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

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{*}

## Abstract

**:**

^{2}values of 1.00, 0.9994, and 0.9997.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Governing Equations

^{3}/s), k is the hydraulic conductivity coefficient (m/s), A is the area of the cross section (m

^{2}), ∂h/∂l is hydraulic gradient, K

_{x}and K

_{y}are hydraulic conductivity in horizontal and vertical directions, respectively (m/s), h is the total water head (m), Q is the applied boundary flux, θ is the volumetric water content, and t is time.

#### 2.2. Numerical Simulation

^{−5}m/s, and a steady-state seepage analysis was performed for all cutoff wall systems during the static condition. The cutoff wall was simulated as an impermeable interface. Moreover, a fully saturated analysis was considered for all materials in the hydraulic structure foundation’s model during the static condition, while a transient analysis was performed during the earthquake shaking (i.e., dynamic loading condition).

#### 2.3. Artificial Neural Networks

^{2}(Equation (6)).

## 3. Results and Discussion

#### 3.1. Uplift Pressure

#### 3.2. Exit Hydraulic Gradient

#### 3.3. Seepage Discharge

#### 3.4. Neural Network Modeling

## 4. Conclusions

^{2}for most of the output parameters achieved 1.00, although RMSE values varied between 0.0021 and 0.06. Overall, this study highlighted the importance of considering both static and dynamic conditions in the design and analysis of hydraulic structures with cutoff walls. However, further studies are needed to improve our knowledge of the hydraulic response of cutoff walls installed beneath hydraulic structures during seismic loads.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**(

**a**) Base case and (

**b**) schematic diagrams indicating different positions and inclination angles.

**Figure 4.**Flowchart for predicting the suitability for uplift pressure, seepage, and exit hydraulic gradient supply using FFNN.

**Figure 5.**(

**a**) Uplift pressure distribution; (

**b**) the total uplift pressure ratio compared with the base case for a static condition at an inclination angle of 90°.

**Figure 6.**Total uplift pressure head for different positions and inclination angles during static conditions.

**Figure 7.**(

**a**) Uplift pressure distributions for inclination angles of 30°, 90°, and 150° at the middle position during the static condition; (

**b**) seepage water flow at the middle position and various inclination angles.

**Figure 8.**Total uplift pressure head for different positions and inclination angles of the cutoff wall during the static condition and at 10 s for the dynamic condition.

**Figure 9.**Uplift pressure distribution for US position and 150° inclination angle during static and dynamic conditions at different times.

**Figure 10.**Excess pore water pressure distribution for US position and 150° inclination angle during dynamic conditions.

**Figure 11.**Exit hydraulic gradient distribution for the base case and with a cutoff wall at an inclination angle of 90° during the static condition.

**Figure 12.**Exit hydraulic gradient distribution for different inclination angles of the cutoff wall at the middle position during the static condition.

**Figure 13.**Exit hydraulic gradient distribution for the cutoff wall at US position with a 45° inclination angle during the static and dynamic conditions at 1.2, 2.14, 2.2, and 10 s.

**Figure 14.**Exit hydraulic gradient distribution for a cutoff wall with a 90° inclination angle at different positions during the dynamic state at 10 s.

**Figure 15.**Exit hydraulic gradient distribution for a cutoff wall at US position with different inclination angles during the dynamic state at 10 s.

**Figure 16.**Seepage discharge without a cutoff wall (BC) and with a cutoff wall at different locations and inclination angles during static conditions.

**Figure 17.**Seepage discharge changing ratios with cutoff walls at different locations and inclination angles during static conditions compared to BC.

**Figure 18.**Inflow seepage discharge distribution for a cutoff wall in the middle position with 90° inclination angles during static and dynamic conditions.

**Figure 19.**Seepage discharge for different positions and inclination angles during the static condition and at 10 s for the dynamic condition.

**Figure 20.**The FFNN model’s (

**a**) uplift, (

**b**) seepage, and (

**c**) exit hydraulic gradient calculated linear regression relationships for training, validation, testing, and overall, per model.

