Steady-state Seepage Research Articles

Proof of multiplicity of solutions for groundwater seepage in recharged heterogeneous unconfined aquifers

Summary A new analytical proof is presented for steady-state seepage in recharged heterogeneous unconfined aquifers. The paper also presents a detailed procedure and important rules for performing correctly numerical studies of unsaturated seepage. Once a numerical solution is calibrated with field data, using a set of spatially distributed values for hydraulic conductivity K and effective infiltration EI, any new numerical analysis with a set of αK and αEI values, where α is a constant, yields an equally good calibration. However, if the effective porosities of each layer are unchanged, the groundwater velocities are multiplied by α, whereas the travel times are divided by α, which may help to select α in order to match known travel time data. This is a clear example of multiple solutions to an inverse problem. The paper underlines the role and the need to finely mesh unsaturated zones and also contacts between layers to reach the asymptotic convergence range, as it was carried out to verify the proof and as it should be completed to study any seepage problem. A few consequences of the new analytical proof and the rigorous procedure are shown with examples. Copyright © 2016 John Wiley & Sons, Ltd.

Investigation of a hybrid polygonal finite element formulation for confined and unconfined seepage

SummaryThis 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.

Influence of structure and water pressure on the hydraulic conductivity of the rock mass around underground excavations

In this study, in situ water injection tests and numerical modeling in conjunction with core logs and television image measurements were applied for an investigation of the hydraulic properties of the rock mass around underground excavations. The aim of our work was to investigate the influence of rock structure and water pressure on the hydraulic conductivity of the rock mass around underground excavations. Thus, water injection tests were conducted in four boreholes that were drilled in the rock mass in underground tunnels in China. Seepage connection initiation and steady state seepage were proposed to identify the seepage evolution course within the rock mass by combining the results of pressure and hydraulic conductivity. Generally, hydraulic conductivity is strongly related to rock structure and water pressure. The results also revealed that a rearrangement of rock structure would occur in the damage zone, resulting in an increase in hydraulic conductivity of nearly one to several orders of magnitude. The results from the modified numerical model showed that the pore water distribution and the groundwater inflow rate are affected by both the hydraulic conductivity and the thickness of the damage zone and they are influenced more by the thickness of this zone.

On the role of partially saturated soil strength in the stability analysis of a river embankment under steady-state and transient seepage conditions

River flood risk is considered being one of the most costly hazards in Europe and under a further major potential impact of climate change, in combination with land-use changes and water management practices, flood risk is expected to increase for many river basins. In engineering practice, the design of river embankments is usually performed using simplified approaches, considering steady-state flow conditions induced by the retained water and almost neglecting issues related to partially saturated soils, thus leading to potentially heavily over conservative results of stability analyses. To provide a realistic assessment of river bank stability conditions and to get a more accurate prediction of flood risk it is necessary to consider river bank soil behaviour at different saturation degrees in connection with transient seepage flow. A numerical study on stability conditions of a specific river embankment focusing on the partially saturated soil strength contribution is presented herein. Seepage and stability analyses have been carried out using the information collected on river Secchia flooding case study, occurred north of the city of Modena (Italy) in January 2014. Limit equilibrium method has been adopted for assessing the overall stability in steady-state and transient flow conditions. Useful indications for accounting unsaturated soil strength in similar circumstances are finally provided in the paper.

Steady-state optimization model and practical design of the fracture network system in tight sand gas reservoirs

Abstract Based on steady-state seepage theory in porous media and the Galerkin method, a finite element model of seepage field in a stimulated reservoir volume of a horizontal well was established. The relationship between fracture conductivity and production under different fractured drainage volumes was studied. For shale gas reservoir, the productivity will increase as the fractured drainage volume enlarges. However for tight sand gas reservoir, this study revealed that the fractured drainage volume should be maintained in the mid-small scale (0.1≤FCI≤0.25) with highly conductive main fractures. For certain fracture network morphology, there exists a critical value or optimal value of SRV curve. The production increase slows down when SRV exceeds its critical value. Cluster spacing and number of clusters for horizontal well fracturing can be determined by critical value of SRV and FCI value. The paper studied the operational conditions for the creation of small and medium-scale fracture network. Firstly, analytical solution of pressure inside the fracture is derived from fracture dynamics of rocks. Pump rate of fracturing fluid, viscosity, rock dynamic fracture toughness, elastic modulus, Poisson's ratio, in-situ stress, natural fracture parameters are input parameters to this analytical solution. Optimized pump rate for small to medium-scale fracture network was derived from the dynamic expanding condition of fracture network.

