Liquefaction resistance of sand is linked to coordination number and contact fabric in DEM simulations, but a mechanical explanation of how these microscopic quantities control stress-dilatancy during cyclic loading is still lacking. This study develops a semi-analytical effective-medium model for the small-strain shear modulus and the volumetric–shear coupling modulus on constant-volume cyclic liquefaction paths. Building on effective-medium theory, the standard framework for linking microstructure to moduli, the model applies the affine kinematic assumption. In real packings, affine deformation induces unbalanced forces and torques of particles that drive non-affine displacements, reducing or enhancing the moduli. In this study, two empirical constants are used to capture this correction. One scales the affine shear modulus according to coordination number: packings with fewer contacts are much softer than affine theory predicts and the shear modulus eventually vanishes at the isostatic limit (a coordination number of 4). The other is a fixed ratio between effective and affine volumetric–shear coupling. Apart from these two constants, the formulation uses macroscopic state variables only. Closed-form expressions show explicitly that coordination number largely governs shear stiffness and contact normal and force anisotropies primarily control volumetric–shear coupling and thus stress-dilatancy. The predicted shear and volumetric–shear moduli agree closely with DEM simulations both at shear load reversals, where cyclic paths are naturally probed, and when small reverse shear increments are applied midway through loading, before the next reversal. The model therefore provides a mechanical link between coordination number, anisotropy, and contractancy during liquefaction.
Active earth pressure acting on retaining walls can be significantly affected by tension cracks that develop within unsaturated marginal backfills. Existing analytical approaches typically idealize these cracks as a continuous zone of uniform depth, neglecting their stochastic nature and the resulting variability in active thrust. This study presents a physics-informed stochastic framework for evaluating active thrust in unsaturated backfills containing spatially variable tension cracks. A physically admissible random field is developed in which crack depth is characterized by its mean, coefficient of variation, and correlation length, while crack location is governed by mean crack spacing. The generated crack field is integrated into a limit-equilibrium formulation incorporating suction stress and a log-spiral failure mechanism. Deterministic analyses first identify an Influence Zone (IZ) along the backfill surface where tension cracks affect active thrust. Monte Carlo simulations are then performed to quantify the influence of crack variability on the 95th percentile of the active earth pressure coefficient, Ka,0.95. Results reveal the existence of a Transitional Regime Domain (TRD) within the IZ where active thrust exhibits maximum sensitivity to crack variability and cracking-zone extent. The location and extent of the TRD depend on the statistical characteristics of the crack field, particularly mean crack spacing and depth variability. Among the stochastic parameters considered, the coefficient of variation of crack depth exerts the strongest influence on Ka,0.95, whereas correlation length has a comparatively minor effect over the conditions and autocorrelation models investigated. The proposed framework provides a practical tool for probabilistic assessment and risk-informed design of retaining walls with unsaturated cracked backfills.
This work presents a comprehensive discrete modeling framework for coupled three-dimensional thermo-hydro-mechanical (THM) applications involving localized failure. The discrete beam lattice formulation for non-isothermal saturated porous materials is capable of capturing complex spatial failure mechanisms. At the same time, the study addresses one of the main limitations of discrete lattice modeling, namely the selection of discrete input parameters and their relationship to continuum-equivalent properties. To overcome this issue, parameter calibration is performed by using a Bayesian inverse modeling procedure. First, a thermoelastic consolidation benchmark is considered, enabling the identification of key thermal, hydraulic, and coupling parameters, along with stiffness correction factors required to reproduce the corresponding continuum response. Next, an undrained heating test on a fully saturated specimen is used to capture thermal pressurization. Finally, the discrete beam lattice model is applied to an undrained compression test, with progressive failure and development of three-dimensional strain localization under coupled THM conditions.
