No abstract

Coulomb's criterion for the shear fracture of a brittle material is that total shearing resistance is the sum of the cohesive shear strength (independent of direction) and the product of the effective normal stress and the coefficient of internal friction (a constant independent of normal stress). Mohr generalized this criterion by extending it to a three‐dimensional state of stress, and by allowing for a variable coefficient. The coefficients of internal and external (sliding) friction are not the same in general. Both tend to decrease with increasing normal stress, and their relative magnitudes may determine if failure occurs by new shear fracturing or by slip on pre‐existing cohesionless surfaces like joints in rocks.

Experiments have shown that the deformation of rocks under high confining pressures cannot be described by terms based on ordinary experience. The writers believe there are only three fundamental macroscopic processes at work: extension fracturing, faulting, and uniform flow. The first involves separation across a plane of no shear normal to the direction of least principal stress and includes tensile fracture as a special case. Faulting involves a shearing displacement and occurs with or without loss of cohesion. It includes shear fracturing as a special case and may occur along a plane inclined at from a few degrees to 45° to the direction of maximum principal stress. From the standpoint of the stress-strain curve, faulting without loss of cohesion is indistinguishable from flow. (The three flow mechanisms-cataclasis, gliding, and recrystallization-cannot always be distinguished either.) Examples of experimental boudins are presented to illustrate these categories of deformation.The field evidence is that earthquakes are accompanied by shearing displacements and are therefore due to faulting in the general sense. Since stored elastic strain energy is released, there must be at least a momentary and local loss of cohesion. A crack then propagates at close to the speed of sound. For deep-focus earthquakes (down to 700 km) certainly, and most probably even for shallow disturbances (a few tens of kilometers), ordinary Coulomb fracture is impossible. The internal friction of dry rocks under tens or hundreds of thousands of bars pressure would demand impossibly high shearing stresses of many kilobars. The most reasonable mechanism of energy release at great depth is a phase change, and the most probable phase change is melting.Calculations suggest that, once a crack or a flaw exists, there is ample elastic energy to propagate the crack by shear melting even if the stress difference is only a few tens of bars. It is, of course, inconceivable that an open crack could exist at depth, so that the most baffling problem is the nature of a flaw of the Griffith type under these conditions. Although it is little more than speculation, we suggest that the flaw may be a pocket of already molten rock or of its more volatile constituents. This idea receives some support from the intimate association of earthquake epicenters and zones of volcanic activity. EXPERIMENTAL EVIDENCE CLASSIFICATION OF FRACTURE AND FLOWObservations by the writers and others indicate that the macroscopic deformation of rocks and minerals deformed at high confining pressures in the laboratory (that is, in triaxial compression tests) can be described in terms of three principal categories of behavior-extension fractures, faults, and uniform flow. How the material will deform appears to depend upon its relative ductility-that is, upon the amount of permanent deformation achievable prior to rupture. Ductility depends upon the composition and structure of the material and also upon the magnitudes of the con-•Publication No. 172,

The mechanical anisotropy of Four‐mile gneiss has been investigated in a series of uniaxial and triaxial, compression and extension experiments performed at confining pressures Pc up to 400 MPa, constant strain rates ε from 1.6×10−6 to 1.5×10−4 s−1, and temperatures T from 25° to 800°C on cylindrical and notched samples oriented with respect to foliation (S) and lineation (L). Differential stresses measured both at the onset of yielding and at failure vary with specimen orientation, with maximum compressive strengths exhibited by samples cored perpendicular to S and minimum strengths exhibited by samples cored at 45° to both S and L. While failure strengths are influenced most strongly by the orientation of S, they appear to depend upon the orientation of L as well. An orthorhombic failure criterion, generalized from a nonlinear Mohr‐Coulomb relation, has been considered with quadratic and linear stress terms resembling those of invariants J2 and I1, respectively, and material parameters estimated by nonlinear regression methods. Satisfactory fits were achieved for results at T = 25°C as well as T = 700°C. Fracture strengths are relatively insensitive to changes in T and ε and the anisotropy exhibited at T = 700°C is remarkably similar to that measured at T = 25°C. Relatively small reductions in strength observed at elevated temperatures are probably due to the influence of thermally induced microcracks. Mechanisms of deformation and sources of anisotropy have been identified by examining microstructures developed in deformed specimens and observing their relationships to those fabric elements initially present in the starting material. Throughgoing shear fractures developed in samples shortened in all orientations with respect to S and L by the coalescence of microcracks in feldspar and quartz grains, as reported for isotropic granites. However, inelastic strains within mica grains were accommodated by slip, frictional sliding, and kinking, and deformation of favorably oriented micas appears to have led to local stress concentrations in neighboring phases that result in nucleation of tensile microcracks. Both S and L are defined by the preferred orientations of micas, and a simple model involving crack nucleation around oriented mica grains is proposed to explain the anisotropy observed.

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.