This paper presents a theoretical analysis addressing the issue of splitting versus shear failure of cylindrical cavities. The analysis is based on bifurcation theory, and employs a Cosserat-Mohr-Coulomb flow theory of elastoplasficity with hardening and softening which is calibrated on conventional triaxial compression test data. The 'preference' for shear rs. splitting failure as a function of load conditions, material properties, etc. is addressed. In addition, the paper elaborates on the entirely different macroscopic features as exhibited by shear and splitting failure. The most important results are: (a) splitting failure shows a pronounced scale effect, whereas shear failure does not, and (b) the 'preference' for either splitting or shear cavity failure depends on constitufive properties, cavity size, and internal cavity support. Splitting failure appears to be favoured in stronger, more dilatant rocks and larger cavities, whereas shear failure appears to be favoured in very weak, non-dilatant rocks and/or smaller cavities. Moreover, small internal cavity support appears to favour shear failure, often leading to a significant increase in failure stress. The above results are in line with laboratory observations to date.
Loading experiments on cylindrical cavities in a wide variety of sandstones have shown that failure can take place either in 'splitting mode', leading to narrow 'cusp-shaped' breakouts, or it can take place in 'shearing mode' leading to broad 'dog-ear' breakouts (Van den Hoek et al. 1992, 1994a,b, 1996, 2000a; Haimson et aL 1993). In the latter case (shear failure), it is also possible that breakouts do not develop at all, but instead the cavity remains circular in shape, while shear bands are spiralling outwards from the cavity wall. The latter phenomenon has been observed especially in very weak sandstones (e.g. Van den Hoek et al. 2000b).
Figure 1 shows a schematic layout of both failure types. In the case of splitting (Fig. la), initial failure is characterised by a "buckling" of the cavity wall, whereas in the case of shear (Fig. lb), initial failure is characterised by curved shear bands. Figure 2 shows experimental examples of cusp-shaped breakouts (Fig. 2a: Castlegate sandstone) and spiralling shear bands (Fig. 2b: weakly consolidated artificial sandstone).
The scope of the paper is to analyze theoretically the issue of splitting versus shear failure at the cavity wall. The analysis is based on bifurcation theory, and employs a Cosserat-Mohr-Coulomb flow theory of elastoplasticity with hardening and softening which is calibrated on conventional triaxial compression test data. Previously, this theory was successfully applied to explain sand production behaviour in the field (Van den Hoek et al. 1996, 2000a), and size dependency of hollow cylinder strength observed in the laboratory on a variety of sandstones (Tronvoll et al. 1993, Papamichos and Van den Hoek, 1995).