Pavement Design

Chapter 2
Stresses and Strains in
Flexible Pavements

1

Layers of Flexible Pavements

Surface (wearing) Course
Binder Course
Base Course
Subbase Course
Subgrade

2

Contents





Single layer analysis
Two-layer system
Three-layer system
Viscoelastic solution

3

Single Layer Analysis

r

t

z
4

Boussinesq Theory (1885)






Homogeneous elastic half-space
A concentrated load is applied
Stresses, strains, and deflections are calculated by integrating concentrated loads on the surface
Further developed by Burmister
(1943)
5

Vertical Normal Stress (σz)

R

2R

Material Properties are more important in higher layers

3R

4R

R is the radius of circular loading
6

Analysis Methods



Charts (Foster and Ahlvin)
Closed form solutions





Flexible plate
Rigid plate

Computer programs





Kenlayer (provided in textbook)
BISAR
ILLI-Layer others 7

Charts developed by
Foster and Ahlvin


Circular load with a radius a and an intensity q




q= P/A = P/(πa2)

Assumed incompressible half-space
(ν = 0.5)
 lateral
Poisson’s ratio (ν) = 



 longitudinal

Bulk modulus




ν = 1/3  K=E ν = 0  K=E/3 ν = ½  K=∞

K

E
3(1  2 )
8

Vertical Stresses Due to
Circular Loading a z/a=3 r/a=2 Also, find radial stress (σr), tangential stress (σt), shear stress
(τrz), and vertical deflection (w) from the consecutive graphs
9

r

t
10

 rz

Vertical displacement (w)

11

Strains
1
 z   z   ( r   t )
E
1
 r   r   ( t   z )
E
1
 t   t   ( z   r )
E
12

Principal Stresses τmax  1, 2 

 z r
2

2

  r 
2
  rz
  z

 2 

σ1

σ2

2

 z  r 
2
  rz

 2 

 max  
3  t

Mohr’s Circle
13

Example 2.1 q= z=

a=5”
14

Flexible Plate v.s. Rigid Plate

15

Closed Form Solutions for