Discrete Element Analysis of Surface Fault Rupture through Granular Media
Earthquake surface fault rupture can cause substantial structural damage and loss of life in near-fault regions. Active fault traces cannot always be avoided, especially by linear infrastructure such as lifelines. With effective design the damaging effects of surface fault rupture can be mitigated. The development of effective mitigation techniques warrants investigation of the fundamental mechanisms of earthquake fault rupture propagation through granular media. The discrete element method (DEM) provides an avenue for analyzing the micromechanics of fault rupture propagation and its interactions with the built environment. In this dissertation, DEM is used to simulate reverse and normal fault rupture in three-dimensions (3D) with assemblages of irregularly shaped sphere-clusters that capture the non-spherical nature of real sand grains.
Simulated dip-slip fault rupture surfaces delineated by particle rotations, frictional dissipation, and strains compare favorably with the results of sandbox-style experiments at various fault dip angles. Reverse fault rupture surfaces become less curved and more linear as the fault dip angle decreases from 90° to 30°, and normal fault rupture simulations successfully capture graben development at shallow fault dip angles. Arched distributions of strong contact forces show a stress arching phenomenon in normal fault rupture that is also seen in trapdoor simulations, and the mechanism of graben formation in shallow normal fault rupture is shown through the collapse of the arched distribution of strong contact forces. Steep reverse fault rupture produces half-arched patterns of strong contact forces that are also present in anchor pull-out simulations, and a widespread distribution of strong contact forces develops over the entire hanging wall during shallow reverse fault rupture. Significant out-of-plane particle rotations highlight the need for 3D DEM even in scenarios of plane-strain shearing.
Simulations with a wide range of void ratio distributions capture the transition from distinct localization to broadly distributed shearing as the void ratio increases, which also produces a smaller gradient of the deformed ground surface. Contractive and dilatant volumetric changes during shearing are associated with increases and decreases in the coordination number of individual particles. In assemblages with the same stress distribution but different relative densities, the inter-particle contact forces are higher on average in looser assemblages because the total force in the system is distributed across fewer contacts. The higher contact forces and more widespread distribution of shear deformation in loose particle assemblages dissipate more friction during fault rupture than in denser particle assemblages. In all particle assemblages, reverse fault rupture increases the number of horizontally oriented inter-particle contacts; whereas, normal fault rupture produces a slight decrease in the number of horizontally oriented inter-particle contacts.
The LIGGGHTS DEM code is modified and used to perform a large suite of direct shear test simulations with different particle shapes, relative densities, and applied pressures. High-performance computing facilitates the simulation of over 100,000 sphere-clusters containing approximately 250,000 constituent spheres. Through homogenization techniques, the mobilized friction angles measured at the rigid-wall boundaries of the test are shown to reflect accurately those that develop along the mid-plane of each specimen, and the angles of dilation measured at the boundaries slightly underestimate those along the mid-plane due to partial absorption of the volumetric expansion through the rest of the specimen. Densely packed particle assemblages exhibit strain-softening, volumetric dilation, and distinctive shear bands seen through localized particle rotations; whereas loosely packed particle assemblages exhibit contraction, no distinct peak strength, and broadly distributed particle rotations throughout the specimen. The shear bands through densely packed sphere-clusters are thicker than those through spheres due to the inability of spheres to interlock. The inability of the particles to crush in the simulations produces little stress dependency in the critical state void ratio, but stress dependency is observed through the coordination number at the critical state and in the initial stiffness of each particle assemblage. Fluid-like characteristics such as vortex structures within the shear bands of densely packed sphere-clusters are seen in the velocity fields of the particle assemblages.
The interaction between a propagating fault rupture surface and a rigid building foundation is simulated for the first time with 3D DEM. High-performance computing with a modified version of the LIGGGHTS DEM code is used to efficiently simulate 400,000 to 1.7 million sphere-clusters containing up to approximately 4.3 million constituent spheres. Physically observed influences of the contact pressure, position, and width of the foundation on fault rupture propagation are captured satisfactorily with high-performance DEM simulations containing hundreds of thousands of sphere-clusters. Micromechanical analyses of particle rotations, void ratios, and contact forces provide valuable insight into mechanisms of reverse and normal fault-foundation interaction. The reverse fault rupture surface is shown to deflect systematically towards the hanging wall edge of the foundation as the foundation contact pressure increases, because higher foundation contact pressures increase the forces between particles and essentially create a barrier to shear rupture beneath the foundation. If the foundation is located sufficiently away from the projected surface fault trace on the footwall during normal fault rupture, a complex sequence of fault rupture propagation develops in which shear activity ceases along one rupture surface propagating towards the hanging wall edge of the foundation and migrates towards a second rupture surface that ultimately outcrops on the footwall edge of the foundation. DEM has great potential for understanding the fundamental granular influences on earthquake surface fault rupture.