Numerical framework for calculating stiffness of liquefied sands during post-shaking re-solidification

Accurate prediction of earthquake-induced settlement in saturated sands remains challenging, primarily due to difficulties in capturing the coupled evolution of excess pore pressure, hydraulic conductivity, and compressibility during and after seismic liquefaction. In particular, quantifying stiffness recovery and consolidation behaviour during the post-shaking re-solidification phase remains problematic, as this stage is characterised by high hydraulic gradients and partially drained conditions. This study presents a physics-constrained numerical and inverse analysis framework to characterise post-shaking re-solidification in liquefied sand deposits. A hybrid explicit–implicit finite difference method (HEI-FDM) is developed to solve the nonlinear one-dimensional consolidation equation governing excess pore pressure dissipation and settlement efficiently and robustly. Building on this forward solver, a joint two-parameter inversion framework is proposed to identify the evolution of constrained modulus and hydraulic conductivity by simultaneously matching excess pore pressure time histories at multiple depths and surface settlement records. The framework is applied to four level-ground free-field dynamic centrifuge tests, enabling systematic investigation of stiffness recovery, hydraulic conductivity correction, and consolidation front propagation. Error-surface mapping and multi-start optimisation demonstrate that the inverse problem is well-constrained, yielding a unique and physically interpretable parameter set. Results show that stiffness inferred directly from conventional compression tests overestimates the stiffness of liquefied sand under partially drained conditions, while joint optimisation of stiffness and hydraulic conductivity accurately reproduces observed pore pressure dissipation and settlement. The proposed framework advances predictive modelling of post-liquefaction re-solidification by providing a mechanistically interpretable representation of hydro-mechanical coupling beyond empirical fitting approaches.