## 1 Introduction  
A large number of large-scale projects, such as bridges and dams, are built in sedimentary valleys. The amplification effect of ground motion in river valley sites has been confirmed by many earthquake damage observations and theoretical studies ([PERSON], [PERSON] et al. [1], [PERSON], [PERSON] et al. [2], [PERSON], [PERSON] et al. [3]). The existing ground motion simulation methods of sediment valleys can be divided into numerical methods and analytical methods. The analytical methods mainly refer to the wave function expansion method ([PERSON], [PERSON] [4, 5], [PERSON], [PERSON] et al. [6], [PERSON], [PERSON] et al. [7] etc.). The numerical methods include the finite element method ([PERSON], [PERSON] et al. [8], [PERSON], [PERSON] et al. [9], etc. ), the finite difference method ([PERSON], [PERSON] et al. [10], etc. ), the boundary element method ([PERSON], [PERSON] et al. [11], [PERSON], [PERSON] et al. [12], [PERSON], [PERSON] et al. [13], etc. ), finite element-boundary element coupling method ([PERSON], [PERSON] et al. [14], etc.) and so on. In order to simplify the calculation, the research models mainly focus on geometric models in ideal uniform elastic space ([PERSON], [PERSON] et al. [15], [PERSON], [PERSON] et al. [16], [PERSON], [PERSON] et al. [17]). However, in fact, soil is not a single-phase ideal elastic medium. Saturated soft soil exists widely in coastal and river valley areas. The propagation characteristics of seismic waves in saturated porous elastic media are quite different from those in elastic media models. For coastal valleys, it is more reasonable to study a saturated soil model. [PERSON] (1964, 1965) established the dynamic equation of a saturated two-phase medium, which laid the theoretical foundation for saturated soft soil. [PERSON], [PERSON] et al. [PERSON] _et al._ (2018) simplified and modified the basic model of [PERSON] to a simpler practical model. [PERSON], [PERSON] et al. [PERSON] _et al._ (2018) extended [PERSON]'s theory to layered saturated sites by dynamic stiffness matrix. [PERSON] et al. [PERSON] _et al._ (2018) studied the reflection and propagation of plane waves in different fluid-saturated porous half-spaces. [PERSON] et al. [PERSON] _et al._ (2018) studied torsional surface waves in fluid-saturated porous half-spaces under heterogeneous layers. [PERSON], [PERSON] et al. [PERSON] _et al._ (2018) studied the reflection and propagation of elastic waves on the non-ideal interface between a micropolar elastic solid half-space and a fluid-saturated porous solid half-space. In recent years, the simulation of saturated sites has developed in the direction of complex site, in combination with seismic resistance of underground engineering, and so on. [PERSON], [PERSON] et al. [PERSON] _et al._ (2018); [PERSON] _et al._ (2018); [PERSON] _et al._ (2018), [PERSON], [PERSON] et al. [PERSON] _et al._ (2018), [PERSON], [PERSON] et al. [PERSON] _et al._ (2018), and others have provided the analytical solutions of P wave and SV wave scattering by various underground structures in saturated half-spaces by using the wave function expansion method, finite element method, and indirect boundary element method (IBEM), respectively. [PERSON], [PERSON] et al. [PERSON] _et al._ (2018); [PERSON] _et al._ (2018); [PERSON] _et al._ (2018) studied the response and behavior of dry sand and saturated sand by experiment. [PERSON], [PERSON] et al. [PERSON] _et al._ (2018) studied the mechanism of compression wave propagation in saturated soil by hydrodynamics coupling analysis and numerical method. It is worth pointing out that most of the current studies are based on the certain saturated site seismic response studies, and there are few studies on uncertain sites. Furthermore, in view of the difficulty of the accurate determination of the geotechnical parameters and the uncertainty of the actual site characteristics (site shape, geotechnical parameters, anisotropy ([PERSON], [PERSON] _et al._ (2018)), etc. ), the research on the randomness of the site develops accordingly.