Orthotropic Seepage Analysis using Hybrid Finite Element Method

A solution procedure using the hybrid finite element method is presented for two-dimensional steady-state linear seepage analysis of orthotropic dams. In the present algorithm, fundamental solutions for orthotropic seepage problems are employed to construct the element interior hydraulic head field and the conventional shape functions are used for the element frame hydraulic head field, then these two independent fields are connected by a hybrid functional. According to the physical definition of fundamental solutions, the elemental interior field can naturally satisfy the orthotropic seepage governing equation and as a result, all twodimensional element domain integrals in the present algorithm can reduce to one-dimensional element boundary integrals. Finally, the present hybrid finite element method with orthotropic fundamental solution kernels is verified by way of analytical solutions and subsequently, numerical experiment is carried out for a practical seepage problem of an orthotropic dam.

Back Analysis of the Permeability Coefficient of a High Core Rockfill Dam Based on a RBF Neural Network Optimized Using the PSO Algorithm

It is important to determine the seepage field parameters of a high core rockfill dam using the seepage data obtained during operation. For the Nuozhadu high core rockfill dam, a back analysis model is proposed using the radial basis function neural network optimized using a particle swarm optimization algorithm (PSO-RBFNN) and the technology of finite element analysis for solving the saturated-unsaturated seepage field. The recorded osmotic pressure curves of osmometers, which are distributed in the maximum cross section, are applied to this back analysis. The permeability coefficients of the dam materials are retrieved using the measured seepage pressure values while the steady state seepage condition exists; that is, the water lever remains unchanged. Meanwhile, the parameters are tested using the unstable saturated-unsaturated seepage field while the water level rises. The results show that the permeability coefficients are reasonable and can be used to study the real behavior of a seepage field of a high core rockfill dam during its operation period.

Soil compressibility in transient unsaturated seepage analyses

Most levee underseepage and uplift analyses are based on steady-state seepage and can yield conservative results. Although computations are simpler and steady-state seepage parameters are easier to determine and readily available, transient unsaturated seepage analyses are more representative of levee seepage conditions because boundary conditions acting on the levee or floodwall and saturation change with time, which induce pore-water pressure and seepage changes with time in the embankment and foundation strata. In addition, these boundary conditions, e.g., flood surge or storm event, are rapid such that steady-state conditions may not have time to develop in the embankment and some foundation materials. Transient seepage analyses using a floodwall case study indicate that as soil compressibility of the underseepage layer decreases, rapid landside pore-water pressures increase and can approach steady-state values. The transient results also indicate that uplift factors of safety during the flood event are about 22% higher than those at steady state. The effect of soil compressibility can delay or accelerate the onset of uplift water pressure increase from the initial steady-state conditions.

Analytical Solution for Contaminant Extraction Using Well Injection Depth Extraction Technology Considering the Effect of Smear Zone

The smear zones are usually caused by the installation of vertical drains in fine-grained soil. An analytical solution for contaminant extraction using well injection depth extraction (WIDE) system considering the smear effect was developed. The injection rate was assumed to be equal to the retrieval rate to maintain full saturation and steady-state seepage flow. The results obtained by the proposed analytical solution agree well with those obtained from the finite element method. An illustrative example was presented to show the influence of the smear zones and results reveal that the smear zone can have a great influence on the contaminant extraction from soils. The 500-hour base concentration of acetone in the middle of the contaminated soil increases by a factor of approximately 1.9 when the effect of the smear zone is considered in the model.

