Reliability-Based Life Prediction of Aging Concrete Bridge Decks

Transcription

1 Reliability-Based Life Prediction of Aging Concrete Bridge Decks Z. Lounis National Research Council, Institute for Research in Construction, Canada. Abstract This paper presents a probabilistic approach to life prediction of concrete highway bridge decks based on Bogdanoff' s cumulative damage model. The condition of the deck is discretized into a finite set of damage states including no damage, onset of corrosion, crack initiation, major damage and failure. The damage accumulation process is modeled using a stationary unit jump Markov chain in which the probability distribution of damage after a duty cycle is assumed to depend only on the length of the duty cycle and the damage accumulated at the start of the cycle. The service life is determined from the time to reaching the absorbing state, which may successively be redefined as the onset of corrosion, cracking, spalling, etc. The proposed model is simple to use and the statistics of the lifetime and damage states at any given time are easily determined. The model yields a practical tool for the condition assessment, life prediction, and maintenance management of highway bridge decks. An example illustrating the application of the proposed approach is presented. 1. Introduction Highway bridges constitute a critical link and a considerable investment in infrastructure that should be kept safe and serviceable. However, in North America, a large number of these bridges are over 50 years old and suffer from extensive deterioration that affects their safety and serviceability, which results in traffic disruption and high user costs. In the OECD countries, the estimated rehabilitation and replacement costs for 800,000 bridges 1 is $ /m 2. In Canada, 40% of the bridges 229

2 are over 40 years old with rehabilitation costs estimated at $10 billion 2. In the U.S.A., about 24% of the bridges were classified as structurally deficient and 18% as functionally obsolete, with maintenance costs estimated at $90 billion 3. Highway bridge decks are identified as the bridge elements with the highest percentage of deficiency 3,4. It is estimated that one-third to one-half of the projected rehabilitation costs in the U.S. are related to bridge deck deterioration 4,5. The main causes of deterioration and failure of reinforced concrete bridge decks are chloride-induced corrosion of the reinforcement, freeze-thaw cycling, traffic overload, inadequate design, protection and construction, in addition to improper inspection and maintenance. Deicing chemicals applied to roadways and bridges during winter in Canada and the snow-belt states of the U.S. are the primary source of chlorides. The high costs associated with preserving the aging highway bridges and the limited funds allocated for their maintenance pose significant technical and economical challenges that require the development and implementation of systematic approaches to bridge management. Such approaches should provide effective decision support in planning the inspection, maintenance and rehabilitation throughout the life of a network of bridge structures. The implementation of such a system ensures adequate safety and reliability of the bridge network, extended service life of bridge structures and low life cycle costs. An effective bridge management system should include the following decision support models 2,5 : (i) Condition assessment using visual inspection and nondestructive evaluation methods 6,7 ; (ii) cumulative damage and service life prediction; and (iii) maintenance optimization 8. However, the prediction of the service life or time to rehabilitation or replacement of a concrete bridge deck is not a straightforward task as it involves the consideration of several criteria 5, including: i. Specified requirements for minimum performance or maximum damage that ensure safety and serviceability; ii. Economy by assessing the life cycle costs of all possible maintenance and rehabilitation strategies, including the do nothing option; iii. User costs associated with the condition and maintenance decision, including vehicle operating costs, crash costs, and traffic delay and disruption costs; iv. Network vs. project level decision, i.e. the decision on the service life and maintenance strategy is taken by considering simultaneously the main components (decks, girders, piers, etc.) of all bridges that constitute the network and prioritize the projects according not only to their condition but also in terms of their importance and risk of failure. In addition to the above criteria, the service life prediction model should also take into account the uncertainty in the damage accumulation. The sources of uncertainty include the physical or inherent uncertainty associated with the variability of concrete cover, chloride concentration and diffusion, freeze-thaw cycles, load traffic, concrete strength, in addition to the uncertainty in damage detection. Reliability-based methods in condition assessment and service life prediction of aging concrete structures have been used in different structural systems 5, 9-12,

