Manual on Service Life of Corrosion-Damaged Reinforced Concrete Bridge Superstructure Elements (2006)

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13 Introduction This chapter reviews the current state-of-the-art modeling of chloride-induced corrosion of steel in concrete and describes a diffusion model to be used for determining poten- tial repair and rehabilitation alternatives for bridge superstruc- ture elements. It concentrates on modeling chloride-induced corrosion of black steel and epoxy-coated rebar resulting from accumulation of chlorides in a bridge superstructure element due to exposure to chloride ions in the external environment, such as deicing salts. This chapter does not consider other cor- rosion mechanisms—such as carbonation or corrosion from chlorides cast into the concrete or other deterioration mecha- nisms such as alkali aggregate reactions, sulfate attack, or freeze-thaw damage. The model both estimates accumulated damage as the function of age from completion of construction of the con- crete element to age 100 years because of the assumption that no repair or corrosion mitigation is applied to the structure and calculates the SI discussed in Chapter 2. This index can then be used to identify appropriate corrosion prevention alternatives along with the repair of the concrete element. Basis of a Model Modeling the durability of reinforced concrete structures due to reinforcement corrosion requires a quantitative under- standing of the environment, transport mechanisms through concrete, the corrosion process, and cracking and physical deterioration processes. Equations or statistics for each part of the process are readily available. Some of the models dis- cussed in the literature have been developed for particular groups of structures, use particular software, and are difficult for others to replicate, while others are generic models designed to have wide application. This chapter summarizes the main research and literature in this area. The process of chloride-induced corrosion of steel in con- crete is described as follows: 1. Chlorides in the environment build up on the concrete surface. 2. Chlorides are transported through the concrete by a num- ber of mechanisms, including diffusion and capillary action. 3. The chloride concentration builds up with time at the steel surface. 4. Once the chloride level achieves a critical threshold level, the passive oxide layer on the steel breaks down and cor- rosion starts. 5. Corrosion products have a higher volume than the steel- consumed products exerting tensile stresses on the concrete. 6. Concrete is weak in tension, so the concrete cracks either vertically to the surface or horizontally to form a delami- nation between reinforcing bars. 7. Cracks form pot holes or spalls, which lead to a degrada- tion in the structure’s appearance, function, and safety, leading to end of service life or time to repair. 8. The repairs may be made, and the cycle continues either in the previously undamaged areas or as the repair system degrades with time. The process of modeling, therefore, requires the following: • Calculating the chloride ion content at the surface of the concrete. This is termed the surface chloride ion concen- tration (C0). • Calculating the rate of transport from the surface to the steel. This is the rate of diffusion of the chloride ions into concrete and is designated by the use of a coefficient termed the diffusion coefficient (D). • Determining the critical chloride concentration required to initiate corrosion. This is referred to as the corrosion threshold (CT). C H A P T E R 3 Service Life Modeling

• Estimating the time to corrosion initiation. This is the age at which corrosion initiates on the reinforcing steel (Ti). • Estimating the time from corrosion initiation to first crack- ing, followed by delamination and spalling. This is referred to as the propagation time (Tp). • Estimating the time from first damage. This is referred to as the time to damage (Td), which equals Ti + Tp. Exposure to Chloride Ions In the simplest terms, if there are no chlorides in the envi- ronment, there is no chloride-induced corrosion. Steel embedded in concrete develops a passive oxide layer that is highly protective and grows at a very slow rate. As long as the steel remains in good alkaline concrete, the passive layer will prevent corrosion initiation on the surface of the steel. This manual is primarily concerned with bridge superstructure elements and exposure to chloride ions from deicing salts. As deicing salts are applied to the surface of the bridge deck, the chloride ions migrate into the deck concrete, and chloride-contaminated runoff through failed joints exposes caps, girders, and columns to chloride ions. Wetting and dry- ing of the concrete increases the rate of accumulation of chlorides inside the concrete and can lead to chloride concentrations in concrete that are higher than in the exter- nal environment because