FInal Tunnel-2 Report.doc

Design Consultancy services for four-Laning of 'Goa/Karnataka Border - Kundapur Section' of NH-17 from Km 93.700 to Km 283.300 in the State of Karnataka

Tunnels- 2 Design Report

5.0 Numerical Analysis

5.0.1 Introduction of Phase2

An essential part of the design of tunnel is the prediction of the response of rocks / rock masses, in terms of

stresses and displacements, which can be well understood by Numerical Methods.

Phase2 is a 2-dimensional windows based program, very popular for the analysis of underground / surface

excavation in rock mass or soil. The program is used for a wide range of geotechnical engineering projects

including complex tunneling problems in weak rock, stress analysis, tunnel design, slope stability, support

design and groundwater seepage analysis etc. Complex multi staged models can easily be created and ana-

lyzed quickly. The program is user friendly, easy to operate and easy to understand. Some of the basic fea -

tures are:

Elasto-Plastic Analysis,

Constant or Gravity Field Stress,

Staged Model,

Plain Strain or Axisymmetric Analysis,

Support analysis (Rock Bolts, Steel Ribs, Lattice Girders Shotcrete / Concrete Liner etc.),

Multiple materials,

Load splitting,

Slope stability analysis,

Ground water seepage analysis etc.

There are three basic components in Phase2 program - Model, Compute and

Interpret. Model is the pre-processing module used for entering and editing

the model boundaries, support, in-situ stresses, boundary conditions,

material properties and creating the finite element mesh. Model, Compute

and Interpret will each run as standalone programs. They also interact with

each other as illustrated in the schematic diagram on the right side.

Compute and interpret can both be started from within the model.

Compute must be run on a file before results can be analyzed with interpret (red

arrow).

Model can be started from interpret.

5.0.2 Input parameters for Phase2

In phase2, field stress can be constant or gravity stress. The gravity field stress option is used to define a

gravity stress field which varies linearly with depth from a user-specified ground surface elevation. Gravity

field stress is typically used for surface or near surface at shallow depth elevations and the areas where

there is the effect of topography in the stress magnitudes and directions.

Material parameters such as Unconfined Compressive Strength of intact rock (σ ci), Hoek-Brown constant

(mi), Geological strength index (GSI), Young‘s Modulus of intact rock (E i), Poisson‘s ratio (ν), Density of the

rock mass (γ) are the material property inputs in Phase2.

AA/HD/1544 24

IM

C



5.0.3 Interpretation of the results

The principal stresses can be displayed. The major and minor principal stresses and angle with horizontal at

any point can be read and the results can be compared with the gravity stress. The strength factor contours

of the rock mass around the tunnel are also displayed. With elastic analysis if the strength factor is greater

than one everywhere around the tunnel, the result will be the same even if Plastic Analysis is done. Hence

there is no necessity of plastic analysis if the strength factor is less than one. The contours of vertical, hori -

zontal and total displacements can be displayed around the tunnel with values marked. The values can be

compared with the results obtained from analytical/semi-analytical methods and measurements of tunnel

convergence in field.

AA/HD/1544 25



5.1.0 Mid Tunnel Section

5.1.0.1 Continuum Modeling

In the Continuum modeling technique rock joints are taken into consideration implicitly, i.e. the rock mass

quality is described by strength and deformability parameters through a failure criterion. Mohr-Coulomb and

Hoek-Brown failure criteria are utilized in the analysis.

5.1.0.2 Finite Element Mesh, Boundary Conditions and Construction Sequence

To eliminate the influence of the applied boundary conditions, the finite element mesh is extended up to the

ground surface and in the lateral direction up to two times the tunnel width. The mesh is of 3272 elements

and 6803 nodes. The gradation factor, ratio of the average length of discretization on excavation boundary

to the length of discretization on the external boundary is 0.2, i.e., the average length of the element on the

external boundary is 20 times the length of the element on the excavation boundary.

Fig 6: Model showing the extent and boundary conditions adopted for the external boundary

AA/HD/1544 26



The modeling starts with generation of the initial stress field, followed by a four stage Excavation process.

Fig.7: Model with stages of sequential excavation

Table 11: Mesh and Discretization Parameters

Mesh type Graded

Element type 6 Noded triangles

Gradation factor 0.2

Default number of nodes on all excavations 110

5.1.0.3 Estimation of In-situ Stresses:

Different in-situ horizontal stress conditions are taken into consideration using stress ratio, k=0.5, 1.0, 1.5

and 2.0. The vertical in-situ stress distribution is considered as the result of weight of the overburden, (σ v =

γH).

