Research Papers

Seismic Reliability Assessment of a Concrete Water Tank Based on the Bayesian Updating of the Finite Element Model

[+] Author and Article Information
Francesca Marsili

Department of Civil and Industrial Engineering,
University of Pisa,
Largo Lucio Lazzarino 2,
Pisa 56126, Italy;
TU Braunschweig,
Beethovenstraße 52,
Braunschweig 38106, Germany
e-mail: francesca.marsili@unifi.it

Pietro Croce

Department of Civil and Industrial Engineering,
University of Pisa,
Largo Lucio Lazzarino 2,
Pisa 56126, Italy
e-mail: p.croce@ing.unipi.it

Noemi Friedman

Institute of Scientific Computing,
TU Braunschweig,
Mühlenpfordtstrasse 23,
Braunschweig D-38106, Germany
e-mail: n.friedman@tu-bs.de

Paolo Formichi

Department of Civil and Industrial Engineering,
University of Pisa,
Largo Lucio Lazzarino 2,
Pisa 56126, Italy
e-mail: p.formichi@ing.unipi.it

Filippo Landi

Department of Civil and Industrial Engineering,
University of Pisa,
Largo Lucio Lazzarino 2,
Pisa 56126, Italy;
Institute of Scientific Computing,
TU Braunschweig,
Mühlenpfordtstrasse 23,
Braunschweig D-38106, Germany
e-mail: filippo.landi@unifi.it

Manuscript received September 30, 2016; final manuscript received December 26, 2016; published online March 1, 2017. Assoc. Editor: Konstantin Zuev.

ASME J. Risk Uncertainty Part B 3(2), 021004 (Mar 01, 2017) (14 pages) Paper No: RISK-16-1131; doi: 10.1115/1.4035737 History: Received September 30, 2016; Revised December 26, 2016

Failure or malfunction of complex engineered networks involves relevant social and economic aspects, so that their maintenance is of primary importance. In assessing the reliability of such networks, it should be duly considered that they are a whole made of different parts, and that some of these individual parts or structures are often crucial to assure the proper operation of the entire network. Moreover, each of these structures can be considered a complex system by itself: structural reliability theory should be thus combined with advanced numerical analysis tools in order to obtain realistic estimates of the probability of failure. Accurate estimations are especially required in seismic zones, aiming to efficiently plan future interventions. This paper presents a method for the reliability assessment of a critical element of engineered networks. The method is discussed with special reference to a relevant case study: a concrete water tank, which is a key component of a water supply system. Special attention is devoted to the reliability assessment of the tank under seismic loads, based on a structural identification approach. The calibration of the finite element model (FEM) of the structure is carried out on probabilistic basis, applying the Bayes theorem and response surface methods. The proposed approach allows to significantly speed up the structural identification process, leading to sounder estimate of the input parameters. Finally, the seismic fragility curves of the structure are developed according to the relevant limit states, demonstrating that information regarding the global structural behavior and local checks can be effectively combined in structural reliability assessments.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.


