Abstract It has been well recognized that the performance of a failure criterion to polyaxial strength data depends on both the type of failure criterion and the varying σ2-dependence of the rock. To incorporate the varying influence of the intermediate principal stress on rock failure at true triaxial or polyaxial stress states, a new modified explicit three-dimensional Hoek-Brown failure criterion has been proposed by combining the Mogi (1967) criterion and the generalized Hoek-Brown criterion. The difference between the modified and the original generalized Hoek-Brown criteria is the introduced term nσ2, which may correspond to the contribution of σ2 to the normal stress on the failure plane and directly quantify the amount of σ2-dependence for different rock types. The failure envelope of the modified three-dimensional Hoek-Brown criterion is a circumscribed curved hexagonal pyramid matching with the three outer apices of the original Hoek-Brown criterion in the principal stress space and a parabolic curve in σ1-σ2 or σ1-σ3 space. The applicability analysis of the proposed three-dimensional Hoek-Brown criterion along with five other failure criteria has been performed by applying them to the polyaxial strength data for eight rocks. The proposed modified Hoek-Brown criterion was validated to reproduce the trend of the test data reasonably and to achieve the least mean misfit in six out of eight rocks. The Zhang-Zhu, the Mogi (1971) and the Mogi-Coulomb criteria derived from the Mogi's postulate yielded comparable average fits to the polyaxial strength data compared to other three criteria. The classical two-dimensional Hoek-Brown criterion only worked well for rocks with intermediate or low σ2-dependence, while the Drucker-Prager criterion performed poorly in most cases. Overall, the formulated explicit three-dimensional Hoek-Brown criterion might make accurate predictions of the polyaxial strength for rocks with low to high σ2-dependence property at a variety of stress states. The best-fitting solutions for all the eight rocks indicate that the value of the weighting factor n accounting for σ2-dependence varies from 0.04 to 0.44 relying on the characteristics of rocks tested. Furthermore, it is reliable to appropriately evaluate the influence of σ2 by applying the modified three-dimensional Hoek-Brown criterion to triaxial strength data as was validated for three out of eight rock types.

中文翻译：

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新的改进显式三维 Hoek-Brown 破坏准则对八块岩石的适用性

摘要 众所周知，多轴强度数据的破坏准则的性能取决于破坏准则的类型和岩石的变化的 σ2 依赖性。为了结合中间主应力对真三轴或多轴应力状态下岩石破坏的变化影响，结合 Mogi (1967) 准则和广义 Hoek-Brown 准则，提出了一种新的改进的显式三维 Hoek-Brown 破坏准则。标准。修改后的和原始的广义 Hoek-Brown 准则的区别在于引入了 nσ2 项，它可能对应于 σ2 对破坏面上法向应力的贡献，并直接量化了不同岩石类型的 σ2 依赖量。修正后的三维 Hoek-Brown 准则的破坏包络线是与原始 Hoek-Brown 准则在主应力空间中的三个外顶点和σ1-σ2 或 σ1-σ3 空间中的抛物线相匹配的外接弯曲六棱锥. 通过将提出的三维 Hoek-Brown 准则和其他五个破坏准则应用于八块岩石的多轴强度数据，对其进行了适用性分析。所提出的修正 Hoek-Brown 准则经过验证，可以合理地再现测试数据的趋势，并在八块岩石中的六块岩石中实现最小的平均失配。与其他三个标准相比，Zhang-Zhu、Mogi (1971) 和源自 Mogi 假设的 Mogi-Coulomb 标准对多轴强度数据产生了可比较的平均拟合。经典的二维 Hoek-Brown 准则仅适用于具有中等或低 σ2 依赖性的岩石，而 Drucker-Prager 准则在大多数情况下表现不佳。总体而言，制定的显式三维 Hoek-Brown 准则可以准确预测在各种应力​​状态下具有低到高 σ2 依赖性的岩石的多轴强度。所有八块岩石的最佳拟合解决方案表明，根据所测试岩石的特性，考虑 σ2 依赖性的权重因子 n 的值从 0.04 到 0.44 不等。此外，通过将修改后的三维 Hoek-Brown 准则应用于三轴强度数据来适当评估 σ2 的影响是可靠的，这已针对八种岩石类型中的三种进行了验证。