5.1.0.4 Estimation of rock mass parameters:

Middle section @ km: 107.645, using data of BH No.5 is used for analysis. The effect of variability and

uncertainty sourced from the complex and variable nature of rock mass cannot be considered by

deterministic approaches using single or mean value. Therefore an effort is made to estimate the required

rock mass properties to construct a reliable FEM-model. Mohr Coulomb (MC) & Hoek- Brown (HB) Failure

criterion are used in the analysis.

AA/HD/1544 27



Table 12: Uniaxial Compressive Strength (UCS) of intact rock samples of BH5 at km: 107.645

Depth UCS(Mpa) E(Mpa) γ(kN/m3)

58.0-59.0 82 46463 2.95

62.5-63.8 183 28932 3.01

67.0-68.0 70 65872 3.06

71.5-72.5 75 71484 3.02

75.5-76.5 35 88223 2.81

80.5-81.5 130 109647 2.99

Mean 96 68437 2.97

Std. dev. 47.75

UCS values on rock core samples from the borehole are highly distributed. Value of standard deviation of

the data is 47.75% of the mean value. Statistical analysis is therefore required to justify a single value for

use. By using statistical analysis it is possible to determine the percentage of values in the data set that

exceeds a certain value. 90% of UCS values measured are exceeding 35 Mpa and that value will be used as

input parameter in the FEM-model.

Fig. 8: Normal distribution of UCS data

The mean value of 96.0 Mpa may also be used but in that case the rock mass in 50% of cases be less

favorable than the parameter used in the design and would be hard to justify. It will however be used here

for comparison purpose. Fig. 9 shows the correlation between UCS and E.

AA/HD/1544 28



Fig.9: Correlation between UCS and E

Fig. 10: Linear correlation between Q and RMR

Residual friction angle, φr = tan-1(Jr/Ja) is worked out to be 56o with field measured values of Jr =1.5 and Ja =

1.So no change is made as regards to the friction angle of rock mass, though the borehole data indicated

friction angle φmean =56o and φ10% = 44o. The stiffness modulus E10% should be around 88.871 Gpa according

to figure 9.

Table 13: The values of cohesion and friction

AA/HD/1544 29

C(Mpa) φ(Degrees)

2.25 49.83

1.45 57.02

0.45 61.05



The following table shows the values considered for Numerical Analysis.

Table 14: Selected Rock Mass Parameters for Numerical Analysis

Confidence Limits 90% 50% Units

Input values of Mohr Coulomb failure Criterion

Cohesion,C 0.350 1.506 Mpa

Friction Angle,φ 44.00 56.00 Degree

Tensile Strength,T 0.300 0.920 Mpa

Modulus of Elasticity,Ei 88.87 68.440 Gpa

Modulus of Deformation,Ed 35.19 30.850 Gpa

Input values of Hoek Brown failure Criterion

Geological Strength Index,GSI 64.00 75.00

Intact Rock Constant,mi 29.00 29.00

Disturbance factor,D 0.00 0.00

Uniaxial compressive strength,UCS 35.00 96.00 Mpa

Modulus of Elasticity,Ei 14.88 40.80 Gpa

Modulus of Deformation,Ed 9.072 33.307 Gpa

Parameter,mb 7.900 11.892

Parameter,s 0.018 0.062

Parameter,a 0.502 0.501

Unit weight,γ 2.870 2.970 kN/cum

Poisson's Ratio,ν 0.130 0.440

5.1.0.5 Stability assessment of tunnels:

Design of effective ground support takes into account the mode of instability so that the support components

can be designed to work efficiently for the anticipated instability mode.

There are three main tunnel instability mechanisms:

Shear Yielding of rock mass is quite common in poor quality rock masses. A plastic zone is formed

around the tunnel and, depending upon the ratio of rock mass strength to in-situ stress, this may

stabilize, or it may continue to expand until the tunnel collapses. The two main mechanisms that

can produce this type of instability are swelling and squeezing conditions. Fig. 11a illustrates, Shear

failure in a plastic zone around tunnels in weak rock

STRUCTURALLY CONTROLLED KINEMATIC INSTABILITY appears in jointed rock masses under

low in-situ stress conditions. Gravity driven wedge instability is typically the dominant instability

mode of the type. The failure involves gravity fall of wedges formed by intersecting geological fea-

AA/HD/1544 30



tures. Fig. 11b illustrates Gravity driven wedge instability along pre-existing geological structures in

blocky ground under low in-situ stress conditions

BRITTLE ROCK FAILURE initiates as a result of the propagation of tensile cracks from defects in

highly stressed massive hard rock. These cracks generally propagate along the maximum principal

stress trajectories, resulting in thin splinters or slabs. Depending upon the ratio of intact rock

strength to in-situ stress, spalling may be limited to small plate-sized slabs, or it may develop into a

massive violent failure or rock burst. Fig. 11c illustrates Stress driven brittle failure tends to domi-

nate in massive brittle rock under high in-situ stress conditions

Fig. 11: Potential Modes of Failure

5.1.1 Elastic Analysis

5.1.1.1 Interpretation of the results:

Different output parameters after the simulation through different stages of excavation in elastic mode are

shown in Fig.12 below.

