Two sides of a fault: Grain-scale analysis of pore pressure control on fault slip

Pore fluid pressure in a fault zone can be altered by natural processes (e.g., mineral dehydration and thermal pressurization) and industrial operations involving subsurface fluid injection and extraction for the development of energy and water resources. However, the effect of pore pressure change on the stability and slip motion of a preexisting geologic fault remains poorly understood; yet, it is critical for the assessment of seismic hazard. Here, we develop a micromechanical model to investigate the effect of pore pressure on fault slip behavior. The model couples fluid flow on the network of pores with mechanical deformation of the skeleton of solid grains. Pore fluid exerts pressure force onto the grains, the motion of which is solved using the discrete element method. We conceptualize the fault zone as a gouge layer sandwiched between two blocks. We study fault stability in the presence of a pressure discontinuity across the gouge layer and compare it with the case of continuous (homogeneous) pore pressure. We focus on the onset of shear failure in the gouge layer and reproduce conditions where the failure plane is parallel to the fault. We show that when the pressure is discontinuous across the fault, the onset of slip occurs on the side with the higher pore pressure, and that this onset is controlled by the maximum pressure on both sides of the fault. The results shed new light on the use of the effective stress principle and the Coulomb failure criterion in evaluating the stability of a complex fault zone.

Figure 1

Schematic of the coupled hydromechanical model based on the discrete element method (DEM) and a pore network flow (PNF) model. (a) Pore network in a five-grain setup (transparent yellow spheres); the pores are shown by purple spheres and the throat by a green cylinder; the edges of the tetrahedral tessellation are shown with red lines. Each pore is composed of the void space within a tetrahedron whose four nodes are the centers of the surrounding grains. Each throat is defined by the open area within a triangular face of a tetrahedron. The pore volumes and throat conductances are calculated based on local geometry. (b) Grain pack (cut in half and rendered in 50% opaque yellow color) and accompanying pore network. (c) Schematic of the couplings in the DEM–PNF model.

Figure 2

Illustration of triangulation, pore network, and pore throat. (a) pore network in a five-grain setup; the pores are shown by purple spheres and the throat by a green cylinder; the edges of the tetrahedral tessellation are shown in red. Each pore is composed of the void space within a tetrahedron whose four nodes are the centers of the surrounding grains. The two pores have volumes $V_i$ and $V_j$, and pressures $p_i$ and $p_j$. Each pore throat having conductance $C_{ij}$ and length $l_{ij}$ is defined as the connection between two neighboring pores ($V_i$ and $V_j$) through the void space. (b) The pore throat conductance $C_{ij}$ is calculated based on the minimum cross-sectional area $A_{ij}^{\text{pt}}$ on a triangular face between tetrahedron $i$ and $j$ (the shaded area), and the perimeter $P_{ij}^{\text{pt}}$ associated with $A_{ij}^{\text{pt}}$.

Figure 3

(a) 3D block–gouge system composed of 7878 particles. The light green particles are unbonded, representing the gouge, while the blue particles are bonded, representing the blocks (fault walls). The origin of axes is placed at the center of the gouge layer. Rigid frictionless walls (not shown) are used to provide mechanical boundary conditions. Loading in the $x$ direction with constant velocity drives the system to slip failure. The front and back walls are assigned zero displacement condition ($u_y=0$). To reproduce relative motion with respect to the gouge layer, we impose zero vertical displacement at the top and bottom of the gouge layer ($u_z^g=0$). (b) Pore pressure cases. Cases 1, 4, and 5 represent continuous pressure across the fault, with Case 4 having a pressure half of that in Case 1, and Case 5 having zero pore pressure (dry system). Cases 2 and 3 represent discontinuous pressure across the fault, with a strong pressure gradient within the gouge layer.

Figure 4

Slip behavior for the block–gouge system. Particle displacement in the $z$ direction (left column) and contact force network with both color and link size representing force magnitude (right column) at horizontal strain ${\varepsilon }_h=3.1\times {10}^{-3}$. (a, b) Pore pressure Case 1; (c, d) Case 2; (e, f) Case 3; (g, h) Case 4; (i, j) Case 5.

Figure 5

Histogram of normal component of contact forces in the gouge layer for the scenario considered in the main text. (a) Pore pressure case 1; (b) pore pressure case 3.

Figure 6

(a) Vertical strain rate $\left[{\mathrm{s}}^{-1}\right]$ as a function of normal stress in the fault gouge. (b) Vertical strain rate $\left[{\mathrm{s}}^{-1}\right]$ as a function of effective normal stress ${\sigma }_n^{\text{eff}}={\sigma }_n-p^f$ with fault pressure $p^f=max(p^L,p^R)$.

Figure 7

Comparison of slip along a block–gouge interface between the fully coupled model and the simplified one-way coupled model. (a) The slip is simulated by providing a constant velocity to the block (as shown in blue); The left side and the right side of the system are given servocontrolled stress boundary The top and bottom boundaries of the gouge are given zero displacement condition; (b) Grain displacement ($z$ component) at $t=4$ ms simulated by the simplified model with one-way coupling; (c) Grain displacement ($z$ component) at $t=4$ ms simulated by the fully coupled model. (d) Pore pressure change (normalized by the horizontal stress) due to slip simulated by the fully coupled model; two cross sections ($y=0$ and $z=0$) are shown.