Cavity expansion in anisotropic rock

The determination of material constants is an important step towards the numerical simulation of boundary value problems. This simulation makes possible to optimize structures and to analyze failures. Cavity expansion tests is an important method to determine material constants and is often applied as field test in geotechnical engineering. It is of particular importance especially if we cannot extract samples and test them in the laboratory. If the considered material is assumed to be cross-anisotropic, cavity expansion tests cannot be used, because a mathematical equation to describe the obtained results, i.e. the displacement of the wall in dependence of the applied pressure and orientation of the lamination with respect to the cavity axis, is still missing. Thus, the measured values cannot be used towards determining the underlying material constants. The applicant has recently derived an approximative solution for the expansion of a cylindrical cavity in a cross- anisotropic material where the lamination axis does not coincide and is not normal to the axis of the cavity. However, the considered cavity expansion problem does inherently not allow to determine all five material constants of a linear elastic cross-anisotropic material. Therefore, further considerations must be introduced. Laying down material stability implies that the stiffness matrix is positive definite and this leads to a set of algebraic inequalities, the incorporation of which into the considered inverse problem is not yet clear. In addition, it is envisaged to evaluate the travel times of elastic waves in order to get the missing information. The underlying approximative solution must be checked against measurements. This can be done numerically, by means of 3D finite element calculations and with physical model tests carried out on artificial cross-anisotropic materials (since extraction of samples from pronouncedly schistous rock fails in most cases due to disintegration of the samples). Such an artificial material can be obtained with sandwich layers of isotropic materials having different stiffnesses. The proposed research will be carried out in cooperation with a research group at the Mining Institute in Novosibirsk of the Siberian Branch of the Russian Academy of Sciences.

Rocks composed of parallel layers are cross-anisotropic materials. The assessment of the material properties of cross-anisotropic rock requires laboratory tests with samples whose foliation has variable orientation relative to the loading axis. However, laboratory testing of rocks with pronounced foliation is associated with insuperable difficulties. The main reason is to be found in the inhomogeneity of natural rocks and difficulties to work with, e.g. disintegration during specimen extraction and preparation. As an alternative, field tests can be performed. Cavity expansion field tests, like radial jack tests and borehole dilatometer tests, seem to be promising methods to determine the properties of linearelastic, cross- anisotropic rock. An analytical solution describing the displacements of the cavity wall with respect to the applied pressure and the orientation of the foliation of linear-elastic, cross- anisotropic rock was missing, until a new approximate solution to determine the material properties of such materials based on cavity expansion tests was developed at the division of geotechnical and tunnel engineering of the university of Innsbruck. Data obtained from radial jack tests served to the inverse analysis of the problem. With known internal radial pressure, radius of the cavity, orientation of foliation and displacements obtained from a field test, the approximation yields material parameters which fit the measured displacements. Three- dimensional finite element modelling was used to simulate cavity expansion in linear-elastic, cross-anisotropic rock. Field measurements were then compared with the numerically calculated cavity wall displacements by implementing the material parameters as obtained from the described approximate solution. The results were also verified by modelling the problem with discrete elements. An alternative way to study the behaviour of cross- anisotropic materials through laboratory small-scale cavity expansion tests in an artificial cross-anisotropic material was also considered. The setup and evaluation of such tests and their feasibility were investigated and it turned out that it is hardly possible to manufacture such a laminate, because the glue applied onto the individual layers would render the response viscoelastic and, thus, the obtained laminate inappropriate to check solutions obtained with linear elasticity.