Mesoscale numerical modelling of freeze–thaw deformation in closed- and open-system soils using a Voronoi–Delaunay lattice

Freeze–thaw deformation in frost-susceptible soils couples heat transfer, phase change, water redistribution and irreversible thaw deformation. This study develops an axisymmetric Voronoi–Delaunay lattice framework with a finite-element-analysis-program (FEAP)-compatible residual–tangent organization, embedded displacement-jump histories and a bounded temperature-dependent creep law. Delaunay edges carry normal–shear interactions, while a circumcentric dual supplies transport faces and storage volumes. The global benchmark implementation combines apparent-heat-capacity heat transfer, a reduced total-water redistribution equation and fixed-reference small-strain lattice mechanics; it is not a complete Darcy-flow, effective-stress or discrete ice-lens formulation. Verification against radial conduction, Stefan-front propagation and confined compression produced errors of 1.45%, 3.53% and 5.88%, respectively. First-cycle heave and thaw-settlement endpoints from one closed Kieler Förde test and six independent open-system tests were used for case-level calibration. The calibrated model reproduced those endpoints with a median absolute percentage error of 0.36%. The subsequent Kieler Förde cycle trend was assessed without further endpoint calibration, and the FEAP jump–creep enrichment retained a median endpoint error of 3.03% without re-optimisation. Predicted temperature, ice fraction, total water, pressure proxy and displacement fields are reported as model outputs because co-registered water-content profiles, pore pressures and freezing-front positions were not available for every case. Four CPU workers produced a measured 3.25-fold batch speedup; an optional GPU sparse-solver route is supplied with deterministic CPU fallback. The framework is therefore intended for rapid laboratory-scale displacement assessment, while finite-strain kinematics and fully coupled ice-lens poromechanics remain future developments.