JSS Mahavidyapeetha Sri Jayachamarajendra College Of Engineering Mysuru – 570 006 HIGHWAY ENGINEERING DESIGN DATA HAND BOOK (Geometric Design and Pavement Design) Compiled By Dr. P. Nanjundaswamy Professor of Civil Engineering DEPARTMENT OF CIVIL ENGINEERING 2015
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JSS Mahavidyapeetha
Sri Jayachamarajendra College Of Engineering Mysuru – 570 006
HIGHWAY ENGINEERING
DESIGN DATA HAND BOOK (Geometric Design and Pavement Design)
Compiled By
Dr. P. Nanjundaswamy Professor of Civil Engineering
DEPARTMENT OF CIVIL ENGINEERING 2015
CONTENTS
Page No.
1 GEOMETRIC DESIGN STANDARDS FOR NON-URBAN HIGHWAYS 1 – 9
1.1. Classification of Non-Urban Roads 1
1.2. Terrain Classification 1
1.3. Design Speed 1
1.4. Cross Section Elements 2
1.4.1 Cross Slope or Camber 2
1.4.2 Width of Pavement or Carriageway 2
1.4.3 Width of Roadway or Formation 2
1.4.4 Right of Way 3
1.5. Sight Distance 3
1.5.1 Stopping Sight Distance (SSD) 3
1.5.2 Overtaking Sight Distance (OSD) 3
1.6. Horizontal Alignment 4
1.6.1 Superelevation 4
1.6.2 Widening of Pavement on Horizontal Curves 6
1.6.3 Horizontal Transition Curves 7
1.6.4 Set-back Distance on Horizontal Curves 8
1.7. Vertical Alignment 8
1.7.1 Gradient 8
1.7.2 Length of Summit Curve 9
1.7.3 Length of Valley Curve 9
2 DESIGN OF FLEXIBLE PAVEMENTS 10 – 18
2.1 Design Traffic 10
2.2 Traffic growth rate 10
2.3 Design Life 10
2.4 Vehicle Damage Factor 11
2.5 Distribution of Commercial traffic over the carriageway 11
2.6 Design Criteria 12
2.7 Design Criteria 12
2.8 Design Charts and Catalogue 13
2.9 Pavement Composition 18
2.10 Final Remarks 18
3 ANALYSIS AND DESIGN OF RIGID PAVEMENTS 19 – 34
3.1 Modulus of Subgrade Reaction 19
3.2 Radius of Relative Stiffness 19
3.3 Equivalent Radius of Resisting Section 19
3.4 Critical Load Positions 20
3.5 Stresses and Deflections due to Wheel Load 20
3.5.1 Corner Loading 20
3.5.2 Interior Loading 21
3.5.3 Edge Loading 21
3.5.4 Dual Tires 22
3.6 Temperature Stresses 23
3.6.1 Warping Stresses (Westergaard Analysis) 23
3.6.2 Frictional Stresses 24
3.7 IRC Recommendations for Design of Plain Jointed Rigid 25
3.7.1 Legal Axle Load Limits 25
3.7.2 Load Safety Factors 25
3.7.3 Tyre Pressure 25
3.7.4 Design Period 25
3.7.5 Design Traffic 25
3.7.6 Characteristics of Sub-grade 26
3.7.7 Characteristics of Concrete 27
3.7.8 Fatigue Behaviour of Cement Concrete 27
3.7.9 Stress Computations 28
3.7.10 Temperature Differential 28
3.7.11 Recommended Design Procedure for Slab Thickness 28
3.7.12 Design of Joints 29
REFERENCES
1
1. GEOMETRIC DESIGN STANDARDS FOR NON-URBAN HIGHWAYS (IRC: 73-1980)
1.1 CLASSIFICATION OF NON-URBAN ROADS
Non-urban roads in India are classified into following five categories based on location and
function according to Nagpur road plan:
National Highways (NH)
State Highways (SH)
Major District Roads (MDR)
Other District Roads (ODR)
Village Roads (VR)
Present system follows modified classification system as per third 20-year road
development plan. The roads are now classified into following three classes, for the
purpose of transport planning, functional identification, earmarking administrative
jurisdictions and assigning priorities on a road network:
Primary system
o Expressways and National Highways (NH)
Secondary system
o State Highways (SH) and Major District Roads (MDR)
Tertiary system (Rural Roads)
o Other District Roads (ODR) and Village Roads (VR)
1.2 TERRAIN CLASSIFICATION
Table 1.1 Classification of terrains
Terrain Classification Cross slope of the country (%)
Plain 0 – 10
Rolling 10 – 25
