A quantificational calculation method of participating mass of foundation vertical vibration is presented in this paper. Vertical subsoil participating mass of strip and rectangular foundation are preliminarily calculated based on Boussinesq’s solution of subsoil additional stress and equivalent-load method. That is, the subsoil participating mass can be calculated only prescribing the isoline of additional stress. The method is suitable for adopting by corresponding codes for it avoids considering complicated influencing factors of subsoil.

The paper analyzes that hoop coefficients of the concrete-filled steel tube influence on dynamic response of the railway bridge height limit protective frame under impact load by using ANSYS/LS-DYNA. Change hoop coefficient of the concrete-filled steel tube structure by changing steel tube wall thickness. The result shows that with increase of steel tube wall thickness, the average impact force of protective frame will increase and the displacement and deformation will reduce, and protective frame can resist greater impact load. It will provide the reference for design of railway bridge height limit protective frame.

The purpose of high-limit protection rack under railway bridge is to protect railway bridge, and avoid passing vehicles under railway bridge colliding bridge. The paper discusses dynamic response and energy transfer of two different structures by analyzing the internal force, deformation, displacement and energy transfer of the steel tube and concrete-filled steel tube protection racks in collision. The result shows that the displacement of concrete-filled steel tube protection rack is smaller, and it can bear larger impact force and have good effect of energy absorption.

In order to simplify the nonlinear analysis of reinforced concrete, a new study on concrete strength criterion under tension condition is made, and more simple and accurate practical calculation equations are put forward. The results from the equations agree well with the experimental data.

Based on the theory of elastic wave in saturated soils, the vertical vibration of a rigid circular footing resting on saturated sands is studied to obtain its analytical solution of dynamic compliance coefficients. Considering the role of water in the soil, the mass-spring-damping model of saturated sands is proposed to realize a practical way for engineering. And the stiffness and damping coefficients of model are calculated by reciprocity law equation. Compared with the solution of elastic half-space with the same Poisson’s ratio, the coefficients of the saturated sands are quite large. To comply with engineering practice, the approximate formula should be modified with multiplying them by factor in the Code for Dynamic Machine Foundation Design.