Theoretical analysis of the damaged zone around the borehole using different failure criteria

Actually, after drilling a borehole, some materials would be eliminated from the original rock mass. The exhumed materials no longer can carry the stresses transferred to the rock surrounding the borehole. The process represents a stress concentration in the rock around the borehole. The so-called borehole breakout failure results from an enhancement in shear stress on the borehole wall because of the excavation-induced increase of the hoop stress surrounding the wall. Vertical borehole breakouts generated via un-equal horizontal in-situ stresses are usually focused in two opposed areas along the least horizontal in-situ stress. Excavation cause loss of balance stresses around the borehole and also cause compressive stress concentration on the walls. Changes in stresses around the borehole may cause formation damage. This status results in other modes of borehole instability such as collapsing of the wall due to shearing failure. Breakout phenomenon (collapsed walls under shear failure) will occur by increased shear stress at the borehole wall which by itself is due to an increase in hoop stress on the wall. In this paper, the goal is to compare four failure criteria including, Mohr-Coulomb, Hoek-Brown, Griffith and Fairhurst to estimate the depth and angular width of the borehole wall in damaged zone, where the stresses are heterogeneous. The results show that damaged zone, undamaged zone and boundary curve of failure around the borehole, can be obtained using the function of failure criteria (F) in σ1-σ3 plane. The more that the area under the curves of these criteria would be in σ1-σ3 plane, the less damaged zone will occur around the borehole.  For instance, the area under the curve for Griffith criteria in σ1-σ3 plane, is less than the area of other criteria. So damaged area in Griffith criteria is more than 3 other criteria. Angular width obtained from Hoek-Brown criterion, Mohr-Coulomb criterion and Fairhrust criterion (unlike Griffith) coincide, because these 3 criteria cut the σ1 axis with the same width in σ1-σ3 plane. Also, with the constant value for difference of in-situ stresses (σd=σH-σh), depth of the failure in minimum in-situ stress direction is more in Griffith and Fairhrust criteria in compare with 2 other criteria. By comparing the failure criteria, it has been observed that, with an increase in in-situ stresses ratio (σH/σh), the results of Griffith and Fairhrust criteria are more close to experimental results in compare with 2 other criteria (Hoek-Brown and Mohr-Coulomb).