Research On Soil-Long Underground Structure Interaction Under The Action Of Seismic Shear Wave Traveling Along Axial Direction Of Structure

The influence of inertia force on interaction between underground structure and soil under action of seismic shear wave propagating along axial direction of long underground structure was theoretically analyzed based on elastic foundation beam model. Forced vibration motion equation and static equilibrium equation are developed based on Winkler foundation model, Pasternak foundation model and nonlinear local foundation model that considering influence of nonlinear factors in the analysis. To solve linear differential equation, analytical method is adopted: By applying mode superposition method and mode orthogonality we simplified partial differential equation into ordinary differential equation, the ordinary differential equation is solved analytically based on differential operator method. To solve nonlinear differential equation, numerical method is adopted: By using finite difference method in place of derivative and discretization we simplified nonlinear partial differential equation into nonlinear algebraic equations, the nonlinear algebraic equations are solved by mathematical software Matlab.Numerical examples are given and the results are compared and analysed. The author come to the following several main conclusions: 1) The influence of axial force N on relative difference D between dynamic and static results is small in most cases. 2) The analysis by using the aforementioned foundation models showed that the influence of inertial force is more significant when stiffness of foundation soil is weaker. 3) For linear foundation models when Pasternak foundation model is used, the relative difference D between dynamic and static results is larger, and influence of inertial force is not obvious when stiffness of foundation soil is moderate. 4) The introduced improved-stiffness ratio R’ can be used to assess the influence of inertial force well for linear foundation models. The influence is weakened with the increase of R’, and could be neglected when R’ is more than 2.5×10-7. 5) For local foundation models, the relative difference D between dynamic and static results for nonlinear foundation model is larger, and the influence of inertial force is not obvious when stiffness of foundation soil is greater than that of moderate rigid soil.