Analytical solutions of stresses and displacements for deep circular tunnels with liners in saturated ground

To investigate the displacement and stress distributions for deep circular tunnels with liners in saturated ground, an analytical model is proposed. For a deep tunnel with drainage conditions, plane strain conditions at any cross-section of the tunnel and the elastic regime of the linear elasticity for the remaining liner are assumed, while the ground is assumed to be linearly elastic and perfectly plastic with a failure surface de?ned by the Mohr-Coulomb criterion. The post-yield behavior of the ground follows the non-associated flow rule defined by the dilation angle. To solve the proposed problem, two procedures are presented. An axisymmetric model for a deep circular tunnel with a steady-state seepage condition is considered, and then a simple closed-form analytical solution is obtained with a common theoretical framework for the boundary conditions of a constant total head along the tunnel circumference. Assuming that certain ground displacements along the tunnel circumference have occurred before the installation of the liner, analytical solutions of stresses and displacements are derived with particular emphasis on the seepage and the stress release effect induced by tunnelling. The proposed analytical model is validated by numerical simulation.

Optimum Size for Clay Core of Alavian Earth Dam by Numerical Simulation

Seepage in embankment dams is one of the important factors in stability and dam's maintenance. Core in earth dam is essential for waterproofing and controlling of seepage. Therefore, selection of proper materials and sizes for core of earth dam are very important. Thick clay core is proper for waterproofing but because of low shear strength of the clay, it would be dangerous for dam's stability. The optimal core would be the core which has proper waterproofing, stability safety factor and also with economic condition. In this study, the aim is to determine the optimum size for clay core of Alavian dam near Maragheh city in steady state seepage condition. For this purposes, Geo-Studio pack is used for numerical simulation. In addition, simulation of seepage and slope stability for the built maps of the dam, 11 more models of the dam with different size of cores were tested to find the optimum core thickness. From these models, data required for objective function and constraints using regression techniques for seepage, hydraulic gradient and stability safety factor were provided. Results showed that optimized volume of the core is 35% smaller than the present core.

Levee failure mechanisms during the extreme rainfall event: a case study in Southern Taiwan

Extreme weather has recently caused many disasters worldwide. In August 8, 2009, Southern Taiwan suffered from serious floods during Typhoon Morakot. In this extreme rainfall event, the Chiuliao first levee in the Laonong River basin experienced catastrophic failure. Therefore, this study focuses on the levee failure mechanisms based on variations in levee water levels. Specifically, this study investigates four mechanisms based on limit state equilibrium. The first mechanism involves the slope stability under hydrostatic conditions at various water levels. The results of this analysis show that the levee cannot fail under this mechanism. The second mechanism involves the levee slope stability with steady-state seepage. Because the water levels are different on the protected and flood sides, the water recedes much faster on the flood side than the protected side. Based on this analysis, the levee slope might fail when the water level at the protected side is close to the top of levee and the water level at the flood side starts to recede. The third and fourth mechanisms involve the levee foundation failure in terms of sliding and overturning failure. The results of this study indicate that the levee foundation is more prone to sliding failure than overturning failure. Based on these results, this study shows that the levee failed when the water level at the protected side neared the top of levee while the water level at flood side started to recede. At this moment, the levee may fail because of both the slope failure with seepage and sliding failure of the levee foundation.

Simulation procedure of unconfined seepage with an inner seepage face in a heterogeneous field

An inner seepage face phenomenon is given and a numerical simulation procedure has been developed. It may appear at the interface of two materials when an unconfined seepage flows from a porous media to a coarser porous media with a higher permeability. Inaccuracy and divergent problems may arise both in a saturated-only and in a variably saturated analysis while an inner seepage face is not simulated with a special procedure. The position of the seepage face is determined during the nonlinear iteration process and the flux of the inner seepage face nodes is transferred to the downstream side nodes. Validity and efficiency of the procedure are illustrated by the simulation of two dimensional steady state seepage examples of heterogeneous zoned dams which is usually used to validate algorithms. An analysis of a three-dimensional earth core rockfill dam is also presented here. The procedure can also be applied to general transient seepage problems.

