Abstract
The most widely used techniques for the study of one-dimensional amplification of vertically propagating seismic waves involve solution of the dynamic equations in the frequency domain with linearly viscoelastic material properties. Material nonlinearities are approximately modeled by iterative use of linear solutions, adjusting values of modulus and damping until they are compatible with computed levels of strain. The program SHAKE is the best known example of a code using this procedure. Several refinements to the iterative scheme originally proposed by Seed and Idriss are presented in this paper. In particular, it is shown that the solution for the layers underlying the control motion can be obtained in one single step, when the mass matrix is diagonal. Use of the shear stress in place of the shear strain as the controlling parameter in determining material properties gives faster convergence and identifies cases of potential non-convergence. Trivial modifications are also proposed to the standard scheme that would enable the researcher to study the amplification or deconvolution of non-vertically incident SH waves with a code like SHAKE. These modifications consist simply in changing the mass density of the soil, and redefining the characteristic strain.
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