Exit Hydraulic Gradient Research Articles

Analytical Solution for the Steady Seepage Field of a Foundation Pit in an Anisotropic Layer

The soil piping and drift sand phenomenon is one of the catastrophic failure forms in foundation pit excavations in coastal buildings. Presently, there is a deficiency in the theoretical research regarding the seepage fields around foundation pits, primarily due to the complexity of theoretical solutions given the difficulty in accurately describing the distribution of the groundwater’s hydraulic head in a seepage field. This study proposes an explicit analytical solution for the steady-state seepage field surrounding a foundation pit under anisotropic conditions. A numerical model, constructed with FLAC3D 7.0 software, was utilized to validate the solution presented in this study. The effects of the foundation pit’s width, the distance between the retaining wall and the impervious layer, and anisotropic seepage conditions on the total head are studied through parameter research. The study shows that the flow behavior of a foundation pit is sensitive to parameters such as the anisotropy of the soil layer and the width of the foundation pit. Further, the study also analyzes the influence of the above parameters on the exit gradient and proposes a simplified algorithm for the exit hydraulic gradient at the base of a foundation pit, which can control the error within 5%. This method makes a certain contribution to improving seepage calculations for foundation pits and is applicable to the seepage problem of anisotropic soil layers.

Modeling and Analysis of Cutoff Wall Performance Beneath Water Structures by Feed-Forward Neural Network (FFNN)

Cutoff walls are widely used to limit seepage, piping, and the uplift under hydraulic structures. Therefore, this study focused on a numerical investigation of the hydraulic performance of cutoff walls beneath hydraulic structures during both static and dynamic conditions, considering location and inclination angle influences. The results confirmed that placing the cutoff wall at the upstream heel was more effective in reducing uplift pressure compared to other placements during static conditions. The inclination angles for the different placements of the cutoff wall had a significant impact on the total uplift pressure, exit hydraulic gradient, and seepage discharge during both static and dynamic states. The earthquakes had a noticeable effect on uplift pressure, seepage discharge, and exit hydraulic gradient. During static conditions, the inclination angle of 90° was the most effective angle for decreasing seepage discharge, irrespective of the cutoff wall position. During an earthquake, the seepage discharge values were high regardless of the inclination angle. In the case of placing a cutoff wall at the upstream heel, the maximum seepage discharge value occurred at an inclination angle of 45°. This study provided insights into the behavior of cutoff walls under different conditions and can inform the design and construction of such structures for effective seepage control. The experimental feed-forward neural network (FFNN) was also successfully built. According to the following criteria (uplift pressure, seepage, and exit hydraulic gradient), the hydraulic performance of cutoff walls beneath hydraulic structures under static conditions can be examined. The FFNN can make predictions with root mean square errors (RMSE) of 0.0697, 0.0021, and 0.0059, respectively, and R2 values of 1.00, 0.9994, and 0.9997.

Impact of inclined double-cutoff walls under hydraulic structures on uplift forces, seepage discharge and exit hydraulic gradient

In hydraulic structures design, using cutoff walls is essential to reduce and control the resultant uplift force (U), seepage discharge (Q), and exit hydraulic gradient (i). This research investigates the effectiveness of inclined double cutoff walls under hydraulic structures, considering the influence of depths, locations, and inclination angles of the upstream and downstream cutoff walls by using Finite Element Method (FEM). The results confirmed that installing a deeper cutoff wall on the downstream reduces the exit gradient even further. In the case of the cutoff walls located in the upstream and downstream ends, the exit gradient will be less than when the cutoff walls are installed at a closer distance. Increasing the inclination angle of downstream cutoff wall has a major impact on exit gradient reduction. Embedment of cutoff walls in the upstream and downstream ends with right angles and equal depths reduces the seepage discharge more than other cases.

