五圆弧平底蛋形断面隧洞临界水深的简易算法
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摘要
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 critical 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 calculating 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.
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 critical 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 calculating 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.
引文
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[3] 卞晓卫,郑新桥,代述兵,等.蛋形断面的正常水深和临界水深的直接计算公式[J].干旱地区农业研究,2017,35(2):191-194.
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[5] 滕凯.无压流六圆弧蛋形断面临界水深近似算法[J].水利水电科技进展,2014,34(1):81-84.
[6] 李若冰,张志昌.明渠六圆弧蛋形断面临界水深和收缩断面水深的计算[J].武汉大学学报(工学版),2012,45(4):463-467.
[7] 文辉,李风铃.平底Ⅰ型马蹄形断面临界水深的直接求解[J].长江科学院院报,2013,30(4):40-42.
[8] 滕凯.蛋形断面隧洞临界水深的简易算法[J].水利水电科技进展,2013,33(6):37-39.
[9] 武周虎.蛋形断面明渠正常水深和临界水深的简化算法[J].人民长江,2014,45(4):73-76.
[10] 张志昌,贾斌,李若冰.六圆弧蛋形断面正常水深直接计算方法[J].西北农林科技大学学报(自然科学版),2015,43(8):231-234.
[11] 孙东坡,丁新求.水力学[M].郑州:黄河水利出版社,2013:198-201.
[12] 中华人民共和国水利部.水工隧洞设计规范:SL 279—2016[S].北京:中国水利水电出版社,2016:14-15.
[2] 张志昌,贾斌.标准Ⅰ型四圆弧蛋形断面的水力计算[J].应用力学学报,2015,32(3):229-234.
[3] 卞晓卫,郑新桥,代述兵,等.蛋形断面的正常水深和临界水深的直接计算公式[J].干旱地区农业研究,2017,35(2):191-194.
[4] 文辉,李风玲,李霞,等.蛋形断面管道临界水深的近似算法[J].人民黄河,2008,30(12):112-113.
[5] 滕凯.无压流六圆弧蛋形断面临界水深近似算法[J].水利水电科技进展,2014,34(1):81-84.
[6] 李若冰,张志昌.明渠六圆弧蛋形断面临界水深和收缩断面水深的计算[J].武汉大学学报(工学版),2012,45(4):463-467.
[7] 文辉,李风铃.平底Ⅰ型马蹄形断面临界水深的直接求解[J].长江科学院院报,2013,30(4):40-42.
[8] 滕凯.蛋形断面隧洞临界水深的简易算法[J].水利水电科技进展,2013,33(6):37-39.
[9] 武周虎.蛋形断面明渠正常水深和临界水深的简化算法[J].人民长江,2014,45(4):73-76.
[10] 张志昌,贾斌,李若冰.六圆弧蛋形断面正常水深直接计算方法[J].西北农林科技大学学报(自然科学版),2015,43(8):231-234.
[11] 孙东坡,丁新求.水力学[M].郑州:黄河水利出版社,2013:198-201.
[12] 中华人民共和国水利部.水工隧洞设计规范:SL 279—2016[S].北京:中国水利水电出版社,2016:14-15.