Scattering Of Incident Plane Waves By Underground Cylindrical Cavity In Unsaturated Poroelastic Medium

With the optimization of engineering technology and the acceleration of urbanization,underground space is being developed and utilized as a resource.When an earthquake occurs,it will cause great damages to underground structures such as tunnels and pipelines in underground space.In the past studies,the soil was regarded as saturated two-phase medium,but most of the soil is unsaturated in practical engineering.At present,the study of the dynamic characteristics of unsaturated porous media is still in its infancy.Therefore,it is particularly important to study the dynamic characteristics of cavity in unsaturated media,which is similar to the actual situation of cylindrical underground structures such as tunnels are encountered with seismic wave.Based on the dynamic theory of unsaturated porous media considering the mixture theory,the analytical solutions of displacement and stress around cylindrical cavity and lined cavity under plane wave incidence are developed in this paper.The main contents are as follows:(1)Starting from the dynamic equation of unsaturated porous media,the analytical solutions of P-wave and SV-wave scattering by cylindrical cavity in cylindrical coordinate system are obtained by using wave function expansion method and variable separation method,and the boundary conditions of impermeability.The validity of the solutions is verified by comparing with the existing literature by degenerating the solutions to saturated state.(2)When the problem of scattering P and SV waves by a lined cylindrical cavity is studied,the lining is regarded as an elastic single-phase medium.Based on the dynamic equations of unsaturated medium and elastic single-phase medium,the analytical solutions of P-wave and SV-wave scattering by a lined cylindrical cavity are obtained by using the wave function expansion method and the separation of variables method,the continuous deformation boundary conditions of unsaturated medium and lining medium.The correctness of the solution are verified by comparing with those in the previous section of cavity.(3)The effect of saturation,shear modulus,porosity and lining thickness on the dynamic stress concentration factor around the cavity is analyzed by an example.The following conclusions are drawn:Saturation has a great influence on displacement and stress around the cavity,and the influence of saturation can’t be ignored.Previous methods of studying dynamic characteristics of soil by using saturated two-phase medium dynamic model are defective.There is a variable relationship between Poisson ratio and shear modulus and bulk modulus.In this paper,the bulk modulus varies with Poisson ratio while the shear modulus remains unchanged,which will affect the displacement and stress around the cavity.But compared with other parameters,Poisson ratio has less influence.The change of porosity will affect the stiffness of soil solid skeleton,which will have a greater impact on the displacement and stress around the cavity.The existence of lining will change the distribution of wave field in unsaturated porous media.Different lining thickness has different influence on wave field.The change of lining thickness has a great influence on the displacement and stress around the tunnel.