for highway users.

3.4 - References In the formulation of this guideline, assistance has been derived from the several publications listed in Appendix - A.

C3.4 –


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4. Relevant Codes/ Standards

The several Codes/Standards are necessary adjuncts to these guidelines and these are listed in Appendix - B.

C4.0 Relevant Codes/ Standards


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5. Scope C5.0 – Scope

The provisions of the present guidelines are applicable for the seismic design of new railway bridges. These provisions are not applicable for the seismic evaluation and retrofitting of the existing railway bridges.

The provisions of these guidelines are for railway bridges wherein, seismic action is mainly resisted through flexure of pier and through abutments, i.e., bridges composed of vertical pier-foundation system supporting the deck structure with or without bearings.

For certain bridges with special geometry and for special locations, additional detailed analysis, not covered in this guidelines, is required. These are mentioned in Clause 6.7. Bridges not requiring seismic analysis are given in clause 6.5.

The present guidelines also cover the seismic design of the bridges with seismic isolation devices.

Some information on post-earthquake operation and inspection is also included

Seismic evaluation of existing railway bridges requires much detailed analysis which is beyond the scope of the present guidelines. Such detailed analysis is required to assess the present strength of the materials, to assess the ductility of the seismic load carrying members, present utility of the bridge, loading conditions etc. Specialized literature shall be referred for this purpose. Some of the references for seismic evaluation and retrofitting are:

1. AASHTO (1994), Manual for Condition Evaluation of Bridges, Second Edition, American Association of State Highway and Transportation Officials, Washington DC, USA.

2. Japan Road Association (1995) - Reference for Applying Guided Specification to New Highway Bridge and Seismic Strengthing of Existing Highway Bridges.

Useful suggestions for evaluation and strengthening of various components such as piers/columns can be derived from the followings documents specially developed for buildings:

1. FEMA 356 (2000) Prestandard and Commentary for the Seismic Rehabilitation of Buildings. Federal Emergency Management Agency, Washington, D. C., USA.

2. ASCE 11-99, Guideline for Structural Condition Assessment of Existing Buildings, American Society of Civil Engineers, USA.

3. IITK-GSDMA Guidelines - Seismic Evaluation and Strengthing of Building, IIT Kanpur. http://www.iitk.ac.in/nicee/IITK-GSDMA/EQ06.pdf


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6. General concepts C6.0 – General concepts

6.1 - Actual forces that appear on portions of bridges during earthquakes may be greater than the design seismic forces specified in these guidelines. However, ductility arising from material behavior and detailing, and over strength arising from the additional reserve strength in them over and above the design forces, are relied upon to account for this difference in actual and design lateral loads.

C6.1 - The earthquake codes provide design forces which are substantially lower than what a structure is expected to actually experience during strong earthquake shaking. Hence, it is important that the structure be made ductile and statically redundant to allow for alternate load transfer paths. Ductile design and detailing enables a designer to use a lower design force (i.e., a higher value of response reduction factor R) than for an ordinarily-detailed structure.

6.2 - The response of a structure to earthquake shaking is a function of the nature of foundation soil, materials, form, size and mode of construction, and characteristics and duration of ground motion. These guidelines specifies design forces for structures standing on soils or rocks which do not settle or slide due to loss of strength during shaking.

C6.2- Provisions of this guidelines deal with the inertia forces induced due to ground shaking. However, other effects of ground shaking like liquefaction of soil, sliding failure of soil strata are not included. Some information on soil liquefaction is included in Appendix – G.

6.3 - The reinforced and prestressed concrete components shall be under-reinforced so as to cause a ductile failure. Further, they should be designed to ensure that premature failure due to shear or bond does not occur. Stresses induced in the superstructure due to earthquake induced ground motion are usually quite nominal. Therefore, ductility demand under seismic shaking has not been a major concern in bridge superstructures during past earthquakes. However, the seismic response of bridges is critically dependent on the ductile characteristics of the substructures. Provisions for appropriate ductile detailing of reinforced concrete members given in Appendix – A shall be applicable to substructures. Bridges shall be designed such that under severe seismic shaking plastic hinges form in the substructure,

C6.3– Provisions for ductile design and detailing for reinforced concrete structures are provided in Appendix – C and IS: 13920-1993. However, provisions for ductile detailing of prestressed concrete, steel and prefabricated structures are not yet available in the form of Indian Standards. If such structures are to be designed for high seismic zones of the country, it is expected that the designer will ensure suitable ductility following the practices of countries, e.g., USA, Europe, New Zealand and Japan, with advanced seismic provisions. The ductile detailing is required for substructures, foundations and connections only and not of the superstructure


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rather than in the deck or the foundation.

6.4 - Masonry and plain concrete arch bridges with spans more than 12 m shall not be built in the seismic zones IV and V.

C6.4– Designers are prohibited to consider masonry and plain concrete arch bridges of spans more than 12 m as structural systems for bridges in high seismic zones, since these systems do not possess adequate ductility or reserve strength and may not withstand forces due to strong ground shaking.

6.5 - Box and pipe culverts need not be analyzed for seismic forces.

C6.5- Existing Bridge Rules also exempt box and pipe culverts from seismic design.

6.6 - Following bridges need not be analyzed for seismic forces :

(a) In Zones II & III, bridges with overall length less than 60m or spans less than 15m

(b) Single span bridges upto 30m span

However, these bridges shall be provided with:

i. The minimum seating width as per Clause 16.3.

ii. The connections in the restrained direction between superstructure and substructure shall be designed for elastic seismic force from superstructure.

C6.6- Single span bridges of spans upto 30m are exempted from seismic analysis. These bridges comprise of single span resting on abutment with no intermediate pier. However, minimum seat width is provided and connections in restrained direction are designed for seismic force.

6.7 - For specific cases of bridges, some additional studies/analysis should be required, which are described in Table 1.

C 6.7 – Specialist literature shall be referred for information regarding additional studies like site specific spectrum, estimation of fault movement, spatial variation of ground motion, soil liquefaction etc.

The site specific spectrum studies requires knowledge about seismic potential of active faults in that region characteristics of the path through which seismic wave travel and soil strata on which structures stands. Such studies


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are to be performed by experts in the field of seismology/geology and these shall be peer reviewed. Following are some of the useful references on site specific design criteria:

1) Reiter L., Earthquake Hazard Analysis: Issues and Insights; Columbia University Press, New York.

2) Kramer S.L., Geotechnical Earthquake Engineering; Indian Reprint, Pearson Education, New Delhi, 2003.

3) Housner, G.W. and Jennings P.C., Earthquake Design Criteria; Earthquake Engineering Research Institute, 1982.

4) AERB (1990), Seismic Studies and Design Basis Ground Motion for Nuclear Power Plant Sites, AERB Safety Guide No. AERB/SG/S-11, Atomic Energy Regulatory Board, India.

Spatial variation of ground motion is relevant for long continuous bridges and for sites where geological discontinuity and large variation in soil property along the bridge length exists. The difference in the characteristics of the ground motion at various locations along the bridge length is of concern in such cases. Information can be obtained in following references:

1) Eurocode 8 (2005) Design of structures for earthquake resistance – Part 2: Bridges, pr En 1998-2, European Committee for Standardization, Brussels.

2) Der Kiureghian A., and Neuenhofer A., 1992, Response spectrum method for multi-support excitations, Journal of Earthquake Engineering and Structural Dynamics, Vol. 21, pp 713-740.


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PROVISIONS

Table 1 - Cases Requiring Special Studies/Analysis

Sr. No.

Cases in which additional special studies/analysis is required

Special studies/analysis

1. In zone IV and V, bridges with individual span length more than 120 m and/or pier height is more than 30 m.

Modeling of the bridge including geometrical nonlinearity, P-delta effect and soil-structure interaction is needed.

Pushover analysis may be done to ascertain the energy dissipation characteristics of ductile members. (Details given in APPENDIX I)

2. Continuous deck bridge of length larger than 600 m

Spatial variation of ground motion shall be considered.

3. Geological discontinuity exists at the site Spatial variation of ground motion shall be considered.

4. Bridge site close to a fault (< 10 km) which may be active.

Site specific spectrum shall be obtained. Else, near-source modifications as per Clause 8.1.1 and 8.8.3 shall be done. Specialist literature shall be required to obtain site specific spectrum.

If bridge is crossing the fault, detailed geological studies shall be performed to estimate past movements across the fault. Bridge to be designed so as to withstand the expected fault displacements. Help from geological / seismological persons with enough experience will be required to calculate fault movement.

5. In zone IV and V, if the soil condition is poor, consisting of marine clay or loose sand (e.g., where the soil up to 30m depth has average SPT N value equal to or less than 20)

Site specific spectrum shall be obtained.

6. Site with loose sand or poorly graded sands with little or no fines. Liquefiable soil.

Liquefaction analysis is required (Details given in APPENDIX I). Liquefaction is the act or process of transforming any substance into a liquid state. In non-cohesive soils it is the transformation of the soil in the solid state to the liquefied state due to the increase in the pore pressure and the consequent reduction in the effective stress.


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6.8- Ground Motion The characteristics (intensity, duration, etc.,) of seismic ground vibrations expected at any location depends upon the magnitude of earthquake, the depth of focus, distance from the epicenter, characteristics of the path through which the seismic waves travel, and the soil strata on which the structure stands. The random ground motions, which cause the structures to vibrate, can be resolved in any three mutually perpendicular directions. Generally, two horizontal and one vertical component of ground motion is considered.

C6.8- Ground Motion

6.8.1- Vertical Component of Seismic Action

In some cases, the effect of vertical component of ground motion has to be specifically considered. The effect of vertical component is particularly important in the following components/situations:

a. Prestressed concrete decks. b. Bearings, hold down devices, and linkages. c. Horizontal cantilever structural elements

such as cantilevers of deck slabs and cantilever bridges.

d. Situations where stability (overturning /sliding) becomes critical.

e. Bridge sites located near fault. The effect of the vertical seismic component on substructure and foundation may, as a rule, be omitted in zones II and III.

C6.8.1 – Vertical Component of Seismic Action

All structures experience a constant vertical acceleration (downward) equal to gravity (g) at all times. Hence, the vertical acceleration during ground shaking can be just added or subtracted to the gravity depending on the direction of motion.

Vertical acceleration shall be of significant consideration in bridges with large spans. Reduction in gravity loads due to vertical component of ground motion can be particularly detrimental for prestressed girders. Vertical seismic forces may cause reduction in stabilizing forces and combined with this, the horizontal seismic force can cause dislocation of structures.

6.9 - Assumptions The following assumptions are made in the earthquake-resistant design of bridges:

C6.9- Assumptions


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a) Earthquake causes impulsive ground motions, which are complex and random in character, changing in period and amplitude, and each lasting for a small duration. Therefore, resonance of the type as visualized under steady-state sinusoidal excitations will not occur, as it would need time to build up such amplitudes.

Note: However, there are exceptions where resonance-like conditions have been seen to occur between long distance waves and tall structures founded on deep soft soils.

The note mentioned after assumption (a) has been necessitated in view of experience such as that in Mexico City (1985).

The earthquake occurred 400 km away from the Mexico City. A great variation in damages was seen in the Mexico City. Some parts experienced very strong shaking whereas some other parts of the city hardly felt any motion. The peak ground acceleration at soft soils in the lake zone was about 5 times higher than that at the rock sites though the epicentral distance was same at both the locations. Extremely soft soils in lake zone amplified weak long-period waves. The natural period of soft clay layers happened to be close to the dominant period of incident seismic waves and it created a resonance-like conditions. Buildings between 7 and 18 storeys suffered extensive damage since the natural period of such buildings was close to the period of seismic waves.

b) Earthquake is not likely to occur simultaneously with wind or maximum flood or maximum sea waves. Similarly, earthquake motion need not be considered to occur simultaneously with other extreme environmental conditions such as thermal, which have low probability of occurrences.

The probability of occurrence of strong earthquake shaking is low. So is the case with strong winds. Therefore, the possibility of strong ground shaking and strong wind occurring simultaneously is very low. Thus, it is commonly assumed that earthquakes and winds of very high intensity do not occur simultaneously. Similarly, it is assumed that strong earthquake shaking and maximum flood or sea waves (Tsunami) and highest temperature will not occur at the same time.

c) The value of a elastic modulus of materials, wherever required, may be taken as for static analysis unless a more definite value is available for use in dynamic conditions

It is difficult to precisely specify the modulus of materials such as concrete, masonry, and soil because its value depends on factors such as stress level, loading condition (static versus dynamic), material strength and age of material.

For such materials, there tends to be large variation in the value of E. For instance, for concrete, IS 456:1978 recommends Ec = 5700fck, where is IS 456:2000 has modified the value to Ec = 5000fck; both under static condition. Further, the actual concrete strength will be different from the specified value. Hence, the code simply allows the modulus of elasticity for static analysis to be used for earthquake analysis also.


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7. Conceptual Considerations Conceptual design suggestions in terms of configuration, superstructure, substructure and ground conditions are given in Table 2, along with the non preferred types, for which special design and detailing are required. These considerations shall be followed as much as practically possible and a balance shall be maintained between functional requirements, cost and seismic resistance features.

7.0 Conceptual Considerations Conceptual considerations are aimed at providing simplicity, symmetry, and displacement capacity in the bridge so as to improve its seismic resistance. This is similar to the role of architectural planning and detailing in the seismic performance of buildings. In the past earthquakes it is seen that bridges with preferred configurations, superstructure, substructure and ground conditions have performed better than non preferred type. Bridges of non preferred types require special considerations in modeling, analysis, design, and construction.

The selection of an appropriate structure type and configuration should take into account the seismic hazard at the site, the soil condition and the bridge performance requirement. In general, site near active faults, site with potentially liquefiable or unstable soil conditions and site with unstable sloping ground conditions should be avoided, if practical, and measures to improve the soil conditions should be considered as an alternative.

Configuration Criteria for determining an adequate structure configuration and layout include simplicity, symmetry and regularity, integrity, redundancy, ductility and ease of inspection and repair. Bridge should be simple in geometry and structural behavior. Simple structure provides a direct and clear load path in transmitting the inertial forces from superstructure to ground. The bridge behavior under seismic loads can be predicted with more certainty and accuracy with fewer dominant modes of vibration.

Bridges with features such as extreme curvature or skew, varying stiffness and mass and abrupt changes in geometry require special attention in analysis and detailing to avoid permanent damages and failure. Superstructure Simple spans of standard configuration are preferred by railways since they have performed well during past earthquakes and are easy to replace if need arises. In simple spans lateral load on piers depends on the weight of adjacent spans. If spans are of equal length, then, all the piers are subjected to almost same lateral seismic force.

In integral bridges, pier and deck constitute a frame action which is beneficial in resisting the seismic forces. Also, unseating of the span does not occur.


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Since all the piers are connected through deck the lateral seismic force on a pier depends on stiffness of pier. In such a case, large lateral force may get transmitted to one single pier of large stiffness. In continuous spans all the seismic forces may get transmitted to one of the abutment. Continuous span however, reduce the likelihood of unseating at the pier. Long spans produce higher load demands on fewer foundations which will increase foundation vulnerability and reduce redundancy. Excessive ballast and other non structural weight should be avoided as far as practically possible. Substructure Wide seat width at the abutment and the pier allow for large displacements without unseating the bridge spans. Multiple columns provide redundancy in the substructure which is needed to survive the higher level ground motions. Ground Conditions The foundation soil should be investigated for susceptibility to liquefaction and slope failure during the seismic ground motion. To the extent possible, bridges in the region of high seismicity should be founded on stiff, stable soil layers. Large diameter pile foundations may be used to withstand the slope failure or carry the bridge loads through liquefiable soil layer to competent material. Foundation Bridges are built either on spread footing or deep foundation. Bridges on spread footing supported by firm soil have performed well during earthquakes. Pile foundation has performed well except when massive soil failure occurred. Generally the column yield first; thus limiting the earthquake demand on foundations. Moreover, the footing and pile cap should be in deeper level to gain passive resistance.


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Table 2 – Seismically Preferred and not Preferred Aspects of Bridges

Seismically preferred Seismically not preferred

1.0 Configuration

1.1 Straight bridge alignment Curved bridge alignment

1.2 Normal piers Skewed piers

1.3 Uniform pier stiffness Varying pier stiffness

1.4 Uniform span stiffness Varying span stiffness

1.5 Uniform span mass Varying span mass

2.0 Superstructure

2.1 a) Simply supported spans

b) Integral bridges

Continuous spans

2.2 Short spans Long spans

2.3 Light spans Heavy spans

2.4 No intermediate hinges within span Intermediate hinges

3.0 Substructure

3.1 Wide seats Narrow seats

3.2 Multiple column Single column

4.0 Ground conditions

4.1 Stiff, Stable soil Unstable soil


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8. Design Criteria

C8.0 – Design Criteria In the existing Bridge Rules, the design seismic forces for bridges are directly specified; this is often misunderstood as the maximum expected seismic force on the bridge under design seismic shaking. The present guidelines distinguishes the actual forces appearing on each bridge component during design earthquake shaking if the entire bridge structure were to behave linear elastically, from the design seismic force for that component. This is in line with the world wide practice in this regard. The actual forces appearing on each bridge component is obtained by dividing the realistic seismic force by factor of 2R, where R is response reduction factor. The realistic seismic force is the one which will act on each component if bridge is to remain elastic.

The guidelines makes it clear to the designer that the design seismic forces on superstructure, substructure and foundations are only a fraction of the maximum elastic forces that would appear on the bridge. Only in connections, the design seismic forces may be equal to (or more than) the maximum elastic forces that would be transmitted through them. This is in stark contrast with the design forces for any other design loading conditions. For instance, in case of design for wind effects, the maximum forces that appear on the structure are designed for and no reductions are employed.

8.1 - Seismic Zone Map For the purpose of determining design seismic forces, the country is classified into four seismic zones. A seismic zone map of India is shown in Fig. 1. The peak ground acceleration (PGA) (or zero period acceleration, ZPA), associated with each zone, is called zone factor, Z. The zone factor is given in Table 3. Zone factors for some important towns are given in Appendix D

Table 3 - Zone Factor Z For Horizontal Motion

Seismic Zone

II III IV V

Z 0.10 0.16 0.24 0.36

C8.1 - Seismic Zone Map The seismic zone map and zone factors are taken from IS 1893 (Part 1): 2002. The seismic zoning map broadly classifies India into zones where one can expect earthquake shaking of the more or less the same maximum intensity. The zoning criterion of the map is based on likely intensity. It does not give us any idea regarding how often a shaking of certain intensity may take place in a location (that is, probability of occurrence or return period). For example, say area A experiences a maximum intensity VIII every 50 years and area B experiences a maximum intensity VIII every 300 years. But both these areas will be placed in zone IV, even though area A has higher seismicity. The current trend worldwide is to specify the zones in terms of ground acceleration that has a certain probability of being


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exceeded in a given number of years. Zone factor (Z) accounts for the expected intensity of shaking in different seismic zones Efforts have been made to specify Z values that represent a reasonable estimate of PGA in the respective zone. For instance, Z value of 0.36 in zone V implies that a value of 0.36g is reasonably expected in zone V. But it does not imply that acceleration in zone V will not exceed 0.36g. For example, during 2001 Bhuj earthquake, peak ground acceleration of approximately 0.6g was inferred from data obtained from the Structural Response Recorder located at Anjar, 44kms away from the epicenter.

8.1.1- Near Source Effect

For bridges which are within a distance of 10 km from a known active fault, seismic hazard shall be specified after detailed geological study of the fault and the site condition. In absence of such detailed investigation, the near-source modification in the form of 20% increase in zone factor may be used.

C8.1.1- Near Source Effect Seismic hazard analysis shall be performed and site specific PGA and design acceleration spectrum shall be developed. Refer table 1 and commentary of clause 6.7.

If bridge is crossing the fault, detailed geological studies shall be performed to estimate past movements across the fault. Bridge to be designed so as to withstand the expected fault displacements. Help from geological/seismological persons with enough experience will be required to calculate fault movement. In case, such studies are not undertaken, 20% increase in zone factor is recommended. Further, the vertical ground motion may be taken as equal to the horizontal ground motion as given in Clause 8.8.3.

8.2 - Importance Factor The values of importance factor I, for different bridges are given in Table 4. The importance factor reflects strategic importance of the route and functionality of the bridge in the post earthquake period.

C8.2 - Importance Factor Seismic design philosophy assumes that a structure may undergo some damage during severe shaking. However critical and important facilities must respond better in an earthquake than an ordinary structure. Importance factor is meant to account for this by increasing the design force level for critical and important structures.

As per IRS for design of substructure and foundation of bridges, Important and Major bridges are defined as follows: Important Bridges: Important Bridges are those having a lineal waterway of 300m or a total waterway of 1000 Sq.m or more and those classified as important by the Chief Engineer/Chief Bridge Engineer, depending on considerations such as depth of waterway, extent of river training works and


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Table 4 - Importance Factor for bridges

Category Importance Factor

Bridges included

Category I

Bridge

1.5 i) All important bridges irrespective of route.

ii) Major bridges on group A, B and C routes.

(For route classification see IRPW Manual)

Category II

Bridge

1.25 i) Major bridges on all other routes.

ii) All other bridges on group A, B and C routes.

Other Bridge

1.0 All other bridges

maintenance problems. Major Bridges: Major Bridges are those which have either a total waterway of 18m or more or which have a clear opening of 12m or more in any one span. The importance factor of 1.5 is suggested for bridges in Group A, B, C routes depending on traffic intensity. The bridges on other routes, if considered strategically important due to non-availability of alternative route nearby, may be designed with importance factor of 1.25 or 1.5.


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8.3 - Methods of Calculating Design Seismic Force

C8.3 - Methods of Calculating Design Seismic Force

8.3.1 -

The seismic forces for bridges shall be generally estimated by Seismic Coefficient Method (Single Mode Method) described in Section 9.0. Response Spectrum Method (Multi Mode Method) described in Section 10 shall be used in zones IV and V in following cases:

(a) Irregular bridge as defined in section 8.3.5.2 (b) Individual span more than 80m (c) Continuous bridge (d) Height of top of pier / abutment from the base

of foundation is more than 30m.

C8.3.1 –

The existing Bridge Rules follow a very simplistic method for calculating design seismic force. In this method, design seismic force computation does not include consideration of flexibility of the bridge. This implies that all the bridges in a seismic zone, irrespective of their span, pier height and structural system adopt the same design acceleration coefficient.

This guideline includes the effect of bridge flexibility in its design force computation. Further, it permits the use of both the Seismic Coefficient Method (single Mode Method) and the Response Spectrum Method (Multi Mode Method). The Seismic Coefficient Method assumes that (a) the fundamental mode of vibration has the most dominant contribution to seismic force, and (b) masses and stiffness are evenly distributed in the bridge resulting in a regular mode shape.

The seismic coefficient method is applicable when dynamic behavior of the bridge can be sufficiently approximated by a single degree of freedom system. This condition is considered to be satisfied in following cases: a) In longitudinal direction of approximately

straight bridges, with continuous deck, the seismic forces are carried by the piers, and the total mass of the piers is less than 20% of the mass of the deck

b) For the above bridge in transverse direction, if the bridge is approximately symmetric about the center of the deck, i.e., when the eccentricity between the center of stiffness of the supporting members and the center of mass of the deck does not exceed 5% of the length of the deck.

c) For bridges with simply supported spans, no significant interaction between piers is expected and the total mass of each pier is less than 20% of the tributary mass of the deck (Tributary mass of the deck on a pier is the half mass of the deck on either side of the pier).


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However, in case of long span bridges, irregular bridges, higher modes may be important and their mode shape may not be regular. Hence, for such bridges this clause suggests the use of multi-mode analysis namely Response Spectrum Method. It may be clarified that mass concrete piers, common in Railway bridges may be analyzed by the Seismic Coefficient method, regardless of the mass ratio of pier weight and the superstructure.

8.3.2 -

The Time History method described in Section 11.0 shall be used in following cases:

(i) To verify the result of Response Spectrum Method for highly irregular bridges in zone IV, and V.

(ii) Bridges with special devices like Shock Transmission Units (STU), and seismic isolation devices, time history method is mandatory.

C8.3.2 -

Ground motion records to be used in the time history analysis shall be obtained after site specific studies. These studies shall be performed by a team of experts and shall be peer reviewed, i.e., reviewed independently by other experts.

8.3.3 -

The Pushover analysis described in Section 12.0 may be used to ascertain the nonlinear load carrying capacity and ductility of pier with more than 50 m height and individual span more than 120 m.

C8.3.3-

International bridge codes are now recommending use of Pushover Analysis for bridges. Pushover analysis is a nonlinear analysis which estimates the nonlinear load carrying capacity of the bridge pier, and assesses the energy dissipating capacity of ductile members. This analysis estimates if the provided ductile detailing is enough to accommodate seismic loads on the bridge.

8.3.4 –

For applying seismic forces obtained using Seismic Coefficient Method or Response Spectrum Method and for applying earthquake ground motion in Time History Method (THM), the mathematical model of bridges shall be used. This model shall appropriately model the stiffness of superstructure, bearings, piers and bridge ends. Analysis of bridge model under dead load, live load and seismic loads gives bending moment, shear and axial forces in various bridge components.

C8.3.4 -


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8.3.5 Regular and Irregular Bridges

8.3.5 Regular and Irregular Bridges

8.3.5.1- Regular Bridge

A regular bridge has no abrupt or unusual changes in mass, stiffness or geometry along its span and has no large differences in these parameters between adjacent supports (abutments excluded). A bridge shall be considered regular for the purposes of this guidelines, if

C8.5.1.1 –

(a) It is straight or it describes a sector of an arc which subtends an angle less than 90 at the center of the arc, and

(a) Fig C1a represents the straight regular bridge. Whereas Fig C1 b show the straight bridge with Φ < 900.

(b) The adjacent piers do not differ in stiffness by more than 25%. (Percentage difference shall be calculated based on the lesser of the two stiffnesses as reference).

(c) If multi-column piers are used then the stiffness of the stiffest columns within piers shall not be 25% more than the stiffness of the most flexible column in that pier.

(c) Multi-column pier (bent) is quite commonly used in highway bridges. They provide frame action in transverse direction. Similarly for continuous bridges, frame action in the longitudinal direction can also be achieved. Details regarding configuration of multi-column pier for regular bridges are given in CALTRANS.

Fig C1a Straight Bridge

Fig C1b Regular Bridge with Φ < 90o

Φ Φ < 90o


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8.3.5.2 - Irregular Bridge

All bridges not conforming to Clause 8.3.5.1 shall be considered irregular. Further, arch bridges of span exceeding 30m, cable stayed bridges, suspension bridges, and other innovative bridge forms shall also be treated as irregular bridges.

C8.3.5.2 -

8.4 - Seismic Weight and Live Load Live load used in the calculation of seismic weight can be different than the live load used in load combinations. Live load for seismic weight is given in Clause 8.4.2, whereas live load for load combination is given in Clause 8.7

C8.4 – Seismic Weight and Live Load

8.4.1- Seismic Weight

The seismic weight of the superstructure shall be taken as its full dead load plus appropriate amount of live load. The seismic weight of the substructure and of the foundation shall be their respective full dead load. Buoyancy and uplift shall be ignored in the calculation of seismic weight.

Note – In the Seismic Coefficient Method (Clause 9.0), for simply supported regular bridges, single degree of freedom (SDOF) model is used to obtain time period and in this model only 80% of pier weight is considered in the seismic weight.

C8.4.1 – Seismic Weight

The dead load of the superstructure also includes the superimposed dead load that is permanently fastened or bonded with its structural self weight. Since there is a limited amount of friction between the live load and the superstructure, only a part of the live load is included in the inertia force calculations.

It is clear that the seismic forces on a bridge component are generated due to its own mass, and not due to the externally applied forces on it. The presence of buoyancy and uplift forces does not reduce its mass. Thus, the clause requires that buoyancy and uplift forces be ignored in the seismic force calculations.

8.4.2- Live load in seismic weight

No live load (train load) shall be considered while calculating horizontal seismic forces along the direction of traffic (Longitudinal direction). 50% live load (excluding impact effect) shall be considered while calculating horizontal seismic forces in the direction perpendicular to traffic (transverse direction).

C8.4.2 – Live load in seismic weight

By the live load , one usually refers to vehicular traffic. Seismic shaking in the direction of traffic causes the wheels to roll once the frictional forces are overcome. The inertia force generated by the vehicle mass in this case is smaller than that if the vehicle mass were completely fastened to the span. Further, the inertia force generated by the vehicle mass due to friction between the superstructure deck and wheels, is assumed to be taken care of in the usual design for braking forces in the longitudinal direction. Thus, live load is ignored while estimating the seismic forces in the direction of traffic.

On the contrary, under seismic shaking in the direction perpendicular to that of traffic (transverse direction), the rolling of wheels is not possible. In

Fig C2: Multi-column Pier (Bent)


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the transverse direction, the train can slide due to gap between wheel and rail. Due to this, during sliding , the entire train load will not contribute to seismic weight. Hence, only 50 % of design live load is considered in transverse direction. Existing Bridge Rules also considers 50% live load in transverse direction and no live load in longitudinal direction.

8.4.3 -

The vertical seismic forces shall be obtained by considering full live load (excluding impact effect) on the bridge.

C8.4.3 –

While calculating vertical seismic forces, the seismic weight shall include full live load. It may be noted that while calculating lateral seismic forces, 50% live load is included in seismic weight for transverse direction, where as no live load is included for seismic weight in longitudinal direction.

8.4.4- Seismic Mass

The seismic mass of a bridge component is its seismic weight divided by the acceleration due to gravity.

C8.4.4- Seismic Mass

Weight = mass x acceleration due to gravity. In SI system, the unit of weight is Newton and unit of mass is kilogram.

8.5 - Combination of Seismic Components The seismic forces shall be assumed to act in any direction. For design purpose, the analysis is done for earthquake motion in two orthogonal horizontal directions and one vertical direction.

Generally, analysis for horizontal seismic forces is adequate. When vertical motion is to be considered, the design seismic forces shall be combined as per clause 8.5.3.

C8.5 - Combination of Seismic Components

The design ground motion can occur along any direction of a bridge. Moreover, the motion has different directions at different time instants. The earthquake ground motion can be thought of in terms of its components in the two horizontal directions and one vertical direction.

8.5.1 -

For regular bridges, the two orthogonal horizontal directions are usually the longitudinal and transverse direction of the bridges (Fig 2a). For such bridges analysis shall be done for seismic forces in longitudinal and transverse directions. The seismic force resultants (Bending Moment, Shear Force and Axial Force) at any component obtained from the analysis in longitudinal and transverse directions shall be considered separately.

