AbstractWe propose a new approach for performing drained and undrained loading of elastoplastic geomaterials over large deformations using smoothed particle hydrodynamics (SPH), a meshfree continuum particle method, combined with the modified Cam Clay (MCC) model of critical state soil mechanics. The numerical approach draws upon a novel oneâparticle twoâphase penaltyâmethod based formulation for handling undrained loading in saturated soils, which allows tracking of the buildup of poreâwater pressures under combined shearing and compression. Largeâscale parallelized simulations are employed to accommodate a significant number of degrees of freedom in a threeâdimensional setting. After verification and benchmark testing, the SPH based formulation is used to analyze the propagation of reverse faults through fluidâsaturated clay deposits and the rupture of strikeâslip faults across earthen embankments. The computational methodology tests the robustness of the meshfree approach in situations where the soil tends to dilate on the âdryâ side of the critical state line and to compact on the âwetâ side, but cannot, because of the incompressibility constraint imposed by undrained loading. Our results extend the current understanding of fault rupture modeling and further demonstrate the potential of our framework together with the SPH method for large deformation analyses of complex problems in geotechnics.