5.1.1.2 Principal Stresses:

In Phase2, σ1 corresponds to the in plane major principal stress and σ3 in plane minor principal stress. The

elastic stress redistribution around the excavation suggests that σ1 increases and σ3 decreases in the rock

mass surrounding the tunnel.

5.1.1.3 Major Principal Stress:

AA/HD/1544 31



Predominant failure modes of the tunnel for different stress ratio’s (k) are predicted based on the limiting

ratio of tangential stress (σ1) to UCS of intact rock.

Fig. 12: Tunnel instability and brittle failure

AA/HD/1544 32



Table 15: Computation of the ratio of Maximum principal stress to uniaxial compressive strength of intact rock

As the stress ratio increases from 0.5 to 2, the failure mode in crown and walls ranges from falling or sliding

of block wedges to localized brittle failure of intact rocks and movement of blocks. The maximum principal

stress being compressive is located in the side wall for k values of 0.5 and 1.0 and in the crown for k values

of 1.5 and 2.0.

5.1.1.4 Strength Factor:

It is defined as the ratio of strength of rock mass to the induced stress. Strength Factor greater than 1.0

indicates that the material strength is greater than the induced stress. A strength factor less than one means

the material will fail, and plastic analysis is necessary.

The tangential stresses in the walls decrease as the stress ratio ‘k’ varied from 0.5 to 2.0 resulting in

improved strength factor values.

The tangential stresses in the roof/crown increase as the stress ratio ‘k’ varied from 0.5 to 2.0 resulting in

decreased strength factor values even though higher horizontal stress provides sufficient constraint and

stability of the roof.

AA/HD/1544 33



Fig. 13: Strength factor Contours for MC-90

Fig. 14: Strength factor Contours for MC-50

AA/HD/1544 34



Fig. 15: Strength factor Contours for HB-90

Fig. 16: Strength factor Contours for HB-50

Table 16: Extent of zone (meters) of Strength Factor below 1.0

AA/HD/1544 35



Strength Factor(Extent of Zone in meter less than 1) k 0.5 1 1.5 2MC-90 Crown 0 0.904 1.066 1.29 Left wall 1.047 0.902 0.904 0.979 Right wall 0.991 0.918 0.822 0.963 Invert 2.174 3.764 5.038 6.071 MC-50 > 1 for all values of k HB-90 Crown 0 0 0.162 0.254 Left wall 0 0 0.145 0.184 Right wall 0 0 0.32 0.389 Invert 1.028 1.451 3.026 3.685 HB-50 > 1 for all values of k

5.1.1.5 Minor Principal Stress induced failure (σ3<0):

The iso-line depicts the region with tensile stresses in the rock exceeding the tensile strength of the rock

mass. Tensile strength is estimated using the Mohr-Coulomb strength relationship, using the formula,

Tensile Strength (σt) = (2c * Cos Φ) / (1+ SinΦ)

Table 17 shows the values of tensile strength adopted in the model using the formula. The maximum

principal stress in tension due to the de-confinement of rock mass in the tunnel floor is lower than the tensile

strength of the rock and hence a flat invert is considered to be adequate.

Table 17: Tensile strength as per Mohr Coulomb failure criteria

c φ σt

MC 90 0.350 44.0 0.30

MC 50 1.506 56.0 0.92

AA/HD/1544 36



Fig. 17: Minor principal Stress Contours (<0, Grey Iso-lines) for MC-90

Fig. 18: Minor principal Stress Contours (<0, Grey Iso-lines) for MC-50

AA/HD/1544 37



Tensile strength of the rock mass as per Hoek Brown failure criteria is

Tensile Strength (σt) = s * σci / mb

Table 18: Tensile strength as per Hoek Brown failure criteria

s mb σci σt

HB 90 0.0180 8.017 35 0.08

HB 50 0.0621 11.875 96 0.50 Th

e region, in which the tensile strength of rock is exceeded, is significant in HB 90 model and a curved invert

can be considered, based on ground conditions met with.

