Analysis of borehole breakouts

Boreholes drilled into rock, which is subjected to stresses that amount to a significant fraction of the strength of the rock, may cause the rock to fail adjacent to the borehole surface. Often this results in the elongation of the cross section of the borehole in the direction of the minimum principal (compressive) stress orthogonal to the borehole axis. Such breakouts are valuable indicators of the direction of the minimum compressive stress orthogonal to the axis of the borehole. Their shapes may provide information about the magnitudes of both the maximum and minimum stresses relative to the strength of the rock. Borehole breakouts also may be impediments to drilling and to in situ measurement techniques, such as hydraulic fracturing. Observations and analyses of borehole breakouts raise three important questions. First, how does the shape of the borehole breakout evolve? Second, why are breakout shapes stable despite the very high compressive stress concentrations that they produce? Third, how is the shape of the breakout related to the magnitudes of the stresses in the rock? In this paper, extensile splitting of rock in unconfined, plane strain compression is assumed to be the process of rock failure adjacent to the circumference of the borehole, by which a breakout forms. To simulate the evolution of a borehole breakout, this process is combined with a numerical boundary element analysis of the stresses around a borehole as its cross section evolves from the originally circular shape to that of a stable breakout. The tangential stresses around a stable breakout cross section are found to be everywhere less than the unconfined, plane strain tensile or compressive strength of the rock. The stresses outside the stable breakout are found to be everywhere less than the limiting values of shear strength given by a Mohr-Coulomb criterion. In the regions of great stress concentrations at the ends of a breakout cross section, which have a pointed shape, the state of stress approaches that of equal biaxial compression in plane strain, as it does ahead of a mathematical crack or notch. The fact that the stresses around a breakout are less than the relevant strength establishes both the stability of the final breakout cross section and the appropriateness of an elastic analysis of the stresses. According to this model, the cross-sectional shapes of stable breakouts are not related uniquely to the state of stress and the strength of the rock. For example, stable breakouts created instantly in rock already subjected to stress are much larger than stable breakouts created in the same rock with a preexisting borehole by subsequently increasing the stresses to the same values. The results of drilling into an actual rock probably lie between these extremes. Modest changes in borehole cross section as a result of breakout do not alter significantly the minimum tangential (tensile) stress around a borehole with internal pressure from that given by the Kirsch solution for a circular hole subjected to the same stresses. Therefore hydraulic fracturing interpretations based on the Kirsch solution give the correct values for the far-field stresses.