摘要
论述了堤坝下游设有棱体和褥垫排水堤坝的渗流计算,排水边界的坡角大于90°。主要内容和成果有:①对于下游水深H2=0的棱体排水,按柯钦娜式q/k=μh0,高精度计算出流量和出逸点高度关系式的比例系数μ的倒值,并提出相应的1/μ拟合式,以便于应用,应用转化的超越几何函数,导出出逸段的坡降计算式,并具体计算出排水边坡坡角90°,135°,180°的出逸坡降分布;②应用速度平面保角变换的简化方法,导出排水棱体临界水深HC的计算式,其推导过程较之努米诺夫的混合函数法大为简化,另提出相应的HC拟合式,以便于应用;③对于下游水深H2≥HC的棱体排水,按努氏式ΔL2=D1H2+D2q/k,高精度计算出下游区附加渗径ΔL2式的比例系数D1和D2,并提出相应的拟合式,以便于应用,应用保角变换求出该型堤坝下游区的精确解,再结合努氏的上游区精确解,举出一具体算例,精确计算出堤坝的流量和渗透系数的比值q/k,出逸点高度hs,出逸段坡降I的分布,以及全程浸润线和上下两反弯点的坐标,可借以校核该型堤坝渗流有限元计算程序和其它近似计算方法的正确性及其计算精度;④对于下游水深0<H2<HC的棱体排水,提出出逸点高度hs和下游区附加渗径ΔL2两近似理论计算式,据此算出的q/k和hs,与有限元计算的结果相符。
The seepage calculations of dams and levees with mound and layer drains on impervious strata are introduced. The slope angle of drain boundary is greater than 90° . The main contents and results are as follows： （1） For the mound drain with the downstream water depthH2=0, according to the Kochina＇s theory q/k=μhl, the reciprocal of ratio μ between the flow quantity and the height h0 of release point is calculated, and the relevant fitting formula for 1μ is presented. By means of the transformed hypergeometric function, a formula for the exit gradient and its distributions with slope angles of 90° , 135 ° , 180° is given. （2） The conformal mapping method is employed to get the critical water depth Hc of the mound drain, and its derivation process is much simpler than that of the Novmurov＇s method. （3） For the mound drain with H2≥Hc, according to the Novmurov＇s theory △L2=D1H2＋D2q/k, the proportional coefficients D1 and D2 of additional length of downstream seepage path are calculated, and two fitting formulae for D1 and D2 with enough precision are presented. The conformal mapping method is used to get the exact seepage solution in downstream district with mound drains, combined with the corresponding solution by Normurov in the upstream district of dams and levees, an example is calculated accurately to get the flow quantity ratio q/k, height of release point hs, distribution of exit gradient I, coordinates of the whole phreatic line and its inflection points to check the corresponding program of finite element and other approximate methods. （4） For the mound drain with 0〈H2〈Hc, two approximate formulae for the height hs of release point and the additional length △L2 of downstream seepage path are presented. The calculated results agree with the results of the finite element methods.
出处
《岩土工程学报》
EI
CAS
CSCD
北大核心
2012年第1期102-109,共8页
Chinese Journal of Geotechnical Engineering
关键词
渗流
堤坝
棱体排水
复变函数
超越几何函数
seepage
dam and levee
mound drain
complex variable
hypergeometric function
作者简介
吴世余（1926—），男，教授级高级工程师，从事土工和渗流研究工作。E—mail：qianfu66@163．com。