C8.5.1 -

For regular bridges, the two orthogonal horizontal directions (say x- and y-directions) are usually the longitudinal and transverse directions of the bridge. For such bridges, it is sufficient to design the bridge for seismic forces acting along each of the x- and y-directions separately. During earthquake shaking, when the resultant motion is in a direction other than x and y, the forces can be resolved into x- and y-components, which the elements in the two principal directions are normally designed to withstand.


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XyM = Bending Moment in y-direction when force is applied in X-

Direction XxM = Bending Moment in x-direction when force is applied in X-

Direction YyM = Bending Moment in y-direction when force is applied in Y-

Direction YxM = Bending Moment in x-direction when force is applied in Y-

Direction

For Straight Bridge, XyM and

YxM are zero.

X- and Y- indicate global axes; x- and y- are local axes for column/pier.

8.5.2 -

For irregular bridges, particularly, skew bridge (Fig. 2b), design seismic force resultants shall be obtained along x-and y-direction. The design seismic force resultant (Bending Moment, Shear Force and Axial Force) at any component shall be obtained as follows:

(a) 21 30±± r.r

(b) 21 ±30± rr.

where

1r Force resultant due to full design seismic

force along x direction,

2r Force resultant due to full design seismic

force along y direction.

C8.5.2 -

In case of irregular bridges, particularly those with skew, design should be done by considering the seismic force component in x-direction and y-direction. In such a case, the bridge should also be designed for earthquake forces acting along the directions in which the structural systems of the substructures are oriented. One way of getting around this without having to consider too many possible earthquake directions is to design the structure for:

(a) full design force along x-direction (ELx) acting simultaneously with 30% of the design force in the y-direction (ELy); i.e., (ELx+0.3ELy), and

(b) full design force along y-direction (ELy) acting simultaneously with 30% of the design force in the x-direction (ELx); i.e., (0.3ELx+ELy).

This combination ensures that the components (particularly the substructure) oriented in any direction will have sufficient lateral strength. In case vertical ground motions are also considered, the same principle is then extended to the design force combinations in the three principal directions.

Fig. 2 a: Seismic forces for Straight Bridge(Clause 8.5.1)

Y

X

XyM

XxM

YyM

YxM

y

x


Page 32

Bridge Plan Global X-Y axes

y x

x

XxM

YxM

y x

YyM

(Local x-x and y-y axes)

XyM

Fig. 2 b: Combination of orthogonal seismic forces for Skew Bridge (Clause 8.5.2).

Design Seismic Force Resultant for Bending Moment

Moments for ground motion along X-axis

Moments for ground motion along Z-axis

Yx

Xxx M.MM 30 Y

yXyy M.MM 30

Design Moments

Yx

Xxx MM.M +30= Y

yXyy MM.M +30=

where, Mx and Mz are absolute moments about local axes.

8.5.3-

When vertical seismic forces are also considered, (Clause 6.8.1), then for regular bridges, the design seismic force resultants shall be obtained for the X-, Y- and Z-direction separately. For irregular bridges, the design seismic force resultant at any component shall be computed as follows:

(a) 321 30±30±± r.r.r

(b) 321 30±±30± r.rr.

(c) 321 ±30±30± rr.r.

Where 21 rr and are as defined in Clause 8.5.2,

and 3r is the force resultant due to full design


Page 33

seismic force along the vertical or z-direction direction.

8.5.4 -

As an alternative to the procedure in 8.5.2 and 8.5.3, the forces due to the combined effect of two or three components can be obtained on the basis of ‘square root of sum of square (SRSS) that is

22

21 rr or 2

322

21 rrr

Where 321 r, rr and are as defined in Clause 8.5.2

or 8.5.3.

C8.5.4 -

When seismic force is applied in X-direction, the

bending moments in column are XxM and X

yM . x-

and y- are local directions. Similarly, for seismic force in Y-direction, the bending moment in column

are YxM and Y

yM . The design moment,XM in x-

direction and in y-direction is given by is given by,

XM 22 + )M()M( Xy

Xx and

YM 22 + )M()M( Yy

Yx

These two orthogonal components are combined by using SRSS rule. The graphical representation is shown in Fig. 2b.

8.6 - Damping and soil Properties C8.6 - Damping and soil properties

8.6.1 - Damping

In general, 5% damping shall be considered.

C8.6.1 – Damping

Damping value of 5% is suggested for all types of bridges. It is expected that in most of the bridges, substructure will be of concrete.

8.6.1.1-

If well foundation is used, then 10% damping shall be used.

C8.6.1.1

Generally piers are considered fixed at the top of the well foundation, i.e., foundation is considered to be rigid. For such models, increased damping of 10% may be used to account for the additional energy dissipation due to interaction between well foundation and adjoining soil. Alternatively, a rigorous soil-structure interaction analysis can be performed by modeling the well foundation and the surrounding soil.


Page 34

8.6.1.2-

In case the guard rails are effectively provided, on single span of bridge upto 30 m length, 10 % damping in longitudinal direction can be considered. However, in the transverse direction damping will not change.

C8.6.1.2-

Railway track along with effectively provided guard rails provides a continuous load path in longitudinal direction. Thus, for short bridges, they help in enhancing the participation of abutment and adjoining soil in the shaking in longitudinal direction. Hence, damping is increased for 10% for such cases. A similar provision is given in AREMA for short bridges.

8.6.2 –Increase in Allowable Pressure in Soils

When earthquake force is included then allowable pressure in soil and rock shall be increased as stipulated in Table 5. Bearing pressure for foundation and pile capacity shall be determined by working stress method only.

C8.6.2 – Increase in Allowable Pressure in Soils

Many modern codes, e.g., the International Building Code (IBC) 2000), classify the soil type as per weighted average in top 30 m based on:

Soil shear wave velocity, or

Standard penetration resistance, or

Soil un-drained shear strength

8.6.3-

The values for allowable bearing pressure in soil given in Table 5 applies to the upper 30m of the soil profile. Profiles containing distinctly different soil layers shall be subdivided into layers, each designated by a number that ranges from 1 (at the top) to n (at the bottom), where there are a total of n layers in the upper 30 meters, and a weighted average will be obtained as follows:

n

1i i

i

n

1ii

N

d

d

N

where

n

iid

1

is equal to 30 m, Ni is the standard

penetration resistance of layer i, not to exceed 100 blows per 300 mm as directly measured in the field without correcting, and di is the thickness of any layer i between 0 and 30m.

C8.6.3-

8.6.4 Soil Structure Interaction

Soil flexibility should be considered in the seismic analysis of bridges, whenever deemed necessary.

C8.6.4 Soil Structure Interaction

Soil flexibility has beneficial as well as adverse effect on seismic response of structures. Due to soil


Page 35

This is particularly important for foundations in soft soil conditions and in cases where deep foundations are used. Soil flexibility leads to longer natural period and hence lowers seismic forces, however, on the other hand, it results in larger lateral deflections. Soil parameters, like, elastic properties and spring constants shall be properly estimated. In many cases, one gets a range of values for soil properties. In such cases, the highest values of soil stiffness shall be used for calculating the natural period and seismic forces, and lowest value shall be used for calculating the deflection.

flexibility, time period increases, which in turn, leads to reduction in seismic forces. On the other hand, due to soil flexibility the lateral deflection of structure increases, which may require inclusion of P-Delta effect in the analysis and may affect the stability of the structure.


Page 36

Table 5 - Percentage of Permissible Increase in Allowable Bearing Pressure or Resistance of Soils

(Clause 8.6.3)

Sl No.

Foundation Type of soil Mainly Constituting the Foundation

Type I Rock or Hard Soil Type II Stiff Soil Type III Soft Soils

(1) (2) (3) (4) (5)

i) Piles passing through any soil but resting on soil type I 50 50 --

ii) Piles not covered under item i -- 25 --

iii) Raft foundations 50 50 --

iv) Combined isolated RCC footing with tie beams 50 25 --

v) Isolated RCC footing without tie beams, or unreinforced strip foundations.

50 25 --

vi) Well foundation 50 25 --

NOTES

1. The allowable bearing pressure shall be determined in accordance with IS 6403 or IS 1888.

2. If any increase in bearing pressure has already been permitted for forces other than seismic forces, the total increase in allowable bearing pressure when seismic force is also included shall not exceed the limits specified above.

3. Desirable minimum field values of N- If soils of smaller N-values are met, compacting may be adopted to achieve these values or deep pile foundations going to stronger strata should be used.

Seismic Zone Level

Depth below Ground (in meters)

N-Values Remarks

III, IV and V ≤ 5 ≥ 10

15 20

II (for important Structures only)

≤ 5 ≥ 10

15 20

For values of depths between 5m and 10m, linear interpolation is recommended.

4. The values of N (uncorrected values) are at the founding level and the allowable bearing pressure shall be determined in accordance with IS 6403 or IS 1888.

5. The piles should be designed for lateral loads neglecting lateral resistance of soil layers liable to liquefy.

6. IS 1498 and IS 2131 may also be referred.

Type of soils

Soil Type Definition

Type I: Rock or Hard Soils

Well graded gravel (GW) or well graded sand (SW) both with less than 5% passing 75 μm sieve (Fines);

Well graded Gravel – Sand mixtures with or without fines (GW-SW);

Poorly graded Sand (SP) or clayey sand (SC), all having N above 30;

Stiff to hard clays having N above 16, where N is the Standard Penetration Test value.

Type II: Stiff Soils Poorly graded sands or Poorly graded sands with gravel (SP) with little or no fines having


Page 37

N between 10 and 30;

Stiff to medium stiff fine-grained soils, like Silts of Low compressibility (ML) or Clays of Low Compressibility (CL) having N between 10 and 16.

Type III: Soft Soils

All soft soils other than SP with N<10. The various possible soils are

Silts of Intermediate compressibility (MI);

Silts of High compressibility (MH);

Clays of Intermediate compressibility (CI);

Clays of High compressibility (CH);

Silts and Clays of Intermediate to High compressibility (MI-MH or CI-CH);

Silt with Clay of Intermediate compressibility (MI-CI);

Silt with Clay of High compressibility (MH-CH).


8.7 - Combination of Seismic Design Forces with Other Forces The design seismic force resultant at a cross-section of a bridge component shall be appropriately combined with those due to other forces as per Table 12 of IRS Concrete Bridge Code (2004). However, in lieu of combination 2 of Clause 11.0 of IRS Concrete Bridge Code, following load combinations shall be used :

(A) Ultimate limit state design

1) 1.25DL + 1.5 DL(S) +1.5EQ + 1.4 PS+ 1.7 EP

2) 1.25DL + 1.5DL(S) + 0.3 (LL + LL(F)) + 1.2EQ + 1.7 EP + 1.4PS + 1. 4HY + 1.4BO

3) 0.9DL + 0.8DL(S) + 1.5EQ + 1.4 PS + 1.7 EP

(B) Serviceability Limit State

1) 1.0 DL+1.2 DL(S) +1.0 EQ

2) 1.0 DL + 1.2 DL(S)+0.3(LL+LL(F))+1.0EQ

(C) During the construction stage, following load combination shall be used:

1.0DL + 1.2DL(S) + 0.8EQ + 1.0ER + 1.3EP + 1.0PS + 1.0HY + 1.0BO

Where,

DL = dead load,

DL(S) = superimposed dead load,

LL = live load,

LL (F) = live load on footpath,

C8.7 - Combination of seismic Design Forces with Other Forces

For a very busy railway track, it is expected that on a bridge, on an average a heavy train will pass once in 15 minutes. A train of 500 m length at a speed of 80 kmph will take about 30 sec to cross a bridge of 30 m span. Thus, there is 1-in-30 chance that train will be present on a bridge during earthquake. For other scenario of train speeds and bridge lengths, the probability of a train being on bridge at any time will vary from 1- in- 20 to 1- in- 50. From this point of view, the partial safety factor for live load is 0.3.

IRS Steel Bridge code and IRS Bridge Sub- structure & Foundation code mention working stress method for steel bridges and substructure and foundation. When working stress method is used, the load combination corresponding to Serviceability Limit State shall be used. The increase in permissible stresses as specified in the respective code may be used for seismic load combinations. Here, it is to be noted that although the earthquake loads have increased but due to recognition of ductility and flexibility and the rationalization of load combinations and importance factor, one will still get a reasonable design.

The load combination A3 is useful not only for assessing the critical combination for overturning effect but also for stress reversal effect. Earthquake load include lateral as well as vertical amount as per clause 8.5


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EQ = earthquake load,

EP = earth pressure,

ER = erection load such as cranes, machines etc.

PS = prestressing load,

HY = hydrodynamic load,

BO = buoyancy load, ,

SH = shrinkage load,

CR = creep load,

TE = temperature load.

The live load (LL) includes impact effect, longitudinal forces (tractive and braking), and centrifugal force.

The seismic load combinations from various codes are listed below:

a) Existing IRS Concrete Code

IRS Concrete Code :

Ultimate Limit State

1) 1.4DL + 2.0DL(S) + 1.6EQ

2) 1.4DL + 2.0DL(S) + 1.25EQ + 1.7EP + 1.25LL(F) + 1.75LL

Serviceability Limit State

1) 1.0DL + 1.2DL(S) +1.0EQ

2) 1.0DL + 1.2DL(S) + 1.0EQ + 1.0LL(F) + 1.0 LL

b) AREMA


1.0 (DL + EP + BO + PS + EQ) -- Concrete Structure

1.0 (DL + EP + BO + EQ) --- Steel structure

c) AASHTO

Ultimate Limit State

(1.25 or 0.9) DC + (1.4 or 0.25) DD + (1.5 or 0.65) DW + (1.5 or 0.9)EH + (1.35 or 0.9) EV + (1.5 or 0.75)ES + 1.0EL + 1.0PS + (1.25 or 0.9) CR + (1.25 or 0.9)SH + 0.5 ( LL + IM + CE + BR + PL + LS ) + WA+ FR +EQ

For permanent loads, the maximum and minimum value of load factor is given. Designer shall use those values which produce the most critical combination or worst effect. For example, if “load A” produces the effect opposite to that of “load B”, then, minimum value of load factor shall be used for “load A” along with the maximum value for “load B”.

d) TRANSIT (New Zealand)

Ultimate Limit State 1) (1.35 or 0.8)DL + EL +1.35EP+1.35OW + SG + ST + EQ + 0.33TP+ GW 2) 1.35DL+ 1.35EL+1.35EP + 1.35OW + 1.35SG + 0.45EQ + 1.49CN + GW Serviceability Limit State DL + EL + GW + EP + OW + SG + ST + EQ + 0.33TP DL + EL + GW + EP + OW + SG + 0.33EQ + CN


Page 39


e) Indian Road Congress (IRC)


1.0DL + 0.5LL + 0.5TR + 0.5BR + 1.0BO + 1.0EQ + 0.5CF + 1 EP + 1.0 WC + 1.0 IM + 1.0TE + 1.0 WP + 1.0 GE + 1.0DE+ 1.0 BF For Construction Condition

1.0DL + 1.0BO + 0.5EQ + 1 EP + 1.0 WC + 1.0 Erection Effect DC = dead load of structural components and nonstructural elements, DD = downdrag force, DL = dead load, DW = dead load of wearing surfaces and utilities, EH = horizontal earth pressure load, EP = earth pressure, ES = earth surcharge load, EL = miscellaneous locked-in force effects resulting from the construction process, including jacking apart of cantilevers in segmental construction, EV = vertical pressure from dead load of earth fill, PS = secondary forces from post-tensioning, CR = force effects due to creep, SH = force effect due to shrinkage, IM = vehicular dynamic load allowance, CE = vehicular centrifugal force, BR = vehicular breaking force, PL = pedestrian live load, LS = live load surcharge, WA = water load and stream pressure, FR = friction load, EQ = earthquake load, OW = ordinary water pressure and buoyancy, SG = shortening effects, ST = settlement, CN = construction loads, including loads on an incomplete structure, TR = tractive effect, BR = breaking effect, TE = temperature effect, GE = grade effect, BF = bearing friction, WC = water current, WP = wave pressure.

8.8 - Vertical Motions The seismic zone factor for vertical ground motions, when required (see Clause 6.8.1), may be taken as two-thirds of that for horizontal motions given in Table 3.

C8.8 - Vertical Motions Usually the vertical motion is weaker than the horizontal motion. On an average, peak vertical acceleration is one-half to two-thirds of the peak horizontal acceleration. While the 1984 edition of IS 1893 and existing Bridge Rules specify vertical coefficient as one-half of horizontal, in the 2002 edition of IS 1893 peak vertical acceleration has been specified as two-thirds of the peak horizontal acceleration.

8.8.1- For superstructure with span upto 80 m, the effect of vertical motion can be considered by analyzing

C8.8.1- Long span bridges are more sensitive to vertical motion and analysis for vertical acceleration shall be


Page 40


the superstructure for 25% additional dead weight in upward and downward direction.

carried out. For spans less than 80 m, simplified approach, taken form CALTRANS is suggested.

8.8.2- For superstructure with span more than 80m, analysis for vertical ground motion shall be done.

Such analysis requires time period of superstructure in vertical direction. Time period for the superstructure has to be worked out separately using the property of the superstructure, in order to estimate the seismic acceleration coefficient (Sa/g) for vertical acceleration. It can be done by free vibration analysis of superstructure using standard structural analysis software. However, for simply supported superstructure with uniform flexural rigidity, the fundamental time period Tv, for vertical motion can be estimated using the expression

EI

mL

πTV

22= , where L is the span, m is the

mass per unit length, and EI is the flexural rigidity of the superstructure.

When ultimate limit state is used, effective flexure rigidity equal to 50% of gross flexural rigidity shall be taken for concrete superstructure (RC and Prestressed girders, slab decks).

C8.8.2- Vertical component of ground shaking can make the superstructure to vibrate in vertical plane. In short span bridges, superstructure will be quite rigid and its time period will be very low. However, in long span bridges, superstructure could be flexible. For continuous superstructure, time period of superstructure can be obtained by modeling it using general purpose structural analysis software.

8.8.3 For locations, within 10 km of active fault, seismic zone factor for vertical ground motion may be taken as equal to that for horizontal motion. (which shall include the 20% increase in horizontal PGA as per Clause 8.1.1).

C8.8.3

In the regions very close to active fault, ground motion characteristics could be quite different. In near-source regions, seismic hazards shall be based on detailed geological study of fault and local site condition. In absence of such detailed study, the zone factor for vertical motion is taken as same as that for horizontal motion. It is to be noted that, for such near source locations, the zone factor for horizontal motion has already been enhanced by 20%. Thus, the zone factor for the horizontal and vertical motion in zone V would be 0.36 x 1.2 = 0.432g.


Page 41


9. Seismic Coefficient Method (Single mode Method) The method can be employed by using the following step-wise procedure:

a) Obtain the horizontal elastic acceleration coefficient due to design earthquake, which is same for all components. (Clause 9.1)

b) Obtain the seismic weight of each component. (Clause 8.4)

c) Obtain the seismic inertia forces generated in each component by multiplying quantities in (a) and (b) above. (Clause 9.2.1)

d) Apply these inertia forces generated in each of the components at the center of mass of the corresponding component, and conduct a linear elastic analysis of the entire bridge structure to obtain the stress resultants at each cross-section of interest.

e) Obtain the design stress resultants in any component by dividing the maximum elastic stress resultants obtained in (d) above by the response reduction factor prescribed for that component. (Clause 9.3)

C9.0 – Seismic Coefficient Method (Single mode Method) The seismic coefficient method is applicable for bridges as described in Clause 8.3.


Page 42


9.1 - Elastic Seismic Acceleration Coefficient The Elastic Seismic Acceleration Coefficient Ah due to design earthquake along a considered direction shall be obtained as

2a

h

SZA I

g

where

Z = Zone Factor, given in Table 3,

I = Importance Factor, given in Table 4,

aS

g= Spectrum Acceleration Coefficient along the

considered direction given as follows:

For rocky, or hard soil sites (Type I)

33.0

/00.1

50.2

Tg

Sa

00.3

00.340.0

40.0

T

T

T

For medium soil sites (Type II)

45.0

/36.1

50.2

Tg

S a

00.3

00.355.0

55..0

T

T

T

For soft soil sites (Type III)

56.0

/67.1

50.2

Tg

S a

00.3

00.367.0

67.0

T

T

T

T = Fundamental natural period of the bridge along the considered direction.

The soil types are described in Table 5.

A plot of aS

g is given in Fig.3 for 5% damping. For

other damping values, the multiplying factors are given in Table 6.

C9.1 - Elastic Seismic Acceleration Coefficient

As compared to the existing Bridge Rules, here, new zone map as per IS 1893(Part 1) and response spectrum similar to IS 1893 (Part 1):2002 is used.

Zone Factor (Z)

Refer commentary of Clause 8.1

Importance Factor (I)

Refer commentary of Clause 8.2

Spectrum Acceleration Coefficient (Sa/g)

This is obtained from the design response spectrum, which is a plot of maximum acceleration of structure as a function of time period of structure. The time period of bridge, depends on its flexibility, and hence, spectrum acceleration coefficient accounts for the effect of flexibility of the bridge on the design acceleration. This design acceleration spectrum is same as the one given in IS 1893 (Part 1):2002, except for its variation in short period range, i.e. T<0.1 sec and in long period range, i.e., T > 3 sec. As compared to the spectrum of IS 1893 (Part 1), in the short period range (0 < T < 0.1), the ascending portion of the spectrum has been replaced by a constant value. This implies that between 0 to 0.1 sec, the value of spectrum acceleration will be on higher side. There are several reasons for this conservatism. For instance, ductility does not help in reducing the maximum forces if natural period is in this range of 0 - 0.1 sec. Hence, it is necessary to raise the level of spectrum in this range. Also, since the acceleration response spectrum has a very steep slope in the range 0-0.1 sec, any small underestimation of the natural period T may lead to a significant reduction in the seismic force. In the long period range, the 1/T variation has been replaced by constant value, which essentially ensures certain minimum level of design acceleration even for very flexible structures.

Damping Factors

The design acceleration spectrum given in Figure 3 is for damping value of 5 percent of critical damping. Ordinates for other values of damping can be obtained by multiplying the value for 5 percent damping with the factors given in Table 6. These factors are same as those given in IS 1893 (Part 1):2002.


Page 43


Table 6 Multiplying Factors for Other Damping percentages

Damping % Factors

0 3.20

2 1.40

5 1.0

7 0.90

10 0.80

15 0.70

20 0.60

25 0.55

30 0.50

9.1.1 Fundamental Natural Period

Fundamental time period of the bridge member is to be calculated by any rational method of analysis.

The fundamental period can also be calculated by the method given below:

(1) For simply supported bridges, the design vibration unit consists of one pier and a superstructure portion supported by it. The fundamental natural period T shall be

C9.1.1 - Fundamental Natural Period

In simply supported bridges, one pier along with appropriate weight of adjoining spans constitute one design vibration unit and is idealized as single-degree-of-freedom (SDOF) system. Figure C3a and Fig. C3b respectively show design vibration unit in longitudinal and transverse directions. Considering pier to be a cantilever, the lateral deflection, due to

Spe

ctru

m A

ccel

erat

ion

Coe

ffic

ient

(S

a/g)

Fundamental Natural Period T (s)

Fig. 3 Response Spectrum for 5% dampingfor Seismic Coefficient Method (Clause 9.0)


Page 44


calculated from the following equation:

δT 2=

Where, = displacement in meter at the acting position of inertial force of the superstructures when the force corresponding to the full weight of superstructure, appropriate amount of live load, and 80% weight of the substructure is assumed to act in the direction of inertial force.

Alternatively, the fundamental natural period T (in seconds) of pier/abutment of the bridge along a horizontal direction may be estimated by the following expression:

21000

WT

F

W = Full Wight of the superstructure, 80% weight of substructure, and appropriate amount of live load in kN.

F = Horizontal force in kN required to be applied at the centre of mass of superstructure for one mm horizontal deflection at the top of pier/abutment for the earthquake in the transverse direction, and the force to be applied at the top of the bearings for the earthquake in the longitudinal direction.

(2) For multi-span integral bridges (continuous bridges), the design vibration unit consists of a number of substructures and superstructure portions supported by it (Fig. C-3c). The fundamental natural period (T ) shall be

calculated by any suitable method. For example, Rayleigh’s method may be used as follows:

δ2T

dssusW

dssusW 2

)()(

)(

sW Weight of the superstructure and

substructure at position s (kN)

)(su Displacement at position s caused in the

acting direction of inertial force when the force corresponding to the weight of the superstructure and substructure above the

lateral force P, can be obtained aseff

p

EI

PH

3

3

In the seismic weight, full weight of superstructure (pier) shall be considered. However, when a single pier and corresponding superstructure is idealized as SDOF system, only 80% weight of substructure (pier) is considered. This is so, because the distributed weight of the pier is lumped at the top level. During lateral ground motion, the lateral seismic force on pier would be distributed along its height. In the SDOF model, the lateral seismic force corresponding to pier weight is to be lumped at the top and hence only 80% pier weight is included in the seismic weight. The appropriate amount of live load implies that 50% live load in transverse direction and no live load in longitudinal direction.

In response spectrum analysis (Clause 10.0), where free vibration analysis is carried out to obtain natural time period, total weight of substructure is considered.

Continuous bridge; F = fixed and M = movable bearings

Fig. C3a – Design vibration unit in longitudinal direction

Fig. C3b – Design vibration unit in transverse

For transverse direction


Page 45


ground surface for seismic design is assumed to act in the acting direction of inertial force.

Note - In general pier shall be considered fixed at the foundation level. However, in case of soft soil or deep foundations, soil flexibility may be considered in the calculation of fundamental natural period as per the Clause 8.6.4.

For some standard bridge spans , with specified pier geometry and heavy mineral loading, time periods are given in Table C1.The values give some idea about the range of time periods of simply supported railway bridges

Table C1 Time period of some standard railway bridges

L. = Longitudinal direction T. = Transverse direction Following assumption are made in the above calculations:

1) Pier diameter is 1.5 m for pier of 6 m and 8 m height. Pier diameter is 2 m for pier of 10 m, 12 m and 15 m height. Pier diameter is 3 m for pier of 20 m, 25 m and 30 m height.

2) Seismic weight has been calculated as: a) Longitudinal direction – Total DL of

superstructure + 80 % DL of pier b) Transverse direction - Total DL of

superstructure + 80 % DL of pier + 50 % LL 3) Effective moment of inertia, I eff = 0.75 Ig

Span (m)

24.4

(HM Std)

45.7

(HM Std)

76.2

(HM Std)

Pier ht.(m)

L. T. L. T. L. T.

6 0.21 0.38 0.30 0.51 0.45 0.69

8 0.34 0.60 0.47 0.79 0.70 1.07

10 0.32 0.50 0.41 0.65 0.57 0.86

12 0.44 0.67 0.55 0.86 0.77 1.13

15 0.65 0.96 0.81 1.22 1.10 1.60

20 0.67 0.82 0.74 0.97 0.90 1.20

25 1.03 1.23 1.12 1.42 1.33 1.73

30 1.46 1.71 1.57 1.95 1.83 2.35

For longitudinal direction

Fig. C-3c Design vibration unit for Continuous Bridge


Page 46


4) DL of superstructure and LL for heavy mineral loading is taken from RDSO’s design document

9.1.1.1-

For ultimate limit state, the cracked flexural stiffness of reinforced concrete pier shall be used. The cracked flexural stiffness is the initial slope of the moment curvature (M-) curve and is given by

where,

My is the moment capacity of the column/pier section at the first yield of the reinforcing steel, and

y is the yield curvature.

In the absence of more rigorous estimate, effective moment of inertia, Ieff, can be taken as 0.75 times gross moment of inertia, Ig.

C9.1.1.1-

CALTRANS, AASSHTO and Eurocode use cracked flexural stiffness. For piers/columns which are compression members, the effective flexural stiffness is considered to be 0.5 to 0.7 times gross flexural stiffness, depending on the level of axial stress.

9.2 - Maximum Elastic Forces and Deformations The inertia forces due to mass of each component or portion of the bridge as obtained from Clause 9.2.1 shall be applied at the center of mass of the corresponding component or portion of the bridge. A linear static analysis of the bridge shall be performed for these applied inertia forces to obtain the force resultants (e.g., bending moment, shear force and axial force) and deformations (e.g., displacements and rotations) at different locations in the bridge. The stress resultants Ve and

deformations so obtained are the maximum elastic force resultants (at the chosen cross-section of the bridge component) and the maximum elastic deformations (at the chosen nodes in the bridge structure), respectively.

C9.2 - Maximum Elastic Forces and Deformations

The seismic forces, thus obtained on each component of bridge are used in linear static analysis of bridge to obtain the response quantities such as bending moment, shear force, axial force and deformation. An adequate mathematical model of bridge shall be made and seismic forces shall be applied at the centre of mass of each component. Mathematical model of 2-span bridge is shown in Fig C3. Here piers (or column) are modeled by three frame elements. Likewise superstructure is modeled using four frame elements. Such mathematical model can also be analyzed by using standard structural analysis software. Seismic forces along with various loads (such as DL, LL) shall be applied on the model and analysis shall be done to obtain the response quantities (bending moment, shear force, axial force and deformation).

Element

Node

Fig C3:- Mathematical Model of Bridge

y

yeffc φ

MIE =


Page 47


9.2.1- Inertia Force Due to Mass of Each Bridge Component

The inertia force due to the mass of each bridge component (e.g., superstructure, substructure and foundation) under earthquake ground shaking along any direction shall be obtained from

ehF A W

where

Ah = Elastic Seismic Acceleration Coefficient along the considered direction of shaking obtained as per Clause 9.1, and

W = Seismic weight as discussed in Clause 8.4.

C9.2.1 - Inertia Force Due to Mass of Each Bridge Component

The inertia force due to the mass of a bridge component under earthquake ground shaking in a particular direction depends on the elastic seismic acceleration coefficient computed for shaking along that direction. Clearly, this acceleration coefficient will be different along different directions owing to different natural periods along those directions. Moreover, seismic weight will also be different in the longitudinal and transverse directions due to different amount of live load in the two directions.

9.2.2- Elastic Seismic Acceleration

Coefficient for Portions of

Foundations below Scour Depth For portions of foundations at depths of 30m or below from the scour depth (as defined in Clause 14.1), the inertia forces as defined in Clause 9.2.1 due to that portion of the foundation mass may be computed using the elastic acceleration coefficient taken as 0.5Ah, where Ah is as obtained from Clause 9.2.

For portions of foundations placed between the scour depth and 30m below the scour depth, the inertia force as defined in Clause 9.2.1 due to that portion of the foundation mass may be computed using the elastic seismic acceleration coefficient obtained by linearly interpolating between the value Ah at scour depth and 0.5Ah at a depth 30 m below scour depth, where Ah is as specified in Clause 9.2.

