Chapter 5 flexible pavement design
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CHAPTER 5 FLEXIBLE PAVEMENT DESIGN. Stresses and Strains in flexible Pavements. • The material properties of each layer are homogeneous • Each layer has a finite thickness except for the lower layer, and all are infinite in lateral directions.

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Chapter 5 flexible pavement design


Stresses and strains in flexible pavements
Stresses and Strains inflexible Pavements

Assumptions in multi layered elastic systems

The material properties of each layer are homogeneous

• Each layer has a finite thickness except for the lower

layer, and all are infinite in lateral directions.

• Each layer is isotropic, that is, the property at a specific

point such as Ai is the same in every direction or


• Full friction is developed between layers at each


• Surface shearing forces are not present at the surface.

• The stress solutions are characterized by two material

properties for each layer, i.e., (μ, E).

Assumptions in Multi LayeredElastic Systems

Stresses in layered systems

At any point, 9 stresses exist. They are 3 normal

stresses (sz, sr, st) and 6 shearing stresses ( trz =tzr; tr t = ttr; ttz =tzt)

• At each point in the system there exists a certain

orientation of the element such that the shearing

stresses acting on each face are zero.

– The normal stresses under this condition are principal stresses and are denoted by s1(major), s2 (intermediate) and s3 (minor).

Stresses in Layered Systems

One layer systems

Boussinseq assumptions:

1.soil is ideal mass;

2.soil are homogenous;

3.possion`s ratio is constant in all directions, and E is constant;

4.soil is isotropic , that mean x = 


Determination of stresses and deflections in multi layer system

Pavement stresses , strains and deflections are caused by:

1.traffic loading,

2.daily or seasonal temperature and moisture changes;

3.changes in the conditions of pavement support.

Determination of stresses and deflections in multi-layer-system:

Chapter 5 flexible pavement design

The general assumptions of the multi-layer theory are:

1.Materials used in each layer is


2.Finite thickness of layer;

3.Infinite lateral dimensions;

4. Isotropic properties;

5. Full friction at layer interfaces;

6 .Shear forces at surface =0;

7 .Each layer’s material is characterized by Poisson’s ratio (u) and elastic modules (E).

Chapter 5 flexible pavement design

Equivalent single wheel load (ESWL)

ESWL defined as the load on a single tire that will cause an equal magnitude of pre-selected parameter (stress, strain, def.), to that resulting from a multiple wheel load at the same location from the pavement.

There are two methods for determination the ESWL , based on equal stress and equal deflection.

Chapter 5 flexible pavement design


(1) For dual system

a = (Q/ p)0.5 = (9000/3.14 x90)0.5 = 5.64 in.

Max. stress at point (a) = 1 + 2

Load (1):

z/a = 30/5.64 =5.32, r/a =0.0

From z influence curve (Fig.58)

stress ratio = 5.1/ 90

1 =Pt x stress ratio = 90 x(5.1/90) =5.1 psi.

Chapter 5 flexible pavement design

load (2):

z/a = 5.32, r/a =5.32

2 = pt x stress ratio = 90x(0.95/90) =0.95 psi.

Total = 5.1 + 0.95 = 6.05 psi

b) For ESWL

max. = Pt x stress ratio = 6.05

stress ratio = 6.05 / Pt = 6.05 / 90 = 0.067

By using the chart:

r/a = 0.0 , stress ratio = 0.067 x 90 = 6.05

z/a = 5 = 30 / a a = 6.0 in.

PE = .Pt. a2 = 3.14x 90x 6x6 = 10.174 Ib.

Chapter 5 flexible pavement design

The design methods are classified to three main groups as follows:

1. Theoretical methods;

2. Empirical methods;

3. Empirical-theoretical methods.

2 empirical methods

These methods can be classified into three groups: follows:

1-Methods based on soil classification tests , as example group index method.

2-Methods based on soil strength tests as CBR-, asphalt institute-and national crushed stone association method.

3-Methods based on the results of road tests as AASHO and road test method.

2. Empirical Methods:

2 1 the group index method

Fig.69 shows an approximation of desirable total permanent th. based on truck traffic volume and the group index of the subgrade. This method is simple, but has many limitations and it could be lead to an over -or under designed pavement.

2.1.The Group Index Method:

2 2 cbr method

2.2. CBR Method: