## 1 Introduction  
Coarse-grained soil (CGS) consists of a pebble (with high elastic modulus) and sand-clay matrix (with rheological properties) surrounding the pebble and pore [1; 2; 3]. It is easily available in nature and thus widely applied in the subgrade, bridge foundation, and structure foundation engineering [4]. For improving the bearing capacity of the foundation, the CGS of different gradations needs to be artificially filled [5; 6; 7; 8]. The slipping and embedding of different gradations CGS particles would lead to a certain height of interface-layer, i.e., the formation of multi-layered CGS [9; 10; 11]. Under long-term loading, the multi-layered CGS may cause uneven settlement due to its rheology properties (depending on its microscopic components and structure) and there exists a potential safety hazard for the foundation engineering [12]. Therefore, it is very important to determine the macroscopic rheological parameters of multi-layered CGS with consideration of the interface-layer for predicting its long-term deformation. Currently, the macroscopic rheological parameters of materials are mainly studied by two theoretical methods: periodic cell method and homogenization method. Since the periodic cell method needs a representative volume unit of a periodic array, it is only used for most metallic alloy materials [13], ceramic material [14], and a few nonmetallic materials with periodic microstructures (e.g., concrete [15]). The homogenization method is widely applied for the geotechnical materialsof a few periodic microstructures, with different solution methods. For example, [PERSON] et al. [16] and [PERSON] et al. [17] calculated equivalent elastic moduli of the concrete and the sandy soil by hollow sphere model and three-phase sphere method, respectively. [PERSON] [18] and [PERSON] et al. [19] predicted equivalent viscoelastic parameters of the asphalt and the saturated frozen soils by Mori-Tanaka equivalent method and improved Hashin model combined with the elastic-viscoelastic corresponding principle. For the one-layered CGS, some solution methods, Hashin model method ([PERSON] and [PERSON] [20]), Mori-Tanaka equivalent method (by [PERSON] et al. [21]), two-phase model method (by [PERSON] [22]), and numerical simulation method based on homogenization method (by [PERSON] et al. [23], [PERSON] et al. [24], [PERSON] et al. [25]) were adopted to predict its elastic parameters. Its viscoelastic parameters could be also obtained by the elastic-viscoelastic corresponding principle. It is worth to note that in all of these homogenization methods, the inclusion (large pebble particles) were simplified to be an ideal sphere or ellipsoid particles, which is obviously inconsistent with the actual irregular shape of the inclusion (polyhedron). Besides, for the multi-layered materials, most works of literature were focused on laminate composites for predicting the elastic parameters [26; 27] and rheological parameters [28] by the homogenization method, regardless of the interface-layers. Very few studies are available on theoretically studying the viscoelastic parameters of the multi-layered CGS. In addition, triaxial compression test was also used to determine macroscopic elastic parameters of the one-layered CGS. Effects of different factors, content [29; 30; 31], and sizes [32; 33] of the coarse pebble, content of the fine particles [34] on its elastic parameters were measured and analyzed by the statistic method and the estimation method, respectively. [PERSON] et al. [35] adopted the triaxial creep test to measure the viscoelastic parameters of the one-layered CGS varying with the clay content. However, the multi-layered CGS is less studied experimentally. This paper aims to propose a new method for predicting the viscoelastic parameters of multi-layered CGS with consideration of interface-layer and actual pebble inclusion shape. Firstly, the calculation model of one-layered CGS and multi-layered CGS with interface-layers were established by the homogenization method.