C9.2.2 - Elastic Seismic Acceleration Coefficient for Portions of Foundations below Scour Depth

The propagation of waves within the body of the earth is modified at the surface of the earth owing to the wave reflections at the boundary surface. For this reason, it is generally accepted that the shaking is relatively more violent at the surface, than below the ground. Hence, the guidelines permit reduction in the elastic seismic acceleration coefficient Ah for portions of foundations below scour depth.

9.3 - Design Seismic Force Resultants for Bridge Components The design seismic force resultant V at a cross-section of a bridge component due to earthquake shaking along a considered direction shall be given

C9.3 - Design Seismic Force Resultants for Bridge Components

Response Reduction Factor

The basic philosophy of earthquake resistant design is that a structure should not collapse under strong


Page 48


by R

VV

e

where

eV = Maximum elastic force resultant at the chosen cross-section of that bridge component from Clause 9.2, and

R = Response Reduction Factor for the component as given in Table 7.

Response Reduction Factor shall not be applied for calculation of design displacements.

earthquake shaking, although it may undergo some structural as well as non-structural damage. Thus, a bridge is designed for much less force than what would be required if it were to be necessarily kept elastic during the entire shaking. Clearly, structural damage is permitted but should be such that the structure can withstand these larger deformations without collapse. Thus, two issues come into picture, namely (a) ductility, i.e., the capacity to withstand deformations beyond yield, and (b) over strength. Over strength is the total strength including the additional strength beyond the nominal design strength considering actual member dimensions and reinforcing bars adopted, partial safety factors for loads and materials, strain hardening of reinforcing steel, confinement of concrete, presence of masonry in fills, increased strength under cyclic loading conditions, redistribution of forces after yield owing to redundancy, etc. Hence, the response reduction factors R used to reduce the maximum elastic forces to the design forces reflect these above factors. Clearly, the different bridge components have different ductility and over strength. For example, the superstructure has no or nominal axial load in it, and hence its basic behavior is that of flexure. However, the substructure (piers) which is subjected to significant amount of axial load undergoes a combined axial load-flexure behavior. It is well known that piers are much more ductile than the superstructures. Also, the damage to the substructure is more detrimental to the post-earthquake functioning of the bridge than damage to the superstructure. In the second case, the span alone may have to be replaced, while the first requires replacement of the entire bridge and minor modifications may not help. Thus, the R factors for superstructures are kept at a lower value than those for substructures. The superstructure is essentially expected to behave elastically and hence R value is taken as unity. A similar argument can be given for the R values of foundations which are also lower than those for substructures.

An important issue is that of connections, which usually do not have any significant post-yield behavior that can be safely relied upon. Also, there is no redundancy in them. Besides, there is a possibility of the actual ground acceleration during earthquake shaking exceeding the values reflected by the seismic zone factor Z. In view of these aspects, the connections are designed for the maximum elastic forces (and more) that are transmitted through them.


Page 49


Thus, the R factors for connections are recommended to have values less than or equal to 1.0.

The R values for ductile frame type pier is taken as 3.25 as against 2.5 for single pier. For ductile RC buildings, the value of R is 5.0 (IS1893 (Part 1:2002)). The lower value of R for pier is due to less redundancy as compared to buildings and non-availability of alternate load path. In American code the value for ductile frame type pier is 5.0 as compared to R = 8 for ductile RC building frames. In Eurocode the behavior factor, q is taken as 3.5 for ductile RC pier as against 5.0 for ductile RC building.

It is expected that ductile structural forms, particularly for substructures are inevitably used in all important bridges and in high seismic zones. As has been observed in the past earthquakes, ductile structures out-perform non-ductile structures even though they may have been designed for lower force.


Page 50

PROVISIONS Table 7: Response Reduction Factor R for Bridge Components and Connections

R Substructure

RCC Piers with ductile detailing - Single Column, Wall Type 2.5 - Frame Type 3.25 RCC Piers without ductile detailing - Single Column, Wall Type 2.0 - Frame Type 2.5 Steel Framed Construction 2.5 Steel Framed Piers (with properly designed cross bracings) 3.5 Masonry/PCC piers (unreinforced )* 1.5 RCC Abutment 2.0 Masonry/PCC Abutment 1.5

Connections (including bearings) Superstructure to abutment 0.8 Superstructure to column or pier 1 Columns or piers to foundations 1 Expansion joints within a span of the superstructure 0.8

Superstructure 1.0

Foundations ** 1.5 * This pier is not allowed in seismic zone IV and V ** For stability analysis of well foundation by conventional method, seismic forces can be further reduced by a factor of 2.0. Notes: 1. Response reduction factor is not to be applied for the calculation of displacements. 2. R value for foundations, also refer Clause 15.1 3. For connections, also refer Clause 16.1.1 4. Usually superstructure are rigid and are unlikely to posses much ductility, and they are

usually designed for elastic forces. However, if Earthquake forces with R=1 , are very high and if they govern the design of superstructure ,then one should obtain the maximum load carrying capacity of the pier ( which is designed as ductile member), and superstructure shall be designed for the forces equal to maximum load carrying capacity of the ductile member i.e. pier.


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10. Response Spectrum Method (Multi mode Method) The Response Spectrum Method requires the evaluation of natural periods and mode shapes of several modes of vibration of the structure. This method requires dynamic analysis, by a competent structural engineer.

C10.0 - Response Spectrum Method (Multi mode Method)

Every structure has finite number of modes of vibrations. For example, a 2-DOF system has two mode shapes as shown in Fig C5. The natural time period corresponding to the kth mode is called natural time period (Tk) of kth mode.

For obtaining the natural frequencies and mode shapes, free vibration analysis (also called eigen value analysis) of the structure is to be carried out.

In seismic coefficient method (single mode method), only one mode of vibration was considered. The time period for this mode was obtained in a very simplistic fashion (Clause 9.1.1) without performing the free vibration analysis. In response spectrum method, the natural periods and mode shapes obtained using free vibration analysis are used to obtain seismic force. Sufficient number of modes shall be used so that sum of modal mass of considered modes is more than 90% of the total mass of the structure.

10.1 - Elastic Seismic Acceleration Coefficient in Mode k

The elastic seismic acceleration coefficient kA

for mode k shall be determined by:

kak g/SIZ

A 2

where Z and I are as defined in Clause 8.1, and

C10.1 - Elastic Seismic Acceleration Coefficient in Mode k

For the fundamental mode of vibration i.e., the first mode of vibration, the shape of acceleration response spectrum is same as the one used in the seismic coefficient method. However, for higher modes (i.e., k > 1), the ascending part of the spectrum between 0 to 0.1 sec can be used. Since, the fundamental mode makes the most significant contribution to the overall response and the contribution of higher modes is

2-DOF Model 1st Mode Shape 2nd Mode Shape

Fig C5 – 2-DOF Model and Mode Shapes


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k

a

g

S

is the seismic acceleration coefficient for

mode k given by expression

For rocky, or hard soil sites (Type I)

003330

003400502

.kT.

.kT0.40 k1.00/T.kT .

kgaS

≥≤

≤

For medium soil sites (Type II)

03450

003550502

.kT.

.kT0.55 k1.36/T.kT .

kgaS

≥≤

≤

F For soft soil sites (Type III)

003560

003670502

.kT.

.kT0.67 k1.67/T.kT .

kgaS

≥≤

≤

where kT is the natural period of vibration of mode

k of the bridge. For modes other than the fundamental mode, the bridge flexibility factor

k

a

g

S

for sec.Tk 10 may be taken

as: kk

a Tg

S151

A plot of k

a

g

S

versus Tk is given in Fig. 4 for 5%

damping. Table 6 gives the multiplying factors for obtaining spectral values for various other damping percentages.

relatively small, this is now permitted by several codes.

Damping factor

For higher modes, the value of acceleration response spectrum at T = 0 will remain unity irrespective of the damping value. Ordinates for other values of damping can be obtained by multiplying the value for 5 percent damping with the factors given in Table 5. Note that the acceleration spectrum ordinate at zero period equals peak ground acceleration regardless of the damping value. Hence, the multiplication should be done for T ≥ 0.1sec only. For T = 0, multiplication factor will be 1, and values for 0≤T<0.1sec should be interpolated accordingly.


Page 53

m


10.2 - Inertia Force due to Mass of Bridge at Node j in Mode k The effect of seismic shaking can be quantified as concentrated seismic inertia forces and moment corresponding to the translational and rotational degrees of freedom, respectively, at each node of the discretised model of the bridge structure (a typical descritised model is shown in Fig. C3). Each mode of vibration contributes to these seismic inertia forces and moments. The maximum elastic force at jth node in kth mode is given by

Fkj = mj k Pk Ak g

The force vector ekF of maximum elastic inertia

forces at different nodes in mode k of vibration due to earthquake shaking along a considered direction shall be obtained as:

ek k k kF m P A g

where = Seismic mass matrix of the bridge structure, as defined in Clause 10.2.1,

k = Mode shape vector of vibration mode k of

the bridge structure obtained from free vibration analysis,

kP = Modal participation factor of vibration

mode k of the bridge structure for a given direction of earthquake shaking

C10.2 - Inertia Force due to Mass of Bridge at Node j in Mode k

The expression for force at jth node in kth mode k is obtained through a routine solution procedure for analysis of elastic structures subjected to seismic ground motion represented by its pseudo-acceleration response spectrum. The mathematical model of the bridge structure (Fig. C3) should properly account for all stiffness and masses. A suitable number of intermediate nodes are required for each bridge component to properly estimate the stress resultants caused by the seismic inertia forces generated. In doing so, it will be advantageous to follow the current AASHTO code practices. Rotational moment of inertia of certain masses in the bridge structure may become important particularly in case of joint elements; the same may be incorporated in the matrix of seismic weights as mass moment of inertia times acceleration due to gravity.

Spe

ctru

m A

ccel

erat

ion

Coe

ffic

ient

(S

a/g)

k

Natural Period (Tk)

Fig. 4 Acceleration response spectrum for 5% damping to be used for response spectrum

method

To be used for k =

To be used for k > 1


Page 54


=

1T

kT

k k

m

m

,

kA = Elastic seismic acceleration coefficient for

mode k as defined in Clause 10.1,

g = Acceleration due to gravity, and

1 = Vector consisting of unity (one) associated

with translational degrees of freedom in the considered direction of shaking, and zero associated with all other degrees of freedom.

10.2.1 Seismic Mass Matrix

The seismic mass matrix of the bridge structure shall be constructed by considering its seismic mass lumped at the nodes of discretisation. The seismic mass of each bridge component shall be estimated as per Clause 8.4, and shall be proportionally distributed to the nodes of discretisation of that bridge component.

C10.2.1 - Seismic Mass Matrix

The seismic weight of each bridge component is proportionally distributed to its end and intermediate nodes as lumped masses considering its geometry. These lumped masses are used to form the matrix of seismic weights keeping in mind that the mass lumped at a node contributes to all the translational degrees of freedom at that node


Page 55


10.3 - Maximum Elastic Forces and Deformations The maximum elastic seismic forces in mode k obtained from Clause 10.2 shall be applied on the bridge and a linear static analysis of the bridge shall be performed to evaluate the maximum

elastic force resultants ekF (e.g., bending moment,

shear force and axial force) and the maximum elastic deformations (e.g., displacements and rotations) in mode k at different locations (or nodes) in the bridge for a considered direction of earthquake shaking.

The maximum elastic force resultants enetF and the

maximum elastic deformations, due to all modes considered, for the considered direction of earthquake shaking, shall be obtained by combining those due to the individual modes as follows:

(a) If the structure does not have closely-spaced modes, then the maximum response due to all modes considered may be estimated by the square root of sum of squares (SRSS) method as:

m

kk

1

2

where

k = Absolute value of response in mode k, and

m = Number of modes being considered

(b) If the structure has a few closely-spaced modes, then the maximum response (*) due to these modes shall be obtained by the absolute sum method as:

r

cc

1*

where the summation is for the closely-spaced modes only. This maximum response due to closely-spaced modes (*) is then combined with those of the remaining well-separated modes by the square root of sum of square (SRSS) method in a) above.

C10.3 - Maximum Elastic Forces and Deformations

The modal response quantities (e.g., bending moment, shear force, axial force, displacements and rotations at any location of the bridge) in each mode k need to be combined to obtain the maximum response due to all modes considered. Studies on modal response combinations show that when modal frequencies are well-separated, the Square Root of Sum of Squares (SRSS) Method provides reasonable estimates. If two modal frequencies are separated from each other upto or equal to 10% of the smaller one, then the two modes may be termed as closely-spaced modes. However, when modal frequencies are closely-spaced or nearly closely-spaced, the SRSS method gives poor results.

There is another method for modal combination, called, Complete Quadratic Coefficient (CQC) Method. This method provides in general, reasonably good estimates of the overall response, irrespective of whether the modal frequencies are closely-spaced or well-separated. However, the CQC method assumes that the modal damping ratio is same for all the modes of vibration. In case it is not so, reference shall be made to literature for suitable expressions for modal response combination.


Page 56


10.3.1

The number of modes to be considered in the analysis shall be such that at least 90% of the total seismic mass of the structure is included in the calculations of response for earthquake shaking along each principal direction. If modes with natural frequency beyond 33 Hz are to be considered, modal combination (Clause 10.3 (a) and 10.3 (b)) shall be carried out only for modes with natural frequency less than 33 Hz. Modes with natural frequency exceeding 33 Hz shall be treated as rigid modes and accounted for through missing mass correction discussed below:

At degree of freedom j, the missing mass is given by

1(1 )

n

j j k kj jk

C m P m

where

kP Modal participation factor for mode k,

kjφ Mode shape coefficient for jth, degree of

freedom in kth mode of vibration jm Total mass of the jth mode,

jc Fraction of missing mass for jth mode.

Lateral force associated with missing mass is

I

ZmcF jj

missingj 2

The structure will be statically analyzed for this set

of lateral inertial forces and response gsinmis will

be obtained. The response gsinmis will be

combined with response for flexible modes by the square root of sum of square (SRSS) method in a) above.

C10.3.1-

Standard text books on structural dynamics cover details of response spectrum method, number of modes to be included and missing mass corrections.

10.4 - Design Seismic Force Resultants in Bridge Components

The design seismic force resultant netV at any

cross-section in a bridge component for a considered direction of earthquake shaking shall

C10.4 - Design Seismic Force Resultants in Bridge Components As discussed in the commentary of 9.3, various components of the bridge do not enjoy the same level of ductility and over strength. Hence, the level of design seismic force vis-à-vis the maximum elastic force that will be experienced by the component if the entire bridge were to behave linearly elastic, varies for


Page 57


be determined as

R

FV

enet

net

where the maximum elastic force resultant enetF

due to all modes considered is as obtained in Clause 10.3, and Response Reduction Factor R of that component of bridge is as per Table 7. However, Response Reduction Factor shall not be applied for calculation of design displacements.

10.5 - Multi-directional Shaking When earthquake ground shaking is considered along more than one direction, the design seismic force resultants obtained from Clause 9.3 or 10.4 at a cross-section of a bridge component due to earthquake shaking in each considered direction, shall be combined as per Clause 8.5.

different bridge components. The values of the response reduction factor R given in Table 7 reflect the same.

C10.5- Multi-directional Shaking


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11. Time History Method In Time History Method, dynamic analysis of bridge is carried out for specified earthquake ground motion. In this method, dynamic response (i.e. response varying with time) is obtained.

C11.0 – Time History Method In Seismic Coefficient Method and Response Spectrum Method, static seismic forces are obtained, and static analysis is carried out to obtain the response. However in Time History Method, dynamic analysis of mathematical model using ground motion time history is performed and dynamic response is obtained.

11.1 - Modeling of Bridge In order to carryout time history analysis, a suitable mathematical model of the bridge shall be developed. The model shall adequately represent the mass distribution and stiffness of superstructure, bearings, pier, abutment and foundation. The damping characteristics shall also be adequately included in the model. For analysis in transverse direction, 50% mass of live load shall be included in the model. The pier can be considered to be fixed at the foundation level.

C11.1 Modeling of Bridge The mathematical model of bridge using frame elements for pier and deck is shown in Fig C3. The pier is divided in three elements. General purpose finite element software can be used to accurately model the mass, stiffness and damping properties of bridge. The column could be considered fixed at the top of the foundation irrespective of scour depth. (Fig. C6)

11.2 - Analysis Analysis may be carried out using modal superposition method or direct numerical integration. In modal superposition method, the number of modes shall be such that more than 90% of bridge mass shall participate in the direction under consideration. Time step to be used in the analysis shall be suitably chosen and sensitivity of the solution to time step shall be ascertained.

C11.2 Analysis Modal superposition method can be used for linear analysis only. Direct numerical integration can be used for linear as well as nonlinear analysis. Time step shall be less than the one twentieth of the time period of highest mode. Time step will also depend on frequency content of the input ground motion.

Pier

Fig. C6 - Pier Fixed at top of foundation

h

Normal ground level

Ground level after scour


Page 59


11.3 - Ground Motion Ground acceleration time histories shall have characteristics that are representative of seismic environment of the site and local site conditions. Time histories from actual recorded events with similar magnitude, fault distance and local site condition shall be selected.

The ground motions selected shall have peak ground acceleration value of Z x I, where, Z is zone factor and I is importance factor. At least three ground motions shall be used, and maximum response of the three cases, shall be taken as design value. If more than seven time histories are used, then, average response can be used as design value.

C11.3 Ground Motion Seismic environment characteristics to be considered are: Tectonic environment, earthquake magnitude, type of fault, seismic source to site distance, local site conditions.

It is desirable that time histories recorded during events with similar magnitude and source-to-site distance shall be used.

Expertise will be needed in selecting time histories to be used in time history analysis.

11.3.1 Scaling of Time Histories

Time histories to be used in the analysis, shall be suitably scaled so as to match the design response spectra. The response spectra of time history shall be matched with the design spectra given by

)g/aS(IZx)T(S γ

The matching shall be such that the average response spectra of the selected time histories shall not be less than the above mentioned design spectra in the periods ranging from 0.2T and 1.5T, where T is the fundamental time period of the bridge in the direction under consideration.

C 11.3.1 Scaling of Time Histories

It is desirable that the recorded ground motions selected for the analysis have a response spectrum which has overall level and shape similar to the design response spectra. This would avoid very large scaling factors and change in the spectral content of ground motions.

The factor corresponds to partial load factor used in load combinations n clause 8.7.

11.3.2 Ground Motions for Two- and Three-Dimensional Analysis

For 2-dimesional analysis, ground motion consists of horizontal acceleration time history in the direction under consideration. If vertical ground motion is to be considered, then, vertical acceleration time history is also used.

For 3-dimenstional analysis, ground motions consist of pairs of time histories of appropriate components of horizontal accelerations. For each pair of horizontal acceleration time histories,

C11.3.2 Ground Motions for Two- and Three-Dimensional Analysis

For a bridge with multi-column piers, the 2-Dimensional model for longitudinal direction is shown in Fig C7. For this model, the X-component of ground motion will be used. For analysis in transverse direction, the model is shown in Fig C8. For this model, the Z-component of ground motion will be used.

On the other hand, if 3-dimensional model of the bridge is used Fig C9, then both the component will be applied


Page 60


SRSS response spectrum shall be obtained. This SRSS response spectrum shall be scaled suitably to match with the design response spectrum as described in Clause 11.3.1. If required the vertical acceleration time history shall also be considered.

together.

If required, the vertical component of ground motion shall also be used along with the horizontal components.

11.4 - Interpretation of Time History Analysis Results

11.4 Interpretation of Time History Analysis Results

11.4.1 Linear Analysis

From the time history of the response quantity of a particular member, the maximum value will be the design value. This maximum value shall be divided by 2R, where R is the response reduction factor for that member. While using this design value in the load combination of Clause 8.7, the factor 2.0 associated with earthquake load shall not be used.

C11.4.1 Linear Analysis

The design response spectra is taken as ZI(Sa/g), and hence, response of each component for a particular load combination is obtained by dividing the result by a factor of 2R.

Fig C7- 2-Dimensional Model for longitudinal Direction Fig C8 - 2-Dimensional

Model for Transverse Direction

Y

X

)t(xg

Y

Z

)t(zg

Fig C9 - 2-Dimensional Model of Bridge

)( txg

)( tzg


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11.4.2 Nonlinear Analysis

Nonlinear analysis is used for verifying if the provided strength is sufficient to accommodate the expected inelastic deformation. For the nonlinear analysis, the bridge model shall include nonlinear properties.

In the analysis, ground motions in two directions shall be applied simultaneously along with the dead loads and other loads.

The results of nonlinear analysis shall not be divided by factor 2R.

C11.4.2 Nonlinear Analysis

In nonlinear analysis, the bridge is analyzed for actual earthquake ground motion and not the design earthquake ground motion. Hence, results are not divided by 2R.

Since nonlinearities in the structure will be explicitly modeled in Nonlinear analysis, the division of 2R is not done.


Page 62


12. Pushover Analysis The design force is obtained by dividing the elastic force by R value. In some instances, mentioned in Table.1 energy dissipating capacity may be ascertained by a push over analysis to ensure that the required displacement demand is being met with. The details regarding push over analysis are given in Appendix – E.

C12.0 Pushover Analysis


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13. Superstructure C13. - Superstructure

13.1- The superstructure shall be designed for the design seismic forces specified in Clauses 9.0 or 10.0 along with the other appropriate loads.

The superstructure shall be designed for lesser of following forces:

a) Elastic seismic forces i.e. seismic forces with R= 1.0

b) Forces developed when over strength plastic moment hinges are formed in the substructure. As described in Appendix A.

C13.1 – For seismic analysis in lateral directions, seismic forces will be governed by the time period of the combined system of substructure and substructure. For obtaining vertical forces on superstructure, time period of superstructure will have to be obtained. Usually superstructures are quite rigid in vertical direction, except for long span bridges. The elastic seismic force obtained as per Clause 9.0 or Clause 10.0 shall be applied along with the other loads (like DL, LL, etc.) on the mathematical model of the superstructure and linear static analysis shall be carried out. If necessary, the vertical seismic forces shall also be considered.

13.2 - Under simultaneous action of horizontal and vertical accelerations, the superstructure shall have a factor of safety of at least 1.5 against overturning. In this calculation, the forces to be considered on the superstructure shall be the maximum elastic forces generated in the superstructure, as calculated using Clauses 9.2 and 10.3.

C13.2 - Since the supporting width of the span in the transverse direction is relatively small in comparison with that in the longitudinal direction, overturning of superstructures (that are resting on the substructure without being monolithically connected) in the transverse direction may be possible under the combined action of seismic forces along transverse and vertical directions. Of course, in these calculations, the direction of vertical seismic force shall be taken so as to produce the worst effect.

Railway bridges invariably contain guard rails, which are likely to provide resistance to overturning in transverse direction.

13.3 - The superstructure shall be secured to the substructure, particularly in seismic zones IV and V, through vertical hold-down devices and anti-dislodging elements in horizontal direction as specified in Clauses 13.3.1 and 13.3.2, respectively. These vertical hold-down devices and anti-dislodging elements may also be used to secure the suspended spans, if any, with the restrained portions of the superstructure. However, the frictional forces shall not be relied upon in the design of these hold-down devices or

C13.3 -

This clause makes it mandatory in high seismic regions to have suitable linking devices provided between the superstructure and substructure if they had not been monolithically connected, and between the suspended spans, if any, and restrained portion of the superstructure.

(a) vertical hold-down devices to prevent the superstructure from lifting off from its supports atop the substructure particularly under vertical seismic forces combined with the transverse seismic forces, and


Page 64


anti-dislodging elements.

(b) Horizontal linkage elements to prevent excessive relative deformations between portions of the superstructure or between the superstructure and substructure.

The vertical hold down devices and anti-dislodging elements provide second line of protection against excessive displacements due to seismic loads. The anti-dislodging elements shall be provided in longitudinal as well as transverse direction, even if appropriate seat width as per clause 16.3 is provided.

13.3.1 - Vertical Hold-Down Devices

In zone IV and V, vertical hold-down devices shall be provided at all supports (or hinges in continuous structures), where resulting vertical force due to the maximum elastic horizontal and vertical seismic forces (combined as per Clause 8.5) opposes and exceeds 50% of the dead load reaction.

C13.3.1 - Vertical Hold-Down Devices

Vertical hold-down devices are considered essential to minimize the potential of adverse effects (like uplifting and overturning) of vertical seismic excitation. The provisions for design force of vertical hold-down devices have been adapted from the AASHTO code.

13.3.1.1 -

Where vertical force U, due to the combined effect of maximum elastic horizontal and vertical seismic forces, opposes and exceeds 50%, but is less than 100%, of the dead load reaction D, the vertical hold-down device shall be designed for a minimum net upward force of 10% of the downward dead load reaction that would be exerted if the span were simply supported.

C13.3.1.1 -

13.3.1.2 -

If the vertical force U, due to the combined effect of maximum horizontal and vertical seismic forces, opposes and exceeds 100% of the dead load reaction D, then the device shall be designed for a net upward force of 1.2(U-D); however, it shall not be less than 10% of the downward dead load reaction that would be exerted if the span were simply supported.

C13.3.1.2 -


Page 65


13.3.2-Horizontal Linkage Elements

Horizontal linkage elements are anti-dislodging devices. Positive horizontal linkage elements (high tensile wire strand ties, cables, and dampers) shall be provided between adjacent section of the superstructure at supports and at expansion joints within a span.

C13.3.2 – Horizontal Linkage Elements

Horizontal linkage elements are used to prevent the dislodging of the superstructure. This second line of defense or the additional safety against the excessive horizontal movement is provided either by connecting the superstructure with substructure with the help of chain (Fig C 10a) or by connecting the two adjoining superstructure spans (Fig. C 10b).

Horizontal linkage elements and anti- dislodging devices are quite commonly used in highway bridges. In case of railway bridges, guard rails are invariably present at both the ends of bridge, These guard rails , which run throughout the length of the bridge and covers all the spans, if fastened properly and anchored, are likely to provide good resistance to sliding and overturning of end spans.

(a) Superstructure connected to substructure

Girder

Substructure Anchor bolt

Fig C10 Horizontal Linkage element

(b) Linkage element connecting adjacent spans

Girder Girder

Pier


Page 66


13.3.2.1 –

The linkage shall be designed for at least the elastic seismic acceleration coefficient Ah times the weight of the lighter of the two connected spans or parts of the structure.

C13.3.2.1 –

The design seismic force for each bridge component is only a fraction of the maximum elastic force that can be sustained by it, if it were to remain completely elastic during earthquake shaking. However, the deformations calculated from the linear analysis of the bridge subjected to these design forces are much smaller than the actual deformations that may be experienced during seismic shaking.

13.3.2.2-

If the linkage is at locations where relative deformation are permitted in the design then, sufficient slack must be allowed in the linkage so that linkages start functioning only when the relative design displacement at the linkage is exceeded.

C13.3.2.2-

Unseating of superstructure from the substructure or the suspended span from the restrained portion are the possible consequences if the actual deformations are not accounted for in the design of the supports at these interface points. Sometimes, the two portions that move relative to each other are securely fastened by positive horizontal linkage elements. These devices are usually high tensile wire strand ties, cables or dampers. For the purposes of the design of these devices, the recommendations from the AASHTO code are used. The design forces specified are conservative to provide increased protection at a minimum increased cost.

13.3.2.3-

When linkages are provided at columns or piers, the linkage of each span may be connected to the column or pier instead of the adjacent span.

C13.3.2.3 –

13.3.2.4-

Reaction blocks (or seismic arrestors) when used as anti-dislodging elements shall be designed for seismic force equal to 1.5 times the elastic seismic coefficient multiplied by tributary weight of spans corresponding to that pier/abutment.

C13.3.2.4-

Due to the presence of guard rails, which are likely to offer resistance to sliding during seismic event, the strength requirements of anti-dislodging elements can be reduced.


Page 67


Shock absorber

Abutment

Concrete block

Steel bracket

Abutment

Shock absorber

Fig C11a Reaction blocks in longitudinal

Reaction block

Reaction block

Pier

Fig C11b Reaction blocks in transverse direction

Rails

Bearings


Page 68


14. Substructure C14.0 – Substructure

14.1 - Scour Depth The scour to be considered for design shall be based on mean design flood. In the absence of detailed data the scour to be considered for design shall be 0.9 times the maximum design scour depth.

Note: The designer is cautioned that the maximum seismic scour case may not always be governing design condition.

C14.1 – Scour Depth IRS on sub-structure and foundation of bridges gives details of scour depth.

14.2 - Hydrodynamic Force C14.2 - Hydrodynamic Force

14.2.1- For the submerged portion of the pier, the total horizontal hydrodynamic force along the direction of ground motion is given by

ehe WACF

where eC is a coefficient given by Table 8,

depending on the height of submergence of the pier relative to that of the radius of a hypothetical enveloping cylinder (Fig. 5); and Ah is the elastic seismic acceleration coefficient as per Clause 9.1 or 10.1; and eW is the weight of the water in the

hypothetical enveloping cylinder. The pressure distribution due to hydrodynamic effect on pier is given in Fig. 6; the coefficients C1, C2, C3 and C4 in Fig. 6 are given in Table 9.

C14.2.1- This clause is retained as given in IS: 1893-1984, except that Ah replaces h. Again, as stated earlier in this guideline, Ah is different from h. Hence, the hydrodynamic forces calculated as per this code will be much higher than those estimated as per IS: 1893-1984.


Page 69


14.2.2- In response spectrum analysis, to account for hydrodynamic pressure, additional weight of water shall be added over the submerged depth of pier. The weight of water to be added at a height of 3/7H from the ground level, is given by:

0 0

3(1 )

4 4P

WP

bH bW W A

a H

for b/H < 2.0

0 0

3(0.7 )

4 10P

WP

bH bW W A

a H

for 2.0 < b/H < 4.0

0 0

9

40P

WP

bHW W A

a

for 4.0 < b/H

where,

b = structural width perpendicular to hydrodynamic

pressure,

a =structural width in the direction of

hydrodynamic pressure,

Ao = sectional area of the substructure, and

Wo= density of water.

Hp = pier height

H = height of submerged portion of pier

C14.2.2- The expression for WWP is taken from Japanese highway bridge code. In response spectrum analysis, mathematical model of the bridge is analyzed. For including the hydrodynamic force effect in this model, an additional weight is to be included. The mass corresponding to this added weight would generate the inertia force which shall be same as the hydrodynamic force. The expression for WWP is similar to CeWe term given in Clause 14.2. A comparison of WWP and CeWe for a wall type pier is shown below:

Pier Height = 8m, Pier sectional area = 1 x 3 m2 , Water depth, H = 2/3 x 8 = 5.33 m Case I) Seismic loading along 3 m face : Radius of enveloping circle = 0.5 m, H = 5.33 m H / radius = 5.33 / 0.5 = 10.66 ; Ce = 0.73 and We = wo x π x (radius)2 x H

= 1 x 3.1428 x (0.5)2 x 5.33 = 4.184

Ce x We = 0.73 x 4.184 = 3.05

b = 1 m, a = 3 m, Ao = 1 x 3 = 3 m2

0 0

3(1 )

4 4P

WP

bH bW W A

a H

WWP = 3.81

Case II) Seismic loading along 1 m face : Radius of enveloping circle = 1.5 m, H = 5.33 m H / radius = 5.33 / 1.5 = 3.5 ; Ce = 0.73 and We = wo x π x radius2 x H

= 1 x 3.1428 x (1.5)2 x 5.33 = 37.7

Ce x We = 0.73 x 37.7 = 27.5

b = 3 m, a = 1 m, Ao = 3 x 1 = 3 m2

0 0

3(1 )

4 4P

WP

bH bW W A

a H


Page 70


WWP = 30.9

Thus, the values of CeWe and WWP are comparable for both the directions of seismic loading.

