A consistent fatigue phase-field model for dynamic pulsed fracture propagation in poroelastic media

This paper presents a thermodynamically consistent dynamic hydraulic-mechanical coupled mixed-mode fatigue phase-field model for simulating fracture propagation in poroelastic rocks under cyclic fluid load. A fatigue degradation function is introduced that significantly reduces fracture toughness as the number of cycles increases and history variables accumulate. Damage is driven by both elastic strain energy density and fluid energy. The model uses the Newmark integration method within a finite element framework and solves the nonlinear system of equations using the Newton-Raphson iterative algorithm. The model is validated through several two-dimensional problems, including a dynamic shear test, a single-edged fracture fatigue test, a Khristianovic-Geertsma-de Klerk model, and a pulse fracturing experiment. The effects of critical energy release rate, injection rate, and injection method on pulse fracture propagation are investigated under single-fracture conditions. Additionally, the effects of different injection rates on fracture propagation are examined for tri-cluster fractures in homogeneous and layered reservoirs. The results demonstrate that the model accurately predicts complex fracture morphology.