Unconfined Seepage Problems Research Articles

A new procedure for locating free surfaces of complex unconfined seepage problems using fixed meshes

The main challenge in the analysis of unconfined seepage flow is that the position of free surfaces is unknown a priori, which needs to be determined through a series of iterative processes. The numerical manifold method (NMM) is a promising method which uses a dual cover system consisting of both mathematical and physical covers. Compared with those traditional methods, NMM is characterized by meshing convenience, approximation accuracy, and being capable of coping with free boundary value problems. Unlike the traditional NMM where the material interface participates in cutting the mathematical cover while forming the physical cover, the physical patches in this study can contain the material interface. The new weight functions for such physical patches are constructed using the refraction law, followed by the application to the analysis of unconfined seepage flow problems. By comparing with analytical or reference solutions of some classic examples, it is validated that the proposed method can accurately locate the free surface, demonstrating its accuracy and convenience in solving unconfined seepage problems.

Simulation of unconfined seepage in soil-rock mixture slope by virtual element method

Abstract The VEM (virtual element method) is commonly used in engineering due to its ability to solve arbitrary node meshes. In this study, we propose a method to determine the free surface of the unconfined seepage problem in soil-rock mixtures slop using the advantages of the VEM. By cutting meshes in the iteration, our method overcomes the limitation of fixed mesh in solving the free surface, and the numerical tests confirm the accuracy of the proposed method in predicting the location of the seepage surface. Moreover, the results demonstrate that the presence of rock blocks significantly impacts the unconfined seepage behavior of soil-rock mixtures slop, revealing the importance of considering rock blocks in the analysis of such systems.

Saturated‐unsaturated seepage simulation and hydrological dam models for quantifying the heterogeneity to hydrological state variables: Impacts of auxiliary structures and leakage anomalies

AbstractSeepage analysis is the central issue in solving the unconfined seepage problems from complex earth‐rock dams. The precision and efficiency of seepage simulation are the major technical barriers to exploring the heterogeneities of hydrological state variables in dams. This paper addresses the heterogeneity of the saturated‐unsaturated zones of dams and develops the smoothed finite element method (S‐FEM) capable of solving the seepage problem in domains with arbitrary geometry and continuously varied permeability. 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, which is used to simplify the solution of seepage problem. To be specific, we employ Van Genuchten method to modify the hydraulic conductivity of unsaturated zones medium and Signorini condition to convert the outflow boundary into the water head boundaries. The precision of the proposed method together with the importance of considering the unsaturated zones are first deliberated by the verification tests. Then, to quantify the impacts on the hydrological state variables, we focus on the heterogeneity of the entire zones through exploratory tests. The results show that the presence of leakage anomalies and auxiliary dam structures has a significant effect on the redistribution of hydrological state variables, which convinces that the findings may lay the foundation for the development of multi‐parameter seepage inversion and the derivation of coupled hydro‐geophysical inversion using the most appropriate starting model.

Optimization variant of the shear strength reduction method and its usage for stability of embankments with unconfined seepage

In this paper, an optimization variant of the shear strength reduction method is introduced and used for the solution of embankment stability problems with unconfined seepage. The optimization framework is based on approximations of non-associated Mohr–Coulomb plastic models with associated ones, especially by using various Davis’ approaches. Next, the finite element method is considered and mesh adaptive solution concepts are developed for both the unconfined seepage and stability problems. In-house codes in Matlab are used for their implementation. Finally, two numerical examples inspired by geotechnical practice are investigated in order to demonstrate the accuracy of the optimization framework and to evaluate three different Davis’ approaches. The results are compared with commercial codes in Plaxis and Comsol Multiphysics.

An equivalent pipe network model for free surface flow in porous media and its comparison with the continuum model

A simple and efficient equivalent pipe network method is developed for unconfined seepage problems in porous media. Instead of the continuum-based method, the porous media is represented by an orthogonal of pipe elements rather than triangular and quadrilateral elements in which water flow occurs. The equivalent expressions of the hydraulic conductivity parameters, the continuity equation, boundary conditions and finite element analysis are reduced to a one-dimensional problem of line elements. Two typical examples are applied to investigate the validity and advantages of the proposed equivalent pipe element method in comparison with the continuum-based method. From the steady-state free surface flow in the homogeneous, the equivalent pipe network method can well reproduce the free surface locations with the numerical solutions. However, the calculated results from the fractured porous media illustrate that the performance of the proposed method is better than the continuum-based method when considering a high- hydraulic conductivity horizontal fracture in the porous media.