**Figure 21.**FFNN predictions for each model for the entire set of experimental data samples for (

**a**) uplift, (

**b**) seepage, and (

**c**) exit hydraulic gradient.

**Figure 22.**The test set of experimental data samples for (

**a**) uplift, (

**b**) seepage, and (

**c**) exit hydraulic gradient are predicted by FFNN for each model.

Model | Error | Number of Neurons | |||
---|---|---|---|---|---|

2 | 5 | 10 | 15 | ||

Uplift (m) | RMSE | 0.4134 | 0.1840 | 0.0830 | 0.0697 |

${R}^{2}$ | 0.9998 | 1.00 | 1.00 | 1.00 | |

Seepage (m^{3}/(s.m)) | RMSE | 0.0163 | 0.0024 | 0.0021 | 0.0032 |

${R}^{2}$ | 0.9567 | 0.9992 | 0.9994 | 0.9985 | |

Exit gradient (dimensionless) | RMSE | 0.0471 | 0.0328 | 0.0059 | 0.0102 |

${R}^{2}$ | 0.9802 | 0.9905 | 0.9997 | 0.9991 |

Model | Activation Function of the Hidden Layer’s | Error | Training Algorithm | ||
---|---|---|---|---|---|

Trainlm | Trainscg | Trainbr | |||

Uplift pressure (m) | tansig | RMSE | 0.0406 | 0.3505 | 0.1862 |

${R}^{2}$ | 1.00 | 0.9998 | 1.0000 | ||

radbas | RMSE | 0.3571 | 1.2833 | 0.1849 | |

${R}^{2}$ | 0.9998 | 0.9978 | 1.00 | ||

tribas | RMSE | 0.2070 | 0.3181 | 0.4286 | |

${R}^{2}$ | 0.9999 | 0.9999 | 0.9998 | ||

Seepage (m^{3}/(s.m)) | tansig | RMSE | 0.0021 | 0.0042 | 0.0014 |

${R}^{2}$ | 0.9994 | 0.9971 | 0.9997 | ||

radbas | RMSE | 0.0024 | 0.0031 | 0.0014 | |

${R}^{2}$ | 0.9991 | 0.9985 | 0.9997 | ||

tribas | RMSE | 0.0028 | 0.0047 | 0.0781 | |

${R}^{2}$ | 0.9987 | 0.9964 | 0.7722 | ||

Exit gradient (dimensionless) | tansig | RMSE | 0.0059 | 0.0457 | 0.0419 |

${R}^{2}$ | 0.9997 | 0.9813 | 0.9844 | ||

radbas | RMSE | 0.0367 | 0.0507 | 0.0668 | |

${R}^{2}$ | 0.9888 | 0.9771 | 0.9605 | ||

tribas | RMSE | 0.0691 | 0.0286 | 0.1088 | |

${R}^{2}$ | 0.9590 | 0.9928 | 0.8996 |

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## Share and Cite

**MDPI and ACS Style**

Alrowais, R.; Alwushayh, B.; Bashir, M.T.; Nasef, B.M.; Ghazy, A.; Elkamhawy, E.
Modeling and Analysis of Cutoff Wall Performance Beneath Water Structures by Feed-Forward Neural Network (FFNN). *Water* **2023**, *15*, 3870.
https://doi.org/10.3390/w15213870

**AMA Style**

Alrowais R, Alwushayh B, Bashir MT, Nasef BM, Ghazy A, Elkamhawy E.
Modeling and Analysis of Cutoff Wall Performance Beneath Water Structures by Feed-Forward Neural Network (FFNN). *Water*. 2023; 15(21):3870.
https://doi.org/10.3390/w15213870

**Chicago/Turabian Style**

Alrowais, Raid, Bandar Alwushayh, Muhammad Tariq Bashir, Basheer M. Nasef, Ahmed Ghazy, and Elsayed Elkamhawy.
2023. "Modeling and Analysis of Cutoff Wall Performance Beneath Water Structures by Feed-Forward Neural Network (FFNN)" *Water* 15, no. 21: 3870.
https://doi.org/10.3390/w15213870