Effect of Two Cut off Rows on Seepage underneath Hy-draulic Structures Using Weak Form Differential Quadra-ture Element Method: A Theoretical Approach

Esraa Ahmed, MSc Student, Irrigation and Hydraulics Department, Faculty of Engineering, Mansoura University, Mansoura 35516, Egypt.Follow
EL-Masry A. A, Professor, Irrigation and Hydraulics Department, Faculty of Engineering, Mansoura University, Mansoura 35516, Egypt.
Hossam A.A. Abdel Gawad, Associated professor, Irrigation and Hydraulics Department, Faculty of Engineering, Mansoura University, Mansoura 35516, Egypt.
Ahmed ELhamrawy, Lecturer, Irrigation and Hydraulics Department, Faculty of Engineering, Mansoura University, Mansoura 35516, Egypt.

Subject Area

Civil and Environmental Engineering

Article Type

Original Study

Abstract

Investigating confined seepage underneath hydraulic structures is crucial to ensure the safety of these structures. The Weak Form Quadrature Element Method (WFQEM) is the basis of this paper, which explores the behavior of confined flow. The seepage flow governing equation is solved numerically to estimate the uplift pressure underneath the hydraulic structures and the exit gradient.The Gauss–Lobatto–Legendre (GLL) type is used as nodal and integration points. Several models were solved to validate the applied numerical method. The obtained results are compared with theoretical and preceding numerical solutions mentioned in the literature. The system of equations generated from applying the WFQEM to the flow governing equation is solved by the aid of Python programming code. The WFQEM achieved pinpoint precision, requiring fewer nodal points and computational effort. Moreover, the WFQEM techniques are applied to investigate the uplift pressure change and exit hydraulic gradient downstream of the structure footing due to a change in the distance between two rows of cut-offs with several layers of thickness under the structure floor. Results show that the least uplift pressure on the floor is produced when the distance between the two cut-off rows is in the range of 0.5 d to 2 d from the constant first cut-off. On the other hand, locating the second cut-off at the end of the floor obtains the minimum exit hydraulic gradient at the last point of the floor

Keywords

Hydraulic structures, Laplace equation, Confined seepage, WFQEM, 2-D, Cut off.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

Recommended Citation

Ahmed, Esraa; A. A, EL-Masry; Abdel Gawad, Hossam A.A.; and ELhamrawy, Ahmed (2026) "Effect of Two Cut off Rows on Seepage underneath Hy-draulic Structures Using Weak Form Differential Quadra-ture Element Method: A Theoretical Approach," Mansoura Engineering Journal: Vol. 51 : Iss. 5 , Article 6.
Available at: https://doi.org/10.58491/2735-4202.3470

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