Fig. 19: Minor principal Stress Contours (<0, Black Iso-lines) for HB-90

Table 19: Extent of tensile stress zone in meters

Extent of Minor principal Stress induced failure (σ3<0) in meter

Invert k MC-90 MC-50 HB-90 HB-50

0.5 1.230 1.268 1.097 1.147

1 1.470 1.551 1.409 1.475

1.5 2.903 2.969 2.889 2.889

2 3.415 3.276 3.481 3.402

AA/HD/1544 38



Fig. 20: Minor principal Stress Contours (<0, Black Iso-lines) for HB-50

5.1.1.6 Critical Shear Strain

The maximum shear strain should be smaller than the critical shear strain (γc). If the maximum shear strain

is larger than the critical shear strain, tunnel support must be installed immediately so as to keep the

maximum shear strain less than the critical shear strain.

Where ‘ν’ is the poisons ratio of the material and ‘εc’ is the critical strain defined as the ratio of uniaxial

compressive strength to the modulus of elasticity of rock mass.

Table 20: Permissible Shear Strain computation for different models

Permissible Shear Strain (γ) Model σci(Mpa) σcm(Mpa) Em(Mpa) σcm/Em (1+νm) σcm/Em (1+νm)MC 90 35 3.45 35190 9.81E-05 1.13 1.11E-04MC 50 96 15.68 30850 5.08E-04 1.13 5.74E-04HB 90 35 3.45 9072.6 3.80E-04 1.44 5.48E-04HB 50 96 15.68 33307 4.71E-04 1.44 6.78E-04

AA/HD/1544 39



Fig.21: Maximum shear strain distribution for MC-90 exceeding permissible values

Fig. 22: Maximum shear strain distribution for HB-90 exceeding permissible values

With increasing stress ratio (k) the need for tunnel support is anticipated in models MC 90 and HB 90. Shear

strain is within limits for model MC 50 and HB 50.

AA/HD/1544 40



5.1.1.7 Principal Stress Cone

The location and thickness of the natural roof arch can be determined by the concept of invert principal

stress cone developed in the numerical modeling. The stress trajectories are displayed in Fig. 23.

Fig. 23: Development and application of concept of principal stress cone

Notations used:

k = Stress Ratio

H = Height of rock load in meter

Preqd = Required Maximum support pressure in ‘MPa’ calculated as the product of Unit weight of rock

and the height of rock load in ‘m’.

AA/HD/1544 41



Fig. 24: Maximum height of rock load for MC-90

End anchored 25φ rock bolts 4.5 m long at 2 m x 2 m spacing, and shotcrete, 50 mm thickness, M25 grade

yield support pressures of 0.051 Mpa and 0.06 Mpa resply., for all values of ‘k’.

Table 21: Support pressures using bolts and shotcrete to resist the rock load for MC-90

Support Pressure reqd (Mpa) Support Pressure (Mpa)Model k H Preqd End Anchored bolts ShotcreteMC 90 0.5 3.827 0.11 0.025 0.12 1 2.567 0.07 0.025 0.06 1.5 1.871 0.05 0.025 0.06 2 1.535 0.04 0.025 0.06

AA/HD/1544 42



Fig. 25: Maximum height of rock load for MC-50

Table 22: Support pressure requirements using bolts and shotcrete to resist the rock load for MC-50

Maximum Support Pressure Calculation

Model k H Preqd End Anchored bolts Shotcrete

MC 50 0.5 3.848 0.11 0.051 0.06

1 1.873 0.06 0.051 0.06

1.5 1.778 0.05 0.051 0.06

2 1.791 0.05 0.051 0.06

AA/HD/1544 43



Fig. 26: Maximum height of rock load for HB-90

End anchored 25 φ rock bolts of 4.5 m length at a spacing of 2 m x 2 m and a shotcrete of M30 grade with

thickness of 100mm resulted in a support pressure of 0.051 Mpa and 0.14 Mpa for k=0.5.For all other values

of k, a shotcrete of M25 grade with thickness of 50mm is found adequate with a support pressure of 0.06

Mpa.

Table 23: Support pressure requirements using bolts and shotcrete to resist the rock load f or HB - 9 0



HB 90 0.5 5.927 0.17 0.051 0.14

1 2.567 0.07 0.051 0.06

1.5 1.871 0.05 0.051 0.06

2 1.535 0.04 0.051 0.06

AA/HD/1544 44



Fig. 27: Maximum height of rock load for HB-50

Table 24: Support pressure requirements using bolts and shotcrete to resist the rock load f or HB-50



HB 50 0.5 2.822 0.08 0.051 0.06

1 2.129 0.06 0.051 0.06

1.5 2.106 0.06 0.051 0.06

2 1.132 0.03 0.051 0.06

Equations used for estimating the support pressure of shotcrete and rockbolts

AA/HD/1544 45



(Ref: https://www.rocscience.com/documents/pdfs/rocnews/winter2012/Rock-Support-Interaction-Analysis-for-Tunnels-Hoek.pdf)

AA/HD/1544 46

https://www.rocscience.com/documents/pdfs/rocnews/winter2012/Rock-Support-Interaction-Analysis-



5.1.1.8 Deviatoric Stress: The difference in the major and minor principal stress referred as deviatoric stress directly relates to the

maximum shear stress. It controls the degree of distortion, allowing for a material to deform in one direction

more than the other (i.e. in the direction of smaller stress.). In effect, this allows fracturing, rupture and

shearing of the rock to occur. The deviatoric stress should be less than UCS of rock mass (σ cm =σci1.5/60). If

the deviatoric stress is high, plastic analysis is required.