Iterative methods for solving seepage problems in multilayer beds in the presence of a point source

This work is devoted to solving steady-state seepage problems of an incompressible fluid that obeys a nonlinear multivalued filtration law with limit gradient in a multilayer bed in the presence of a point source. The seepage problem is formulated as a mixed variational inequality with an inversely strongly monotone operator in a Hilbert space. An iterative splitting method is proposed to solve the variational inequality. Unlike the earliermethods, the method proposed allows one to find not only approximate values of the fluid pressure, but also the filtration rates, in particular, on the sets corresponding to multivalued points in the filtration law. The convergence of the method is analyzed.

A way to calculate the seepage attached to the flow around the Zhukovskii rabbet with more than one-sheeted area of complex velocity

Under the definition of a hydrodynamic problem, a problem is solved on flat steady-state seepage under a Zhukovskii rabbet through irrigated soil bedded by a very permeable pressure horizon, whose left semi-infinite roof is simulated by an impenetrable inclusion. The movement in the case when the velocity of the flow at the rabbet’s end is equal to infinity, which causes more than one sheeted area of complex velocity, is examined. The results are compared with the results obtained for the case when the velocity of the flow at the rabbet’s end is a finite quantity.

Rules for confidence intervals of permeability coefficients for water flow in over-broken rock mass

Based on the steady-state seepage method, we used the Mechanical Testing and Simulation 815.02 System and a self-designed seepage instrument for over-broken stone to measure seepage properties of water flows in three types of crushed rock samples. Three methods of confidence interval in describing permeability coefficients are presented: the secure interval, the calculated interval and the systemic interval. The lower bound of the secure interval can be applied to water-inrush and the upper bound can solve the problem of connectivity. For the calculated interval, as the axial pressure increases, the length of confidence interval is shortened and the upper and lower bounds are reduced. For the systemic interval, the length of its confidence interval, as well as the upper and lower bounds, clearly vary under low axial pressure but are fairly similar under high axial pressure. These three methods provide useful information and references for analyzing the permeability coefficient of over-broken rock.

사력댐의 정상상태 침투량 예측식

본 연구에서는 한국수자원공사가 건설 및 관리하고 있는 8개 대규모 사력댐을 대상으로 불포화 침투류해석을 실시하고 저수위의 변화, 차수죤의 형상변화와 포화 및 불포화 수리특성의 변화에 대한 사력댐 제체의 침투량을 분석하여, 불포화 영역을 통한 침투량을 고려할 수 있고 높이 50m 이상의 국내 대규모 사력댐에 적용 가능한 사력댐 제체의 침투량 예측식을 제안하였다. 제안된 예측식에 의한 침투량은 불포화 흐름을 고려하지 않는 기존 이론식 (Sakamoto, 1998)에 비하여 전반적으로 큰 값을 나타내었고, 그 차이는 저수위가 낮아지면서 증가하고, 저수위가 높아지면서 감소하였다. 기존 사력댐에서 측정된 실측 침투량을 제안된 예측식에 의한 예측치와 비교한 결과 잘 일치하는 것을 확인할 수 있었다. 제안된 예측식은 차수죤의 상 하류 사면경사가 1V:(0.2 ~0.3)H의 범위인 사력댐에 대한 불포화 침투류해석 결과에 기초하며, 불포화 흐름을 고려하므로 기존 예측식(Sakamoto, 1998, Chapuis와 Aubertin, 2001)에 비해 실제 현상에 가까운 예측결과를 얻을 수 있다. In this study unsaturated seepage analysis of 8 large rockfill dam managed by Korea Water Resources Corporation, were carried out, and the seepage rate of rockfill dam was analyzed by changing reservoir water level, shape, saturated and unsaturated seepage properties of core zone to present an equation to estimate steady-state seepage rate of rockfill dam. This equation considers unsaturated seepage flow and is applicable to domestic large scale Rockfill dam with the height of more than 50m. Estimated values by the proposed equation are greater than those by the method of Sakamoto (1998), which does not consider unsaturated seepage flow. The difference of estimated values increases with the lower reservoir water level and decreases with the higher reservoir water level. We can be sure that the comparison between the measured seepage rate and the estimated seepage rate by the proposed equation for the existing rockill dam was well-matched. The proposed equation is close to the actual phenomenon compared with the existing equations (Sakamoto, 1998; Chapuis and Aubertin, 2001) because it is based on the results of unsaturated seepage analysis of dams, has upstream and downstream slopes in the range of 1Vertical: (0.2~0.3)Horizontal.

