Theoretical Solution for Temperature Profile in Multi-layered Pavement Systems Subjected to Transient Thermal Loads

摘要

This technical report focuses on developing easily implemented analytical solutions to predict rapidly varying temperature profiles in concrete pavements subjected to transient thermal loadings generated by vertical take-off aircraft engines. The general closed-form solution for the one-dimensional (1-D) temperature profile in a homogeneous half-space with specified pavement surface temperatures is well known; efficient numerical algorithms to accurately resolve the integrals involved in the general solution are identified through literature review and recommended based on numerical experiments in this report. 1-D analytical solutions for temperature fields in a two-layered pavement system using Laplace transforms are proposed for two different surface boundary conditions, i.e., specified transient surface temperature and mixed boundary condition involving heat flux emanating from the aircraft engine. Furthermore, two-dimensional (2-D) axisymmetric temperature field in a homogeneous half-space subjected to transient thermal loading was solved under the specified surface temperature condition. Two solution methods were introduced: one based on the Hankel transforms and the method of separation of variables; another based on the Hankel and Laplace transforms. Numerical experiments suggest that the combined results based on those two methods give reasonable approximation to the rapidly varying temperature profile.