The paper suggests an algorithm for determining characteristics of the initial stress field in an intact rock mass based on the interpretation of field measurements of cross-section diameter length changes of a circular borehole (or opening).
When designing underground structures constituting with the surrounding rock mass a single deformable system the results obtained are essentially influenced by the characteristics of the initial stress field in the intact rock which are used as input - the principal stress value N1, the ratio of the principal stresses Λ= N2/N1 and the slope of the main axes of the initial stresses to the vertical and horizontal lines. These characteristics determine to a considerable degree the qualitative character of distribution of normal and tangential contact stresses (loads) along the perimeter of the support cross-section and therefore stresses and forces in the support sections. If, given the rock sale weight, the slope of the main axes γ = 0, the vertical principal initial stress N1 = H (- rock weight per unit volume, H - excavation depth), and rock lateral pressure coefficient can be approximately derived from the Academician A.N. Dinnik's formula λ = V o/(1-V), where Vo - Poisson's ratio of or the rock, then to design a support in a rock mass subjected to the action of tectonic forces the above characteristics should be determined from field measurements. One of the measuring procedures in current use is the method of parallel boreholes consisting in measuring changes in the lengths of the diameters of the cross-section of a circular unsupported borehole (opening) when excavating a parallel one near it, which causes additional displacements of the surface points. In order to interprete the results of the measurements performed by the method of parallel boreholes the authors use the solution of the plane problem of the elasticity theory for a medium weakened by two unequal circular holes (Fig. 1) and having the initial stresses б x(o), б y(o), τ(o). The problem is stated as an inverse one and consists in determining, from the known changes in diameter length of one of the holes caused by the presence of another hole the initial stresses б x(o), б y(o), τ(o) as well as the principal initial stresses N1, N2 and the slope of the greater principal stress to the line of the centres. If one of the principal stresses (N1 or N2) is known (e.g. N1 = H), the above solution can be used to determine the rock deformation modulus E o. In the primal problem the basic formulas for determining displacements of the points of the borehole cross-section contour are derived by D.I. Sherman's method using the theory of analytical functions of complex variable and the apparatus of complex series. In treating the inverse problem the increments of the diameter length changes caused by the influence of the second hole, i.e. the differences Δ d = Δ d2- Δ d1 are used as initial data rather than the changes themselves (Δd2).
