Effects of the intermediate principal stress on the failure of limestone, dolomite, and glass at different temperatures and strain rates

Abstract

Strength and ductility of ordinarily brittle substances are commonly observed to increase with mean pressure. However, since the pioneering work of von Kármán and of Böker fifty years ago, it has been recognized that the effects differ from compression (σ1 > σ2 = σ3) to extension (σ3 < σ2 = σ1) tests, where subscripts denote maximum, intermediate, and minimum principal (compressive) stresses. This difference has been ascribed to the influence of σ2, but, to our knowledge, it has not previously been quantitatively demonstrated. By subjecting jacketed cylinders to combined triaxial compression or extension and torsion, one can obtain relative values of σ2 that lie between the limits σ2 = σ1 and σ2 = σ3; in torsion alone σ2 lies midway between. The data from different types of test are conveniently compared by plotting octahedral stress τoct against mean pressure Pm at fracture or yielding. Tests have been done at temperatures of 25 to 500°C, confining pressure to 10 kb, and different strain rates (10−4 to 10−7 per second) on 1‐ by 2‐cm solid cylinders and 1.2‐ by 2.5‐cm hollow cylinders (0.7‐mm wall) of homogeneous, statistically Isotropic Solenhofen limestone, Blair dolomite, and glass. At strain rates near 10−4 per second at 25°C, the τoct versus Pm curves for limestone are essentially linear and reflect brittle behavior at relatively low pressures. In compression, failure occurs by shear fracturing; in extension and torsion, tensile fracture dominates. The shear strength is dependent upon mean pressure but tensile breaking strength is not. At intermediate pressures the curves become concave toward the Pm axis. This is associated with transitional behavior, faulting in all three types of test. This brittle‐ductile transition occurs at 2.7 and 5.4 kb in compression and extension, respectively; in torsion it is near 4.0 kb. This strongly suggests that ductility is a linear function of the relative magnitude of the intermediate principal stress. At high pressures all curves tend to approach the same asymptote, τoct = constant. The results for dolomite and glass are similar. Increasing the temperature or decreasing the strain rate tends to lower the transition confining pressures for all states of stress.

A Failure Criterion for Rocks Based on True Triaxial Testing

“…(1) is that when applied to individual plots of r 1 at failure as a function of r 2 for constant r 3 (Fig. 1a, for example), it predicts that the strength when r 2 = r 1 is the same as when r 2 = r 3 , which is not in agreement with previous conventional triaxial test results, in which strength in triaxial extension was shown to be generally higher by some 10-20 % than that in triaxial compression (Murrell 1963;Handin et al 1967). Two counter arguments are noted: (1) the failure criterion represented by Eq.…”

“…The significant observation by Murrell (1963) and Handin et al (1967) that rock compressive strength in experiments conducted in conventional triaxial extension (r 1 = r 2 [ r 3 ) is higher than in conventional triaxial compression (r 1 [ r 2 = r 3 ), provided convincing evidence that the effect of the intermediate principal stress on rock failure cannot be ignored and should be further studied. In a 1971 seminal paper, Mogi (1971) reported the results of tests conducted in a true triaxial testing apparatus that enabled the application of three independent and unequal orthogonal compressive loads to each pair of faces of a rectangular prismatic rock sample.…”

The Mohr–Coulomb criterion for intact rock strength and friction – a re-evaluation and consideration of failure under polyaxial stresses

“…3). This arrangement was first described and used by Heard (1960Heard ( , 1963Heard ( , 1972). Thus specimens are tested in axisymmetric extension (not tension), in which the radial hydrostatic confining pressure provides the maximum (and intermediate) principal stresses, and the axial stress becomes σ 3 .…”

“…Several studies have been made of rock failure under more general polyaxial stress states, σ 1 = σ 2 = σ 3 (e.g. Handin et al, 1967;Mogi, 1967Mogi, , 1971Kern and Karl, 1969;Reches and Dieterich, 1983;Takahashi and Koide, 1989;Song and Haimson, 1997;Chang and Haimson, 2000;Chang, 2000, 2002;Smart, 1995), and there have been many reanalyses of such previously published data in attempts to find the most appropriate failure criterion to describe them (e.g. Colmenares and Zoback, 2002;Zimmerman, 2005, 2006;You, 2009;Kwaśniewski, 2012Kwaśniewski, , 2013 and applications of these criteria to problems such as the estimation of far-field stresses from the analysis of hydraulic fractures and borehole breakouts (e.g.…”

A compressive strength criterion for anisotropic rock materials

“…Nevertheless, in many cases none of these criteria is satisfactory. They fail to correlate experimental results under complex stress states (10,11). There have been more recently several attempts to develop more adequate criteria such as those depicted in (12,13).…”