3 In this paper, a probabilistic approach to service life prediction of deteriorating concrete bridge decks exposed to chlorides from deicing salts is presented. It is based on Bogdanoff s cumulative damage model that provides a reliable and practical prediction tool, which is applicable at both project and network levels and accommodates initial damage, time-dependent rate of deterioration, uncertainty in initial damage, condition assessment, environmental factors, and loading. 2. Damage Assessment in Concrete Bridge Decks The concrete slab-on-girder system is one of the most common bridge superstructure systems in North America and the deterioration of its deck accounts for an estimated one-third to one-half of the projected rehabilitation costs 4,5 in the U.S. The termination of the service life of concrete bridge decks is associated with the accumulation of irreversible damage resulting from corrosion of reinforcement, freeze thaw cycles, traffic loading, in addition to the initial damage resulting from poor design and /or construction and inadequate inspection and maintenance practices. The deck is exposed to aggressive environmental factors such as deicing salts and freeze-thaw cycles in addition to ever-increasing traffic loads that make it the weakest link of the bridge system in terms of performance and service life. The deterioration of the deck affects the quality of the riding surface and traffic safety, stiffness, load distribution characteristics, and load carrying capacity. The main factors that control the durability of concrete bridge decks include: Depth and permeability of its cover that provides a mechanical barrier to the action of chlorides, water, oxygen and carbonation front; Protection of the deck (membrane, epoxy coating, cathodic protection); Routine inspection and maintenance such as deck washing, maintenance of the drainage and joint systems and repair of cracks. It should be pointed out that most failures of bridge decks are due to loss of serviceability and functionality and not loss of strength and collapse. The ultimate limit state strength of concrete bridge decks is greatly enhanced by the high level of compressive membrane action that makes failure due to punching shear the governing failure mode as opposed to the flexural failure mode. Chloride-induced reinforcement corrosion is recognized as the major cause of deterioration of concrete decks. Depending on the quality of the initial design and protection, the time to damage initiation can vary considerably. Once corrosion is initiated, irreversible changes accumulate such as cracking, delamination and spalling that lead to a loss of cross-sectional area of concrete and steel, loss of bond between the steel and concrete, loss of serviceability and strength of the deck, and complete failure. The time at which the deck ceases to perform satisfactorily is the service life or lifetime of the deck. This irreversible damage accumulation is the result of the pressure exerted by the corrosion products (which occupy a much larger volume than the metallic iron due to the lower density of iron oxides), freeze thaw cycles and traffic loads. The specific volume of the hydrated iron oxides can be up to nearly seven times 231

4 of the iron from which they were formed 13, depending on the oxidation state. This volume increase induces tensile stresses in the concrete surrounding the reinforcement, which in turn lead to cracking and spalling of the concrete cover as these stresses exceed the concrete fracture strength. However, the corrosion process does not always lead to cracking as the oxides can diffuse through the pores to the external surface of the concrete and generate rust stains without cracking when the concrete is wet 13. Damage assessment in bridge decks is carried out using discrete damage rating systems. It consists in mapping the observed/measured condition using visual inspection and non-destructive evaluation methods (e.g. measurements of potentials, chloride content, resistivity, ground penetrating radar, etc.) onto a rating scale of 5, 7 or 9 ratings that describe the type, severity and extent of different distresses 6,7,8,12. Such a discrete rating system provides a practical tool in the assessment and management of highway bridges. In this paper, to ensure compatibility with the current practice of inspection and maintenance of concrete bridge decks, we assume that the evolutionary process of damage accumulation can be discretized into seven damages states D(i), i=1, 7, as follows: State1: This is the reference state and represents the initial deck condition with effective protection and no damage. State 2: Following the aging and failure of the protection, the deck becomes exposed to the ingress of chlorides. However, there is no corrosion activity as the chloride concentration at the reinforcement level is low. State 3: As the chlorides accumulate around the reinforcing steel and reach the socalled threshold level, depassivation of the reinforcing steel and initiation of corrosion become probable. The time to reach this damage state depends on the rate of diffusion of chlorides, depth of concrete cover, and presence of early-age cracks in the cover. State 4: Following the initiation of corrosion, corrosion products start accumulating and induce tensile stresses in the concrete that lead to longitudinal cracking. At this state, we assume minor cracks and light scaling on less than 10% of the deck with no spalling. State 5: The rate of corrosion is accelerated by the generation for longitudinal cracks along the reinforcing steel. About 20% to 30% of the deck is contaminated including repaired areas, delamination and spalling on 5% of the deck, in addition to some full depth failures. State 6: This state is characterized by an advanced loss of reinforcing steel cross sectional area and spalling of concrete on more than 15% of the deck. About 30% to 50% of the deck is deteriorated or contaminated. Extensive and wide cracks with local overstresses that make some deck sections not capable of supporting heavy wheel loads. The deck surface is rough with difficult vehicle control. State 7: Deck in failed condition. Full depth failures over much of the deck. Some sections of the deck have punched through. The deck surface is irregular producing a rough ride with extreme difficulty in vehicle control. The bridge should be closed. 232