Table 25: Extent of zone greater than UCS of rock mass

Extent of Degree of Distortion in meter

k Crown Walls Invert

MC-90 0.5 0.00 3.287 0.000

σci =35 1.0 2.032 2.797 0.000

σcm =3.45 1.5 4.569 2.531 10.545

2.0 9.445 2.214 full

HB-90 0.5 0.00 3.367 0.000

σci =35 1.0 2.074 2.791 0.00

σcm =3.45 1.5 4.676 2.491 10.667

2.0 9.208 2.287 full

MC-50 0 for all values of k

HB-50 0 for all values of k

Fig. 28: Deviatoric stress distribution (more than UCS of rock mass)

5.1.2 Plastic Analysis:

AA/HD/1544 47



5.1.2.1 Yielded Elements:

The depth of the shear (x) and tensile (o) failure zones in the surrounding rock without any support is an

important factor to be considered in the design of required support system.

Fig. 29: Plastic Zones around the tunnel for MC 90

Table 26: Extent of yield zone around tunnels for MC 90 Model.

Extent of zone in m

MC 90

Shear zone

k = 0.5 k = 1 k = 1.5 k = 2

Crown 0.0 1.85 1.84 3.73

Walls 2.0 1.90 1.86 2.85

Invert 2.2 3.45 5.20 5.50

Tension zone

k = 0.5 k = 1 k = 1.5 k = 2

Crown 0.00 0.60 0.78 0.66

Walls 0.80 0.90 0.86 0.87

Invert 1.22 1.34 2.68 2.52

AA/HD/1544 48



Fig. 30: Plastic Zones around the tunnel for HB 90

5.1.2.2 Depth of Spalling:

The concentration of compressive stress in sidewalls for k values of 0.5 and 1 is not to the level of intact rock

strength and may not lead to spalling.

Fig. 31: Major Principal stress concentration for k = 0.50 & 1.0

The concentration of compressive stress is shifted to crown and invert for k values of 1.5 and 2. The

potential for spalling may also depend on the joint pattern. The rock bolt length is so chosen to extend

beyond the zone of stress concentration.

AA/HD/1544 49



Fig. 32: Major Principal stress concentration for k = 1.5 & 2.0

5.1.2.3 Support System:

Each support component in a support system is intended to perform one of the three functions illustrated in

figure 33.

Reinforce the rock mass to strengthen it and control bulking.

Retain broken rock to prevent key block failure and unraveling.

Hold key blocks and securely tie back the retaining element(s) to stable ground.

While each support element may simultaneously provide more than one of these functions, it is convenient

to consider each function separately:

The goal of reinforcing the rock mass is to strengthen it, thus enabling the rock mass to

support itself. Reinforcing mechanisms generally restrict and control the bulking of the rock mass,

thus ensuring that inter block friction and rock mass cohesion are fully exploited. Typically,

reinforcing behave as stiff support elements or ductile or yielding elements

While retaining the broken rock at the excavation surface is required for safety reasons, it may also

become essential under high stress conditions to avoid the development of progressive failure

process that lead to unraveling of the rock mass. Qualitative observations indicate that full aerial

coverage by retaining elements becomes increasingly important as the stress level increases.

The holding function is needed to tie the retaining elements of the support system back to stable

ground, to prevent gravity-driven falls of ground.

AA/HD/1544 50



Fig 33: Three primary functions of support elements

The support system adopted for the Tunnel Section under consideration is shown in Fig. 34.

Fig. 34: Proposed support system

Tension bolts with resin point anchorage are used to apply a compressive force across layered rock strata.

Tension bolts are applied using fast setting resin as the point anchorage in conjunction with slow setting

cement as a corrosion protection for the free stress length. Bolt tension is applied after the fast setting resin

has cured but before the slow setting cement cures.

As seen in Fig. 35, the rock bolts had marginal reduction effect on the roof settlement once a natural roof

arch is formed, and after systematic rock bolting, the roof arch is more stable. A pretension of 10 ton is

applied to the rock bolts to prevent rock dilation of 1.0 m. The application of pre-tensioned bolts is intended

to provide stiffer support by reacting faster to the rock movement.

