Analytical Modelling Of Pavements Under Moving Loads

On a global scale, substantial financial resources are allocated for developing safe roads and the maintenance of existing ones. As a result, it is desirable to ensure there is no unnecessary spending and that allocated budgets are utilised as efficiently as possible. Conventionally, analytical pavement design and analysis takes place through the development of an axi-symmetric solution. These models are based on making several assumptions as well as transforming a given problem into an axi-symmetric system, which simplifies and undermines the accuracy of output that is achieved. CIRCLY is an example of a software package that evaluates pavement parameters through the utilisation of axisymmetric solutions. In making these mathematical simplifications, models become restricted to axi-symmetric systems, stationary loads (i.e. a moving coordinate system is not considered), and static cases as the effects due to inertia are ignored. To eliminate these constraints, this paper aims to develop an alternative analytical approach which can be used to efficiently and accurately determine pavement responses under stationary and moving loads. The governing equation that forms the basis of the model is Cauchy’s theorem for examining the deformation characteristics of a pavement structure. Several substitutions and simplifications have been made in order to incorporate a moving coordinate system and to transform Cauchy’s theorem to a relationship that is entirely based on displacements. This will then allow for the calculation of associated stresses and strains. The relationship developed is solved through the utilisation of Fourier transformations and complex numbers, which is the main focus of this paper. Based on the derivations and associated formulations, a program has been developed which can be used to calculate solutions for flexible pavements under variable loading conditions. Several case studies have been carried out and the output analysed. It was concluded that, the method is able to address the assumptions made in conventional analytical models. Additionally, the program is capable of accurately carrying out calculations at substantially reduced computational effort, a main restriction that is encountered with numerical approaches.