Investigation of Seepage, uplift forces and hydraulic gradient in hydraulic structures with Different Configurations of Dual-Cutoff Walls

In design of hydraulic structures cutoff walls are needed for reduction of uplift force and exit hydraulic gradient. Upstream cutoff wall is used for reduction of the uplift force and downstream cutoff wall is used for reduction of the exit hydraulic gradient. This study tends to numerically investigate the double-cutoff beneath the hydraulic structures with variation in their location, distance and depth. Governing equations with boundary conditions are solved using the finite element method (FEM). Results showed that if the downstream cutoff wall is deeper than upstream cutoff wall, the resultant of uplift force would be more than the uplift force without cutoff walls. With a constant value for hydraulic structures width (B), decreasing in distance between two cutoffs (L), results the reduction in uplift force. Increasing in impermeable depth (D) and reduction in B, yields lower uplift force. Increasing in downstream cutoff depth (d2) and L, results reduction in exit hydraulic gradient (GR). When the two cutoffs are located in the end of the hydraulic structure, GR is lower than that when the downstream cutoff is located in L/B=0.33 and L/B=0.66 from upstream cutoff. Comparison between the available analytical solutions for two equal ending cutoffs with FEM, showed that FEM can predict PC and GR with maximum 5% error.

Effect of Drain Pipes on Uplift Force and Exit Hydraulic Gradient and the Design of Gravity Dams Using the Finite Element Method

The effects of diameter and location of drain pipes on the uplift force and exit hydraulic gradient for a gravity dam are investigated. A numerical model of a gravity dam is simulated using the finite element method. The results indicate that drain pipes under a gravity dam reduce the uplift force and exit hydraulic gradient. The optimal location of the drain pipe with respect to reducing uplift force is 0.25 L (where L is the dam width) from the dam heel, and is 0.75 L with respect to the exit hydraulic gradient. In addition, with increasing drain depth, the uplift force first decreases and then increases. The drain pipe diameter has little effect on uplift force and exit hydraulic gradient and thus its selection should depend on other considerations. When the drain pipe is located at its optimum location with respect to minimizing the uplift force, the volume of dam materials is reduced ~ 30–50%.

Upstream Cutoff and Downstream Filters to Control of Seepage in Dams

The finite element method was used in this study to investigate cutoff walls and downstream filters to control seepage, the exit hydraulic gradient, and uplift forces for dams. Experimental data was used for validating the numerical modelling. The effective parameters are the length of filter and its distance downstream from the dam, the depth of the cutoff walls, the upstream dam head, and the thickness of alluvial foundation. The results show that by increasing filter length, the exit hydraulic gradient, uplift force, and seepage are reduced. The optimum relative length of the filter is L/H = 0.028 which results in a decrease of about 65% in the exit hydraulic gradient, a 35% decrease in seepage and 10% reduction in the uplift force at the upstream foundation and a 60% decrease in the uplift force at the downstream foundation. Increase of cutoff wall depth reduces the exit hydraulic gradient, uplift force, and seepage. Using two cutoff walls both upstream and downstream of the dam decreases seepage, hydraulic gradient, and uplift force 132%, 450% and 11% respectively. However, using an upstream cutoff and downstream filter decreases seepage, hydraulic gradient, and uplift force by 180%, 490%, and 119% respectively. Thus, based on this study, recommendations for suitable combinations of upstream cutoff and downstream filter are provided.

Investigation of the effect of depth and distance between cutoff walls on uplift force for gravity dams

The purpose of this study was to investigate the effect of the location of cutoff walls, the number of walls (or their spacing), and their depth in the foundation of dam on the uplift force and the exit hydraulic gradient. The solutions are obtained with the finite element method; the effect of depth and location of the walls was studied. In addition, multiple cutoff walls at six different depths and separations were considered. As the depth of a cutoff wall at the heel of dam increases, the uplift pressure and the exit hydraulic gradient decrease if there is only one cutoff wall. The uplift pressure was 51.58% and the exit hydraulic gradient was 49.33% lower than the non-cutoff wall state and for a ratio of d/D = 0.96. In the case with two or three cutoff walls, reducing their distance from each other decreases the uplift pressure, while increasing the distance reduces the exit hydraulic gradient. The results indicate that when multiple walls are used, their spacing should be such that the length of the water flow path is prolonged. In order to validate the present study, the present numerical model was evaluated against analytical calculations for a given condition. The results showed excellent agreement between the numerical calculations and the expected results, thereby adding confidence in the results.

