The Finite Element Method For Dynamic Analysis Of Foundation Under Moving Loads

The dynamic responses of ground subjected to moving loads have always been very important for engineers and academics. In recent years, the speed of railway vehicles has obtained great improvement, and new types of high-speed railway will be built in the near future, which will make vehicles faster. In many areas of southeast China, Rayleigh wave velocity of the earth surface is very small; therefore, high-speed trains are nowadays in the range of Rayleigh wave velocity. Low-speed vehicles will have little effect on strains and stresses when the speed is less than 0.4 times the surface wave velocity, whereas high-speed vehicles will cause greater stresses and strains than low-speed vehicles and cause damage to the nearby construction when the speed of vehicles reach more than 0.8 times as large as the surface wave velocity. Obviously, high-speed vehicles will have greater influence on their surrounding.The purpose of present work is to investigate the dynamic responses of foundation under moving and time-harmonic loads. The quasi-static Finite Element is established by making use of the weighted residual method and the dynamic problems are regarded as quasi-static. It is more practical to consider the influence of load frequency together with the layered ground on the dynamic responses, and it is found that there have few researches on this topic according to the author's understanding; Furthermore, this research work have great interest to engineering and theory. The main contents are as follows:1. Based on theory of fundamental equations of dynamic considerations, the quasi-static Finite Element is established by making use of the weighted residual method and the dynamic problem are regarded as 'quasi-static'. It is found that the principal diagonal component in stiffness matrices can be modified according to static stiffness matrices. Influences of moving velocity and vibration frequency on the dynamic responses of foundation are studied in the paper. The displacements and stresses are calculated by the quasi-static Finite Element Method. 2. Based on the general methods, with the consideration of boundary conditions, the final expression of displacements and stresses are established for layered ground.3. Influences of the moving velocity, vibration frequency and soil parameters on the stresses and displacements are studied, and some numerical solutions of the stresses and displacements are presented and compared with the corresponding analytical solutions, which prove the results are reliable. The results obtained reveal that the strains and stresses of foundation vary obviously with increasing the moving velocity; layered ground has the same calculated characteristic.