Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 31108
Reliability Levels of Reinforced Concrete Bridges Obtained by Mixing Approaches

Authors: Adrián D. García-Soto, Alejandro Hernández-Martínez, Jesús G. Valdés-Vázquez, Reyna A. Vizguerra-Alvarez


Reinforced concrete bridges designed by code are intended to achieve target reliability levels adequate for the geographical environment where the code is applicable. Several methods can be used to estimate such reliability levels. Many of them require the establishment of an explicit limit state function (LSF). When such LSF is not available as a close-form expression, the simulation techniques are often employed. The simulation methods are computing intensive and time consuming. Note that if the reliability of real bridges designed by code is of interest, numerical schemes, the finite element method (FEM) or computational mechanics could be required. In these cases, it can be quite difficult (or impossible) to establish a close-form of the LSF, and the simulation techniques may be necessary to compute reliability levels. To overcome the need for a large number of simulations when no explicit LSF is available, the point estimate method (PEM) could be considered as an alternative. It has the advantage that only the probabilistic moments of the random variables are required. However, in the PEM, fitting of the resulting moments of the LSF to a probability density function (PDF) is needed. In the present study, a very simple alternative which allows the assessment of the reliability levels when no explicit LSF is available and without the need of extensive simulations is employed. The alternative includes the use of the PEM, and its applicability is shown by assessing reliability levels of reinforced concrete bridges in Mexico when a numerical scheme is required. Comparisons with results by using the Monte Carlo simulation (MCS) technique are included. To overcome the problem of approximating the probabilistic moments from the PEM to a PDF, a well-known distribution is employed. The approach mixes the PEM and other classic reliability method (first order reliability method, FORM). The results in the present study are in good agreement whit those computed with the MCS. Therefore, the alternative of mixing the reliability methods is a very valuable option to determine reliability levels when no close form of the LSF is available, or if numerical schemes, the FEM or computational mechanics are employed.

Keywords: Monte Carlo Simulation, structural reliability, reinforced concrete bridges, point estimate method, mixing approaches

