Abstract A new area of application of Fracture Mechanics methods is proposed: the determination of surface deformation induced by internal volume change (e.g. due to underground hydrocarbon extraction). The finite layer-like zone of volume alteration is modelled as a crack, that is as a continuous distribution of dislocation loops. This approach allows the determination of surface deformation and can serve as the basis for monitoring of the volume alteration from surface measurements. In a limiting case of nearly uniform deformation of the reservoir boundaries the model consists of a single dislocation loop (an inserted cylindrical body of a constant height) in half-space and results in simple approximate expressions for the normal and tangential displacement components of the free surface. For the example of subsidence in the Groningen gas field the proposed method produces more realistic results describing reality better than the traditional models based on representing the reservoir as a collection of independent dilation centres. Also, analytical expressions are proposed for the nuclei – the basic Green’s function type expressions that allow representation of a planar horizontal reservoir layer of an arbitrary shape as a distribution of infinitesimal dislocation loops. For the case of a cylindrical reservoir, the nuclei integration recovers the exact distribution of the surface displacements.

中文翻译：

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资源开采沉降问题的断裂力学方法

摘要 提出了断裂力学方法的一个新应用领域：确定由内部体积变化（例如，由于地下碳氢化合物提取）引起的表面变形。体积变化的有限层状区域被建模为裂纹，即位错环的连续分布。这种方法允许确定表面变形，并可作为监测表面测量体积变化的基础。在储层边界几乎均匀变形的极限情况下，该模型由半空间中的单个位错环（一个恒定高度的插入圆柱体）组成，并导致自由的法向和切向位移分量的简单近似表达式表面。对于格罗宁根气田下沉的例子，与基于将储层表示为独立膨胀中心集合的传统模型相比，所提出的方法产生了更真实的结果，更好地描述了现实。此外，还提出了核的解析表达式——基本的格林函数类型表达式，允许将任意形状的平面水平储层表示为无限小的位错环分布。对于圆柱形储层，核积分恢复了表面位移的精确分布。为核提出了解析表达式——基本的格林函数类型表达式，允许将任意形状的平面水平储层表示为无限小的位错环分布。对于圆柱形储层，核积分恢复了表面位移的精确分布。为核提出了解析表达式——基本的格林函数类型表达式，允许将任意形状的平面水平储层表示为无限小的位错环分布。对于圆柱形储层，核积分恢复了表面位移的精确分布。