普通城门洞形断面临界水深的近似计算法

Approximate method of calculating critical water depth to arched section tunnel

【目的】建立普通城门洞形断面临界水深的简捷计算方法。【方法】针对目前普通城门洞形过水断面临界水深计算过程繁琐、误差较大,且依赖图表、不便应用的现状,应用数学变换及逐步优化拟合原理,提出普通城门洞断面临界水深的计算公式,并采用实例对公式进行验证。【结果】得到了城门洞形断面临界水深的近似计算式,实例计算及误差分析结果表明,在工程实用范围内(临界水深与拱顶半径之比为1.13～1.85),所建立的公式最大相对误差仅为0.33%。【结论】所建立的公式物理概念清晰明确、形式简捷,为工程设计及水工设计手册的编制提供了有益参考。

[Objective] It is difficult to calculate critical depth of arched section tunnel for its complex geometrical shape. The aim was to find a direct calculating formula for critical water depth to arched section tunnel. [Method] Using a mathematics transformation method and the theory of optimization and regression to deal with the basis equation of the critical depth in arched section tunnel,a new brief and exact direct formula was derived in this study. [Result] This method was simpler and more accurate than other approximate methods with a maximum error of less than 0.33% in the utility range （ratio of critical depth to arch radius of 1.13-1.85）. [Conclusion] So,it will be useful in engineering practice and in course of compiling handbook of hydraulic structure design.