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This study aims to develop a novel ensemble modeling approach that integrates artificial neural networks with finite element analysis to optimize the stability of hydraulic structures, particularly through the design of cutoff wall configurations. The research investigates the effects of varying cutoff wall positions and inclination angles on key parameters such as uplift pressure, seepage discharge, and exit gradient. Numerical simulations were performed using Geostudio SEEP/W to analyze seepage patterns across multiple configurations. The proposed methodology combines a Feed-Forward Neural Network (FFNN), XGBoost Regressor, and Support Vector Machine (SVM) with a Genetic Algorithm (GA) to create a predictive optimization framework. The findings reveal that the optimal cutoff wall inclination angle for minimizing both uplift pressure and exit gradient is 165° across all positions, while for seepage discharge, the optimal angle varies by position, ranging from 60° to 120° and increasing incrementally by 15° from upstream to downstream. The ensemble model demonstrated robust predictive performance across 5-fold cross-validation trials, achieving mean R-squared values of 0.99 ± 0.01 for uplift pressure, 0.94 ± 0.02 for seepage discharge, and 0.97 ± 0.01 for exit gradient. The small standard deviations indicate consistent performance across different data partitions, validating model stability and generalizability. The Genetic Algorithm results closely aligned with the numerical model outputs, validating the robustness of the proposed framework. This study introduces a significant improvement over traditional analytical methods by providing an integrated approach that enhances the safety and efficiency of hydraulic infrastructure design, particularly under complex conditions where conventional techniques may fall short.

Al-Hindiya barrage is an important project to ensure safety of structures is considered as one of the important projects in Iraq, so it’s very important to checking it’s the extent of the efficiency of the cut-off wall can be determined by calculating the amount of seepage flow that occurred under the structure in different conditions, such as the difference in water levels in the upstream and downstream, using the Geo-studio SEEP/W program by taking a natural analysis and a differential analysis. Cut off and a significant drop, and also when the most dangerous flood situation occurs at the greatest level in the Upstream In this case, all the gates must be opened, i.e., a quick descent into the origin. This case was studied, and the efficiency of the cut-off wall was proven in the most dangerous case, and it is considered one of the indicators of peace for the Al-Hindiya barrage The finite element method was used to investigate cutoff walls and downstream filters to control seepage, exit hydraulic gradient, and uplift forces for dams, The Al-Hindiyah Bridge was studied and the error rate was less than 1%, studying the unloading situation at the highest level at a time approved by the executing company, and delaying the unloading process at this time at the start of the project operation This case was analyzed by studying the uplift pressure, seepage rate, seepage velocity, gradient and discharge at the upstream, i.e. from a point close to the face of the sheet pile and a point far from the face of the sheet pile at the downstream we conclude through this case the efficiency of the sheet pile at the point located in the backside, which shows the efficiency of the sheet pile significantly The study proved that when facing the Al-Hindiya Bridge, the state of flooding, all gates must be opened at an average speed for a period of 12 hours to get rid of the water in excess of the permitted storage The study proved the efficiency of the sheet bale when confronting the flood situation and at different times, by calculating the safety factor 2.24 within the permissible limits. Recommendations for suitable combinations of upstream cutoff and downstream filter are provide. Recommendations for suitable combinations of upstream cutoff and downstream filter are provide

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.

An analytical study was carried out on an anchored circular pit with a submerged free surface in layered soil. The seepage field around the anchor circular pit was divided into three zones. Separate variable method was used to obtain the graded solution forms of head distribution in the column coordinate system for each of the three regions. Combined with the continuity condition between the regions the Bessel function orthogonality was used to obtain the explicit analytical solution of the seepage field in each region, and the infiltration line was determined. Comparison with the calculation results of Plaxis 2D 8.5 software verified the correctness of the analytical solution. Based on the analytical solution, the influence of the radius of the pit and the distance of the retaining wall from the top surface of the impermeable layer on the total head distribution on both sides of the retaining wall was analyzed. And the variation in the infiltration line was determined with the above parameters. The results show that as the pit radius, r, decreased, the total head on both sides of the retaining wall gradually increased, and the height of the submerged surface drop also increased. As the distance, a, between the retaining wall and the impermeable boundary at the bottom increased, the hydraulic head on the outer side of the retaining wall decreased and the head on the inner side increased. The height of the submerged surface drop increased with decreasing depth of insertion of the retaining wall. The depth of insertion of the retaining wall had a greater influence on the degree of diving surface drop than the pit radius.