Croce, P. , and Holicky, M. , 2015, Operational Methods for the Assessment and Management of Aging Infrastructure, TEP, Pisa, Italy.
Diamantidis, D. , and Holicky, M. , 2012, “ Innovative Methods for the Assessment of Existing Structures,” Klokner Institute, Czech Technical University, Prague, Czechia.
Huang, Q. , Gardoni, P. , and Hurlebaus, S. , 2015, “ Adaptive Reliability Analysis of Reinforced Concrete Bridges Subject to Seismic Loading Using Nondestructive Testing,” ASCE-ASME J. Risk Uncertainty Eng. Syst., Part A, 1(4).
Sykora, M. , Markova, J. , Holicky, M. , Jung, K. , Thiis, T. , Flo, I. A. , and Kvaal, K. , 2010, “ Structural Assessment of Industrial Heritage Buildings,” Klokner Institute, Czech Technical University, Prague, Czechia.
Der Kiureghian, A., 1994, “ Structural Reliability Methods for Seismic Safety Assessment,” Earthquake Engineering, Tenth World Conference 1994, Balkema, Rotterdam, The Netherlands, pp. 6519–6533.
Ditlevsen, O. , and Madsen, H. O. , 1996, Structural Reliability Methods, Wiley, Chichester, UK.
Melchers, R. E. , 1999, Structural Reliability Analysis and Prediction, Wiley, Chichester, UK.
Melchers, R. E. , and Hough, R. , 2007, Modeling Complex Engineering, ASCE, Reston, VA.
Lemaire, M. , 2009, Structural Reliability, Wiley, Hoboken, NJ, and ISTE, London.
Faravelli, L. , 1989, “ Response-Surface Approach for Reliability Analysis,” J. Eng. Mech., 115(12), pp. 2763–2781. [CrossRef]
Sudret, B. , 2007, “ Uncertainty Propagation and Sensitivity Analysis in Mechanical Models: Contributions to Structural Reliability and Stochastic Spectral Methods,” Rapport d'activitée scientifique présenté en vue de l'obtention de l'Habilitation à Diriger des Recherches, Blaise Pascal University–Clermont II, Clermont-Ferrand, France, Report No. HDR 239.
Çatbaş, N. F. , Kijewski-Correa, T. , and Aktan, A. E. , 2013, Structural Identification of Constructed Systems, ASCE, Reston, VA.
Ang, H.-S. , and Tang, W. H. , 2007, Probability Concepts in Engineering: Emphasis on Applications to Civil and Environmental Engineering, Vol. 1, 2nd ed., Wiley, Hoboken, NJ.
Marsili, F. , Croce, P. , Klawonn, F. , and Landi, F. , 2016, “ A Bayesian Network for the Definition of Probability Models for Compressive Strength of Concrete Homogeneous Population,” 14th International Probabilistic Workshop, Ghent, Belgium, pp. 269–283.
Beconcini, M. L. , Croce, P. , Marsili, F. , Muzzi, M. , and Rosso, E. , 2016, “ Probabilistic Reliability Assessment of a Heritage Structure Under Horizontal Loads,” Probab. Eng. Mech., 45(7), pp. 198–211. [CrossRef]
Kolios, A. , Quinio, A. , Antoniadis, A. , and Brennan, F. , 2010, “ An Approach to Stochastic Expansion for the Reliability Assessment of Complex Structures,” 8th International Probabilistic Workshop, Szczecin, Poland, pp. 223–232.
Sudret, B. , 2012, “ Meta-Models for Structural Reliability and Uncertainty Quantification,” Fifth Asian-Pacific Symposium on Structural Reliability and Its Applications (5APSSRA), Paper No. 321.
Der Kiureghian, A. , and Ditlevsen, O. , 2009, “ Aleatory or Epistemic? Does It Matter?” Struct. Saf., 31(2), pp. 105–112. [CrossRef]
Giannini, R. , Sguerri, L. , Paolacci, F. , and Alessandri, S. , 2014, “ Assessment of Concrete Strength Combining Direct and NDT Measures Via Bayesian Inference,” Eng. Struct., 64(4), pp. 68–77. [CrossRef]
Pereira, N. , and Romão, X. , 2016, “ Assessment of the Concrete Strength in Existing Buildings Using a Finite Population Approach,” Constr. Build. Mater., 110(5), pp. 106–116. [CrossRef]
Ghanem, R. , and Spanos, P. , 1991, Stochastic Finite Elements: A Spectral Approach, Springer-Verlag, New York.
Stefanou, G. , 2009, “ The Stochastic Finite Element Method: Past, Present and Future,” Comput. Methods Appl. Mech. Eng., 198(9–12), pp. 1031–1051. [CrossRef]
Matthies, H. G. , 2007, “ Uncertainty Quantification With Stochastic Finite Elements,” Encyclopedia of Computational Mechanics, Vol. 1, E. Stein, R. de Borst, and T. J. R. Hughes, eds., Wiley, Chichester, New York, Chap. 27.
