13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- Table 2. Unbalanced forces of cracks and dam heel in scheme 3 (104 N) No. Crack Dam weight Water pressure 1.5 times water pressure 2 times water pressure 2.5 times water pressure 1 13lf-1 0.11 0.88 1.59 3.11 38.11 2 13lf-2 0.04 1.98 25.22 67.44 92.83 3 20lf-1 0.13 0.00 0.00 0.00 14.30 4 20lf-2 0.00 18.05 597.84 1902.98 3216.86 5 22lf-1 0.00 0.00 0.00 0.00 0.00 6 22lf-3 0.06 0.00 0.00 0.00 0.00 7 22lf-4 0.00 0.00 0.00 0.00 0.00 8 25lf-1 0.25 0.00 0.00 0.00 0.47 9 28lf-1 155.71 0.00 0.95 20.05 110.01 10 28lf-2 0.65 18.39 2321.18 9522.02 18778.98 11 30lf-1 69.33 0.19 29.91 124.81 897.03 Dam heel 4005.15 40225.05 257428.3 415430.9 561604.5 Table 1 and Table 2 show that unbalanced forces of dam heel increase earlier than cracks in the dam. Dam heel contributes the major unbalanced forces in all condition. Namely, dam heel cracking occurs before any crack propagates. Among all existing cracks, 20lf-2 and 28lf-2 are the dominating cracks in the process of fracture propagation. The final crack status of upstream dam surface in geo-mechanical model test is shown in Fig. 7. In normal working condition, dam cracks are mostly in compression-shear state, and neither yielding nor tension fracture is involved. Dam heel cracking occurs as the work load increases to 1.7~3.0 times normal pressure. There is no sign of crack propagation in the dam during the test. Instead, cracks that occur on the dam surface begin to extend after the work load reaches 4.0 times normal pressure. Experimental results indicate that dam heel cracking, compared with dam cracks, is the dominating problem of Xiaowan arch dam, which is corresponding to FEM results. Figure 7. The final crack status of upstream dam surface 4. Conclusions This paper presents a new approach to deal with cracks in stability and fracture analysis of 3-D structure. Unbalanced force, derived from the Deformation Reinforcement Theory (DRT), could be the criterion of initiation of fracture, the distribution area and magnitude of which could indicate fracture propagation direction. FEM expression of DRT is deduced and implemented in a three dimensional nonlinear FEM program, and successfully applied in dam heel cracking and multi-crack analysis of arch dam. Both elasto-plastic FEM analysis and geo-mechanical experiments are performed on Baihetan and Xiaowan arch dams. Dam heel cracking and multi-crack propagation analysis are presented. Results of geo-mechanical experiments show great agreement with FEM analysis. Unbalanced forces can be used as the indication of fracture initiation and propagation.
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