厚壁空心透水球体中流体诱导裂缝的起裂
Initiation of fluid-induced fracture in a thick-walled hollow permeable sphere
摘要：
在准稳态流动过程（排水响应）下，渗透性地质材料地层中的流体诱导断裂的起始受到Biot系数和地层尺寸的强烈影响。本文的目的是分析这些参数对厚壁空心可渗透球在孔内受注液作用下的初始破裂过程的影响。假设裂缝在起裂过程的硬化阶段是均匀分布的，将流固耦合问题描述为一个非线性常微分方程，并采用有限差分结合打靶法和牛顿法进行数值求解。有限差分程序也在弹性范围内得到了验证，即，在断裂开始之前，相对于上述微分方程的原始封闭形式的解析解。结果表明，球的名义强度随比奥系数的增大而增大，随尺寸的增大而减小。
英文摘要：
The initiation of fluid-induced fracture in formations of permeable geomaterials subjected to quasi-stationary flow processes (drained response) can be strongly affected by Biot's coefficient and the size of the formation. The aim of this paper is to analyse the influence of these parameters on the initial fracture process of a thick-walled hollow permeable sphere subjected to fluid injection in the hole. Assuming that fracture patterns are distributed uniformly during the hardening stage of the fracture initiation process, the coupled fluid-solid problem is described by a nonlinear ordinary differential equation, which is solved numerically by means of finite differences combined with shooting and Newton methods. The finite difference code has also been validated in the elastic range, i.e., before initiation of fracture, against an original closed-form analytical solution of the above differential equation. The results show that the nominal strength of the sphere increases with increasing Biot's coefficient and decreases with increasing size.
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