平底蛋形断面隧洞正常水深直接计算方法
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摘要
平底蛋形断面具有施工相对简单、适应性强的特点,但断面形状较复杂,正常水深计算需要求解超越方程,计算过程繁琐且无法直接求解。利用面积分割法计算出普通平底蛋形断面的水力要素方程,得到3种典型断面的过水断面面积、湿周和水深方程。根据正常水深基本方程和优化拟合理论,推导出求解3种平底蛋形典型断面正常水深超越方程的直接简化计算公式,并进行公式精度分析。结果表明,直接简化计算公式具有形式简单、计算方便、精度高的特点,在适用范围内正常水深相对误差最大值仅为0.34%。
The egg-shaped section with flat bottom has the characteristics of simple construction and strong adaptability, but its normal depth calculation formula must be derived from a transcendental equation which is a complicated process and difficult to solve with complex geometry. Using area segmentation method, the hydraulic factor equations of egg-shaped section with flat bottom were computed and then the area,wetted perimeter and depth of three typical sections were obtained. Based on the basic equation of normal depth and optimum matching theory, the direct and simplified formula was proposed to solve the normal depth transcendental equation of the three typical sections and their errors were analyzed and evaluated.The results show that the proposed simplified formulas are simple form, convenient calculation and high precision, and the maximum error of calculated normal depth is less than 0.34% in the practical range.
The egg-shaped section with flat bottom has the characteristics of simple construction and strong adaptability, but its normal depth calculation formula must be derived from a transcendental equation which is a complicated process and difficult to solve with complex geometry. Using area segmentation method, the hydraulic factor equations of egg-shaped section with flat bottom were computed and then the area,wetted perimeter and depth of three typical sections were obtained. Based on the basic equation of normal depth and optimum matching theory, the direct and simplified formula was proposed to solve the normal depth transcendental equation of the three typical sections and their errors were analyzed and evaluated.The results show that the proposed simplified formulas are simple form, convenient calculation and high precision, and the maximum error of calculated normal depth is less than 0.34% in the practical range.
引文
[1] 吕宏兴,裴国霞,杨玲霞.水力学[M].2版.北京:中国农业出版社,2011:6.
[2] 赵延风,刘军,梅淑霞,等.普通城门洞形断面正常水深的近似计算方法[J].武汉大学学报(工学版),2009,42(6):773.
[3] 赵延风,王正中,方兴,等.排灌输水隧洞正常水深的简捷算法[J].排灌机械工程学报,2011,29(6):523-528.
[4] 赵延风,王正中,芦琴,等.马蹄形断面正常水深的直接计算公式[J].水力发电学报,2012,31(1):173-177.
[5] 吕宏兴,辛全才,花立峰.马蹄形过水断面正常水深的迭代计算[J].长江科学院院报,2001,18(3):7-9.
[6] 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):229-234.
[7] 张志昌,贾斌.明渠六圆弧蛋形断面水面线的近似计算[J].应用力学学报,2015,32(3):229-234.
[8] 滕凯.蛋形断面隧洞正常水深的简易计算方法[J].长江科学院院报,2013,30(12):39-42.
[9] 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(6):229-234.
[10] 索丽生,刘宁.水工设计手册[M].2版.北京:中国水利水电出版社,2011:426.
[11] 中华人民共和国水利部.水工隧洞设计规范:SL279—2016[S].北京:中国水利水电出版社,2016:15.
[2] 赵延风,刘军,梅淑霞,等.普通城门洞形断面正常水深的近似计算方法[J].武汉大学学报(工学版),2009,42(6):773.
[3] 赵延风,王正中,方兴,等.排灌输水隧洞正常水深的简捷算法[J].排灌机械工程学报,2011,29(6):523-528.
[4] 赵延风,王正中,芦琴,等.马蹄形断面正常水深的直接计算公式[J].水力发电学报,2012,31(1):173-177.
[5] 吕宏兴,辛全才,花立峰.马蹄形过水断面正常水深的迭代计算[J].长江科学院院报,2001,18(3):7-9.
[6] 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):229-234.
[7] 张志昌,贾斌.明渠六圆弧蛋形断面水面线的近似计算[J].应用力学学报,2015,32(3):229-234.
[8] 滕凯.蛋形断面隧洞正常水深的简易计算方法[J].长江科学院院报,2013,30(12):39-42.
[9] 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(6):229-234.
[10] 索丽生,刘宁.水工设计手册[M].2版.北京:中国水利水电出版社,2011:426.
[11] 中华人民共和国水利部.水工隧洞设计规范:SL279—2016[S].北京:中国水利水电出版社,2016:15.