Modelling partially-emptied compaction bands induced by borehole drilling

Drilling into rock blocks subjected to critical far-field stresses can result in localized failure around the created borehole, manifested by the formation of two diametrically opposed breakouts. In weakly bonded quartz-rich porous sandstones breakouts take the form of narrow tabular (slot-like) openings extending along a plane perpendicular to the maximum applied-stress direction. SEM images strongly suggest that these breakouts are compaction bands (CB's) that have been emptied to different degrees. Debonded grains, some whole, others cracked or crushed, within the compaction band are totally or partially removed by the circulating drilling fluid, creating the breakout. A new analytical model is developed here, which computes the stress field around partially-emptied CBs and predicts the expected lengths of these defects and their dependence on borehole radius and the extent of the CB emptying by the drilling fluid. It is found that boreholes with larger radius generate longer partially-emptied CBs. The results also demonstrate that when the ratio of the filled to the emptied part of a CB increases (addressing a smaller drilling fluid flow rate), the resulting total length of partially-emptied CB decreases. Both of these findings are in good agreement with results of drilling experiments conducted by Sheets and Haimson (2004).