| The study on the propagation law of train vibration in rock-soil semi-infinite media is of great significance to determine the vibration limit of various buildings and optimize the vibration damping technology,so as to ensure the stability of the structures on the ground,twin-parallel tunnels and surrounding soils.Compared with the finite element method,the boundary element method has a unique advantage in dealing with semi-infinite problems.It does not require artificial boundaries and can obtain higher accuracy.In order to simulate the propagation process of subway vibration waves in semi-infinite rock and soil with high precision,time domain boundary element formulation for the elastoplastic dynamic plane problem with doubly connected domains in a semi-infinite medium is developed.In this paper,the establishment,numerical treatment and solving process of time domain boundary integral equations for the elastoplastic dynamic plane problem with doubly connected domains in a semi-infinite medium are given in detail.In the process of establishing time domain boundary integral equations,some virtual boundaries are constructed between finite boundaries and the free boundary to form a boundary to refer to the theory of developing time domain boundary integral equations for the single connected domain problem in infinite media.The suspicious plastic region appearing in the boundary integral equations is formed by plastic element generation algorithm,which narrows precisely the calculation range.Infinite boundary elements are introduced to simulate the infinity of free boundaries during spatial discretization for semi-infinite domain problems.For the singular integrals,a pure analytical method is adopted to calculate both time and space integrals.For non-singular integrals,the semianalytical and semi-numerical solution method is used.For the time integrals,the finite integral method is used,and solve spatial integrals with Gauss numerical integration.In order to deal with geotechnical engineering problems,constitutive relationship based on the Drucker-Prager criterion(D-P yield criterion)is introduced into the time domain boundary element method system.According to the solution strategy of time domain boundary integral equations for elastoplastic dynamic plane problems,the corresponding MATLAB computing program is written.The validity of the time domain boundary element formulation and MATLAB codes by the time domain boundary element method are verified by two deliberately designed examples.By analyzing the influence of different spacing and burial depth on the calculation results,the rationality of the TD-BEM formulation is also verified. |
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