Abstract
AbstractShear‐based fracture propagation in fluid‐saturated porous materials is investigated using a displacement–pressure formulation that includes acceleration and inertial effects of the fluid. Pressure‐dependent plasticity with a nonassociated flow rule is adopted to realistically represent the stresses in the porous bulk material. The domain is discretized using unequal order T‐splines and cast into a finite element method using Bézier extraction. An implicit scheme is used for the temporal integration. The solid acceleration‐driven fluid flow reacts to stress waves, but it results in pressure oscillations. Adding fluid acceleration terms dampens these oscillations and increases the fluid pressure near the fracture tips. By simulating a typical shear fracture case, it is shown that stick‐slip like, or stepwise, fracture propagation occurs for a high permeability, also upon mesh refinement. The acceleration driven fluid flow results in a build‐up of pressure near the fracture tip. Once this pressure region encompasses the fracture tip, propagation arrests until the pressure has diffused away from the crack tip, after which propagation is resumed and the build‐up of pressure begins anew. This results in a stick‐slip like behavior, with large arrests in the fracture propagation. Stepwise propagation related to the initial conditions has also been observed, but disappears once the fracture length exceeds the size of the region influenced by the initial conditions.
Highlights
Seismic activity, either involving preexisting faults or new fractures, is related to changes in the interstitial fluid pressure in the surrounding porous rock.[1,2,3,4] Observations and laboratory experiments have shown that the presence of fluids can induce instabilities[5] and that increases in the fluid pressure can trigger earthquakes.[6]
The effect of terms that account for acceleration-driven fluid flow in the mass balance and separate inertia terms in the momentum balance is analyzed by adding these terms one-by-one
A pressure–displacement formulation has been presented for fluid-saturated porous media that includes accelerationdriven fluid flow and separate inertia terms
Summary
Either involving preexisting faults or new fractures, is related to changes in the interstitial fluid pressure in the surrounding porous rock.[1,2,3,4] Observations and laboratory experiments have shown that the presence of fluids can induce instabilities[5] and that increases in the fluid pressure can trigger earthquakes.[6]. Simulations have shown that the presence of these accelerations invalidates the assumption of a low-frequency response and that neglecting the fluid acceleration terms results in different solutions.[20] the fluid acceleration term in Darcy’s law damps the pressure and stress waves,[21,22,23] and results in different values for the stresses near the fracture tip, which has been shown using a simplified formulation.[24] when simulating porous materials with a relatively high porosity and permeability, neglecting this term causes differences in the solution.[25]. Our aim is to investigate stepwise shear fracture propagation observed in fluid-saturated porous materials For this purpose, we will first derive the governing equations, neglecting as few terms as possible, while adhering to the standard displacement–pressure formulation.
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