Numerical simulation of stick-slip behaviours of typical faults in biaxial compression based on a frictional-hardening and frictional-softening model

Abstract

Stick-slip behaviours of typical faults and interactions among faults are numerically modelled using a proposed frictional-hardening and frictional-softening elastoplastic continuum model. Forty numerical tests in biaxial compression are conducted quasi-statically or dynamically in plane strain and in small or large strain mode using FLAC-3D. Faults are modelled by square or quadrilateral elements from a viewing angle perpendicular to the maximum surface of a specimen. An incremental plastic shear strain in a stick-slip cycle is involved in the model, which is calculated at the beginning of slip and then is set to be zero upon reaching its maximum at the end of stick. Thus, the repeated stick-slip behaviour can be modelled using the same set of equations, and only the evolution of an internal frictional angle is required to be different at different stages. At the slip stage, a decrease of the angle leads to an increase of the incremental plastic shear strain, while at the following stick stage, it is updated according to the present incremental plastic shear strain. Nodal velocities change at the two stages because of the use of dynamic equations even though a rate-and state-dependent law is not introduced. Effects of loading rate, fault width and maximum incremental plastic shear strain are investigated. To obtain size-independent stress-deformation curves, a slower loading is required for a finer mesh to ensure the same propagating distance of stress wave. For two intersecting faults or an echelon fault, a few small events are observed at the stick stage because of interactions among faults, whereas only one large event is observed at the slip stage. For a specimen with a bending fault, as the angle between two fault segments is large, the asynchronic softening and hardening of fault elements lead to a small stress drop at loading ends (stable sliding) rather than a saw-tooth-like behaviour (stick-slip). To validate the proposed model, a laboratory test is modelled quasi-statically that was performed on a specimen including an inclined fault oriented an angle of 60° with the horizontal direction in biaxial compression. The physical and numerical results agree well. Numerical results show that the stick-slip period is doubled if the loading velocity is halved. Compared with the rate-and state-dependent law, the present model is simple and can be implemented in FLAC-3D, capable of modelling the effects of creep, seepage and temperature. For complex faults under complex loading conditions, the proposed model can be used to identify faults prone to sliding or those with large stress drops, and to investigate active sequences of faults and their interactions. Advantages and disadvantages of square or quadrilateral meshes are also addressed, especially on the aspect of stick-slip modelling. For a bending or a single straight fault, a long stick-slip period and a low load-carrying capacity are obtained for quadrilateral meshes, but not for square meshes. © The Authors 2013.