基于实域总势能计算渗流溢出点的位置

发布时间：2018-03-04 14:31

本文选题：渗流自由面　切入点：渗流溢出点　出处：《烟台大学》2017年硕士论文　论文类型：学位论文

【摘要】：渗流自由面问题的研究已成为岩土工程方向一个重要的研究课题。渗流计算的主要任务是计算渗流场的渗流量、水头、水力坡降等渗流要素,从而为稳定性分析及选取合理的渗控设计方案提供依据。渗流自由面的确定是求解渗流场的关键,而溢出点位置的确定是精确计算渗流自由面的前提。基于有限单元法提出了一种确定二维稳定渗流场溢出点位置和计算渗流自由面的方法,研究成果包括:(1)采用以往有限元法计算渗流溢出点时,全域总势能法求解精度高且无需同自由面迭代。但是全域总势能包含了自由面以上区域的势能,给计算结果带来了误差。本文在全域总势能的基础上,提出了实域总势能的概念,将虚域势能从全域总势能中剔除,消除了因虚域势能造成的误差,提高了渗流溢出点的计算精度。工程实例计算结果表明,基于实域总势能求解溢出点具有更高的精度和稳定性。(2)基于实域总势能最小原理,对自由面以上的虚域单元做不同处理:调整虚域单元的渗透系数或在有限元计算时将虚域单元丢弃,以及对实域总势能最小值计算方式的不同,提出了变渗透系数调节点法、变渗透系数曲线拟合法、丢单元调节点法、丢单元曲线拟合法四种确定溢出点位置的方法。分别采用四种方法计算工程实例,丢单元调节点法有较高的计算精度。(3)求解渗流自由面常采用虚单元法,但是该法需不断调整通过自由面的单元,迭代效率慢且易造成单元畸形。本文对有限元法求解的自由面节点水头做曲线拟合,无需调整单元,即可得到高精度的渗流自由面曲线。应用本文方法求解实际工程算例表明,该方法精度高,稳定性好,效率高,与实际自由面形状更吻合。
[Abstract]:The study of seepage free surface has become an important research topic in geotechnical engineering. The main task of seepage calculation is to calculate seepage flow, water head, hydraulic gradient and other seepage elements. This provides the basis for the stability analysis and the selection of reasonable seepage control design scheme. The determination of seepage free surface is the key to solve the seepage field. The location of overflow point is the premise of accurate calculation of seepage free surface. Based on finite element method, a method to determine the location of overflow point and calculate seepage free surface of two-dimensional steady seepage field is proposed. The results include: 1) when the seepage overflow point is calculated by the former finite element method, the global total potential energy method has high accuracy and does not need to be iterated with the free surface, but the total potential energy of the whole domain contains the potential energy of the region above the free surface. On the basis of the total potential energy of the whole domain, the concept of the total potential energy in the real domain is put forward in this paper. The virtual domain potential energy is eliminated from the total potential energy of the whole domain, and the error caused by the virtual domain potential energy is eliminated. The calculation accuracy of seepage overflow point is improved. The result of engineering example shows that it is more accurate and stable to solve overflow point based on the total potential energy of real domain, which is based on the principle of minimum total potential energy in real domain. The virtual domain element above the free surface is treated differently: adjusting the permeability coefficient of the virtual domain element or discarding the virtual domain element in the finite element calculation, and the method of adjusting point of variable permeability coefficient is put forward to calculate the minimum value of the total potential energy of the real field. There are four methods to determine the location of overflow point: curve fitting method of variable permeability coefficient, adjusting point method of unit loss and curve fitting method of missing element. The virtual element method is often used to solve the seepage free surface, but the method needs to adjust the element passing through the free surface constantly. The iteration efficiency is slow and the element deformity is easy to be caused. In this paper, the free surface water head of the free surface node solved by the finite element method is fitted by curve, and the seepage free surface curve with high accuracy can be obtained without adjusting the element. The practical engineering example shows that the method in this paper is used to solve the seepage free surface curve. This method has the advantages of high precision, good stability and high efficiency, which is more consistent with the actual free surface shape.
【学位授予单位】：烟台大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TV139.1

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