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An approach is presented for the analysis of the unconfined steady-state seepage through homogeneous trapezoidal dams based on a bijective mapping between the flow domain, having an unknown shape, and a fixed triangular domain. It is shown that the geometrically non-linear unconfined analysis is equivalent to the problem of determining the unknown distribution of permeability, within a triangular domain with known shape, that satisfies the set of transformed boundary conditions. The flow problem in the triangular domain is solved through a finite-element technique analogous to that adopted for confined analyses and, on the basis of this solution, the shape of the free surface in the physical space is evaluated. The proposed approach is applied to the determination of the influence of the water levels in the upper and lower reservoirs on the elevation of the free surface seepage point. 相似文献
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A practical and efficient numerical scheme for the analysis of steady state unconfined seepage flows
The scaled boundary finite‐element method (SBFEM), a novel semi‐analytical technique, is applied to the analysis of the confined and unconfined seepage flow. This method combines the advantages of the finite‐element method and the boundary element method. In this method, only the boundary of the domain is discretized; no fundamental solution is required, and singularity problems can be modeled rigorously. Anisotropic and nonhomogeneous materials satisfying similarity are modeled without additional efforts. In this paper, SBFE equations and solution procedures for the analysis of seepage flow are outlined. The accuracy of the proposed method in modeling singularity problems is demonstrated by analyzing seepage flow under a concrete dam with a cutoff at heel. As only the boundary is discretized, the variable mesh technique is advisable for modeling unconfined seepage analyses. The accuracy, effectiveness, and efficiency of the method are demonstrated by modeling several unconfined seepage flow problems. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
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提出了求解有自由面渗流问题的三维数值流形方法,通过构造任意形状流形单元的水头函数,推导了流形单元的渗透矩阵和无压渗流分析的总体控制方程,并给出了自由面的迭代求解策略和渗透体积力的计算方法。典型算例的数值分析表明,该方法采用数学网格覆盖整个材料区域,在自由面的迭代求解过程中数学网格保持不变,只考虑自由面以下渗流区的介质,只对自由面以下的流形单元形成总体渗透矩阵,具有精度高、收敛速度快、编程简单等优点,而且能够通过单纯形积分精确计算被自由面穿越单元的渗透作用力,因此,特别适用于有自由面渗流问题的模拟。 相似文献
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A finite element, variable mesh analysis of unconfined steady-state seepage problems is presented based on a nonlinear programming algorithm. It is shown that the minimization of an objective function which merely represents a measure of the total flux leaving or entering the mesh at the free surface nodes (except those that belong also to pervious boundaries) does not permit a unique definition of the free surface geometry. This problem, which is apparently related to the numerical instabilities often met when using variable mesh approaches, can be eliminated by adding to the objective function a term representing a sort of overall ‘regularity’ condition for the shape of the free surface. The modified solution procedure turns out to be stable and able to provide meaningful results for practical problems even when rather coarse meshes are adopted. 相似文献
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Investigation of a hybrid polygonal finite element formulation for confined and unconfined seepage 
