Subjects: Mathematics >> Mathematics （General） Subjects: Hydraulic Engineering >> Basic Disciplines of Hydraulic Engineering submitted time 2023-04-28
Abstract： In this paper, we mainly provide a proper maintenance plan for the Kariba Dam in Africa which falls into disrepair and is facing to collapse. Firstly, we make a threshold analysis of the three options about their costs which include people’s moving, old dam’s removing, new dams’ building, later repairing, ecological destruction and their incomes which include generation energy, avoiding of flood disasters’ loss, providing employment, tourism resources and ecological protection. Then we get the specific relationship between benefits and years with some collected data. Both of the results show that the third option is the best choice from the economic view. And the result is completely as same as the conclusion we get after studying deeply on Option 3. Secondly, we regard water management capabilities as the safety coefficient of dams. We select 30 seed points along the riverbank for preparing the establishment of dams. With flow-between-riverway model, Manning equations, large Cauchy distribute function we get the scores of the seed points. We give an advice that the number of dams should be more and the positions of dams should be well-distributed. Then, we build an assessment model by analytic hierarchy process. We select three factors among all the factors, safety, economy and population. After testing the consistency, we get the weights of each factor: 0.6442, 0.2705, 0.0852. Then we value the factors and get an optimal scheme during the assessment with 0-1 integer programming: the number of dams is 17 and the longitude and latitude of them are shown in Table 17. The sensitivity of the result is tested as well. We also provide some strategies for the managers of ZRA to use. We suggest that they should use the dams normally in general. With the Dam-break model, we find 13 points among 17 points which are shown in Table 20. The dams at the 13 points need to be closed when there is a flood and it is just the opposite when the drought happens. For the extreme water flow, we assume an ideal water flow at first. The extreme water flow has to be adjusted to satisfy the ideal one. As for the restrictions in extreme conditions, the biggest impact happens at the 8th point among the 17 points. If the duration of maximum flow is t0, the drainage time t to make the water flow return to the normal level equals to 4.95t0.
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