5 Depending on the maximum acceptable damage state, economy, and risk, several definitions and values of service life are possible, which can vary from the time of damage initiation to the time of complete deck failure as shown in Fig.1. Damage State corrosion initiation loss of protection extensive spalling/ local failure delamination/ spalling cracking collapse Possible values of mean service life Time Fig.1 Service life model of concrete bridge decks exposed to chlorides In the following section, a probabilistic cumulative damage model based on the above damage discretization is proposed for the prediction of the performance and service life of concrete bridge decks. 3. Life Prediction using Bogdanoff s Cumulative Damage Model As mentioned earlier, the termination of the service life of concrete bridge decks is associated mainly with the accumulation of irreversible damage induced by reinforcement corrosion, freeze thaw cycles, traffic load and initial damage. Furthermore, under service conditions, the signal-to-noise ratios are significantly lower than those obtained under controlled laboratory conditions. The fluctuations from mean performance and mean life are sufficiently large and cannot be ignored without serious consequences owing to the large fluctuations in the in-service environment, deck response, initial damage, etc. Hence, a probabilistic modeling of the damage accumulation and service life is required to achieve reliable results. In this paper Bogdanoff s cumulative damage model 14,15,16 is used to predict the future performance and service life of reinforced concrete bridge decks. The model assumes a probabilistic evolutionary structure of the damage accumulation process. The condition of the bridge is discretized into a finite state space with seven damage states as described in the previous section. A basic element of the model is the concept of duty cycle, which is a repetitive period of operation in the life of a component in which the accumulation is assumed non-negative. In this paper, a duty cycle is defined as oneyear in which the deck is subjected to de-icing salts in winter, freeze-thaw cycles, 233

6 traffic load and its own weight. The probability distribution of damage after a duty cycle is assumed to depend only on the duty cycle itself and the damage accumulated at the start of the duty cycle; thus its is assumed independent of how the damage was accumulated at the start of the duty cycle. These assumptions lead to the fact that the damage process can be modeled as a discrete-time and discrete-state Markovian process The probabilistic evolution of damage is completely determined by the transition matrix for each duty cycle and initial damage state. The transition matrix for a duty cycle is given by : P=[p j,k ] j=1,b; k=1,b (1a) P jk = P(D t+1 =k D t =j) (1b) where p jk represents the probability of the deck being in damage state k at the end of the duty cycle given it was in damage state j at the start of the duty cycle (with j<k for nonmaintained systems). Damage states 1 to 6 are transient states, whereas damage state 7 (denoted state b) is called an absorbing state, which is a state that cannot be vacated without rehabilitation. If we assume that there are no multiple damage states transitions within a duty cycle, the transition matrix is greatly simplified and has only two elements per row, namely p k,k and p k,k+1, which is referred to as the unit jump Markov chain 14,17. Given the uncertainty in defining the end of life or failure criterion, it is possible to have different definitions of the absorbing state, depending on the requirements of the decision maker, economical criteria and importance or criticality of the bridge in the highway network. The initial state of damage D 0 is identified by the vector P 0 =[p o (i)] i=1,b, where p o (i) is the probability of being in state i at time t=0. This initial damage may arise from poor materials, inadequate design and/or construction. It follows from Markov chain theory 14,17, that the state of damage at time t is given by: p t = p o P 1 P 2..P t = [p t (1) p t (2) p t (b)] (2a) where P j is the transition matrix for the j th duty cycle, and p t (k) is the probability of being in state k at time t. If we assume that the duty cycles are all of constant severity throughout the deck lifetime, then the transition matrix is time-invariant and equal to P, which yields a stationary stochastic process. Therefore, Eq. (2a) simplifies to: p t = p o P t (2b) The above transition matrix is generated from the in-service data collected during the inspections of the bridge decks. Contrary to lifetime models, the transition matrix and thus the proposed cumulative damage model can be developed from a limited set of data, which then can be further refined using the Bayesian updating approach 5,8,12. The probability that the deck be in damage state j at time t is given by: P(D t = j)= p t (j) (3a) The cumulative distribution function of damage at time t, D t, is defined by: j F Dt (j)= P(D t j) = p t ( k) (3b) k = 1 The expected damage at time t µ Dt is given by: 234