evaporation increases the chloride concentration on the surface of the concrete. In literature, the chloride ion concentration at some depth just below the sur- face is often referred to as the surface concentration of chlo- ride ions. It is this concentration of chloride ions that with time diffuses into the concrete element. Chloride profiles obtained from 210 cores collected from decks of six bridges indicated that the chloride concentration in the first 0.25 inch of concrete from the surface is very dependent on exposure conditions [13]. The accumulation of chloride ions occurs at about the depth of 0.5 inches because of the exposure of the surface of the concrete to moisture. Rain, snow, and water from other sources that flow over the bridge deck can wash away the chloride ions from the first 0.25 inch of concrete. However, the accumulation occurring a little deeper in the concrete is not affected by such exposure. The areas not exposed to wetting and drying will normally be either too wet or too dry for corrosion. A resistivity below 50 kΩ-cm is needed to support a significant corrosion rate [14]; very dry concrete with high resistivity does not corrode even in the presence of chlorides. Also, if the concrete is too dry, there is no mechanism for transport of chloride into the concrete. Tuutti found that below a relative humidity of 60%, chloride-induced corrosion rates are negligible [15]. The wet- ting and drying environment will affect the transport of chlo- rides into concrete as discussed in the next section. Diffusion of Chloride Ions Chloride ions are transported in solution through the porous concrete cover in various processes. These include dif- fusion (driven by the concentration gradient between various sections of the concrete) and capillary action of water in a porous medium. Other mechanisms, such as wetting and dry- ing, concentrate chloride ions more rapidly in concrete. Dif- fusion is affected by “sinks” within the concrete, such as binding with aluminate phases to form chloroaluminates, physical absorption of ions onto pore surfaces, and trapping in closed pores. One way of dealing with sinks is to use an “apparent” or “effective” diffusion coefficient, which is derived empirically from field or laboratory data. For exam- ple, if the diffusion coefficient is calculated from chloride pro- files obtained from cores, this accounts for all effects and provides a reasonable estimate of effective rate of migration of chloride ions into the concrete. Meijers developed a finite element analysis model that uses convection and conduction (i.e., diffusion) modeling of the chloride transport process [16]. However, most models assume that the dominant process is diffusion or that, for a reasonably well-constructed structure with rea- sonably good cover and concrete quality, the diffusion cal- culation is a reasonable approximation of the overall “real world” process. The diffusion process is modeled by solving the one- dimensional equation for Fick’s second law of diffusion: (1) where C = chloride ion concentration t = time D = diffusion coefficient This is usually solved by using the error function solution: (2) where C(x,t) = chloride concentration at depth x at time t C0 = surface concentration erf = error function Kranc et al. showed that the simple one-dimensional, semi- infinite solid approach is conservative because the reinforcing bar blocks the chloride transport, thus “backing up”chlorides at the steel-concrete interface because they cannot proceed through any further [17]. C C erf x Dt x t( , ) = − ⎛⎝⎜ ⎞⎠⎟ ⎡ ⎣⎢ ⎤ ⎦⎥0 1 2 ∂ ∂ = ∂ ∂ ⎛ ⎝⎜ ⎞⎠⎟ C t D C C 2 2 14

Corrosion Initiation Corrosion initiation is generally deemed to occur once chloride concentration exceeds a given value or threshold. However, there is no fixed value of the corrosion threshold. Figure 1 shows data taken from a series of U.K. highway bridges by Vassie [18]. From Figure 1, it is clear that corrosion can initiate at a range of values from the low chloride levels of 0.1% to 1.8% by mass of cement. The observation of only 80% of bars cor- roding at 1.8% chloride by mass of cement can be explained by the presence of cathodic sites on the remaining 20% required for macrocell corrosion. With regards to corrosion initiation at 0.1% chloride by mass of cement, lowering of chloride threshold due to carbonation of the concrete and the effects of bound and unbound chlorides are suspected [14]. This issue, along with other variables, such as local exposure and variable permeabilities, led Bentz to use Monte Carlo calculations to look at the sensitivity of modeling to such variables [19]. There is extensive discussion of thresh- olds in the report on corrosion of metals in concrete pre- pared by ACI Committee 222 [20]. How to determine the effective chloride threshold for a concrete element is dis- cussed later in this chapter. Time to Damage Time to damage is the sum total of the time required for chloride ions to diffuse down