Investigation of the effect of the different configurations of double-cutoff walls beneath hydraulic structures on uplift forces and exit hydraulic gradients

In the design of hydraulic structures, cutoff walls are needed to reduce uplift force (U) and the exit hydraulic gradient (GR). Usually two cutoff walls are required; an upstream cutoff wall is used to reduce the resultant of uplift force and a downstream cutoff wall is used to reduce the exit hydraulic gradient. This study numerically investigates double-cutoff walls beneath hydraulic structures with variations in their location and depth. Governing equations with specified boundary conditions are solved using the finite element method (FEM). Results show that if the downstream cutoff wall is deeper than the upstream cutoff wall, the resultant of uplift force will increase (compared to the no-cutoff wall case). With a constant hydraulic structure width (B), decreasing the distance between the two cutoffs (L), results in a reduction of uplift force. For L/B = 0.7, the change in the slope of the uplift force is large. Increases in the permeable depth (D) and reductions of B will lower the uplift forces. Increases in the downstream cutoff depth (d2) and L result in a reduction in the exit hydraulic gradient (GR). When the two cutoffs are located at the end of the hydraulic structure, GR is lower than when the downstream cutoff wall is located at a more downstream location. Comparisons between the available analytical solutions and computational results for two equal cutoffs show that the FEM can predict U and GR with a maximum of 5% error.

Effect of using grouted vertical barrier on seepage characteristics under small hydraulic structures

This study investigated the effect of using Grouted Vertical Barrier (GVB) on the seepage characteristics (uplift force, seepage rate, and exit hydraulic gradient) under small hydraulic structures. The GVB’s variables, viz., position, depth, width and hydraulic conductivity, were studied experimentally using sand model and numerically employing SEEP/W software. A parametric study investigated several cases of the variables after numerical model verification. The results depicted that the heal and toe ends were the best positions for uplift force and exit gradient, respectively. The maximum reduction in the seepage occurred at both ends. The seepage characteristics swiftly decreased by increasing the GVB’s depth in the pre-mentioned best positions. Upsurge of the GVB’s width sequentially reduced the exit gradient and the seepage rate, whilst negatively impacted the uplift force. Declining the ratio between the hydraulic conductivity of the GVB (K) and the reference soil one (Ko) significantly lowered the seepage until reaching a stationary proportion K/Ko = 1E−4. Beyond this, decreasing K/Ko ratio do-nothing. Through regression analysis, three equations were developed to estimate the seepage characteristics affected by GVB’s variables. The indications of comparative studies revealed a better effect of the GVB compared to any of the sheet pile or the upstream blanket.

Optimum layout of weep holes in concrete irrigation canals to control uplift pressure and hydraulic gradient

In this study, the effect of weep holes on controlling uplift pressure and hydraulic gradient under concrete canals was investigated in different groundwater levels. For this purpose, three weep holes were embedded in different locations and combinations on the bottom and the sidewall of a laboratory canal. The amounts of seepage discharge were measured from these weep holes in single and combined modes. The corresponding values of seepage discharge, uplift pressure, and exit hydraulic gradient were calculated through simulation with the Seep/W model. The comparison of the observed and the simulated seepage values was indicative of the model’s high accuracy with a mean error of 6.23%. The results showed that uplift pressure values in the single modes of weep holes in three different groundwater levels are similar. Uplift pressure in the binary combinations had a significant reduction compared to the single modes (an average of 73%). The maximum exit hydraulic gradient occurred at the weep hole located at the corner of the canal bottom. In general, the binary combinations of the weep holes were the best choice in terms of the minimum uplift pressure and the suitable exit hydraulic gradient.

Validity of the Method of Fragments for Seepage Analysis in Circular Cofferdams

The method of fragments (MoF) is a simple solution method for confined seepage problems. MoF based seepage solutions have been proposed and validated in the literature on cofferdams analyzed in the 2D Cartesian plane (i.e., double-walled cofferdams). More recently, this method has been extended by the authors for determining the flow rate and exit hydraulic gradient for axisymmetric cases (circular cofferdams). The accuracy of the MoF solutions for circular cofferdams relies on the assumption that the equipotential surface along the cofferdam perimeter at the tip of the cut-off wall is vertical. Therefore, in the first part of the paper, the validity of this assumption and the effect of any deviation on the seepage solutions for circular cofferdams were studied. For that, series of circular cofferdam geometries were studied using numerical simulations, and then the seepage solutions (flow rate and exit hydraulic gradient values) obtained were compared with corresponding MoF solutions. It shows that the MoF solutions are conservative in all the cases and also the error is limited to 10% for most of the cases. In the second part of the paper, an attempt is made to simplify the MoF solutions, further developing expressions for the form factors of the two fragments and the exit hydraulic gradient without relying on the graphical solutions proposed by the authors. The equations presented herein enable the MoF to be implemented in spreadsheet and hence be used as an effective tool for parametric studies.

