关键词: 地下结构抗震分析, 简谐振动, 动力响应, 分离变量法, 解析解

Abstract: Starting from the calculation model of the two-dimensional soil-cantilever rigid wall under horizontal simple harmonic resonance action, and based on the theory of wave mechanics, the dynamic response characteristics of two-dimensional soil-cantilever rigid wall were studied considering the vertical stress and vertical displacement of soil layer. Firstly, the vibration equation of the soil layer was transformed to obtain the equation of the volumetric strain ? , which was solved by the method of separation of variables. Then, the inhomogeneous equation of the displacement motion equation was obtained by substituting the solution back to the vibration equation. The definite solution of the vibration equation was obtained by combining the interaction conditions between the wall and the soil layer as well as the far-field boundary conditions. Then more strict analytical solutions of the earth pressure on the wall, the shear force at the bottom of the wall and the bending moment of the rigid underground wall were obtained. Compared with the vertical stress-neglected solution and the vertical displacement-neglected solution, it is shown that the obtained solution can reflect one more resonance frequency, and when the Poisson’s ratio of soil is greater than 0.45, the vertical displacement-neglected solution is meaningless. Through parameter analysis, it is shown that the excitation frequency and soil damping factor have great influence on the dynamic response of the wall, whereas the vibration mode order considered has less impact.

Key words: seismic analysis of underground structures, simple harmonic vibration, dynamic response, method of separation of variables, analytical solution