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True Triaxial Stresses and the Brittle Fracture of Rock

机译：真三轴应力与岩石脆性断裂

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This paper reviews the efforts made in the last 100 years to characterize the effect of the intermediate principal stress σ 2 on brittle fracture of rocks, and on their strength criteria. The most common theories of failure in geomechanics, such as those of Coulomb, and Mohr, disregard σ 2 and are typically based on triaxial testing of cylindrical rock samples subjected to equal minimum and intermediate principal stresses (σ 3=σ 2). However, as early as 1915 Böker conducted conventional triaxial extension tests (σ 1=σ 2) on the same Carrara marble tested earlier in conventional triaxial compression by von Kármán that showed a different strength behavior. Efforts to incorporate the effect of σ 2 on rock strength continued in the second half of the last century through the work of Nadai, Drucker and Prager, Murrell, Handin, Wiebols and Cook, and others. In 1971 Mogi designed a high-capacity true triaxial testing machine, and was the first to obtain complete true triaxial strength criteria for several rocks based on experimental data. Following his pioneering work, several other laboratories developed equipment and conducted true triaxial tests revealing the extent of σ 2 effect on rock strength (e.g., Takahashi and Koide, Michelis, Smart, Wawersik). Testing equipment emulating Mogi's but considerably more compact was developed at the University of Wisconsin and used for true triaxial testing of some very strong crystalline rocks. Test results revealed three distinct compressive failure mechanisms, depending on loading mode and rock type: shear faulting resulting from extensile microcrack localization, multiple splitting along the σ 1 axis, and nondilatant shear failure. The true triaxial strength criterion for the KTB amphibolite derived from such tests was used in conjunction with logged breakout dimensions to estimate the maximum horizontal in situ stress in the KTB ultra deep scientific hole.
机译：本文回顾了过去100年中为表征中间主应力σ2 对岩石的脆性断裂及其强度标准所做的努力。地质力学中最常见的破坏理论，例如库仑和莫尔的破坏理论，忽略了σ2 ，并且通常基于圆柱岩样在三轴试验中受到相同的最小和中间主应力（σ3 =σ2 ）。然而，早在1915年，博克（Böker）就对同一卡拉拉大理石进行了常规的三轴拉伸试验（σ1 =σ2 ），该大理石早些时候由vonKármán在常规三轴压缩试验中表现出不同的强度性能。通过Nadai，Drucker和Prager，Murrell，Handin，Wiebols和Cook等人的工作，在上世纪下半叶，继续努力整合σ2 对岩石强度的影响。 1971年，Mogi设计了一种高容量的真三轴试验机，并且是第一台根据实验数据获得完整岩石真三轴强度标准的设备。在他的开创性工作之后，其他几个实验室开发了设备并进行了真正的三轴测试，揭示了σ2 对岩石强度的影响程度（例如Takahashi和Koide，Michelis，Smart，Wawersik）。威斯康星大学开发了模仿Mogi的但更紧凑的测试设备，用于一些非常坚固的晶体岩石的真正三轴测试。测试结果显示了三种不同的压缩破坏机理，具体取决于载荷模式和岩石类型：由微裂纹局部扩展引起的剪切断裂，沿σ1 轴的多次分裂以及非膨胀剪切破坏。由此类测试得出的KTB闪石的真实三轴强度标准与测井的突破尺寸一起用于估算KTB超深科学孔中的最大水平原位应力。

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