Strength criterion for rocks under compressive-tensile stresses and its application

Estimating in-situ stress with hydraulic borehole fracturing involves tensile strength of rock. Several strength criteria with three parameters result in tensile strengths with great differences, although they may describe the relation between strength of rock and confining pressure with low misfits. The exponential criterion provides acceptable magnitudes of tensile strengths for granites and over-estimates that for other rocks, but the criterion with tension cut-off is applicable to all rocks. The breakdown pressure will be lower than the shut-in pressure during hydraulic borehole fracturing, when the maximum horizontal principal stress is 2 times larger than the minor one; and it is not the peak value in the first cycle, but the point where the slope of pressure-time curve begins to decline.