Experiments and field monitoring have revealed that in block caving, fractures over the cave crown tend to form in narrow curved bands that are parallel or subparallel to the cave back surface. These fractures delineate curved shells of orebody between the bands and the cave back. The effectiveness of block caving hinges on the subsequent fracturing and fragmentation of these orebody shells. This study adopts a dual approach, combining thin spherical shell theory and full 3D numerical simulations along with principles of linear elastic fracture mechanics, to investigate the fracturing behaviour of these shells. Analytical analysis indicates that under axisymmetric loading, latitudinal tensile fractures predominantly initiate across the most part of the shell, occurring on both the upper and lower surfaces, except at a localised area. Additionally, longitudinal tensile fractures may initiate at the central area of the upper surface, while shear fractures tend to occur around the edge of the shell. Consequently, the shells become susceptible to fracturing, leading to the collapse or cave‐in of the orebody. Numerical simulations agree with these findings, illustrating that fracturing points within the shell region are longitudinally dispersed throughout the entire shell. Most of these fracturing points satisfy the criteria for tensile fracturing, particularly within the middle portion of the shell, aligning with the analytical results. Furthermore, simulations considering nonaxisymmetric loading patterns demonstrate that regions surrounding the caving cavity, aligned with the minimum principal in situ stress, exhibit heightened susceptibility to fracture initiation. This insight holds potential significance for optimising the design of the caving process.

中文翻译：

---

块体回落上方压裂分析：球壳理论方法和 BEM 数值模拟


实验和现场监测表明，在块状崩落中，洞冠上的裂缝往往形成与洞穴背面平行或次平行的狭窄弯曲带。这些裂缝在带和洞穴背面之间描绘了弯曲的矿体壳。块体崩落的有效性取决于这些矿体壳的后续破裂和碎裂。本研究采用双重方法，将薄球壳理论和全 3D 数值模拟以及线性弹性断裂力学原理相结合，以研究这些壳的断裂行为。分析表明，在轴对称载荷下，纬度拉伸断裂主要始于壳的大部分，发生在上表面和下表面，局部区域除外。此外，纵向拉伸断裂可能始于上表面的中心区域，而剪切断裂往往发生在壳的边缘周围。因此，贝壳变得容易破裂，导致矿体坍塌或塌陷。数值模拟与这些发现一致，表明壳区域内的断裂点纵向分散在整个壳中。这些压裂点中的大多数都满足拉伸压裂的标准，尤其是在壳体的中间部分，这与分析结果一致。此外，考虑非轴对称载荷模式的模拟表明，与最小主原位应力对齐的落洞腔周围区域表现出对裂缝萌生的高度敏感性。这种洞察力对于优化落落过程的设计具有潜在的意义。