The Lumped mass Chebyshev spectral element method for seismic response analysis of horizontally layered soil sites

A time-domain high-order explicit method for the seismic response analysis of horizontally layered soil sites is proposed. The upper soil and bedrock are discretized by several Chebyshev spectral elements. The multi-transmitting artificial boundary is set at the bottom of the model. The Chebyshev orthogonal polynomials are employed for establishing high-order element displacement field. By means of the Gauss-Lobatto quadrature, the lumped mass matrix, which has diagonal form, for the Chebyshev spectral element is rigorously derived. Combined with the central difference time-stepping scheme, an efficient lumped mass Chebyshev spectral element method for simulating wave motion is constructed. Earthquake records obtained from different kinds of sites provided by the Kik-net strong earthquake network are used to examine the validity of the proposed method. This method overcomes the shortage in efficiency of conventional Chebyshev spectral element method resulted from having consistent form ofmass matrix. Numerical results show that the proposed method can give reasonable prediction on the ground motions of Ⅰ ₁, Ⅱ and Ⅳ type sites under weak or moderate earthquakes, and good accuracy can be achieved only by deploying a small number of elements per wavelength.