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Fault propagation and surface rupture in geologic materials with a meshfree continuum method

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Abstract

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. 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, \(\varTheta _{\mathrm{A}}=45^{\circ } \pm (\psi +\phi )/4\), with respect to the principal stresses. Additionally, we conduct simulations to explore the fault propagation problem, where a blind fault in rigid basement rock propagates through an overlying weak layer to reach the surface. Our results demonstrate that the resulting shear band rotates as the blind fault progressively accumulates more slip, initially taking the orientation given by the Roscoe angle, \(\varTheta _{\mathrm{R}}=45^{\circ } \pm \psi /2\), then that of the Arthur angle, and lastly, that of the familiar Coulomb orientation, \(\varTheta _{\mathrm{C}}=45^{\circ } \pm \phi /2\), in both extensional and contractional setups. 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. 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.

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Acknowledgements

This material is based upon work supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, Geosciences Research Program, under Award Number DE-FG02-03ER15454. Support for materials and additional student hours were provided by the National Science Foundation under Award Number CMMI-1914780. The first author acknowledges the support by the US National Science Foundation (NSF) Graduate Research Fellowship under Grant DGE 1656518, as well as by the Stanford Graduate Fellowship.

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  1. Department of Civil and Environmental Engineering, Stanford University, Stanford, CA, 94305, USA

    Enrique M. del Castillo & Ronaldo I. Borja

  2. Department of Civil and Environmental Engineering, Bucknell University, Lewisburg, PA, 17837, USA

    Alomir H. Fávero Neto

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  1. Enrique M. del Castillo
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del Castillo, E.M., Fávero Neto, A.H. & Borja, R.I. Fault propagation and surface rupture in geologic materials with a meshfree continuum method. Acta Geotech. 16, 2463–2486 (2021). https://doi.org/10.1007/s11440-021-01233-6

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