to the steel depth and accumu- late in concentrations in excess of the corrosion threshold (Ti) plus the time required for sufficient corrosion to have occurred to generate the required amount of rust (or expansion) to pro- duce cracking and/or delamination of the concrete (Tp). The rate of accumulation of rust (i.e., rate of expansion) can be estimated by measuring the rate of corrosion of the steel.Sev- eral techniques and equipments are available to measure the in situ corrosion rate. Corrosion rate is a function of many factors, is not constant, and varies with time; it is very difficult to calcu- late the total accumulation of rust. In addition, the amount of expansion generated by the products of corrosion highly depends on the level of oxidation of the corrosion product.Sev- eral techniques are available to estimate the accumulation of rust or section loss of steel (section loss of steel is directly pro- portional to the amount of rust generated). Determining the time when cracking, delamination, or spalling occurs presents a series of significant problems because of the following factors: • There is no easy way of converting section loss to cracking rate. 15 0 10 20 30 40 50 60 70 80 0 0.5 1.0 1.5 2.0 % Cl Concentration by Mass of Cement % P ro ba bi lit y Figure 1. Corrosion initiation (% probability) vs. chloride concentration.

• Cracking patterns will be a function of steel layout and shape of the reinforced concrete member. • Loading, especially live loading, will affect cracking rate. One quantitative equation for converting section loss to cracking has been developed by Rodriguez et al. [21]. The crack width W at the concrete surface is: (3) where β = 0.01 for top cast steel and 0.0125 for bottom cast steel X = bar radius decrease due to corrosion to produce crack width W X0 = bar radius decrease due to corrosion to induce crack initiation (at surface) X0 = 83 + 7.4c/φ − 22.6fc,sp where c = cover φ = bar diameter fc,sp = tensile splitting strength of concrete The tensile strength of concrete fc,sp can be derived from its compressive strength fc [22]. fc,sp = 0.12(fc)0.7 To calculate time to cracking, Equation 3 is used to deter- mine the reduction in the bar radius for a given crack width. Corrosion rate measurements can then be used to determine when such a reduction will occur. Liu proposed a different approach that is based on the mechanics of the generation of rust and the resulting stress in the concrete [23]. Liu idealized a rebar in concrete as a thick- walled cylinder and derived the following equation for the critical amount of rust required to produce a crack: (4) where Wcrit = critical volume of corrosion product required to induce a crack ρrust = density of rust C = clear concrete cover fi = tensile strength of concrete Eef = effective elastic modulus of concrete a = inner radius of the thick-walled cylinder (clear concrete cover – d0) b = outer radius of the thick-walled cylinder (clear concrete cover + D/2) W Cf E a b b a v di ef ccrit rust= + − + ⎛ ⎝⎜ ⎞ ⎠⎟ + ⎡ ⎣⎢ ρ π 2 2 2 2 0 ⎤ ⎦⎥ + ⎛ ⎝⎜ ⎞ ⎠⎟D Wst stρ W X X= + − < <0 05 10. ( )β for 0 W mm νc = Poisson’s ratio for concrete d0 = thickness of the porous zone around the steel-concrete interface D = diameter of the rebar Wst = mass of steel corroded ρst = density of steel The rate of production of rust is given by: (5) where α = molecular weight of steel or corrosion products icorr(t) = rate of corrosion as a function of time t = time The critical volume of rust required to generate a crack is calculated from Equation 4, and the time required to generate that volume of rust is then obtained by solving Equation 5. This model was validated against laboratory slabs. This model indicates that the time to cracking is dependent on physical properties of concrete (elastic modulus and Poisson’s ratio), clear concrete cover, rebar diameter, and corrosion rate. The problem with using this model is that once corrosion initiates, the corrosion rate varies with time. Andrade and Gonzalez have suggested measuring the corrosion rate several times a year using the average of the measured corrosion rates [24]. Diffusion Models Proposed in Literature As stated earlier, there are a number of models for corrosion of steel in concrete. Some are designed for use in new con- struction and are computed from data from construction details and environment, predicting time to first and subse- quent repairs and life cycle costs for a new structure to compare durability options (such as changing cement types, adding cor- rosion inhibitors, changing the concrete cover, or changing bar types). Others are designed for projecting present data forward from existing structures to estimate time to damage. Bazant developed a complete physical-mathematical model that describes the corrosion process in submerged concrete exposed to sea water [25]. A set of equations has been derived for the transport of oxygen and chloride ions through the concrete cover, the mass sources and sinks of oxy- gen and corrosion products, the cathodic and anodic electric potential, and the flow of ionic current through the concrete electrolyte. This model is largely based on theoretical assump- tions and is completed by formulating the problem as an initial- boundary-value problem that can be solved by using the finite element method. In order to arrive at numerical solu- tions, the spatial distribution and geometry of anodic and W Di t dt t crit corr 2 6 0 2 2 59 10 1 = × ⎛⎝⎜ ⎞⎠⎟−∫ . ( )α π 16

cathodic areas on the reinforcing bars have to be assumed. This model has been applied to several illustrative numerical examples, and the results obtained show that for submerged concrete, diffusivities for chloride ions and oxygen—not only at the anodic (i.e., rusting) area, but also, and mainly, at cathodic areas—usually are the controlling factors. Although the model takes into account all relevant chemical and phys- ical processes involved in reinforcement corrosion, several processes are not adequately addressed and the polarization behavior of the anodic and cathodic reactions has not been fully described. However, the model results in an improved understanding of the complex nature of the problem. Similar models based on the same relationships, but expressed in more simplified forms, have been presented by Sagues and Kranc, Noeggerath, Naish et al., and Raupach and Gulikers [26–29]. These models have shown that these ana- lytical electrochemical approaches lead to suitable results for specific corrosion problems. In November 1998, a consortium was established under the Strategic Development Council (SDC) of ACI to develop an initial life cycle model based on the existing service life model developed at the University of Toronto. The life cycle model [30] provides insight into the durability of a given construc- tion practice, thereby allowing designers to ascertain the impact of additives to concrete and corrosion prevention strategies applied to new construction on the long-term dura- bility of the concrete element. In October 2000, Life-365 Ver- sion 1.0 software was released, and Version 1.1 followed in December 2001. In Life-365 software, the analyses are divided into four steps: predicting initiation period, predicting prop- agation period, determining repair schedule after the first repair, and estimating life cycle costs based on initial con- struction and future repair costs. The Life-365 software predicts the initiation period assum- ing ionic diffusion to be the dominant mechanism. This soft- ware differs from other diffusion models in that it accounts for the variability of the diffusion coefficient with age and with temperature. It also attempts to model the impact of var- ious additives, such as silica fume and fly ash (by reducing the diffusion coefficient to reflect the lower permeability) and corrosion inhibitors (by raising the chloride threshold required to initiate corrosion). The rate of accumulation and the maximum accumulation of surface chloride in this pro- gram are based on the type of structure, geographic location, and exposure. A diffusion model developed by Sagues et al. to predict the future performance of existing structures has been validated on marine piles of several structures [31, 32]. Initially, Sagues et al. used specialized software to calculate the diffusion coefficient from field cores and the solution to the error function to evalu- ate marine piles of two structures [31]. Later, Sohanghpurwala and Diefenderfer developed a methodology to perform the modeling in a standard spreadsheet program and validated the model on marine piles of another structure [32]. The approach of Sagues et al. obtains probability distribution information on diffusion coefficient, clear concrete cover, and surface chloride ion concentration from the existing structure. It subdivides the concrete element into finite elements and determines the time to corrosion initiation for each finite element using the error solution to Fick’s second law of diffusion. To calculate the time to corrosion initiation (Ti) for each finite element, values of diffusion coefficient, clear concrete cover, and surface chlo- ride concentration are required. These are obtained from the probability distributions defined for each variable. The time for propagation (Tp) is assumed to be 3 to 6 years. A similar software program has been developed in the United Kingdom. The diffusion coefficient is calculated from data taken from concrete blocks exposed to a marine tidal/splash zone environment and other laboratory data and is used to estimate time to initiation [33]. The time to failure is obtained from the Rodriguez formulas. Similarly, Broomfield used the method of collecting chlo- ride profiles from the structure under investigation to estimate the apparent diffusion coefficient [34]. The effective chloride diffusion coefficient was calculated using a parabolic approx- imation to the error function