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1.
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
2.
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
3.
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
4.
A new artificial boundary approach for transient seepage problems in unbounded domain is presented. The artificial boundary condition at the truncated boundary is derived from the analytical solutions for transient seepage problems in one dimension, including solutions, respectively, for flow in one‐dimensional infinite space and for radial flow in an infinite layer, and then it is tentatively applied for some two dimensional problems in addition to the one‐dimensional problems mentioned above. The boundary conditions derived relate the time‐dependent boundary flux with the time derivative of the hydraulic head at the truncated boundary, which makes the implementation much easier compared with the infinite element method. The accuracy and efficiency of the artificial boundary are validated by several numerical examples, which shows that the proposed boundary can give very good results for one‐dimensional transient seepage problems, as expected, whereas reasonable results can be also obtained for two‐dimensional problems, such as two‐dimensional axisymmetric flow and flow in an infinite plane. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
5.
A local artificial boundary for transient seepage problems with unsteady boundary conditions in unbounded domains 
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下载免费PDF全文 Numerical analysis of transient seepage in unbounded domains with unsteady boundary conditions requires a more sophisticated artificial boundary approach to deal with the infinite character of the domain. To that end, a local artificial boundary is established by simplifying a global artificial boundary. The global artificial boundary conditions (ABCs) at the truncated boundary are derived from analytical solutions for one‐dimensional axisymmetric diffusion problems. By applying Laplace transforms and introducing some specially defined auxiliary variables, the global ABCs are simplified to local ABCs to significantly enhance the computational efficiency. The proposed local ABCs are implemented in a finite element computer program so that the solutions to various seepage problems can be calculated. The proposed approach is first verified by the computation of a one‐dimensional radial flow problem and then tentatively applied to more general two‐dimensional cylindrical problems and planar problems. The solutions obtained using the local ABCs are compared with those obtained using a large element mesh and using a previously proposed local boundary. This comparison demonstrates the satisfactory performance and obvious superiority of the newly established boundary to the other local boundary. Copyright © 2017 John Wiley & Sons, Ltd. 相似文献
6.
A finite element procedure is developed to accurately locate the free surface of unconfined seepage flow through porous media. The free surface is taken as the boundary between wet and dry soils, with flow in the saturated region characterized by Darcy's law. The method involves equations and meshing which are fully consistent with a general formulation for geotechnical engineering problems involving simultaneous solution of pore fluid pressures and soil skeleton displacements. Accuracy and versatility of the proposed procedure are demonstrated by solving various unconfined seepage flow problems through earth structures. Free surfaces and flownets are presented for the calculated flow fields. 相似文献
7.
A high‐frequency open boundary for transient seepage analyses of semi‐infinite layers by extending the scaled boundary finite element method 下载免费PDF全文
下载免费PDF全文 Suriyon Prempramote 《国际地质力学数值与分析法杂志》2016,40(6):919-941
A high‐frequency open boundary has been developed for the transient seepage analyses of semi‐infinite layers with a constant depth. The scaled boundary finite element equation of pore water pressure is formulated first in the frequency domain. With the eigenvalue problem, the equation can be decoupled into modal equations whose modal dynamic permeability equation can be determined. The continued fraction technique is adopted to formulate the continued fraction solution in the frequency domain. All constants in the solution are determined recursively at the high‐frequency limit. By introducing auxiliary variables and the continued fraction solution to the relationship between the prescribed seepage flow and the pore water pressure in the frequency domain, the open boundary condition is obtained. After transformed to the time domain, the open boundary condition is expressed as a system of fractional differential equations. No convolution integral is required. The accuracy of the analysis results increases with the increasing orders of continued fraction. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
8.
One dimensional solutions for the classic critical upward seepage gradient/quick condition and the time rate of consolidation problems are obtained using coupled routines for the finite volume method (FVM) and discrete element method (DEM), and the results compared with the analytical solutions. The two phase flow in a system composed of fluid and solid is simulated with the fluid phase modeled by solving the averaged Navier–Stokes equation using the FVM and the solid phase is modeled using the DEM. A framework is described for the coupling of two open source computer codes: YADE-OpenDEM for the discrete element method and OpenFOAM for the computational fluid dynamics. The particle–fluid interaction is quantified using a semi-empirical relationship proposed by Ergun [12]. The two classical verification problems are used to explore issues encountered when using coupled flow DEM codes, namely, the appropriate time step size for both the fluid and mechanical solution processes, the choice of the viscous damping coefficient, and the number of solid particles per finite fluid volume. 相似文献
9.
