Module II : Analysis and design of concrete pavements
Lecture 2 : Analysis of Concrete Pavement
 

Temperature stress analysis
Most of the studies show that the temperature distribution in concrete pavement is nonlinear.

Let, $T(z)$ represent the pavement temperature at depth $z$ from the mid-surface (positive downward) and $T_0$ is the reference temperature at which the slab is free from any temperature stress. It is also assumed that elastic modulus ($E$) and Poisson's ratio ($\mu$) does not change with temperature and also the pavement temperature distribution of the pavement, with respect to time, is fixed. So, if the slab is fully restrained, the restrained strain ( $\epsilon^T$) due to temperature change from $T_0$   to  $T(z)$   will be:
$\displaystyle \epsilon_{xx}^{total,T}(z)$
 $\textstyle =$ $\displaystyle \epsilon_{yy}^{total,T}(z) = \alpha \left ( T(z)-T_0 \right )$
(17)

The corresponding stress ( $\sigma^{total,T}$), may be expressed as:
$\displaystyle \sigma_{xx}^{total,T}(z)$ $\textstyle =$ $\displaystyle \frac{E(z)}{1-\mu^2} \epsilon_{xx}^{total,T}(z)+\mu \frac{E(z)}{1... ...}\epsilon_{yy}^{total,T}(z)=- \frac {E \alpha \left (T(z)-T_0 \right )} {1-\mu}$
(18)
$\displaystyle \sigma_{yy}^{total,T}(z)$ $\textstyle =$ $\displaystyle \frac{E(z)}{1-\mu^2} \epsilon_{yy}^{total,T}(z)+\mu \frac{E(z)}{1... ...} \epsilon_{xx}^{total,T}(z)=- \frac {E \alpha \left( T(z)-T_0 \right )}{1-\mu}$
(19)

where, $\alpha$ is coefficient of thermal expansion of concrete. The positive strain indicates the compressive stress (negative). It may be noted that the shape of the stress diagram is similar to the temperature profile. The above stresses (equation 18 and 19) can be divided into three components, (i) axial, (ii) bending and (iii) residual. This has been explained schematically in Fig. 17 and Fig. 18, for day time and night time conditions respectively (Choubane and Tia 1992). The various stress components are discussed further in the following.

                                   Figure 17. Various components of stress during day time comdition


                                           Figure 18: Various components of stress during night time condition

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