Some facility for the prevention of piping, reducing exit gradient and seepage amount under hydraulic structures, is construction of cutoff wall and drain. Therefore, this study compares the efficiency of cutoff wall on some design parameters in an assumed diversion dam cross-section. For this purpose, different placements of cutoff wall with various angle of inclination were used in the dam foundation. Results of this study showed that minimum uplift pressure happens when cut off wall is in the heel (upstream) of the dam. With fixing of longitudinal cut off wall placement, inclination of cutoff wall respect to the vertical position, results in reducing of uplift pressure. Effect of inclination of cutoff wall in upstream of the dam; respect to vertical position, in reducing of uplift pressure is very high.

This study is focused on a numerical method to investigate the performance of cutoff walls system against uplift pressure and piping phenomenon. The parametric study has been conducted on the variation of cutoff wall parameters such as inclination angle of one cutoff wall in upstream and downstream side of the hydraulic structure, their length in upstream side, their spacing and number of cutoff walls under hydraulic structure. The results showed that using inclined upstream cutoff wall θ = 70° and θ = 90° was beneficial in increasing the safety the hydraulic structure against piping phenomenon and uplift pressure, respectively. Using downstream cutoff wall with any inclination angle decreased the safety against uplift pressure, and the best inclination angle of the cutoff wall at the toe of the hydraulic structure in increasing the safety against piping phenomenon was θ = 130°. Increasing the length of the upstream cutoff wall increased the safety against uplift pressure and piping phenomenon. The use of the larger spacing between two vertical cutoff walls decreased the safety against uplift pressure and increased the safety against piping phenomenon. Finally, the best number of cutoff walls in increasing the safety against uplift pressure was three and also increasing the number of cutoff walls increased the safety against piping phenomenon.

Seepage under hydraulic structures is considered to be a dangerous phenomenon which may cause the collapse of the structure over time if neglected. In this research, a SEEP/W model was developed to find the seepage rate and exit gradient under a concrete dam provided with two sheet piles. The independent variables were head difference; coefficient of soil permeability; and the spacing, lengths, and inclined angles of the sheet piles. The model was run for three different values of each independent variable. The results obtained from SEEP/W model were then used to create two neural artificial network (ANN) models (A and B) in which the output variables were the seepage rate (model A) and exit gradient (model B). The most appropriate structure, which gave minimum relative errors, was (7 3 1) nodes for both models. The results of the ANN models indicated that the variable with the most effect on seepage rate was the coefficient of soil permeability, with an importance ratio of about 76%, followed by the difference in the head (8%), the distance between piles (5.5%), length of downstream pile (5%), length of upstream pile (4%), and downstream and upstream inclined angles of the sheet piles, with ratios of about 1% and 0.5%. In terms of exit gradient, the most influential factor was the distance between piles at 35%, followed by the downstream inclination angle, length of downstream pile, head difference, length of upstream pile, inclined angle of upstream pile, and soil permeability with importance of about 23%, 19%, 14%, 7.5%, 1% and 0.5%, respectively. These results are in agreement with an analysis of the SEEP/W model.

Although the impervious layer under a hydraulic structure is rarely flat, the effect of the impervious layer’s slope, under the hydraulic structure, on seepage characteristics has not been studied to date. Therefore, this study investigated the effect of the downhill and uphill impervious layer’s slope (downhill/uphill foundation slopes) on the uplift pressure, seepage discharge and exit gradient under hydraulic structures. In order to reach this goal, a numerical model has been developed in which the general equation of fluid flow in non-uniform; anisotropic soil is solved by the finite volume method on a structured grid. The model validation was performed using the measured data from experimental tests. The results of the model validation indicated that the model calculates the seepage discharge and uplift pressure with a maximum error of less than 3.79% and 3.25%, respectively. The results also indicated that by increasing the downhill foundation slope (DFS) the uplift force decreases, but the exit gradient and seepage discharge increase. Moreover, by increasing the uphill foundation slope (UFS), the uplift force increases but the exit gradient and seepage discharge decrease. In addition, the results demonstrate that by increasing the length of the cut-off wall the effect of the DFS on decreasing and UFS on increasing the uplift pressure force becomes more severe. However, the effect of the DFS on increasing the seepage discharge and UFS on decreasing the seepage discharge becomes milder as the length of the cut-off wall increases. By increasing the DFS, from zero to −15%, the exit gradient increases 19.75% and 14.4% for 1 m and 6 m cut-off lengths, respectively.

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%.

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.