In fractured poroelastic media under high differential stress, the shearing of pre-existing fractures and faults and propagation of wing cracks can be induced by fluid injection. This paper presents a two-dimensional mathematical model and a numerical solution approach for coupling fluid flow with fracture shearing and propagation under hydraulic stimulation by fluid injection. Numerical challenges are related to the strong coupling between hydraulic and mechanical processes, the material discontinuity the fractures represent in the medium, and the strong effect that fracture deformation and propagation have on the physical processes. The solution approach is based on a two-level strategy that is classified into the coarse and fine levels. In the coarse level, flow in and poroelastic deformation of the matrix are coupled with the flow in the fractures and fracture contact mechanics, allowing fractures to frictionally slide. Fracture propagation is handled at the fine level, where the maximum tangential stress criterion triggers the propagation of fractures, and Paris' law governs the fracture growth processes. Simulations show how the shearing of a fracture due to fluid injection is linked to fracture propagation, including cases with hydraulically and mechanically interacting fractures.

在高差应力作用下的裂缝性多孔弹性介质中，流体注入可以引起预先存在的裂缝和断层的剪切以及翼裂缝的扩展。本文提出了一种二维数学模型和数值求解方法，用于在流体注入水力刺激下耦合流体流动与裂缝剪切和扩展。数值挑战与水力和机械过程之间的强耦合、裂缝在介质中所代表的材料不连续性以及裂缝变形和扩展对物理过程的强烈影响有关。解决方法基于分为粗略和精细级别的两级策略。在粗略的层面上，基质的流动和孔隙弹性变形与裂缝中的流动和裂缝接触力学相结合，使裂缝摩擦滑动。裂缝扩展在精细级别进行处理，其中最大切向应力准则触发裂缝扩展，而巴黎定律支配裂缝扩展过程。模拟显示了由于流体注入导致的裂缝剪切如何与裂缝扩展相关联，包括水力和机械相互作用裂缝的情况。