Mountainous 25 – 60
Steep > 60
1.3 DESIGN SPEED
Table 1.2 Design Speeds on Non-urban Roads
Road Classification
Design Speed (km/h)
Plain Rolling Mountainous Steep
Ruling Min Ruling Min Ruling Min Ruling Min
Expressways 120 100 100 80 80 60 80 60
NH and SH 100 80 80 65 50 40 40 30
MDR 80 65 65 50 40 30 30 20
ODR 65 50 50 40 30 25 25 20
VR 50 40 40 35 25 20 25 20
2
1.4 CROSS SECTION ELEMENTS
1.4.1 Cross Slope or Camber
Table 1.3 Recommended values of camber for different types of road surfaces
Sl No
Types of Road Surface Range of Camber in areas of
Heavy rainfall Light rainfall
1 Cement concrete and high type bituminous surface 1 in 50 (2.0%) 1 in 60 (1.7%)
2 Thin bituminous surface 1 in 40 (2.5%) 1 in 50 (2.0%)
3 Water bound macadam and gravel pavement 1 in 33 (3.0%) 1 in 40 (2.5%)
4 Earth Road 1 in 25 (4.0%) 1 in 33 (3.0%)
1.4.2 Width of Pavement or Carriageway
Table 1.4 Recommended values for width of carriageway
Sl No
Class of Road Width of Carriageway (m)
1 Single lane 3.75
2 Two lanes, without raised kerbs 7.0
3 Two lanes, with raised kerbs 7.5
4 Intermediate carriageway (except on important roads) 5.5
5 Multi-lane pavements 3.5 m per lane
Notes:
The lane width of Expressways is 3.75 m in plain and rolling terrains and 3.5 m in mountainous terrian
The width of single lane for village roads may be decreased to 3.0 m
On urban roads without kerbs the single lane width may be decreased to 3.5 m and in access roads to residential areas to 3.0 m
The minimum width recommended for kerbed urban road is 5.5 m
1.4.3 Width of Roadway or Formation
Table 1.5 Recommended values for width of roadway of various classes of roads
Sl No
Road Classification
Roadway width (m)
Plain & Rolling terrain
Mountainous & Steep terrain
1 National & State Highways
a. Single Lane b. Two Lane
12.0 12.0
6.25 8.80
2 Major District Roads
a. Single Lane b. Two Lane
9.0 9.0
4.75 ---
3 Other District Roads
a. Single Lane b. Two Lane
7.5 9.0
4.75 ---
4 Village Roads – single lane 7.5 4.0
3
1.4.4 Right of Way
Table 1.6 Recommended land width for different classes of non-urban roads
Sl No
Road Classification
Plain & rolling terrain Mountainous &
steep terrain
Open areas Built-up areas Open areas
Built-up areas
Normal Range Normal Range Normal Normal
1 Expressways 90 - - - 60/30
2 National & State Highways 45 30-60 30 30-60 24 20
3 Major District Roads 25 25-30 20 15-25 18 15
4 Other District Roads 15 15-25 15 15-20 15 12
5 Village Roads 12 12-18 10 10-15 9 9
1.5 SIGHT DISTANCE
1.5.1 Stopping Sight Distance (SSD)
SSD = Lag distance + Braking distance
��� = �� +��
2�(� ± 0.01�) (1.1)
� = Design speed (m/s) � = Reaction time of driver (s) (2.5 seconds as per IRC guidelines) � = Design longitudinal friction coefficient (Refer Table 1.7) � = Acceleration due to gravity = 9.8 m/s2 � = Gradient of road (%) (+ for ascending and – for descending)
Table 1.7 Recommended longitudinal friction coefficient for providing SSD
Table 1.8 Recommended Stopping Sight Distance for different speeds
Speed (km/h) 20 25 30 40 50 60 65 80 100
SSD (m) 20 25 30 45 60 80 90 120 180
1.5.2 Overtaking Sight Distance (OSD)
��� = �� + �� + �� (1.2a)
��� = ��� + (��� + 2�)+ �� (1.2b)
��∗ = (�∗ − 16) (As per IRC guidelines) (1.2c)
� = (0.2��∗ + 6) (As per IRC guidelines) (1.2d)
� = �4� �⁄ (1.2e)
4
� = Design speed or Speed of overtaking vehicle (m/s) �� = Speed of overtaken vehicle (m/s) � = Reaction time of driver (s) (2.0 seconds as per IRC guidelines) � = Time taken for overtaking operation (s) � = The minimum spacing between vehicles (m) �∗ = Design speed or Speed of overtaking vehicle (km/h) ��∗ = Speed of overtaken vehicle (km/h) � = Average acceleration during overtaking (m/s2)