PROVISIONS Table - 8. Values of eC

Cylinder Enveloping of Radius

(H) Portion Submerged of Height

1.0

2.0

3.0

4.0

Ce

0.39

0.58

0.68

0.73

Table - 9. Coefficients C2, C3 and C4 as a function of C1 1C 2C 3C 4C

0.1 0.410 0.026 0.9345

0.2 0.673 0.093 0.8712

0.3 0.832 0.184 0.8013

0.4 0.922 0.289 0.7515

0.5 0.970 0.403 0.6945

0.6 0.990 0.521 0.6390

0.8 0.999 0.760 0.5320

1.0 1.000 1.000 0.4286


Page 71

PROVISIONS

Direction of Seismic Shaking

Fig. 5: Hypothetical Enveloping Cylinders to Estimate Hydrodynamic Forces on Substructures due to Seismic Shaking (Clause 14.2)

Fig. 6: Hydrodynamic Pressure Distribution on the Substructure due to Steam Flow (Clause14.2.2)

C1H

C4H

C3F

(Resultant of pressure on shaded area up to depth C1H) C2pb

pb = 1.2F/H

pb

H


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14.2.3 - Analysis for Vertical Acceleration

While carrying out the analysis for vertical acceleration, the added mass of water for hydrodynamic effect shall not be considered.

C14.2.3 -Analysis for Vertical Acceleration

In vertical direction, water mass will not apply any hydrodynamic pressure on substructure. Hence, added mass of water is n ot considered for vertical direction.

14.3 - Design Seismic Foce The design seismic forces for the substructure shall be obtained as the maximum elastic force on it (as defined in Clause 14.3.1) divided by the appropriate response reduction factor given in Table 7.

C14.3 - Design Seismic Force The clause is meant to ensure ductile behavior of the substructure. In R.C. members, flexural failure can be ductile if the member is detailed appropriately. On the other hand, shear failure is brittle. Hence, the columns are designed and detailed for flexure first. Then, using the principle of capacity design, one calculates how much is the maximum possible earthquake force that this column can sustain in the event of strong shaking. Since the shear failure is a brittle failure, shear design for columns is carried out for this upper bound load.

14.3.1 - Maximum Elastic Seismic Forces

The maximum elastic seismic force resultants at any cross-section of the substructure shall be calculated considering the following forces:

(a) Maximum elastic seismic forces transferred from the superstructure to the top of the substructure

(b) Maximum elastic seismic forces applied at its center of mass due to the substructure’s own inertia forces. Reduction due to buoyancy shall be ignored in the calculation of seismic weight.

(c) Hydrodynamic forces acting on piers as per Clause 14.2, and

(d) Modification in earth-pressure due to earthquake acting on abutments as per Appendix F.

C14.3.1 - Maximum Elastic Seismic Forces


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14.4 - Substructure of Continuous Girder Superstructure

C14.4 – Substructure of Continuous Girder Superstructure.

14.4.1 -

When the superstructure of a multi-span bridge consists of a single continuous girder resting on a restrained bearing (in longitudinal direction) over one of the piers and on sliding bearings over the other piers, the design seismic force at the top of the substructures along the longitudinal direction of the bridge shall be taken as follows:

(a) For the pier supporting the restrained bearing, it shall be the full elastic seismic force transmitted from the superstructure to the top of the pier in the longitudinal direction divided by the appropriate response reduction factor, assuming no friction between the other sliding bearings and the corresponding piers.

(b) For the other piers supporting the sliding bearings, it shall be the horizontal friction force generated on the pier due to the superstructure resting on the pier considering the maximum possible friction between the sliding bearings and the top of the pier.

C14.4.1

14.4.2 –

In transverse direction, the seismic force from superstructure is to be transmitted to the substructures in proportion to their lateral stiffness.

C14.4.2 -

14.4.3 -

While considering the stability of the substructure, such as, wingwalls, abutments etc., against overturning, the minimum factor of safety shall be 1.5 under simultaneous action of maximum elastic seismic forces in both horizontal and vertical directions during the earthquake.

C14.4.3 -


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15. Foundations C15.0 - Foundations

15.1 - The foundations of all bridges shall be designed to resist lesser of the following forces:

(a) Design seismic forces obtained from Clauses 9.3 or 10.4 using value of R as 1.5.

(b) Forces developed when over strength plastic moment hinges are formed in the substructure, as described in Appendix A.

Note – For stability analysis of well foundation by conventional method, seismic forces can be further reduced by a factor of 2.0.

C15.1 -

15.2 - Not withstanding the provisions in relevant codes, the following factor of safety shall be adopted for seismic design of foundation under ultimate condition:

Factor of safety against overturning - 1.5

Factor of safety against sliding - 1.25

Notes:

Note 1: No live load to be considered when the net effect has a stabilizing effect.

Note 2: Area under tension need not be checked provided above criteria for overturning and sliding is satisfied.

C15.2 -

15.3 - In loose sands or poorly graded sands with little or no fines, vibrations due to earthquake may cause liquefaction or excessive total and differential settlements. In Zones IV and V, the founding of bridges on such sands should be avoided unless appropriate methods of compaction or stabilization are adopted. Liquefaction analysis procedure is given in APPENDIX G. Foundation should be taken to sufficient depth below the layers of soil which are

C15.3 – Damages to foundations have very serious implications from structural safety considerations. Also, foundation repairs are very expensive as it is very difficult to access and to make alterations in them. Hence, it is required to ensure that these are not damaged. This clause is intended to achieve the objective that in case of severe ground shaking, the foundation is not damaged. This is done first by requiring a much lower value of response reduction factor for foundation than for the substructure, i.e., a much higher design seismic


Page 75


susceptible to liquefaction.

coefficient for foundation than that for the substructure. However, this is qualified through the concept of capacity design.

Since the seismic forces are inertia induced, the foundation can never experience a seismic force higher than what the substructure is capable of transmitting to it. The attempt is to obtain this upper-bound force that can be transmitted by the substructure by calculating its overstrength plastic moment capacity. The code requires the lower of (a) and (b) of Clause 15.1 to be used in design of the foundation.


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16. Connections The connection between the superstructure and substructure is achieved through bearings. The primary functions of the bearings are to resist the vertical loads due to dead load and live load and to allow for superstructure movements (translation and rotation) due to live load and temperature changes. The design of bearings is governed by the force to be resisted and the extent of movement (translation and rotation) it can accommodate. During seismic event, the lateral seismic forces from superstructure are transferred to substructure through bearings. The bearing shall possess sufficient strength to resist these seismic forces.

C16.0 - Connections Usually bearings are provided at the connection between superstructure and substructure. The connection between adjacent sections of superstructure (expansion joints etc.) and the connections between substructure and foundation also needs to be adequately designed and detailed for seismic loads.

16.1 - Design Force for Connections

C16.1 - Design Force for Connections

16.1.1 –Seismic Zone II and III

The connections between adjacent sections of the superstructure or between the superstructure and the substructure shall be designed to resist at least horizontal seismic force in the restrained directions equal to 0.2 times the vertical dead load reaction at the bearing, irrespective of the number of spans.

C16.1.1 – Seismic Zone II and III

In low seismic regions, the effort in the seismic design of the bridges is reduced to some extent by this clause by requiring only a simple design force calculation for the restrained supports (e.g., rocker or elastomeric bearings). The clause, same as that in the AASHTO code, is considered to provide a somewhat overestimate of the design force.

16.1.2 –Seismic Zone IV and V

The connection between the superstructure and substructure, and the substructure and foundation shall be designed to resist the smaller of the following forces:

a) Maximum elastic horizontal seismic force obtained from analysis and transferred through the connection in the restrained directions, divided by the appropriate Response reduction factor R as applicable to connections, which are given in Table 7.

b) Maximum horizontal force, when over strength plastic moment hinges are formed in the substructure.

C16.1.2 –Seismic Zone IV and V

The most common cause for earthquake disasters in case of bridges is the failure of connections, particularly those between superstructure and the substructure. Hence, extra caution is needed to ensure the safety of connections. This is done in this guidelines by requiring the value of response reduction factor for bridges as 0.8 or 1.0, which implies that the design force for connections obtained is equal to (or more than) the maximum expected elastic force. However, by allowing the designer to use the lower value from (a) and (b) above for design of connections, the code brings in the capacity design concept. Force obtained by (b) above provides an upper-bound on the inertia force that can be developed in the superstructure before the substructure becomes plastic. Once the


Page 77


substructure becomes plastic, the bridge will not be able to sustain higher inertia forces.

16.2 - Displacements at Connections

C16.2 – Displacement at Connections

16.2.1 - Separation between Adjacent Units

When relative movement between two adjacent units of a bridge are designed to occur at a separation/expansion joint, sufficient clearance shall be provided between them, to permit the calculated relative movement under design earthquake conditions to freely occur without inducing damage. Where the two units may be out of phase, the clearance to be provided may be estimated as the square root of the sum of squares of the calculated displacements of the two units under maximum elastic seismic forces given by Clauses 9.2 or 10.3.

C16.1.1 - Separation Between Adjacent Units

When two adjacent units are designed such that relative movement between them is expected to occur at their separation joint, then adequate clearance is necessary between them to avoid pounding and the consequential damage. Probability that the maximum out of phase movement of the two adjacent portions will occur at the same time is very low. To provide the clearance equal to cumulative sum of the displacements of the two units at the separation would be too conservative. Thus, this clause proposes that the square root of the sum of squares of the calculated displacements of the two units under the earthquake forces may be provided as the clearance.

16.3 - Minimum Seating Width Requirements The widths of seating W (in mm) at supports measured normal to the face of the abutment/pier/pedestal of bearings/restrained portion of superstructure from the closest end of the girder shall be the larger of the following:

(a) 1.4 times the calculated displacement under the maximum elastic seismic forces estimated as per Clauses 9.2 or 10.3, to account for uncertainty in deflection calculation; and

(b) the value specified below: 300 + 1.5L + 6Hp for seismic zones

II and III

W = 500 + 2.5L + 10 Hp for seismic zones IV and V

where

C16.3 - Minimum Seating Width Requirement

The connections between superstructures and substructures are designed for forces specified under Clause 16.1. Even though these values are conservative, there still will remain possibilities of the actual seismic force in the connections exceeding the actual strength of the connections. Also, in bridges the substructures are liable to undergo large displacements due to dynamic earth-pressures. Under these conditions, it is possible that the superstructure span may get separated from the connection. At this instance, if adequate width is available on top of the substructure for the superstructure span to rest (despite being separated from the connections), then at least the superstructure span is prevented from being dislodged from its support. Clearly, if the superstructure is still resting atop the substructure, the cost of repairing the connection and restoring the superstructure to its desired position is far more economical than having to rebuild the superstructure afresh if it falls off from the substructure.


Page 78


L = Length (in meters) of the superstructure to the adjacent expansion joint or to the end of superstructure. In case of bearings under suspended spans, it is sum of the lengths of the two adjacent portions of the superstructure. In case of single span bridges, it is equal to the length of the superstructure.

For bearings at abutments, Hp is the average height (in meters) of all columns supporting the superstructure to the next expansion joint. It is equal to zero for single span bridges. For bearings at columns or piers, Hp is the height (in meters) of column or pier. For bearings under suspended spans, Hp is the average height (in meters) of the two adjacent columns or piers.

Graphical representation of seating widths is shown in Fig. 7.

Hence, this clause attempts that even under maximum expected deformations, possibility of collapse or loss of span are minimized through conservative provisions of minimum seating widths. The values of seating widths recommended for high seismic regions are higher than those for low seismic regions; this is because of higher potential of connection failures in high seismic zones. The minimum seat width is required in longitudinal as well as transverse direction.

Based on the data supplied by RDSO, minimum seat width for different types of bridges is given in Table C2

The Minimum seating width given in various codes are:

(A) AREMA:

W =(305+2.5L+10Hp)x(1+0.000125S2) mm

S = skew angle in degrees

(B) TAIWAN HSR:

W =(500+2.5L+10Hp) mm

( C) JAPAN HIGHWAYS

700 + 5 L

Slab/Girder

Abutment

(a) Abutment W

Slab/Girder Slab/Girder

Pier Top

(b) Column or Pier

L1 L2

W1 W2

Suspended Restrained Portion

(c) Suspended Span on Restrained Portion of Superstructure

L1 L2

W

Fig. 7: Minimum Width of Seating of Spans on Supports (Clause 16.3)

L

G.L.

Height of Pier (Hp)


Page 79

Table C2 Seating width for standard Railway bridges (supplied by RDSO)

a

b

cg g

e e

f f

d

a = Nominal Clear Spanb = Centres of Bearingsc = Over all length of Girder/Slabd = Centres to Centres of Pierse = Width of Piers at Topf = Centres of Bearings on piersg = Clearance between spans

w ww

w

SLAB/GIRDER

cg g

d

e a eb ff

PIERS

BEARINGS

w = Minimum width of seating of spans on supports

aw w(c-a)/2

SPAN

b cPIERS

d e

PIERS

f g

2559154575450043203660 632420752559955565549053104570 6344607525510657165709069106100 6384957530011501030010200109009150 646525100300120013400133001310012200 654550100

600180026200260502560024400 686825150700210032600324503190030500 702975150

900245048150478504725045700 74010753001000300064000637006300061000 7801350300

1100370079900796007880076200 81917003001800430095800952009400091500 858185060018005000 8982200600

40018300 19400 19650 150019800 675150 670

5500 2000 700 2400 937

Note:- 1. ALL DIMENSIONS ARE IN MILLIMETRES.

WIDTH FROM SEISMIC

ELEVATION

PLAN

*

-W=500+2.5L+10Hp. for Seismic Zones IV and V.*

Hp = Height of Pier in meters.L = Length in meters of Superstructure to the adjacent expansion joint

or to the end of Superstructure.

(NOT TO SCALE)

3050 3710 3890 3960 915 255 76 420 629

B-PSC GIRDERS12200 1330013100 13400 1200 300 100 550 654

45100 4685046150 48150 20003050 60 875 740

122009150

1330010200

1310010900

1340010300

12001150

300300

100100

550525

654646

305002440018300

324502605019650

2560031900

194002620032600

198006001800

2100 700

1500 400150150

150825925

675686702

670

MINIMUM SEATING WIDTH REQUIREMENT FOR SLABS (PSC & RCBALASTLESS), PSC GIRDERS & STEEL/COMPOSITE GIRDERS

421

515539563

402

444

492

468

421411

388392

444

388

392

411402

392

381383

378379

-W=300+1.5L+6Hp. for Seismic Zones II and III.*

A-SLABS (PSC & RC BALLASTLESS)

C-STEEL/COMPOSITE GIRDERS

******

*

**

* 2. RETROFITTING REQUIRED IN ZONE IV & V.3. MINMUM SEATING WIDTH SHOWN IN THIS TABLE IS SUTABLE UPTO 12 HIGH PIERS.


Page 80


17. Special Ductile Detailing Requirements for Bridges Substructures The design seismic force for bridges is lower than the maximum expected seismic force on them. However, to ensure good performance at low cost, the difference in the design seismic force and the maximum expected seismic force shall be accounted for through additional safety provisions in design / detailing. (These provisions are meant for bridges having reinforced concrete substructures; however, if steel substructures are used in high seismic zones, reference should be made to specialist literature.) APPENDIX C describes the detailing procedure.

C17.0 – Special Ductile Detailing Requirements for Bridges Substructures


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18. Special Devices Special devices like seismic isolation devices, shock transmission units (STU) and dampers may be employed to improve the seismic performance of bridges. However, appropriate analysis and testing shall be carried out before installation.

C18.0 – Special Devices

18.1 - Seismic Isolation Devices Section 19 provides details regarding bridges with seismic isolation.

C18.1 – Seismic Isolation Devices

18.2 - Shock Transmission Units Multi-span bridges with continuous superstructure may be provided with restrained bearings over only one pier/abutment. In order to distribute the seismic forces generated by the superstructure to other pier(s)/abutment(s), STUs’ may be introduced after adequate testing, between superstructure and other pier(s)/abutment(s) where free/guided bearings are used. However, specialist literature shall be consulted for the details of such STUs and for their design in bridges subjected to seismic effects. STUs should facilitate the breathing of the bridge due to thermal and shrinkage effects.

STUs shall be accessible for inspection and maintenance/replacement.

C18.2 – Shock Transmission Units Shock Transmission Unit (STU) also called Lock-Up Device (LUD) creates a rigid link at a movable connection between superstructure and pier/abutment during a shock loading. This facilitates the transfer of lateral load (of shock loading) to piers. An STU comprises of a cylinder filled with fluid and a piston with holes moves against the fluid. This fluid with thexotropic property moves smoothly and slowly under slow motion causing loads (Like temperature related movements). But when subjected to sudden motion causing loads (like during breaking or seismic loads), the fluid can’t flow through. This creates a rigid link.

Pier

Super Structure

STU unit

Fig C12 Typical Shock Transmission Unit


Page 82



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19. Bridges with Seismic Isolation

C19.0 – Bridge With Seismic Isolation

19.1 - General Seismic isolation devices (bearings) are deployed below the deck and on the top of the pier (Fig. 8). These shall be used for stiff bridges with time period less than 1 sec. The reduction in forces is achieved either by lengthening of time period or increase of damping or both of them. The effect of lengthening of period and increase of damping on the design force is explained in Fig. 9. The increase in damping is achieved by hysteretic energy loss. The isolation bearing is idealized as bilinear spring with hysteresis as shown in Fig. 10; where, Ku is elastic stiffness, Kd is post elastic stiffness, Qd is characteristic strength and Keff is effective stiffness.

With the use of isolation devices, the lateral displacement of superstructure increases. This increase in displacement shall not cause any adverse effect. Isolation bearings shall not be used for bridges which (a) are on soft soil, (b) which have long natural time period, and (c) which may experience uplift at bearing support. Isolation bearings shall be firmly fixed to the superstructure and substructure by anchor bolts and shall be easily accessible for replacements.

C19.1 – General A bridge without base isolation has lower time period. In Fig. 9, the spectral acceleration corresponding to non – isolated bridge is A1. With the deployment of base isolation, the time period increase to Te and damping also increases. For this increased damping the spectral acceleration is given by solid line in Fig 9. Thus, the spectral acceleration for time period Te become A3. Thus, presence of base isolation reduces spectral acceleration from A1 to A3. Seismic isolation consists essentially of the mechanism, which decouple the structure, or its contents, from potentially damaging earthquake – induced ground, and support, motions. This decoupling is achieved by increasing the flexibility of the system, together with providing appropriate damping. In many, but not all, the seismic isolation system is mounted beneath the structure and is referred to as “base isolation”.

The basic intent of seismic isolation is to increase the fundamental period of vibration such that the structure is subjected to lower earthquake forces. However, the reduction in forces is accompanied by an increase in displacement demand that must be accommodated within the flexible mount. Furthermore, flexible bridges can move under service loads. When seismic isolation is used, the overall structure is considerably more flexible and provision must be made for substantial horizontal displacement.

The concept of isolation for bridge is fundamentally different than for building structures. There are a number of features of bridges which differ from building and which influence the isolation concept:

1) Most of the weight is concentrated in the superstructure, in a single horizontal plane.

2) The superstructure is robust in terms of resistance to seismic loads but the substructure (piers and abutments) are vulnerable.

3) The seismic resistance is often in two orthogonal horizontal directions, longitudinal and transverse.

4) The bridge must resist significant service lateral loads and displacements from wind and traffic loads


Page 84


and from creep, shrinkage and thermal movements.

The objective of isolation a bridge structure also differs. In a building, isolation is installed to reduce the inertia force transmitted into the structure above in order to reduce the demand on the structural elements. A bridge is typically isolated immediately below the isolators by reducing the inertia loads transmitted from the superstructure.

Although the type of installation shown in Fig. 8 is typical of most isolated bridges, there are number of variations. For example, the isolator may be placed at the bottom of bents; partial isolation may be used if piers are flexible (bearing at abutments only): a rocking mechanism for isolation may be used.


Page 85


0

0.2

0.4

0.6

0.8

1

0.0 0.5 1.0 1.5 2.0 2.5 3.0

PERIOD (sec)

SP

EC

TR

AL

AC

CE

LE

RA

TIO

N (

S a/g

)

Period of non-isolated bridge

Period of isolated bridge

Isolated modes with damping equal to effective damping of

Structural modeswith 5% damping

Composite spectrum for isolated bridge

Period Shift

Teff

A2

A3

A1

IS 1893 Zone V Soil Type I

(5% damped)

Fig.8 Bridge with seismic isolation (Clause 19.0)

Fig.9 Effect of isolator on spectral acceleration (Clause 19.0)


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19.2 - Design Criteria A site-specific seismic hazard analysis shall be carried out to develop design ground motion for base-isolated bridges. This study shall be carried out by professionals with acknowledged expertise to do so and will usually involve geological, seismological, geotechnical and structural inputs. However, if the design ground motion thus arrived at gives a design less conservative than that from

design response spectrum given by . .2

aSZI

g

,

then the latter shall govern the design. The response reduction factor for the substructure shall be taken as half of the values given in Table7. However, the value of response reduction factor shall not be less than 1.0.

C19.2 – Design Criteria

Fig.10 Bilinear force-deflection model for isolator (Clause 19.0)

Force Fmax

Kd Fy

Qd

Displacement

max

EDCQd = Characteristics Strength Fy = Yield Force Fmax = Maximum Force Kd = Post-elastic stiffness Ku = Elastic (unloading) stiffness Keff = Maximum bearing displacement EDC = Energy dissipated per cycle = Area of hysteresis loop (shaded)

Ku Keff Ku


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19.3 - Analysis Procedure The seismic coefficient method (single mode method) or response spectrum method (multimode method) can be used. The isolation system shall be idealized as bilinear system (Fig. 10) with linear stiffness as Keff. The analysis shall be done using upper bound properties and lower bound properties. The upper bound properties, which would result in higher value of Keff, would give higher force, and the lower bound properties would give higher deflection. The maximum and minimum values are obtained by multiplying Kd and Qd with the property modification factors, which depend on velocity, temperature, aging, scragging, travel and contamination. The values of property modification factors are described in Appendix – H.

From the analysis, the isolator deflection, di, shall be obtained. Then, the design force for isolator is F = Keff . di. If uniform load method is used, then, isolator displacement is given by

2250 h eff

iI

A Td

Bmm,

where, 2effeff

WT

K g

Since, the isolator unit has low stiffness, the displacement increases. The clearance in the two orthogonal directions shall be the maximum displacement determined in each of the directions from the analysis. The clearance shall not be less than

2200 h eff

I

A T

B mm

where, BI is the damping coefficient corresponding to the effective damping ratio of the isolator unit.

The value of BI shall be taken from Table 10.

C19.3 – Analysis Procedure Details regarding uniform load method are given in AASHTO Guide Specifications for Isolated Bridges (Reference No. 13 in Annexure A1)


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Table 10. Damping Coefficient for Isolated Bridges, BI

Damping (Percentage of critical)

2 5 10 20 30 40 50

BI 0.8 1 1.2 1.5 1.7 1.9 2.0

In the uniform load method, earthquake force, F = (Ah). W is applied on the structure. Here, W is weight of the bridge, and Ah is the design seismic coefficient corresponding to time period, Teff and damping coefficient, BI.

19.4 - Requirements on Isolator Unit

C19.4 – Requirement on Isolator Unit

19.4.1 - Non-seismic Lateral Forces

The isolation system must resist all Non-seismic lateral load combinations applied above the isolation unit. The rigidity against these lateral forces shall be established with the help of tests. If the temperature is likely to be very low in winter, then, the effect of low temperature on either coefficient of friction, shear modulus etc. shall be properly considered. The isolator shall not lose its effectiveness due to low temperature.

C19.4.1 – Non-seismic Lateral Forces

This requirement is to ensure that the flexible isolator has enough rigidity to resist frequently occurring wind and other service loads.


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19.4.2 - Lateral Restoring Force

The isolator unit has more flexibility and high energy dissipating capacity. Hence, in order to avoid cumulative displacement, it must have sufficient restoring force at any given displaced position. In order to ensure that the restoring force is not too less, it is recommended that at any displacement less than the design displacement, the tangent stiffness shall be such that the natural period shall not be more than 6 sec. The restoring force at any displacement shall be more than the restoring force at lower displacement. If the restoring force is constant for all displacements, then, this force shall be at least equal to 1.05 times the characteristics strength, Kd. It is important to note that the forces which do not depend on the displacements, such as damping force may not be used to meet the minimum restoring force requirement.

C19.4.2 – Lateral Restoring Forces

In the long period range, response spectrum gives very low value of design acceleration. Hence, there is a limit of 6 sec on fundamental natural period.

19.4.3 - Vertical Load and Rotational Stability

In laterally undeformed state, the isolation system shall provide a factor of safety of at least three against the vertical loads. It shall also be shown to be stable under 1.2 times the dead load and vertical load due to seismic force. Further, its stability against the lateral displacement equal to the offset displacement and 1.1 times the total design displacement shall be checked.

The isolator shall have the rotation capacity to accommodate rotation due to dead load, live load and construction misalignment, which shall not be less than 0.005 radians.

C19.4.3 – Vertical Load and Rotational Stability

The buckling load capacity of bearing can be calculated using following relation:

1 2

1 2

2 2

6

r

cr

r

S S GA

P

S S GA

S1 = shape factor of the rubber bearing and for the lead-plugged rubber bearing it is defined as

b pl

r r

A A

B t

, Ab = bonded area and Apl = area of

lead-plug

S2 = second shape factor (aspect ratio) defined as r

B

T

Ar = overlap area between the top-bonded and bottom-bonded elastomer areas of a displaced bearing, as shown in Fig. 12

Buckling load capacity under vertical load can be calculated for non-seismic displacement by replacing Ar by Ab in the above relation.

For circular

For square


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19.5 - Tests on Isolation System C19.5 – Tests on Isolation System

19.5.1 – System Characterization Test

This is to establish characteristics of isolation unit and its various components.

C19.5.1 – System Characterization Test

19.5.2 – Prototype Test

This is to establish deformation and damping characteristics of the isolator unit.

C19.5.2 – Prototype Test

Rectangular

2

1

sin4

2 cos

r

r

BA

d

B

Circular

B1

Bonded dimension

B2

2 1 1 rA B B d

dt

Fig. C12 Overlap area Ar

B

Bonded dimension


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19.5.3 –

These tests are done at manufacturing units and the specimens involved in the test are not used. The prototype test is to be conducted on at least two specimen of full size. The system characterization tests are conducted on various components as per the requirements of the corresponding IS codes.

C19.5.3 –

19.5.4 –

A shake table test on model not less than 1/4th of full model shall be done. Scale factors for this test shall be well established. Wear or travel and fatigue tests are conducted to check if the movements due to thermal displacements and live load rotation can be accommodated. The thermal displacements and live load rotations shall correspond to at least 30 years of expected movement. The tests shall be applied at the design contact pressure and at 200C 80C. The rate of application shall be not less than 63.5 mm/minute.

C19.5.4–

19.5.5 –

The tests shall be done for following minimum :

Bearings – 1.6 km

Dampers attached to the web of the neutral axis – 1.6 km

Dampers attached to the girder bottom – 3.2 km.

C19.5.5

19.5.6 –

The prototype specimen shall be tested in the following sequence for prescribed number of cycles:

C19.5.6


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Table – 11: Sequence for Testing of Bearing

Test Description

(A) Component

Thermal Three fully reversed cycle of loads at a lateral displacement corresponding to the maximum thermal displacement. The test velocity shall not be less than 0.075 mm per minute.

Wind and braking

Twenty fully reversed cycles between limits of plus and minus maximum load for a total duration not less than 40 seconds. After the cyclic testing, the maximum load shall be held for 60 seconds.

Seismic -1

Three fully reversed cycles of loading at each of the following multiples of the total design displacement: 1.0, 0.25, 0.50, 0.75, 1.0, and 1.25 in the sequence mentioned. The results of test corresponding to design displacement are used for finding stiffness and damping properties.

Seismic -2 Fully reversed cycles of loading at design displacement for 25 cycles. The test shall be started from a displacement equal to the offset displacement.

The prototype specimen shall be tested in the following sequence for prescribed number of cycles: Wind and braking

Three fully reversed cycles between limits of plus and minus the maximum load for a total duration not less than 40 seconds. After the cyclic testing, the maximum load shall be held for 60 seconds. This test is done to ascertain the survivability of the isolator after the major earthquake.

(B) Prototype

Seismic performance verification

Three fully reversed cycles of loading at the deign displacement. The test verifies service load performance after the major earthquake.

Vertical load The vertical load carrying capacity shall be demonstrated under 1.2DL + LL (seismic) + additional vertical load due to overturning moment.


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19.5.7 –

The force deflection characteristics of the isolator shall be based on cyclic load test results (seismic test described above) for each fully reversed cycle of loading (Fig. 10). The effective stiffness of an isolator unit shall be calculated for each cycle of loading as follows:

p neff

p n

F FK

where, P and n are maximum positive and negative displacements and FP and Fn are maximum positive and negative forces at P and n respectively (Fig. 10).

C19.5.7 –

19.5.8 –

The equivalent viscous damping ratio () is given by

The total EDC area shall be taken as the sum of the areas of all isolator units. The hysteresis loop area of each isolator unit shall be taken as the minimum area of the three loops established at the design displacement, di is the design displacement at the centre of rigidity of the isolation system in the direction under consideration.

C19.5.8–

Δn Δp

Fn

Fp

Displacement

Force keff

Force

Displacement

Δn Δp

Fn

Fp

keff

Fig. C13 Hysteretic Behavior

Fig. C14 Visco-elastic Behavior

2

1

2eff i

Total EDC area

K d


Page 94


19.6 - System Adequacy In the above mentioned tests, the performance of isolator unit is considered to be satisfactory, if the following conditions are satisfied:

(i) The force deflection plots, of all tests on prototype specimen (excluding viscous damper component) shall show positive incremental force-carrying capacity so as to meet the restoring force requirements.

