Dynamic response of soil deposits to vertical SH waves for different rigidity depth-gradients

The response of soils to vertically propagating shear waves has hitherto been analytically studied by assuming a rigidity increase with depth according to some power-law. Solutions in terms of Bessel functions are well-known. However, the near-surface stress distribution due to the static foundation load or the presence of a stiff surface layer leads to a notable rigidity value at the surface that may decrease with depth. In the present paper, a three-parameter depth-function with bounded value at large depths, one that is capable of reproducing both positive and negative depth-gradients, is adopted. The analytical solution derived in terms of power series is used to study elastic-rock amplification characteristics and modal shapes. Approximate expressions for the fundamental natural frequency of an elastic layer are given, covering a wide range of the parameters involved. Using the transfer matrix approach for multi-layered ground and the solution for a linear depth-profile for the individual layers, the accuracy of discretization schemes is examined. Finally, the case of a 2D rigidity variation is investigated by means of a numerical code.

► Analytical solution for non-linearly increasing or decreasing shear modulus depth-profiles.
► Elastic rock amplification for this class of soil profiles.
► Approximate formula for the eigenfrequency of a layer.
► Transfer-matrix approach for multi-layered ground with linear modulus variation in each layer.
► Numerical analysis for 2D variation of shear modulus due to the stiffness stress-dependency