Table 1.9 Maximum overtaking acceleration at different speeds
Speed (km/h) 25 30 40 50 65 80 100
Max overtaking Acc
(kmph/s) 5.00 4.80 4.45 4.00 3.28 2.56 1.92
(m/s2) 1.41 1.30 1.24 1.11 0.92 0.72 0.53
Table 1.10 Overtaking Sight Distance on two-lane highways for different speeds
Speed (km/h) 40 50 60 65 80 100
SSD (m) 165 235 300 340 470 640
Note:
��� = �� + �� for one-way roads
��� = �� + �� + �� for two-way roads
Intermediate Sight Distance (ISD) = 2 SSD
Head Light Distance (HSD) = SSD
1.6 HORIZONTAL ALIGNMENT
1.6.1 Superelevation (e)
� + �� =��
�� (1.3)
� = Rate of superelevation �� = Design value of transverse or lateral friction coefficient (0.15 as per IRC guidelines) � = Design speed vehicle (m/s) � = Radius of the horizontal curve (m) � = Acceleration due to gravity = 9.8 m/s2
Maximum Superelevation
In order to account for mixed traffic conditions in India, IRC has defined the maximum limit
of superelevation (���� ) as given in Table 1.11
Table 1.11 Recommended maximum limit of superelevation 7 % - Plain and rolling terrains and in snow bound areas
10 % - Hill roads not bound by snow 4 % - Urban road stretches with frequent intersections
5
Minimum Superelevation
From drainage considerations it is necessary to have a minimum cross slope to drain off the
surface water. If the design superelevation works out to be less than the camber of the
road surface, then the minimum superelevation to be provided on horizontal curve may be
limited to the camber of the surface. Thus, after elimination of the crown a uniform cross
slope equal to the camber is maintained from outer to inner edge of pavement at the
circular curve.
In very flat curves with large radius, the normal cambered section may be retained on the
curves. However, in such cases, a check is performed for negative superelevation against
allowable lateral friction coefficient.
The IRC recommendation giving the radii of horizontal curves beyond which normal
cambered section may be maintained and no superelevation is required at horizontal
curves, are presented in Table 1.12, for various design speeds and rates of cross slope.
Table 1.12 Recommended radii beyond which superelevation is not required
Design Speed (km/h)
Radius (m) of horizontal curve for camber of
4% 3% 2.5% 2% 1.7%
20 50 60 70 90 100
25 70 90 110 140 150
30 100 130 160 200 240
35 140 180 220 270 320
40 180 240 280 350 420
50 280 370 450 550 650
60 470 620 750 950 1100
80 700 950 1100 1400 1700
100 1100 1500 1800 2200 1600
Design of Superelevation (as per IRC guidelines)
The superelevation is calculated for 75% of design speed neglecting the friction
� =(0.75�)�
�� (1.4)
If the calculated value of ‘e’ is less than the specified maximum limit of superelevation
(���� ) the value so obtained is considered as design value of superelevation.
If the calculated value of ‘e’ exceeds ���� then ���� is considered as design value of
superelevation and developed lateral friction coefficient is verified at the full value of
design speed.
6
�� =��
��− ���� (1.5)
If �� calculated is less than 0.15, then ���� is accepted as the design superelevation.
If not, either the radius of the horizontal curve has to be increased or the speed has to
be restricted to the safe value �� given in equation 1.6 which will be less than the design
speed.
�� = �(���� + ��)�� (1.6)
Appropriate warning sign and speed limit regulation sign are installed to restrict and
regulate the speed to �� at such curves.
