Fluid Flux Crack «FAST →»

Abstract: This paper presents a novel computational framework for modeling the interaction between fluid flux and crack propagation in saturated porous media. We derive a thermodynamically consistent model coupling the phase-field approach to fracture with the theory of porous media. Unlike traditional discrete fracture models, the proposed method treats the crack geometry as a diffuse interface, allowing for the simulation of complex crack patterns—including nucleation, branching, and coalescence—driven by fluid pressure. We analyze the influence of fluid flux viscosity and injection rates on the stress intensity factors and crack tip velocity. Numerical examples demonstrate the robustness of the scheme in capturing the transition from toughness-dominated to viscosity-dominated propagation regimes.

Keywords: Fluid-Structure Interaction, Phase-Field, Hydraulic Fracturing, Porous Media, Crack Propagation.

We consider a domain $\Omega$ containing a crack $\Gamma$. The system is defined by two primary variables: the solid displacement field $\mathbfu$ and the fluid pressure field $p$.

To avoid tracking the discrete crack, we introduce a phase-field variable $d(\mathbfx, t) \in [0, 1]$, where $d=0$ represents the intact solid and $d=1$ represents the fully broken material. The crack surface density is approximated as: $$ \Gamma_l(d) = \int_\Omega \left( \frac12ld^2 + \fracl2|\nabla d|^2 \right) dV $$ where $l$ is a length scale parameter governing the width of the diffuse crack.