This paper examines the axisymmetric problem of a penny-shaped crack located in a poroelastic halfspace that is modelled by Biot poroelasticity. The paper first examines the axisymmetric problem of the mechanics of fluid injection over a circular area within a halfspace that would create the skeletal stress state necessary to initiate fracture. The triggering of the fracture is assumed to create an axisymmetric penny-shaped crack whose surfaces will be subjected to fluid pressure. The mechanics of the penny-shaped crack in terms of its potential to extend in an axisymmetric fashion is examined by formulating the poroelastic mixed boundary value problem and solving the coupled Fredholm integral equations of the second-kind obtained through successive applications of integral transform techniques. The analysis of the poroelasticity problem of fluid-injection into the crack gives rise to time-dependent skeletal stress intensity factors (SIFs) at the crack tip; these are combined with a mixed-mode brittle skeletal fracture criterion to establish the injection pressures that can lead to the extension of the penny-shaped crack in a self-similar fashion.

本文研究了用Biot多孔弹性模型建模的位于多孔弹性半空间中的一分钱形裂纹的轴对称问题。本文首先研究了半空间内圆形区域上流体注入力学的轴对称问题，该问题将产生引发断裂所需的骨架应力状态。假定断裂的触发会产生一个轴对称的便士形裂缝，其表面将承受流体压力。通过公式化多孔弹性混合边值问题并求解通过连续应用积分变换技术获得的第二类耦合的Fredholm积分方程，研究了便士形裂纹就其以轴对称方式扩展的潜力而言的力学。对流体注入裂纹的孔隙弹性问题的分析导致了裂纹尖端的随时间变化的骨架应力强度因子（SIF）。这些与混合模式脆性骨骼断裂准则相结合，以建立可导致自相似形裂纹扩展的注射压力。