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1.
The main objective of this work is to develop a novel moving‐mesh finite‐volume method capable of solving the seepage problem in domains with arbitrary geometries. One major difficulty in analysing the seepage problem is the position of phreatic boundary which is unknown at the beginning of solution. In the current algorithm, we first choose an arbitrary solution domain with a hypothetical phreatic boundary and distribute the finite volumes therein. Then, we derive the conservative statement on a curvilinear co‐ordinate system for each cell and implement the known boundary conditions all over the solution domain. Defining a consistency factor, the inconsistency between the hypothesis boundary and the known boundary conditions is measured at the phreatic boundary. Subsequently, the preceding mesh is suitably deformed so that its upper boundary matches the new location of the phreatic surface. This tactic results in a moving‐mesh procedure which is continued until the nonlinear boundary conditions are fully satisfied at the phreatic boundary. To validate the developed algorithm, a number of seepage models, which have been previously targeted by the other investigators, are solved. Comparisons between the current results and those of other numerical methods as well as the experimental data show that the current moving‐grid finite‐volume method is highly robust and it provides sufficient accuracy and reliability. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
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Farhang Daneshmand 《国际地质力学数值与分析法杂志》2012,36(6):780-797
One major difficulty in seepage analyses is finding the position of phreatic surface which is unknown at the beginning of solution and must be determined in an iterative process. The objective of the present study is to develop a novel non‐boundary‐fitted mesh finite‐element method capable of solving the unconfined seepage problem in domains with arbitrary geometry and continuously varied permeability. A new non‐boundary‐fitted finite element method named as smoothed fixed grid finite element method (SFGFEM) is used to simplify the solution of variable domain problem of unconfined seepage. The gradient smoothing technique, in which the area integrals are transformed into the line integrals around edges of smoothing cells, is used to obtain the element matrices. The solution process starts with an initial guess for the unknown boundary and SFGFEM is used to approximate the field variable. The boundary shape is then modified to eventually satisfy nonlinear boundary condition in an iterative process. Some numerical examples are solved to evaluate the applicability of the proposed method and the results are compared with those available in the literature. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
3.
针对数值流形方法特有的覆盖剖分方式,提出了一种模拟岩土工程中开挖过程的算法。该算法采取某种措施,在覆盖剖分过程中将开挖面视为特殊的不连续面,这种不连续面将其所在的数学网格剖分成不同的流形单元,但却不对所在的数学覆盖作剖分。这样,开挖面两侧虽分属不同的流形单元,但开挖面两侧同一数学网格内的流形单元却具有相同的物理覆盖。采用该算法,无需对开挖面处的单元进行特殊处理,可在整个分析域采用统一的网格形式;同时,打破了原有数值流形方法的限制,将开挖面的位置完全当作连续介质来处理,避免了因将其视为不连续面而产生的误差。验证了算法的可靠性后,将其应用于某假想隧道的开挖模拟,计算结果表明该算法具有一定的应用前景。 相似文献
4.
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
5.
In this paper, the numerical manifold method (NMM) is extended to study wave propagation across rock masses. First, improvements to the system equations, contact treatment, and boundary conditions of the NMM are performed, where new system equations are derived based on the Newmark assumption of the space–time relationship, the edge‐to‐edge contact treatment is further developed for the NMM to handle stress wave propagation across discontinuities, and the viscous non‐reflection boundary condition is derived based on the energy minimisation principle. After the modification, numerical comparisons between the original and improved NMM are presented. The results show that the original system equations result in artificial numerical damping, which can be overcome by the Newmark system equations. Meanwhile, the original contact scheme suffers some calculation problems when modelling stress wave propagation across a discontinuity, which can be solved by the proposed edge‐to‐edge contact scheme. Subsequently, the influence of the mesh size and time step on the improved NMM for stress wave propagation is studied. Finally, 2D wave propagation is modelled, and the model's results are in good agreement with the analytical solution. Copyright © 2013 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
7.
