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Chapter 11 of 12

Pavement Design (Flexible & Rigid)

In the DSSSB JE Civil syllabus under Transportation Engineering · 2 parts

Flexible Pavement Design · Rigid Pavement Design

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📑 Contents (19 sections)

Part 1 of 2

Flexible Pavement Design

Last reviewed 16 Sept 2026 · 9 min read

Types of pavements

Flexible pavement	Rigid pavement
Layers of granular material with a bituminous surface; low flexural strength	Portland cement concrete slab with high flexural strength
Load transferred by grain-to-grain contact — spreads through layers in a cone	Load distributed over a wide area by slab (beam) action
Design depends heavily on subgrade strength	Less sensitive to subgrade strength
Deforms with the subgrade; surface follows undulations	Bridges minor subgrade irregularities
Lower initial cost, higher maintenance; can be opened soon after construction	Higher initial cost, low maintenance, long life; needs curing
Temperature affects binder stiffness	Temperature causes warping stresses; joints needed

Other types: composite pavements (bituminous over concrete or cement-treated base), semi-rigid pavements (cement-treated layers), interlocking concrete block pavements.

Layers of a flexible pavement

Layer	Function / typical material
Surface (wearing) course	Resists abrasion and skidding, provides a smooth riding surface, waterproofs the pavement — bituminous concrete (BC), stone matrix asphalt (SMA), semi-dense BC, premix carpet, surface dressing
Binder course	Transfers load to the base and bonds the surface to the base — dense bituminous macadam (DBM), bituminous macadam
Base course	Main load-spreading layer — wet mix macadam (WMM), water bound macadam (WBM), cement-treated or bitumen-treated bases, crushed rock
Sub-base course	Spreads load to the subgrade, drainage and filter layer, prevents intrusion of fines — granular sub-base (GSB), cement/lime-treated soil
Subgrade	Compacted natural/borrow soil (top 500 mm compacted to high density) — foundation of the pavement

Also: prime coat (between granular base and bituminous layer) and tack coat (between bituminous layers).

Stresses in flexible pavements

A wheel load is applied over a contact area (often assumed circular) with contact pressure roughly equal to tyre pressure.
Boussinesq's theory (homogeneous elastic half-space): vertical stress below the centre of a uniformly loaded circular area of radius $a$ :

σ_{z} = p [1 - \frac{z ^{3}}{( a ^{2} + z ^{2} ) ^{3/2}}]

Burmister's layered theory — two or three elastic layers of different moduli; basis of modern analysis (a stiffer upper layer reduces stresses below).

Equivalent single wheel load (ESWL)

The single wheel load that produces the same effect (stress or deflection) at a given depth as a group of wheels (dual or tandem).

Boyd–Foster equal stress method (graphical): on a log–log plot of load against depth, ESWL = $P$ (one wheel of the dual) at depth $d /2$ and $2 P$ at depth $2 S$ ( $d$ = clear gap between tyres, $S$ = centre-to-centre spacing), with a straight line between:

lo g (E S W L) = lo g P + \frac{0.301 lo g ( 2 z / d )}{lo g ( 4 S / d )} for \frac{d}{2} \leq z \leq 2 S

Design approaches

Approach	Method
Empirical	Group index method; CBR method (early IRC:37); California method
Semi-empirical / semi-theoretical	Triaxial method (Kansas), layered-system methods
Mechanistic–empirical	Compute critical strains with a layered elastic model; limit them using performance (transfer) functions — IRC:37-2012 and IRC:37-2018

CBR method (empirical)

t = P [\frac{1.75}{C B R} - \frac{1}{p π}]^{1/2}

$t$ = total pavement thickness (cm) above the layer of given CBR; $P$ = wheel load (kg); $p$ = tyre pressure (kg/cm²). Thickness above each layer is found using that layer's CBR.

Design traffic

Standard axle and equivalency

The standard axle in IRC:37-2018 is a single axle with dual wheels carrying 80 kN. Damage by other axle loads is expressed by the fourth power law:

FormulaAxle load equivalency factors (IRC:37-2018)

Single axle (dual wheels): $E F = (\frac{W}{80})^{4}$
Tandem axle: $E F = (\frac{W}{148})^{4}$
Tridem axle: $E F = (\frac{W}{224})^{4}$ ( $W$ = axle load in kN.)

