On the fundamental resonant mode of inhomogeneous soil deposits

Abstract

The problem of estimating seismic ground deformation is central to state-ofpractice procedures of designing and maintaining infrastructure in earthquakeprone areas. Particularly, the problem of estimating the displacement field in a soft shallow layer overlying rigid bedrock induced by simple SH wave excitation has been favored by engineers due to its simplicity combined with inherent relevance for practical scenarios. We here derive analytical, accurate estimates for both the fundamental frequency and the amplitude of the first resonant mode of such systems by applying an intuitive argument based on resonance of single-degree-of-freedom systems. Our estimates do not presuppose a continuous velocity distribution, and can be used for fast assessment of site response in seismic hazard assessment and engineering design. On the basis of the said estimates of fundamental frequency and amplitude, we next propose a novel definition of "equivalent homogeneous shear modulus" of the inhomogeneous deposit; and we show that the response of the fundamental mode of these systems is governed by the mechanical properties of the layers closer to the bedrock. We finally discuss the validity of our argument, and evaluate the accuracy of our results by comparison with analytical and numerical solutions.

Data‐driven 1D wave propagation for site response analysis

“…Also in Figure 7B, the fact that the analytical fundamental frequency matches the first peak inferred from the DD results means that the material stiffness at the lower layers is properly reflected, 44,45 while the greater amplitudes in the low frequency regime could be due to the model's lack of precision in accounting for the upper layers' stiffness and their non‐linear behavior.…”