One-dimensional temperature profile prediction in multi-layered rigid pavement systems using a separation of variables method

Abstract

This paper presents an analytical solution for prediction of the one-dimensional (1D) time-dependent temperature profile in a multi-layered rigid pavement system. Temperature at any depth in a rigid pavement system can be estimated by using the proposed solution with limited input data, such as pavement layer thicknesses, material thermal properties, measured air temperatures and solar radiation intensities. This temperature prediction problem is modelled as a boundary value problem governed by the classic heat conduction equations, and the air temperatures and solar radiation intensities are considered in the surface boundary condition. Interpolatory trigonometric polynomials, based on the discrete least squares approximation method, are used to fit the measured air temperatures and solar radiation intensities during the time period of interest. The solution technique employs the complex variable approach along with the separation of variables method. A FORTRAN program was coded to implement the proposed 1D analytical solution. Field model validation demonstrates that the proposed solution generates reasonable temperature profile in the concrete slab for a four-layered rigid pavement system during two different time periods of the year.