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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• 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 (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
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 = ONE – LAYER SYSTEMS
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:
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).
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.
(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
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.
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.
1. Theoretical methods;
2. Empirical methods;
3. Empirical-theoretical methods.
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:
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: