Abstract Rock indentation is the basic process in drilling and excavation from the mechanical points of view. A better understanding of the fundamental mechanism of rock-indenter interaction is of great significance. This paper proposes a semi-analytical model (SAM) to analyze rock fragmentation processes induced by indentation loads. In SAM, the analytical expressions of the stress and strain relationship of each two elements are obtained based on the theory of continuum mechanics. The numerical approaches including the conjugate gradient methods, fast Fourier transform, and fix-point iteration are applied to solve the unknowns of the model. In the proposed model, rocks are considered as elasto-brittle, and the damage threshold is described by the Mohr-Coulomb failure criterion. Also, a fracture element is treated as an inhomogeneity and tackled by the equivalent inclusion method. The present model can precisely capture the coupling between rock fragmentation and contact status. Thus, the developments of the crushed zone and cracked zone can be duplicated well. To reveal the potential applications of the model, the effects of confining pressure, rock inhomogeneity, and indenter geometry on rock indentation are also carefully investigated.

中文翻译：

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用于分析压头引起的岩石破碎的半解析接触模型

摘要 从力学角度看，岩石压痕是钻孔和开挖过程中的基本过程。更好地理解岩石-压头相互作用的基本机制具有重要意义。本文提出了一种半解析模型（SAM）来分析压痕载荷引起的岩石破碎过程。在SAM中，基于连续介质力学理论，得到了每两个单元应力应变关系的解析表达式。应用共轭梯度法、快速傅立叶变换和定点迭代等数值方法求解模型的未知数。在所提出的模型中，岩石被认为是弹性脆性的，损伤阈值由 Mohr-Coulomb 破坏准则描述。还，断裂元素被视为不均匀性，并通过等效包含方法处理。本模型可以精确捕捉岩石破碎与接触状态之间的耦合。因此，破碎区和裂纹区的发展可以很好地复制。为了揭示模型的潜在应用，还仔细研究了围压、岩石不均匀性和压头几何形状对岩石压痕的影响。