7 b µ Dt = jp t ( j) (3c) j= 1 The service life T of the deck may be defined as the time to absorption at state b. For the case of initial damage vector with p 0 (1)=1, its cumulative distribution function F T is given by 14 : F T (t) = P(T t) = p t (b) t=1, 2,., n (4) The mean service life µ T is given by the mean time to absorption 14, i.e.: µ = [1 F ( t )] (5) T t = 1 T In this paper, the service life is defined as the time at which the probability of absorption is equal to a specified maximum acceptable value p max (b), e.g. 10%. It is also possible to specify maximum acceptable probabilities of reaching the other states, e.g. 10% for the absorbing state b or 7 and 30% for state 6. Hence, a criterion for the end of life may be defined by a vector of maximum damage probabilities, i.e.: p t p max = [p max (1) p max (2).. p max (6) p max (b)] (6) For the case of an initial damage vector with multiple nonzero elements, the cumulative distribution function of service life (or time to absorption) is given by 14 : b F T (t) = P(T t) = 1 k= 1 p (7) 0 ( k ) F Tk ( t ) where F Tk (t)is the cumulative distribution function of the time at which the damage state first enters the absorbing state, given the initial damage state is k. The probabilistic prediction of accumulation of damage in the bridge deck using Eq.(2a) is illustrated in Fig.2, which indicates the evolution with time of the probability mass function of the damage. In Fig.2, it is seen that in the early stages of the deck life, the probability mass of the damage is near state 1, but with aging and damage accumulation, this probability mass shifts to high damage states. Ultimately, if no rehabilitation is undertaken, all the probability mass accumulates in the absorbing state 7, referred to as b. Damage State t Time 1 t 2 t 3 Fig.2. Evolution of damage probability mass functions in concrete bridge decks 235

8 4. Illustrative Example The approach presented in this paper is applied for the prediction of the damage accumulation and service life of a reinforced concrete bridge deck. A constant severity duty cycle is assumed throughout the deck lifetime that consists in one-year exposure of the deck to chloride-induced reinforcement corrosion due to deicing salts, freeze thaw cycles and traffic loading. In addition to a constant severity duty cycle, a unit-jump Bogdanoff cumulative damage model is assumed with a stationary transition matrix having the following elements 2,12 : p 11 =0.70, p 22 =0.75, p 33 =0.85, p 44 =0.90, p 55 =0.98, p 662 =0.98, and p 77 =1.0. The probability mass function of the current deck condition is shown in Fig.3(a), and is given by the following initial damage vector: P 0 = [ ] (8a) Frequency (a) Frequency years 30 years 50 years (b) Damage state Damage state Fig.3. Damage distributions at different deck ages: (a) Current deck condition; (b) Deck conditions after 10, 30 and 50 years Expected damage Time (years) Fig.4. Time-variation of expected damage in bridge deck 236

9 Using Eq.(2b), the condition of the deck after 10, 30, and 50 years is shown in Fig.3(b). For example after 30 years, the deck condition is given by the following vector: P 30 = [ ] (8b) The above vector illustrates that after 30 years, 90% of the deck is in the damage state 5 or higher (i.e, advanced damage level). Using Eq.(3c), the time-variation of the expected damage is shown in Fig.4, which shows that the expected damage increases from 3.36 to 5.33 after 30 years. The probability of absorption increases with time as shown in Fig.5, which yields a service life of 36 years for a 10% maximum probability in the absorbing state. F(t) Time (years) Fig.5. Time-variation of probability of absorption in bridge deck 5. CONCLUSIONS A stochastic damage and life prediction model based on Bogdanoff s cumulative damage process is proposed for concrete bridge decks subjected to chloride induced reinforcement corrosion. The model captures in a probabilistic evolutionary structure the time-dependence and uncertainty associated with bridge deck deterioration, and provides a reliable prediction of future macroscopic behavior of concrete bridge decks that is compatible with the current condition assessment methodology. The model encompasses all major sources of variability that affect the performance of concrete bridge decks, which include the uncertainty in environmental and traffic loads, quality of materials, protection, and construction, inspection and routine maintenance practices, in addition to the identification of failure or replacement criteria. The proposed predictive model of cumulative damage and service life of concrete bridge decks provides effective decision support in maintenance management and design. Such a model becomes necessary in network level analysis, where optimal decisions on rehabilitation and replacement need to be made on a large number of structures and at different points in time. 237

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