Perhaps the most important mechanical property of rock is its compressive strength. Strength criteria such as the Coulomb, Mohr, or Hoek-Brown, are strictly correct only when the intermediate and least principal stresses are equal (σ2 = σ3). At the University of Wisconsin we employ a new true triaxial testing apparatus that enables the application of three unequal principal stresses to rectangular prismatic specimens. Comprehensive series of tests on several rock types have demonstrated that, contrary to common criteria, the compressive strength (peak σ1) for a given 3 increases significantly with the magnitude of σ2, reaching levels of up to 10–100% higher than the peak σ1 when σ2 = σ3. The true triaxial strength criterion is obtained by plotting all test results in a modified Nadai (1950) domain, in which the data points are best fit by a power function in which the octahedral shear stress, τ oct, at failure is related to the mean stress acting on the plane of failure, σ m,2: τ oct = A σm,2B τ increases with the magnitude of 2, thus retarding the onset of the failure process. Moreover, the dip angle of the fault at failure rises monotonically with 2 for fixed σ3, again contrasting commonly used criteria.


The most common rock strength criteria presently in use, such as Mohr-Coulomb, and Hoek-Brown, are in essence two dimensional, in that they do not incorporate the third (intermediate) principal stress. In this keynote paper I briefly review previous work over the last century that revealed that the intermediate principal stress σ2 does contribute to and should be included in rock strength criteria. The effect of σ2 was first observed in conventional triaxial tests in which failure, or brittle fracture, was brought about in cylindrical specimens that were subjected axially to one principal stress, and laterally to confining fluid pressure, simulating the case in which the other two principal stresses are equal. The results of axial compression tests versus those under axial extension, lead to a strong suspicion that the role of the intermediate principal stress cannot be ignored, although it required further studies. This brought about the design and use of true triaxial (also called polyaxial) testing machines that enable a more detailed recording of rock strength under a general state of stress (Mogi, 1971, Haimson, 2006).

We highlight several aspects of rock strength and deformation under true triaxial loading obtained at the University of Wisconsin on several igneous metamorphic, and sedimentary rocks, all showing a consistent mechanical behavior and strength criterion, clearly affected by the intermediate principal stress, and not previously recognized from conventional triaxial tests.


The role of the applied stresses in the brittle failure of rock has been appreciated since the early stages of civilization.

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