[ Détermination des lois de distribution des éléments structurels des évacuateurs de crue par la méthode d’indice de condition ]
Guy-de-Patience FTATSI MBETMI1, François Juvenaul TAMO CHEKAM2, Frédéric DUPRAT3, and GUY EDGARD NTAMACK4
1 LASE, Université de Ngaoundéré, IUT, P.O. Box 455, Ngaoundéré, Cameroon
2 LASE, Université de Ngaoundéré, IUT, P.O. Box 455, Ngaoundéré, Cameroon
3 LMDC, Université de Toulouse, INSA, UPS, 135 Avenue de Rangueil, 31077 Toulouse cedex 04, France
4 Group of Mechanics, Materials and Acoustics, Department of Physics, Faculty of Sciences, University of Ngaoundéré B.P. 454, Ngaoundéré, Cameroon
Original language: French
Copyright © 2025 ISSR Journals. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Structural components are the least studied in the literature because of their properties that vary from one design to another, which explains the scarcity of statistical data on them. The objective of this work is to determine the Weibull parameters of the reliability laws of the structural components of a spillway using the Condition Index method. To this end, the partial Top-Down Structural Analysis of a spillway was presented. A structural fault tree served as a starting point for the determination of the Weibull parameters of the corresponding component reliability laws. Then, the state condition tables associated with each element were drawn from the analyses carried out by the experts during the dam inspections. The determination of the Condition Indices was carried out by following a succession of steps developed in detail in this paper. After a variable change and a linear regression on the empirical data, a first approximation of the Weibull parameters of each component was performed. Then, the parameters obtained were optimized using the generalized gradient reduction nonlinear solver of the Excel software, on points of distinct reliability, and starting from the previous approximations. The resulting reliability models are very close to discrete data, and generally conservative. Finally, the Kolmogorov-Smirnov conformity test performed in each case validates the law and the determined parameters with a confidence interval greater than 95%. They can be used as a basis for determining the structural reliability of spillways.
Author Keywords: distribution law, spillway, condition index, structural elements, reliability.
Guy-de-Patience FTATSI MBETMI1, François Juvenaul TAMO CHEKAM2, Frédéric DUPRAT3, and GUY EDGARD NTAMACK4
1 LASE, Université de Ngaoundéré, IUT, P.O. Box 455, Ngaoundéré, Cameroon
2 LASE, Université de Ngaoundéré, IUT, P.O. Box 455, Ngaoundéré, Cameroon
3 LMDC, Université de Toulouse, INSA, UPS, 135 Avenue de Rangueil, 31077 Toulouse cedex 04, France
4 Group of Mechanics, Materials and Acoustics, Department of Physics, Faculty of Sciences, University of Ngaoundéré B.P. 454, Ngaoundéré, Cameroon
Original language: French
Copyright © 2025 ISSR Journals. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Structural components are the least studied in the literature because of their properties that vary from one design to another, which explains the scarcity of statistical data on them. The objective of this work is to determine the Weibull parameters of the reliability laws of the structural components of a spillway using the Condition Index method. To this end, the partial Top-Down Structural Analysis of a spillway was presented. A structural fault tree served as a starting point for the determination of the Weibull parameters of the corresponding component reliability laws. Then, the state condition tables associated with each element were drawn from the analyses carried out by the experts during the dam inspections. The determination of the Condition Indices was carried out by following a succession of steps developed in detail in this paper. After a variable change and a linear regression on the empirical data, a first approximation of the Weibull parameters of each component was performed. Then, the parameters obtained were optimized using the generalized gradient reduction nonlinear solver of the Excel software, on points of distinct reliability, and starting from the previous approximations. The resulting reliability models are very close to discrete data, and generally conservative. Finally, the Kolmogorov-Smirnov conformity test performed in each case validates the law and the determined parameters with a confidence interval greater than 95%. They can be used as a basis for determining the structural reliability of spillways.
Author Keywords: distribution law, spillway, condition index, structural elements, reliability.
Abstract: (french)
Les composants structurels sont les moins étudiés de la littérature à cause de leurs propriétés variables d’une conception à une autre, ce qui explique la rareté de données statistiques sur ces derniers. L’objectif de ce travail est de déterminer les paramètres de Weibull des lois de fiabilité des composants structurels d’un évacuateur de crues en utilisant la méthode d’Indice de Condition. À cet effet, l’Analyse Structurelle Descendante partielle d’un évacuateur de crues a été présentée. Un arbre de défaillances d’origine structurelle a servi de point de départ pour la détermination des paramètres de Weibull des lois de fiabilité des composants correspondants. Ensuite, les tableaux de conditions d’états associés à chaque élément ont été tirés des analyses effectuées par les experts lors des inspections de barrages. La détermination des Indices de Condition a été menée en suivant une succession d’étapes développées en détails dans ce papier. Après un changement de variable et une régression linéaire sur les données empiriques, une première approximation des paramètres de Weibull de chaque composant a été effectuée. Ensuite, les paramètres obtenus ont été optimisés en utilisant le solveur non linéaire à réduction de gradient généralisé du logiciel Excel, sur des points de fiabilité distincte, et partant des approximations précédentes. Les modèles de fiabilité obtenus sont très proches des données discrètes, et généralement conservateurs. Enfin le test de conformité de Kolmogorov Smirnov effectué dans chaque cas valide la loi et les paramètres déterminés avec un intervalle de confiance supérieur à 95%. Ils pourront servir de base à la détermination de la fiabilité structurelle d’évacuateurs de crues.
Author Keywords: loi de distribution, évacuateur de crue, indice de condition, éléments structurels, fiabilité.
