Types of stresses in cement concrete pavement

A cement concrete (rigid) pavement slab resting on the subgrade is subjected to stresses from wheel loads and from changes in temperature and moisture. The types of stress (Westergaard's analysis, IRC:58-2015 for design) are:

1. Wheel load stresses

Caused by the load of the vehicle, treated by Westergaard's theory (slab on a Winkler foundation). Three critical positions:

$$\begin{aligned} \text{Interior:}\ \sigma_i &= \frac{0.316P}{h^2}\left[4\log_{10}\frac{l}{b} + 1.069\right]\\ \text{Edge:}\ \sigma_e &= \frac{0.572P}{h^2}\left[4\log_{10}\frac{l}{b} + 0.359\right]\\ \text{Corner:}\ \sigma_c &= \frac{3P}{h^2}\left[1 - \left(\frac{a\sqrt{2}}{l}\right)^{0.6}\right] \end{aligned}$$

where $P$ = wheel load, $h$ = slab thickness, $a$ = radius of the loaded area, $b = a$ if $a \ge 1.724h$ and $b = \sqrt{1.6a^2 + h^2} - 0.675h$ otherwise, and $l$ = radius of relative stiffness:

$$l = \left[\frac{E\,h^3}{12(1-\mu^2)\,k}\right]^{1/4}$$

($E$ = modulus of elasticity of concrete, $\mu$ = Poisson's ratio, $k$ = modulus of subgrade reaction.) The edge and corner stresses are the highest, so they control the design (corner cracks develop at the joint corners).

2. Temperature (warping) stresses

The top and bottom of the slab are at different temperatures. During the day the top is hotter and tends to expand, so the slab curls down at the edges; at night it curls up. The self-weight and the subgrade restrain this, giving tensile stresses:

$$\sigma_{te} = \frac{C\,E\,\alpha\,t}{2}\ \ \text{(edge)},\qquad \sigma_{ti} = \frac{E\alpha t}{2}\left[\frac{C_x + \mu C_y}{1-\mu^2}\right]\ \ \text{(interior)}$$

where $\alpha$ = coefficient of thermal expansion ($10 \times 10^{-6}$ per $^\circ$C), $t$ = temperature difference between top and bottom, and $C$, $C_x$, $C_y$ = Bradbury's coefficients (functions of slab length/$l$). The hot-afternoon edge warping stress is tension at the bottom; night curling gives tension at the top.

3. Frictional stresses

When the slab contracts due to a fall in temperature or shrinkage, friction with the subgrade resists the movement and causes tension at the middle of the slab:

$$\sigma_f = \frac{W\,L\,f}{2 \times 10^4}\ \text{kg/cm}^2$$

where $W$ = unit weight of concrete (2400 kg/m$^3$), $L$ = slab length (m) and $f$ = coefficient of friction (about 1.5). It governs the joint spacing and the steel in the slab.

4. Other stresses

Moisture-warping and shrinkage stresses, stresses due to subgrade settlement and swelling, and stresses at joints.

Combination for design (IRC:58): at the edge, summer midday: load + warping − friction, and winter midday: load + warping + friction; at the corner (critical at night): corner load stress + corner warping stress. The critical value is compared with the flexural strength of concrete with a factor of safety (fatigue is also checked).