Vehicle damage factor (VDF) — number of standard axle repetitions caused by one passage of a commercial vehicle; found from axle load surveys (or indicative values).
Lane distribution factor (LDF) — proportion of commercial vehicles in the design lane: single-lane road 1.0; two-lane single carriageway 0.50; four-lane single carriageway 0.40; dual carriageway — two lanes in each direction 0.75, three lanes 0.60, four lanes 0.45.

FormulaCumulative design traffic

N = \frac{365 A [ ( 1 + r ) ^{n} - 1 ]}{r} \times D \times F

$N$ = cumulative standard axles (msa — million standard axles) during the design period
$A$ = initial commercial vehicles per day (both directions) in the year of opening: $A = P (1 + r)^{x}$ , where $P$ = count in the last year and $x$ = years between count and opening
$r$ = annual growth rate of commercial vehicles (decimal; about 5% where data are lacking)
$n$ = design period (years)
$D$ = lane distribution factor; $F$ = vehicle damage factor

Only commercial vehicles (laden weight above 3 tonnes) are considered. Design periods of about 20 years are commonly used for National and State Highways (longer for expressways and high-density corridors, shorter for lower categories). IRC:37-2018 is applicable for design traffic of 2 msa and above; low-volume roads are designed as per IRC:SP:72.

IRC:37-2018 mechanistic–empirical design

Design criteria

Bottom-up fatigue cracking of the bituminous layer — controlled by the horizontal tensile strain $ε_{t}$ at the bottom of the bituminous layer.
Rutting (permanent deformation) — controlled by the vertical compressive strain $ε_{v}$ on top of the subgrade.
Additional checks for cement-treated bases (fatigue of CTB) and top-down cracking considerations.

FormulaPerformance (transfer) functions (IRC:37-2018)

Fatigue:

N_{f} = 1.6064 \times C \times 1 0^{- 4} [\frac{1}{ε _{t}}]^{3.89} [\frac{1}{M _{R m}}]^{0.854} (80% reliability)

N_{f} = 0.5161 \times C \times 1 0^{- 4} [\frac{1}{ε _{t}}]^{3.89} [\frac{1}{M _{R m}}]^{0.854} (90% reliability)

$C = 1 0^{M}$ , $M = 4.84 (\frac{V _{b e}}{V _{a} + V _{b e}} - 0.69)$ — $V_{b e}$ = effective binder volume, $V_{a}$ = air voids (%); $M_{R m}$ = resilient modulus of the bituminous mix (MPa).

Rutting:

N_{R} = 4.1656 \times 1 0^{- 8} [\frac{1}{ε _{v}}]^{4.5337} (80%), N_{R} = 1.4100 \times 1 0^{- 8} [\frac{1}{ε _{v}}]^{4.5337} (90%)

Reliability: 90% for design traffic of 20 msa and above; 80% for lower traffic.

Material inputs

Subgrade — effective CBR (considering embankment and subgrade layers) → $M_{R}$ from CBR relations.
Granular layers — modulus depends on thickness and support: $M_{R, g r an} = 0.2 h^{0.45} M_{R, s u pp or t}$ ( $h$ in mm).
Bituminous layers — resilient modulus from IRC tables depending on binder grade (e.g. VG-30, VG-40) and pavement temperature (commonly 35 °C in design).
Cement-treated layers — modulus and flexural strength as given in the code.
Poisson's ratio — typically 0.35 for bituminous and granular layers and subgrade (0.25 for cemented layers).

Procedure

Estimate design traffic (msa) and subgrade effective CBR.
Select pavement composition (e.g. bituminous surface + DBM + WMM + GSB, or with CTB/CTSB layers) with trial thicknesses.
Analyse the pavement with the IITPAVE multilayer elastic program under the standard axle (dual wheels, 20 kN each, tyre pressure 0.56 MPa, 310 mm spacing).
Compute allowable $ε_{t}$ and $ε_{v}$ from the transfer functions for the design traffic.
Adjust thicknesses until computed strains do not exceed allowable strains; check minimum layer thicknesses and drainage.
IRC:37-2018 also provides design catalogues of layer thicknesses for different CBR and traffic combinations.

Part 2 of 2

Rigid Pavement Design

Last reviewed 16 Sept 2026 · 10 min read

Components of a rigid pavement

Layer	Function / typical specification
Pavement quality concrete (PQC)	Main structural slab carrying loads by flexure; high-strength concrete (commonly M40, design flexural strength about 4.5 MPa at 28 days)
Separation membrane / debonding layer	Polythene sheet or bitumen layer between PQC and sub-base to reduce friction and restraint cracking
Dry lean concrete (DLC) sub-base	Uniform, non-erodible support; commonly about 150 mm thick with a minimum compressive strength (e.g. 10 MPa)
Granular sub-base / drainage layer	Drains water, prevents pumping, provides construction platform
Subgrade	Compacted soil; strength expressed by modulus of subgrade reaction $k$

Unlike flexible pavements, the thickness of a rigid pavement depends mainly on the flexural strength of concrete; subgrade support has a relatively smaller effect.

