Numerical Simulation Of Earthquake Wave And Stability Of Calculation

In this paper, explicit finite element-finite difference method is studied systematically, including theoretical analysis, algorithm improvement, and practical application. The effect of the numerical simulation method on wave propagation and the calculation stability of the method combination of local artificial boundary conditions are studied quantitatively through theoretical derivation. Improvements about simulating source problems and scattering problems are presented, and these approaches are approved by the numerical simulation. A finite element and explicit finite element-finite difference method coupled method is presented, and using this method to simulate process of vibrator working. In the earthquake using the data obtained, the site effect is analyzed with the Wenchuan earthquake data. Main tasks are as follows:1. Based on the recursion formula of the integration method which can be used to solve dynamic equation of structural system, the transfer function of wave is presented. For one-dimensional uniform discrete model, the transfer function of numerical wave is put forward and numerical experiments are provided to demonstrate the correctness of the result. The effect of the explicit integration formula on cut-off frequency, frequency dispersion and numerical dissipation of wave propagation in finite element meshes is studied. The present paper aims to provide academic reference for the explicit integration formula application in infinite domain wave problem.2.Considering the numerical simulation of wave with explicit finite element-finite deference method and Local Transmitting boundary, the circulation coefficient is derived and calculated, the stability condition of numerical simulation is presented and tested by the numerical experiment; Based on the circulation coefficient, the effect of the explicit integration depressing and eliminating the high-frequency induced by local transmitting boundary is studied quantitatively; And how to use this effect to calculate steadily is discussed, that is how to take the time-discrete step and size of the space model values to ensure stability of calculation and decrease calculation amount to the full.3. In this chapter, improvements about simulating source problems and scattering problems using explicit finite element-finite difference method combined Local Transmitting boundary are presented respectively. For wave source problems,the artificial wave velocity is suggested to be different value, which can be calculated through correlation processing of data. Numerical experiments show that solving wave source problems with this approach can improve numerical accuracy without increasing the risk of calculation instability. For wave scattering problems, a improvement about wave inputting is presented, that is incident wave in the wave field separating use the discrete numerical solution instead of using the analytical solution, numerical experiments approve the measure can eliminate the drift instability.4. This chapter gives an explicit finite element and finite element-finite difference method coupling method. The calculation model is divided into two regions, the general structure and the surrounding area is simulated with finite element method, and the other part of the soil using explicit finite element finite difference method, the data of the two region communicate in the overlap region, This method is approved by numerical experiments representing the wave source problem and the scattering problem. Proposed coupling method used for establishing numerical model to simulate the vibrator working process, the effect of various factors, including soil density and stiffness, surface layer thickness, soft, hard interlayer, and the radius of the bottom plate of the vibrator on energy is studied, providing references for how to input energy to earth.5. Based on the strong motion accelerations recorded by the topographical effect observation array in Xishan park, Zigong city from the mainshock of Wenchuan earthquake,2008, the site effects of the ridge in the observation array site are studied through Horizontal-to-Vertical Spectral Ratio (HVSR) method, and the reliability of results is discussed. The strong motion accelerations of the observation array site are also simulated by the two-dimensional site model and analysis method, which are based on the explicit finite element-finite deference method and local transmitting boundary. This study indicates that the results of the numerical simulation and the observation data are strong consistent, and the simple two-dimensional site model is suitable for simulating the topographical effects on ground motions.