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下载免费PDF全文 This study presents a formulation for field problems using hybrid polygonal finite elements, taking steady state seepage through a porous material as the focus. We make comparisons with a conventional finite element formulation based on a single primary variable, focussing on the advantages of the hybrid formulation in terms of flux field accuracy and extension to convex polygonal shaped elements. For the unconfined case, we adopt a head dependent hydraulic conductivity that does not require remeshing. The performance of the hybrid polygonal element formulation is demonstrated through a series of numerical examples. The results show a sensitivity of the location of the free surface in unconfined seepage to mesh configuration for hybrid quadrilateral meshes with various aspect ratios, but not for hybrid polygonal meshes with various orientations and irregularity. Examination of the free surface location results for several conforming shape function options shows an insensitivity to choice of interpolation function, provided that it conforms with the assumptions in the formulation. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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B‐bar based algorithm applied to meshfree numerical schemes to solve unconfined seepage problems through porous media 下载免费PDF全文
下载免费PDF全文 The object of this work is to establish a meshfree framework for solving coupled, steady and transient problems for unconfined seepage through porous media. The Biot's equations are formulated in displacements (or u − w) assuming an elastic solid skeleton. The free surface location and its evolution in time are obtained by interpolation of pore water pressures throughout the domain. Shape functions based on the principle of local maximum entropy are chosen for the meshfree approximation schemes. In order to avoid the locking involved in the fluid phase of the porous media, a B‐bar based algorithm is devised to compute the average volumetric strain in a patch composed of various integration points. The efficiency of such an implementation for one phase problems is shown through the Benchmark problem, Cook's membrane loaded by a distributive shear load. The proposed methodology is firstly applied to various classical examples in unconfined steady seepage problems through earth dams, then to the dynamic consolidation of a soil column. The results obtained for both problems are quite satisfactory and demonstrate the feasibility of the proposed method in solving coupled problems in porous media. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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An approximate step-by-step procedure is presented for the finite element analysis of transient unconfined flow problems. At each step the free surface is modelled by means of segments coinciding with sides of the elements. This leads to an approximate but extremely simple solution scheme which can be readily incorporated into standard codes for confined analysis. The solutions of some significant problems are presented and compared with other non-approximate solutions. They show that the technique, in spite of its approximation, is capable of giving meaningful results from an engineering viewpoint. 相似文献
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Stochastic analysis of free surface flow through earth dams 总被引：1，自引：0，他引：1
This research investigated the unconfined flow through dams. The hydraulic conductivity was modeled as spatially random field following lognormal distribution. Results showed that the seepage flow produced from the stochastic solution was smaller than its deterministic value. In addition, the free surface was observed to exit at a point lower than that obtained from the deterministic solution. When the hydraulic conductivity was strongly correlated in the horizontal direction than the vertical direction, the flow through the dam has markedly increased. It is suggested that it may not be necessary to construct a core in dams made from soils that exhibit high degree of variability. 相似文献
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裂隙岩体因含有发育程度不同的裂隙、节理和断层等不连续面,致其渗透性具有各向异性、不连续性等特点,因此传统的有限元法对分布密集的裂隙岩体渗流场求解有一定的难度。本文提出了采用无单元Glaerkin法求解有自由面裂隙渗流问题,并推导了无单元法求解渗流场的基本方程和积分格式,给出了应用罚函数法处理渗流边界条件和自由面处理方法。采用IDL语言编制了二维无单元法计算软件LIDAREFM。文中以北京怀柔桥梓镇某裂隙岩体边坡渗流场计算为例,研究了复杂裂隙共同作用下渗流场特性和自由面分布,讨论了不同开度、不同连通程度的裂隙对渗流场的影响。研究结果表明:无单元法可以较好地解决有密集裂隙的岩体渗流场的求解问题,实现了裂隙处结点任意加密以及积分网格的独立布置,避免了对有自由面和裂隙穿越的子域的重新处理,简化了渗流问题的求解过程。 相似文献
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岩体裂隙网络非稳定渗流分析与数值模拟 总被引：1，自引：0，他引：1
