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Abstract We 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 one‐particle two‐phase penalty‐method based formulation for handling undrained loading in saturated soils, which allows tracking of the buildup of pore‐water pressures under combined shearing and compression. Large‐scale parallelized simulations are employed to accommodate a significant number of degrees of freedom in a three‐dimensional setting. After verification and benchmark testing, the SPH based formulation is used to analyze the propagation of reverse faults through fluid‐saturated clay deposits and the rupture of strike‐slip faults across earthen embankments. The computational methodology tests the robustness of the meshfree approach in situations where the soil tends to dilate on the ‘dry’ side of the critical state line and to compact on the ‘wet’ 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. 

Abstract We develop an analytical solution to the problem of one‐dimensional consolidation of unsaturated soil subjected to cyclic loads with arbitrary waveforms. The solution predicts the excess pore water and pore air pressures and the accompanying vertical compression in a poroelastic, unsaturated soil material. Cyclic loading occurs in a variety of engineering applications and often generates higher excess pore fluid pressures and larger vertical compression than does a time‐invariant load. In the present study, the loading function is allowed to take on any arbitrary waveform represented by a Fourier trigonometric series. Analytical solution to the boundary‐value problem in one dimension is given in closed form describing the frequency‐independent and frequency‐dependent components of the poroelastic response. We verify the analytical solution through representative examples involving cyclic loads with square and triangular patterns. Apart from the shape of the forcing function, we also investigate the effects of initial water saturation, soil texture, and excitation frequency on the system response. 

Permanent deformation and uplift caused by fault rupture is one of the most significant hazards posed by earthquakes on the built environment. In this paper, we use Smoothed Particle Hydrodynamics (SPH) to explore the effects of soil layering or stratification on the trajectories and deformation patterns caused by rupturing reverse faults in bedrock, as well as in the foundations of engineered earth structures. SPH is a continuum meshfree numerical method highly adept at modeling large deformation problems in geotechnics. Through the use of constitutive models involving softening behavior as well as critical state type models, we isolate the effects of rigid body rotation from critical state behavior of soil in helping explain the frequently observed rotation of shear bands emanating from the bedrock fault. This analysis is facilitated by the fact that the SPH method allows us to track the propagation of shear bands over substantial amounts of vertical uplift (more than 50\% of the total height of the soil deposit), far beyond many previous computational studies employing the finite element method (FEM). We observe and characterize various emergent features including fault bifurcations, stunted faults, and tension cracking, while providing insights on practical guidelines regarding the potential surface distortion width, and the critical amount of fault displacement required for surface rupture depending on the multilayered constitution of the soil deposit. Finally, we predict the expected amount of surface distortion and internal damage to earthen embankments depending on varying fault location and soil makeup.