【摘要】：滲流自由面的求解是滲流分析中的難題之一。滲流自由面是滲流場中的待求邊界,需同時(shí)滿足水頭值等于高程(第一類邊界條件)和流量交換為零(第二類邊界條件)。在以往的研究工作中,采用虛單元法、初流量法等有限元法求解滲流自由面,為提高計(jì)算精度,通常通過提高迭代次數(shù)來逐步逼近第一類邊界條件或第二類邊界條件,計(jì)算復(fù)雜。本文提出了基于實(shí)域能量損失率最小求解穩(wěn)定滲流場自由面的逐步剖分法,該方法物理意義明晰,計(jì)算精度高。主要研究成果包括:1、基于六節(jié)點(diǎn)三角形單元優(yōu)化了滲流自由面。六節(jié)點(diǎn)三角形單元在以往的平面滲流自由面求解中是未曾被采用的。本文對平面滲流計(jì)算常用的三角形單元和等參四邊形單元比較分析,六節(jié)點(diǎn)三角形單元具有如下優(yōu)勢:(1)能適應(yīng)形狀復(fù)雜的滲流邊界;(2)能以完全二次多項(xiàng)式表達(dá)非線性水頭插值函數(shù)。基于六節(jié)點(diǎn)三角形單元劃分網(wǎng)格,應(yīng)用優(yōu)化的虛單元法求解了矩形滲流模型的滲流自由面,與電模擬試驗(yàn)解的比較表明,求得的滲流自由面精度更高,更接近其真實(shí)狀態(tài)。2、基于實(shí)域能量損失率最小提出求解滲流自由面的逐步剖分法。對有確定上、下游邊界以及自由滲出邊界的滲流場,進(jìn)行有限單元劃分,由滲流溢出點(diǎn)逐步向滲流匯入點(diǎn)推進(jìn)求解滲流自由面點(diǎn),每推進(jìn)一層單元,基于實(shí)域能量損失率最小求解該剖面上的自由面點(diǎn)位置,直到得到完整的滲流自由面以及完整的滲流實(shí)域。3、應(yīng)用Fortran語言編寫了逐步剖分法的計(jì)算程序,求解了有電模擬試驗(yàn)解的矩形壩、有模型試驗(yàn)解的矩形壩、有解析解的梯形壩的滲流自由面。逐步剖分法計(jì)算結(jié)果分別與電模試驗(yàn)解、甘油試驗(yàn)解和解析解對比,最大相對誤差分別是4.94%、1.37%和2.57%。結(jié)果表明,逐步剖分法具有很高的計(jì)算精度。
[Abstract]:The solution of seepage free surface is one of the difficult problems in seepage analysis. The seepage free surface is the boundary to be solved in the seepage field, and the head value is equal to the elevation (the first type boundary condition) and the flow exchange is zero (the second type boundary condition) at the same time. In previous research work, the finite element method such as virtual element method and initial flow method was used to solve the seepage free surface. In order to improve the calculation accuracy, the boundary conditions of the first or the second kind are approximated gradually by increasing the number of iterations. The calculation is complicated. In this paper, a step-by-step method for solving the free surface of steady seepage field based on the minimum real-domain energy loss rate is presented. The physical meaning of this method is clear and the calculation accuracy is high. The main results are as follows: 1. The seepage free surface is optimized based on the six-node triangular element. The six-node triangular element has never been used in solving the free surface of plane seepage. In this paper, the triangle element and isoparametric quadrilateral element commonly used in plane seepage calculation are compared and analyzed. The six-node triangular element has the following advantages: (1) it can adapt to the seepage boundary with complex shape; (2) the nonlinear head interpolation function can be expressed by complete quadratic polynomials. Based on the mesh of six-node triangular element, the seepage free surface of the rectangular seepage model is solved by using the optimized virtual element method. Compared with the experimental solution of electrical simulation, the obtained seepage free surface is more accurate and closer to its real state. Based on the minimum real-domain energy loss rate, a step-by-step partition method is proposed to solve the seepage free surface. For the seepage flow field with definite upstream, downstream boundary and free exudation boundary, the finite element division is carried out, and the seepage free surface point is solved gradually from the seepage overflow point to the seepage flow convergence point, with each layer of element advancing. Based on the minimum real-domain energy loss rate, the point position of the free surface on the profile is solved, until the complete seepage free surface and the complete seepage real domain are obtained. 3. The program of the progressive partition method is programmed with Fortran language. The seepage free surface of rectangular dam with electric simulated test solution, rectangular dam with model test solution and trapezoidal dam with analytical solution is solved. The maximum relative errors are 4.94%, 1.37% and 2.57%, respectively, compared with the electrical model test solution, glycerin test solution and analytical solution. The results show that the step-by-step method has high accuracy.
【學(xué)位授予單位】：煙臺大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TV139.1

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