Analytical Solution for Biot Flow–Induced Damping in Saturated Soil during Shear Wave Excitations

Abstract

This paper presents a theoretical study of Biot flow–induced damping in saturated soil during shear wave excitations. The solid skeleton is treated as equivalent linear. Biot flow–induced damping is evaluated for the cases of resonant column tests and site response analysis, based on the spectral response of a soil column/layer under harmonic torsional/horizontal excitations. Closed-form analytical solutions indicate that Biot flow–induced damping is hydraulic conductivity and frequency dependant. At the first resonance in a resonant column test, Biot flow–induced damping is dependent on a dimensionless hydraulic conductivity parameter K. For K within the range of 0.01 to 100, corresponding to coarse sands and clean gravels, Biot flow–induced damping may have an important contribution to total soil damping, especially at small strain levels. For site response analysis, Biot flow–induced damping should be considered for coarse sands and clean gravels, but can be practically neglected for fine sands, silts, and clays. The effects of soil porosity, mass coupling, and non-Poiseuille flow on Biot flow–induced damping are discussed.