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Numerical determination of the state of stress in a wall of a building under the influence of discon |
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Numerical determination of the state of stress in a wall of a building under the influence of discontinuous ground deformation Author: L. Florkowska
The structures situated in the areas influenced by mining exploitation are subjected to a very complex system of loads. Some of those loads are caused by ground deformations. It is possible to predict the deformations quantity but only if trough of subsidence is of regular shape, however, due to different reasons (geological or connected with exploitation system) discontinuous deformations or irregularities in the shape of trough may appear. In the paper, the following problem was discussed: how would the answer of the building look like if the ground was subjected to discontinuous deformation? In particular: how would stress distribution in the wall change? Assumed physical model was presented on Fig. 3. It consisted of two elastic shields: upper shield represented wall of the building and a lower one represented the ground. Both shields were totally fastened together. Suitable material constants were set in the Table. Two different schemes were discussed: - with the edge of the wall not supported and forming something like a cantilever of "a" - reach (Fig. 2a, 4a), - with a cavern of "k" - width appearing under the wall (Fig. 2b, 4b). The mathematical model consisted of linear elasticity equations system with suitable boundary conditions. Analytical solution of the system was abandoned in favour of numerical solution by means of Finite Element Method (FEM). The problem was formulated according to calculus of variation rules. The numerical calculations were made by means of FEM-program ALGOR. T h e f ir s t s c h e m e Normal stress s[sigma] sub yy distribution change as a function of increase of cantilever reach "a" was presented on Fig. 6. On Fig. 7, changes in szz due to changes in "a" - value were presented. The propagation of tensioned zone in the wall with the increase of length of unsupported wall edge was presented on Fig. 8. The calculations were stopped, when tensions appeared in connection between wall and building, on the side of building opposite to landslide. That phenomenon testified loss of contact between the wall and the ground. T h e s e c o n d s c h e m e Changes in s sub yy and s sub zz stresses as functions of increase of cavern width "k" were presented on Fig. 10 and 11. Fig. 12 showed distribution of compressed and tensioned zones for consecutive values of "k". It was visible, that those changes were insignificant.
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2011