Module 4: Pavement Design

Lecture 29 Rigid pavement design

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Wheel load stresses - Westergaard's stress equation

The cement concrete slab is assumed to be homogeneous and to have uniform elastic properties with vertical sub-grade reaction being proportional to the deflection. Westergaard developed relationships for the stress at interior, edge and corner regions, denoted as $\sigma_i,~\sigma_e,~\sigma_c$ in kg/cm$^2$ respectively and given by the equation 1-3.

$$\sigma_i=\frac{0.316~P}{h^2}\left[4~\log_{10}\left(\frac{l}{b}\right)+1.069\right]$$ (1)

$$\sigma_e=\frac{0.572~P}{h^2}\left[4~\log_{10}\left(\frac{l}{b}\right)+0.359\right]$$ (2)

$$\sigma_c=\frac{3~P}{h^2}\left[1-\left(\frac{a\sqrt{2}}{l}\right)^{0.6}\right]$$ (3)

where $h$ is the slab thickness in cm, $P$ is the wheel load in kg, $a$ is the radius of the wheel load distribution in cm, $l$ the radius of the relative stiffness in cm and $b$ is the radius of the resisting section in cm

Figure 1: Critical stress locations