Fuzzy reliability analysis of RC structures by using an improved time-dependent model of chloride ingress

Steel bars pitting corrosion is a process that strongly jeopardises the reliability of the reinforced concrete structures exposed to chlorides. The proper treatment of uncertainties that affects geometrical, mechanical and chemical involved parameters is for some aspects still an open question because the probabilstic approach, ordinarily adopted, presents some limitations not only when few data are available to characterise involved variables but especially when some parameters are ambiguously defined, not only in terms of distribution type. In these circumstances a possibilistic approach could respresent a reasonable alternative to perform this specific reliability analysis. In the present study, the problem parameters are modelled by using a complete fuzzy criterion and a time-dependent fuzzy safety factor is defined in order to evaluate how the residual flexural resistance is greater or less than the bending moment. Moreover, the study provides a more proper mathematical analysis of the chloride penetration into concrete.

[1]  B. Elsener.  Corrosion rate of steel in concrete : Measurements beyond the Tafel law , 2005 .

[2]  Edward Beltrami,et al.  Uncertainty and Information , 2020, What Is Random?.

[3]  Isaac E. Elishakoff,et al.  Fuzzy sets based interpretation of the safety factor , 2006, Fuzzy Sets Syst..

[4]  Paul Sandberg.  Critical evaluation of factors affecting chloride initiated reinforcement corrosion in concrete , 1995 .

[5]  Robert E. Melchers,et al.  Effect of reinforcement corrosion on reliability of highway bridges , 1998 .

[6]  L. Nilsson,et al.  Chloride diffusivity in high strength concrete at different ages , 1992 .

[7]  Mark G. Stewart,et al.  Structural reliability of concrete bridges including improved chloride-induced corrosion models , 2000 .

[8]  F. Duprat,et al.  Reliability of RC beams under chloride-ingress , 2007 .

[9]  H JavierGuachalla.  The Mathematics , 2007 .

[10]  Siegfried Gottwald,et al.  Fuzzy Sets and Fuzzy Logic , 1993 .

[11]  Isaac Elishakoff,et al.  Four Alternative Definitions of the Fuzzy Safety Factor , 2006 .

[12]  David W. Law,et al.  Prediction of the ultimate limit state of degradation of concrete structures , 2003 .

[13]  Mark G. Stewart,et al.  Spatial variability of pitting corrosion and its influence on structural fragility and reliability of RC beams in flexure , 2004 .

[14]  T. Luping,et al.  On the mathematics of time-dependent apparent chloride diffusion coefficient in concrete , 2007 .

[15]  Andrew Chan,et al.  Residual capacity of corroded reinforcing bars , 2005 .

[16]  Christine M. Anderson-Cook,et al.  Impact of specification changes on chloride-induced corrosion service life of bridge decks , 2002 .

[17]  W. F. Chen,et al.  Closure of "Effective Length Factor of Columns in Semirigid and Unbraced Frames" , 1997 .

[18]  Terje Haukaas,et al.  Probabilistic capacity models and seismic fragility estimates for RC columns subject to corrosion , 2008, Reliab. Eng. Syst. Saf..

[19]  Baoding Liu,et al.  Uncertainty Theory - A Branch of Mathematics for Modeling Human Uncertainty , 2011, Studies in Computational Intelligence.

[20]  A C Smith,et al.  CORROSION OF STEEL BY CONCRETE , 1982 .

[21]  J. Westwater,et al.  The Mathematics of Diffusion. , 1957 .

[22]  Wolfgang Graf,et al.  Time-dependent reliability of textile-strengthened RC structures under consideration of fuzzy randomness , 2006 .

[23]  Tang Luping,et al.  Chloride Transport in Concrete - Measurement and Prediction , 1996 .

[24]  Leif Mejlbro,et al.  The Complete Solution of Fick's Second Law of Diffusion with Time-dependent Diffusion Coefficient and Surface Concentration , 1996 .

[25]  E J Wallbank,et al.  The Performance of Concrete in Bridges: a Survey of 200 Highway Bridges , 1989 .

[26]  K. Takewaka,et al.  Quality and Cover Thickness of Concrete Based on the Estimation of Chloride Penetration in Marine Environments , 1988, SP-109: Concrete in Marine Environment.

[27]  Lotfi A. Zadeh,et al.  Fuzzy Sets , 1996, Inf. Control..

[28]  P. B. Bamforth,et al.  The derivation of input data for modelling chloride ingress from eight-year UK coastal exposure trials , 1999 .

[29]  Mark G. Stewart,et al.  Time-dependent reliability of deteriorating reinforced concrete bridge decks , 1998 .

[30]  Michael P. Enright,et al.  Probabilistic analysis of resistance degradation of reinforced concrete bridge beams under corrosion , 1998 .

[31]  Robert E. Melchers,et al.  RELIABILITY OF DETERIORATING RC SLAB BRIDGES , 1997 .

[32]  Mark G. Stewart,et al.  Pitting corrosion and structural reliability of corroding RC structures: Experimental data and probabilistic analysis , 2008, Reliab. Eng. Syst. Saf..

[33]  Franco Bontempi,et al.  Fuzzy reliability analysis of concrete structures , 2004 .

[34]  Michael D. A. Thomas,et al.  Modelling chloride diffusion in concrete: Effect of fly ash and slag , 1999 .

[35]  Dimitar P. Filev,et al.  Fuzzy SETS AND FUZZY LOGIC , 1996 .

[36]  Cruz Alonso,et al.  Comparison of rates of general corrosion and maximum pitting penetration on concrete embedded steel reinforcement , 1995 .

[37]  B. T. Molloy,et al.  Prediction of long term chloride concentration in concrete , 1994 .

[38]  Mark G. Stewart,et al.  Spatial time-dependent reliability analysis of corrosion damage and the timing of first repair for RC structures , 2007 .

[39]  Baoding Liu.  Uncertainty Theory: An Introduction to its Axiomatic Foundations , 2004 .

[40]  A W Beeby,et al.  CONCISE EUROCODE FOR THE DESIGN OF CONCRETE BUILDINGS. BASED ON BSI PUBLICATION DD ENV 1992-1-1: 1992. EUROCODE 2: DESIGN OF CONCRETE STRUCTURES. PART 1: GENERAL RULES AND RULES FOR BUILDINGS , 1993 .

[41]  R. Langley.  UNIFIED APPROACH TO PROBABILISTIC AND POSSIBILISTIC ANALYSIS OF UNCERTAIN SYSTEMS , 2000 .

[42]  M. Collepardi,et al.  Penetration of Chloride Ions into Cement Pastes and Concretes , 1972 .

[43]  Michael D.A. Thomas,et al.  The use of bulk diffusion tests to establish time-dependent concrete chloride diffusion coefficients , 2003 .

[44]  Gert Heshe,et al.  DS/ENV 1992-1-1 NAD. National Application Document for Eurocode 2: Design of Concrete Structures, Part 1-1: General Rules and Rules for Buildings , 1993 .

[45]  F. H. Wittmann,et al.  Chloride Penetration into Concrete , 2008 .