Seismic harmonic response of inhomogeneous soil: scaling analysis

Abstract

The study of the seismic response of inhomogeneous soil deposits, underlying rigid bedrock, has traditionally been framed as a one-dimensional wave propagation problem in a linear viscoelastic medium. When it comes to modelling soil inhomogeneity, the current trend to model the continuous variation of soil stiffness with depth employs a ‘generalised parabolic function’. Exact solutions have already been obtained, but these come in terms of Bessel functions, which muddle the interpretation of results and obstruct assessment of the parameters’ influence. This also hinders the definition of an ‘equivalent homogeneous’ soil deposit (a relevant concept utilised in many seismic codes). It is shown herein that the so-called inhomogeneity factor plays a secondary role in determining the response in many cases; thus straightforward guidelines are suggested for simplifying the problem, leading to elementary scaling relations. The scalings provide simple yet meaningful relations that reveal and explain the fundamental traits of the dynamic behaviour of these systems.

On the fundamental resonant mode of inhomogeneous soil deposits

“…Likewise, an estimate particularly well-suited for the high-frequency regime has been furnished previously by the authors [15]. Regarding the ground surface amplification relative to the profile base, it was found…”

Geometrical Optics applied to 1D Site Response of Inhomogeneous Soil Deposits

“…In a previous work [Garcia-Suarez et al, 2020], the authors focused on a specific, commonly used, distribution of S-wave velocity, the so-called "generalized parabola" (density is assumed to be constant):…”

“…This work has been occupied, chiefly, with a generalization of previous results obtained under the assumption of S-wave velocity profile abiding by eq. (2) [Garcia-Suarez et al, 2020] to any profile meeting two simple requirements: 1) continuity and boundedness of first derivative of f (η), 2) positive (non-zero) values of c s throughout the deposit, including at the free-surface. It has been shown that this result stems from a classical result in Physics, the so-called Geometrical Optics approximation.…”

Linear one-dimensional site response analysis in the presence of stiffness-less free surface for certain power-law heterogeneities

“…As discussed in previous work by the authors [10][11][12], coming up with equivalent homogeneous properties valid over the whole frequency range appears an irreducible task. Instead, it seems more feasible to assess equivalent homogeneous properties for either the fundamental mode [10], or relatively high frequencies in general [11].…”