Design factors

Wheel load and axle configuration — axle load spectrum, tyre pressure, contact area.
Traffic — number of repetitions of different axle loads over the design period (commonly 30 years for rigid pavements).
Modulus of subgrade reaction $k$ — from plate load tests (or from CBR correlations), increased for the effect of DLC/granular sub-base (effective k).
Concrete properties — flexural strength (modulus of rupture), modulus of elasticity (about 30 000 MPa), Poisson's ratio (0.15), coefficient of thermal expansion (about $10 \times 1 0^{- 6}$ per °C).
Temperature differential between top and bottom of the slab — causes warping.

Radius of relative stiffness

FormulaRadius of relative stiffness (Westergaard)

l = [\frac{E h ^{3}}{12 ( 1 - μ ^{2} ) k}]^{1/4}

$E$ = modulus of elasticity of concrete; $h$ = slab thickness; $μ$ = Poisson's ratio; $k$ = modulus of subgrade reaction.

It measures the stiffness of the slab relative to the subgrade — the distance over which the slab spreads the load.

Equivalent radius of resisting section

For a load of contact radius $a$ on a slab of thickness $h$ (thin-plate theory correction):

b = 1.6 a^{2} + h^{2} - 0.675 h when a < 1.724 h; b = a when a \geq 1.724 h

Load stresses (Westergaard)

Westergaard considered three critical positions of the wheel load:

Interior — load well away from edges and corners.
Edge — load at the edge, away from corners.
Corner — load at the corner of the slab.

FormulaWestergaard's stress equations (modified)

( $P$ = wheel load in kg; $h$ in cm; $l$ , $b$ , $a$ in cm; stresses in kg/cm²)

Interior:

σ_{i} = \frac{0.316 P}{h ^{2}} [4 lo g_{10} \frac{l}{b} + 1.069]

Edge:

σ_{e} = \frac{0.572 P}{h ^{2}} [4 lo g_{10} \frac{l}{b} + 0.359]

Corner:

σ_{c} = \frac{3 P}{h ^{2}} 1 - (\frac{a 2}{l})^{0.6}

Interior and edge stresses are tensile at the bottom of the slab; corner stress is tensile at the top.
Edge load stress is generally the most critical of the load stresses (without load transfer).

Temperature stresses

Warping stresses

A temperature differential between the top and bottom of the slab makes it curl (warp); self-weight and subgrade restraint resist this, inducing stresses.

Day (summer, mid-day): top hotter → slab tends to curl down at edges → tension at the bottom (adds to wheel load tension at the edge).
Night (winter): top cooler → edges curl up → tension at the top (adds to corner load stress).

FormulaWarping stresses (Bradbury)

Interior: $σ_{t i} = \frac{E α t}{2} [\frac{C _{x} + μ C _{y}}{1 - μ ^{2}}]$

Edge: $σ_{t e} = \frac{C _{x} E α t}{2}$ (or with $C_{y}$ , whichever is greater)

Corner: $σ_{t c} = \frac{E α t}{3 ( 1 - μ )} \frac{a}{l}$

$α$ = coefficient of thermal expansion; $t$ = temperature differential; $C_{x}$ , $C_{y}$ = Bradbury's coefficients depending on $L_{x} / l$ and $L_{y} / l$ (slab length and width ÷ radius of relative stiffness), read from Bradbury's chart.

Frictional stresses

Uniform temperature change makes the slab expand or contract; friction with the sub-base restrains it.

S_{f} = \frac{W L f}{2 \times 1 0 ^{4}}

( $S_{f}$ in kg/cm²; $W$ = unit weight of concrete, kg/m³; $L$ = slab length, m; $f$ = coefficient of friction, about 1.5.) This governs the spacing of contraction joints.

Critical combinations

Condition	Critical combination
Summer, mid-day	Edge load stress + warping stress at edge (bottom tension) − frictional stress
Winter, mid-day	Edge load stress + warping stress + frictional stress (contraction)
Night	Corner load stress + corner warping stress (top tension)

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