An improved FE-Meshfree method for solving steady seepage problems

An improved FE-Meshfree method, formulated as a combination of finite element method (FEM) and radial point interpolation method (RPIM), has been proposed in this paper, aiming for obtaining a more accurate and robust solution for steady seepage problems. Two main aspects are mainly investigated: firstly, the traditional cell-based discretization and assembly procedure as normally seen in FEM is replaced by a support domain based one, which potentially improves the computed results with a higher tolerance with the mesh distortion; secondly, an adaptation procedure of inserting extra field nodes on the boundaries/interfaces is proposed and incorporated, which shows an improved computational accuracy and stability. The superiority of the method is demonstrated via some applications to both confined and unconfined seepage problems.

A practical adaptive moving-mesh algorithm for solving unconfined seepage problem with Galerkin finite element method

One of the great challenges of unconfined seepage through a dam lies in the accurate determination of free surface that depends on the complexity of the seepage model, especially if the model is characterized with complex geometry and sharp variations in permeability distribution. This study presents a practical methodology that combines the adaptive moving-mesh algorithm and the Galerkin finite element method (FEM) to solve an unconfined seepage problem with high efficiency and precision. The methodology employs a set of improvement terms, such as remainder factor, step-size parameter and termination condition, all of which guarantee that the simulation and the refinement fitting can be implemented efficiently until the free surface converges within a given allowable error. In particular, a specialized discussion is presented for the significant relation between the location of the exit point and the corresponding grid fineness. To validate the practicability of the proposed method, a series of examples are performed. Comparing the result with those of other numerical approaches, we conclude that even though the unconfined seepage model may be complicated with arbitrary complex geometry and sharp variations in permeability distribution, the proposed algorithm provides a great improvement in efficiency and accuracy in free-surface searching.

Isogeometric analysis in solution of unconfined seepage problems

This article investigates the numerical solution of saturated unconfined seepage problems in which a fluid with a free surface passes through a porous media. In such cases, the geometry of the wet region is unknown in advance and must be obtained through an iterative process. Such problems are known as variable domain problems. Since the use of traditional mesh based numerical methods is not straight forward due to remeshing difficulties, the isogeometric analysis is proposed here which eliminates the meshing process and accordingly makes this method an attractive tool to deal with such problems. On the other hand, the use of isogeometric analysis accounts for other difficulties which this paper aims to address. In the isogeometric analysis the boundary control points are not located on the domain boundary. Therefore, in this article, a new boundary updating formula is proposed to reconstruct the free surface. For modifying the control net, the transfinite interpolation is used in order to update the control net when the geometry undergoes any change. The domain is considered inhomogeneous with spatially varied permeability. Three benchmark examples are solved to demonstrate the applicability of the proposed method. Finally, the results are compared with those available in the literature.

Isogeometric boundary element analysis of problems in potential flow

The aim of the paper is to show that the isogeometric Boundary Element Method (isoBEM) has advantages over other numerical methods when applied to problems in potential flow. The problems presented here range from the flow past an obstacle to confined and unconfined seepage problems in isotropic and anisotropic media. It is shown how accurate results can be obtained with very few unknowns. The superior capability of NURBS to describe geometry and the variation of the unknowns is exploited.

Unconfined Seepage Analysis Using Moving Kriging Mesh-Free Method with Monte Carlo Integration

The unconfined seepage problem is a classic moving boundary problem, in which the position of phreatic surface is unknown at the beginning of solution and should be determined through iteration. Mesh-free methods are especially suitable for solving this problem. In this work, the moving Kriging mesh-free method with Monte Carlo integration is proposed. Additionally, a corresponding procedure for handling material discontinuity is presented, which extends the approach to inhomogeneous medium. The present method is a true mesh-free method, which does not require a mesh for either shape function construction or numerical integration. Another advantage of the present method is the convenient numerical implementation. Numerical examples show that the present method can achieve better convergence and higher accuracy with rational computation cost when compared with the original mesh-free method. The present method is also verified to be applicable in analyzing transient seepage through homogeneous and inhomogeneous media.