Teughels, A. , and De Roeck, G. , 2005, “ Damage Detection and Parameter Identification by Finite Element Model Updating,” Arch. Comput. Methods Eng., 12(2), pp. 123–164. [CrossRef]
Marwala, T. , 2010, Finite-Element-Model Updating Using Computational Intelligence Techniques, Springer-Verlag, London.
Reich, G. W. , and Park, K. C. , 2001, “ A Theory for Strain-Based Structural System Identification,” ASME J. Appl. Mech., 68(4), pp. 521–527. [CrossRef]
Friswell, M. , and Mottershead, J. , 1995, Finite Element Model Updating in Structural Dynamics, Kluwer Academic Publishers, Dordrecht, The Netherlands.
Schlune, H. , Plos, M. , and Gylltoft, K. , 2009, “ Improved Bridge Evaluation Through Finite Element Model Updating Using Static and Dynamic Measurements,” Eng. Struct., 31(7), pp. 1477–1485.
Yao, C. R. , and Li, Y. D. , 2008, “ Updating of Cable-Stayed Bridges Model Based on Static and Dynamic Test Data,” J. China Railw. Soc., 30(3), pp. 65–70.
Zong, Z. H. , and Xia, Z. H. , 2008, “ Finite Element Model Updating Method of Bridge Combined Modal Flexibility and Static Displacement,” China J. Highw. Transp., 21(94), pp. 43–49.
Simoen, E. , De Roeck, G. , and Lombaert, G. , 2015, “ Dealing With Uncertainty in Model Updating for Damage Assessment: A Review,” Mech. Syst. Signal Process., 56–57(5), pp. 123–149. [CrossRef]
Beck, J. , and Katafygiotis, L. , 1998, “ Updating Models and Their Uncertainties—I: Bayesian Statistical Framework,” ASCE J. Eng. Mech., 124(4), pp. 455–461. [CrossRef]
Katafygiotis, L. , and Beck, J. , 1998, “ Updating Models and Their Uncertainties—II: Model Identifiability,” ASCE J. Eng. Mech., 124(4), pp. 463–467. [CrossRef]
Tarantola, A. , 2005, Inverse Problem Theory and Methods for Model Parameter Estimation, SIAM, Philadelphia, PA.
Box, G. , and Tiao, G. , 1973, Bayesian Inference in Statistical Analysis, Addison-Wesley, Reading, MA.
Ka Veng, Y. , 2010, Bayesian Methods for Structural Dynamics and Civil Engineering, Wiley, Singapore.
Tiernay, L. , 1994, “ Markov Chains for Exploring Posterior Distribution,” Ann. Stat., 22(4), pp. 1701–1728. [CrossRef]
Kalman, R. , and Bucy, R. , 1961, “ New Results in the Linear Prediction and Filter Theory,” ASME J. Basic Eng., 83(1), pp. 85–108. [CrossRef]
Evensen, G. , 2009, Data Assimilation, The Ensemble Kalman Filter, Springer-Verlag, Berlin.
Bertsekas, D. P. , and Tsitsiklis, J. N. , 2000, Introduction to Probability (Lecture Notes), Athena Scientific, Belmont, MA, MIT Course 6.041–6.431.
Ernst, O. G. , Sprungk, B. , and Starkloff, H.-J. , 2014, “ Bayesian Inverse Problems and Kalman Filters,” Extraction of Quantifiable Information From Complex Systems (Lecture Notes in Computational Science and Engineering), Springer, Switzerland, pp. 133–159.
Matthies, H. G. , Zander, E. K. , Rosic, B. V. , Litvinenko, A. , and Pajonk, O. , 2015, “ Inverse Problems in a Bayesian Setting, Inst. of Scientific Computing,” T.U. Braunschweig, Braunschweig, Germany.
Zhao, Y.-G. , and Ono, T. , 1999, “ A General Procedure for First/Second-Order Reliability Method (FORM/SORM),” Struct. Saf., 21(2), pp. 95–112.
Xiu, D. , 2010, Numerical Methods for Stochastic Computations, Princeton University Press, Princeton, NJ.
Rosic, B. , Sykora, J. , Pajonk, O. , Kucerova, A. , and Matthies, H. G. , 2014, “ Comparison of Numerical Approaches to Bayesian Updating,” T.U. Braunschweig, Braunschweig, Germany, Report No. 10.
Zander, E. K. , 2015, “ Nonlinear Minimum Mean Square Error Estimation,” Institute of Scientific Computing, T.U. Braunschweig, Braunschweig, Germany, Internal Report.
Marsili, F. , Friedman, N. , Croce, P. , Formichi, P. , and Landi, F. , 2016, “ On Bayesian Identification Methods for the Analysis of Existing Structures,” 19th IABSE Congress, Stockholm, Sweden, Sept. 21–23, pp. 194–201.
Belluzzi, O. , 1961, Scienza Delle Costruzioni, Vol. III, Zanichelli Bologna, Italy.