1.6.2 Widening of Pavement on Horizontal Curves
Extra width = Mechanical widening + Psychological widening
� � = � � + � �� (1.7a)
� � =���
2�+
�∗
9.5√� (1.7b)
� = Number of traffic lanes � = Length of wheel base (m) (normally 6.1 m or 6.0 m) � = Radius of horizontal curve (m) �∗ = Design speed (km/h)
Table 1.13 Recommended Extra Width of pavement at horizontal curves
The design traffic is considered in terms of cumulative number of standard axles (in the lane
carrying maximum traffic) to be carried during the design life of pavement using
� =���[(� + �)� − �]
�∗� ∗� ∗� (2.1 a)
N The cumulative number of standard axles to be catered for in the design life in terms of msa
A Initial traffic in the year of completion of construction in terms of the number of commercial vehicles per day
D Lane distribution factor F Vehicle damage factor n Design life in years r Annual growth rate of commercial vehicles
The traffic in the year of completion is estimated using
� = �(� + �)� (2.1 b)
P Number of commercial vehicles as per last count x Number of years between the last count and the year of completion of
construction
2.2 TRAFFIC GROWTH RATE
Traffic growth rates should be estimated
by studying the past trends of traffic growth, and
by establishing econometric models, as per the procedure outlined in IRC:108
“Guidelines for traffic prediction on rural highways”.
If adequate data is not available, it is recommended that an average annual growth rate of
7.5 percent may be adopted.
2.3 DESIGN LIFE
For the design of pavement, the design life is defined in terms of the cumulative number of
standard axles that can be carried before strengthening of pavement is necessary.
It is recommended that pavements for National Highways (NH) and State Highways (SH)
should be design for a life of 15 years. Expressways and Urban roads nay be designed for a
longer life of 20 years. For other categories of roads, a design life of 10 to 15 years may be
adopted.
11
2.4 VEHICLE DAMAGE FACTOR
��� =�� �
� �
� ���
+ �� �� �
� ���
+ �� �� �
� ���
+… …
�� + �� + �� +… …
(2.2 a)
��� =������� + ������� + ������� +… …
�� + �� + �� +… … (2.2 b)
���� = ���������
������������������
(2.2 c)
Standard Axle Load Single Axle : 8160 kg Tandem Axle : 14968 kg
Where sufficient information on axle loads is not available and project does not warrant
conducting an axle load survey, the indicative values of vehicle damage factor as given
below may be used.
Table 2.1 Indicative VDF Values (Table 1 of IRC:37-2001)
Initial traffic volume (CVPD)
Terrain
Rolling/Plain Hilly
0-150 1.5 0.5
150-1500 3.5 1.5
More than 1500 4.5 2.5
2.5 DISTRIBUTION OF COMMERCIAL TRAFFIC OVER THE CARRIAGEWAY
In the absence of adequate and conclusive data for Indian conditions, it is recommended to
assume the following distribution.
Table 2.2 Indicative Lane Distribution Values
No. of Traffic lanes
in two directions
Percentage of trucks in Design Lane
Undivided Roads
(Single Carriageway)
Divided Roads
(Dual Carriageway)
1 100 100
2 75 75
3 ---- 60
4 40 45
12
2.6 DESIGN CRITERIA
The flexible pavements has been modeled as a three layer structure and stresses and strains
at critical locations have been computed using the linear elastic model. To consider the
aspects of performance, the following three types of pavement distress resulting from
repeated (cyclic) application of traffic loads are considered:
Vertical compressive strain at the top of the sub-grade which can cause sub-grade
deformation resulting in permanent deformation at the pavement surface.
Horizontal tensile strain or stress at the bottom of the bituminous layer which can
cause fracture of the bituminous layer.
Pavement deformation within the bituminous layer.
Figure 2.1 : Critical Locations in Pavement
While the permanent deformation within the bituminous layer can be controlled by meeting
the mix design requirements, thickness of granular and bituminous layers are selected using
the analytical design approach so that strains at the critical points are within the allowable
limits. For calculating tensile strains at the bottom of the bituminous layer, the stiffness of
dense bituminous macadam (DBM) layer with 60/70 bitumen has been used in the analysis.
2.7 FAILURE CRITERIA
As shown in figure 2.11, A and B are the critical locations for tensile strains (εt). Maximum
value of the strain is adopted for design. C is the critical location for the vertical subgrade
strain (εz) since the maximum value of the εz occurs mostly at C.
