Small-Strain Stiffness, Shear-Wave Velocity, and Soil Compressibility: Fid-Bau Portal

Small-Strain Stiffness, Shear-Wave Velocity, and Soil Compressibility

Cha, Minsu / Santamarina, J. Carlos / Kim, Hak-Sung / Cho, Gye-Chun

Abstract

The small-strain shear modulus depends on stress in uncemented soils. In effect, the shear-wave velocity, which is often used to calculate shear stiffness, follows a power equation with the mean effective stress in the polarization plane $V_{s} = α {(σ_{m}^{'} / 1 kPa)}^{β}$ , where the $α$ factor is the velocity at 1 kPa, and the $β$ exponent captures the velocity sensitivity to the state of stress. The small-strain shear stiffness, or velocity, is a constant-fabric measurement at a given state of stress. However, parameters $α$ and $β$ are determined by fitting the power equation to velocity measurements conducted at different effective stress levels, so changes in both contact stiffness and soil fabric are inherently involved. Therefore, the $α$ and $β$ parameters should be linked to soil compressibility $C_{C}$ . Compiled experimental results show that the $α$ factor decreases and the $β$ exponent increases as soil compressibility $C_{C}$ increases, and there is a robust inverse relationship between $α$ and $β$ for all sediments: $β \approx 0.73 - 0.27 \log [α / (m / s)]$ . Velocity data for a jointed rock mass show similar trends, including a power-type stress-dependent velocity and inverse correlation between $α$ and $β$ ; however, the $α - β$ trend for jointed rocks plots above the trend for soils.