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《Transactions of the Chinese Society of Agricultural Engineering》 2009-04
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Direct calculation of critical depth of horseshoe section tunnel

Zhang Kuandi1,2,L Hongxing1,Chen Junying1 (1. College of Water Conservancy and Architectural Engineering,Northwest Agriculture and Forestry University,Yangling 712100,China; 2. State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau,Institute of Soil and Water Conservation,Chinese Academy of Sciences and Ministry of Water Resources,Yangling 712100,China)  
Horseshoe section tunnel is a common type in the free-flow tunnel. There is no analytical expression to solve the critical depth of horseshoe section tunnel under free flow. The traditional solving methods,such as trial method and chart method,are very complicated with low precision. In this study,by mathematical transformation of critical flow equation of horseshoe section tunnel,the relationship between the dimensionless parameters and relative critical depth was analyzed and simulated. Using the gradual optimization and fitting principle,a direct formula for calculating the critical depths of standard Ⅰ-type and Ⅱ-type horseshoe section tunnel was established. Results of the example calculation and error analysis show that the maximum relative error of critical depth is 0.8%,in agreement with the application scope of engineering. The characteristics of this formula is exact and simple,which supplies a reference to manual compilation of engineering design and hydraulic design.
【Fund】: 国家973计划课题(2007CB407201);; 国家自然科学基金重点项目(40335050);; 西北农林科技大学创新团队建设计划(01140202);; 黄土高原土壤侵蚀与旱地农业国家重点实验室基金项目(10501-182)
【CateGory Index】: TV135
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