Fatigue Criteria:
Bituminous surfacing of pavements display flexural fatigue cracking if the tensile strain at
the bottom of the bituminous layer is beyond certain limit. The relation between the fatigue
life of the pavement and the tensile strain in the bottom of the bituminous layer is
expressed as
13
�� = �.������� ��
����.��
��
���.���
(2.3)
Nf Allowable number of load repetitions to produce 20% cracked surface area εt Tensile strain at the bottom of surface layer (micro strain) E Elastic modulus of bituminous surfacing (MPa)
Rutting Criteria:
The allowable number of load repetitions to control permanent deformation can be
expressed as
�� = �.��������� ��
����.����
(2.4)
Nr Allowable number of load repetitions to produce rutting of 20 mm εz Vertical subgrade strain (micro strain)
Standard axle load considered is 80 kN. One dual wheel set with a wheel load of 20kN,
center-to-center tyre spacing of 310 mm and tyre pressure of 0.56 MPa is considered for
analysis.
2.8 DESIGN CHARTS AND CATALOGUE
Based on the performance of existing designs and using analytical approach, simple design
charts (Figure 2.2 and 2.3) and a catalogue of pavement designs are added in the code. The
pavement designs are given for subgrade CBR values ranging from 2% to 10% and design
traffic ranging from 1 msa to 150 msa for an average annual pavement temperature of 35 C.
The later thicknesses obtained from the analysis have been slightly modified to adapt the
designs to stage construction. Using the following simple input parameters, appropriate
designs could be chosen for the given traffic and soil strength:
Design traffic in terms of cumulative number of standard axles; and
CBR value of subgrade.
The designs relate to ten levels of design traffic 1, 2, 3, 4, 5, 10, 20, 30, 50, 100 and 150 msa.
For intermediate traffic ranges, the pavement layer thickness may be interpolated linearly.
For traffic exceeding 150 msa, the pavement design appropriate to 150 msa may be chosen
and further strengthening carried out to extend the life at appropriate time based on
Binder course : BM, DBM, mix seal surfacing, SDBC and BC
Wearing surface used is open-graded premix carpet of thickness upto 25 mm, it
should not be counted towards the total thickness
2.10 FINAL REMARKS
The present guidelines follows mechanistic empirical approach and developed new
set of designs up to 150 msa
Thickness charts are still available for CBR values of up to 10% only
Design charts are available for only a pavement temperature of 35o C
The contribution of individual component layers is still not realized fully with the
system of catalogue thicknesses. The same can be done with the analytical tool for
design.
19
3. ANALYSIS AND DESIGN OF RIGID PAVEMENTS
3.1 MODULUS OF SUBGRADE REACTION (K)
� =�
∆
(3.1 a)
p Pressure sustained by a rigid plate of diameter 75 cm at design deflection ∆ ∆ Design deflection = 0.125 cm
Allowance for Worst Subgrade Moisture
�� = ������
(3.1 b)
pus Pressure required in the plate bearing test for design deflection of 0.125 cm which produces a deformation of δ in unsoaked consolidation test
ps Pressure required to produce the same deformation δ in the soaked consolidation test
K Modulus of subgrade reaction for the prevailing moisture condition Ks Corrected modulus of subgrade reaction for worst subgrade moisture
Correction for Small Plate Size
� = ��
���
(3.1 c)
K1 Modulus of subgrade reaction determined using plate of radius a1 K Corrected modulus of subgrade reaction for standard plate of radius a
3.2 RADIUS OF RELATIVE STIFFNESS (�)
� = ����
���(� − ��)�
���
(3.2)
E Modulus of elasticity of cement concrete μ Poisson’s ratio of concrete = 0.15 h Slab thickness K Modulus of subgrade reaction
3.3 EQUIVALENT RADIUS OF RESISTING SECTION (b)
� = ��.��� + �� − �.��������� < 1.724ℎ (3.3)
� = ������ ≥ �.���� A Radius of wheel load distribution H Slab thickness
20
3.4 CRITICAL LOAD POSITIONS
The three typical locations namely the interior, edge and corner, where differing conditions
of slab continuity exist, are treated as critical load positions.
