# Break-Out of Boreholes

When the mass of rock (or concrete) in which a borehole has been drilled is subjected to large compressive stresses, it may suddenly collapse in a brittle manner. This type of failure is called the break-out. The classical approach to the break-out has been by plasticity. However, because the failure occurs by cracking, fracture mechanics appears to be more appropriate. Its use, of course, inevitably leads to size effect, which is known to occur in the break-out of boreholes in rock, as experimentally demonstrated by Nesetova and Lajtai (1973), Carter (1992), Carter, Lajtni and Yuan (1992), Yuan, Lajtai and Ayari (1993), and Haimson and Herrick (1989).

An approximate energy-based analytical solution of the break-out has been obtained (Bazant, Lin and Lippmann 1993) under the simplifying assumption that the splitting cracks occupy a growing elliptical zone as sketched in Fig. 10.5.9 (although in reality this zone is narrower and closer to a triangle). The assumption of an elliptical boundary permits the energy release from the surrounding infinite solid to be easily calculated (Bazant, Lin and Lippmann 1993) according to Fshelby’s (1956) theorem for uniform eigenstrains in ellipsoidal inclusions in infinite medium. According to the theorem (see, e. g., Mura 1987), the following approximate expression for the energy release from the infinite rock mass has been derived:

in which R ~ borehole radius, a — principal axis of the ellipse (Fig. 10.5.9), !>0 and ayao – remote

principal stresses, E = Young’s modulus of the rock, and iz — Poisson ratio. A similar analysis as that for the propagating band of axial splitting cracks, already explained in Section 9.5, has provided a break-out stress formula of the type

where Co and C are constants.

Figure 10.5.10 Hillerborg’s (1990) analysis of bending of reinforced concrete beam: (a) sketch of the failure cross section; (b) stress-strain curve in compression; (c) no-tension zone (L-y1), clastic zone (A-В), and softening zone (В-C)’, (d) strain profile;, (e) stress profile; (f) moment-curvature diagrams for various sizes; (g) stress-strain curve in compression according to the CEB-F1P Model Code; (h) stress-strain curve with size-dependent cut-off proposed by Hillerborg (1990).