There is a wealth of experimental evidence that fracture initiation and breakdown pressures differ depending on in-situ stress status, rock properties, and injection conditions. However, the mechanism is not fully understood from a theoretical modeling perspective. In this study, a fully coupled plain-strain fracture model is proposed to interpret the mechanism of fracture initiation and breakdown pressures. The fracture model consists of fracture initiation and propagation governed by linear elastic fracture mechanics. The effects of wellbore compliance (or compressibility), solid-fluid coupling, and fracture multiscale propagation behavior are fully considered. The solid-fluid coupling equations are solved using the Newton–Raphson iterative method. The explicit time marching method is used to capture the fracture initiation process. An implicit time-stepping with the fracture tip asymptotic solution is used to capture fracture propagation fronts. The model is validated against the analytical solutions of the plane-strain model. Sensitivity analysis demonstrates that the initiation pressure mainly depends on rock properties, especially the fracture toughness. The peak pressure (breakdown pressure) is related to rock properties and injection conditions and usually occurs before the peak of the pressurization rate is reached. It increases with the injection rate, fluid viscosity, Young's modulus, and fracture toughness. The dimensionless inlet flux into the fracture can be used to determine the fracture initiation pressure. The pressurization rate during the fracture initiation stage is constant and can be used to assess wellbore compliance. Using a low injection rate and a low-viscosity fluid is beneficial to capturing the fracture initiation pressure. This study can help understand fracture initiation and propagation and interpret hydraulic fracture initiation and breakdown pressures.

大量实验证据表明，裂缝起始压力和破裂压力因地应力状态、岩石特性和注入条件而异。然而，从理论建模的角度来看，该机制并未完全理解。在这项研究中，提出了一个完全耦合的平应变断裂模型来解释裂缝起始和破裂压力的机制。断裂模型由线弹性断裂力学控制的断裂起始和扩展组成。充分考虑了井筒顺应性（或可压缩性）、固液耦合和裂缝多尺度扩展行为的影响。使用Newton-Raphson求解固流耦合方程迭代方法。显式时间推进法用于捕捉裂缝起始过程。使用裂缝尖端渐近解的隐式时间步长来捕获裂缝扩展前沿。该模型根据平面应变模型的解析解进行了验证。敏感性分析表明，起爆压力主要取决于岩石性质，尤其是断裂韧性。峰值压力（破坏压力）与岩石性质和注入条件有关，通常发生在加压速率达到峰值之前。它随着注入速率、流体粘度、杨氏模量和断裂韧性的增加而增加。进入裂缝的无量纲入口通量可用于确定裂缝起始压力。裂缝起始阶段的加压速率是恒定的，可用于评估井筒顺应性。使用低注入速率和低粘度流体有利于捕获裂缝起始压力。这项研究可以帮助了解裂缝的起始和扩展，并解释水力裂缝的起始和破裂压力。