Numerical Modeling of Swelling Rock

Abstract

This master thesis is focusing on numerical modeling of a swelling rock called anhydrite. If water gets in contact with the rock anhydrite (CaSO4) it transforms into gypsum (CaSO4•2H2O). This chemical process can result in an increase of the solid matter up to 61%. This increase in volume can result in major swelling deformations.The motivation for this thesis is Staufen, a medieval town in Germany, which after completing the drilling of seven thermal wells started to heave. The city center was rising with a rate of approximately 1cm/month. This heave has created considerable damages to more than 200 houses in the city center. The heave in this city is numerical back calculated in both 2D and 3D in this master thesis. The FEM program Plaxis 2D version 9.02 is used for the 2D calculations and Plaxis 3D version2010.0 beta version are used for the 3D calculations.The swelling problem in Staufen is presented in this report. The investigations and counter measures that are done in connection to the swelling heave problem are also discussed.Laboratory test from Staufen was back calculated to get an overview of in which range the swelling parameters were in the Staufen case. Some new parameters were added to the material model used for the numerical back calculation. These parameters detect numerical errors arising from the explicit implementation of the swelling strains. Back calculating the lab tests with different time intervals showed that as long as short enough time intervals were used in the calculation the explicit approach to the swelling strains gives good results.The swelling in the subsurface of Staufen was first back calculated in 2D, and a material parameterset was found. A prognosis for the continuing development of the swelling in Staufen for the next tenyears was made. The maximum heave after ten years was calculated to be approximately 28 cm.The swelling was next calculated for a “slice” in 3D, which was a one meter deep projection of the 2D model. This gave quite similar result as the 2D calculation, and the small different could be due to the coarse mesh used in the 3D “slice” model. Finally a full 3D model was made. This one did not giveresults that was consistent with the measurements and the two other calculation models. This isdespite the fact that exactly the same parameters were used. This indicates that the 2D model does not capture all aspects of the real case.The conclusion in this thesis is that the problem is to be considered as a 3D problem. Therefore, the prognosis from the 2D calculations is not overly reliable. A 3D approach should be strived for instead.The material parameters back calculated from 2D cannot be transferred in the 3D calculation. A back calculation of the measured time history with the 3D approach would be needed. This back calculation could not be performed within this thesis due to time constraints.