<  Back to the Polytechnique Montréal portal

Stability of cracked concrete hydraulic structures by nonlinear quasi-static explicit finite element and 3D limit equilibrium methods

Flavien Vulliet, Mahdi Ben Ftima and Pierre Léger

Article (2017)

Open Access document in PolyPublie
Open Access to the full text of this document
Accepted Version
Download (1MB)
Show abstract
Hide abstract


Several hydraulic concrete structures suffer from severe tridimensional (3D) discrete cracking, producing an assembly of concrete blocks resting one on top of the other. It is important to consider the 3D particularities of the cracked surfaces in the nonlinear sliding safety evaluation of these structures. A methodology to assess a sliding safety factor (SSF) and a sliding direction D for any structure with an a priori known 3D discrete crack surface geometry using the quasi-static explicit nonlinear finite elements method (QSE-FEM) is presented herein in the context of the strength reduction approach. QSE-FEM is known for its efficiency in solving highly nonlinear problems compared to implicit FEM. However, in QSE-FEM, the determination of the incipient failure motion is challenging. In addition to the ratio of kinetic to internal strain energy, a new criterion is proposed to identify sliding initiation based on absolute displacements of a control point. As part of the proposed methodology, a complementary simple tool, 3D-LEM, has been developed as a 3D extension of the classical limit equilibrium method (LEM). It is useful in preliminary sliding analyses to estimate the critical friction coefficient inducing sliding and the corresponding direction D. Three benchmark examples, of increasing complexities, are presented to verify the performance of the proposed methodology. Finally, a case study is adapted from an existing cracked hydraulic structure to evaluate its sliding stability using the QSE-FEM and 3D-LEM approaches. In the three benchmark examples, the same results are found for SSF and D for the two approaches. In the hydraulic structure example, SSFLEM, computed with 3D-LEM, is a lower bound of SSFFEM from QSE-FEM, and a strong correlation is found between the sliding directions computed with the two approaches.

Uncontrolled Keywords

Finite elements; Quasi-static explicit analyses; Limit equilibrium; Three-dimensional analyses; Sliding safety assessment, concrete hydraulic structure

Subjects: 1100 Structural engineering > 1100 Structural engineering
1100 Structural engineering > 1103 Concrete: materials and structures
1100 Structural engineering > 1104 Structural analysis
Department: Department of Civil, Geological and Mining Engineering
Grant number: RGPIN137122-04
PolyPublie URL: https://publications.polymtl.ca/2482/
Journal Title: Computers & Structures (vol. 184)
Publisher: Elsevier
DOI: 10.1016/j.compstruc.2017.02.007
Official URL: https://doi.org/10.1016/j.compstruc.2017.02.007
Date Deposited: 15 Mar 2017 15:00
Last Modified: 13 May 2023 03:55
Cite in APA 7: Vulliet, F., Ben Ftima, M., & Léger, P. (2017). Stability of cracked concrete hydraulic structures by nonlinear quasi-static explicit finite element and 3D limit equilibrium methods. Computers & Structures, 184, 25-35. https://doi.org/10.1016/j.compstruc.2017.02.007


Total downloads

Downloads per month in the last year

Origin of downloads


Repository Staff Only

View Item View Item