针对裂隙岩体的非稳定渗流问题,通过将Darcy定理扩展到包含干区的整个裂隙网络区域,并令潜在溢出边界条件为Signorini型互补边界条件,将湿区上的非稳定渗流问题转化为全域上的一个新的初边值问题。为降低试探函数选取的难度,建立与定义在整个裂隙网络区域上的偏微分方程（PDE）提法等价的抛物型变分不等式（PVI）提法,并给出裂隙网络非稳定渗流分析的有限元数值分析格式和迭代算法,与砂槽模型试验数据的对比分析,验证其有效性。最后,将文中发展的计算方法应用到含复杂裂隙网络的边坡非稳定渗流分析,计算结果很好地反映出边坡内部自由面随库水降落的变化规律,并能准确地描述裂隙网络内部渗流运动特征及流量分布的不均匀性。 相似文献
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A major challenge in seepage analysis is to locate the phreatic surface in an unconfined aquifer. The phreatic surface is unknown and assumed as a discontinuity separating the seepage domain into dry and wet parts, thus should be determined iteratively with special schemes. In this study, we systematically developed a new numerical manifold method (NMM) model for unconfined seepage analysis. The NMM is a general numerical method for modeling continuous and discontinuous deformation in a unified mathematical form. The novelty of our NMM model is rooted in the NMM two‐cover‐mesh system: the mathematical covers are fixed and the physical covers are adjusted with iterations to account for the discontinuity feature of the phreatic surface. We developed an energy‐work seepage model, which accommodates flexible approaches for boundary conditions and provides a form consistent with that in mechanical analysis with clarified physical meaning of the potential energy. In the framework of this energy‐work seepage model, we proposed a physical concept model (a pipe model) for constructing the penalty function used in the penalty method to uniformly deal with Dirichlet, Neumann, and material boundaries. The new NMM model was applied to study four example problems of unconfined seepage with varying geometric shape, boundary conditions, and material domains. The comparison of our simulation results to those of existing numerical models for these examples indicates that our NMM model can achieve a high accuracy and faster convergence speed with relatively coarse meshes. This NMM seepage model will be a key component of our future coupled hydro‐mechanical NMM model. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
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改进的遗传算法及其在渗流参数反演中的应用 总被引：11，自引：5，他引：6
利用水头实测资料,以裂隙组的渗透系数比例因子为待反演的参数向量,在采用基本遗传算法进行参数反演研究的基础上,针对裂隙岩体无压渗流参数反问题计算量过大,目标参数众多以及参数可能变化范围大等特点,提出了一种混合遗传算法求解此类问题,力求克服简单遗传算法在解决此类问题时存在的局部搜索能力弱、易出现早熟收敛及计算量大等缺陷,并通过典型岩坡渗流算例进行验证,同时给出了基本遗传算法、传统单纯形算法的反演成果。计算结果表明,该方法保持了基本遗传算法优点,并有效地提高了算法的运行效率,从而为求解裂隙岩体无压渗流参数反问题等计算量大的系列问题提供了新的途径。 相似文献
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针对无压渗流问题,在传导矩阵调整法的基础上,对穿越自由面的单元用复合单元来处理,每个复合单元具有两套结点水头,一套用于饱和区的水头插值;另一套则用于无水区。通过变分原理,推出了控制方程并在程序中实现。应用复合单元法可以较好地解决自由面的插值问题,消除了穿过自由面单元的水上部分对自由面附近结点水头的贡献,同时对逸出面边界条件的处理也更加方便和准确。算例表明了该方法的有效性。 相似文献
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Grid adaptive methods combined with domain adaptation are discussed for two-dimensional seepage flow problems with free boundaries through porous media. Examples of grid and domain adaptive methods are presented to demonstrate several ways to predict grids and shapes of free boundaries using an iterative scheme. Finally, the combined adaptive methods are applied to obtain smooth non-oscillatory shape of a free boundary of seepage flow through non-homogeneous porous media. 相似文献
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考虑初始面非水平条件,建立河流边界控制下的半无限含水层渗流模型,提出非水平初始面及其相关参数（a、tN）的简易计算方法,并探讨模型的适用条件。分析表明,该法适用于观测数据较少、地下水水位变幅相对于潜水含水层厚度较小、且观测孔距河岸较近条件下河流附近潜水含水层渗流计算。结合实例,采用查表法和配线法求解模型。计算结果表明:参数a和tN的计算值不同,水位计算误差在0.02 m以内,较原公式精度有明显提高。新模型为初始面非水平条件下的潜水渗流计算提供一种简易方法。 相似文献
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岩土体的渗透破坏、地下工程的防渗设计等无不与渗流计算有关。针对渗流自由面问题,提出一种重心拉格朗日插值的配点型无网格方法。由于渗流自由面问题的求解区域是不规则区域,该方法通过将不规则求解区域嵌入一个正则矩形区域,在正则区域上采用重心拉格朗日插值近似未知函数,利用配点法离散渗流问题的控制方程,将重心拉格朗日插值的微分矩阵离散成代数方程表达的矩阵形式。将自由面上的边界条件通过重心拉格朗日插值离散,通过置换方程法和附加方程法施加边界条件,利用正则区域上的重心插值配点法,通过迭代确定最终自由面的位置。数值算例表明所提出的无网格方法对于求解渗流自由面问题的正确性和高精度。 相似文献
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由含水层底部向上施工疏放水孔（井）进行疏水降压是保证煤矿安全开采的重要措施之一,该类疏放水孔与地面抽水井的渗流特征具有显著差别。为了研究井下疏放水孔的渗流特征,以非承压含水层底部单井疏放水孔为例,采用数值模拟的方法对其渗流特征进行研究。研究结果表明,当疏放水井的井长lw小于临界长度lc时,即lwc,疏放水井上部含水层孔隙水压力大于0,且由下而上呈先增加后减小的分布规律,渗流量与井长呈指数函数关系增加;当lw ≥ lc时,疏放水非完整井的渗流特征及渗流量与完整井相同;渗流量随井半径增加呈指数关系增加,且指数小于1;将s+lw代替水位降深s对裘布依（Dupuit）潜水完整井计算公式进行修正,当lwc时,采用修正的Dupuit潜水完整井计算公式计算疏放水非完整井渗流量更精确。该研究结果对认识井下疏放水井上部孔隙水压力分布特征及合理布置疏放水井具有重要的借鉴意义。 相似文献