On ground water seepage under hydraulic structures

This present paper continues paper [1] of the authors and is concerned with the following problems regarding seepage flows with unknown boundaries under hydraulic structures, with use being made of the theory of two-dimensional (2D) steady state seepage of incompressible fluid according to Darcy’s law in a uniform isotropic soil. Below we construct a smooth underground contour of a rectangular subsurface dam of constant seepage rate in the case when a pervious abutment is underlain by a blanket consisting of two curvilinear and one (middle) horizontal elements which are also characterized by constant incident velocity. We are concerned with the fluid flow below Joukowski’s cutoff wall through the watered soil mass underlain by a highly permeable aquifer with confined groundwater; the left semi-infinite part of its roof is simulated by impermeable inclusion. These motions are examined using multiparameter problems of the theory of analytic functions. Their solutions are obtained by the semi-inverse method of the velocity hodograph by P.Ya. Polubarinova-Kochina and I.N. Kochina, by Polubarinova-Kochina’s approach dependent on the analytic theory of linear Fuchsian equations, and using the available conformal mappings of domains of special kinds peculiar for underground hydrodynamics. The results of the numerical calculations are given and the hydrodynamic effect of the physical parameters of models on the flow pattern is ascertained. The limiting cases previously examined in [1] are singled out.

Seismic Slope Stability of Embankments Constructed with Pond Ash

Utilization of pond ash in large earthworks for geotechnical applications like construction of highway embankments, raising of ash dykes and filling low lying areas (construction fills), solves the waste disposal problem besides conserving the natural soils. However, design and construction of such geotechnical structures particularly in earthquake prone areas, requires thorough understanding of dynamic response of these structures under different seismic loading conditions. Here in this article, dynamic stability of embankments raised around the perimeter of ash ponds by the upstream and down stream methods of construction with coarse (ash from inflow point) and fine (ash from outflow point) pond ash materials, has been computed for different site specific earthquake scenarios appropriate for Delhi region. The performance of the embankments is analyzed using Quake/w and Slope/w software packages for steady-state seepage condition. The required dynamic properties of the materials are obtained form the various field and laboratory tests. The geotechnical structures constructed with ash exhibited similar type of response as that of with the natural soils. The performance of the structures is influenced by number factors such as type of construction (e.g. upstream or downstream), insitu conditions (e.g. stresses, density, phreatic line), and magnitude of dynamic loads, besides on the static and dynamic characteristics of the materials. The structures with the fine ash exhibit higher vulnerability to liquefaction related failures, which emphasizes need for carrying site-specific studies and adoption of proper construction measures to ensure design parameters.

Normalized Relationships for Depth of Embedment of Sheet Pile Walls and Soldier Pile Walls in Cohesionless Soils

Normalized, non-dimensional relationships for calculating the depths of embedment of sheet pile walls and soldier pile walls embedded in cohesionless soils are presented. Rankine theory for lateral earth pressures in active and passive conditions are used in the analyses. Relationships are presented for cantilever walls and walls propped at crest. The proposed relationships can be used in dry soil conditions and as well as in saturated soil conditions with steady state seepage. The embedment depth relationships are presented in terms of non-dimensional parameters and can be used for a variety of soil conditions, dimensions and spacing of the walls, and depths of excavation. The presented relationships are simple, easy to use, and do not require tedious calculations.