(ii) In the thermal test on prototype, the maximum measured force shall be less than the design value.

(iii) In the other tests on prototype, the maximum displacement shall be less than the design displacement.

(iv) In the three cycles of seismic tests, the average effective stiffness shall be within 10% of the value used in the design.

(v) In the seismic test, in each of the three cycles, the measured minimum effective stiffness shall not be less than the 80% of the maximum effective stiffness.

(vi) In the second seismic test (Seismic -2), the minimum effective stiffness shall not be less than 80% of the maximum effective stiffness. Similarly, the minimum area under EDC shall not be less than 70% of the maximum EDC area.

C19.6 – System Adequacy

19.7 - Requirements for Elastomeric Bearings In addition to the normal tests and designs, which are done for non-seismic conditions, the elastomeric bearings shall comply with the design described in this section. The elastomeric bearings shall use steel reinforcement; the use of fabric reinforcement is not permitted.

C19.7–Requirements for

Elastomeric Bearings

19.7.1 Shear Strain Components for Isolation Design

The various components of shear strain in the bearing shall be computed as:

19.7.1 – Shear Strain Components for Isolation Design


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Table .12 Shear Strain Components

Component Shear strain

Shear strain due to vertical load

12

21

3

2 (1 2 )

83 1

4

r

c

r

S P

A G kS

GkSP K

GkSA

Shear strain due to non-seismic lateral displacement ,

ss s

rT

Shear strain due to seismic lateral displacement ,

is e q

r

d

T

Shear strain due to rotation 2

2ri r

B

t T

Where,

K is the bulk modulus of the elastomer, in the absence of measured data, the value of K may be taken as 2000 MPa. The shape factor, S1 shall be taken as the plan area of the elastomer layer divided by the area of perimeter free to bulge.

s is non seismic lateral displacement resulting from creep, post-tensioning, shrinkage and thermal effects,

di is seismic lateral displacement,

θ is design rotation and shall not be less than 0.005 rad.

Tr is total elastomer thickness,

k is the material constant, and

ti is the thickness of ith layer.

B is bonded plan dimension or bonded diameter in loaded direction of rectangular bearing or diameter of circular bearing

for S1 15

for S1 > 15


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19.7.2 - Load Combinations

The elastomeric bearing shall satisfy the following load combinations of shear strains:

c 2.5

c + s,s + r 5.0

c + s,eq + 0.5r 5.5

where, shear strains are as explained in Table 12 above.

C19.7.2 – Load Combinations

19.7.3 - Construction Requirements

In addition to non-seismic construction requirements following shall be met with:

(i) The layers of elastomeric bearings shall integrally bond during vulcanization and cold bonding is not allowed.

(ii) A 5-minute proof load test with 1.5 times the dead load and live load shall be conducted on each bearing. There shall be no bulging due to poor lamination.

(iii) All bearings shall be tested in combined compression and shear. The bearings may be tested in pairs. The compressive load shall be average dead load of all bearings and they shall be subjected to five fully reversed cycles of loading at the total design displacement or 50% of elastomer thickness. For each group of similar types of bearings, the effective stiffness and EDC shall be averaged. For individual bearings, the effective stiffness shall be within 20% of design values and EDC shall not be less than 25% of the design value. The average value of effective stiffness of a group shall be within 10% of design value and the EDC value shall not be less than 15% of the design value.

After all the tests, all the bearing shall be visually inspected for defects. If there is lack of bond between rubber and steel, or laminate placement fault, or permanent deformation or surface cracks on rubber that are wider or deeper than 2/3rd rubber thickness, then, the bearing shall be rejected.

C19.7.3 – Construction Requirements


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20. Post earthquake Operation and Inspection

C20. Post earthquake Operation and Inspection

The response of railway tracks and bridges to an earthquake would depend on distance from epicenter and nature of attenuation.The post earthquake train operations in the region shall be cautiously started. The guidelines given in Appendix - I shall be followed, which have been based on AREMA Railway Engineering Manual. Detailed procedure for post earthquake operations and inspection is explained in Appendix – I.


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Appendix – (A) References In the formulation of this guideline, assistance has been derived from the following publications:

1) “Manual for Railway Engineering”, American Railway Engineering and Maintenance-of-Way Association (AREMA), USA, 2007.

2) “AASHTO LRFD Bridge Design Specifications”, American Association of State Highway and Transportation Officials (AASHTO), USA, 2007.

3) Seismic Design Criteria”, California Department of Transportation (CALTRANS), USA, 2006.

4) Design of Structures for Earthquake Resistance”, Eurocode 8: Part 2: Bridges, European Committee for Standardization, 2005.

5) Bridge Manual”, TRANSIT, Wellington, New Zealand, 2005.

6) “Specifications for Highway Bridges”, Part V Seismic Design Japan Road Association, 2003.

7) “Seismic Design for Railway Structures”, Railway Technical Research Institute (RTRI), Japan, 2000.

8) “Seismic Design Criteria for High Speed Rail Project“, National Center for Research on Earthquake Engineering, Taiwan, 1992.

9) Murty, C.V.R. and Jain, S.K. “A Proposed Draft for Indian Code Provisions on seismic design for bridges-Part I: Code”, Journal of Structural Engineering, Vol.26, No. 3, 223-234, 2000.

10) Murty, C.V.R. and Jain, S.K. “A Proposed Draft for Indian Code Provisions on seismic design for bridges-Part II: Code”, Journal of Structural Engineering, Vol.27, No. 2, 79-89, 2000

11) Skinner ,R.I. , Kelly , T.E. and Robinson , B. “ Seismic Isolation for Designers and Structural Engineers”, Robinson Seismic Ltd.

12) “AASHTO Guide Specifications for Seismic Isolation Design “American Association of State Highway and Transportation Officials (AASHTO), USA, 2000.


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Appendix – (B) Relevant Codes and Standards

The following Codes/Standards are necessary adjuncts to these guidelines:

1) IRC:6 Standard Specification and Code of Practice for Road Bridges, 2000

2) IRC:83 (Part III) Standard Specification and Code of (Part III) Practice for Road Bridges

Section IX: - Bearings, 2002

3) IRS Code of Practice For Plain, Reinforced & Prestressed Concrete For General Bridge Construction, Third Revision, 2004

4) IRS Code of Practice For the Design of Sub-Structures and Foundation of Bridge, Second Revision,2004

5) IRS Code of Practice For the Design of Steel or Wrought Iron Bridges Carrying Rail, Road or Pedestrian Traffic, Second Revision, 2004

6) IRS Bridge Rules specifying the Loads for Bridge Design of Super Structure and Sub- Rules Structure of bridges, Second Revision, 2004

7) IS 1893 Criteria for Earthquake Resistant Design of Structures, 1984

8) IS 1893 (Part I) Criteria for Earthquake Resistant Design of Structures, Part I: General Provisions and Buildings, 2002

9) IS 1893 (Part 3) Draft Criteria for Earthquake Resistant Design of Structures, Bridges and Retaining Walls, 2008

10) IS 13920 Ductile Detailing of Reinforced Concrete Structure Subjected to Seismic Forces-Code of Practice, 1993


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Appendix – (C) Ductile Detailing Specifications (Clause 17.0)

C-0 General The detailing rules given have been chosen with the intention that reliable plastic hinges should

form at the top and bottom of each pier column, or at the bottom only of a single stem pier under horizontal loading and that the bridge should remain elastic between the hinges (Fig. C-1). The aim is to achieve a reliable ductile structure. Repair of plastic hinges is relatively easy.

Design strategy to be used is based on assumption that the plastic response will occur in the substructure. However, in case of a wall type substructure, the nonlinear behavior may occur in the foundation-ground system.

C-1 Specification

C-1.1 Minimum grade of concrete should be M25 (fck = 25 MPa).

C-1.1 Steel reinforcement of grade Fe 415 (see IS 1786: 1985) or less only shall be used. However, high strength deformed steel bars of grades Fe 500, having elongation more than 14.5 percent and conforming to other requirements of IS 1786 : 1985 may also be used for the reinforcement.

C-2 Layout (a) The use of circular column is preferred for better plastic hinge performance and ease of

construction.

(b)The bridge must be proportioned and detailed by the designer so that plastic hinges occur only at the controlled locations (e.g., pier column ends) and not in other uncontrolled places.

C-3 Longitudinal Reinforcement The area of the longitudinal reinforcement shall not be less than 0.8 percent nor more than 6

percent, of the gross cross section area Ag. Splicing of flexural region is not permitted in the plastic hinge region. Lap shall not be located within a distance of 2 times the maximum column cross-sectional dimension from the end at which hinging can occur. The splices should be proportioned as a tension splice.

C-3.1 Curtailment of longitudinal reinforcement in piers due to reduction in seismic bending moment towards top.

C-3.1.1 The reduction of longitudinal reinforcement at mid-height in piers should not be carried out except in tall pier.

C-3.1.2 In case of high bridge piers such as of height equal to 30m or more, the reduction of reinforcement at mid height may be done. In such cases the following method should be adopted:

(i) The curtailment of longitudinal reinforcement shall not be carried out in the section six times the least lateral column dimension from the location where plastic hinge is likely to occur.


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(ii) The interval between hoop ties is specified to be less than 150mm in a reinforcement position. The interval between hoop ties shall not change abruptly, the change must be gradual.

C-4 Transverse Reinforcement The transverse reinforcement for circular columns shall consist of spiral or circular hoops.

Continuity of these reinforcements should be provided by either (Fig. C -.2(a) or C-2.(b)):

(a) Welding, where the minimum length of weld should be 12 bar diameter, and the minimum weld throat thickness should be 0.4 times the bar diameter. (b) Lapping, where the minimum length of lap should be 30 bar diameters and each end of the bar anchored with 135 hooks with a 10 diameter extension into the confined core.

Splicing of the spiral reinforcement in the plastic hinge region should be avoided.

In rectangular columns, rectangular hoops may be used. A rectangular hoop is a closed stirrup, having a 135 hook with a 10 diameter extension at each end that is embedded in the confined core (Figure C.2.c). When hoop ties are joined in any place other than a corner the hoop ties shall overlap each other by a length 40 bar diameter of the reinforcing bar which makes the hoop ties with hooks as specified above.

Joint portion of hoop ties for both circular and rectangular hoops should be staggered.

C-5 Design of Plastic Hinge Regions

C-5.1 Seismic Design Force for Substructure

Provisions given in Appendix - C for the ductile detailing of RC members subjected to seismic forces shall be adopted for supporting components of the bridge. The design shear force at the critical section(s) of substructures shall be the lower of the following:

(a) Maximum elastic shear force at the critical section of the bridge component divided by the response reduction factor for that components as per Table 7, and

(b) Maximum shear force that develops when

(i) the substructure has maximum moment that it can sustain (i.e., the overstrength plastic moment capacity as per Clause C-5.2) in single-column or single-pier type substructure.

(ii) plastic moment hinges are formed in the substructure so as to form a collapse mechanism in multiple-column frame type or multiple-pier type substructures, in which the plastic moment capacity shall be the overstrength plastic moment capacity as per Clause C-5.2.

In a single-column type or pier type substructure, the critical section is at the bottom of the column or pier as shown in Figure C-1(a). And, in multi-column frame-type substructures or multi-pier substructures, the critical sections are at the bottom and/or top of the columns/piers as shown in Figure C-1(b).

C-5.2 Over strength Plastic Moment Capacity

The over strength plastic moment capacity at a reinforced concrete section shall be taken as 1.3 times the ultimate moment capacity based on the usual partial safety factors recommended by relevant design codes for materials and loads, and on the actual dimensions of members and the actual reinforcement detailing adopted.

C-5.3 Special Confining Reinforcement:

Special confining reinforcement shall be provided at the ends of pier columns where plastic hinge


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can occur. This transverse reinforcement should extend for a distance from the point of maximum moment over the plastic hinge region over a length l0. The length l0 shall not be less than,

(a) 1.5 times the column diameter or 1.5 times the larger cross sectional dimension where yielding occurs (b) 1/6 of clear height of the column for frame pier (i.e when hinging can occur at both ends of the column) (c) 1/4 of clear height of the column for cantilever pier (i.e when hinging can occur at only one end of the column) (d) 600 mm

C-5.4 Spacing of Transverse Reinforcement

The spacing of hoops used as special confining reinforcement shall not exceed

(i) 1/5 times the least lateral dimension of the cross section of column, (ii) 6 times the diameter of the longitudinal bar, (iii) 150 mm

The parallel legs of rectangular stirrups shall be spaced not more than 1/3 of the smallest dimension of the concrete core or more than 350 mm centre to centre. If the length of any side of the stirrups exceeds 350 mm, a cross tie shall be provided. Alternatively, overlapping stirrups may be provided within the column.

C-5.5 Amount of Transverse Steel to Be Provided

C-5.5.1 The area of cross section, Ash, of the bar forming circular hoops or spiral, to be used as special confining reinforcement, shall not be less than

y

ck

c

gksh f

f

A

ASDA

109.0

or,

whichever is the greater

where

Ash = area of cross-section of circular hoop

S = pitch of spiral or spacing of hoops in mm

Dk = Diameter of core measured to the outside of the spiral or hoops in mm

fck = characteristic compressive strength of concrete

fy = yield stress of steel (of circular hoops or spiral )

Ag = gross area of the column cross section

Ac = Area of the concrete core = 2

4 kDπ

y

ckksh f

fSD.A 0240=


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C-5.5.2 The total area of cross-section of the bar forming rectangular hoop and cross ties, Ash to be used as special confining reinforcement shall not be less than

0.24 1.0g cksh

r y

A fA Sh

A f

or,

0.096 cksh

y

fA Sh

f

where

h = longer dimension of the rectangular confining hoop measured to its outer face

Ar = Area of confined core concrete in the rectangular hoop measure to its outer side dimensions.

Note: Crossties where used should be of the same diameter as the peripheral hoop bar and Ak shall be measured as the overall core area, regardless the hoop area. The hooks of crossties shall engage peripheral longitudinal bars.

C-5.5.2.1 Unsupported length of rectangular hoops shall not exceed 300mm.

C-5.5.3 For ductile detailing of hollow cross-section of pier special literature may be referred. Some of the provisions for hollow RC piers are:

i) For hollow cylindrical piers, in the plastic hinge region, the ratio of internal diameter to thickness should not exceed 8.0.

ii) For wall type hollow piers, in the plastic region, the ratio of clear width of the wall to thickness should not exceed 8.0.

C-6 Design of Components between the Hinges

Once the position of the plastic hinges has been determined and these regions detailed to ensure a ductile performance, the structure between the plastic hinges is designed considering the capacity of the plastic hinges. The intention here is:

(i) To reliably protect the bridge against collapse so that it will be available for service after a major shaking.

(ii) To localize structural damage to the plastic hinge regions where it can be controlled and repaired.

The process of designing the structure between the plastic hinges is known as “capacity design”.

C-6.1 Column Shear and Transverse Reinforcement

To avoid a brittle shear failure design shear force for pier shall be based on overstrength moment capacities of the plastic hinges and given by:

h

MV

O

u

∑=


Page 104

where

∑ =OM the sum of the overstrength moment capacities of the hinges resisting lateral loads, as

detailed. In case of twin pier this would be the sum of the overstrength moment capacities at the top and bottom of the column. For single stem piers the overstrength moment capacity at the bottom only should be used.

h = clear height of the column in the case of a column in double curvature; height to calculated point of contra-flexure in the case of a column in single curvature.

Outside the hinge regions, the spacing of hoops shall not exceed half the least lateral dimension of the column, nor 300 mm.

C-7 Design of Joints:

Beam-column joints should be designed properly to resist the forces caused by axial loads, bending and shear forces in the joining members. Forces in the joint should be determined by considering a free body of the joint with the forces on the joint member boundaries properly represented.

The joint shear strength should be entirely provided by transverse reinforcement. Where the joint is not confined adequately (i.e. where minimum pier and pile cap width is less than three column diameters) the special confinement requirement should be satisfied.

C-7.1 Ductility of all the joints in the structure may be ensured by offsetting the splices / couplers where the area of reinforcement provided is at least twice the required by analysis staggered 600 mm minimum.

C-7.2 The pier – foundation joint or the slab – pier joint (in case of integral slab – bridges ) must be checked for principal tensile stress in the concrete around the junction , following an appropriate prevailing method. The un-cracked joint may be designed by keeping the principal stresses in the joint region below direct tension strength of concrete. If the joint cannot be prevented from cracking, additional vertical stirrups may be added to the external concrete region around the column.

The joint stresses may be assumed to disperse 45º around the column as per prevailing practices. Following references may be useful:

1. Paulay, T. and Priestley, M.J.N., “Seismic Design of Reinforced Concrete and Masonry Buildings” John Wiley and Sons. Inc., 1992.

2. Xiao, Y., “Seismic Design of Reinforced Concrete Bridges”, McGraw Hill , 1989.


Page 105

Elevation Section AA

a. Single column or pier type substructures

Elevation Section AA

(b) Multi-column or frame type substructures

Fig. C-1: Potential location of plastic hinges in substructures (Clause C-0).

Earthquake

Earthquake

Force

Potential Plastic

Hinge Regions

Pile Cap

Pile

Column Cap

A

A

Piles

Column Cap

Earthquake Force

Earthquake

Potential Plastic

Hinge Regions

A

A


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(c) Rectangular hoops

(Fig. C-2: Transverse reinforcement in column (Clause C-4)

(a) Welding in Circular hoops (b) Lapping in circular hoops


Page 107

Appendix – (D) Zone Factors for Some Important Towns (Clause 8.1)

Town Zone Zone Factor, Z Town Zone Zone Factor, Z Agra III 0.16 Kanchipuram III 0.16 Ahmedabad III 0.16 Kanpur III 0.16 Ajmer II 0.10 Karwar III 0.16 Allahabad II 0.10 Kohima V 0.36 Almora IV 0.24 Kolkata III 0.16 Ambala IV 0.24 Kota II 0.10 Amritsar IV 0.24 Kurnool II 0.10 Asansol III 0.24 Lucknow III 0.16 Aurangabad II 0.10 Ludhiyana IV 0.24 Bahraich IV 0.24 Madurai II 0.10 Bangalore II 0.10 Mandi V 0.36 Barauni IV 0.24 Mangalore III 0.16 Bareilly III 0.16 Monghyr IV 0.24 Belgaum III 0.16 Moradabad IV 0.24 Bhatinda III 0.16 Mumbai III 0.16 Bhilai II 0.10 Mysore II 0.10 Bhopal II 0.10 Nagpur II 0.10 Bhubaneswar III 0.16 Nagarjunasagar II 0.10 Bhuj V 0.36 Nainital IV 0.24 Bijapur III 0.16 Nasik III 0.16 Bikaner III 0.16 Nellore III 0.16 Bokaro III 0.16 Osmanabad III 0.16 Bulandshahr IV 0.24 Panjim III 0.16 Burdwan III 0.16 Patiala III 0.16 Calicut III 0.16 Patna IV 0.24 Chandigarh IV 0.24 Pilibhit IV 0.24 Chennai III 0.16 Pondicherry II 0.10 Chitradurga II 0.10 Pune III 0.16 Coimatore III 0.16 Raipur II 0.10 Cuddalore III II 0.16 Rajkot III 0.16 Cuttack III 0.16 Ranchi II 0.10 Darbhanga V 0.36 Roorkee IV 0.24 Darjeeling IV 0.24 Rourkela II 0.10 Dharwad III 0.16 Sadiya V 0.36 Dehra Dun IV 0.24 Salem III 0.16 Dharampuri III 0.16 Simla IV 0.24 Delhi IV 0.24 Sironj II 0.10 Durgapur III 0.16 Solapur III 0.16 Gangtok IV 0.24 Srinagar V 0.36 Guwahati V 0.36 Surat III 0.16 Goa III 0.16 Tarapur III 0.16 Gulbarga II 0.10 Tezpur V 0.36 Gaya III 0.16 Thane III 0.16 Gorakhpur IV 0.24 Thanjavur II 0.10 Hyderabad II 0.10 Thiruvananthapuram III 0.16 Imphal V 0.36 Tiruchirappali II 0.10 Jabalpur III 0.16 Thiruvennamalai III 0.16 Jaipur II 0.10 Udaipur II 0.10 Jamshedpur II 0.10 Vadodara III 0.16 Jhansi II 0.10 Varanasi III 0.16 Jodhpur II 0.10 Vellore III 0.16 Jorhat V 0.36 Vijayawada III 0.16 Kakrapara III 0.16 VIshakhapatnam II 0.10 Kalapakkam III 0.16


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Appendix – (E) Pushover Analysis (Clause 12.0)

E-1 Pushover analysis is performed to explicitly ascertain the displacement capacity of the bridge structure. This analysis is explained for the reinforced concrete structures. This is done with the help of static nonlinear analysis, in which nonlinear properties of concrete and reinforcing steel are used. The displacement capacity shall be greater than the displacement demand. The procedure explained herein, is based on Caltrans (2006).

E-2 Displacement demand

The displacement demand is twice the elastic displacement obtained using a linear analysis. This displacement demand is doubled due to use of factor Z/2 in the seismic force calculation for linear analysis. The single mode method (Clause 9.0) or multi mode method (Clause 10.0) may be used as per the requirements of Clause 8.3.1. From the displacement demand, D, the displacement ductility demand is obtained as

YDD Δ/Δμ =

where, Y is yield displacement of the system from its initial position to the formation of plastic hinge.

E-3 Displacement capacity

The local displacement capacity of a member is obtained from its curvature capacity, which is determined from the moment curvature (M-) analysis. The expected stress strain curve or material properties of concrete and steel are used. For confined concrete, the Mander’s model shown in Fig. E-1 is used, and the stress-strain model shown in Fig. E-2 is used for steel. The moment curvature analysis obtains the curvatures associated with a range of moments for a cross-section, based on the strain compatibility force equilibrium conditions. The M- curve (Fig. E-3) can be idealized with an elastic perfectly plastic curve to estimate the plastic moment capacity of a cross-section. The idealized plastic moment capacity is obtained by balancing the areas between the actual curve and the idealized curve beyond the first reinforcing bar yield point (Fig. E-3).

Fig E-1 Stress strain model for concrete Fig E-2 Stress strain model for steel


Page 109

Here, Mp is the plastic moment capacity , My is the first reinforcing bar yield point & Mne is the expected nominal moment capacity, u is the curvature capacity at the failure limit state defined as the concrete strain reaching cu or the confinement reinforcing steel reaching the reduced ultimate strain cu

R. Similarly, Y is the idealized yield curvature defined by an elastic-perfectly plastic representation of M- curve (Fig. E-3).The idealized plastic curvature capacity, P, which is assumed constant over plastic hinge length, LP is given by P = u - Y. The hinge length, LP in mm is given by

LP = 0.08L + 0.022fyedbl 0.044fyedbl for columns (mm, MPa)

LP = G + 0.044fyedbl for horizontally isolated flared columns

Here, G is the gap between the isolated flare and the soffit of the bent cap. With reference to Fig. E-4, the plastic rotation capacity, P = LP x P and

Then, the total displacement capacity of the column is given by

c = Ycol + P

where, Ycol is the idealized yield displacement of the column (Fig. E-4).

Fig. E-4 Lateral displacement capacity of fixed base column

2P

PP

LL

Fig. E-3 Moment curvature (M- ) curve

Idealized curve Actual curve


Page 110

The displacement capacity c thus obtained shall be greater than the demand D obtained from linear static analysis. The above described procedure to obtain the displacement capacity is for a cantilever column, fixed at the base and free at the top. Similarly, analysis can be done for fixed-fixed column. For a frame type substructure, M- curve is to be given for each member and the analysis becomes more involved, for which help of standard software may be required.

It shall be ensured that the flexural hinge occurs prior to shear failure of column, and hence, the nominal shear capacity shall be greater than the shear force corresponding to plastic hinge. Similarly, capacity protection shall be provided to the other adjacent components such as bent cap, pile cap etc.


Page 111

Appendix – (F) Dynamic Earth Pressure (Clause 14.3.1)

F-1. Dynamic earth pressure on abutments

F-1.1 Lateral Earth Pressure - The pressure from earth fill behind retaining walls during an earthquake shall be as given in F.1.1.1 to F.1.4.1. In the analysis, cohesion has been neglected. This assumption is on conservative side.

F-1.1.1 Active Pressure Due to Earth fill - The general conditions encountered for the design of retaining walls are illustrated in Fig. F 1. The total active pressure exerted against the wall shall be the maximum of the two given by the following expression:

21(1 )

2AE h AEE H A K (F.1.)

Where the seismic active earth pressure coefficient KAE is given by

22

2

cos ( ) sin( )sin( )1

cos( )cos( )cos cos cos( )AE

iE

i

(F.2.)

and where

= unit weight of soil (kN/m3)

H = height of wall in (m)

Ф=angle of friction of soil (0)

δ=angle of friction between soil and abutment (0)

Ah=elastic seismic coefficient [see Clause 9.1]

Av= vertical seismic coefficient– it’s value being taken consistently throughout the stability analysis of wall

Failure Surface

Kh W w (1-Kv ) Gravity Wall

Active wedge

EAE Failure Surface

(1-Kv )

w Kh W

Cantilever Wall

Figure F 1: Seismic Active Earth Pressure on Retaining Walls

Active wedge

EAE

i kv ws

kh Ws

Ws -

R

ha

H

EAE


Page 112

equal to 2/3 Ah. (0)

i=backfill slope angle (0)

β=slope of wall to the vertical, negative as shown (0)

F.1.1.2 Point of Application – From the total pressure computed as above subtract the static active pressure obtained by putting in the expression given by equation F.1and F.2. The remainder is the dynamic increment. The static component of the total pressure shall be applied at an elevation H/3 above the base of the wall. The point of application of the dynamic increment shall be assumed to be at mid-height of the wall.

F.1.2 Passive Pressure Due to Earth fill –The total passive pressure against the walls shall be the minimum of the two given by the following expression:

21(1 )

2PE V PEE H A K (F.3.)

Where the seismic passive earth pressure coefficient KPE is given by

22

2

cos ( ) sin( )sin( )1

cos( )cos( )cos cos cos( )PE

iE

i

(F.4.)

F.1.2.2 Point of application - From the static passive pressure obtained by putting 0h vk k in the

expression given by equation F.3 and F.4, subtracts the total pressure computed as above. The remainder is the dynamic decrement .The static component of the total pressure shall be applied at an elevation H/3 above the base of the wall. The point of application of the dynamic decrement shall be assumed to be at an elevation 0.66 H above the base of the wall.

F.1.3 Active Pressure Due to Uniform Surcharge - The active pressure against the wall due to a

uniform surcharge of intensity q per unit area of the inclined earth fill surface shall be:

cos( ) (1 )

cos( )AE q V AE

qHE A K

i

(F.5.)

F.1.3.1 Point of application- The dynamic increment in active pressure due to uniform surcharge shall be applied at an elevation of 0.66H above the base of the wall, while the static component shall be applied at mid-height of the wall.

F.1.4 Passive Pressure Due to Uniform Surcharge-The passive pressure against the wall due to a uniform surcharge of intensity q per unit area of the inclined earth fill shall be:

cos( )

cos( )PE q PE

qHP K

i

(F.6.)

F.1.4.1 Point of application- The dynamic decrement in passive pressures due to uniform surcharge shall be applied at an elevation of 0.66h above the base of the walls while the static component shall be applied at mid-height of the wall

0=== θAA hv

vAhA

tan

1

1-θ


Page 113

F.2 Effect of Saturation on Lateral earth Pressure

F.2.1 For saturated earthfill, the saturated unit weight of the soil shall be adopted in the Equation F.1

F.2.2 For submerged earthfill, the dynamic increment (or decrement) in active and passive earth pressures during earthquakes shall be found from expressions given in equation F.2 and F.4 with the following modifications:

a) The value of shall be taken as the value 1/2 of for dry backfill.

b) The value of θ shall be taken as follows:

)1(tan 1

vb

ht

A

A

(F.7.)

Where

= saturated unit weight of soil (kN/m3)

= submerged unit weight of soil (kN/m3)

Ah= elastic seismic coefficient

=vertical seismic coefficient= 2/3 Ah

c) Buoyant unit weight shall be used in equation F.1 and F.3 as the case may be

d) From the value of earth pressure found out as above, subtract the value of earth pressure determined by putting but using buoyant unit weight. The remainder shall be dynamic increment.

F.2.3 Hydrodynamic pressure on account of water contained in earthfill shall not be considered separately as the effect of acceleration on water has been considered indirectly.

F.3 Partially Submerged Backfill

The situations with partial submerged backfill may be handled by weighing unit weights based on the volume of soil in the failure wedge above and below the phreatic surface as shown in Figure F2. Equation F.7 shall be used to calculate θ using instead of . Then total active and passive pressure can be obtained from equation F.1 and F.2 using equivalent unit weight ( )

F.4 Concrete or Masonry Inertia Forces - Concrete or masonry inertia forces due to 'horizontal and vertical earthquake accelerations are the products of the weight of wall and the horizontal and vertical seismic coefficients respectively.

NOTE - To ensure adequate factor of safety under earthquake condition, the design shall be such that the factor of safety against sliding shall be 1.2 and the resultant of all the forces including earthquake force shall fall within the middle three-fourths of the base width provided. In addition, bearing pressure in soil should not exceed the permissible limit.

vA

0=== θAA hv


Page 114

Figure F 2: Effective unit weight for partially submerged backfills

Tan(900-) =

OR

Area = Area1 + Area2

e =

e =

e =

l

h2

h1

h l2

Notes: (1) Exact solution when ru = 0. (2) Approximate Solution when ru > 0.


Page 115

Appendix – (G) Simplified Procedure for Evaluation of

Liquefaction Potential

(Clause 15.4)

G-1 Cohesionless Soils Due to the difficulties in obtaining and laboratory testing of undisturbed representative samples from most potentially liquefiable sites, in-situ testing is often relied upon for assessing the liquefaction potential of cohesionless soils. Liquefaction potential assessment procedures involving both the SPT and CPT are widely used in practice. The most common procedure used in engineering practice for the assessment of liquefaction potential of sands and silts is the Simplified Procedure1. The procedure may be used with either SPT blow count, CPT tip resistance or shear wave velocity measured within the deposit as discussed below:

Step 1: The subsurface data used to assess liquefaction susceptibility should include the location of the

water table, either SPT blow count (N), or tip resistance of a standard CPT cone cq or the shear wave

velocity, mean grain size 50D , unit weight, and fines content of the soil (percent by weight passing the

IS Standard Sieve No. 75 ).

Step 2: Evaluate the total vertical stress v and effective vertical stress v for all potentially

liquefiable layers within the deposit.

Step 3: The following equation can be used to evaluate the stress reduction factor dr :

m 32z9.15 for z0267.0174.1r

and m 9.15z for z00765.01r

d

d

where z is the depth below the ground surface in meters.

