# Application of Finite Layer Method in Pavement Structural Analysis
## 1 Introduction
Exploiting its orthogonal properties, a problem of such a class can be simplified into a series of 2D solutions. This method is so called semi-analytical FEM and was first developed in linear analysis by [PERSON] [8]. The analysis was extended to an elasto-plastic body by [PERSON] [9] based on [PERSON]'s work. A visco-plastic formulation was used by [PERSON] and [PERSON] [10] to tackle material nonlinearity. To analyze the consolidation of elastic bodies subjected to non-symmetric loading, [PERSON] and [PERSON] [11] provided an effective solution by using the continuous Fourier series. [PERSON] and [PERSON] [12] successfully applied a discrete Fourier technique to analyze the stress state of solids with nonlinear behavior under 3D loading conditions. Further developments were made by [PERSON] [13] and [PERSON] et al. [14], who programed simple FE codes to apply the semi-analytical FEM for the analysis of asphalt pavements. Recently, an FE code named SAFEM with more features was developed by [PERSON] et al. [15; 16; 17; 18; 19]. Viscoelastic material property and dynamic analyses were integrated in this code. Here, the partial bonds between pavement layers can be considered and the infinite element was applied to reduce the influence of the boundary on the computational results. The finite layer method (FLM) is proposed as another alternative way for analyzing the structural response of pavements, whilst reducing the computational requirements without decreasing the computational accuracy. This method combines a one-dimensional (1D) FEM discretization in the pavement depth direction with Fourier series in the two horizontal directions, which can be considered as a further development of the semi-analytical FEM. The idea is particularly suitable for multilayered structures. Furthermore, due to the use of Fourier series in two directions, the computational cost of FLM is significantly lower than that of conventional FE analysis methods. The FLM started to be applied in the analysis of elastic, horizontally layered foundations from 1979 [20], when the basic theory and application were proposed. Thereafter, the approach was further developed for the analysis of nonhomogeneous soils whose modulus increases linearly with depth [21]. An exact finite layer flexibility matrix was introduced to overcome the difficulties when the conventional finite layer stiffness approach was applied to incompressible materials [22; 23]. Meanwhile, soil consolidation and surface deformation entailing the extraction of water was also investigated by using this approach [24; 25; 26]. In the next several years, researchers applied the FLM in groundwater flow models [27] and analyses of 3D Biot consolidation of layered transversely isotropic soils [28]. Recently, the FLM was applied for modeling the noise transmission through double walls [29]. analytical model, called 3D-Move uses a continuum-based FLM to compute pavement responses [30; 31]. The 3D-Move model can account for important pavement response factors such as moving loads, 3D contact stress distributions (normal and shear) of any shape, and viscoelastic material characterization for the pavement layers. Although the 3D-Move is freely available, it is not open source, and it still lacks some specific features such as the interlayer behavior for the pavement modeling. Therefore, a re-implementation of the FLM in code is necessary. As mentioned in the manual of 3D-Move, the accuracy of the calculated results is not guaranteed. Therefore, an algorithm or a technique that can provide more accurate results is of significant importance. In recent years, the research on super-convergence has increasingly drawn attention since it can provide higher order accuracy. A number of research studies have been conducted on this subject [32; 33]. In recent years, a super-convergence technique named Element Energy Projection (EEP) method was proposed by [PERSON] et al. [34; 35; 36].