equation. Time to corrosion can be predicted from the individual sets of measurements based on the actual diffusion and exposure characteristics of the measurement location. The Rodriguez equations are then used in a separate module of the program to predict time to cracking. The chloride diffusion model was validated against field data in one case where surveys were conducted approxi- mately 9 years apart. The earlier data set agreed with the later survey predictions of time to corrosion ± 2 years in five out of six cases where the initial prediction was greater than 10 years. In another seven out of nine cases, the earlier and later data sets agreed that corrosion was imminent, but at the point of measurement there was no damage. Model Development Two separate models were developed to deal with black steel and epoxy-coated rebar. The models were validated against field structures and/or data on field structures avail- able in literature. As this manual is primarily concerned with chloride-induced corrosion, these models are chloride diffu- sion based. However, to assist in the case where no chloride information can be obtained, a damage-based model is also proposed. The damage-based model has not been validated. Model for Black Steel The proposed chloride diffusion model is based on devel- oping statistical distribution functions of diffusion coefficient, 17

surface chloride ion content, and clear concrete cover from the structure. It assumes that the past diffusion behavior and chlo- ride accumulation will continue at the same rates in the future. However, it is clear that the diffusion process is affected by many factors, such as temperature, humidity, and concrete cure, and each of these factors varies with time and season. To model each factor and its variations would be a significantly more complex problem. In addition, knowledge of the exact processes and variations in these factors is not known. To over- come this complexity and lack of information, this model is based on measuring the structure’s “effective or apparent dif- fusion” coefficient that represents the average diffusion that has resulted from the impact of all factors over the life of the structure, thereby eliminating the necessity to model each and every factor and its variation. Similarly, the chloride ion con- centration just below the surface of the concrete can be used to represent the surface chloride ion concentration that repre- sents the sum total of the chloride exposure that the concrete element has experienced. The clear concrete cover is the intrinsic property of a concrete element, which is the function of the design and construction practice and remains constant over time. The diffusion coefficient, surface chloride ion concentra- tion, and clear concrete cover all vary from one location to another. The measurement process has an error associated with it. Therefore, the distribution of each of these can be described by a probability function. The distribution of the clear concrete cover and the surface chloride ion concentra- tions are generally described by the normal distribution func- tion. The diffusion coefficient is best described by the gamma distribution function. In general, the probability distribution function selected to represent the field data should be evalu- ated for good fit. However, the normal and the gamma func- tions have been found to best describe the field data and are used in this model. Once the probability distribution func- tions for diffusion coefficient, surface chloride concentration, and clear concrete cover have been developed, they are used in the model to represent field data. The “apparent or effective diffusion”coefficient is estimated by measuring the profile of chloride ion concentrations as a function of depth (C(x,t) − chloride ion concentration at depth x at age t at a specific location in the concrete element) in con- crete cores collected from the subject concrete element. The profile is obtained by collecting powdered concrete samples from various depths from the concrete core and analyzing them for total chloride ion content using the total acid soluble analysis. The following function is then fitted to the chloride profile obtained from each core using nonlinear regression analysis: (6)C C erf x Dt x t( , ) = − ⎛⎝⎜ ⎞⎠⎟ ⎡ ⎣⎢ ⎤ ⎦⎥0 1 2 The nonlinear regression is performed by minimizing the sum-of-squares of vertical distances of the chloride profile data points from Equation 6. The best fit provides an estimate of diffusion coefficient D for that core. The fit is performed for t equal to the age of the structure at the time of collection of the core and C0 equal to the concentration of chloride ions in the top layer of the core. If sufficient time has elapsed between the collection of the core and the analysis of the chloride pro- file, then the age at which the analysis is conducted should be used. Because the cores are not exposed to the environment after they have been