Step 4: Calculate the critical stress ratio induced by the design earthquake, CSR , as;

vvdmax /rg/a65.0CSR

where v and v are the total and effective vertical stresses, respectively, at depth z, maxa is the peak

horizontal ground acceleration (PHGA), and g is the acceleration due to gravity. In the absence of site-

specific estimates of maxa , the PHGA may be estimated by max / /a g ZIS g , where Z is the zone factor

obtained from Table-3 as described earlier, I is the importance factor as per Table-4 and /Sa g is

spectral acceleration coefficient obtained from Clause 9.1. For estimating the vertical total and effective stresses, the water table should be assumed at the highest piezometric elevation likely to be encountered during the operational life of the dam or the embankment except where there is a free standing water column. For assessing liquefaction potential of soil layers underneath free standing water column, the height of free standing water should be neglected and water table should be assumed at the soil surface.

1 Youd, T.L., Idriss, I.M., Andrus, R.D., Arango, I., Castro, G., Chtristian, J.T., Dobry, R., Finn, W.D.L., Harder, L.F., Hynes, M.E., Ishihara, K., Koester, J.P., Liao, S.S.C., Marcuson III, W.F., Martin, G.R., Mitchell, J.K., Moriwaki, Y., Power, M.S., Robertson, P.K., Seed, R.B., Stokoe II, K.H. 2001. Liquefaction resistance of soils: Summary report from the 1996 NCEER and 1998 NCEER/NSF workshops on evaluation of liquefaction resistance of soils. J. of Geotech. and Geoenv. Engrg., ASCE. 127(10): 817-833.


Page 116

For assessing liquefaction susceptibility using the SPT go to Step 5a, for the CPT go to Step 5b, and the shear wave velocity go to Step 5c, to compute cyclic resistance ratio (CRR7.5) for Mw 7.5 earthquakes. Cyclic resistance ratio, CRR for sites for earthquakes of other magnitudes or for sites underlain by non-horizontal soil layers or where vertical effective stress exceeds 1 atmospheric pressure is estimated by multiplying CRR7.5 by three correction factors, Km, Kα and Kσ respectively. Here correction factors for magnitude sloped stratigraphy and effective stress has been denoted with symbols Km, Kα and Kσ,

respectively. These correction factors are obtained from figures G-1, G-2 and G-3.

Step 5a:

Evaluate the standardized SPT blow count ( 60N ) which is the standard penetration test blow count for a

hammer with an efficiency of 60 percent. Specifications of the “standardized” equipment corresponding to an efficiency of 60 percent are given in Table G-1 in the absence of test-specific energy measurement. The standardized SPT blow count is obtained from the equation:

6060 .CNN

where 60C is the product of various correction factors. Correction factors recommended by various

investigators for some common SPT configurations are provided in Table G-2.

Calculate the normalized standardized SPT blow count, 601N using 60601 NCN N , where 601N is

the standardized blow count

normalized to an effective overburden pressure of 98 kPa in order to eliminate the influence of confining pressure. Stress normalization factor CN is calculated from following expression:

2/1/ vaN PC

Subjected to 2NC , where Pa is the atmospheric pressure. However, the closed-form expression

proposed by Liao and Whitman (1986) may also be used:

2/1/179.9 vNC

The Critical Resistance Ratio (CRR) or the resistance of a soil layer against liquefaction is estimated from

Figure A-5 for representative 601N value of the deposit.

Step 5b:

Calculate normalized cone tip resistance, csNcq 1 , using acn

vaccsNc PqPKq 1

where cq is the measured cone tip resistance corrected for thin layers, exponent n has a value of 0.5 for

sand and 1 for clay, and Kc is the correction factor for grain characteristics estimated as follows.

64.1for 88.1775.3363.21581.5403.0

and 641for 0.1234

cccccc

cc

IIIIIK

.IK

The soil behavior type index, cI , is given by 22 log22.1log47.3 FQIc

where nvaavc PPqQ , 100qfF vc , f is the measured sleeve friction and n

has the same values as described earlier. Assess susceptibility of a soil to liquefaction using Figure G-6.

The CRR for a soil layer is estimated from Figure A-6 using the csNcq 1 value representative of the layer.

Although soils with Ic >2.6 are deemed non-liquefiable, such deposits may soften and deform during earthquakes. General guidance is not available to deal with such possibilities.

Softening and deformability of deposits with Ic>2.6 should thus be treated on a material specific basis.


Page 117

Step 5c:

Calculate normalized shear wave velocity, 1sV , for clean sands using: 25.01 vass PVV subjected to

ss VV 3.11 .

The CRR for a soil layer is estimated from Figure G-7 using the 1sV value representative of the layer.

Appropriate CRR- 1sV curve should be used in this assessment depending on the fines content of the

layer.

Step 6: Correct CRR7.5 for earthquake magnitude (Mw), stress level and for initial static shear using correction factors km, k and k, respectively, according to:

kkkCRRCRR M ..5.7

where, km, k k are correction factors, respectively for magnitude correction (Figure G-1), effective overburden correction (Figure G-2) and sloping ground correction (Figure G-3), in combination with Figure G-4. The Critical Stress ratio CRR7.5 is estimated from Figure G-5 for SPT, Figure G-6 for CPT and Figure G-7 for shear wave velocity data.

Step 7: Calculate the factor of safety against initial liquefaction, FS , as:

CSRCRRFS /

where CSR is as estimated in Step 4 and CRR is from Step 6a, 6b or 6c. When the design ground motion is conservative, earthquake-related permanent ground deformation is generally small if 1.1FS .

G-2 Cohesive Soils Cohesive soils are often deemed to be non-liquefiable if any one of the following conditions is not satisfied (Figure G-8a): Percent (by weight) finer than 5 μm 15 % wl 35 % wn 0.9 wl

where wl is the Liquid Limit and and wn is the Natural Moisture Content, respectively. These conditions are collectively referred to as the Chinese Criteria. Since the Chinese Criteria are not always conservative, Seed et al. (2003)2 recommend the following alternative (Figure G-8b):

Cohesive soils should be considered liquefiable if wl 37 %, Ip 12 % and wn 0.85 wl, where Ip is the Plasticity Index

Liquefaction susceptibility of soils should be considered marginal if wl 47 %, Ip 20 % and wn 0.85 wl, where Ip is the Plasticity Index and for such soils liquefaction susceptibility should be obtained from laboratory testing of undisturbed representative samples

Cohesive soils should be considered non-liquefiable if wl 47 % or Ip 20 % or wn 0.85 wl, where Ip is the Plasticity Index

2 B. Seed, K. O. Cetin, R. E. S. Moss, A. M. Kammerer, J. Wu, J. M. Pestana, M. F. Riemer, R.B. Sancio, J.D. Bray, R. E. Kayen, and A. Faris 2003. Advances in Soil Liquefaction Engineering: A Unified and Consistent Frame Work, Proceedings of 26th Annual ASCE Los Angeles Geotechnical Spring Seminar, Keynote Presentation, Long Beach, California.


Page 118

Table G-1: Recommended “Standardized’ SPT Equipment.

Element Standard Specification

Sampler Standard split-spoon sampler with: (a) Outside diameter = 51 mm, and Inside Diameter = 35 mm

(constant – i.e., no room for liners in the barrel)

Drill Rods A or AW-type for depths less than 15.2 m; N- or NW-type for greater depths

Hammer Standard (safety) hammer: (a) drop hammer (b) weight = 65 kg; (c) drop = 750 mm (d) delivers 60% of the theoretical potential energy

Rope Two wraps of rope around the pulley

Borehole 100 to 130mm diameter borehole

Drill Bit Upward deflection of drilling mud (tricone or baffled drag bit)

Blow Count Rate 30 to 40 blows per minute

Penetration Resistant Count Measured over range of 150 to 450 mm of penetration into the ground

Notes:

(1) If the equipment meets the above specifications, N = N60 and only a correction for overburden are needed.

(2) This specification is essentially the same to the ASTM D 1586 standard.


Page 119

Table G-2: Correction Factors for Non-Standard SPT Procedures and Equipment.

Notes : N = Uncorrected SPT blow count. C60 = CHT CHW CSS CRL CBD

N60 = N C60

CN = Correction factor for overburden pressure (N1)60 = CN N60 = CN C60 N

Correction for Correction Factor

Nonstandard Hammer Type

(DH= doughnut hammer; ER = energy ratio)

CHT =0.75 for DH with rope and pulley

CHT =1.33 for DH with trip/auto and ER = 80

Nonstandard Hammer Weight or Height of fall

(H = height of fall in mm; W = hammer weight in kg)

7625.63

WH

CHW

Nonstandard Sampler Setup (standard samples with room for liners, but used without liners

CSS =1.10 for loose sand

CSS =1.20 for dense sand

Nonstandard Sampler Setup (standard samples with room for liners, but liners are used)

CSS =0.90 for loose sand

CSS =0.80 for dense sand

Short Rod Length CRL =0.75 for rod length 0-3 m

Nonstandard Borehole Diameter CBD =1.05 for 150 mm borehole diameter

CBD =1.15 for 200 mm borehole diameter

Figure G-1: Magnitude Correction factor

Mag

nit

ud

e S

calin

g F

acto

r, K

m


Page 120

Figure G-2: Stress correction factor

Figure G-3: Correction for initial static shear (Note: Initial static shear for an embankment may be estimated from Figure A-4)

vho /


Page 121

Z

Px

2

1

2 logx e

Rx x

R

xz

PZ

11 2 22 2

2 1

( log )e

RPx z

R

12 22 2max

1

( )e

RPZLog

R

Figure G-4: Initial static shear under an embankment


Page 122

Figure G-5: Relationship between CRR and (N1)60 for sand for Mw, 7.5 earthquakes

CR

R7.

5

(N1)60


Page 123

Figure G-6: Relationship between CRR and (qc1N)cs for Mw, 7.5 earthquakes

CR

R7.

5 C

RR

7.5

(qc1N)cs

Vs1 m/s

Figure G-7: Relationship between CRR and Vs1 for Mw, 7.5 earthquakes


Page 124

Figure G-8a: The Chinese Criteria (Seed et.al., 2003)

Figure G-8b: Proposal of Seed et al. (2003)

Liquefiable if %finer than 5µm ≤15

wl (

%)

0 100 0

100

wn = 0.9wl

wl = 35

Not Liquefiable

I p (%

)

0 100 0

100

Liquefiable if Wn ≤ 0.85Wl

12

20

47

Test if Wn ≤ 0.85Wl

37

Wl (%)


Page 125

Appendix – (H) System property modification factors

(Clause 19.3)

H-1 General

Kd,max = Kd x max,Kd and Kd,min = Kd x min,Kd

Qd,max = Qd x max,Qd and Qd,min = Qd x min,Qd

These factors are given by

min,Kd = min,t,Kd x min,a,Kd x min,v,Kd x min,tr,Kd x min,c,Kd x min,scrag,Kd

max,Kd = max,t,Kd x max,a,Kd x max,v,Kd x max,tr,Kd x max,c,Kd x max,scrag,Kd

min,Qd = min,t,Qd x min,a,Qd x min,v,Qd x min,tr,Qd x min,c,Qd x min,scrag,Qd

max,Qd = max,t,Qd x max,a,Qd x max,v,Qd x max,tr,Qd x max,c,Qd x max,scrag,Qd

Where,

t = factors to account for effect of temperature

a = factors to account for effect of aging

v = factors to account for effect of velocity (including freq. for elastomeric bearings)

tr = factors to account for effect of travel (wear)

c = factors to account for effect of contamination (in sliding system)

scrag = factors to account for effect of scragging a bearing (in elastomeric systems)

H-2 Elastomeric bearings

Factors for min

min = 1.0 for Kd and Qd

Factors for max

max,v = Established by test

max,c = 1.0

max,tr = Established by test

max,a = See Table G 2.1

max,t = See Table G 2.2

max,scrag = See Table G 2.3


Page 126

max,t Minimum Temp

for design dQ dK

C0 1HDRB 2HDRB 2LDRB 1HDRB 2HDRB 2LDRB

21 1.0 1.0 1.0 1.0 1.0 1.0

0 1.3 1.3 1.3 1.2 1.1 1.1

-10 1.4 1.4 1.4 1.4 1.2 1.1

-30 2.5 2.0 1.5 2.0 1.4 1.3

HDRB = High damping rubber bearing

LDRB = Low damping rubber bearing 1 Large difference in scragged and unscragged properties (more than 25%) 2 Small differences in scragged and unscragged properties

max,scrag

dQ dK

LDRB HDRB

with 150.βeff ≤

HDRB with 150.βeff ≤ LDRB

HDRB with 150.βeff ≤

HDRB

with 150.βeff ≤

1.0 1.2 1.5 1.0 1.2 1.8

max,a

dK dQ

Low-Damping

natural rubber

1.1 1.1

High-Damping rubber with small difference between scragged and unscragged properties

1.2 1.2

High-Damping rubber with large difference between scragged and unscragged properties

1.3 1.3

Lead - 1.0

Neoprene 3.0 3.0

Table H - 2.1: Value of max,a

Table H - 2.2: Value of max,t

Table H - 2.3: Value of max,scrag


Page 127

H-3 Sliding Isolation system

Factors for min

min = 1.0 for Kd and Qd

max,a

Unlubricated

PTFE

Lubricated

PTFE

Bimetallic Interfaces

Sealed Unsealed Sealed Unsealed Sealed Unsealed

Normal 1.1 1.2 1.3 1.4 2.0 2.2

Severe 1.2 1.5 1.4 1.8 2.2 2.5

max,c

Unlubricated

PTFE

Lubricated

PTFE


Sealed with stainless steel surface facing down 1.0 1.0 1.0

Sealed with stainless steel surface facing up* 1.1 1.1 1.1

Unsealed with stainless steel surface facing down 1.1 3.0 1.1

Unsealed with stainless steel surface facing up Not Allowed Not Allowed Not Allowed

max,c Cumulative Travel

(M) Unlubricated

PTFE*

Lubricated

PTFE


1005

< 2010 1.1 1.1 To be established by test

> 2010 1.1 3.0 To be established by test

Factors for max

max,scrag = does not apply

max,v = does not apply

max,a = See Table H 3.1

max,c = See Table H 3.2

max,tr = See Table H 3.3

max,t = See Table H 3.4

Condition

Environment

Table H – 3.1 : Value of max,a

Table H – 3.2: Value of max,c

Table H – 3.3: Value of max,tr


Page 128

* Test data based on 1/8-inch sheet, recessed by 1/16 inch and bonded.

Minimum Temp

for design

max,t

C0 Unlubricated

PTFE

Lubricated

PTFE


21 1.0 1.0

0 1.1 1.3

-10 1.2 1.5

-30 1.5 3.0

To be established by test

Table H – 3.4: Value of max,t


Page 129

Appendix – (I) Post Earthquake Operations and Inspections

I.0 - Post Earthquake Operations and Inspections The response of railway tracks and bridges to an earthquake would depend on distance from epicenter and nature of attenuation. The post earthquake train operations in the region shall be cautiously started. The following guidelines have been based on AREMA Railway Engineering Manual.

I.1 - Operations After an earthquake is reported, the train dispatcher shall notify all the trains and engines within 150 km radius of the reporting area to run at restricted speed until magnitude and epicenter have been determined by proper authority. After determination of the magnitude and epicenter, response levels given in Table I-1 and I-2 will govern the operations.

Table – I-1 Specified Radius of Different Earthquake

Earthquake Magnitude

(Richter)

Response Level

Specified Radius

0- 4.9 I

5.0 – 5.9 II 80 km

6.0 – 6.9 III

II

160 km

240 km

7.0 or above III

II

*

*

* As directed but not less than 6.0-6.9

Table – I-2 Details of Response Level

Response level

Details

I Resume maximum operation speed. The need for the continuation of inspections will be determined by proper authority responsible for maintenance of P.Way.

II All trains and engines will run at restricted speed within a specified radius of the epicenter until inspections have been made and appropriate speeds established by proper authority.

III

All trains and engines within the specified radius of the epicenter must stop and may not proceed until proper inspections have been performed and appropriate speed restrictions established by proper authority. For earthquakes of Richter magnitude 7.0 or above, operations shall be directed by proper authority, but the radii shall not be less than that specified for earthquakes between 6.0 and 6.99.


Page 130

I.2 - Post Earthquake Inspection The following list provides general guidelines for an inspection procedure:

I.2.1 - Track and Roadbed

During the post earthquake inspection, following items shall be observed:

o Line, surface and cross level irregularities caused by embankment slides or liquefaction o Track buckling or pull apart due to soil movement o Offset across fault rupture o Disturbed ballast o Cracks or slope failures in embankments o Slides and/or potential slides in cuts, including loose rocks that could fall in an aftershock o Scour due to tsunami in coastal area Potential for scour or ponding against embankment due to changes in water course

I.2.2 - Bridges

Following an earthquake, inspectors may need to travel by rail between bridges. River bed may get flooded, hence, to quickly reach the bearings; alternate access routes shall be made. In steel bridges following shall be observed carefully:

o Displaced or damaged bearings o Stretched or broken anchor bolts o Distress in viaduct tower o Buckled columns or bracings o Tension distress in main members or bracings o Displaced substructure elements Concrete bridge inspection shall include the following :

o Displacement at bearings o Displaced substructure elements o Cracks in superstructure o Cracks in substructure Inspection team shall also look for items which may fall on track. At an overpass, attention shall be given to reduced span at bearings, damages to column and restrainer system. If there are adjacent buildings to railway track, then such buildings shall also be inspected to ensure if they can withstand aftershocks. Inspection team shall also look for damages to the powerlines passing over the track.


Page 131



Part 2 – Explanatory Examples


Page 132

Example 1 – Railway Bridge with Simply Supported Steel Superstructure

1. Problem Statement:

A three span simply supported Railway Bridge with steel superstructure of open web girder and ballast less track has equal spans of 76.2 m. Train load is Heavy Mineral type (HM loading). Bridge is located in Zone V. The soil at the bridge site is of hard type (Type I). The circular RC pier has 12 m height and 2 m diameter. Height of submerged pier is 4 m. Analyze the bridge for seismic loads at Ultimate Limit State.

Solution: The lateral loads in transverse and longitudinal directions are calculated. Since the spans of the bridge are simply supported, one pier can be considered as single degree of freedom system with half weight of spans on either side. Hence, seismic coefficient method can be used for seismic load calculation. Seismic loads will be obtained from IITK-RDSO Guidelines and also from provisions of existing Bridge Rules and IRS Concrete Code. A comparison of loads obtained from IITK-RDSO Guidelines and existing Bridge Rules will be presented.

1.1. Preliminary Data

The schematic diagram of the bridge is shown below in Figure 1.1. Grade of pier concrete and reinforcement are M30 and Fe415 respectively. Density of concrete is 25 kN/m3. RC pier has ductile detailing.

76.2 m

Pier Height = 12 m

G.L.

76.2 m 76.2 m

Figure 1.1 Geometric details of the bridge


Page 133

1.2. Weight Calculation

1.2.1. Dead Load Calculation

Dead Load (DL) per meter of 76.2 m girder without track load = 43.7 kN/m

(As per data supplied by RDSO)

DL per meter of ballast less track = 0.4 kN/m


DL per meter of superstructure

= DL of girder + DL of track

= 43.7 + 0.4 = 44.1 kN/m

Total DL of superstructure

= 44.1 x 76.2 = 3360 kN

DL of one pier =

= π x 22 /4 x 12 x 25 = 942 kN

Total DL of structure

= DL of superstructure + 80% DL of pier

(Section 9.1.1)

= 3360 + 0.8 x 942 = 4114 kN

1.2.2. Live Load

Live Load (LL) for HM loading on 76.2 m span = 128.6 kN/m


Total live load = 128.6 x 76.2 = 9800 kN

Coefficient of Dynamic Augment (CDA) ,

80.15

(6 )CDA

L

80.15

(6 76.2)CDA

= 0.25

Impact Load = CDA X L.L.

= 0.25 X 9800 = 2450 kN

1.3. Seismic Wight

Seismic weight in longitudinal direction

= Total DL of structure + No LL

(Section 8.4)

= 4114kN

Seismic weight in transverse direction

= Total DL of structure +50 % LL

(Section 8.4)

= 4114 + 0.50 x 9800 = 9014 kN

1.4. Fundamental Natural period

For simply supported bridges, the fundamental natural period (T) in seconds is given by:

δ2T =

(Section 9.1.1)

Where, δ = horizontal deflection in meters due to lateral force, F equal to weight of superstructure and 80 % of weight of substructure and appropriate amount of live load

Since, the superstructure has roller / hinge supports, it is reasonable to assume that pier will behave like cantilever, fixed at the base and free at the top. Hence

pH/D 42


Page 134

EI

FH p

3

3

Where,

H p = Pier height from top of foundation

= 12 m

E = Modulus of elasticity of pier material

=5000√fc

(Section 6.2.3.1, IS456:2000)

= 5000√30 = 27386 N/mm2

= 27386130 kN/m2

I g = Gross moment of inertia of pier section

= π/64 х D4 = π x 24 /64

= 0.785 m4

Ieff = effective moment of inertia of pier section

Ieff = 0.75 x Ig (Section 9.1.1.1)

= 0.75 x 0.785 = 0.589 m4

1.4.1. Longitudinal Direction

In longitudinal direction, no live load is considered. (Section 8.4)

Lateral force to be applied, F = 4114 kN

Lateral deflection,

= 4114 х 123/ (3 х 27386130 х 0.589)

= 0.15 m

Time period 2T

= 2 х 15.0 = 0. 77 sec

1.4.2. Transverse Direction

In transverse direction, 50% live load is considered. (Section 8.4)

Lateral force to be applied, F = 9014 kN

= 9014х 123 / (3 х 27386130 х 0.589) = 0.32 m

δ2T = = 2 х 32.0 = 1.13 sec

1.5. Seismic Load as per IITK-RDSO Guidelines

1.5.1 Horizontal Elastic Seismic Acceleration Coefficient

Horizontal elastic seismic acceleration coefficient, Ah

2a

h

SZA I

g (Section 9.1)

Where,

Z = 0.36 (zone V; Table 3)

I = 1.5 (Table 4)

Damping = 5% (Section 8.6.1)

Site has hard soil (Type I)

Longitudinal direction :

Sa/g = 1.0 / 0.77 = 1.31

Ah = (0.36 / 2) x 1.5 x 1.31 = 0.35

Transverse direction:

Sa/g = 1.0 / 1.13 = 0.88

Ah = (0.36 / 2) x 1.5 x 0.88 = 0.24

1.5.2. Elastic and Design Horizontal Seismic Load

1.5.2.1 Elastic Seismic load

ehF A W

EI

FH p

3

3

EI

FH p

3

3


Page 135

(Section 9.2.1)

In longitudinal direction

Fe = 0.35 x 4114 = 1440 KN

In transverse direction

Fe = 0. 24 x 9014 = 2163 KN

1.5.2.2 Design Seismic load

Design seismic load is obtained by dividing the elastic seismic by response reduction factor, R (Section 9.3)

Since, RCC Pier with ductile detailing,

R = 2.5 (Table 6 of Section 9.3)

Design seismic load in longitudinal direction

= 1440 / 2.5 = 576 kN

Design seismic load in transverse direction

= 2163 / 2.5 = 865 kN

1.5.3. Hydrodynamic Force

1.5.3.1. Elastic Hydrodynamic Force

For the submerged portion of the pier, the total horizontal hydrodynamic force along the direction of ground motion is given by

(Section 14.2)

H = Height of submerged portion of pier

= 1/3 of pier height = 4 m

r = Radius of enveloping cylinder

= 1 m

H/r = 4,

Hence ,

Ce = 0.73

(Table 8 of Section 14.2)

Ah in longitudinal direction = 0.35

Ah in transverse direction = 0.24

We = Weight of the submerged portion of enveloping cylinder = ρw x π a2 H

= 9800 x π x 12 x 4 / 1000 = 123 kN

F = Total horizontal hydrodynamic force

in longitudinal direction

= 0.73 x 0.35 x 123 = 32 kN


in transverse direction

= 0.73 x 0.24 x 123 = 21 kN

1.5.3.2. Design Hydrodynamic Force

Design horizontal hydrodynamic force is ratio of total hydrodynamic force and response reduction factor.

R = 2.5


Design hydrodynamic force in longitudinal direction

= 32 / 2.5 = 13 kN

eWAeCF h ××=

12

4 m F (Resultant Pressure)

2 m

Hydrodynamic Pressure Distribution

on the Pier due to stream flow


Page 136

Design hydrodynamic force in transverse direction

= 21 / 2.5 = 9 KN

1.5.4. Vertical Seismic Acceleration

The elastic vertical Seismic Acceleration Coefficient

gI

ZA aS

v

23

2 (Section 8.8)

As the superstructure is very rigid, the time period in vertical direction will be very less.

Hence, Sa/g = 2.5.

Now,

Z = 0.36 (Table 3 of Section 8.1)

I = 1.5 (Table 4 of Section 8.2)

Av = (2/3) x 0.36/2 x 1.5 x 2.50

= 0.45

Since the vertical seismic acceleration coefficient is less than 0.5, no vertical hold-down devices will be required.

(Section 13.3.1)

The design vertical seismic acceleration coefficient will be

Av / R = 0.45 / 2.5 = 0.18

This implies that total axial force acting on pier will increase or decrease by 18 %. In the present example, this 18 % additional force has been neglected.

1.5.5 Load Combinations

Following two load combinations are given:

(1) 1.25 DL + 1.5 EQ

(2) 1.25DL + 0.3 (LL+IL) + 1.2EQ + 1.4HY

(Section 8.8)

Where, DL = Dead Load, LL = Live Load,

EQ= Earthquake Load , IL = Impact Load Note – Other loads i.e. Superimposed dead Load (DL(S)), Live load on footpath (LL(f)), Hydrodynamic Pressure (HY), Prestressing force (PS), Buoyancy load (BO), Earth Pressure (EP) etc. are not considered.

Loads on pier as per two load combination are shown below:

1.6. Seismic Loads as per existing Bridge Rules and IRS Concrete Bridge Code

Dead load, live load are same as given in section 1.2.1, 1.2.2

1.6.1. Seismic Weight


= Total DL of structure

= 4111 kN


= Total DL of structure + 50 % of LL

= (4111 + 0.5 x 9800) = 9011 kN

1.6.2. Design Seismic Coefficient

The design values of horizontal seismic

5143 kN 1287 kN

869 kN

Load Combination (1)

8818kN 1042 kN

713 kN



Page 137

coefficient αh shall be computed by the following expression:

oh I (Section 2.12.4.2, Bridge Rule)

Where,

β = coefficient for soil foundation system

= 1 (Section 2.12.4.3, Bridge Rule)

I = coefficient for importance of bridge

= 1.5 (Section 2.12.4.4, Bridge Rule)

α0 = Basic horizontal seismic coefficient


αh = 1x 1.5 x 0.08 = 0.12

1.6.3. Seismic Load

Total seismic load in longitudinal direction

= 0.12 x 4111 = 493 kN

Total seismic load in transverse direction

= 0.12 x 9011 = 1081 kN

1.6.4. Load Combinations


(1) 1.4DL + 1.6EQ

(2) 1.4DL + 1.75 ( LL+ IL ) + 1.25 EQ

(Table 12, Section 11.3 of IRS Concrete Bridge Code)

Note – Other loads i.e. Superimposed dead Load (DL(S)), Live load on footpath (LL(f)), Prestressing force (PS), Buoyancy load (BO) etc are not considered.


1.7. Seat Width Calculation

Seat width W (mm) = 500 + 2.5L + 10 HP

(Section 16.3)

L = Length (in meters) of the superstructure to the adjacent expansion joint or to the end of superstructure = 76.2 m

W = 500 + 2.5x76.2 + 10x12

= 810 mm

This is the minimum seat width to be provided here. If the value of the seat width obtained from load requirement comes less than this value, still the minimum seat width will have to be provided.

27198kN 1352 kN

617 kN


5760 kN 1731 kN

790 kN



Page 138

Table 1.1 Comparison of seismic forces from proposed IITK-RDSO guidelines and existing Bridge Rules + IRS Concrete Code (Hard soil)

Span = 76.2m, Pier Height = 12 m, Pier diameter = 2m, Hard soil

Longitudinal Direction

Proposed IITK-RDSO Guidelines existing Bridge Rules + IRS concrete code Time period = 0.77 sec; Ah/R = 0.35 / 2.5 = 0.14 h = 0.12

Transverse Direction

Proposed IITK-RDSO Guidelines existing Bridge Rules + IRS concrete code

Time period = 1.15 sec;

Ah/ R = 0.24/2.5 = 0.096 h = 0.12

Notes –

1) The circular pier will be designed for the worst load case. From the above cases it is seen that as per the Bridge Rule and IRS Concrete code, the pier will be designed for Axial force of 5760 kN and horizontal force of 1731 kN. As per the proposed guidelines, the pier will be designed for Axial force of 5143 kN and lateral force of 1287 kN. Thus, the design forces from the proposed guidelines are almost same as those from the existing Bridge Rules.

2) The bridge is also subjected to other lateral loads like Racking force and Braking/Tractive forces. As per Clause 2.9.1 of Bridges Rules, the racking force which acts in the transverse direction will be 448 kN and As per Appendix XIII of existing Bridge Rules the Tractive / Braking force, which acts in longitudinal direction will be 1325 kN.

713 kN

5143 kN

869 kN

1.25 DL + 1.5 EQ 1.25DL +0.3(LL+IL)+1.2EQ

8818 kN

617 kN

1.4 DL + 1.6 EQ 1.4DL +1.75(LL+IL)+1.25EQ

5760 kN

790 kN

27198 kN

5143 kN

1287 kN

1.25 DL + 1.5 EQ 1.25DL +0.3(LL+IL)+1.2EQ

8818 kN

1042kN

1.4 DL + 1.6 EQ1.4DL +1.75(LL+IL)+1.25EQ

27198 kN

1352 kN

5760 kN

1731 kN


Page 139

In the above comparison, hard soil condition is considered. The comparison of seismic forces from IITK-RDSO Guidelines and existing Bridge Rules will get affected if soil type changes. The above example is again worked out for the soft soil condition and the comparison of results is given in Table 1.2. In the existing Bridge Rules, the soil factor for soft soil also depends on the type of foundation. Here, well foundation is considered.

