Rocks composed of parallel layers (sedimentation or schistosity) belong to the so-called cross-anisotropic materials. The determination of the material properties of these rocks requires laboratory tests in samples whose foliation has variable orientations with respect to the loading axes. However this is often not feasible for rocks with pronounced foliation: the rock disintegrates during the extraction of the samples.

Another possibility for the estimation of the material properties could be the execution of field tests which capture the behavior of the rock mass in-situ, e.g. cavity expansion tests. An analytical solution describing the displacements of the cavity wall with respect to the applied pressure and the orientation of the foliation is still missing. Thus, the determination of the material properties by means of in-situ measurements has been impossible.

A new approximate solution is presented in this paper. Based on the known analytical expression for the ground line in elastic isotropic rock, it is observed that the displacement of the cavity wall can be obtained by considering the stress state in the rock adjacent to the cavity wall, i.e. the consideration of the entire stress field in the rock is not required. This result was transferred to the case of linear-elastic cross-anisotropic rock and thus, yielded the approximate solution. Measurements from large-scale cavity expansion tests (radial jack tests) were used to back calculate the material constants.