The seismic site response analysis requires the dynamic soil properties (i.e., the modulus and damping). While it is well understood that the shear modulus and damping ratio are nonlinearly shear-strain dependent, the knowledge on the constrained modulus and damping ratio of compressional waves is still very limited due to lack of laboratory testing equipment. This study aims to simulate cyclic tests of constrained compression for granular specimens by discrete element method (DEM) to understand the dynamic soil properties of compressional waves, i.e., the nonlinearity in constrained modulus and damping ratio with the compression strain. The evolution in microstructure of granular specimens is revealed to provide micromechanical interpretations for the compressional soil nonlinearity. The results show that the dependency of constrained modulus on compression strain is different in compression and extension stages, and the modulus reduction is only observed in the extension path. The damping ratio of samples under cyclic constrained compression is smaller than that of cyclic shear. The nonlinear soil behavior is more obvious at lower confining pressure and for dense sample. The nonlinearity of constrained modulus depends on the coordination number, contact normal force and fabric anisotropy, while the associated damping ratio is only related to fabric anisotropy.

Expansive soil is known for its ability to undergo significant volume changes in response to changes in moisture levels. Several investigations have been conducted to explore the stabilisation of expansive soils, encompassing a variety of reinforcement techniques and stabilisation approaches. Analysing dynamic properties such as shear modulus and damping ratio in expansive soil is imperative as they provide vital insights into the soil's response to dynamic loads. The use of lime and fibre treatment for stabilising expansive soil offers a comprehensive solution that addresses both chemical and physical stabilisation. This approach enhances soil properties and reduces the risk of damage to structures. To understand the complex behaviour of soil systems under varying conditions, cyclic triaxial tests on expansive soil were conducted using fibre-lime treatment. The variations in dynamic shear modulus and damping ratio with respect to shear strain amplitude, as well as the dynamic shear stress-strain curves, were studied across various confining pressures. The paper also presents the small strain shear modulus and modulus reduction curves. Besides, for a comprehensive understanding of the microstructural reactions of the fibre-lime-treated soil, specimens subjected to cyclic loading were examined using SEM analysis. A comparative analysis, examining the dynamic properties of soil under varying lime percentages, with and without 0.5% polypropylene (PP) fibre, as well as comparing scenarios with different lime contents between 0 and 0.5% PP fibre conditions has been presented. The experimental findings suggests that the fibre-lime treatment led to an enhancement in the dynamic shear modulus and damping ratio, with the increase of confining pressure. From the SEM analysis of the fibre-lime-treated soil, the microstructure displays a fabric-like pattern with cementitious gel connecting soil particle clusters. The images also show clay particles bonding together, forming a compact structure.