Comparison of Thermal Stress Calculation: Hopkins and Hamming’s Algorithm and Laplace Transformation Approach

Low-temperature cracking is a severe distress for asphalt pavement built in cold regions. When a steep drop in temperature is experienced, thermal stress develops in the different pavement layers and, as a critical temperature value is reached, cracking occurs. Hence, thermal stress represents a relevant parameter for predicting the low-temperature performance of asphalt pavements. Conventionally, thermal stress is calculated by converting the experimental results of creep compliance to a relaxation modulus and then by numerically solving the convolution integral. Hopkins and Hamming's algorithm is commonly used for this purpose in many research efforts. In this paper, the use of Laplace transformation is evaluated as an alternative approach since, by using this method, thermal stress and critical temperature can be directly and easily derived without relying on a traditional two-step computation process. The results obtained from Hopkins and Hamming's solution and from the Laplace transformation are then graphically and statistically compared. It is found that the approach based on Laplace transformation provides reliable and reasonably close results to those obtained from the more complex Hopkins and Hamming's method.