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.

我们利用平滑粒子流体动力学 (SPH)，一种基于拉格朗日粒子的连续介质方法，研究大变形下地质材料中剪切带或断层的起始和传播。我们表明 SPH 能够自然地捕获剪切带的形成，而无需引入异质性或“种子”。在移动挡土墙后面的主动或被动加载回填土中，我们表明穿过表面的剪切带以亚瑟角给定的方向倾斜，\(\varTheta _{\mathrm{A}}=45^{\circ } \pm (\psi +\phi )/4\)，关于主应力。此外，我们还进行了模拟以探索断层传播问题，即刚性基底岩石中的盲断层通过上覆的弱层传播到达地表。我们的结果表明，随着盲断层逐渐积累更多的滑动，最终的剪切带旋转，最初采用 Roscoe 角给出的方向，\(\varTheta _{\mathrm{R}}=45^{\circ } \pm \ psi /2\)，然后是亚瑟角，最后是熟悉的库仑方向，\(\varTheta _{\mathrm{C}}=45^{\circ } \pm \phi /2\), 在伸展和收缩设置中。最后，我们还评估了描述剪切带传播路径的经验解的有效性，并考虑了不同材料参数对合成剪切带几何形状以及表面位移和变形的影响。我们的结果表明，SPH 可以很好地处理外部载荷，例如由挡土墙施加的载荷，或由构造运动引起的载荷，如断层传播问题。