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 966


[1] R. E. Melchers, Structural Reliability Analysis and Prediction. Chichester, England: John Wiley and Sons Ltd, 1999, ch. 2.
[2] Rosenblueth E. Aproximaciones de segundos momentos en probabilidades. Boletín del Instituto Mexicano de Planeación y Operación de Sistemas Vol. 26 (in Spanish), 1974; 1–12.
[3] Rosenblueth E. Point estimates for probability moments. Proc. Natl. Acad. Sci., USA, 1975; 3812–3814.
[4] Rosenblueth E. Two-point estimates in probability. Appl. Math. Modelling, 1981; 329–335.
[5] Harr ME. Probabilistic estimates for multivariate analyses. Appl. Math. Model., Vol. 13, 1989; 313–318.
[6] Hong HP. An efficient point estimate method for probabilistic analysis. Eng. Syst. Safety, Vol. 52, 1998; 161–167.
[7] Lin Z, Li W. Restrictions of point estimate methods and remedy. Reliability Engineering and System Safety. Vol. 111, 2013; 106–111.
[8] Tsai CW, Franceschini S. Evaluation of probabilistic point estimate methods in uncertainty analysis for environmental engineering applications. Journal of Environmental Engineering 2005; 131:387–95.
[9] Zhao YG, Ono T. New point estimates for probability moments. Journal of Engineering Mechanics 2000; 126:433–436.
[10] Franceschini S, Tsai C, Marani M. Point estimate methods based on Taylor Series Expansion – The perturbance moments method – A more coherent derivation of the second order statistical moment. Applied Mathematical Modelling 2012; 36:5445–5454.
[11] Zhang Y, Lam JSL. A Copula Approach in the Point Estimate Method for Reliability Engineering. Quality and Reliability Engineering International 2015; 1–8.
[12] A.D. García-Soto, A. Hernández-Martínez, and J.G. Valdés-Vázquez, “Assessment of reliability levels for reinforced concrete beams using different methods and codes”, Structural Engineering International (Journal of the International Association for Bridge and Structural Engineering (IABSE)), submitted for publication.
[13] A.D. García-Soto, A. Hernández-Martínez, and J.G. Valdés-Vázquez, “Probabilistic assessment of a design truck model and live load factor from WIM data for Mexican highway bridge design”, Canadian Journal of Civil Engineering, vol. 42, pp. 970–974, 2015.
[14] R.A. Vizguerra-Alvarez, “Development of a live load model for Guanajuato state bridge design using extreme value analysis and considering multiple presence” (“Desarrollo de un modelo de cargas vivas para el diseño de puentes en el estado de Guanajuato mediante un análisis probabilista de valores extremos y considerando presencia múltiple”). Master Thesis, National Autonomous University of Mexico (UNAM), 2015 (in Spanish).
[15] ASSHTO. LRFD Bridge design specifications. American Association of State Transportation Officials, 6th edition, Washington D.C., 2014.
[16] CAN/CSA-S6-06. Canadian highway bridge design code. Canadian Standards Association, CSA International, 2012.
[17] NTC04. Normas técnicas complementarias para el diseño de estructuras de concreto. Reglamento de Construcciones para el Distrito Federal, Gaceta Oficial del Departamento del Distrito Federal, 2004 (in Spanish).
[18] J. Bojórquez-Mora and S.E. Ruiz, “Factores de carga y de resistencia para el diseño de estructuras de c/r ante cargas viva y muerta”. Serie Investigación y Desarrollo del Instituto de Ingeniería UNAM, SID 692, January 2015 (in Spanish).
[19] American Concrete Institute (ACI). Building code requirements for structural concrete. ACI 318-14, Farmington Hills, MI, 2014.
[20] European Committee for Standardization (CEN). Design of concrete structures. EN 1992-1-1, Eurocode, Brussels, Belgium, 2004.
[21] S. E. Ruiz, “Reliability associated with safety factors of ACI 318-89 and the Mexico City concrete design regulations”. ACI Structural Journal, 1993. 90-S27: 262-268.
[22] A.D. García-Soto, A. Hernández-Martínez, J.G. Valdés-Vázquez and L.F. Gay-Alanís, “Confiabilidad de Vigas de Concreto Reforzado Empleando Información Reciente de Laboratorio”. Journal del Instituto Mexicano del Cemento y del Concreto (IMCYC), Mexico 2015 (in Spanish); submitted for publication.
[23] H.P. Hong, “Short reinforced concrete column capacity under biaxial bending and axial load”, Canadian Journal of Civil engineering, 2000, Vol. 27, pp 1173-1182.
[24] SCT. “Nueva normatividad para diseño de puentes. N-PRY-CAR-6-01-001/01 a N-PRY-CAR-6-01-006/01”, Secretaria de Comunicaciones y transportes, 2001 (in Spanish).
[25] A. D. García-Soto, F. Calderón-Vega, R. Gómez, J. A. Escobar. “Analysis of live load effects on bridges modeled as plates considering multiple presence from WIM data”. Proceedings of the 9th International Conference on Short and Medium Span Bridges, SMSB 2014, Calgary, Alberta, Canada. 10 p paper in proceedings.
[26] H. Baji, and H. R. Ronagh. “A reliability-based investigation into ductility measures of RC beams designed based on fib Model Code 2010”. Structural Concrete 2015 (Accepted article).
[27] Joint Committee on Structural Safety: “JCSS: Probabilistic Model Code”, 2001.
[28] T. Braml and O. Wurzer. “Probabilistische Berechnungsverfahren als usätzlicher Baustein der ganzheitlichen Bewertung von Brücken im Bestand”, Verlag für Architektur und technische Wissenschaften GmbH & Co. KG, Berlin. Beton- und Stahlbetonbau 107, 2012, Heft 10 (in German)
[29] D. E. Allen. “Canadian highway bridge evaluation: reliability index”. Can. J. Civ. Eng. 1992, 19(6), 987–991
[30] J. R. Benjamin and C. A. Cornell. “Probability, Statistics, and Decision for Civil Engineers”. McGraw-Hill Book Company, New York, 1970.
[31] M. H. Faber. “Statistics and Probability Theory. In pursuit of engineering decision support”. Springer, Topics in safety, reliability and quality Vol. 18, 2012.
[32] M. Lemaire. “Structural reliability”, ISTE-Wiley, London-Hoboken, 2009.
[33] H. O. Madsen, S. Krenk, and N. C. Lind. “Methods of Structural Safety”. Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1986.