When tunneling is carried out beneath the groundwater table, hydraulic boundary is altered, resulting in seepage entering into the tunnel. The development of flow into the tunnel induces seepage stresses in the ground and the lining is subjected to additional loads. This can often cause fine particles to move, which clog the filter resulting in the long‐term hydraulic deterioration of the drainage system. However, the effect of seepage force is generally not considered in the analysis of tunnel. While several elastic solutions have been proposed by assuming seepage in an elastic medium, stress solutions have not been considered for the seepage force in a porous elasto‐plastic medium. This paper documents a study that investigates the stress behavior, caused by seepage, of a tunnel in an elasto‐plastic ground and its effects on the tunnel and ground. New elasto‐plastic solutions that adopt the Mohr–Coulomb failure criterion are proposed for a circular tunnel under radial flow conditions. A simple solution based on the hydraulic gradient obtained from a numerical parametric study is also proposed for practical use. It should be noted that the simple equation is useful for acquiring additional insight into a problem on a tunnel under drainage, because only a minimal computational effort is needed and considerable economic benefits can be gained by using it in the preliminary stage of tunnel design. The proposed equations were partly validated by numerical analysis, and their applicability is illustrated and discussed using an example problem. Comments on the tunnel analysis are also provided. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
8.
By extending Darcy's law to the dry domain above the free surface and specifying the boundary condition on the potential seepage surfaces as Signorini's type, a partial differential equation (PDE) defined in the entire domain of interest is formulated for non‐steady seepage flow problems with free surfaces. A new parabolic variational inequality (PVI) formulation equivalent to the PDE formulation is then proposed, in which the flux part of the complementary condition of Signorini's type in the PDE formulation is transformed into natural boundary condition. Consequently, the singularity at the seepage points is eliminated and the difficulty in selecting the trial functions is significantly reduced. By introducing an adaptive penalized Heaviside function in the finite element analysis, the numerical stability of the discrete PVI formulation is well guaranteed. The proposed approach is validated by the existing laboratory tests with sudden rise and dropdown of water heads, and then applied to capture the non‐steady seepage flow behaviors in a homogeneous rectangular dam with five drainage tunnels during a linear dropdown of upstream water head. The non‐steady seepage flow in the surrounding rocks of the underground powerhouse in the Shuibuya Hydropower Project is further modeled, in which a complex seepage control system is involved. Comparisons with the in situ monitoring data show that the calculation results well illustrate the non‐steady seepage flow process during impounding and the operation of the reservoir as well as the seepage control effects of the drainage hole arrays and drainage tunnels. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
9.
Development of a discontinuous approach for modeling fluid flow in heterogeneous media using the numerical manifold method 
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下载免费PDF全文 In the numerical modeling of fluid flow in heterogeneous geological media, large material contrasts associated with complexly intersected material interfaces are challenging, not only related to mesh discretization but also for the accurate realization of the corresponding boundary constraints. To address these challenges, we developed a discontinuous approach for modeling fluid flow in heterogeneous media using the numerical manifold method (NMM) and the Lagrange multiplier method (LMM) for modeling boundary constraints. The advantages of NMM include meshing efficiency with fixed mathematical grids (covers), the convenience of increasing the approximation precision, and the high integration precision provided by simplex integration. In this discontinuous approach, the elements intersected by material interfaces are divided into different elements and linked together using the LMM. We derive and compare different forms of LMMs and arrive at a new LMM that is efficient in terms of not requiring additional Lagrange multiplier topology, yet stringently derived by physical principles, and accurate in numerical performance. To demonstrate the accuracy and efficiency of the NMM with the developed LMM for boundary constraints, we simulate a number of verification and demonstration examples, involving a Dirichlet boundary condition and dense and intersected material interfaces. Last, we applied the developed model for modeling fluid flow in heterogeneous media with several material zones containing a fault and an opening. We show that the developed discontinuous approach is very suitable for modeling fluid flow in strongly heterogeneous media with good accuracy for large material contrasts, complex Dirichlet boundary conditions, or complexly intersected material interfaces. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
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Numerical simulation of groundwater flowing to horizontal seepage wells under a river 总被引：6，自引：0，他引：6
A horizontal seepage well, consisting of an interconnected vertical well, galleries, chambers and small-diameter radiating
bores, is used to acquire relatively clean water that has been filtered through natural alluvial deposits in a riverbed. It
has wide application, especially in arid and semi-arid areas. The lack of calculation formulae or models for horizontal seepage
wells, up until now, has resulted in several false applications. Based on the analysis of groundwater flow characteristics,
it has been concluded that several flow regimes coexist and hydraulic head loss exists in the horizontal seepage well. To
avoid the difficulty of confirming the flux or head distribution in such a complex system, the model boundary of the whole
horizontal seepage well has been moved to that of just the vertical well, and the well-aquifer system was treated as a heterogeneous
medium, where the horizontal seepage well itself is a highly permeability medium. A mathematical model has been developed,
based on the coupled seepage-pipe flow, by the introduction of equivalent hydraulic conductivity according to different flow
regimes. Then a three-dimensional finite difference numerical model, based on the mathematical model, was developed and applied
to a horizontal seepage well in China. The numerical model verified the groundwater flow characteristics of the horizontal
seepage well.
