# Scattering of Plane Waves by Cylindrical Cavity in Unsaturated Poroelastic Medium +
## 1 Introduction  
Nowadays, many underground structures such as subways, water-conveyance tunnels, mineral prospecting, and military facilities have been constructed all around the world. In earthquake events, seismic action may cause great damage to underground structures. The existence of underground cavities will cause wave scattering and stress concentration around the cavities, so as to change the seismic response of underground structures. Therefore, theoretical studies on the scattering of seismic waves by a cavity or tunnel are not only meaningful in revealing the induced amplification of and reduction in earthquake motion but are also helpful in guiding its anti-seismic design in a qualitative way. In previous studies, scholars have carried out detailed research on the dynamic response characteristics of the soil around underground cavities. Initially, when considering the fluctuation of an elastic medium, the soil is usually simplified as a pure elastic medium without considering the influence of pores in the soil. For example, [PERSON] and [PERSON] [1] studied the dynamic response of a lined tunnel embedded in an infinite elastic medium, subjected to an incident wave; [PERSON] with his cooperators [2; 3; 4] carried out a series of works to investigate the scattering of the P-wave, SH-wave, and SV-wave by a cavity or a circular tunnel in a half-space. For some water-rich grounds, underground structures are usually contained in a porous medium, which is filled with fluids in the pores. The presence of the fluids will significantly affect the mechanical behavior of the tunnels. To illustrate the influence of the fluids, on the basis of [PERSON]'s model [5], [PERSON] et al. [6] investigated the wave scattering by a circular cavity in a saturated porous medium by using the boundary layer approximation. [PERSON] et al. [7] studied the wave propagation of a plane harmonic wavedisturbed by a fluid-filled cylindrical cavity in a saturated porous medium. [PERSON] and [PERSON] [8] proposed a method to analyze the dynamic response of cylindrical tunnels within the soft ground. The mechanical responses of lined and non-lined tunnels under a harmonic wave were investigated by [PERSON] et al. [9]. [PERSON] and [PERSON] [10] solved the problem of plane wave scattering from cylindrical cavities in the saturated poroelastic half-space using the wave function expansion method. [PERSON] et al. [11] solve the two-dimensional scattering of plane waves by a lined cylindrical cavity in the poroelastic half-plane approximating the half-plane surface as a convex circular surface. [PERSON] et al. [12] investigated the wave scattering by a shallowly buried lining in a poroelastic half-space considering the non-local effect. As can be seen in Ref. [13], the research on the scattering of seismic waves by underground caverns in saturated media is well understood. However, in reality, unsaturated poroelastic media are encountered in many areas. In general cases, two types of fluids coexist within the porous space: either two liquids, such as oil and water in oil fields, or a gas and a liquid, such as air and water in unsaturated soil geomaterials. Therefore, studying the dynamic responses in unsaturated porous media is of considerable interest. As summarized by [PERSON] et al. [14], numerous unsaturated poroelasticity models have been established, and the dynamic behaviors of unsaturated porous media have been studied. According to these studies, the dynamic response of an unsaturated medium is significantly different from that of a traditional saturated porous medium in many respects owing to the existence of the gas phase. However, to date, there have several reports on the dynamic responses of underground cavities in unsaturated poroelastic media. [PERSON] et al. [15] considered the transient responses of pressurized cylindrical unlined and lined cavities in an infinite unsaturated poroelastic medium for the first time.