B. Nath 《国际地质力学数值与分析法杂志》1981,5(2):139-163
A novel finite element method has been proposed in this paper for the solution of seepage problems economically and accurately. In this method the governing equation and the prescribed boundary conditions are transformed so that they refer to a suitable logarithmically condensed ‘image’ space; the physical problem domain is also mapped into the image space. The transformed equation is then solved in the image space using standard finite elements, subject to the transformed boundary conditions. Because physical space is logarithmically condensed in the image space, the proposed method is capable of dealing with large or very large aspect ratio seepage problems economically and accurately. The validity of the method has been demonstrated by means of a number of examples including anisotropy and non-linearity. In all cases an excellent degree of accuracy was achieved, efficiently and economically. 相似文献
10.
为解决城区渗流场中缝隙多、区域的大尺度与物体的小尺寸相差了几个数量级,有限元分析上存在的困难,根据缝隙流动的解析解,经适当地简化,将缝隙附近的渗流场分为缝外区和缝内区两部分,将缝外区流动简化为一个半径为半缝宽的井流,缝内区流动简化为一个均匀流。引入附加阻力系数,考虑缝隙出入口附近的由于过水断面突然变化而引的局部水头损失,并得到附加阻力系数的表达式。利用该式,结合渗流场中井点水头的修正公式,得到了能有效模拟渗流场中建筑物间缝隙的修正线单元公式。利用该线单元编制了相关程序模拟城区渗流场中的缝隙,使得缝隙出入口处的网格尺寸为缝隙两边的建筑物边长1/3～1/4时就能得到较为准确的结果,避免了区域性渗流场中小尺寸物体的网格划分问题,通过算例验证了该公式的精度和边界适应性。 相似文献
11.
为解决城区渗流场中缝隙多、区域的大尺度与物体的小尺寸相差了几个数量级，有限元分析上存在的困难，根据缝隙流动的解析解，经适当地简化，将缝隙附近的渗流场分为缝外区和缝内区两部分，将缝外区流动简化为一个半径为半缝宽的井流，缝内区流动简化为一个均匀流。引入附加阻力系数，考虑缝隙出入口附近的由于过水断面突然变化而引的局部水头损失，并得到附加阻力系数的表达式。利用该式，结合渗流场中井点水头的修正公式，得到了能有效模拟渗流场中建筑物间缝隙的修正线单元公式。利用该线单元编制了相关程序模拟城区渗流场中的缝隙，使得缝隙出入口处的网格尺寸为缝隙两边的建筑物边长1/3～1/4时就能得到较为准确的结果，避免了区域性渗流场中小尺寸物体的网格划分问题，通过算例验证了该公式的精度和边界适应性。 相似文献
12.
Abbas El‐Zein 《国际地质力学数值与分析法杂志》2008,32(3):265-287
Finite‐element models of contaminant transport through composite landfill liners require highly refined meshes around the interface between the geomembrane and the clay layer, especially if leakage through holes in the geomembrane is considered. In addition, no general formulation for transport through leaking geomembranes can be found in the literature. The paper develops a general approach to time‐dependent contaminant migration through composite liners with intact or leaking geomembranes. Equations are derived for various combinations of system conditions including Dirichlet and Neumann boundary conditions in the waste, constant mass of contaminants in the waste, steady state or transient transport in the geomembrane, and steady state or transient seepage velocities in the mineral liner. The effect of the geomembrane on transport in the soil is converted into an equivalent boundary condition applicable at the top of the clay layer. Hence, only the media underlying the top geomembrane are explicitly represented in the numerical model, yielding a computationally efficient algorithm. The new formulation is validated in conjunction with finite‐layer, finite‐element and boundary‐element methods, by comparing its predictions to those of more conventional approaches which represent the geomembrane explicitly. The scope of the method is illustrated by modelling a landfill liner with a geomembrane leaking in five locations. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
13.
A challenging computational problem arises when a discrete structure (e.g. foundation) interacts with an unbounded medium (e.g. deep soil deposit), particularly if general loading conditions and non‐linear material behaviour is assumed. In this paper, a novel method for dealing with such a problem is formulated by combining conventional three‐dimensional finite‐elements with the recently developed scaled boundary finite‐element method. The scaled boundary finite‐element method is a semi‐analytical technique based on finite‐elements that obtains a symmetric stiffness matrix with respect to degrees of freedom on a discretized boundary. The method is particularly well suited to modelling unbounded domains as analytical solutions are found in a radial co‐ordinate direction, but, unlike the boundary‐element method, no complex fundamental solution is required. A technique for coupling the stiffness matrix of bounded three‐dimensional finite‐element domain with the stiffness matrix of the unbounded scaled boundary finite‐element domain, which uses a Fourier series to model the variation of displacement in the circumferential direction of the cylindrical co‐ordinate system, is described. The accuracy and computational efficiency of the new formulation is demonstrated through the linear elastic analysis of rigid circular and square footings. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
14.