collected from the concrete element, C0 measured from the core may be lower than the actual in situ concrete because chloride ions will continue to diffuse, albeit at a different rate in the core. The surface chloride ion concentration, C0, is measured from core samples at the depth of 0.25 to 0.5 inch. Clear con- crete cover information is obtained by nondestructively measuring the clear concrete cover at numerous locations using a covermeter or a pachometer. The concrete element is subdivided into numerous finite elements. For each element, the diffusion coefficient (D), sur- face chloride ion concentration (C0), and clear concrete cover (x) are selected from the statistical distribution functions such that the probability of selection of any value from the function is the same and can be applied to Equation 6. It should be noted that this particular solution of the Fick’s second law assumes that C0 is constant during the diffusion process, although for an actual structure C0 increases with time as chloride ions from the environment accumulate in the concrete. However, there is a limit beyond which the accu- mulation of chloride ions in the top layer of the concrete would cease to increase. This limit is presently not known. To account for the increasing C0, it was assumed that C0 increases linearly satisfying the following equation: (7) where m is the rate of chloride accumulation and t is the age of the concrete element. The solution to Fick’s second law is modified as follows to account for the variation of C0: (8) where t is the time that varies from age 0 years to T years, and T is the age at which the value of C(x,T) is calculated. The goal is to determine the age at which C(x,T) will exceed the threshold required to initiate corrosion (i.e., the time to initiation, Ti). Time to propagation is assumed to be 5 years. Liu has found that, for highway concretes with average, 2-inch, clear concrete cover, the time to cracking is several C m erf x Dt dtx T T ( , ) = − ⎛⎝⎜ ⎞⎠⎟ ⎡ ⎣⎢ ⎤ ⎦⎥∫0 1 2 C mt0 = 18

orders of magnitude smaller than the time to initiation and ranges from 3 years to 5 years. The time to propagation, as modeled by Liu, depends on concrete properties, clear con- crete cover, and corrosion rate. For much deeper clear con- crete cover, or for concretes with higher tensile strength, the time to propagation would be longer than 3 to 5 years. Once time to corrosion initiation is known, time to damage, Td, for each finite element at each age is calculated as follows: Td = Ti + tp (9) The number of elements that meet the following requirement is calculated to produce a cumulative damage distribution: Td < T (10) The model is first evaluated at threshold levels as low as 300 ppm of chloride ion concentration. The cumulative dam- age results from the model at the age of the field evaluation are compared with the actual measured damage. If the two are not in agreement, the threshold value is adjusted upward until the model produces results comparable to the field measurements. Analysis of modeling data obtained in this project indicates that the cumulative damage distribution can be best described by using the Weibull distribution, which is widely used for failure analysis and, therefore, is applicable to serv- ice life modeling. As diffusion modeling results in a Weibull distribution, it is reasonable to expect that if data on the quantity of concrete damage at several ages are available, then the Weibull distribution could be used to model the damage distribution of the concrete element. The modeling can be accomplished by obtaining concrete damage quantities at several ages and using the data to fit the Weibull curve. Once the Weibull parameters are estimated, the cumulative Weibull curve can be used to estimate future progression of damage. Model for Epoxy-Coated Rebar The epoxy-coated rebar diffusion model is very similar to the black reinforcing steel model discussed with one excep- tion. The epoxy-coated rebar model also uses a probability distribution function to ascertain if the coating is damaged in the finite element. On black steel, corrosion initiates at all locations where the threshold concentration has been exceeded, whereas on epoxy-coated rebar, corrosion initiates only at the defects where the chloride ion concentration has exceeded the threshold. Epoxy coating is a barrier system that is designed to keep chlorides and other chemical species that can initiate and sus- tain corrosion away from the reinforcing steel. It also provides a physical barrier between the steel and concrete interface. Epoxy is a very effective barrier because it does not allow dele- terious species to permeate through it. However, the epoxy uptakes some amount of moisture, which results in temporary reduction in bond between the epoxy and the steel surface. The effectiveness of the epoxy as a barrier is not impacted by the reduction or loss of bond; it is impacted by the presence of coating damage or defect