Introduction to Suggested Methods for Failure Criteria

Accurate assessment of rock strength is necessary for the rational design of underground structures, for the evaluation of wellbore stability, for the determination of in situ stresses (e.g., hydraulic fracturing, borehole breakouts, drilling-induced cracks), and as part of geophysical research such as faulting and earthquake mechanics. In engineering fields, the stress condition by which ultimate strength is reached is referred to as the ‘‘failure criterion’’. Failure criteria are often expressed in terms of the major principal compressive stress r1 that rocks can sustain for given values of the other two principal stresses, r2 and r3. In its most general form, this can be expressed as r1 = f1 (r2, r3 )o rf2 (r1, r2, r3) = 0 (Scholz 1990) where f1 or f2 are functions that vary with the selected criterion and can be determined theoretically, empirically or from laboratory tests (in some failure criteria, the effect of r2 is not considered and in that case the functions f1 or f2 are independent of r2). The convention used is positive for compression, and it is implied that failure is expressed in terms of effective stresses; correspondingly, expressions such as f2 (r1, r2, r3) = 0 and f2 (r 0 1, r 0 2, r 0 3) = 0 are used interchangeably.