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 Vs = α(σm/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 ϹϹ. Compiled experimental results show that the α factor decreases and the β exponent increases as soil compressibility ϹϹ 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.