Breysse, D. , 2012, “ Non-Destructive Evaluation of Concrete Strength: An Historical Review and a New Perspective by Combining NDT Methods,” Constr. Build. Mater., 33(8), pp. 139–163. [CrossRef]
Huang, Q. , 2010, “ Adaptive Reliability Analysis of Reinforced Concrete Bridges Using Nondestructive Testing,” Ph.D. dissertation, Texas A&M University, College Station, TX.
Beconcini, M. L. , and Formichi, P. , 2003, “ Resistenza del calcestruzzo, misure sclerometriche e di velocità di propagazione degli ultrasuoni in strutture esistenti: risultati di una campagna di indagini,” 10th Congresso Nazionale dell'AIPnD, Ravenna, Italy, pp. 372–380 (in Italian).
CEN, 2002, “ Eurcode Basis of Structural Design,” CEN, Brussels, Belgium, Standard No. EN1990:2002.
Computers and Structures, 2009, “ SAP2000: Static and Dynamic Finite Element of Structures (Version 14),” Computers and Structures, Berkeley, CA.
Neville, A. M. , 2004, Properties of Concrete Fourth and Final Edition Standards Updated to 2002, Pearson Education Limited, Essex, UK.
Lu, X. , Sun, Q. , Feng, W. , and Tian, J. , 2013, “ Evaluation of Dynamic Modulus of Elasticity of Concrete Using Impact-Echo Method,” Constr. Build. Mater., 47(10), pp. 231–239. [CrossRef]
Jurowskia, K. , and Grzeszczyka, S. , 2015, “ The Influence of Concrete Composition on Young's Modulus,” 7th Scientific-Technical Conference Material Problems in Civil Engineering (MATBUD’2015), pp. 584–591.
Yıldırım, H. , and Sengul, O. , 2011, “ Modulus of Elasticity of Substandard and Normal Concretes,” Constr. Build. Mater., 25(4), pp. 1645–1652. [CrossRef]
Zhu, B. F. , 2009, “ On the Dynamic Modulus of Elasticity of Concrete in Anti-Earthquake Design of Concrete Dams,” Water Res. Hydropower Eng., 40(11), pp. 19–22.
HBM, 2000, “ Inductive Displacement Transducer HBM W20: Mounting Instructions,” Hottinger Baldwin Measurements, Darmstadt, Germany.
HBM, 2000, “ Accelerometer HBM B/200: Mounting Instructions,” Hottinger Baldwin Measurements, Darmstadt, Germany.
Zander, E. , 2016, “ A Matlab/Octave Toolbox for Stochastic Galerkin Methods,” Github, San Francisco, CA.
Marsili, F. , Friedman, N. , and Croce, P. , 2015, “ Parameter Identification Via gPCE-Based Stochastic Inverse Methods for Reliability Assessment of Existing Structures,” International Probabilistic Workshop 2015, Liverpool, pp. 112–123.
Housner, G. W. , 1957, “ Dynamic Pressures on Accelerated Fluid Containers,” Bull. Seismol. Soc. Am., 47(1), pp. 15–35.
Davidovici, V. , and Haddadi, A. , 1982, “ Calcul pratique de réservoirs en zone sismique,” Ann. Inst. Tech. Batim. Trav. Publics, 409.
CEN, 2006, “ EN 1998-4: Eurocode 8: Earthquake Resistant Design of Structures—Part 4: Tanks, Silos and Pipelines,” CEN, Brussels, Belgium, Standard No. EN 1998-4: Eurocode 8.
CEN, 2004, “ EN 1998-1: Eurocode 8: Design of Structures for Earthquake Resistance—Part 1: General Rules, Seismic Actions and Rules for Buildings,” CEN Brussels, Belgium, Standard EN 1998-1: Eurocode 8.
Ellingwood, B. , 1977, “ Statistical Analysis of RC Beam–Column Interaction,” J. Struct. Div., ST7(103), pp. 1377–1388.
Neuenhofer, A. , and Zilch, K. , 1993, “ Probabilistic Validation of Eurocode 2 Partial Safety Factors Using Full Distribution Reliability Methods,” 5th International Federation for Information Processing (IFIP) WG 7.5 Conference, Reliability and Optimization of Structural Systems, Takamatsu, Japan, Mar. 16–24.
Floris, C. , and Mazzucchelli, A. , 1991, “ Reliability Assessment of RC Column Under Stochastic Stress,” ASCE J. Struct. Eng., 117(11), pp. 3274–3292. [CrossRef]
Frangopol, D. M. , Ide, Y. , Spacone, E. , and Iwaki, I. , 1996, “ A New Look at Reliability of Reinforced Concrete Columns,” Struct. Saf., 18(2/3), pp. 123–150. [CrossRef]
Stewart, M. G. , and Attard, M. M. , 1999, “ Reliability and Model Accuracy for High-Strength Concrete Column Design,” J. Struct. Eng., 125(3), pp. 167–177.
