the density of the filled material could not be neglected compared with the rock density, the initial mass of the filled joint could affect wave propagation [20]. Therefore, it is crucial to investigate the seismic response of the joints filled with a viscoelastic medium.  
Many analytical models were proposed to characterize the seismic response of the filled joints. [PERSON]. [24] applied the displacement discontinuity model (DDM) to study wave propagation through a filled rock joint. The model assumed that the stress was continuous, but the displacement was not when the stress wave impinged on the filled joint which was controlled by the fracture compliance [25]. Based on the DDM, [26] proposed a three-phase medium model for the filled rock joint considering the interaction of the three-phase system consisting of gas, liquid and granular solid. [PERSON]. [20] proposed a displacement and stress discontinuity model (DSDM) to study wave propagation through filled joints considering the initial mass effect of the filled material. This model assumes that not only the displacement but also the stress is discontinuous in the front and rear interface of the filled joint. However, the above studies mainly have two limitations: (1) Wave reflection in the filled layer was neglected when it needs to be considered as the ratio of filled thickness to the wavelength is relatively large; (2) There are many parameters in these analytical models which are difficult to determine by laboratory tests, such as the viscosity and stiffness of the filled joint. To overcome these problems, a simple and feasible way is to model the filled joint as a layer of independent continuum solid medium. Properties of the filled joint are controlled by those of the filled medium such as the density, filled thickness (aperture), wave velocity and quality factor (Q) that can be readily determined. Furthermore, multiple reflections in the filled layer can be taken into account. It was found that a joint or an interface between two solids can be represented as a thin-layer interface [27]. Ref. [28] pointed out that a thin-layer interface or a zero-thickness interface for a joint should be essentially the same from the physical point of view. The thin-layer medium model (TLMM) was also proved to be reasonable and feasible to characterize stress wave propagation through filled joints in previous studies [29]. They found that predicted results of stress wave propagation through joints by the purely elastic TLMM are nearly the same as the zero-thickness interface model if the ratio of the wavelength to the filled thickness is large enough. [PERSON] et al. in 2012 [30] investigated the propagation of the stress waves normally impinging on a single rock joint filled with a viscoelastic medium. By modeling the interface between two solids as a thin viscoelastic layer with stiffness and inertia term, wave propagation through a single filled joint was addressed by [31]. However, thus far, analytical models based on the TLMM were rarely reported to investigate seismic response of viscoelastic filled joints as the water content of the filling varied.  
The purpose of this paper is to establish an analytical model on the seismic response of the rock joints filled with a viscoelastic medium, considering the water content, the filled thickness (aperture), viscosity of the filled material (quality factor), the joint spacing (related to joint density) as well as the incident angle and frequency of the incident wave.