五圆弧平底蛋形断面隧洞临界水深的简易算法

Simple Calculation Method for Critical Depth of Five Arc Egg-Shaped Section Tunnel with Flat Bottom

五圆弧平底蛋形断面隧洞具有结构相对简单、断面形状尺寸容易控制和易于施工的特点,是工程中较常采用的水工隧洞断面形式之一,但其断面临界水深计算公式复杂,且为分段的超越方程,在求解过程中计算繁琐,无法直接给出解析解.为此,本文计算了五圆弧平底蛋形断面的水力要素,得到3种典型断面的过水断面面积和水面宽度计算公式,并对临界水深的基本计算公式进行简单的数学变换,对无量纲临界水深和无量纲参数的关系进行研究分析,利用优化拟合理论,在工程适用的范围内推导了3种典型五圆弧平底蛋形断面临界水深的直接简易计算公式,并进行了精度分析.结果表明:公式计算误差绝对值的最大值小于0.24%,且大部分区域相对误差在0.1%内正负波动,完全满足实际工程的精度需求.

The five arc egg-shaped section with flat bottom has the characteristics of relatively simple structure, easy control of cross-sectional shape and easy construction, and is one of the hydraulic tunnel cross-sections often used in engineering. However, the expression of the criti-cal depth is complicated and divided into several sections. Beyond the equation, the calculation is cumbersome in the solution process, and the analytical solution cannot be directly given. For this purpose, this paper had calculated thehydraulic factor equations of five arc egg-shaped section with flat bottomin detail, and obtained the cross-sectional area and water surface width of three typical sections, and performed a simple mathematical transformation of the basic calculation formula of critical depth. The relationship between dimensionless critical depth and dimensionless parameters were studied and analyzed. Using the optimized fitting theory, a simple and straightforward formula for calculat-ing the critical depthof three typical five arc egg-shaped section with flat bottomwas deduced within the applicable scope of the project, and accuracy analysis was performed. Finally, it gave an application example. Through precision analysis and example calculations, the results show that the absolute value of the formula's maximum calculation error is less than 0.24%, and the relative error of most regions is within plus or minus 0.1%, which fully meets the precision requirements of the actual project.