The viability and success of a deep mining or tunnelling project is dependent on a safe, reliable support design. In highly-stressed brittle rock, this design must properly account for the excessive deformations and bulking that can occur due to stress-induced extensional fracturing (referred to as spalling or slabbing) near the excavation boundary. Important is the recognition that stress-induced brittle fracturing is dominated by an extensional fracture mode with a directional dilation component that is highly sensitive to 3-D confinement. This behaviour differs from that represented by popular elastoplastic yield and dilation models used in commercial numerical modelling software (e.g., Mohr-Coulomb) that have been developed based on experiences involving ductile behaviour and shear in soils and weak rocks. Recent experiences suggest that these are inappropriate for robust design in brittle rock and can be dangerously misleading. The importance of the dilation model and its implementation through a flow rule – which determines the relative incremental plastic straining under a specific stress state and at a specific plastic straining history – has particularly been overlooked. Numerical analyses in most cases adopt the oversimplifying assumption of a uniform dilation model (that is independent of confinement and plastic strain history), using as input a constant dilation angle $\psi$. This imposes significant limitations in modelling the extent of the yielding zone and the resulting displacements. More advanced dilation models exist. However, they suffer from two key deficiencies: i) most do not account for the influence of the intermediate principal stress, ${\sigma }_2$, on the directionality and magnitude of dilation; and ii) many require numerous empirical parameters or variables that do not have physical meaning (neither phenomenologically, nor micro-mechanically), making it difficult for practitioners to intuitively understand the influence and sensitivity of each parameter on the modelled response. This paper, presented in two parts, reviews the mathematical expression of the flow rule and its physical meaning in relation to brittle fracturing, and addresses the deficiencies in current dilation models by developing a new non-potential flow rule that accounts for the directionality and 3-D confinement-dependency of dilation (i.e., both ${\sigma }_3$- and ${\sigma }_2$-dependency), and uses parameters/variables that have physical meaning. In Part 1, we present a new framework for understanding and modelling the 3-D directionality of plastic deformations in Cartesian coordinates using what we call Plastic Strain Increments Ratios (PSIRs). The 3-D PSIRs are phenomenologically meaningful as they describe relative plastic straining. More importantly, we show that they are micro-mechanically meaningful as they associate the 3-D directionality of dilation with the different 3-D fracturing modes observed in intact brittle rock under various polyaxial stress states. In the Part 2 companion paper, we use these PSIRs to develop and derive the formulation of a new dilation model involving a non-potential 3-D confinement-dependent flow rule.

深部采矿或隧道工程的可行性和成功取决于安全、可靠的支撑设计。在高应力脆性岩石中，这种设计必须适当考虑由于开挖边界附近的应力引起的拉伸破裂（称为剥落或板裂）而可能发生的过度变形和膨胀。重要的是认识到应力诱导的脆性压裂由具有对 3-D 限制高度敏感的定向膨胀分量的拉伸断裂模式支配。这种行为不同于商业数值建模软件（例如，Mohr-Coulomb）中使用的流行弹塑性屈服和膨胀模型所代表的行为，这些模型是基于土壤和软弱岩石中的延性行为和剪切的经验开发的。最近的经验表明，这些不适用于脆性岩石的稳健设计，并且可能会产生危险的误导。膨胀模型及其通过流动法则实现的重要性——它决定了在特定应力状态和特定塑性应变历史下的相对增量塑性应变——尤其被忽视了。在大多数情况下，数值分析采用均匀膨胀模型的过度简化假设（与约束和塑性应变历史无关），使用恒定膨胀角作为输入 膨胀模型及其通过流动法则实现的重要性——它决定了在特定应力状态和特定塑性应变历史下的相对增量塑性应变——尤其被忽视了。在大多数情况下，数值分析采用均匀膨胀模型的过度简化假设（与约束和塑性应变历史无关），使用恒定膨胀角作为输入 膨胀模型及其通过流动法则实现的重要性——它决定了在特定应力状态和特定塑性应变历史下的相对增量塑性应变——尤其被忽视了。在大多数情况下，数值分析采用统一膨胀模型的过度简化假设（独立于约束和塑性应变历史），使用恒定膨胀角作为输入$\psi$. 这对模拟屈服区的范围和由此产生的位移施加了很大的限制。存在更高级的扩张模型。然而，它们有两个关键缺陷：i) 大多数没有考虑中间主应力的影响，${\sigma }_2$，关于膨胀的方向性和幅度；ii) 许多需要大量没有物理意义的经验参数或变量（无论是现象学上还是微观机械上），这使得从业者很难直观地理解每个参数对建模响应的影响和敏感性。本文分为两部分，回顾了流动法则的数学表达式及其与脆性压裂相关的物理意义，并通过开发一种新的非势能流动法则来解决当前膨胀模型的不足，该法则考虑了方向性和 3 -D 限制依赖的扩张（即，两者都${\sigma }_3$- 和 ${\sigma }_2$-dependency），并使用具有物理意义的参数/变量。在第 1 部分中，我们提出了一个新框架，用于使用我们所谓的塑性应变增量比 (PSIR)来理解和建模笛卡尔坐标中塑性变形的 3D 方向性。3-D PSIR 具有现象学意义，因为它们描述了相对塑性应变。更重要的是，我们表明它们在微观力学上是有意义的，因为它们将膨胀的 3-D 方向性与在各种多轴应力状态下在完整脆性岩石中观察到的不同 3-D 破裂模式相关联。在第 2 部分配套论文中，我们使用这些 PSIR 来开发和推导新的膨胀模型的公式，该模型涉及非潜在的 3-D 约束相关流动规则。