Simple solutions for square and rectangular cofferdam seepage problems

Cofferdams are widely used temporary structures at construction sites. Two of the main parameters required in designing a cofferdam are the flow rate and exit hydraulic gradient at the bottom of the excavation. Commonly, these two parameters are evaluated by using two-dimensional (2D) ground water flow models. However, when the flow pattern is three-dimensional (3D), such as flow into the square or rectangular cofferdams, predictions by the 2D models underestimate the flow rate and exit gradients considerably. Therefore, it is necessary to incorporate the 3D flow effect through a correction factor. It is shown that treating a square cofferdam as a circular one of the same width or treating a rectangular cofferdam as a 2D double-walled cofferdam significantly underestimates the flow rate. In this study, simple expressions are developed and validated for accurately estimating the flow rate and exit hydraulic gradient values of square and rectangular cofferdams, based on hundreds of finite element simulations in both 2D and 3D. It is suggested that the expressions given in the Canadian foundation engineering manual be improved.

Probabilistic analysis of seepage for internal stability of earth embankments

Internal erosion, or piping, has been attributed as a major cause of dam and embankment failures. Most prediction models for predicting piping use the hydraulic gradient between the upstream and downstream water levels as an indicator. No explicit consideration is made regarding preferential pathways, although piping usually initiates from a discrete downstream location. The local seepage velocity is investigated here through stochastic seepage analysis incorporating consideration of soil heterogeneity. The results show that when the coefficient of variation of hydraulic conductivity is small, the location of the maximum local velocity is typically near the downstream toe of the embankment, as for a deterministic analysis. In contrast, increasing the coefficient of variation scatters the possible locations of the maximum local velocity. The heterogeneity of hydraulic conductivity also leads to an increase in the average exit hydraulic gradient, as well as having a significant influence on the global kinetic energy and kinetic energy distribution.

Plausible failure mechanisms of wildlife-damaged earth levees: insights from centrifuge modeling and numerical analysis

Earth levees are subject to a wide range of wildlife intrusion patterns that cause mass removal and subsequent serious deformations. Such invasive activities leave the body of an earth embankment with burrow systems too complex to map and model using conventional techniques. This study investigates the impact of different idealized configurations of animal burrows on the geotechnical performance of levees. For this purpose, centrifuge testing was conducted on homogenous scaled-down 1 horizontal : 1 vertical (1H:1V) levee models built from silty sand material. Modeling involved introducing horizontal cylinder-shaped waterside and landside burrows at different elevations within the levee section. The reference (intact) and deteriorated levee models were subject to a centrifugal acceleration of 35g, which was kept constant as the water level behind the levee model was gradually increased. The deformation profile of the model was tracked, and the crest displacements were concurrently measured. Miniature pore pressure transducers (PPTs) embedded within the levee body provided pore pressure measurements. A three-dimensional finite element model was developed to investigate the hydraulic performance and verify the failure patterns of the deteriorated levees. Compared with an intact levee, the presence of animal intrusions was found to increase the exit hydraulic gradient for both waterside and landside intrusions. Lower animal burrows appeared to cause larger exit gradients than higher ones. Similarly, waterside burrows exhibited a notably higher pore pressure and larger hydraulic gradient. Waterside damage resulted in a quicker and more violent failure than landside burrows. The failure mechanisms for both the waterside and landside burrows are dissimilar despite their similarly abrupt nature.

Stochastic analysis of seepage under water-retaining structures

This paper investigated the problem of confined flow under dams and water-retaining structures using stochastic modelling. The approach advocated in the study combined a finite-element method based on the equation governing the dynamics of incompressible fluid flow through a porous medium with a random field generator that generates random hydraulic conductivity based on log normal probability distribution. The resulting model was then used to analyse the confined flow under a hydraulic structure. Cases for a structure provided with cut-off wall and when the wall did not exist were both tested. Various statistical parameters that reflected different degrees of heterogeneity were examined and the changes in the mean seepage flow, the mean uplift force and the mean exit gradient observed under the structure were analysed. Results reveal that under heterogeneous conditions, the reduction made by the sheet pile in the uplift force and exit hydraulic gradient may be underestimated when deterministic solutions are used.

