The geothermal energy program has resulted in an increased interest in the deformation and stability of relatively large diameter holes drilled deep into crystalline rocks in regions where the geothermal gradient is high. Knowledge of the response of the rock surrounding such holes can be gained providing that an adequate model can be constructed. For complete generality the model should be capable of analysis of a hole which is arbitrarily orientated with respect to the principal axes of the initial stress field and also any planes of elastic symmetry of the rock. Under these conditions the deformation of the rock around the hole will not, in general, be in plane strain. Taking the ¿ axis as the axis of the hole then, providing the hole is long, the axial strain will be constant and the axial displacement will be a linear function of ¿. The other components of displacement, and therefore all the components of the stress and strain tensors, are independent of ¿. This kind of deformation is a particular case of a kind referred to as antiplane-strain. In this paper, it is shown how this condition can be modeled very simply without resorting to a full three-dimensional analysis. The formulation of a finite element code making use of this approach is presented very briefly and shown to give results in good agreement with those obtained analytically. Finally, some calculations of stresses and displacements around chilled holes deep in hot, dry crystalline rock are introduced.
Drilling a borehole in any rock will result in disturbance of the initial stress and temperature states. When the hole is deep and the rock hot, these disturbances may be of practical significance as far as borehole closure and stability are concerned. Reviewing the literature, it is clear that this problem has not been extensively studied for the conditions that are likely to be encountered when drilling deep into hot, dry rock of the crystalline basement. Analysis of stresses around borehole has been mainly related to drilling in soft rock. In some cases the influence of the bottom of the hole is taken into account, but more commonly the hole is considered to be long and. an analysis conducted on the basis that the deformation will be in plane-strain. Often it is further assumed that the axial stress will be the intermediate principal stress and that it has no effect upon the strength of the rock. Whether these simplifications are reasonable depends-upon the nature of the rock and also the initial state of stress. To be completely general, however, full account should be taken of:
The magnitude and orientation of the principal initial stresses
The orientation of the hole
If all these factors are taken into account a conventional two-dimensional analysis assuming the deformation to be in plane-strain will not be adequate. In particular, such an analysis would not represent axial, or out of plane, displacements and associated stresses.