Study On Stability Problems Of Local Transmitting Boundary In Wave Simulation Of Site Seismic Effect

In this paper, stability problems of local transmitting boundary in wave simulation on of site seismic effect is studied. Based on the analysis and comparison of existing stability measures for transmitting boundary, the applicability of each measure is given. A new measure for eliminating the drift instability is proposed based on the combination of the multi-transmitting boundary with the viscous-spring elements, and a new measure for eliminating the high-frequency instability is proposed. Validities of these two suggested measures was tested by numerical experiment. Compared with analytical solution, calculation accuracy of the method which combining the explicit finite element-finite difference method with local transmitting boundary is verified. Ground motion response of the overlaying soil and ridge terrain in Zigong Xishan park was simulated by the explicit finite element-finite difference method. Compared with the observed values of strong motion records in Wenchuan earthquake, Validity of this method to practical wave simulation was tested.The works in this study include:1. The method which combining the explicit finite element-finite difference method with local transmitting boundary is compared with Fourier-Bessel wave function expansion method combined with big circle assumption. At different frequencies, mesh size requirement of numerical solution corresponding to analytical solution is also different. The precision can be satisfied and the calculation efficiency can be improved by suitable time step without too small step.2. Based on the Cause of drift instability and high-frequency instability, the applicability of previously used stability measures is discussed by numerical experiment. To the perfect elasticity problem, the filtering method is more suitable to eliminate high-frequency instability; to the situation existing damping itself such as viscoelastic problem, explicit difference scheme with damps is effective to eliminate high-frequency instability by energy consumption of difference scheme. As for drift instability, the method of adding modified operator?B00 is needed to be carefully used because of the empirical feature and uncertainty of parameter value. We recommend the method of reduced order because of the certainty and controllability of parameter value.3. The measure was studied for eliminating instability of the transmitting boundary by means of adding viscous-spring elements in the artificial boundary area. In the measure, the springs and dampers are emplaced on the finite element nodes next to the artificial boundary in the artificial boundary area. Validity of the suggested measure is tested by numerical analysis for the topographical site. The results show that the measure is a valid one to solve the drift instability of multi-transmitting boundary, which is effective for eliminating the drift instability but no visible effect on the high-frequency instability.4. The filtering method using the neighbor node of boundary node is suggested to eliminate high-frequency instability. In this method, the errors of high frequency oscillation in the vertical and parallel direction are all considered. The value of smoothing coefficient is also suggested in this paper. The results show that the measure is a valid one to solve the high-frequency instability of multi-transmitting boundary. According to this filtering method, a preliminary multi-direction transmitting formula is suggested.5. Site amplification was analyzed for the ridge terrain of Zigong Xishan park using the strong motion record obtained in Wenchuan earthquake by traditional spectral ration method. The reference seismic station of spectral ration is located near the foot of the ridge. Ground motion response of the ridge terrain in Zigong Xishan park was simulated by the explicit finite element-finite difference method. The results of numerical simulation were compared with the observed values of strong motion records, which shows that this numerical simulation model could reflect the ridge terrain basically. Numerical modeling results show these conclusions as follows. Amplification action of the overlaying soil to seismic acceleration is more obvious than that of the topographic change. Horizontal component of the seismic ground motion is amplified by topography variation more evidently than vertical component. The two-dimensional model built in this paper could well simulate the ground motion on overlaying soil and the results coincided well with the observation results. Simulation for bedrock could reflect the ground motion response of the ridge terrain in low frequency range.At last, the work in this study is summarized, and the problems need to be studied moor deeply are pointed out.