Approximate equations for the method of fragment

The method of fragment is a simple and approximate technique for solving confined seepage flow problems. In this method, the flow domain is divided into few fragments along the equipotential lines that are assumed to be vertical and a dimensionless form factor is defined for each fragment. The flow rate and the exit hydraulic gradient can be computed using the form factors. Griffiths proposed three types of fragments that are adequate to solve most configurations, incorporating anisotropy in permeability, and presented design charts for determining the form factors. In this paper, through extensive numerical modeling simulations, equations are developed for the form factors and they are validated. These equations enable quicker computations and the method of fragment be implemented in spreadsheets.

Experimental evaluation of the performance of earth levees deteriorated by wildlife activities

In this study, an earth levee model is constructed to investigate the impact of animal burrows on the integrity and performance of earthen structures. A series of centrifuge experiments are conducted on homogenous scaled-down 1H:1V levee models built from the natural Kasama soil. Both intact and deteriorated models were subject to a 35g acceleration level. Invasive animal intrusions were introduced in the form of horizontal array of idealized cylindrical burrows at the mid-height of the levee. The water level was gradually increased during the centrifuge flight, and the response of the levee was monitored throughout the test. Pore pressures were recorded using pressure transducers placed at preselected locations within the model. Surface displacements were measured using laser LVDTs and supplemented with three digital cameras for tracking the overall deformation pattern of the levee model. A summary of the test procedure and selected results is presented herewith. The observed deformation mechanism due to the presence of animal burrows is also described. As compared with the intact levee, the presence of burrows is found to alter the pattern of the water flow through the deteriorated levee structure—leading to a notable increase in the exit hydraulic gradient, internal erosion, and subsequently slope failure.

3D Analysis of Seepage under Hydraulic Structures with Intermediate Filters

Seepage flow under hydraulic structures provided with intermediate filters has been investigated. The flow through the banks of the canal has been included in the model. Different combinations of intermediate filter and canal width were studied. Different lengths of the floor, differential heads, and depths of the sheet pile driven beneath the floor were also investigated. The introduction of an intermediate filter to the floor of hydraulic structures reduced the uplift force acting on the downstream floor by up to 72%. The maximum uplift reduction occurred when the ratio of the distance of filter location downstream from the cutoff to the differential head was 1. Introducing a second filter in the downstream side resulted in a further reduction in the exit hydraulic gradient and in the uplift force, which reached 90%. The optimum locations of the two filters occurred when the first filter was placed just downstream of the cutoff wall and the second filter was placed nearly at the middistance between the cutoff and the end toe of the floor. The results showed significant differences between the three-dimensional (3D) and the two-dimensional (2D) analyses.

Hydraulic structures with defective sheet pile walls

A sheet pile wall driven to form a barrier wall below the floor of a hydraulic structure is frequently assumed to be watertight. Although the leakage through the interlocks of the sheet piles is usually small, damage and other factors can result in significant leakage. Consequently, this assumption is rarely, if ever, satisfied in reality. The present study used a finite-element model to investigate the effect of leaks through sheet piles driven under the floor of a hydraulic structure on seepage losses, on the uplift force and on the exit hydraulic gradient. Flow through the channel banks was considered to obtain accurate and robust calculations. The study indicated that when the leak existed in a sheet pile wall, driven centrally below the floor of the hydraulic structure, it has a small impact on seepage losses, the exit hydraulic gradients and the uplift force. However, when the leak existed at a sheet pile wall driven at the downstream end of the floor, its impact was significant, particularly on the exit hydraulic gradient with consequent risk to the stability against piping and undercutting of the structure. A combination of both cut-off walls did not provide a significant benefit, should leakage occur.

Stochastic Analysis of Seepage under Hydraulic Structures Resting on Anisotropic Heterogeneous Soils

AbstractThis research investigated the confined flow under hydraulic structures. The hydraulic conductivity of the soil was modeled as a spatially random field, which followed a lognormal distribution. Only porous media that have anisotropic heterogeneity were investigated. Results showed that larger anisotropic heterogeneity ratios (the ratio of horizontal to vertical scale of fluctuation) dramatically increased the seepage flow. This increase of flow was more pronounced at larger coefficients of variations. A similar trend was observed in the case of uplift force, although it was less sensitive to the increase in the anisotropic heterogeneity ratio. Moreover, both the seepage flow and the uplift force tended to their deterministic values as the ratio of anisotropic heterogeneity increased. Results also showed that the exit hydraulic gradient attained its greatest value at particular values of the anisotropic heterogeneity ratio.