Half-Space Dynamic Stiffness Models Compatible with the Thin Layer Formulation for Use in Response Analysis of Soil Profiles

This work presents two new wave propagation models for the half-space compatible with the thin layer formulation (TLF). The TLF is based on a polynomial expansion in the wave number κ of the exact matrix of the dynamic stiffness of a layer. The advantage of the TLF with respect to the exact model is that it allows transforming the soil profile response between wave number and spatial domains in analytical form through the decomposition of response in wave propagation modes. The expansion in κ applied to the exact matrix of the half-space does not produce a satisfactory approximation for moderate or large values of κ. Therefore, the TLF in its original form only reproduces with good accuracy the response of soil profiles composed by an assembly of layers over an infinitely stiff half-space. The proposed models eliminate such shortcomings and adequately represent the half-space stiffness in the wave number domain. The techniques used for adjustment of mechanical soil profiles generally represent the half-space through an assembly of strata with increasing thickness in depth. Such approach produces acceptable accuracy in the wave propagation velocity of the fundamental mode for normally dispersive profiles (with increasing stiffness in depth), although it generates spurious modes not related with higher propagation modes. The adjustment of mechanical parameters of inversely dispersive profiles requires an adequate approximation of the half-space dynamic behavior given the significant contribution of the higher propagation modes to the response. The proposed models are suitable for the adjustment of soil profiles with an arbitrary distribution of stiffness in depth and for evaluating the dynamic stiffness of foundations.