The existence of high horizontal in-situ stress resulted in higher tunnel crown subsidence, floor uplift and

deformations. This may be explained by rock mass yielding, which is caused by differential principal stress.

AA/HD/1544 51



Fig. 35: Total displacement of crown

Fig. 36: Total displacement of side wall

AA/HD/1544 52



Table 27: Number of yielded elements in Elastic Perfectly plastic analysis

(Static Analysis/) Yielded elements

k No sup RB SC RB & SC

0.5 259 254 261 249

1.0 295 301 299 290

1.5 320 324 323 320

2.0 351 347 342 337

Redistribution of stresses is concentrated in the rock mass at a distance of 3.0 m from the tunnel boundary

which delineates the Plastic and Elastic zones. Pattern bolting and SFRS result in a near triaxial stress

condition.

Fig. 37: Principal stress Distribution near side wall from tunnel boundary for k=0.5

Fig. 38: Principal stress Distribution near side wall from tunnel boundary for k=1

AA/HD/1544 53



Fig. 39: Principal stress Distribution near side wall from tunnel boundary for k=1.5

Fig. 40: Principal stress Distribution near side wall from tunnel boundary for k=2

Examination of the distribution of radial and tangential stresses indicates the function of the radial

reinforcement. It reduces the radial displacement (ur) and generates a higher magnitude of σr in the fractured

zone, resulting in a higher gradient in the σt distribution. The effect is to shift the plastic–elastic transition

closer to the excavation boundary. Thus, both closure of the excavation and the depth of the zone of yielded

rock are reduced.

AA/HD/1544 54



5.1.3 Seismic Design

5.1.3.1 Pseudo-Static Analysis:

For most underground structures, the inertia of the surrounding rock is large, relative to the inertia of the

structure and therefore the seismic response of the tunnel is dominated by the response of the surrounding

rock mass. In phase2, seismic loading is based on pseudo-static approach, where the seismic force is

calculated as the product of the specified seismic coefficient, a dimensionless vector, and the amplitude of

the body force, which is the self weight of the finite element.

5.1.3.2 Seismic Coefficient Method:

The inertial forces due to earthquake are obtained by multiplying the rock load with the design coefficient

(0.08) which is expressed by the following equation (IS: 1893- 1984:Cl.3.4.2.3 (a))

Where

AA/HD/1544 55



Selected Values in Blocks from Tables 2, 3 & 4 of IS: 1893:1984

AA/HD/1544 56



Fig. 41: Mesh Generation for Seismic Analysis

Fig. 42: Stages of sequential excavation, support application and application of seismic loadA large zone of tensile failure is seen in the upper left hand corner in all models, which can be attributed to

the effect of boundary conditions, when horizontal seismic loading is applied from left to right. .At the

AA/HD/1544 57



external boundary, the material when pulled away by applied seismic force, creates a large tensile stress

due to the applied boundary conditions and their effect can be minimized by increasing the extent of the

external boundary, or by placing the an elastic material away from the tunnel.

Fig. 43: Tensile zone in Upper left corner due to earthquake loading

Table 28: Number of yielded elements in Elastic Perfectly plastic seismic analysis

Seismic

k No sup RB SC RB & SC

0.5 466 452 458 443

1.0 410 398 401 388

1.5 393 379 380 375

2.0 415 403 399 395

5.1.3.3 Interaction Diagrams of shotcrete and final lining:

Interaction diagrams are therefore useful to estimate if the tunnel lining is able to tolerate applied loading

from the rock mass. Results of analysis for static and seismic loading are presented in fig.44 to 51. Lining is

never loaded by the stress which is initially prevailed in the ground. Initial stress is reduced by deformation of

the ground that occurs during excavation. The Stress relaxation of the rock mass when considered

eliminates the data points outside the envelope.

AA/HD/1544 58



Fig. 44: Interaction diagrams of of shotcrete for k=0.5 (Static case)

Fig. 45: Interaction diagrams of shotcrete for k=1.0 (Static case)

Fig. 46: Interaction diagrams of of shotcrete for k=1.5 (Static case)

AA/HD/1544 59



Fig. 47: Interaction diagrams of shotcrete for k=2.0 (Static case)

Fig. 48: Interaction diagrams of final lining for k=0.5 (Seismic case) with M25 Grade concrete


AA/HD/1544 60





5.1.3 Conclusions:

5.1.3.1 Numerical Analysis of twin tube tunnels using Phase2 with poor rock mass properties is carried out.

In-situ stress ratio, k (σH / σv) varies along the length of tunnel due to variation in the direction/mag-

nitude of σH and σv with geology and topography. k= 0.5, 1.0, 1.5 and 2.0 are considered for critical

condition. In-situ vertical stress is due to gravity. Mohr- coulomb and Hoek Brown failure criteria are

utilized. Excavation of tunnels is by heading and bench method.