Pipe network model for unconfined seepage analysis in fractured rock masses

An efficient unconfined seepage analysis method is developed for analysing fluid flow in fractured rock mass. The proposed method discretises both porous rock matrix (a low permeability medium) and discrete fracture networks (a high permeability medium) as permeable pipe networks. A finite volume based approach is used to determine the equivalent flow parameters in the undirected pipes for the porous rock matrix such that seepage analysis in a fractured rock mass is carried out in a consistent mathematical framework which gives excellent computational accuracy and efficiency. Using an auxiliary boundary method, pipe networks in the vicinity of the phreatic surface can be adapted in unconfined seepage problems. Validated by finding the phreatic surface in dam structures, it has been found that the fracture orientation, hydraulic aperture, fracture set number and fracture distribution can affect the phreatic surface significantly in a fractured rock mass. The proposed method is applied to investigate the effectiveness of the water curtain system in a water-sealed underground crude oil storage cavern. Grouting effect can also be conveniently investigated by the unified pipe network system. Results show that the proposed method is robust in seepage analysis for both fractured and porous rock masses.

Integration of Thiele Continued Fractions and the method of fundamental solutions for solving unconfined seepage problems

Unconfined seepage through an earth dam or a levee is recognized as a challenging problem. This complexity is mainly due to the fact that determination of the phreatic line through the dam/levee body is not straightforward. For simulation purposes, mesh generation as well as accurate and smooth alteration of the phreatic line at the junction with the downstream slope (referred to as exit point) for an unconfined seepage problem with complex geometry generally makes cumbersome numerical solutions. This study presents an innovative boundary-type meshfree method to determine the phreatic line location in unconfined seepage problems. The current study explicitly addresses the problem that alternative methods commonly face to deal with the exit point. The method is developed based upon integrating the Method of Fundamental Solutions (MFS), Particle Swarm Optimization (PSO) algorithm, and Thiele Continued Fractions (TCF). To accurately estimate the phreatic line location, the proposed framework uses MFS to solve the flow continuity equation, TCF to generate the phreatic line and PSO to optimize the phreatic line location generated by TCF. As a boundary method, MFS only deals with the boundaries of the domain and consequently, it only takes the exact position of phreatic line as a variable boundary. The proposed approach employs TCF to guarantee that the phreatic line is tangent to the downstream slope at the exit point, a characteristics which is important especially for the cases where abrupt changes occur in the phreatic line near the exit point. For comparison and validation purposes, the phreatic lines determined by the proposed approach for two unconfined seepage problems are compared and verified against those obtained from alternative analytical and numerical methods as well as a set of experimental results. An excellent agreement is demonstrated upon comparison of the proposed method to the results attained from the analytical solutions and experimental tests.

Constrained optimization based F.E. mesh deforming algorithm for unconfined seepage problems

In this paper, a nonlinear programming technique is presented to calculate the location of the phreatic line in earth dams. Homogeneous and zoned earth dams with and without horizontal drain are considered in this study. A polynomial with unknown coefficients is assumed as equation of the phreatic line in the homogeneous dams. For zoned earth dams, phreatic line is considered as a multi-segment non smooth curve. Coefficients of the polynomials are calculated optimizing an objective function which is defined based on the physical conditions on the phreatic line. Seepage boundary conditions are introduced as constraints for the objective function. Linear finite elements method with adjustable mesh is used to calculate the distribution of the water pressure in the dam. An algorithm based on the location of the phreatic line is presented to construct the finite elements mesh. The result of the present method is verified by the results of the nonlinear finite elements and other mesh deforming methods.

B-bar based algorithm applied to meshfree numerical schemes to solve unconfined seepage problems through porous media

Summary 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.

The variational inequality formulation for unconfined seepage through three-dimensional dense fracture networks

The space block search technology is used to determine a connected three-dimensional fracture network in polygonal shapes, i.e., seepage paths. After triangulation on these polygons, a finite element mesh for 3D fracture network seepage is obtained. Through introduction of the generalized Darcy’s law, conservative equations for both fracture surface and fracture interactions are established. Combined with the boundary condition of Signorini’s type, a partial differential equation (PDE) formulation is presented for the whole domain concerned. To solve this problem efficiently, an equivalent variational inequality (VI) formulation is given. With the penalized Heaviside function, a finite element procedure for unconfined seepage problem in 3D fracture network is developed. Through an example in a homogeneous rectangular dam, validity of the algorithm is verified. The analysis of an unconfined seepage problem in a complex fracture network shows that the proposed algorithm is very applicable to complex three-dimensional problems, and is effective in describing some interesting phenomenon usually encountered in practice, such as “preferential flow”.