An erratum to this article can be found at 相似文献
12.
Particle manifold method (PMM) is a new extension of the numerical manifold method (NMM). PMM uses a mathematical cover system to describe the motion and deformation of a particle‐based physical domain. By introducing the concept of particle into NMM, PMM takes the advantages of easy topological and contact operations with particles. In this article, the methodology, formulations and implementation of the method are presented, together with modelling examples for validation. It is found that good solutions for both continuous and discontinuous problems are obtained by the new developed PMM. Due to the underlying coupled continuum‐discontinuum property of PMM, it has great potential for modelling of geomechanical problems. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
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In this study, a simplified analytical closed‐form solution, considering plane strain and axial symmetry conditions, for analysis of a circular pressure tunnel excavated underwater table, is developed. The method accounts for the seepage forces with the steady‐state flow and is based on the generalized effective stress law. To examine the effect of pore pressure variations and also the boundary conditions at the ground surface, the formulations are derived for different directions around the tunnel. The proposed method can be applied for analysis and design of pressure tunnels. Illustrative examples are given to demonstrate the performance of the proposed solution and also to examine the effect of seepage forces on the stability of tunnels. The simplified analytical solution derived in this study is compared with numerical analyses. It is concluded that the classic solutions (Lame's thick‐walled solution), considering the internal pressure as a mechanical load applied to the tunnel surface, are not applicable to pervious media and can result in an unsafe design. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
15.
Transient seepage analysis in zoned anisotropic soils based on the scaled boundary finite‐element method 下载免费PDF全文
下载免费PDF全文 The scaled boundary finite‐element method, a semi‐analytical computational scheme primarily developed for dynamic stiffness of unbounded domains, is applied to the analysis of unsteady seepage flow problems. This method is based on the finite‐element technology and gains the advantages of the boundary element method as well. Only boundary of the domain is discretized, no fundamental solution is required and singularity problems can be modeled rigorously. Anisotropic and non‐homogeneous materials satisfying similarity are modeled with no additional efforts. In this study, firstly, formulation of the method for the transient seepage flow problems is derived followed by its solution procedures. The accuracy, simplicity and applicability of the method are demonstrated via four numerical examples of transient seepage flow – three of them are available in the literature. Homogenous, non‐homogenous, isotropic and anisotropic material properties are considered to show the versatility of the technique. Excellent agreement with the finite‐element method is observed. The method out‐performs the finite‐element method in modeling singularity points. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
16.
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
17.
A numerical model to predict landslide movements along pre‐existing slip surfaces from rainfall data is presented. The model comprises: a transient seepage finite‐element analysis to compute the variations of pore water pressures due to rainfall; a limit equilibrium stability analysis to compute the factors of safety along the slip surface associated with transient pore pressure conditions; an empirical relationship between the factor of safety and the rate of displacement of the slide along the slip surface; an optimization algorithm for the calibration of analyses and relationships based on available monitoring data. The model is validated with reference to a well‐monitored active slide in central Italy, characterized by very slow movements occurring within a narrow band of weathered bedrock overlaid by a clayey silt colluvial cover. The model is conveniently divided and presented in two parts: a groundwater model and a kinematic model. In the first part, monthly recorded rainfall data are used as time‐dependent flow boundary conditions of the transient seepage analysis, while piezometric levels are used to calibrate the analysis by minimizing the errors between monitoring data and computed pore pressures. In the second part, measured inclinometric movements are used to calibrate the empirical relationship between the rate of displacement along the slip surface and the factor of safety, whose variation with time is computed by a time‐dependent stability analysis. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
18.
Analytical solutions for the two-dimensional problem of unconfined seepage towards semi-infinite slopes are described. The analysis employs complex variable techniques. Conformal mappings have been used to reduce the problem to solving an ordinary differential equation. The resulting integrals are presented in terms of special functions. The solutions for the location of the phreatic surface and the exit point have been obtained in parametric form. Some additional results and asymptotic expansions of the solutions are also presented. The numerical results have been calculated and plotted for different values of the slope angle in dimensionless co-ordinate space. 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