AA/HD/1544 61



5.1.3.2 ELASTIC Analysis:

A strength factor less than one in MC 90 and HB 90 models indicated that the material will fail and

plastic analysis is necessary.

As the stress ratio increases from 0.5 to 2.0, the failure mode in crown and walls range from falling

or sliding of block wedges to localized brittle failure of intact rocks and movement of blocks.

The tangential stresses in the walls decrease as the stress ratio k varied from 0.5 to 2.0 resulting in

improved strength factor values. In roof/crown it increase as k varied from0.5 to 2.0 resulting in de-

creased strength factor values, even though higher horizontal stress provides sufficient constraint

and stability of the roof.

The region in which the tensile strength of rock is exceeded is significant in HB 90 model and can

be attributed to the use of a lower modulus of deformation value which stressed the use of a curved

invert.

With increasing stress ratio (k) the need for immediate tunnel support is anticipated for stability in

models MC 90 and HB 90

For MC 90 and HB 90 models, the max. height of rock load above crown determined by the concept

of invert principal stress cone, is 3.848m for k=0.5. As k increases the rock load decreases. But MC

50 model indicates the height of rock load is 5.927m for k=0.5. End anchored 25dia rock bolts 4.5m

long at 2m x 2m spacing, and shotcrete, 50mm, M25 grade is adequate for the rock load except for

HB 90 model with k=0.5. Since this approach is based on empirical formulas,

The deviatoric stress (σ1-σ3) which directly relates to shear stress, controlling the degree of distor-

tion and fracturing, rupture and shearing of tunnel section, is more than UCS of rock mass, for MC

90 and HB 90 models for k=0.5-2.0, indicating Plastic analysis is necessary.

5.1.3.3 PLASTIC Analysis:

The depth of the shear and tensile failure zones in the rock mass without any support is an impor-

tant factor in the design of required support system.

The extent of yielded zone in crown is 3.73m, walls 2.85 and invert 5.5m for k=2 and reduces with k

for MC 90 model. But plastic zone is limited to invert in HB-90model.

25dia rock bolts, resin end anchored + slow setting cement capsules, 4.5m long, shotcrete 50mm

thick and 200mm thick SFRS final lining is considered.

Redistribution of stresses is concentrated in the rock mass at a distance of 3m from the tunnel

boundary which delineate the plastic and elastic zones.

5.1.3.4 Seismic Design:

The tunnels are located in Zone III of seismic map of India. Tunnel section with Liner 1 of 50mm shotcrete

and Liner 2 of 200mm SFRS lining is analysed with Phase2 for its adequacy with and without seismic. Inter-

action diagrams are generated. Thrust, Shear and Moments in tunnel section during different stages of con-

struction are plotted on the interaction diagrams. Though some of the values are outside the diagram, stress

relaxation of the rock mass when considered eliminates the data points outside the envelope.

AA/HD/1544 62



5.2 Portal Section

5.2.1 Estimation of rock mass parameters:

Portal section @ km: 107.845 and Borehole No.6 is used for the calculations. Mohr Coulomb Failure

criterion is used in the analysis. It is assumed similar rock conditions prevail at new north portal section after

shifting by 30 m.

Table 29 : Test results on intact rock samples of BH 6 at km: 107.845

Depth UCS(Mpa) E(Mpa) γ(kN/m3)

17.0-18.0 102.70 42062 2.67

21.5-22.5 94.200 34673 2.66

26.0-27.0 115.30 45709 2.64

30.5-31.5 76.10 36119 2.68

35.0-36.0 116.50 38438 2.66

39.5-41.0 125.40 79032 2.74

Mean 105.00 46005.5 2.67

St dev 16.400

Value of standard deviation of the UCS data is 16.40 % of the mean value. 90% of UCS values measured

are exceeding 84.0 MPa and the value will be used as input parameter in the FEM-model. Fig. 52 shows the

correlation between UCS and E.

Fig. 52: Linear Correlation between UCS vs E

Measurements of cohesive strength in the same borehole indicates Cmean=4.14 MPa and C10%=2.5 MPa.

AA/HD/1544 63



Fig. 53: Linear correlation between Q and RMR

Friction angle in the borehole indicates φmean=70o and φ10%=68o.is Residual friction angle, φr = tan-1(Jr/Ja)

is worked out to be 36o with Jr =1.5 and Ja = 2.0. So friction angle of rock mass equal to residual friction is

considered in the analysis. The stiffness modulus E10% is 33.0 GPa according correlation in Fig. 52.

Table 30: Test results of cohesion and friction of rock mass

C(Mpa) φ(degrees)

3.80 71.36

2.76 68.91

5.85 67.61

After doing the Probabilistic Analysis, the following Rock Properties are considered for Numerical Modeling.

