Estimating the Uplift Pressure under Hydraulic Structures with Dual end Cutoff Walls with Finite Element, Regression and Intelligent Approaches

ABSTRACT
The amount of uplift pressure in under hydraulic structures plays a significant role in the dimensions and stability of engineering designs, so its determination and estimation by accurate methods is very important. The purpose of this study is to model and estimate the uplift pressure force at key points under floors with dual end cut-off walls. For this aim, first numerical simulations with finite element method (FEM) using SEEP/W software was performed and after extracting the results, three intelligent models ANN (MLP), ANN (RBF) and GEP and multiple nonlinear regression (MNLR) model were used to estimate the amount of uplift pressure at key points using the parameters affecting it and their performance were evaluated together. Evaluation of the obtained results was performed using statistical criteria R2, RMSE, RE% and KGE as well as graphic diagrams. The results of statistical criteria indicated the superiority of ANN (MLP) model over other approaches. Comparison of violin plots and related indexes showed that the data estimated by the ANN (MLP) model are very closely correlated with the FEM data. It should also be noted that in the this study, a series of nonlinear and explicit regression equations were presented to estimate the amount of uplift pressure at key points with the extracted data, which can be used by design engineers due to its higher accuracy.
KEYWORDS
Cut-off Walls, Finite Element Method, Hydraulic Structure, Intelligent Model, Uplift Pressure.
BACKGROUND AND OBJECTIVES:
Uplift pressure exerted beneath hydraulic structures is a critical factor governing their structural stability and design dimensions. The accurate prediction of this force is therefore paramount for safe and economical engineering. While cutoff walls are widely used as an effective countermeasure to control seepage and reduce uplift, the specific configuration of dual end cutoff walls—particularly those of unequal depth—has remained a less explored area in existing literature. Traditional methods, including physical modeling and numerical simulations like the Finite Element Method (FEM), often involve significant computational cost, time, and expertise. This research gap necessitates the development of robust, accurate, and computationally efficient predictive models. The primary objective of this study is to model and estimate the uplift pressure force at key points (designated as C at the upstream point and E at the downstream point) beneath hydraulic structure floors equipped with dual end cutoff walls. To achieve this, the study leverages data from extensive numerical simulations to develop and compare the performance of multiple intelligent and regression models.
METHODOLOGY:
The research methodology was executed in a systematic, multi-stage process. First, a comprehensive numerical simulation was conducted using the Finite Element Method (FEM) implemented in SEEP/W software (part of the Geo-Studio package). A total of 90 numerical models were developed, encompassing various configurations of dual cutoff walls, including both equal-depth (30 models) and unequal-depth (60 models) scenarios. The influential dimensionless parameters considered were the ratio of floor width to foundation depth (B/D), the ratio of floor width to downstream cutoff depth (B/d₂), and the ratio of upstream to downstream cutoff depths (d₁/d₂). The model was validated against established analytical solutions, confirming its high accuracy.
Subsequently, the dataset generated from the FEM analysis (90 data points) was utilized to develop and train four distinct predictive models:
1. Intelligent Models:
• Artificial Neural Network - Multi-Layer Perceptron (ANN-MLP)
• Artificial Neural Network - Radial Basis Function (ANN-RBF)
• Gene Expression Programming (GEP)
2. Regression Model:
• Multiple Non-Linear Regression (MNLR)
For all models, 70% of the data (63 points) was used for training, and the remaining 30% (27 points) was used for testing. The models were designed to predict the percentage of uplift pressure at the key points (PC% and PE%) based on the three input parameters. The performance of each model was evaluated using a suite of statistical metrics, including the Coefficient of Determination (R²), Root Mean Square Error (RMSE), Relative Error Percentage (RE%), and Kling-Gupta Efficiency (KGE), supplemented by graphical analyses such as scatter plots, violin plots, and density diagrams.
FINDINGS:
The findings of this study provide significant insights into both the physical phenomenon and the performance of the predictive models:
• Numerical Simulation Results: The FEM analysis successfully demonstrated the impact of varying cut-off wall configurations on seepage patterns and uplift pressure. For instance, increasing the B/d₂ ratio led to a rise in PC% (at C-key point) and a concurrent decrease in PE% (at E-key point). The study also produced a set of explicit, high-accuracy MNLR equations for directly estimating PC% and PE%, which are valuable for practical engineering design.
• Model Performance Comparison: The evaluation of the predictive models revealed a clear ranking in performance. The ANN-MLP model consistently outperformed all other approaches, achieving near-perfect agreement with the FEM data.
• For the test phase, the ANN-MLP model yielded exceptional statistical results: For PE%, R²=0.997, RMSE=0.223%, RE=0.069%, KGE=0.997. For PC%, R²=0.999, RMSE=0.015%, RE=0.184%, KGE=0.997.
• The relative error (RE%) for the superior ANN-MLP model was confined within an impressive range of less than ±2%.
• Graphical analyses, particularly the violin and density plots, visually confirmed that the data estimated by the ANN-MLP model closely matched the distribution and statistics of the original FEM data.
• The overall ranking of models based on a comprehensive scoring system was: 1. ANN-MLP, 2. ANN-RBF, 3. GEP, and 4. MNLR for key point E, and a similar order for key point C, affirming the superiority of the ANN-MLP approach.
CONCLUSION:
This study successfully demonstrates the application of intelligent computing techniques in geotechnical and hydraulic engineering. The research conclusively establishes that the ANN-MLP model is a highly superior, reliable, and accurate tool for estimating uplift pressure under hydraulic structures with complex dual cutoff wall configurations. Its performance surpasses that of other intelligent models (ANN-RBF, GEP) and regression (MNLR) methods. Furthermore, the study provides practicing engineers with two practical tools: a set of explicit MNLR equations for quick estimations and a highly precise ANN-MLP model for critical design scenarios. The methodologies and findings are directly applicable to the design and safety assessment of hydraulic infrastructures, enabling more efficient and risk-mitigated engineering solutions. Future work could focus on integrating a wider range of soil properties and structural geometries to further generalize the developed models.