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ANAIS DO 55 CONGRESSO BRASILEIRO DO CONCRETO - CBC2013 55CBC 1

Life-Cycle Reliability Assessment of Concrete BridgesExposed to Corrosion

Fabio Biondini

Department of Civil and Environmental Engineering, Politecnico di MilanoPiazza Leonardo da Vinci 32 20133 Milan, Italy

[email protected]

Abstract

For concrete bridges exposed to damaging environments the structural performance must be considered astime-dependent. Therefore, a life-cycle approach to design of concrete bridges should lead to structureswhich are able to comply with the desired performance not only at the initial stage when the system is intact,but also during the expected lifetime. At present, design for durability with respect to chemical-physicaldamage phenomena is based on threshold values for concrete cover, water-cement ratio, amount and typeof cement, among other prescriptive requirements, to limit the effects of structural damage induced bycarbonation of concrete and corrosion of reinforcement. However, a durable design cannot be based only onsuch indirect evaluations of the effects of structural damage, but also needs to consider the global effects ofthe local damage phenomena on the overall performance of the structure. To this aim, a life-cycleprobabilistic approach to structural assessment and design of concrete structures exposed to the diffusiveattack from external aggressive agents has been proposed in previous works. This approach allows toreproduce the diffusion process of aggressive agents, such as chlorides, and to describe the mechanicaldamage coupled to diffusion, including corrosion of steel reinforcement and deterioration of concrete. Theglobal effects of local damage are evaluated by means of nonlinear and limit analysis procedures and thetime-variant structural reliability is evaluated at the system level by Monte Carlo simulation. An overview ofthe proposed methodology is presented in this paper, with application to time-variant reliability analysis andlifetime assessment of a concrete arch bridge exposed to corrosion.

Keywords: Concrete Bridges; Diffusion Processes; Corrosion; Life-Cycle Reliability; Structural Lifetime.

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1 Introduction

The structural performance of concrete bridges is time-variant due to deterioration effects ofaging and damage processes of materials and components (Ellingwood 2005). The mainsources of damage include chemical processes associated to sulfate and chloride attacksand alkali-silica reactions, physical processes due to freeze/thaw cycles and thermal cycles,and mechanical processes such as cracking, abrasion, erosion, and fatigue (Kilareski1980, CEB 1992, Bertolini et al.2004). The detrimental effects of these phenomena canlead over time to unsatisfactory levels of structural reliability. This problem presents amajor challenge to bridge engineering, since the classical time-invariant structural designcriteria and methods need to be revised to account for a proper modeling of the structural

system over its entire life-cycle by taking the effects of deterioration processes underuncertainty into account (Frangopol & Ellingwood 2010, Frangopol 2011).

In recent years, a considerable amount of research has been conducted in the area of life-cycle performance of structural systems under uncertainty (Frangopol & Furuta 2001,Frangopol et al.2004a, 2004b, 2007, 2012, Estes & Frangopol 2005, Nowak & Frangopol2005, Cho et al. 2007, Biondini & Frangopol 2008a, Biondini 2009, Chen et al. 2010,Frangopol & Ellingwood 2010, Biondini & Frangopol 2011, Strauss et al. 2012), andrelevant advances have been accomplished in the fields of modeling, analysis, design,maintenance, monitoring, and management of deteriorating bridges (Frangopol et al.1997a, 1997b, Frangopol 1999, Frangopol et al.2002, Casas et al.2002, Watanabe et al.

2004, Cruz et al.2006, Furuta et al.2006, Kho & Frangopol 2008, Frangopol et al. 2010,Biondini & Frangopol 2012, Malerba 2013, Zhu & Frangopol 2013). Despite this researchtrend, life-cycle concepts are not yet explicitly addressed in design codes and the checkingof system performance requirements is referred to the initial time of construction when thesystem is intact. In this approach, design for durability of concrete structures with respectto chemical-physical damage phenomena is based on simplified criteria associated withclasses of environmental conditions. Such criteria introduce threshold values for concretecover, water-cement ratio, amount and type of cement, among others, to limit the effects oflocal damage due to carbonation of concrete and corrosion of reinforcement. However, adurable design cannot be based only on such indirect evaluations of the effects ofstructural damage, but also needs to take into account the global effects of the local

damage phenomena on the overall performance of the structure.

