Asymmetric deformation has been observed in the α other than 0° or 90° cases, which is mainly attributable to the different relative principal directions between the stress and the fabric at the two sides of the domain. The bearing capacity is found to decrease with an increasing α and the reduction can reach as high as 25%. The inherent fabric anisotropy of sand is reflected by the bedding plane angle α of the RVEs composed of elliptic particles, where α measures the average angle between the long axes of the particles and the horizontal direction. In the approach, the material constitutive responses are captured by DEM simulations on representative volume elements (RVEs) assigned to the FEM Gauss points. The influence of inherent fabric anisotropy of sand and its evolution on the footing bearing capacity and the failure mechanism has been modelled and analysed with a multiscale approach that couples the finite element method (FEM) and the discrete element method (DEM). Our results show that SPH deals well with external loadings such as those applied by a retaining wall, or those induced by tectonic movement like in the fault propagation problem. Finally, we also evaluate the validity of empirical solutions describing the shear band propagation path and consider the effect of different material parameters on the geometry of the resultant shear bands, as well as on displacement and deformation at the surface. We show that SPH is able to capture the formation of shear bands naturally without needing to introduce a heterogeneity or “seed.” In an actively or passively loaded backfill behind a moving retaining wall, we show that shear bands crossing the surface are inclined at an orientation given by the Arthur angle, \(\varTheta _ \pm \phi /2\), in both extensional and contractional setups. We utilize smoothed particle hydrodynamics (SPH), a Lagrangian particle-based continuum method, to study the initiation and propagation of shear bands or faults in geologic materials over large deformations. The micromechanics study also sheds lights on the possible detriment of heavy foundations for the superstructure despite the rupture surface diversion.
By examining the responses and microstructural evolutions of local RVE packings, it is found that the RVEs located in- or outside the shear bands (SBs) behave distinctly, and may change their stress states from initial at-rest to active in the normal fault case.
The fault rupture surfaces and shear localization patterns under normal faults with or without foundation atop have been well captured by the multiscale approach and verified with available centrifuge experimental and numerical results. In the approach, the soil constitutive responses are obtained from DEM solutions of representative volume elements (RVEs) embedded at the FEM integration points so as to effectively bypass the phenomenological hypotheses in conventional FEM simulations. A multiscale approach that couples the finite element method (FEM) and the discrete element method (DEM) is employed to model and analyses the earthquake fault rupture-soil-foundation interaction (FR-SFI) problem.
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