Table 31: Selected Rock Mass Properties for Numerical Analysis

Soil (Assumed)

Cohesive Strength,C 0.11 Mpa

Friction Angle,φ 16.00 Degree

Tensile Strength, T 0.00 Mpa

Modulus of Deformation, Ed 0.045 Gpa

Highly weathered Rock (Assumed)

Cohesive Strength, C 0.11 Mpa

Friction Angle, φ 35.00 Degree



Rock

Confidence Limit 90% units

Input values of Mohr Coulomb failure Criterion

AA/HD/1544 64



Cohesive Strength, C 2.50 Mpa

Friction Angle, φ 36.0 Degree


Modulus of Elasticity, Ei 32.94 Gpa


5.2.2 In-situ Rock Stress

Close to the ground surface k value is small due to weathering and hence k values of 0.35 and 0.50 are

considered for the analysis of portal section. Analysis with k=0.35 is reported since k=0.5 is not found critical.

Fig. 54: Model showing the extent and boundary conditions adopted for the external boundary

5.2.3 Elastic Perfectly Plastic Analysis

The direction of total displacement is semi horizontal parallel to the hill slope, as in near valley side model.

The deformation behavior in both tube tunnels indicates that the right wall and crown are in de-stressed

mode due to the excavation and there is stress concentration on the left wall. The intensity of distressed rock

in the tube tunnel roofs decrease as the tunnel advances into the hill.

AA/HD/1544 65



Fig. 55: Displacement vectors and deformed excavation shapes at portal

The maximum principal stress in tension due to the de-confinement of rock mass in the tunnel floor is lower

than the tensile strength of the rock and hence a flat invert is considered to be adequate.

Fig. 56: Extent of Plastic Zone in tension(unsupported with Static)

AA/HD/1544 66



Fig. 57: Extent of Plastic Zone in tension(Unsupported with Earthquake)

5.2.4 Design of Initial Support System

A top heading excavation with steel sets fully embedded in shotcrete to form a very strong structural shell on

enlarged footings (“elephant’s feet”) have been used. In addition to steel ribs, fully grouted rock bolt anchors

4.00 m long are installed at elephant foot location. The normal force in the footing of the lining, 0.4m wide, is

1.204 MN/m, resulting in stress of 3.10 Mpa, which is well below the sustainable stress of the rock mass.

Spilling is proposed to reduce the vertical stress ahead of the tunnel face to increase the stability.

Fig. 58: Extent of Plastic Zone in tension (supported with static)

AA/HD/1544 67



Fig. 59: Extent of Plastic Zone in tension (supported with Earthquake)

The extent of plastic zones with support system is insignificantly small in without and with earthquake. The

interaction diagrams with primary support system of steel ribs and shotcrete are given below.

Fig. 60: Interaction diagrams of Steel rib embedded in shotcrete for k=0.35

AA/HD/1544 68



Fig. 61: Interaction diagrams of 50 mm Shotcrete for k=0.35

The moment-axial thrust capacity curves plotted in Figure 60 & 61 are calculated for a factor of safety of 1.0.

5.2.5 Design of Final lining

The final unreinforced final concrete lining is designed with a factor of safety of 2, in the portal section.

Fig. 62: Interaction diagrams of final lining 250 mm thick M 25 grade PCC for k=0.35

AA/HD/1544 69



The moment-axial thrust capacity diagram for a 250 mm thick lining of M25 grade, unreinforced concrete, is

plotted in Fig. 62. In the same figure, the induced moment-axial thrust combinations are also plotted. The

points all fall within the capacity envelope. Hence an unreinforced final concrete lining 250mm thick is

adequate in the portal.

5.2.6 Conclusions:

Mohr coulomb failure criteria is used in the analysis. Properties of rock mass of BH 6 are consid-

ered with k = 0.35, since tunnel is at shallow depth below ground level.

Elastic Perfectly plastic analysis indicates direction of total displacement is parallel to the hill slope

and thereby stresses concentration is on hill side walls of both the tubes. Seismic condition is in-

cluded.

Interaction diagrams are generated for shotcerete, steel rib, and final concrete lining. Thrust, shear

and moments in tunnel section are within the interaction diagrams.

Excavation is by heading and bench with spiling umbrella. Initial support system is steel sets

W200x35.9, fully embedded in shotcrete. Steel ribs rest at bench on elephant foot footing. The final

lining is 250mm thick plain cement concrete M 25 grade.

AA/HD/1544 70

FInal Tunnel-2 Report.doc

Documents

stress analysis

numerical analysis

gravity stress field

axisymmetric analysis

elastic analysis

support analysis rock

slope stability analysis

elastoplastic analysis