| The problem domain of two-phase saturated medium in soil dynamics includes explosive source problem, dynamic foundation problem, dynamic rigidity problem of piles, wave diffraction problem, rupture problem of faults, and such practical problems. Connected with examples of practical engineering, there are two solutions to solve the problems above, exactly numerical solution and analytic solution. Boundary Element Method as one of the numerical solutions, its Green function is an effective methods to solve fluctuation and soil-structure interaction. The application of Green function can reduce the problems' dimensions, and we only need to do the discrete treatment in boundary, it can greatly reduce the complexity of calculation. Proper Green function can simulate the layered medium exactly, especially for solving infinite domain and semi-infinite domain, and it also plays a significant role in analyzing the displacement and scattering of waves, and such relevant studies.The thesis outlines Biot's dynamic equations on two-phase saturated medium firstly, and based on these dynamic equations and the forerunners' studies, adopting proper Green function, taking several tunnels with normal section geometry as example, then work out any field point's displacement expression located in boundary of model. Therefore, the thesis introduces the analysis model of object-oriented for the problem domain of finite geometrical cavum in the problem domain of two-phase saturated medium in soil dynamics. Adopt the encapsulation idea of object-oriented to compose the model object with Green function and Lamb integral equation on two-phase saturated medium. Finally, under the help of my tutor, I successfully completed the derivation of Green function under the condition of drainage on two-phase saturated medium by our joint effort, also on basis of this, we figure out fluid phase pressure expression and solid phase displacement expression under the condition of drainage on two-phase saturated medium.
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