Optimizing Lysmer-Kuhlemeyer Boundary Parameters for Different Incident Angles in DDA Seismic Simulation

抄録

In seismic engineering problems, artificial boundaries are often introduced in finite-volume models within an infinitely large earth. The reflection and refraction of seismic waves at these boundaries can distort waveforms within the model, making it an important issue to mitigate their effects. Absorbing Boundary Condition (ABC) has been widely used for this purpose since Berenger introduced it in 1994. However, the Lysmer-Kuhlemeyer (LK) viscous boundary, which employs dimensionless parameters a and b, is often recommended with values of 1.0 for both parameters, which is not always optimal for absorbing energy at different incident angles. This study aims to find the optimal a and b values for different incident angles. First, the discontinuous deformation analysis (DDA) method is used to simulate the usual artificial boundaries, such as free and fixed boundaries, demonstrating the waveform disturbance phenomenon caused by reflections inside the model. Next, it is shown that the LK boundary with a = 1.0 and b = 1.0 can effectively absorb reflection interference when the incident wave is perpendicular to the artificial boundary. However, for cases with incident angles, the LK boundary with a = 1.0 and b = 1.0 fails to provide effective absorption. Consequently, the Monte Carlo simulation method is employed to randomly select a and b values, using DDA to simulate seismic wave propagation within the model. The optimal a and b values corresponding to the incident angle are found based on the maximum absorption rate. A large number of calculations are performed for different incident angles, and the empirical formulas for a and b are derived.