Lattice Boltzmann method for elastic viscoplastic modelling of soil consolidation

A novel fully coupled framework integrating the Lattice Boltzmann Method (LBM) with an elastic viscoplastic (EVP) constitutive model is presented to model the one-dimensional, time-dependent consolidation and creep in saturated soils. The EVP creep strain rate is embedded directly as a local source term within the LBM collision step, enabling fully explicit treatment of the nonlinear coupling between pore-pressure dissipation and viscous skeleton deformation without global matrix assembly or iterative convergence procedures. A Chapman–Enskog expansion rigorously demonstrates that the LBM recovers the governing EVP consolidation equation. An explicit analytical relationship is established between the microscopic LBM relaxation time and the macroscopic coefficient of consolidation, bridging mesoscopic lattice dynamics with continuum-scale soil mechanics. Model performance is verified against Terzaghi's analytical solution and validated against multi-increment oedometer tests on Drammen clay, a numerical benchmark under different over-consolidation ratios, and field settlement measurements from a multi-layered embankment under staged loading. Validations confirm reliable prediction of both transient pore-pressure dissipation and long-term creep deformation. Overall, the framework is inherently parallelisable and extensible to two- and three-dimensional problems, establishing LBM as a robust, scalable alternative solver for nonlinear coupled geomechanical problems.