# Scattering of Plane Waves by Cylindrical Cavity in Unsaturated Poroelastic Medium +
## 4 Conclusions  
In this research, the scattering of plane waves (P and SV waves) by a cylindrical cavity with a permeable surface in an unsaturated poroelastic medium was solved based on Ref. [17]. The results can be used to calculate the dynamic stress concentration factor around the cavity. The influences of saturation, porosity, and Poisson's ratio on the dynamic stress concentration factor around the cavity under different incident frequencies and boundary conditions were studied in detail. The main conclusions are as follows,  
The distributions of the hoop stress around the surface of the cavity change with saturation. The responses of the stress around the cavity for \(S_{\rm r}=1.0\) are significantly different from that for \(S_{\rm r}<1.0\). When \(S_{\rm r}<1.0\), saturation has little effect on the distribution  
Figure 5: Effects of porosities on distributions of \(\sigma_{\theta\theta}^{S}/\sigma_{0}\) around the surface of the cavity for P\({}_{1}\) wave incidence for \(S_{\rm r}=0.6\). (**a**) \(k_{0}a\)\(=0.5\). (**b**) \(k_{0}a\)\(=1.0\). (**c**) \(k_{0}a\)\(=2.0\).  
Figure 6: Effects of porosities on distributions of \(\sigma_{\theta\theta}^{S}/\sigma_{0}\) around the surface of the cavity for P\({}_{1}\) wave incidence for \(S_{\rm r}=1.0\). (\(k_{0}\) is the wave number of the incident P1 wave). (**a**) \(k_{0}a\)\(=0.5\). (**b**) \(k_{0}a\)\(=1.0\). (**c**) \(k_{0}a\)\(=2.0\).  
of stress. For the same saturation, the frequency of the incident wave will change the angle at which the maximum value occurs.  
For \(S_{\rm r}\) = 1.0, the dynamic stress concentration factor of an impermeable cavity is slightly larger than that of a permeable cavity. For \(S_{\rm r}\) < 1.0, the responses have no obvious differences between the permeable and impermeable cavities.  
The distribution of stress around the cavity varies with Poisson's ratio. With the increase in Poisson's ratio, the dynamic stress concentration factor around the cavity increases gradually, and the angle at which the maximum value occurs gradually approaches the direction of the incident wave direction.  
The porosity does not affect the dynamic stress concentration factor around the cavity for an unsaturated medium. However, it has great influences on the hoop stress distribution around the cavity for \(S_{\rm r}\) = 1.0. That is mainly because the ratio of the P\({}_{1}\) wave velocity to the S wave velocity varies greatly with the porosity of the saturated poroelastic medium.  
Conceptualization, W.L.; methodology, W.L. and F.F.; software, Z.Y. and F.F.; validation, F.F.; formal analysis, W.L.; investigation, W.L.; resources, W.L.; data curation, W.L. and Z.Y.; writing--original draft preparation, Z.Y. and A.Z.; writing--review and editing, W.L.; visualization, W.L. and Z.Y.; supervision, W.L.; project administration, W.L.; funding acquisition, W.L. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the Fundamental Research Funds for the Central Universities (Grant No. 2022 JBZY010) and the National Natural Science Foundation of China (Grant No. 52078033).  
Not applicable.  
The data used in this study are available from the corresponding author upon reasonable request.  
The authors declare no conflict of interest.  
The expressions of coefficients \(S_{\rm j}\), \(W_{\rm j}\), \(X_{\rm j}\), and \(Y_{\rm j}\) in Equations (32) and (33) are as follows: (For P\({}_{1}\)