Odemarks equivalent thickness concept

Odemark s method is based on the assumption that the stresses and strains below a layer depend only on the stiffness of that layer. If the thickness, modulus and Poisson s ratio of a layer are changed, but the stiffness remains unchanged, the stresses and strains below the layer should also remain (relatively) unchanged.  

According to Odemark (1949), the stiffness of the layer is proportional to the term hence, two layers are structurally equivalent when 

If a two-layer system is to be transformed into an equivalent one-layer system, the above equation becomes 

In order to achieve better agreement between the stresses and strains calculated using Odemark s concept and those from the theory of elasticity, a correction factor f is applied to the above equation. Thus, 

A recent study has confirmed that there is good agreement between the vertical stresses at the interface between the two layers, in a two-layer system, calculated using the theory of elasticity and Odemark s concept when using a correction factor (f) in the range of 0.8 to 0.9 (El-Badawy and Kamel 2011). 

---

Odemark s equivalent thickness concept consists of the transformation of a two or more layer system with different characteristic properties, E and p, into an equivalent one-layer system with equivalent thickness but one elastic modulus, that of the bottom (last) layer. Thus, one elastic, isotropic and homogeneous layer results and calculations of stresses and strains are easier. The transformation a two-layer system into an equivalent one-layer system is explained in Figure 11.13. 

Surface deformation using Odemark s equivalent thickness concept... 

From the nomograph in Figure 11.14, the vertical stress, at any depth, t, can also be calculated provided the three-layer system is transformed into a one-layer system using Odemark s equivalent thickness concept. In this case, the left y-axis and the top x-axis in Figure 11.14 are used. 

---