Figure 3.1: Critical Load Positions
3.5 STRESSES AND DEFLECTIONS DUE TO WHEEL LOAD
3.5.1 Corner Loading
Westergaard (1926)
�� =��
���� − �
�√�
��
�.�
� (3.4 a)
∆�=�
�����.� − �.���
�√�
���
(3.4 b)
Westergaard analysis modified by Kelly
�� =��
���� − �
�√�
��
�.�
� (3.4 c)
Ioannides et al (1985)
�� =��
���� − �
�
���.��
� (3.4 d)
∆�=�
�����.��� − �.�� �
�
���
(3.4 e)
21
3.5.2 Interior Loading
Westergaard (1926)
�� =�(� + �)�
�������
�
�+ �.����� (3.5 a)
∆�=�
������ +
�
����� �
�
��� − �.���� �
�
���
� (3.5 b)
3.5.3 Edge Loading
Westergaard (1926)
�� =�.����
���� ����
�
��+ �.���� (3.6 a)
Westergaard’s analysis Modified by Teller and Sutherland (1948)
�� =�.����
��(� + �.���)�� ����
�
��+ ���(�)− �.����� (3.6 b)
Ioannides et al (1985) – Semicircular loaded area
�� =�(� + �)�
�(� + �)������
���
������� + �.�� −
��
�+(� + ��)
��� (3.6 c)
∆�= ���� + �.��
����� �� −
(�.��� + �.���)�
�� (3.6 d)
When μ = 0.15
�� =�.����
���� ����
�
��+ �.����
�
�� + �.���� (3.6 e)
∆�=�.����
����� − �.����
�
��� (3.6 f)
22
Ioannides et al (1985) – Circular loaded area
�� =�(� + �)�
�(� + �)����� �
���
������� + �.�� −
��
�+� − �
�+�.��(� + ��)�
�� (3.6 g)
∆�= ���� + �.��
����� �� −
(�.�� + �.��)�
�� (3.6 h)
When μ = 0.15
�� =�.����
���� ����
�
��+ �.����
�
�� − �.���� (3.6 i)
∆�=�.����
����� − �.�� �
�
��� (3.6 j)
σc, σi, σe Maximum stress at corner, interior and edge loading respectively ∆c, ∆i, ∆e Maximum deflection at corner, interior and edge loading respectively
h Slab thickness P Wheel load K Modulus of subgrade reaction a Radius of wheel load distribution l Radius of relative stiffness b Radius of resisting section c Side length of square contact area = 1.772a E Modulus of elasticity of cement concrete μ Poisson’s ratio of concrete = 0.15
3.5.4 Dual Tires
Figure 3.2: Method for Converting Duals into a Circular Area
23
If Pd is the load on one tire and q is the contact pressure, the area of each tire is
σtc, σti, σte Maximum warping stress at corner, interior and edge region respectively
a Radius of wheel load distribution
l Radius of relative stiffness
E Modulus of elasticity of cement concrete
μ Poisson’s ratio of concrete = 0.15
α Thermal coefficient of concrete
Cx, Cy, Bradbury warping stress coefficient
24
L/l C L/l C
1 0.000 7 1.030
2 0.040 8 1.077
3 0.175 9 1.080
4 0.440 10 1.075
5 0.720 11 1.050
6 0.920 12 1.000
Figure 3.3: Warping Stress Coefficient or Stress Correction Factor for Finite Slab (Bradbury – 1938 and IRC : 58-2002)
3.6.2 Frictional Stresses
����� = ��
����� (3.9 a)
Or
��� = �
���� (3.9 b)
σtf Frictional Stress developed in cement concrete pavement
h Slab Thickness
B Slab width
L Slab length
f Coefficient of subgrade restraint (maximum value is about 1.5)
γc Unit weight of concrete (about 2400 kg/m3)
25
3.7 IRC RECOMMENDATIONS FOR DESIGN OF PLAIN JOINTED RIGID
PAVEMENTS FOR HIGHWAYS (IRC : 58-2002)
3.7.1 Legal Axle Load Limits
Single 10.2 tonnes
Tandem 19.0 tonnes
Tridem 24.0 tonnes
3.7.2 Load Safety Factors
Expressway/NH/SH/MDR 1.2
Lesser importance with lower truck traffic 1.1
Residential and other streets 1.0
3.7.3 Tyre Pressure
Range 0.7 to 1.0 MPa
No significant effect on pavements ≥ 20cm thick
0.8 MPa is adopted
3.7.4 Design Period
Normal – 30 years
Accurate prediction not possible – 20 years
3.7.5 Design Traffic
a. 2-lane 2-way road – 25% of total for fatigue design
b. 4-lane or multi-lane divided traffic – 25% of total traffic in the direction of
predominant traffic.
c. New highway links where no traffic data is available - data from roads similar
classification and importance
d. Average annual growth rate – 7.5%
e. Cumulative Number of Repetitions of Axles
� =���[(� + �)� − �]
�� (3.10 a)
� = �(� + �)� (3.10 b)
A Initial number of axles per day in the year when the road is operational R Annual rate of growth of commercial traffic N Design period in years P Number of commercial vehicles as per last count X Number of years between the last count and the year of completion of
construction
26
3.7.6 Characteristics of Sub-grade
Modulus of sub-grade reaction (K)
a. Pressure sustained per unit deflection
b. Plate bearing test (IS : 9214 – 1974)
c. Limiting design deflection = 1.25mm
d. K75 = 0.5 k30
e. One test/km/lane
Approximate K-Value
Approximate K-value corresponding to CBR values for homogeneous soil subgrade
k-Value of subgrade (kg/cm3) 2.1 2.8 4.2 4.8 5.5 6.2
Effective k over 100 mm DLC (kg/cm3) 5.6 9.7 16.6 20.8 27.8 38.9
Effective k over 150 mm DLC (kg/cm3) 9.7 13.8 20.8 27.7 41.7 -
27
3.7.7 Characteristics of Concrete
Modulus of Elasticity
Experimentally determined value
3.0 x 105 kg/cm2 for M40 Concrete
Poisson’s ratio
µ = 0.15
Flexural strength of Cement Concrete
fcr = 45 kg/cm2 for M40 Concrete
Coefficient of thermal expansion
α = 10 x 10-6 per °C
3.7.8 Fatigue Behaviour of Cement Concrete
� = ��������� for SR < 0.45 (3.11 a)
� = ��.����
�� − �.������.���
when 0.45 ≤ SR ≤ 0.55 (3.11 b)
������ = ��.���� − ��
�.����� for SR > 0.55 (3.11 c)
N Fatigue life SR Stress ratio
Stress Ratio and Allowable Repetitions in Cement Concrete
Stress Ratio Allowable
Repetitions Stress Ratio
Allowable Repetitions
Stress Ratio Allowable
Repetitions
0.45 62,790,761 0.59 40,842 0.73 832
0.46 14,335,236 0.60 30,927 0.74 630
0.47 5,202,474 0.61 23,419 0.75 477
0.48 2,402,754 0.62 17,733 0.76 361
0.49 1,286,914 0.63 13,428 0.77 274
0.50 762,043 0.64 10,168 0.78 207
0.51 485,184 0.65 7,700 0.79 157
0.52 326,334 0.66 5,830 0.80 119
0.53 229,127 0.67 4,415 0.81 90
0.54 166,533 0.68 3,343 0.82 68
0.55 124,526 0.69 2,532 0.83 52
0.56 94,065 0.70 1,917 0.84 39
0.57 71,229 0.71 1,452 0.85 30
0.58 53,937 0.72 1,099 --- ----
28
3.7.9 Stress Computations
Edge Stress
Due to Load – Picket & Ray’s chart
Due to Temperature –Westergaard’s equation (Equation 2.7 b)
Corner Stress
Due to Load –Westergaard’s analysis modified by Kelly (Equation 2.3 c)
Due to temperature – negligible and hence ignored
3.7.10 Temperature Differential
Recommended Temperature Differentials for Concrete
3.7.11 Recommended Design Procedure for Slab Thickness
Stipulate design values for the various parameters
Decide types and spacing between joints
Select a trial design thickness of pavement
Compute the repetitions of axle loads of different magnitudes during design period
Calculate cumulative fatigue damage (CFD)
If CFD is more than 1.0 revise the thickness
Check for load+temperature stress at edge with modulus of rupture
Check for corner stress
29
3.8 Design of Joints
Expansion Joint
If δ' is the maximum expansion in a slab of length Le with a temperature rise from T1 to T2,
then δ' = Le α (T1 to T2) where α is the coefficient of thermal expansion of concrete.
