SH Wave Scattering In Elastic Half Space By Lining Structures With Inhomogeneous And Anisotropy Medium

With the developing of science technology,varies kinds of new material are applied in practical engineering.Many artificial materials can adopt to complex condition due to some unique mechanical and physicochemical properties.Moreover,with the enrichment and perfection of infrastructure,a large number of underground tunnels and pipelines appears in cities and villages in order to satisfy the equirement of people.Due to reinforced concrete and artificial material are widely used in constructing underground pipelines and tunnels,research on dynamic response of lining structures made by complex materials under elastic waves can provide worthy references for practrical engineering.Considering the complexity of the mechanical property,governing equations of SH wave propagation in anisotropic medium,inhomogeneous medium and inhomogeneous and anisotropic medium are constructed.Then,methodologies are provided in solving the governing equations analytically.Referring to the actual engineering application,the research content of this paper is divided into three parts:(1)Analytical solution of SH wave scattering by a single inhomogeneous anisotropic lining in half space.Let the half space be a homogeneous and isotropic linear elastic medium,while the lining medium is inhomogeneous and orthotropic.The density and shear modulus of the medium are described by functions.The shear elastic modulus is orthotropic along the radial and circumferential directions of the lining.According to the function form of medium density and shear modulus of inhomogeneous lining,the corresponding control equation of out plane wave propagation is established.The control equation is separated into the form of multiplying the radial coordinate term and the circumferential coordinate term by the method of separating variables,and then the separated differential equation is solved.The analytical expression of the wave field in the lining is obtained by integrating the separated solutions.The dynamic stress concentration around the lining and the influence of a single lining on the amplitude of surface displacement are analyzed through calculation cases.(2)Dynamic response of inhomogeneous anisotropic lining with cylindrical cavity under SH wave incidence.According to the actual conditions that underground tunnels and transportation pipelines are often buried together,a model of SH wave scattering by semiinfinite space lining and circular cavity is established.Based on the research content(1),the zero-stress condition of the cylindrical cavity boundary is added,and the influence of the scattered wave excited by the circular cavity on the boundary condition must be considered at the same time.In order to solve this problem,the transformation relationship between the local coordinate systems and the global coordinate system is established by using the complex variable function method.Through a series of parametric examples,the interaction between the lining and the circular cavity is studied,including the influence of the buried depth of the structures,the relative spatial coordinates between the two structures,and the incident wave parameters on the dynamic stress concentration factor at the boundary of the double structure and the displacement amplitude at the horizontal surface of the half space.(3)Dynamic response of multiple inhomogeneous anisotropic linings in half space under SH wave incidence.According to the actual conditions of several similar underground tunnels,a model of SH wave scattering by lining groups in semi-infinite space is established.Based on the analytical solution of SH wave scattering by a single inhomogeneous anisotropic lining,the general solution of SH wave scattering by any number of inhomogeneous anisotropic lining is derived.Through the image method and a series of multipole coordinate transformation,the expressions of displacement field and stress field are obtained.Taking the double inhomogeneous anisotropic lining as an example,the effects of model geometric parameters,medium parameters and incident wave parameters on SH wave scattering are analyzed.Finally,through the investigation of dynamic stress concentration factor and surface displacement with different parameters,it is shown that the distribution of dynamic stress concentration factor has a clear regularity when the density-decreased lining is embedded.Hence,the distribution of DSCF with different parameters can be forecast more easily,which is more applicative in practical engineering.