Numerical study on the seismic response of the underground subway station-surrounding soil mass-ground adjacent building system

Ground buildings constructed above metro station have increased very quickly due to the limited land resources in urban areas. In this paper, the seismic response of the Underground subway station-Surrounding soil mass- Ground adjacent buildings （USG） system subjected to various seismic loading is studied through numerical analysis. The numerical model is established in terms of the calculation domain, boundary condition, and contact property between soil and structure based on the real project. The reciprocal influence between subway station and ground adjacent building, and their effects on the dynamic characteristics of surrounding soil mass are also investigated. Through the numerical study, it is found that the impact of underground structure on the dynamic characteristics of the surrounding soil mass depends on its own dimension, and the presence of underground structure has certain impact on the seismic response of ground adjacent building. Due to the presence of underground structure and ground adjacent building, the vertical acceleration generated by the USG system cannot be ignored. The outcomes of this study can provide references for seismic design of structures in the USG system.

Closed-form solution of beam on Pasternak foundation under inclined dynamic load

The dynamic response of an infinite Euler–Bernoulli beam resting on Pasternak foundation under inclined harmonic line loads is developed in this study in a closed-form solution.The conventional Pasternak foundation is modeled by two parameters wherein the second parameter can account for the actual shearing effect of soils in the vertical direction.Thus,it is more realistic than the Winkler model,which only represents compressive soil resistance.However,the Pasternak model does not consider the tangential interaction between the bottom of the beam and the foundation;hence,the beam under inclined loads cannot be considered in the model.In this study,a series of horizontal springs is diverted to the face between the bottom of the beam and the foundation to address the limitation of the Pasternak model,which tends to disregard the tangential interaction between the beam and the foundation.The horizontal spring reaction is assumed to be proportional to the relative tangential displacement.The governing equation can be deduced by theory of elasticity and Newton’s laws,combined with the linearly elastic constitutive relation and the geometric equation of the beam body under small deformation condition.Double Fourier transformation is used to simplify the geometric equation into an algebraic equation,thereby conveniently obtaining the analytical solution in the frequency domain for the dynamic response of the beam.Double Fourier inverse transform and residue theorem are also adopted to derive the closed-form solution.The proposed solution is verified by comparing the degraded solution with the known results and comparing the analytical results with numerical results using ANSYS.Numerical computations of distinct cases are provided to investigate the effects of the angle of incidence and shear stiffness on the dynamic response of the beam.Results are realistic and can be used as reference for future engineering designs.