| The geological conditions are varied due to natural formation or artificial backfill,the development and construction of underground structures are changed rapidly.When the elastic wave propagation in solid media encountered the holes and other defects,which are embedded in continuous or intermittent geological conditions,elastic wave will be reflected,refracted and scattered.These elastic waves will generate reflection,refraction and scattering wave field.The wave field increased destructive dynamic force and ground surface displacement of the holes and other defects.They will be directly related to people’s lives and property,the mine tunnel of metro tunnel and other underground structures construction and the use of safety.Therefore,it is necessary to master the propagation law of elastic wave and underground structure dynamic effect on the elastic wave.However,the SH wave is a kind of elastic waves of out-of-plane motion.It provides a simple mechanical model and mature theory to solve many unknown boundary value problems.Therefore,the problem of SH wave scattering studied on the mechanics model in thesis,which are abstracted the model of vertical half space with an interface crack and a cylindrical cavity on the bi-material horizontal interface on engineering problems.The research contents of this paper are briefly summarized as follows:(1)The scattering problem of out-of-plane line source load is studied on right-angle plane with a semi-cylindrical cavity on the horizontal interface.It are necessary resort to "division" and "conjunction" technology in order to the scattering problem of SH wave in bi-material is solved using Helmholtz control equation,which the scope of its application be applied to a homogeneous isotropic medium.The first are the study of "division" for the two parts along two different medium interfaces respectively,and then the two parts "conjunction" into one based on the interface stress and displacement continuity conditions.However,it is the precondition of "conjunction" that the Green function solution of displacement field is solved,which the Green function on the horizontal boundary in quarter plane with a semi-cylindrical cavity on the interface.The analytical solution of the scattering problem is build using the "image method",it is used to construct a scattering wave of Green function.Finally,the numerical solutions of surface displacement amplitudes are give by the calculation method of direct discrete based on combined with the scattering wave attenuation and analytical solution.(2)The scattering problem of SH wave is studied on vertical half space with a cylindrical cavity on the bi-material horizontal interface.First of all,the half space is divided into two quarter plane along the bi-material horizontal interface.Secondly,the bi-material media model of "conjunction" is constructed by has obtained the Green function and the interface continuity conditions,which put together out of an upper and a lower rectangular domain space.The series of infinite algebraic equations for ascertain the sealed forces can be established through balance of stress and displacement continuous conditions on interface,it is the analytical solution of the scattering problem.Finally,the numerical solutions of dynamic stress distribution around the circular cavity whole edge are made by numerical calculation method.(3)The scattering problem of SH wave is investigated on vertical half space when a circular cavity and the crack on the bi-material horizontal interface.Firstly,one vertical half space is divided into two quarter plane along the bi-material horizontal interface by means of the crack-division technique and "division".Secondly,the bi-material media model is assembled with the aid of the Green function and the"conjunction" conditions on interface.Finally,the dynamic analytic solution and numerical solution at circular cavity whole edge and crack tips are researched using Helmholtz control equation and numerical calculation method. |
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