Table 1.2 Comparison of seismic forces from proposed IITK-RDSO guidelines and existing Bridge Rules + IRS Concrete Code (Soft soil)

Span = 76.2 m, Pier Height = 12 m, Pier diameter = 2m, Soft soil & Well foundation




Ah/R = 0.59 / 2.5 = 0.24 h = 0.18


Proposed IIT-RDSO Guidelines existing Bridge Rules + IRS concrete code


Ah /R = 0.40 / 2.5 = 0.16 h = 0.18

925 kN

1.25DL +0.3(LL+IL)+1.2EQ 1.4DL +1.75(LL+IL)+1.25EQ

1191 kN

2028 kN

1.25DL +0.3(LL+IL)+1.2EQ

8818 kN

1.25 DL + 1.5 EQ

5143 kN

1452 kN

5143kN

2149 kN

1.25 DL + 1.5 EQ

8818 kN

1739 kN

1.4 DL + 1.6 EQ

22293 kN 5143 kN

2595 kN

1.4 DL + 1.6 EQ 1.4DL +1.75(LL+IL)+1.25EQ

5760 kN

1184 kN

27198 kN


Page 140

Example 2 – Comparison of Design Seismic Forces for Short and Long Span Railway Bridges

2. Problem Statement: In Example 1, details on seismic load calculations are covered. Also, a comparison of seismic forces from the proposed guidelines and the existing Bridge Rules is given. In order to assess the difference in design seismic forces obtained from the IITK-RDSO for various types of railway bridges, two examples considered. These two examples represent two extreme types of bridges. The first one (Bridge A) has short span and low pier height and the second one (Bridge B) has long span and tall pier height. The preliminary geometric details of the two bridges are: Bridge A: Span = 12.2 m, Pier Height = 8m, Pier diameter = 2 m Bridge B: Span = 76.2 m, Pier Height = 30 m, Pier diameter = 3 m These are regular, multi-span, and simply supported bridges. Hence, only one unit comprising of one span and pier need to be considered using seismic coefficient method. The bridges are considered in seismic zone V, with hard soil type. Piers are of reinforced concrete and are provided with the ductile detailing.

Solution: Here details of the seismic load calculations will not be given. Rather, values of all the major quantities will be mentioned. Seismic loads are obtained using IITK-RDSO guidelines and existing Bridge Rules.

2.1 Weight Calculations

Table 2.1 Weight Calculations

Component Bridge A Bridge B

Span 12.2 m 76.2 m

Height 8 m 30 m

Diameter of pier 2 m 3 m Soil type Hard, = 1.0 Hard, = 1.0 Importance Factor (I) 1.5 1.5 Seismic zone Z = 0.36, 0 = 0.08 Z = 0.36, 0 = 0.08 Response reduction factor, R 2.5 2.5 Dead Load (DL) per meter girder without track load 8.80 kN/m 43.7 kN/m DL per meter of ballast less track 0.4 kN/m 0.4 kN/m

DL per meter of superstructure 9.2 kN/m 44.1 kN/m

Total DL of superstructure 112 kN 3360 kN DL of one pier 628 kN 5301 kN

Total DL of structure 615 kN 7602 kN

Live Load (LL) for HM loading on span 166.2 kN/m 128.6 kN/m Total live load 2028 kN 9800 kN Impact Load 1197 kN 2450kN Seismic Wight Longitudinal direction Transverse direction

615 kN

1629 kN

7602 kN

12502 kN Gross moment of inertia of pier section 0.785 m4 3.976 m4

Effective moment of inertia of pier section 0.589 m4 2.982 m4


Page 141

2.2 Seismic Loads

Table 2.2 Seismic Loads for Bridge A

Quantity IITK-RDSO Guidelines

existing Bridge Rules

Fundamental period Longitudinal Transverse

0.16 sec 0.26 sec

- -

Spectrum Acceleration Coefficient Longitudinal Transverse

2.5 2.5

- -

Horizontal Elastic Seismic Acceleration CoefficientLongitudinal Transverse

0.68 0.68

- -

Design Seismic Acceleration Coefficient Longitudinal Transverse

0.68/2.5 = 0.27 0.68/2.5 = 0.27

0.12 0.12

Elastic Seismic load Longitudinal Transverse

415 kN

1100 kN

- -

Design Seismic load Longitudinal Transverse

166 kN 440 kN

74 kN

195 kN Total horizontal hydrodynamic force Longitudinal Transverse

36 kN 36 kN

- -

Design Hydrodynamic Force Longitudinal Transverse

14 kN 14 kN

- -

Vertical Seismic Acceleration Av 0.45 -

Design vertical seismic acceleration coefficient 0.45/2.5 = 0.18 -


Page 142

Table 2.3 Seismic Loads for Bridge B

Quantity IITK-RDSO Guidelines

existing Bridge Rules

Fundamental period Longitudinal Transverse

1.83 sec 2.35 sec

- -

Spectrum Acceleration Coefficient Longitudinal Transverse

0.55 0.43

- -

Horizontal Elastic Seismic Acceleration Coefficient Longitudinal Transverse

0.15 0.12

- -

Design Seismic Acceleration Coefficient Longitudinal Transverse

0.15/2.5 = 0.06

0.12/2.5 = 0.048

0.12 0.12

Elastic Seismic load Longitudinal Transverse

1121 kN 1438 kN

- -

Design Seismic load Longitudinal Transverse

488 kN 575 kN

912kN

1500 kN Total horizontal hydrodynamic force Longitudinal Transverse

75 kN 58 kN

- -

Design Hydrodynamic Force Longitudinal Transverse

30 kN 23 kN

- -

Vertical Seismic Acceleration Av 0.45 - Design vertical seismic acceleration coefficient 0.18 -


Page 143

Table 2.4 Comparison of seismic forces for Bridge A from proposed IITK-RDSO guidelines and existing Bridge Rules + IRS Concrete Code (Hard Soil)

Span = 12.2 m, Pier Height = 8 m, Pier diameter = 2m, Hard soil




Ah/R = 0.68 / 2.5 = 0.27

h = 0.12




Ah/R = 0.68 / 2.5 = 0.27 h = 0.12

Notes –

1. The circular pier will be designed for the worst load case. From the above cases it is seen that as per the Bridge Rule and IRS Concrete code, the pier will be designed for axial force of 861 kN and horizontal force of 313 kN. As per the proposed guidelines, the pier will be designed for Axial force of 769 kN and lateral force of 665 kN. Thus, the design lateral forces from the proposed guidelines is double than that from the existing Bridge Rules.

2. The bridge is also subjected to other lateral loads like Racking force and Braking /Tractive forces. As per Clause 2.9.1 the racking force which acts in transverse direction will be 72 kN and As per Appendix XIII of existing Bridge Rules the Tractive / Braking force, which acts in longitudinal direction will be 510 kN.

769 kN

251 kN

1.25 DL + 1.5 EQ 1.25DL +0.3(LL+IL)+1.2EQ

1736 kN

221 kN

1.4 DL +1.75(LL+IL)+1.25EQ

6505 kN

92 kN

1.4 DL + 1.6 EQ

861 kN

118 kN

1.25 DL + 1.5 EQ

665 kN

769 kN

1.25DL +0.3(LL+IL)+1.2EQ

1736kN

552 kN

1.4DL +1.75(LL+IL)+1.25EQ

244 kN

1.4 DL + 1.6 EQ

769 kN

313 kN

5284 kN


Page 144

Table 2.5 Comparison of seismic forces for Bridge B from proposed IITK-RDSO guidelines and existing Bridge Rules + IRS Concrete Code (Hard Soil)

Span = 76.2 m, Pier Height = 30 m, Pier diameter = 3 m, Hard soil




Ah / R = 0.15 / 2.5 = 0.06

h = 0.12




Ah / R = 0.12/2.5 = 0.048 h = 0.12

Notes –

1. The circular pier will be designed for the worst load case. From the above cases it is seen that as per the Bridge Rule and IRS Concrete code, the pier will be designed for axial force of 10642 kN and horizontal force of 2400 kN. As per the proposed guidelines, the pier will be designed for Axial force of 9502 kN and lateral force of 863 kN. Thus, the design lateral forces from the proposed guidelines are almost one-third than that from the existing Bridge Rules. 2. The bridge is also subjected to other lateral loads like Racking force and Braking /Tractive forces. As per Clause 2.9.1 the racking force which acts in transverse direction will be 448 kN and As per Appendix XIII of existing Bridge Rules the Tractive / Braking force, which acts in longitudinal direction will be 1325 kN.

580 kN

1875 kN

1.25DL+0.3(LL+IL)+1.2EQ

9502 kN

673 kN

1.25 DL + 1.5 EQ

13177 kN

9502 kN

863 kN

1.25 DL + 1.5 EQ 1.25DL +0.3(LL+IL)+1.2EQ

13177 kN

723 kN

1.4DL +1.75(LL+IL)+1.25EQ

32080 kN

1140 kN

1.4 DL+ 1.6 EQ

10642 kN

1460 kN

1.4 DL + 1.6 EQ

10642kN

2400 kN

1.4DL +1.75(LL+IL)+1.25EQ

32080 kN


Page 145

Example 3 – Calculation of Seismic Forces for Superstructure

3. Problem Statement: A simply supported railway bridge with steel superstructure of plate girder – welded type has a span of 24.4 m. Train load is Heavy Mineral type (HM loading). Bridge is located in Zone V. The soil at the bridge site is of hard type (Type I). The circular RC pier has 12 m height and 2 m diameter. Calculate lateral seismic forces on bridge superstructure. Bridge pier has isolated spread footing type foundation.

Solution: 3.1. Preliminary Data

Section Property of Superstructure

Outside height (t3) = 2.05 m

Top flange width (t2) = 0.620 m

Top flange thickness (tf) = 0.045 m

Web thickness (tw) = 0.014 m

Bottom flange width (t2b) = 0.620 m

Bottom flange thickness (tfb) = 0.045 m

Fig 4.1:- Sketch of superstructure

2.05 m

1.98 m

0.62m 0.045m

0.014 m

0.045 m


Page 146








= 23.96 + 0.4 = 24.4 kN/m


= 24.4 x 24.4 = 594 kN

DL of one pier =

= π x 22 /4 x 12 x 25 = 942 kN

3.2.2. Live Load

Live Load (LL) for HM loading on 24.4m span = 146.52 kN/m



3.3. Seismic Wight


= Total DL of superstructure + No LL

(Section 8.4)

= 594 kN


= Total DL of superstructure +50 % LL

(Section 8.4)

= 594 + 0.50 x 3575 = 2382 kN

3.4. Fundamental Natural period

For simply supported bridges, the fundamental natural period (T) in seconds is given by:

δ2T =

(Section 9.1.1)

Where, δ = horizontal deflection in meters due to lateral force, F equal to weight of superstructure and 80 % of weight of substructure and appropriate amount of live load

Since, the superstructure has roller / hinge supports, it is reasonable to assume that pier will behave like cantilever, fixed at the base and free at the top. Hence

2

3PFH

EI

where,

H p = 12 m


=5000√fc = 27386130 kN/m2

(Section 6.2.3.1, IS456:2000)

I g = π/64 х D4 = 0.785 m4

Ieff = 0.75 x Ig =0.589 m4 (Section 9.1.1.1)

3.4.1. Longitudinal Direction

In longitudinal direction, no live load is considered. (Section 8.4)

Lateral force to be applied, F =

= 594 + 0.8 x 942 = 1348 kN

Lateral deflection,

pH/D 42


Page 147

2 31348 12

3 3 27386130 0.589PFH

EI

= 0.05 m

Time period 2T = 0.44 sec

3.4.2. Transverse Direction

In transverse direction, 50% live load is considered. (Section 8.4)

Lateral force to be applied, F =

= 594 + 0.8 x 942 + 0.5 x 3575 = 3136 kN

Lateral deflection,

2 33136 12

3 3 27386130 0.589PFH

EI

= 0.11 m

Time period 2T = 0.67 sec


3.5.1 Horizontal Elastic Seismic Acceleration Coefficient

Horizontal elastic seismic acceleration coefficient, Ah

2

ah

SZA I

g (Section 9.1)

Where,


I = 1.5 (Table 4)

Damping = 5% (Section 8.6.1)

Site has hard soil (Type I)

Longitudinal direction :

Sa/g = 1.0 / 0.44 = 2.28

Ah = 0.36 / 2 x 1.5 x 2.28= 0.62

Transverse direction:

Sa/g = 1.0 / 0.67 = 1.49

Ah = 0.36 / 2 x 1.5 x 1.49 = 0.40

3.5.2. Elastic and Design Horizontal Seismic Load

3.5.2.1 Elastic Seismic load

ehF A W

(Section 9.2.1)

In longitudinal direction

Fe = 0.62 x 594 = 366 kN

In transverse direction

Fe = 0.40 x 2382 = 961 kN

3.6. Seismic Loads as per Bridge Rules and IRS Concrete Bridge Code

Dead load, live loads are same as given in section 4.2.1, 4.2.2

3.6.1. Seismic Weight


= 594 kN


= 2382 kN

3.6.2. Design Seismic Coefficient

The design values of horizontal seismic coefficient αh shall be computed by the following expression:


Page 148

oh I (Section 2.12.4.2, Bridge Rule)

Where,

β = coefficient for soil foundation system

= 1 (Section 2.12.4.3, Bridge Rule)

I = coefficient for importance of bridge


α0 = Basic horizontal seismic coefficient


αh = 1x 1.5 x 0.08 = 0.12

3.6.3. Seismic Load

Total seismic load in longitudinal direction

= 0.12 x 594 = 71 kN

Total seismic load in transverse direction

= 0.12 x 2382 = 286 kN

3.7. Racking force and Braking force

3.7.1. Racking force

Lateral load in transverse direction due to racking force of moving load = 5.88 kN / m

(Section 2.9.1, IRS Bridge Rules, 2004)

= 5.88 x 24.4 = 144 kN

3.7.2. Braking force

Lateral load in longitudinal direction due to braking force of moving load

= 882 kN

(APPENDIX – XIII, IRS Bridge Rules, 2004)

Lateral forces

IITK –RDSO Guidelines Existing bridge rules Racking / Braking force


366 kN 71 kN 882 kN


961 kN 286 kN 144 kN

Table 3.1: – Seismic Force for superstructure


Page 149

3.8. Calculations for Wind Forces

Wind load on windward girder

t91.91000

6.25581.2150

Wind load on leeward girder = 25% of Windward girder = 9.91 x 0.25 = 2.47t

(cl.2.11.3.1 of B.R)

W.L. on moving load

1980 mm

2581

mm

600

mm

3505

mm

( 215

0 W

EB

+ 1

00 F

LA

NG

E +

150

SL

EE

PE

R+

156

RA

IL +

25

PA

CK

ING

= 2

581)


Page 150

1980

mm

7.6 t

A

15.2 t 15.2 t

B C

15.2 t C

D

15.2 t15.2 t

E

15.2 t

F G

11.4 t 3.8 t

H I

25600 mm1706.5

R = 56.75 t R = 56.75 t

t46.131000

6.25505.3150

W.L. due to above transverse load = 9.91 + 2.47 + 13.46 = 25.84 t = 256 kN

3.9 Seismic Calculation

Transverse seismic load as per IIT-RDSO guidelines (Table 3.1 above)

961KN>256KN

Hence, seismic forces are governing by Racking force @ 600 kg/m (eff. Span > 20m) (cl.2.9.1 of B.R)

=(600 x 25.6)/1000=15.36 t

Total lateral load = 98.1 + 15.36 = 113.5t

End Reaction t75.562

5.113

Force at intermediate node = 5.75.113

(since

there are 7.5 panels) = 15.2t

Force at node ‘A’ = 2

2.15=7.6t

Force at node ‘H’ = 2.1543 = 11.4t

Force at node I = t8.32.1541

Shear in end way = 56.75 – 3.8 = 52.95t

Eff. Length of bracing =

22 6.1701987.0

= 0.7 x 261.36 = 182.95 cm

Force in end lateral = t70198

36.26195.52


Page 151

Design of top Lateral Bracing

Using two angles 130*130*10

Area = 50.12cm2

rmin =4.01mm

Slenderness ratio = 182.95/4.01 =46

Pac = 13.95-(13.95-12.59)*6/20 (From table (iv) of SBC)

= 13.95-.408=13.54 kg/mm2

Pac (with occasional load) = 13.54*7/6 =15.8kg/mm2 = 1.58t/cm2 (From table (i) of SBC)

Area required = 70/1.58 = 44.3 cm2

Area provided =50.12 cm2 > 44.3 cm2 safe

3.10 DESIGN OF CONNECTION BETWEEN GUSSETS PLATE TO TOP LATERAL BRACING

Rivet Value

Use 22 power driven field rivets

Strength of rivet in single shear

f = t08.494.035.24

2

Strength of one rivet in bearing against 10mm thick gusset plate = 2.35 x 1 x 2.2

=5.17t

Rivet value R = 4.08t

R (with occ-load) = 4.08 x 1.167 = 4.76t

Calculation of No. of Rivets

No. of rivets required

n = 7.1476.4

70

Say 16 Nos. 22 power driven field rivets

3.11 DESIGN OF GUSSET PLATE (SIZE 325 x 10 x 370)

Welded Design of End Gusset Plate

L = 2 (325 + 181) = 1012 mm

Permissible stress in weld = (Cl.13.4.1 of Weld Bridge Code)

Strength of weld = 0.7 X 5 X 101.2 X 1.02

= 72.25 X 5t/cm

Force in gusset due to end lateral = 70t

Size of weld cm96.025.72

70s

Provide 10mm weld size

Welded Design of Intermediate Gusset Plate

Welded length of gusset plate (size 370 x 10 x 820)

L = 820 + 2 x 181 + 510 = 1692mm

Strength of weld = 0.7 x S x 189.2 x 1.02

= 120.80 x S t/cm

Force in gusset plate due to end lateral = 2 x 52.95 = 105.0t

2Ls. 130x130x10

181

10325

10

325x10x370GUSSET PL.

TOP ;AT. BRACINGS

820

510

181

GUSSET PL.370x10x820

10

10


Page 152

Size of weld S = 8.1209.105

= 0.877cm Provide 10mm weld

3.11 DESIGN OF BOTTOM LATERAL BRACING

A lateral bracing system between the bottom flange of sufficient strength to transmit 1/4th of total lateral load (Cl. 5.13.2 of SBC)

Force in end lateral = 4

70 = 17.5t

Eff. Length of bottom bracings L = 0.7 x 261.36 = 182.95 cm

Using s 110 x 110 x 10mm

a = 21.06 cm2

rvv = 2.14 cm

8614.2

95.182

min

r

left

Pac with occasional loads

675.057.10620

57.1032.857.10

= 9.89 kg/mm2

Area required of bottom lateral bracing

22 06.2122.1515.1

5.17cmcm O.K.

3.12 ANALYSIS OF DESIGN FORCE FOR BEARING DESIGN

Analysis of Transverse forces for design

Fy = maximum S.F./Bearing = 4

57.554 =

138.39 t (From DD/2000/2)

Transverse seismic force/bearing

Fz = t52.248.9x4

961

(as per table 3.1 of draft IITK)

Fx = Longitudinal Force/Bearing =

2366882

(as per table 3.1 of draft IITK)

= 624 kN = t8.9

624= 63.7t

50% of L.L. = 0.5 x 3575 = 1788 kN (appendix xii of B.R)

Seismic Load on moving load

= 1788 x Ah = 1788 x 0.4 = 715.2 kN = 73t

(Ah=0.4 as per draft IITK)

Seismic force on fixed structure

= D.L. Ah = 594 x 0.4 = 237.6 kN =

24.3t

Additional vertical effect of seismic on lee-ward girder due to O.T. effect

980.1

)75.16.0581.2(733.13.24

xx= 198t

Load/bearing = 198/2 =99t

ANALYSIS OF VERTICAL FORCES

Due to D.L.

Seismic force = D.L. x Av = 594 x 0.45 (Ah=0.45 as per draft IITK)

= 267.3 kN = 27.3t

Due to L.L. (Shear)

Seismic force = L.L. (50%) x Av

= 1788 x 0.45 = 804.6 kN = 82.1t (Appendix XII of B.R)

Force/bearing = 4

1.823.27 = 27.35t

Loads/Bearing

W/o Seismic

With seismic

Fy 138.39t 138.39+99+27.3 = 265t

Fx 45.0t 63.7t

Fz - 24.52t


Page 153

3.13 DESIGN OF ROCKER & ROLLER BEARING

Design of Expansion End

Size of base plate = 1100 x 560 x 40 mm

With Seismic

Actual base pressure

= 2t/m 43156.01.001

265

Permissible stress = 711 x 1.167 (M-25 grade concrete)

= 829.7 t/m2 O.K.

Design of Roller

Fy (with seismic) = 265 t

Provide 4 rollers of dia 150 mm

Load/roller = 4

265= 66.25t

Allowable working load/mm length = 0.517

= 0.5 x 150 = 75 kg/mm

Net length of roller required

= 31075

25.66 = 884 mm

Total length = 884 + 2 x 30 + 52 = 996 mm < 1010 mm provided

Design of Base slab thickness

Actual bearing pressure

= 23

cm/kg4356110

10265

B.M. at ‘A’ = 2

7110432

=115885 kgcm

B.M. at ‘B’ =

32

101425.662

2111043

= 1042965 – 927500 = 115465 Kg cm

1.5.3 t = 24/236/71570110

6115885

=

1.9 cm

provided = 40 mm O.K.

3.14 IMPLICATIONS OF PROPOSED SEISMIC PROVISION ON EXISTING DESIGN OF ROCKER ROLLER BEARING

BEARING

TYPE COMPONENT EXISTING NEW REMARKS

Base plate 750mm*460mm*50mm 1100mm*560mm*40mm Rollers Two rollers 150mm dia. Four rollers 150mm dia.

Knuckle slab thickness

60mm 75mm

Knuckle thickness

65mm 65mm

Saddle thickness 40mm 60mm

Saddle bolts Four turned bolts 40mm

dia. Four turned bolts 40mm dia.

property clause 6.6

A) Roller bearing

Anchor bolts Four bolts 40mm dia. Eight bolts 40mm dia.

B) Rocker

bearing

Base plate

650mm*900mm*50mm

740mm*1100mm*40mm


Page 154

Example 4 – Analysis of Superstructure for Vertical Component of Earthquake

4. Problem Statement: A simply supported railway bridge with steel superstructure of plate girder – welded type has a span of 24..4 m. Train load is Heavy Mineral type (HM loading). Bridge is located in Zone V. The soil at the bridge site is of hard type (Type I). The circular RC pier has 12 m height and 2 m diameter. Analyze bridge superstructure for vertical component of seismic forces

Solution: 4.1 Preliminary Data

Section Property of Superstructure

Outside height (t3) = 2.05 m

Top flange width (t2) = 0.620 m

Top flange thickness (tf) = 0.045 m

Web thickness (tw) = 0.014 m

Bottom flange width (t2b) = 0.620 m

Bottom flange thickness (tfb) = 0.045 m

Fig 4.2:- Elevation of superstructure

Fig 4.1:- Cross – Section of superstructure

2.05 m

1.98 m

0.62m

0.045m

0.014 m

0.045 m


Page 155

4.2 Weight Calculation

4.2.1 Dead Load Calculation






= 23.96 + 0.4 = 24.4 kN/m

4.2.2 Live Load

Live Load (LL) for HM loading on 24.4m span = 146.5 kN/m


4.3 Seismic Wight for Horizontal motion

Seismic weight for horizontal motion

= Total DL of superstructure + 100 % LL

= 24.4 + 146.52 = 170.9 kN/m

4.4 Method of Analysis

4.4.1 Simplified Approach

As per Section 8.8.1 of IITK – RDSO Guidelines,

For superstructure with span less than 80 m, the effect of vertical motion can be considered by analyzing the superstructure for 25 % additional dead weight in upward and downward direction.

Additional dead weight for vertical motion

= 25 % of seismic weight for horizontal motion

= 0.25 x 170.92 = 42.7 kN/m

Thus , in addition to vertical loads due to Dead load and Live load , 25 % of additional dead load in vertical direction.

Total forces in vertical direction

= DL of superstructure + LL + 25 % additional DL

= 24.4 +146.5 + 42.7 = 213.6 kN / m

4.4.2 Static Analysis

In this analysis, vertical seismic forces are obtained by calculating the time period in vertical direction.

For a simply supported span, the fundamental time period Tv, for vertical motion is given as:-

22V

mT L

EI

(Section 8.8.2)

where,

L = Span of superstructure = 24.4 m


= 5000√fc = 27386130 kN/m2

(Section 6.2.3.1, IS 456:2000)

m = mass per unit length

= (DL + 100 % LL) / g

= (24.4 + 146.52) / 9.81 = 17.42 ton / m

The superstructure comprises of two I-girders, which are connected by horizontal members as shown in figure 4.1. The moment of inertia

24.4 m

213 6 kN / m


Page 156

varies along length. Thus, one will have to use equivalent moment of inertia for the span.

Here , without getting in to details of calculation of moment of inertia , it is assumed that, the time period of the span in vertical direction will be less than 0.4 sec , so that the value of Sa/ g = 2.5

Spectral Acceleration Coefficient for vertical motion is taken as two – thirds of horizontal spectral acceleration.

(Section 8.8)

(Sa/ g) v = 2 / 3 x 2.5 = 1.67

Elastic Seismic Acceleration Coefficient,

2

2 3a

h

SZA I

g

= 0.36 / 2 x 1.5 x 2 / 3 x 2.5

= 0.45

4.5 Vertical Seismic Force

Vertical Seismic Force (EQ) V = Av x W

= 0.45 x 213.65 = 96.1 kN / m

Note: - 1) using the simplified approach, the seismic forces in vertical direction is 42.7 kN/ m where as by static analysis seismic forces in vertical direction is 96.1 kN/m.

2) If time period in vertical direction, Tv is obtained preciously then, Sa/ g will get further reduced.


Page 157

Example 5 – Base Isolated Railway Bridge with Simply Supported Steel Superstructure


A three span simply supported Railway Bridge with steel superstructure of open web girder and ballast-less track has equal spans of 76.2 m. It is proposed to provide Lead Rubber bearings (LRB) above pier to support superstructure. Train load is Heavy Mineral type (HM loading). Bridge is located in Zone V. The soil at the bridge site is of hard type (Type I). The circular RC pier has 12 m height and 2 m diameter. Height of submerged pier is 4 m. Analyze the bridge for seismic loads at Ultimate Limit State.

Solution:

The lateral loads in transverse and longitudinal directions are calculated. Since the spans of the bridge are simply supported, one pier can be considered as single degree of freedom system with half weight of spans on either side. Two bearings will be provided below each super structure girders above a pier sharing equal loads. Hence, seismic coefficient method can be used for seismic load calculation. Seismic loads will be obtained from IITK-RDSO Guidelines. A comparison of loads obtained from Base Isolation bearings and fixed bearings will be presented.

5.1. Preliminary Data

The schematic diagram of the bridge is shown below in Figure 1.1. Grade of pier concrete and reinforcement are M30 and Fe415 respectively. Density of concrete is 25 kN/m3. RC pier has ductile detailing.

76.2 m

Pier Height = 12 m

G.L.

76.2 m 76.2 m

Figure 5.1 Geometric details of the bridge


Page 158








= DL of girder + DL of track

= 43.7 + 0.4 = 44.1 kN/m


= 44.1 x 76.2 = 3360 kN

DL of one pier =

= π x 22 /4 x 12 x 25 = 942 kN

DL of Pier to be lumped

= 80% DL of pier

= 0.8 x 942 = 754 kN

5.2.2. Live Load

Live Load (LL) for HM loading on 76.2 m span = 128.6 kN/m



Coefficient of Dynamic Augment (CDA),

8

0.156

CDAL

8

0.156 76.2

CDA

= 0.25

Impact Load = CDA X L.L.

= 0.25 X 9800 = 2450 kN

5.3. Seismic Wight


= DL + No LL (Section 8.4)

= 3360 kN (W2) for superstructure

= 754 kN (W1) for pier


= DL + 50 % LL (Section 8.4)

= 3360 + 0.50 x 9800

= 8260 kN (W2) for superstructure

= 754 kN (W1) for pier

5.4. Lead Rubber Bearing

5.4.1. Properties

A circular bearing of 600mm overall diameter with central lead core of 100mm diameter is proposed. It has following properties.

Size of bearing, B = 600 mm

Effective size, rB = 590 mm

Modulus of rubber, rG = 0.45 MPa

Thickness of rubber layer, rt = 10 mm

No. of rubber layers, rn = 15

Thickness of steel shims, st = 3 mm

Total rubber Thickness, rT = 150 mm

Total bearing height, h = 192 mm

2 / 4 pD H


Page 159

Elastic modulus of rubber, rE= 4.0 rG

Material constant, k = 0.82

Lead plug diameter, pld = 100 mm

Area of lead plug, plA = 7854 mm2

Yield stress of lead, ply = 8.7 MPa

Characteristic strength, Q = 68.33 kN

Area of bearing, bA= 2.734 x 105 mm2

Post yield stiffness, rk = /b r rA G T

= 820 kN/m

Initial stiffness, uk = 6.5 (1 12 / )r pl bk A A

= 7169 kN/m

Yield displacement, yu r

Q

k k

= 10.76 mm

5.4.2. Design

Due to higher seismic weight in transverse direction, the LRB will be designed for seismic weight = 8260 kN (to be distributed to four LRBs). Primarily, LRB will be designed by assuming SDOF system. Later, it is will be verified by modeling as 2-DOF system. The response spectrum ordinates are amplified by a factor of 1.5 to account for the 1st load case in Ultimate Limit State (1.25 DL + 1.5 EQ).

Seismic weight per LRB, W = 8260 / 4

= 2065 kN

Assuming, target displacement, = 150 mm

Force required, m rF Q k = 191 kN

Effective Stiffness, meff

Fk

= 1275.5 kN/m

Effective time period of the system,

2effeff

WT

gk = 2.55 sec

Total EDC Area = 4 ( )yQ

Equivalent viscous damping,

2

4 ( )

2y

eff

Q

k

= 21.10%

Damping coefficient, BI = 1.52 (Table 10)

Spectral acceleration coefficient,

/aS g = 0.39 (Fig. 3, Damping = 5%)

Horizontal seismic acceleration coefficient,

1.52

ah

SZA I

g

where,


I = 1.5 (Table 4)

hA= 0.16

Displacement, 2250 h eff

m

A T

B

= 169.82 mm

since m , re-iterate by assuming target

displacement m till the convergence is

achieved, i.e. m .

In present case, convergence is achieved with displacement = 182.5 mm. The property of LRB at above displacement is given below.

effk = 1194.3 kN/m (K2)

eT = 2.64 sec

β = 18.78% and B = 1.46

Similar calculations can be done for longitudinal direction with seismic weight as 3360 kN. The convergence is achieved at displacement Δ = 90 mm. The property of LRB at above displacement is given below.

effk = 1573.9 kN/m (K2)


Page 160

eT = 1.47 sec

β = 26.87% and B = 1.64

5.4.3. Check

Shape factor,

1

2

14.326

4

b pl

r r

r

A AS

B t

BS

T

Reduced area, 2

sin4

r

BA

12cos 2.56tdrad

B

taking dt as seismic displacement = 169.82 mm

Ar =1.81 x 105 mm2

Ratio /r bA A = 0.66 > 0.3, hence OK.