To this purpose, a life-cycle probabilistic approach to structural assessment and design ofconcrete structures exposed to the diffusive attack from external aggressive agents hasbeen proposed in previous works (Biondini et al.2004b, 2006a, 2006b, 2008, 2011, 2013,Biondini & Frangopol 2008b, 2009, Biondini 2011, Biondini & Vergani 2012). This approachallows to reproduce the diffusion process of aggressive agents, such as chlorides, and todescribe the mechanical damage coupled to diffusion, including corrosion of reinforcementand deterioration of concrete. The global effects of local damage are evaluated by meansof nonlinear and limit analysis procedures and the time-variant structural reliability isevaluated at the system level by Monte Carlo simulation. An overview of the proposedmethodology is presented in this paper, with application to time-variant reliability analysisand lifetime assessment of a concrete arch bridge exposed to corrosion.

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2 Simulation of Diffusion Processes

The diffusion process of chemical components in solids can be described by the Ficks lawswhich, in case of single component diffusion in homogeneous, isotropic and time-invariantmedia, lead to the following second order partial differential linear equation (Glicksman 2000):

t

CCD

=2 (1)

where D is the diffusivity coefficient of the medium, C=C(z, t) is the concentration of the

chemical component at point z=(x,y,z) and time t, C= gradC(z, t)and 2

=.

For one-dimensional diffusion (1D) the Ficks equation can be solved analytically. The 1Ddiffusion model is frequently used to simulate the chloride diffusion process in concretestructures (fib 2006). However, the actual diffusion process is generally characterized bytwo- or three-dimensional patterns of concentration gradients and 1D diffusion models canlead to a loss of accuracy depending on the exposure conditions, geometrical shape ratioof the cross-section, and location of points where concentration is evaluated (Titi &Biondini 2012). For this reason, a numerical solution of the Ficks diffusion laws in two orthree dimensions may be necessary for accurate life-cycle evaluations.

The diffusion differential equation can be effectively solved numerically by means ofcellular automata which, in their basic form, consists of regular uniform grids of cells with adiscrete variable in each cell which can take on a finite number of states (Wolfram 1994). Itcan be shown that the Ficks laws in d-dimensions can be accurately reproduced byadopting the following evolutionary rule (Biondini et al.2004b):

=

++ +

+=

d

j

k

ji

k

ji

k

i

k

i CCd

CC1

,1,10

0

1 )(2

1 (2)

where the discrete variable Cik = C(zi,tk) represents the concentration of the component at

time tk in the cell i located at point zi=(xi,yi,zi), k jiC ,1 is the concentration in the adjacent cells

i1 in the direction j=1,..,d, and 0is a suitable evolutionary coefficient related to the rateof mass diffusion. In order to regulate the process according to a given diffusivity D, aproper discretization in space and time should be chosen in such a way that the grid

dimension x=y=z and the time step tsatisfy the following relationship:

t

x

dD

=2

0

2

1 (3)

A proof is given in Biondini et al. (2008). The value 0= 1/2 usually ensures a goodaccuracy of the automaton. A validation of this approach can be found in Biondini (2011).

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3 Modeling of Corrosion Damage

3.1 Reduction of the Cross-section of Reinforcing Steel Bars

The most relevant effect of corrosion is the reduction of the cross-section of the reinforcingsteel bars. The time evolution of the areaAsof a corroded bar is represented as follows:

0)](1[)( sss AttA = (4)

whereAs0is the area of the undamaged steel bar and s=s(t) is a dimensionless damage

index which provides a measure of cross-section reduction in the range [0; 1]. The damagefunction s=s(t) depends on both corrosion rate and corrosion mechanism. The relationship

between the damage index sand the corrosion penetration depth associated to uniformcorrosion, pitting corrosion, and mixed type of corrosion with components of uniform andpitting corrosion, can be found in Biondini & Vergani (2012).

3.2 Reduction of Ductility of Reinforcing Steel

Pitting corrosion may involve a significant reduction of steel ductility. Tensile tests oncorroded bars show that for a relatively small mass loss (about 13%) steel behavior may

become brittle (Almusallam 2001). The results of experimental tests reported inApostolopoulos & Papadakis (2008) indicate that ductility reduction of corroded steel bars

depends on the loss of resistant area. Based on these results, the steel ultimate strain su

can be related to the damage index sas follows (Biondini & Vergani 2012):

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