One-Dimensional Rigid Pavement Temperature Prediction Using Laplace Transformation

This paper presents an analytical solution for the prediction of the time-dependent one-dimensional temperature profile in an N-layered rigid pavement system using Laplace transformation. Temperature at any depth in a rigid pavement system can be estimated by using the proposed solution with input data such as pavement layer thicknesses, material thermal properties, and the measured air temperature and solar radiation intensities. The associated initial boundary value problem is governed by the classic heat conduction equation with the air temperature and solar radiation considered in the surface boundary condition. Interpolatory trigonometric polynomials, based on the method of discrete least-squares approximation, are used to fit the measured air temperature and solar radiation intensities during a user-defined time period. The relationship between the constants of integration for the $i$th layer and the first layer are deduced, which simplifies the solution process. Model validation with the measured data confirms that the proposed solution generates a reasonable temperature profile in the concrete slab of a four-layer rigid pavement system during two different time periods of the year.