CAJ | 학술논문

针对现有水面线计算采用的逐段试算法计算较繁琐等问题，对典型无压长隧洞如城门洞形、卵形无压隧洞恒定渐变流沿程水深的计算进行了数学推导。根据渐变流水力微分方程，利用数值计算理论及无量纲化原理，将恒定渐变流基本微分方程转换为高精度的可解析积分函数形式，进而得到典型无压长隧洞水面线计算得解析式，利用该解析式可直接算得沿程水深。该解析算法比《水工隧洞设计规范》建议的逐段试算法更简捷，并通过工程算例分析，该新解析法成果精度可靠，方便快捷，完全满足工程实践要求。
침대현유수면선계산채용적축단시산법계산교번쇄등문제，대전형무압장수동여성문동형、란형무압수동항정점변류연정수심적계산진행료수학추도。근거점변류수력미분방정，이용수치계산이론급무량강화원리，장항정점변류기본미분방정전환위고정도적가해석적분함수형식，진이득도전형무압장수동수면선계산득해석식，이용해해석식가직접산득연정수심。해해석산법비《수공수동설계규범》건의적축단시산법경간첩，병통과공정산례분석，해신해석법성과정도가고，방편쾌첩，완전만족공정실천요구。
The existing analytical method for calculating water surface profile adopts section by section trial calculation which is tedious and inconvenient .Here the gradually varied steady flow depth of the typical long non-pressure tunnels with horseshoe-shaped cross-section and oval cross-section was mathematically deduced ,and then its basic differential e-quation was transformed into an analytical integral function with high-precision based on the numerical analysis theory and dimensionless principle ,from which the analytical formula for calculating water surface profile of gradually varied steady flow for typical long non-pressure tunnels was obtained .The water depth can be calculated directly according to this for-mula and it’s more convenient and simple than the recommended method in the specification for design of hydraulic tun-nel .According to the analysis of its application in an actual construction project ,this method is more convenient and simple ,and it can provide more accurate and reliable results that meet the requirements of the construction .