Assessing the strength evolution of cement-stabilized clay using small-strain shear modulus: a modified Gompertz model conversion approach

This study introduces an innovative approach for estimating the unconfined compressive strength ( q u ) of cement-stabilized soil using the non-invasive measurement of small-strain shear modulus ( G max ). This approach provides a practical alternative to conventional time-consuming laboratory strength tests. However, converting small-strain stiffness to strength in cement-stabilized clay is challenging due to mismatched evolution curves at different curing stage. Strength evolution typically adheres to a three-phase pattern, whereas small-strain stiffness evolution exhibits a two-phase pattern. This study adapts the Gompertz model to parameterize the varying strength and stiffness geometric trends of cement-soil mixtures throughout the entire curing period. Renowned for its simplicity and flexibility, the modified Gompertz model, with its three key parameters—maximum asymptote, growth rate, and inflection time—effectively captures the evolution curve for both strength and stiffness. The accuracy is validated using OPC-stabilized clay with various mixing ratios, in addition to published data from a wide range of cement and soil types. The study finds that the maximum strength asymptote linearly correlates with the square of the maximum asymptote for small-strain stiffness. Additionally, the growth rate and inflection time parameters exhibit relative consistent value, which are influenced by the type of cement used. Subsequently, the strength evolution curve is linearly converted from shear modulus using three transfer coefficients, each linked to the Gompertz model parameters. Laboratory tests validate the accuracy of this model-based conversion, showing that refining parameters within the Gompertz function yields greater precision than direct empirical correlations between strength and stiffness.