# Application of Finite Layer Method in Pavement Structural Analysis
## 1 Introduction  
The analysis of stress states is of considerable importance for the design, construction, maintenance, and rehabilitation of asphalt pavements in practice. In the past several decades, a lot of computer software has been developed and is increasingly used routinely in pavement design and assessment processes. In Germany, the guidelines for the analytical design of asphalt pavement superstructures RDO Asphalt 09 [1] propose the use of layer elastic theory (LET), e.g., the program BISAR, (Shell global, The Hague, The Netherlands) as the kernel of its pavement response model to calculate stresses, strains and displacements for different temperatures at critical locations within the pavement structure. Due to its simplicity, the LET has been utilized by pavement engineers for several decades. Currently, LET has been expanded to handle some problems with the material properties of viscoelasticity andnonlinearity as well as non-uniform loads [2]. However, the features of the software application based on the LET are still limited. For example, in BISAR, each layer is assumed homogeneous, isotropic, and linear elastic; all materials are weightless (no inertial effects are considered); all layers are assumed to be infinite in lateral extent and have a finite thickness except for the sub-grade, which is assumed to be infinite; the pavement systems are loaded statically over a uniform circular area; the compatibility of strains and stresses is assumed to be satisfied at all layer interfaces [3; 4]. However, the reality of asphalt pavements may be very different to the assumptions made in the BISAR, e.g., finite geometrical scale in lateral extent, non-uniform loading conditions, and inelastic material properties. These differences may result in significant deviations between the calculated and the real responses of asphalt pavements. With the finite element method (FEM), which is a numerical analysis technique proposed for obtaining approximate solutions for a wide variety of engineering problems, these specific requirements can be met and the asphalt pavement responses can be predicted more realistically. Some representative software applications have been widely used in pavement engineering, such as CAPA-3D (Delft University of Technology, Delft, The Netherlands) and APADS 2D (Austroads, Sydney, Australia). The development history of CAPA-3D goes back to the late 1980s. Currently, CAPA-3D is a linear/nonlinear, static/dynamic finite element (FE) system for the solution of very large scale three-dimensional (3D) solid models such as those typically encountered in pavement and soil engineering. It includes several constitutive material models, e.g., linear elasticity, hyperelasticity, elastoplasticity and viscoelasticity. As such, it can simulate a very broad range of engineering materials under various loading conditions [5]. Unfortunately, due to its 3D characteristics, the high hardware demands and long execution times render it suitable, primarily for research purposes [6]. APADS 2D was developed from 2008, in the scope of the Austroads project Developments of Pavement Design Models. It applies a two-dimensional (2D) axisymmetric concept to reduce the computational time and considers the effect of multiple loads through superposition. Due to the inherent limitations of axisymmetric models, it is difficult to simulate a pavement model with a determined geometry and complex loading conditions [7]. Other general-purpose FE software, such as ABAQUS (SIMULIA, Johnston, RI, USA) and ANSYS (ANSYS, Canonsburg, PA, USA), may provide more powerful capabilities to simulate the response of asphalt pavements to a certain extent. However, the expensive costs to get valid licenses and the time-consuming training process often render it impractical to be used by a road engineer. One proposed method to overcome the aforementioned difficulties assumes that the displacements in one geometrical direction can be represented using Fourier series.