An Improved Thermodynamic Energy Equation for Stress–Dilatancy Behavior in Granular Soils

This study proposes an advanced thermodynamic energy equation to accurately simulate the stress–dilatancy relationship in granular soils for both uncrushed and crushed sands. Traditional energy formulations primarily consider dissipation energy and often neglect the role of free energy. Recent developments have introduced free energy components to account for plastic energy contributions from dilation and particle crushing. However, significant discrepancies between theoretical predictions and experimental observations remain, largely due to the omission of complex mechanisms such as contact network rearrangement, force-chain buckling, grain rolling, rotation without slip, and particle crushing. To address these gaps, the proposed model incorporates dual exponential decay functions into the free energy framework. Rather than explicitly modeling each mechanism, this formulation aims to phenomenologically capture the interplay between fundamentally opposing thermodynamic forces arising from complex mechanisms during granular microstructure evolution. The model’s applicability is validated using the experimental results from both uncrushed silica sand and crushed calcareous sand. Through extensive comparison with over 100 drained triaxial tests on various sands, the proposed model shows substantial improvement in reproducing stress–dilatancy behavior. The average discrepancy between predicted and measured η–D relationships is reduced to below 15%, compared to over 60% using conventional models. This enhanced energy equation provides a robust and practical tool for predicting granular soil behavior, supporting a wide range of geotechnical engineering applications.