Small-strain stiffness, shear-wave velocity, and soil compressibility

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 a factor decreases and the b exponent increases as soil compressibility C_C increases, and there is a robust inverse relationship between α and β for all sediments: β≈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.