Practical Estimates of Tensile Strength and Hoek-Brown Strength Parameter mi of Brittle Rocks
Practical Estimates of Tensile Strength and Hoek-Brown Strength Parameter mi of Brittle Rocks
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DOI：
10.1007/s00603-009-0053-1
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发表时间：
2010-03-01
影响因子：
6.2
通讯作者：
Cai, M.
中科院分区：
文献类型：
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作者：
Cai, M.
通过应用脆性破坏的格里菲斯应力准则，可以发现岩石的单轴抗压强度（σ(c)）是单轴抗拉强度（σ(t)）的8倍。即使考虑裂纹闭合，格里菲斯强度比也小于通常对岩石所测量的值。原因是格里菲斯理论仅涉及破坏的起始。在拉伸条件下，裂纹扩展是不稳定的，因此拉伸裂纹扩展应力（σ(cd))(t)和峰值抗拉强度σ(t)几乎与拉伸裂纹起始应力（σ(ci))(t)相同。另一方面，在以受压为主的条件下，裂纹起始后的裂纹扩展是稳定的。在受压时需要额外加载，以使应力从裂纹起始应力σ(ci)达到峰值强度σ(c)。建议根据强度比R = σ(c)/|σ(t)| = 8σ(c)/σ(ci)来估算坚硬脆性岩石的抗拉强度：σ(c)/σ(ci)这一项考虑了单轴压缩试验中拉伸和压缩时裂纹增长或扩展的差异。σ(c)/σ(ci)取决于岩石的非均质性，粗粒岩石比细粒岩石的值更大。σ(ci)可通过体积应变测量或声发射（AE）监测获得。确定强度比R后，可间接从|σ(t)| = σ(c)/R = σ(ci)/8得出抗拉强度。发现使用这种方法预测的抗拉强度与试验数据吻合良好。最后，给出了霍克 - 布朗强度参数m(i)的一种实用估算方法，并建议对某些脆性岩石采用双线段或多线段来表示霍克 - 布朗强度包络线。通过这种方式，像σ(t)和m(i)这样需要特殊试验（如直接拉伸（或巴西）试验和三轴压缩试验）来确定的岩石强度参数，可以从单轴压缩试验中合理估算出来。
By applying the Griffith stress criterion of brittle failure, one can find that the uniaxial compressive strength (sigma(c)) of rocks is eight times the value of the uniaxial tensile strength (sigma(t)). The Griffith strength ratio is smaller than what is normally measured for rocks, even with the consideration of crack closure. The reason is that Griffith's theories address only the initiation of failure. Under tensile conditions, the crack propagation is unstable so that the tensile crack propagation stress (sigma(cd))(t) and the peak tensile strength sigma(t) are almost identical to the tensile crack initiation stress (sigma(ci))(t). On the other hand, the crack growth after crack initiation is stable under a predominantly compressive condition. Additional loading is required in compression to bring the stress from the crack initiation stress sigma(ci) to the peak strength sigma(c). It is proposed to estimate the tensile strength of strong brittle rocks from the strength ratio of R = sigma(c)/vertical bar sigma(t)vertical bar = 8 sigma(c)/sigma(ci) : The term sigma(c)/sigma(ci) accounts for the difference of crack growth or propagation in tension and compression in uniaxial compression tests. sigma(c)/sigma(ci) depends on rock heterogeneity and is larger for coarse grained rocks than for fine grained rocks. sigma(ci) can be obtained from volumetric strain measurement or acoustic emission (AE) monitoring. With the strength ratio R determined, the tensile strength can be indirectly obtained from vertical bar sigma(t)vertical bar = sigma(c)/R = sigma(ci)/8 : It is found that the predicted tensile strengths using this method are in good agreement with test data. Finally, a practical estimate of the Hoek-Brown strength parameter m(i) is presented and a bi-segmental or multi-segmental representation of the Hoek-Brown strength envelope is suggested for some brittle rocks. In this fashion, the rock strength parameters like sigma(t) and m(i), which require specialty tests such as direct tensile (or Brazilian) and triaxial compression tests for their determination, can be reasonably estimated from uniaxial compression tests.