Module 4: Pavement Design

Lecture 29 Rigid pavement design

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Modulus of sub-grade reaction

Westergaard considered the rigid pavement slab as a thin elastic plate resting on soil sub-grade, which is assumed as a dense liquid. The upward reaction is assumed to be proportional to the deflection. Base on this assumption, Westergaard defined a modulus of sub-grade reaction $K$ in kg/cm$^3$ given by $K=\frac{p}{\Delta}$ where $\Delta$ is the displacement level taken as 0.125 cm and $p$ is the pressure sustained by the rigid plate of 75 cm diameter at a deflection of 0.125 cm.

Relative stiffness of slab to sub-grade

A certain degree of resistance to slab deflection is offered by the sub-grade. The sub-grade deformation is same as the slab deflection. Hence the slab deflection is direct measurement of the magnitude of the sub-grade pressure. This pressure deformation characteristics of rigid pavement lead Westergaard to the define the term radius of relative stiffness $l$ in cm is given by the equation 1.

$$l = \sqrt[4]{\frac{Eh^3}{12K(1-\mu^2)}}$$ (1)

where E is the modulus of elasticity of cement concrete in kg/cm$^2$ (3.0$\times$10$^5$), $\mu$ is the Poisson's ratio of concrete (0.15), $h$ is the slab thickness in cm and $K$ is the modulus of sub-grade reaction.