Numerical modelling of wave propagation in anisotropic soil using a displacement unit-impulse-response-based formulation of the scaled boundary finite element method |
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| Institution: | 1. School of Civil Engineering and Architecture, Beijing Jiaotong University, Beijing 100044, China;2. MCC Capital Engineering Research Incorporation Limited, Beijing 100176, China;3. Civil Engineering Department, University of Southern California, KAP 216D Vermont Avenue, Los Angeles, CA 90089-2531, USA;1. Aristotle University of Thessaloniki, Research Unit of Soil Dynamics and Geotechnical Earthquake Engineering, Department of Civil Engineering, PO Box 424, GR-54124 Thessaloniki, Greece;2. University of Catania, Department of Civil and Environmental Engineering, Sicily, Italy;1. Department of Civil Engineering, Zanjan Branch, Islamic Azad University, Zanjan, Iran;2. Department of Civil Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran;1. The State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian, Liaoning 116024, China;2. School of Hydraulic Engineering, Dalian University of Technology, Dalian, Liaoning 116024, China |
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| Abstract: | An efficient method for modelling the propagation of elastic waves in unbounded domains is developed. It is applicable to soil–structure interaction problems involving scalar and vector waves, unbounded domains of arbitrary geometry and anisotropic soil. The scaled boundary finite element method is employed to derive a novel equation for the displacement unit-impulse response matrix on the soil–structure interface. The proposed method is based on a piecewise linear approximation of the first derivative of the displacement unit-impulse response matrix and on the introduction of an extrapolation parameter in order to improve the numerical stability. In combination, these two ideas allow for the choice of significantly larger time steps compared to conventional methods, and thus lead to increased efficiency. As the displacement unit-impulse response approaches zero, the convolution integral representing the force–displacement relationship can be truncated. After the truncation the computational effort only increases linearly with time. Thus, a considerable reduction of computational effort is achieved in a time domain analysis. Numerical examples demonstrate the accuracy and high efficiency of the new method for two-dimensional soil–structure interaction problems. |
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| Keywords: | Wave propagation Unbounded domain Scaled boundary finite element method Displacement unit-impulse response matrix Anisotropic soil Truncation time |
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