Three dimensional smoothed fixed grid finite element method for the solution of unconfined seepage problems

A three dimensional numerical analysis for unconfined seepage problems in inhomogeneous and anisotropic domains with arbitrary geometry is presented in this paper. The unconfined seepage problems are nonlinear in its nature due to unknown location of the phreatic surface and nonlinear boundary conditions which complicates its solution. The presented method is based on the application of non-boundary-fitted meshes and is an extension of the recently proposed two dimensional smoothed fixed grid finite element method. The main objective of using this method is to facilitate solution of variable domain problems and improve the accuracy of the formulation of the boundary intersecting elements. In this method, the gradient smoothing technique is used to obtain the element matrices. This technique simplifies the solution significantly by reducing the volume integrals over the elements into area integrals on the faces of smoothing cells. To locate the free surface, an initial guess for the unknown geometry is selected and modified in each iteration to eventually satisfy nonlinear boundary condition. The application of the proposed technique for three dimensional seepage problems is carried out for different examples including rectangular, trapezoidal and semi-cylindrical dams and the results are compared with those available in the literature.

The solution of unconfined seepage problem using Natural Element Method (NEM) coupled with Genetic Algorithm (GA)

Phreatic line detection is a major challenge in seepage problems which should be solved by iterative solving procedures. In conventional methods such as finite element method (FEM), an updating mesh is needed in each iteration where the qualities of the mesh and the nodal connectivity have significant impact on the results. The main aim of this study is to use a method not to be sensitive to mesh generation.In this study, to obtain the optimal phreatic line by the 4th degree polynomial, Natural Element Method (NEM) and Genetic Algorithm (GA) are implemented. Based on the energy principle, an objective function is defined to control the phreatic line position. In the optimization procedure, NEM is utilized to analyze the problem. NEM is a domain type mesh-free method, adapted to geometry of the problem in each iteration. Results display more convergence and flexibility of the present method in comparison with previous studies.

Displacement based coupled model for unconfined seepage problems applied to the Gasset Dam (Ciudad Real, Spain)

The present work shows the application of a new methodology, to find out the free surface inside earth fill dams under steady flow conditions, to a real field case: the Gasset Dam, in Ciudad Real, Spain. An accurate and fast computation of the free surface is of paramount importance, since it is a previous and necessary step for evaluating the safety of an earth dam in terms of its stress–strain behavior. This new methodology is based on a coupled numerical model formulated in terms of displacements (so called u–w formulation) instead of a more usual approach of water heads. The developed general code has been previously validated using several theoretical seepage problems through porous media. The selected field case is an earth dam built a century ago, which has been subjected to several rehabilitation works since then. Hence, it is a very irregular and nonhomogeneous dam. The comparison of computations and real field measurements, in terms of the free surface location and the total discharge through the dam under steady conditions, is presented in this paper, demonstrating the accuracy and applicability of this formulation to this kind of problems.

Analysis for 3-D Seepage Field of Gravity Dam Foundation

An equivalent method that simulate drainage holes is adopted in the analysis of 3-D seepage field. The Initial Flow Method is applied in this paper to deal with the unconfined seepage problem. In this paper, the finite element model of a gravity dam project is established and the seepage field is analyzed.

Changing impermeability boundary conditions to obtain free surfaces in unconfined seepage problems

A coupled numerical model of flow through porous media, formulated in terms of the fluid displacements and changing the impermeability boundary conditions, is applied to calculate the free surface in unconfined, steady-seepage problems. In this new methodology, the domain of computation is kept constant, and the free surface is iteratively obtained by imposing impermeability conditions at the free boundaries, which are updated at the end of each iteration, aiming to simulate the physics of the problem. By doing so, a line of pore-water pressure equal to zero (free surface) is obtained in a few iterations, usually two or three. The results obtained with the proposed method have been successfully compared to analytical and numerical solutions in several examples to show the usefulness of the method in practical seepage problems.