This paper proposed a numerical formulation for unsaturated flow problems with nonlinear boundaries of seepage face and soil–atmosphere interface via the concept of parabolic variational inequality (PVI) method. A unified unilateral boundary condition was first proposed to represent the conditions on the seepage face and soil–atmosphere interface boundaries within the partial differential equation (PDE) formulation. A PVI formulation mathematically equivalent to the PDE formulation was then proposed, which automatically transforms the flux part of the unified unilateral boundary condition into the natural boundary condition and eliminates the singularity at seepage points. By discretizing the PVI formulation, a finite element procedure together with an iterative algorithm was suggested. An existing experiment of unsaturated flow in a layered hillside and a laboratory test of unsaturated flow through sand flume performed in this study were used to validate the proposed method, with a good agreement between the measured and computed results and a satisfactory balance of mass being maintained during the simulations. The numerical results also indicated that the problem of mesh dependence associated with unsaturated flow simulations is well addressed with the proposed numerical method. Finally, the process of unsaturated flow in a soil slope with layers of horizontal drains subjected to rainfall/evaporation was further examined. The numerical results reveal that the deployment of drains in a soil slope can significantly lower the pore water pressure around the drains, with the bottom layer drains being most effective in controlling the seepage flow. 相似文献
15.
Noboru Kikuchi 《国际地质力学数值与分析法杂志》1977,1(3):283-297
The theory of variational inequalities enables us to formulate and solve free boundary problems in fixed domains, while most other methods assume the position of the unknown domain in solving the problem. Here the problem of seepage flow through a rectangular dam with a free boundary is formulated as a vertical inequality following the ideas of Baiocchi. In order to demonstrate the essential ideas of extending the domain of the solution of problems with free boundaries, the problem of the deflection, of a string on a rigid support is first examined. Next, variational inequalities are derived which are associated with several cases of seepage problems. An approximation theory, including a priori error estimates, is developed using finite element methods, and an associated numerical scheme is given. It is shown that for linear and quadratic finite element methods, the rates of convergence are 0(h) and 0(h1.25-δ), 0 < δ < 0.25, respectively, if the permeability is constant. 相似文献
16.
A finite element approach based on an advanced multi‐surface kinematic constitutive model is used to evaluate the bearing capacity of footings resting on granular soils. Unlike simple elastic‐perfectly plastic models, often applied to granular foundation problems, the present model realistically accounts for stress dependency of the friction angle, strain softening–hardening and non‐associativity. After the model and its implementation into a finite element code are briefly discussed, the numerical difficulty due to the singularity at the footing edge is addressed. The bearing capacity factor Nγ is then calculated for different granular materials. The effect of footing size, shape, relative density and roughness on the ultimate bearing capacity are studied and the computed results compare very favourably with the general experimental trends. In addition, it is shown that the finite element solution can clearly represent counteracting mechanisms of progressive failure which have an important effect on the bearing capacity of granular foundations. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
17.
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
18.
This paper is concerned with the transient vibration analysis of railway-ground system under fast moving loads. A 3D finite element method in a convected coordinate system moving with the load is formulated, together with viscous-elastic transmitting boundary conditions in order to limit the finite element mesh. A method is proposed to introduce Rayleigh type material damping in the finite element formulation in the moving coordinate system, while measures have also been taken to improve the numerical stability of the solution procedure. The performance of the transmitting boundary and the entire solution procedure are assessed via comparison with the ordinary finite element solution of some relatively simple problems and through a comparison with field measurements. The reasonable agreement found from these comparisons demonstrates the validity of the proposed method. 相似文献
19.
A set of mapping functions in the form of convergent series for an infinite element, which is capable to include the infinitely distanced constant head boundary condition from the area of disturbance (e.g. pumping), is proposed based on the asymptotic far-field behaviour of typical seepage flow problems. The derived mapping functions have been successfully used in three-dimensional point symmetric, two-dimensional axi-symmetric and one-dimensional unidirectional flow for the fixed head boundary at infinite distance. The result shows excellent agreement with analytical solution. For the first time, the mapping function of an infinite element is presented in the form of a convergent series. The infinite elements are really capable of reducing the cost and efficiency of conventional finite element analysis. Finally, a figure is also proposed to indicate the required size of the near field to obtain accurate drawdown at specified locations based on some calculations for two-dimensional radial flow case. 相似文献