A semi-empirical relationship for the small-strain shear modulus of soft clays

The small-strain shear modulus (G_max) is a soil property that has many practical applications. The authors compiled a database of G_max measurements for 40 normally consolidated to slightly overconsolidated low to high plasticity clays. Using these data, the authors propose a semi-empirical relationship between G_max, effective stress (σ'_v or σ'_c), preconsolidation stress (σ'_p) and in-situ void ratio (e₀) for four ranges of plasticity index (I_p): I_p < 30%, 30% ≤ I_p < 50%, 50% ≤ I_p < 80% and 80% ≤ I_p < 120%. With results from bender element tests on a Gulf of Mexico clay subjected to multiple load-unload consolidation loops, the authors were able to validate the proposed relationships for 30% ≤ I_p < 50% and 50% ≤ I_p < 80%. The proposed relationship for 30% ≤ I_p < 50% and 50% ≤ I_p < 80% captures changes in laboratory G_max resulting from variations in effective stress (σ'_c), maximum past stress (σ'_v,max), and void ratio. The proposed relationships are a simple and efficient tool that can provide independent insight on G_max if the stress history of a clay is known, or on stress history if G_max is known.