The Estimation of the Cavity Effect by Higher Degree Finite Element Approximation

The measurements of tide-induced tilts and deformations are usually performed in underground cavities (mostly man-made). Therefore, the data obtained must be debugged of the influence of the cavity itself (cavity effect) and of the effect of elastic parameter inhomogeneities in the vicinity of the point of measurement (geological effect), if they are to he presented. Since these effects are reflected as a modulation of tidal waves (in both amplitude and phase), the only way to perform this can be modelling of the strain and stress field around the cavity as precisely as possible. The finite element method (F.E.M.) seems to be a very useful tool for this purpose. To justify some conclusions in this paper, a number of numerical runs of the F.E.M. models of the tide-induced strains and stresses (in two dimensions) were performed. A higher degree of approximation (up to the value of 7) was used in these calculations. To estimate the cavity effect, the correction factors (relative changes of particular strain components due to the presence of the cavity) were determined and plotted in the cavity's close neighbourhood. The distribution of the deformation energy (and also the work of external forces) over the whole domain of interest is given, and the conclusions for subsequent error estimation are drawn. An attempt was made to compare the real tilt data to the theoretical deduced from the numerical model.