Shear strain from vertical loads,

1

21

3

2 1 2

c

r

S P

A G kS = 1.614 < 2.5, hence OK.

Shear strain form lateral load, where di = 169.82

,i

s eqr

d

T = 1.013

Shear strain due to rotation, assuming θ to be a minimum value of 0.005 rad

2

2

ri r

B

t T=0.6

Neglecting shear strain due to imposed non-seismic lateral displacement

Therefore, total shear strain,

, 0.5 t c s eq r = 2.93< 5.5, hence OK.

Buckling load capacity of rubber bearing at seismic displacement is given by

, 1 22 2

cr eq rP S S GA

= 5184 kN > 2065 kN,

hence OK.

Buckling load capacity under vertical loads for non-seismic displacement assuming Δs = 0 is calculated as

, 1 22 2

cr c bP S S GA

= 7831kN

This capacity should be compared with the maximum vertical load possible on the bearing due to dead and live load combination to provide a safety factor of at least 3.

5.5. Response Spectrum Analysis

5.5.1. Modeling

The bridge pier and base isolation bearing is modeled as 2-DOF system as shown in figure 5.2 below. The weight W1 is the 80% weight of pier, as calculated earlier. For 1st mode, the system damping is considered as 26.87% and 18.78% for longitudinal and transverse direction, respectively, as calculated earlier. However, 5% damping is considered for 2nd mode.

Figure 1.2 2-DOF Idealization

Here, pier stiffness, 1 3

3EIK

L

where,

L = Pier height from top of foundation = 12 m


= 5000√fc (Clause 6.2.3.1, IS456:2000)

= 5000√30 = 27386 N/mm2

= 27386130 kN/m2

I = moment of inertia of pier section

= π/64 х D4 = π x 24 /64

= 0.785 m4

1K = 37342 kN/m

W2

W1

K2

K1


Page 161

Stiffness K2 of LRB is taken as effective stiffness ( effk ) with 4 LRBs in parallel. The

seismic weight of superstructure W2 is taken as 3360 kN and 8260 kN along longitudinal and transverse direction, respectively.

5.5.2. Result

The modal analysis was carried out to find system dynamic properties and tabulated in Table 5.1 below. The deformations and base shear were calculated for two modes and were combined using SRSS rule.

Table 5.1 Response spectrum analysis results for 1.5EQ hazard level

Description Long. Dir

Trans. Dir

Seismic weight (W2, kN) 3360 8260

Total stiffness (K2, kN/m) 6296 4777

1st mode period (sec) 1.59 2.80

2nd mode period (sec) 0.26 0.27

LRB displacement (mm) 79.3 167.5

Seismic coefficient for 1st mode (Ah)

0.1555g 0.0989g

Seismic coefficient for 2nd mode (Ah)

1.0125g 1.0125g

Base shear (kN) 782 1026


5.6.1. Horizontal Elastic Seismic force

The lateral load on the pier due to seismic load

1.5EQ is calculated and tabulated in Table 5.1

above. Similar calculations can be done for

seismic load 1.2EQ. The results are tabulated in

Table 5.2 below.

Table 5.2 Response spectrum analysis results for 1.2EQ hazard level

Description Long. Dir

Trans. Dir

Seismic weight (W2, kN) 3360 8260

Total stiffness (K2, kN/m) 7570 5398

1st mode period (sec) 1.47 2.66

2nd mode period (sec) 0.26 0.27

LRB displacement (mm) 55.2 116.9

Seismic coefficient for 1st mode (Ah)

0.1296g 0.0781g

Seismic coefficient for 2nd mode (Ah)

0.8100g 0.8100g

Base shear (kN) 624 807

5.6.2. Hydrodynamic Force

For the submerged portion of the pier, the total horizontal hydrodynamic force along the direction of ground motion is given by

(Section 14.2)

eWAeCF


Page 162

H = Height of submerged portion of pier

= 1/3 of pier height = 4 m

r = Radius of enveloping cylinder

= 1 m

H/r = 4,

Hence ,

Ce = 0.73


A in longitudinal direction = 0.81

A in transverse direction = 0.81

W e= Weight of the submerged portion of enveloping cylinder

= ρw x π a2 H

= 9800 x π x 12 x 4 / 1000 = 123 kN

F = Total horizontal hydrodynamic force in longitudinal direction

= 0.73 x 0.81 x 123 = 72.7 kN


in transverse direction

= 0.73 x 0.81 x 123 = 72.7 kN

5.6.3 Load Combinations


(1) 1.25 DL + 1.5 EQ

(2) 1.25DL +0.3 (LL+IL) +1.2EQ + 1.4HY

(Section 8.8)

Where, DL = Dead Load, LL = Live Load, EQ= Earthquake Load, IL = Impact Load

Note – Other loads i.e. Superimposed dead Load (DL(S)), Live load on footpath (LL(f)), Hydrodynamic Pressure (HY), Prestressing force (PS), Buoyancy load (BO), Earth Pressure (EP) etc. are not considered.


4m

12m

F (Resultant pressure)

2m Hydrodynamic Pressure Distribution on the pier due to stream flow

5378 kN 1026 kN

782 kN


9053 kN 909 kN

726 kN



Page 163

Table 5.3 Comparison of seismic forces between fixed base system and proposed base isolated system as per IITK-RDSO guidelines

Span = 76.2m, Pier Height = 12 m, Pier diameter = 2m, Hard soil


Fixed base system Proposed base isolated system

Period = 0.77 s; Ah = 0.35/2.5 = 0.14 As shown in Table 5.1 and Table 5.2 above

Period =1.59 s; Ah=0.16g Period =1.47s; Ah=0.13g


Fixed base system Proposed base isolated system

Period = 1.15 s; Ah = 0.24/2.5 = 0.096 As shown in Table 5.1 and Table 5.2 above

Period =2.8 s; Ah=0.10g Period=2.66s; Ah=0.07g

Notes:

1. Site specific study is required for hazard evaluation corresponding to DBE and MCE conditions.

2. LRB design shall be checked for MCE hazard level.

3. Effect of vertical acceleration shall be considered in case of near fault region.

726 kN

5378 kN

782 kN

9053 kN

713 kN

5143 kN

869 kN

8818 kN

LC 2 LC 1LC 2LC 1

1042kN

5143 kN

1287 kN

LC 1

8818 kN

LC 2

LC 1

9053 kN

909 kN

5378 kN

1026 kN

LC 2

Draft IITK-RDSO Guidelines for Seismic Design of Railway Bridges

164

Example 6 – M- curve for a Reinforced Concrete (RC) Section


Determine the moment curvature curve (M- curve) of a Reinforced Concrete (RC) section shown in Fig. 6.1. The M- calculations shall be done manually and also using structural analysis software.

Solution: 6.1 Preliminary Data:

The cross section details are given below.

Fig. 6.1 RC section

M- curve is the relationship between the moment of resistance (M) and the curvature () of the cross-section. When applied moment is very small, concrete and steel are in elastic range, and there is linear relationship between M and (point A in Fig. 6.2). However, as the moment increases, the concrete in tensile region cracks. Beyond this stage the tension is taken by the tensile steel. As the moment is further increased, the tensile steel reaches its first yield (point B in Fig. 6.2). After this stage, the yielding of tensile steel continues and the compression steel and concrete in compression also undergo plastic deformations. At the end, the entire section reaches its maximum moment carrying capacity, i.e., plastic moment, MP.

The calculation of moment of resistance (M) and curvature () for these two points (A, B in Fig. 6.2) is demonstrated in this example.

6.2 Elastic range (Point A)

Concrete and steel are in elastic range and the distribution of strains and stresses as

shown below:

A = Area of transformed section

= b.D + (1.5m-1) Asc + (m-1) Ast

= 92100 mm2.

Centroid of transformed section is obtained as

= 187.917 mm.

Moment of Inertia of transformed section about the centriodal axis is I = 1.165 x109 mm4

Concrete looses its elasticity when it first cracks in the tensile region. At this stage, stress in

2-12

350 mm 375 mm

2-12, 2-10 230 mm

25 mm b = 230 mm, D = 375 mm, d = 350 mm, d’ = 25 mm,

Asc = 226 mm2 (0.26%), Ast = 383 mm2 (0.44%),

fck = 20 N/mm2, fy = 415 N/mm2, fcr = 3.1305 N/mm2,

Modular ratio = m = 8.94, ES=200000 N/mm2,

Ec = 22360 N/mm2.

y1

y2

Effective section

Transformed section stresses strains

fcr

c

y

s

fc

y


165

concrete in tensile region is fcr and the moment of resistance is given by

Mcr = = 19.497 x 106 Nmm

Curvature () is given by =

= 7.483 x 10-7 rad/mm.

These values of M and are shown in the M- curve shown in Fig. 6.5.

6.3 Tensile steel yields (Point B)

This is the stage at which concrete in tension is already cracked and tensile steel has reached yield stress, fy.

The distribution of strains stresses and forces as shown below.

Neutral axis (N.A.) coefficient is obtained as

K =

1/ 2

2 2 2( ' ) ( )d

m m md

K=0.238

Here, = % steel in tension (.0044), ’ = % steel in compression (0.0026).

The depth of N. A., n = k d = 83.11 mm.

when the steel reaches its first yield, the strain in tension steel is obtained as

s = = 0.00275

From strain diagram we find,

c= s = 0.0006472

fc = c Ec = 14.471 N/mm2 < fck

Therefore, the triangular stress block is an assumption. Strain in concrete at the level of compression steel is obtained as

’s = C = 0.0004527

Stress in concrete at the level of compression steel.

f’s = 0.0004527 ES = 90.549 N/mm2

Compressive force in concrete =

Cc = 0.5 fc b n = 138.48 kN.

Compressive force in concrete at the level of steel = CS =Asc f’S = 20.464 kN.

Resultant Total compressive force = C = Cc + CS

= 158.945 N.

Centroid of resultant compressive force from top fiber = y = 27.385 mm.

lever arm = jd = d -y = 322.615 mm.

yield moment = My = As fy jd

= 51.278 106 Nmm

Yield curvature = c

n

= 7.778 x 10-6 rad/mm.

This is shown in Fig. 6.5

6.4 Limit state

As the applied moment is increased further, concrete in compression region also yield. The tensile steel reaches maximum yield strain. Stress strains of concrete and steel enter into nonlinear stage. The stress distribution in cracked section will take the shape of idealized parabola. This occurs because the fundamental assumption of a linear strain distribution holds good at all stages of loading. The manual calculation for this phase is quite cumbersome due to iteration process for the plastic moment and curvature, so this part is explained briefly here. However it can be easily done on the structural analysis software like SAP. The determination of M- curve by using SAP software is presented in section 6.5.

Stress-strain relationship for concrete is

c

sc n

fc f’s

CC

CS

TS fs

S Strains Stresses Forces Effective

section


166

considered as given in IS456:2000. However, the same for steel is given below, as considered for the present problem (Andriono and Park, 1987) with usual notations.

yf = 415 MPa, suf = 477.3 MPa, sE = 200 GPa,

sh = 0.025, su = 0.14, shE = 3851 MPa

a) Elastic region ( 0 s y ): s s sf E

b) Yield Plateau ( y s sh ): s yf f

c) Strain Hardening region ( sh s su ):

P

su ss su y su

su sh

f f f f

Where,

su shsh

su y

P Ef f

From equilibrium, C T , we get

1 ck sc sc s stk f bn f A f A

Here, k1 is area factor corresponding to maximum concrete strain in the section.

since /stA bd , ' /scA bd ,

c

c s

kd d

, sc sc sf E and

1sc c

n y

n

, we get

11 'c

ck s c c sc s

s

yk f E

df

The above equation is a function of strain in concrete & reinforcement and stress in reinforcement for a given section. Hence, different plots can be obtained by selecting strain in concrete c. If we overlap these plots above the actual stress-strain curve of reinforcement assumed, from the intersecting point one can get stress and strain in reinforcement for a selected value of strain in concrete as illustrated in Fig. 6.2.

Fig 6.2: Stress strain curves for reinforcement

After obtaining fs and s, depth of neutral axis can be calculated as

1

1

'

'

c s

cck c s s

c s

y En

k f E f

Further, strain (sc) and hence stress (fsc) in compression steel can be calculated, as shown earlier. Moment capacity M and curvature can be calculated equations given from below.

1 2 1( ) ( )ck sc scM k f bn d k n f A d y

and c

n

, here k2 is depth of NA factor.

For c = 0.001, we get k1 = 0.471 & k2 = 0.375. From Fig 6.2, intersection of two plots can be found as s = 0.00474 and fs = 415 MPa. Depth of neutral axis n can be calculated as 61 mm. Further, strain and hence stress in compression reinforcement bars is calculated as sc = 0.00059


167

and fsc = 118.029 MPa. From above relation, M = 51.398 kN-m and = 1.639 x 10-5 rad/mm.

Table 6-1: Stepwise results in Tabular Form:

Manual Calculation

SAP Results

Stage M

(kNm)

(rad/mm) M

(kNm)

(rad/mm)

Cracking 19.497 7.483 x 10-7 - -

Yielding 51.278 7.778 x 10-6 50.850 7.916 x 10-6

c=0.0010 51.938 1.639 x 10-5 52.075 1.570 x 10-5

c=0.0015 52.558 3.145 x 10-5 52.736 3.180 x 10-5

c=0.0020 52.875 4.934 x 10-5 52.967 5.000 x 10-5

c=0.0025 52.978 6.842 x 10-5 53.044 6.870 x 10-5

c=0.0030 54.036 8.645 x 10-5 53.414 8670 x 10-5

c=0.0035 56.013 1.031 x 10-4 54.219 1.038 x 10-4

Similar calculations can be done for different value of strain in concrete. (See table 6.1)

6.5 M- curve using software

Software for nonlinear analysis for reinforced concrete provides facility to obtain moment curvature relationship for a given RC section. Section Builder module of SAP 2000 is one such software. In the manual calculations shown in the previous sections, M- calculations are done at three points only. In the software, the M- calculations are done at many points and a smooth curve is obtained. The input to software are geometrical details of cross section, quantity of steel in tensile and compression region and all the material properties, viz., Young’s Modulus, Poisson’s Ratio, characteristic strength of concrete and yield stress for steel.

The stress-strain of concrete and steel are also required. In this context, it is to be noted that IS 456 (2000) provides stress-strain curve of concrete and steel. For the present problem, the stress-strain curve of steel and concrete shown in Fig.6.3 and Fig.6.4 are used. For concrete, stress-strain curve depends on level of confined steel. The details of The M- curve obtained using this software is shown in Fig 6.5. A comparison of moment and curvature values obtained from manual calculations and software is given in Table 6.1.

Fig. 6.5 M- Curve obtained by manual calculations and by section builder of SAP 2000 software

Fig. 6.4 Stress-strain curve used in section builder forFe415 reinforcement bars.

Fig. 6.3 Stress-strain curve used in section builder forconcrete (Mander, Priestley and Park 1988)


168

Example 7 – Obtain plastic moment, MP for RC pier and the maximum seismic coefficient required for plastic hinge formation

7. Problem Statement: For the pier of bridge considered in Example 1, Calculate the plastic moment (Mp) of reinforced concrete pier and the maximum seismic coefficient required to form the plastic hinge in the pier.

Solution:

7.1 Preliminary Data

From Example 1, following data is taken:

Height of pier =12 m, Diameter of pier = 2 m, Seismic weight in longitudinal direction = 4114 kN,

Seismic weight in transverse direction = 9014 kN, Time period in longitudinal direction = 0.77 sec,

Time period in transverse direction = 1.13 sec.

Seismic forces obtained in Example 1 for Load combination 1.4 DL + 1.75(LL+IL) + 1.25EQ are:

Vertical force = 22293 kN, Lateral forces in longitudinal direction = 925 kN

Lateral forces in transverse direction = 2028 kN.

7.2 Calculation of % of steel

Pu = Axial load on pier = 22293 kN

Mu = Transverse moment

= 2928 x 12 = 24336 kNm

0.186

0.101

From chart 55, (SP 16: 1980): pt/fck = 0.1

pt = 3 %

Provide 60 numbers of bar of 45 mm diameter. The clear spacing between two bars is 54 mm, which gives the total steel of 3.1%.

7.3 Calculation of Plastic Moment (Mp)

In a very simplistic fashion, the plastic moment can be taken as 1.4 x Mu = 34070 kNm.

However, the provided steel is slightly more than the steel required, hence, the plastic moment will be slightly on higher side.

For 3.1% steel: pt/fck = 3.1 / 30 = 0.103

For this value of pt/fck , and

one gets

M u, lim = 0.105 x 30 x 20003 / 106

= 25200 kN-m

Plastic moment, Mp = 1.4 x M u, lim

= 1.4 x 25200

= 35280 kN-m

2Df

P

ck

u

=3Df

M

ck

ux

10503

.Df

M

ck

ux

18602

.Df

P

ck

u


169

This value is slightly higher than 1.4x Mu (i.e. 34070 kNm).

Using the Section Builder module of SAP 2000 software and following the procedure described in Example 6, the value of plastic moment for this RC section is obtained as 32530 kNm.

7.4 Maximum Seismic Coefficient

Here, the maximum seismic coefficient (Ah)max, required to produce the plastic hinge in the pier section is obtained.

Lateral force required to develop plastic moment is Pmax.

Mp = Pmax x h

Pmax = Mp / h = 35280 / 12 = 2940 kN

For this pier, In the transverse direction the seismic weight, W = 9014 kN (as per example 1)

Pmax = (Ah) max x W

Where, (Ah)max is lateral seismic coefficient required to achieve lateral force of Pmax.

(Ah) max = Pmax / W = 2940 / 9014 = 0.33g

Thus, lateral seismic coefficient required to achieve plastic moment is (Ah) max = 0.33g

For superstructure design, if elastic forces

( i.e. forces with R = 1 ) are quite large , then, superstructure shall be designed for (Ah) max, i.e. maximum lateral seismic coefficient at which plastic hinge gets developed in the ductile member, i.e., pier.

170

Example 8 - Liquefaction Analysis using SPT data

8. Problem Statement: The measured SPT resistance and results of sieve analysis for a site in Zone IV are given in Table 8.1. Determine the extent to which liquefaction is expected for a 7.5 magnitude earthquake. The site is level, the total unit weight of the soil layers is 18.5 kN/m3, the embankment height is 10 m and the water table is at the ground surface. Estimate the liquefaction potential immediately downstream of the toe of the embankment.

Table 8.1: Result of the Standard penetration Test and Sieve Analysis

Depth (m)

60N Soil Classification Percentage fine

0.75 9 Poorly Graded Sand and Silty Sand (SP-SM) 11 3.75 17 Poorly Graded Sand and Silty Sand (SP-SM) 16 6.75 13 Poorly Graded Sand and Silty Sand (SP-SM) 12 9.75 18 Poorly Graded Sand and Silty Sand (SP-SM) 8 12.75 17 Poorly Graded Sand and Silty Sand (SP-SM) 8 15.75 15 Poorly Graded Sand and Silty Sand (SP-SM) 7 18.75 26 Poorly Graded Sand and Silty Sand (SP-SM) 6

Solution:

Site Characterization:

This site consists of loose to dense poorly graded sand to silty sand (SP-SM). The SPT values ranges from 9 to 26. The site is located in zone IV. The peak horizontal ground acceleration value for the site will be taken as 0.24g corresponding to zone factor Z = 0.24

Liquefaction Potential of Underlying Soil

Step by step calculation for the depth of 12.75m is given below. Detailed calculations for all the depths are given in Table 8.2. This table provides the factor of safety against liquefaction (FS), maximum depth of liquefaction below the ground surface.

max

max 0.24 1 1 0.24

a Z I S

a

5.7M w , 318.5 /sat kN m ,

389 m/kN.w

Considering water table at ground surface, sample calculations for 12.75m depth are as follows.

Initial stresses:

kPa9.2355.1875.12v

kPa95.1248.9)00.075.12(u0

'0 235.9 124.95v v u

= kPa95.110

Stress reduction factor:

83.075.120267.0174.1z0267.0174.1rd

Critical stress ratio induced by earthquake:

g24.0amax , 5.7M w

'vvdmaz /rg/a65.0CSR

0.65 0.24 0.83 235.9 /110.95CSR

= 28.0

Correction for SPT (N) value for overburden pressure:

60N601 NCN

2/1'vN /179.9C

93.095.110/179.9C 2/1N

161793.0N 601

Cyclic stress ratio resisting liquefaction:

171

For 16N 601 , fines content of %8

22.0CRR 5.7 (Figure G-5)

Corrected Cyclic Stress Ratio Resisting Liquefaction:

kkkCRRCRR m5.7

mK Correction factor for earthquake

magnitude other than 7.5 (Figure G-1) 00.1 for 5.7M w

K Correction factor for initial driving

static shear (Figure G-3) 00.1 , since no initial static shear

K Correction factor for stress level

larger than 96 kPa (Figure G-2) 88.0

19.088.01122.0CRR

Factor of safety against liquefaction:

70.028.0/19.0CSR/CRRFS

It shows that the considered strata are liable to liquefy.

Summary:

The extent of liquefaction for the strata of considered site on be read from Table 8.2, where F. S. < 1.0 indicates the possibility of liquefaction.

Table 8.2: Liquefaction Analysis: Water Level at GL

Depth %Fine v

(kPa)

'v

(kPa) 60N NC 60N dr

CSR 5.7CRR CRR FS

0.75 11.00 13.9 6.5 9.00 2.00 18 0.99 0.33 0.24 0.27 0.82 3.75 16.00 69.4 32.6 17.00 1.71 29 0.97 0.32 0.32 0.34 1.04 6.75 12.00 124.9 58.7 13.00 1.28 17 0.95 0.31 0.21 0.20 0.65 9.75 8.00 180.4 84.8 18.00 1.06 19 0.91 0.30 0.23 0.21 0.69 12.75 8.00 235.9 110.9 17.00 0.93 16 0.83 0.28 0.22 0.19 0.70 15.75 7.00 291.4 137.0 15.00 0.84 13 0.75 0.25 0.16 0.13 0.53 18.75 6.00 346.9 163.1 26.00 0.77 20 0.67 0.22 0.22 0.18 0.80

172

Example 9 - Liquefaction Analysis using CPT data

9. Problem Statement: Prepare a plot of factors of safety against liquefaction versus depth. The results of the cone penetration test (CPT) of 15m thick layer in Zone V are provided in Table 9.1. Assume the water table to be at a depth of 2.35 m, the unit weight of the soil to be 18 kN/m3 and the magnitude of 7.5 and the peak horizontal ground acceleration as 0.15g.

Table 9.1: Result of the Cone penetration Test

Depth (m) cq sf Depth (m)

cq sf Depth (m) cq sf

0.50 64.56 0.652 5.50 49.70 0.235 10.50 116.1 0.248

1.00 95.49 0.602 6.00 51.43 0.233 11.00 97.88 0.159

1.50 39.28 0.281 6.50 64.94 0.291 11.50 127.5 0.218

2.00 20.62 0.219 7.00 57.24 0.181 12.00 107.86 0.193

2.50 150.93 1.027 7.50 45.46 0.132 12.50 107.2 0.231

3.00 55.50 0.595 8.00 39.39 0.135 13.00 124.78 0.275

3.50 10.74 0.359 8.50 36.68 0.099 13.50 145.18 0.208

4.00 9.11 0.144 9.00 45.30 0.129 14.00 138.53 0.173

4.50 33.69 0.297 9.50 102.41 0.185 14.50 123.95 0.161

5.00 70.69 0.357 10.00 92.78 0.193 15.00 124.41 0.155

Solution:

Liquefaction Potential of Underlying Soil:

The result of assessment of liquefaction potential provided in the last column of Table 9.1, where FS denotes the factor of safety against liquefaction (= CRR7.5/CSR). Step by step calculation for the soil at depth of 4.5m is given below for illustration. Detailed calculations are given in Table 9.2, which provides the factor of safety against liquefaction (FSliq).

amax/g = 0.15, Mw=7.5,

3sat m/kN81 , 3

w m/kN8.9

Depth of water level below G.L. = 2.35m

Depth at which liquefaction potential is to be evaluated = 4.5m

Initial stresses:

kPa00.81185.4v

kPa07.218.9)35.25.4(u0

kPa93.5907.2181u0v'v

Stress reduction factor:

965.05.400765.01

z00765.01rd

Critical stress ratio induced by earthquake:

'max //65.0 vvdrgaCSR

13.0

93.59/81965.015.065.0CSR

Correction factor for grain characteristics:

64.1I for

88.17I75.33I63.21I581.5I403.0K

and 64.1I for 0.1K

c

c2

c3

c4

cc

cc

where the soil behavior type index, cI , is

given by

22c Flog22.1Qlog47.3I

173

19.2

903.0log22.119.42log47.3I 22c

Where,

100qfF vc

903.0100813369/7.29F and

nvaavc PPqQ

19.42

93.5935.10135.101813369Q 5.0

64.1 88.1719.275.3319.263.21

19.2581.519.2403.0K2

34c

Normalized Cone Tip Resistance:

acn

vaccsN1c PqPKq

77.70

35.101336993.5935.10164.1q 5.0

csN1c

Factor of safety against liquefaction:

For 77.70q csN1c ,

11.0CRR 5.7 (Figure G-6)

Corrected Critical Stress Ratio Resisting Liquefaction:

kkkCRRCRR m5.7

mK Correction factor for earthquake

magnitude other than 7.5 (Figure G-4) 00.1 for 5.7M w

K Correction factor for initial driving

static shear (Figure G-6) 00.1 , since no initial static shear

K Correction factor for stress level

larger than 100 kPa (Figure G-5) 00.1

11.011111.0CRR

CSR/CRRFS

86.013.0/11.0FS

Summary:

The analysis shows that the strata between depths 4-9m are liable to liquefy under earthquake shaking corresponding to peak ground acceleration of 0.15g. The plot for depth verses factor of safety is shown in Figure 9.1.

174

Table9.2: Liquefaction Analysis: Water Level 2.35 m below GL (Units: kN and Meters)

Depth v v ' rd

qc (kPa)

fs (kPa) CSR F Q Ic Kc (qc1N)cs CRR7.5

CRR FS

0.50 9.00 9.00 1.00 6456 65.20 0.10 0.45 241.91 1.40 1.00 242.06 0.20 0.20 2.10

1.00 18.00 18.00 0.99 9549 60.20 0.10 0.63 159.87 1.63 1.00 160.17 100.00 100.00 1033.55

1.50 27.00 27.00 0.99 3928 28.10 0.10 0.72 65.43 1.97 1.27 83.53 0.13 0.13 1.39

2.00 36.00 36.00 0.98 2062 21.90 0.10 1.08 33.54 2.31 1.99 68.04 0.11 0.11 1.14

2.50 45.00 43.53 0.98 15093 102.70 0.10 0.68 226.55 1.53 1.00 227.23 100.00 100.00 1011.48

3.00 54.00 47.63 0.98 5550 59.50 0.11 1.08 79.10 2.01 1.31 105.02 0.19 0.19 1.74

3.50 63.00 51.73 0.97 1074 35.90 0.12 3.55 13.96 2.92 5.92 87.81 0.14 0.14 1.24

4.00 72.00 55.83 0.97 911 14.40 0.12 1.72 11.15 2.83 5.01 60.64 0.10 0.10 0.83

4.50 81.00 59.93 0.97 3369 29.70 0.13 0.90 42.19 2.19 1.64 70.77 0.11 0.11 0.89

5.00 90.00 64.03 0.96 7069 35.70 0.13 0.51 86.63 1.79 1.10 96.60 0.16 0.16 1.24

5.50 99.00 68.13 0.96 4970 23.50 0.14 0.48 58.62 1.93 1.22 72.68 0.12 0.12 0.85

6.00 108.00 72.23 0.95 5143 23.30 0.14 0.46 58.85 1.92 1.21 72.45 0.12 0.12 0.83

6.50 117.00 76.33 0.95 6494 29.10 0.14 0.46 72.50 1.83 1.13 83.61 0.13 0.13 0.95

7.00 126.00 80.43 0.95 5724 18.10 0.14 0.32 62.00 1.83 1.13 71.56 0.11 0.11 0.79

7.50 135.00 84.53 0.94 4546 13.20 0.15 0.30 47.66 1.92 1.21 59.46 0.10 0.10 0.68

8.00 144.00 88.63 0.94 3939 13.50 0.15 0.36 40.04 2.02 1.33 55.18 0.10 0.10 0.64

8.50 153.00 92.73 0.93 3668 9.90 0.15 0.28 36.26 2.02 1.33 50.45 0.09 0.09 0.61

9.00 162.00 96.83 0.93 4530 12.90 0.15 0.30 44.09 1.95 1.24 56.79 0.10 0.10 0.64

9.50 171.00 100.93 0.92 10210 18.50 0.15 0.37 48.78 1.95 1.24 62.62 0.18 0.18 1.16

10.00 180.00 105.03 0.91 9278 19.30 0.15 0.43 43.22 2.02 1.33 59.94 0.15 0.15 0.97

10.50 189.00 109.13 0.89 11610 24.80 0.15 0.44 53.40 1.95 1.23 68.16 0.21 0.21 1.36

11.00 198.00 113.23 0.88 9788 15.90 0.15 0.34 43.84 1.98 1.27 58.01 0.15 0.15 1.01

11.50 207.00 117.33 0.87 12750 21.80 0.15 0.35 56.56 1.88 1.17 68.51 0.23 0.23 1.53

12.00 216.00 121.43 0.85 10786 19.30 0.15 0.37 46.67 1.97 1.26 61.23 0.17 0.17 1.12

12.50 225.00 125.53 0.84 10720 23.10 0.15 0.45 45.53 2.01 1.31 62.48 0.16 0.16 1.09

13.00 234.00 129.63 0.83 12478 27.50 0.15 0.46 52.39 1.96 1.25 68.09 0.20 0.20 1.37

13.50 243.00 133.73 0.81 14518 20.80 0.14 0.40 44.79 2.00 1.29 60.67 0.26 0.26 1.81

14.00 252.00 137.83 0.80 13853 17.30 0.14 0.35 41.93 2.00 1.30 57.21 0.23 0.23 1.61

14.50 261.00 141.93 0.79 12396 16.10 0.14 0.37 36.68 2.06 1.39 53.90 0.18 0.18 1.29

15.00 270.00 146.03 0.77 12441 15.50 0.14 0.35 36.23 2.06 1.38 53.24 0.18 0.18 1.29

175

0

3

5

8

10

13

15

0.0 0.5 1.0 1.5 2.0

FSliq

Dep

th (

m)

Figure 9.1: Factor of Safety against Liquefaction

Non-Liquefiable Liquefiable