in the form of holidays, mashed areas, and bare areas. The defects in the coating are normally generated during application of the coating, storage and han- dling, transportation to site, placement in forms, and place- ment of the concrete. Corrosion on epoxy-coated rebars initiates at defects in the form of crevice corrosion and can spread by undercutting the coating. The rate of corrosion is controlled by the availability of cathodic sites and chloride ions. In addition, the coating may deteriorate with time, and more defects may appear on it. To account for corrosion spreading under the coating and deterioration of the coating, the amount of damage on the coating is varied with age. At age 0, the percentage of exposed surface area (i.e., damage or defect in the epoxy coating that exposes the steel surface) is assumed to be that allowed by the governing specifications or whatever the user believes it may have been. At the time of the field evaluation, cores that contain one or more epoxy-coated rebar sections are extracted, and the percentage of exposed surface area on each extracted section is documented. The average percentage of exposed steel observed on the extracted sections of epoxy-coated rebars is then used to determine the growth rate of deterioration. It is assumed that the rate of growth is linear, and this rate is used to determine when 100% of the surface of the epoxy-coated rebar will be exposed (i.e., no epoxy coating is left on the rebar). This rate of increase of deterioration is used by the model, and it is assumed that the rate will remain the same in the future. The model allows cor- rosion initiation on epoxy-coated rebars in the finite elements that have suffered epoxy coating damage. A probability distri- bution is used to determine if the epoxy coating in the finite element has suffered damaged or not. Susceptibility Index (SI) The distribution of chloride ions at the steel depth can be used to quantify both the susceptibility of the concrete ele- ment to corrosion in areas that are not presently damaged and the future susceptibility to corrosion-induced damage. If suf- ficient chloride ions are present to initiate corrosion, then corrosion-induced damage in the near future is expected, and only very aggressive corrosion mitigation techniques, such as cathodic protection and electrochemical chloride extraction, can be used to control the corrosion process. However, if the chloride ion concentration distribution at the steel depth is low and corrosion is not expected to initiate in the near future, less expensive corrosion control systems—such as 19

sealers, membranes, and/or corrosion inhibitors—can be used to either control or stop the rate of corrosion. Therefore, an index that provides a good representation of the distribu- tion of chloride ions at the steel depth would be very useful in selecting a corrosion control system. The distribution of chloride ions can be obtained by col- lecting samples of the concrete and analyzing for chloride ion content at the steel depth. There are two methods of accomplishing this. One method requires locating reinforc- ing steel on the deck surface, drilling down, measuring the clear concrete cover over the reinforcing steel, and then col- lecting a powdered concrete sample from concrete adjacent to the reinforcing steel from the depth at which the reinforc- ing bar is located. Although this method has been and often is being used, it has many disadvantages, and the amount of time required for sampling is large, which means that the structure has to be closed down for a long period of time. The second method uses the field data collected for the serv- ice life model. The diffusion coefficients, the surface chloride concentrations, and the clear concrete cover can be used in conjunction with the diffusion model presented for black steel to determine the distribution of chloride ions at a given steel depth at a given age. The following equation is proposed to represent the SI. (11) where Clth = chloride concentration threshold Xi = chloride concentration in the ith finite element or location n = number of finite elements used in the model or locations where measurements were made This index is a ratio of the average moment from threshold over the threshold. It is scaled to 10 for ease of use. The value of this index is 0 if all the chloride ion concentration every- where at the steel depth is at the threshold and is 10 if there are no chloride ions anywhere at the steel depth. The threshold for corrosion initiation would be based on either the information available in the literature or the value used in the diffusion model that provides the best estimate of present damage. Because the threshold from literature may not be applicable to that particular structure, using the diffu- sion model to calculate the distribution of chloride ions and the apparent threshold seems to be more appropriate. SI Cl X n Clth i n th= −( )( ) ×( ) ×( )∑ 1 10/ 20