Expansion joint gap δ = 2 δ'
Maximum expansion joint gap = 25 mm
Maximum Spacing between expansion joints
for rough interface layer
140 m – all slab thicknesses
for smooth interface layer
when pavement is constructed in summer
90 m – upto 200 mm thick slab
120 m – upto 250 mm thick slab
when pavement is constructed in winter
50 m – upto 200 mm thick slab
60 m – upto 250 mm thick slab
Contraction Joint
����� = �������� (3.12)
σtc Allowable tensile stress in concrete
h Slab thickness
B Slab width
Lc Slab length or spacing b/w contraction joints
γc Unit weight of concrete
f Coefficient of subgrade restraint (max 1.5)
If Reinforcement is provided, replace LHS by σts As
Maximum Spacing between contraction joints
for unreinforced slabs
4.5 m – all slab thicknesses
for reinforced slabs
13 m – for 150 mm thick slab
14 m – for 200 mm thick slab
30
Dowel Bar Design
Load transfer capacity of a single dowel bar in
Shear ��� = �.������� (3.13 a)
Bending ��� =
�����
�� + �.�� (3.13 b)
Bearing ��� =
������
��.�(�� + �.��) (3.13 c)
P' Load transfer capacity of a single dowel bar, kg d Diameter of dowel bar, cm Ld Total length of embedment of dowel bar, cm δ Joint width, cm Fs Permissible shear stress in dowel bar, kg/cm2 Ff Permissible flexural stress in dowel bar, kg/cm2 Fb Permissible bearing stress in concrete, kg/cm2
Balanced design for equal capacity in bending and bearing gives
�� = �� ����
����� + �.��
�� + �.���� (3.14)
Minimum dowel length L = Ld + δ
Load capacity of dowel system = 40% of wheel load
Required load capacity factor = ��%�����������
(�′)���
Effective distance upto which there is load transfer = 1.8 (radius of relative stiffness)
Variation of capacity factor linear from 1.0 under the load to 0.0 at effective distance
Design spacing = The spacing which conforms to required capacity factor
Recommended Dimensions of Dowel Bars for Rigid Pavements (Axle Load of 10.2t)
Slab thickness, cm Dowel Bar Details
Diameter, mm Length, mm Spacing, mm
20 25 500 250
25 25 500 300
30 32 500 300
35 32 500 300
Note : Dowel bars shall not be provided for slabs of less than 15 cm thickness
31
3.9 Tie Bar Design
Area of steel per unit length of joint is obtained by equating the total friction to the total
tension developed in the tie bars
����� = ����� (3.15)
Length of embedment required to develop a bond strength equal to working stress of steel
����� =������� or �� =
�
�������
(3.16)
σts Allowable tensile stress in steel = 1400 kg/cm2 As Area of tie bar B distance b/w the joint and nearest free edge h Slab thickness γc Unit weight of concrete f Coefficient of subgrade restraint (max 1.5) Lt Length of tie bar P Perimeter of tie bar d Diameter of tie bar
σbc Allowable bond stress in concrete = 24.6 kg/cm2 for deformed tie bars
= 17.5 kg/cm2 for plain tie bars
Details of Tie Bars for Longitudinal Joint of Two-Lane Rigid Pavements
Slab Thickness
cm
Tie bar details, cm
Diameter mm
Max. spacing, cm Minimum Length, cm
Plain bars
Deformed bars
Plain bars
Deformed bars
15 8 33 53 44 48
10 52 83 51 56
20 10 39 62 51 56
12 56 90 58 64
25 12 45 72 58 64
16 80 128 72 80
30 12 37 60 58 64
16 66 106 72 80
35 12 32 51 57 64
16 57 91 72 80
Note: The recommended details are based on the following values of design parameters
σts Allowable tensile stress in steel = 2000 kg/cm2 for deformed bars
= 1250 kg/cm2 for plain bars
σbc Allowable bond stress in concrete = 24.6 kg/cm2 for deformed bars
IRC: 73 – 1980 “Geometric Design Standards for Rural (Non-urban) Highways”, Indian Roads Congress, New Delhi IRC: 37 – 2001 “Guidelines for the Design of Flexible Pavements”, Second Revision, Indian Roads Congress, New Delhi IRC: 58 – 2002 “Guidelines for the Design of Plain Jointed Rigid Pavements for Highways”, Second Revision, Indian Roads Congress, New Delhi Khanna S K, Justo C E G and Veeraragavan A (2014) “Highway Engineering” Nem Chand & Bros, Roorkee Rajib B. Mallick and Tahar El-Korchi (2009) “Pavement Engineering – Principles and Practice”, CRC Press, Taylor & Francis Group Yang H Huang (2004) “Pavement Analysis and Design”, 2nd edition, Prentice Hall Yoder and Witzack (1975) “Principles of Pavement Design”, 2nd edition, John Wileys and Sons