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1. Introduction A growing attention on highway development has raised many questions about the comfort of transportation and the economic maintenance of systems, which consist of vehicles, road construction proper and sub-soil. Rational design and maintenance procedures for road structures, such as pavement and subgrade, require elaborate predictive methods to assess the long-term performance of any particular kind of geotechnical structure. One of the major concerns is the ability to determine the dynamic stresses and deformations of the road structure induced by repeated traffic loading. The fairly complex phenomena involved in road structures can be analysed by analytic/numerical methods and experimental measurements. The history of the development of stresses and deformations due to traffic loads on road structures began with the use of analytic methods in the early 1950s (Sneddon [1] in 1952, Criner and Mccann [2] in 1953, Kenney [3] in 1954, Mathews [4] and [5] in 1958 and 1959, Cole and Huth [6] in 1958). In these studies, the road structure was simplified as elastic beams or plates supported on the Winkler-type foundation or elastic half-space. Clearly, these studies cannot offer sufficient information about the behaviour of each substructure because they did not precisely represent the structure of the road; however, the simple model solutions are still useful and important as a way to easily understand the nature of the problem and for serving as benchmarks when developing and testing numerical methods of the solution. In recent years, the increase in traffic and weight on the roadways has accentuated the imperfections of empirical methods to evaluate the road structure behaviour. In the methods that analyse the pavement under traffic, the road structure layers are assumed homogeneous and linearly elastic, and the load is often considered static. The use of the multi-layered elastic theory with a static load is a reasonable approach compared with the older empirical models. Therefore 更多：https://www.bmcx.com/ , a variety of specifications and corresponding mechanical analysis software for highway design have been developed based on the elastic multi-layered theory and static load hypothesis (China Technical Specifications for Design and Construction of Highway Embankment on Soft Ground [7], China Specifications for Design Highway Asphalt Pavement [8], Elsym5 [9], Bisar [10], Modulus [11]). However, a heterogeneous road structure exhibits a different behaviour from these ideal conditions and is subjected to dynamic and cyclic loadings. For this type of loading, studies have used the elastodynamic approach or dynamic finite element method, where the traffic loads are usually assumed to be stationary or moving time-harmonic loads. There are many kinds of analytical and numerical methods that can be used to calculate the stresses and the deformations of the layered road structure. For example, Kausel and Roesset [12] and Kausel and Peek [13] presented a simple technique based on layer stiffnesses to determine the displacements and stresses due to any dynamic loads on or within the layered elastic media. Chow et al. [14] applied the aforementioned methodology to predict the response of a layered elastic medium to a stationary strip footing subjected to a vertical or horizontal harmonic load. To consider a load in actual motion, De Barros and Luco [15] and [16] developed a semi-analytical model for a point load moving on a viscoelastic multi-layered half-space by determining the stiffness matrices and combining the stiffness matrices of each layer. This model is based on a double Fourier transform and shows the presence of Mach cones in the first layer at super-Rayleigh speeds. This method was then used by Gunaratine and Sanders in analysing a road [17] and by Auersh [18], Picoux et al.[19], Picoux and Houedec [20] for analysing track excitation. It has also been used by Jones and Petyt for rectangular loads or strip loads with different ground conditions: half space [21], elastic layers on a half space [22] or on a rigid foundation [23]. More recently, a number of semi-analytical tools have been developed by Lefeuve-Mesgouez and Mesgouez to study ground vibrations induced by dynamic loads on multilayered viscoelastic media [24] and [25] or poroviscoelastic media [26] and [27].