The elastic moduli of porous or clastic rocks are not always constant but may increase with increasing minor principal stress. Previous studies of circular excavations in hydrostatic stress fields have shown that, for this class of rock, classical constant modulus linear elastic theory can lead to erroneous predictions of the initiation and extent of failure around excavations. A plane strain finite element program has been adapted to extend these solutions to the case in which the in situ stresses in the plane of the excavation cross-section are not hydrostatic. Previous conclusions are confirmed for non-axisymmetric loading. The influences of the ratio of the major and minor principal stresses in the plane of the cross-section and of the internal borehole pressure are evaluated. The boundary conditions used are shown to influence the numerical results obtained for cases involving stress dependent elastic moduli.
The development of reliable methods of predicting instabilities in deep boreholes provides a major challenge of considerable current interest. Any universally applicable method of analysis must be capable of accounting for a range of rock mass characteristics and environmental conditions (Guenot 1987, Guenot & Santarelli 1988). Among the factors to be considered is the fact that many of the porous or clastic rocks encountered in oil-and gas-field environments have elastic moduli which are not constant but increase with increasing minor principal Stress. Santarelli & Brown (1987) and Brown et al (1988) have shown that the use of classical linear elastic theory in these cases can lead to erroneous predictions of the initiation and extent of failure around axisymmetric excavations and to poor predictions of excavation induced deformations. Only rarely will the hydrostatic in situ stress fields assumed in the previous analyses be encountered in practice. More frequently, the principal in situ stresses in the plane of the borehole cross-section can be expected to be anisotropic. Accordingly, it is important that the previous studies be extended to the non-axisymmetric case. This paper presents plane strain finite element solutions for circular excavations (boreholes) with and without internal pressure made in rock whose modulus varies with minor principal stress in the manner determined by Santarelli (1987) for Carboniferous sandstone. The principal in situ stresses in the plane of the borehole cross-section may be either equal or unequal. Calculations are made only of elastic stresses and displacements. Important aspects of the overall problem including the complete poroelastic response of the rock (Detournay & Cheng, 1988) and localisation phenomena (Vardoulakis et al, 1988) are not considered.
Fig. 1 shows a circular excavation subject to an in situ stress field in which one of the principal stresses in the plane of the cross-section is parallel to the y-axis and of magnitude 100 MPa. (This represents a realistic value of the total overburden stress at a depth of about 4 km). The other in situ principal stress acts parallel to the x-axis and is allowed to vary from 100 to 300 MPa.
