A simple method to estimate tensile strength and Hoek-Brown strength parameter mi of brittle rocks

Rock Engineering 2009 - Rock Engineering in Difficult Conditions
Abstract Direct tensile strength test of rocks is not routinely conducted because of the difficulty in specimen preparation. The Hoek-Brown strength parameter mi values need to be determined from a series of triaxial tests. Quite often, triaxial tests are not routinely conducted for most projects and engineers are forced to determine the mi values empirically, which could lead to large error and uncertainty. Hence, a simple and yet reliable method to estimate the tensile strength and Hoek-Brown strength parameter mi is desired.
Griffith’s theory is first reviewed in this study. The Griffith stress criterion of brittle failure predicts that the uniaxial compressive strength (?c) of rocks is eight times the value of the uniaxial tensile strength (?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 the Griffith’s theory addresses only the initiation of failure. Under tensile conditions, the crack propagation is unstable so that the tensile crack propagation stress (?cd)t and the peak tensile strength ?t are almost identical to the tensile crack initiation stress (?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 ?ci to the peak strength ?c.
It is proposed to estimate the tensile strength of strong brittle rocks from a strength ratio which is a modified version of the Griffith strength ratio, using the values of ?ci and ?c. The new strength ratio considers the difference of crack growth or propagation in tension and compression in uniaxial compression tests. It depends on rock heterogeneity and is larger for coarse grain sized rocks than for fine grain sized rocks. ?ci can be reliably obtained from volumetric strain measurement or acoustic emission (AE) monitoring. With the modified strength ratio determined, the tensile strength can be indirectly obtained. 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 mi is presented and a bi-segmental representation of the Hoek-Brown strength envelope is suggested. In this fashion, the rock strength parameters like ?t and mi, 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.
Keywords: Uniaxial compressive strength, crack propagation, AE, crack initiation, Volumetric strain, Griffith’s theory, Tensile strength
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