Jiang, Y. , and Yang, W. , 2013, “ An Approach Based on Theorem of Total Probability for Reliability Analysis of RC Columns With Random Eccentricity,” Struct. Saf., 41(3), pp. 37–46. [CrossRef]
Ghersi, A. , and Muratore, M. , 2004, “ Verifica e progetto allo stato limite ultimo di pilastri in c.a. a sezione rettangolare: un metodo semplificato,” Ing. Sismica, XXI(3), pp. 41–49 (in Italian).
Verderame, G. M. , Stella, A. , and Cosenza, E. , 2001, “ Le proprietà meccaniche degli acciai impiegati nelle strutture in c.a. realizzate negli anni ’60,” X Congresso Nazionale L'ingegneria Sismica, Potenza-Matera, Italy, Sept. 9–13, pp. 203–216 (in Italian).
Ellingwood, B. , 1980, “ Development of a Probability Based Load Criterion for American National Standard A58: Building Code Requirements for Minimum Design Loads in Buildings and Other Structures,” Vol. 13, National Bureau of Standards Washington, DC, Special Publications 577.
Holicky, M. , 2014, Introduction to Probability and Statistics for Engineers, Springer-Verlag, Berlin, Heidelberg.
JCSS, 2011, “ JCSS Probabilistic Model Code,” Joint Committee on Structural Safety, DTU, Lyngby, Denmark.
Gardoni, P. , 2002, “ Probabilistic Models and Fragility Estimates for Structural Components and Systems,” Ph.D. dissertation, University of California, Berkeley, Berkeley, CA.
Choi, E. , Des Roches, R. , and Nielsen, B. , 2004, “ Seismic Fragility of Typical Bridges in Moderate Seismic Zones,” Eng. Struct., 26(2), pp. 187–199. [CrossRef]
Gardoni, P. , Mosalam, K. M. , and Der Kiureghian, A. , 2003, “ Probabilistic Seismic Demand Models and Fragility Estimates for RC Bridges,” J. Earthquake Eng., 7(1), pp. 79–106.
Pejovic, J. , and Jankovic, S. , 2015, “ Seismic Fragility Assessment for Reinforced Concrete High-Rise Buildings in Southern Euro-Mediterranean Zone,” Bull. Earthquake Eng., 14(1), pp. 185–212. [CrossRef]
Kafali, C. , and Grigoriu, M. , 2007, “ Seismic Fragility Analysis: Application to Simple Linear and Non Linear Systems,” Earthquake Eng. Struct. Dyn., 36(13), pp. 1885–1900. [CrossRef]
Karim, K. R. , and Yamazaki, F. , 2001, “ Effect of Earthquake Ground Motions on Fragility Curves of Highway Bridge Piers Based on Numerical Simulation,” Earthquake Eng. Struct. Dyn., 30(12), pp. 1839–1856. [CrossRef]
Hwang, H. , Jernigan, J. B. , and Lin, Y. , 2000, “ Evaluation of Seismic Damage to Memphis Bridges and Highway Systems,” ASCE J. Bridge Eng., 5(4), pp. 322–330. [CrossRef]
Shinozuka, M. , Feng, M. Q. , Kim, H. , and Kim, S. , 2000, “ Nonlinear Static Procedure for Fragility Curve Development,” ASCE J. Eng. Mech., 126(12), pp. 1287–1295. [CrossRef]
Bourinet, J.-M. , Mattrand, C. , and Dubourg, V. , 2009, “ A Review of Recent Features and Improvements Added to FERUM Software,” 10th International Conference on Structural Safety and Reliability (ICOSSAR'09), Osaka, Japan, Paper No. 205.
ISO, 2001, “ Basis for Design of Structures, Assessment of Existing Structures,” International Organization for Standardization, Geneva, Switzerland, Standard No. ISO13822.


Grahic Jump Location
Fig. 1

General methodology for reliability assessment of existing structures based on response surface methods and Bayesian updating

Grahic Jump Location
Fig. 2

The water tank structure considered in the case study

Grahic Jump Location
Fig. 3

The FEM of the structure

Grahic Jump Location
Fig. 4

The loading device

Grahic Jump Location
Fig. 5

Position of transducers and accelerometers along the structure

Grahic Jump Location
Fig. 6

Response surfaces for the displacement δ1 recorder by the first sensor (a) and for the frequency ν (b, c, d)

Grahic Jump Location
Fig. 7

Sample points of the posterior pdfs, as obtained applying MCMC

Grahic Jump Location
Fig. 8

Seismic fragility curve (empty tank)

Grahic Jump Location
Fig. 9

Seismic fragility curve (full tank)




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Articles from Part A: Civil Engineering
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In