https://doi.org/10.14311/APP.2022.33.0344 Acta Polytechnica CTU Proceedings 33:344–349, 2022 © 2022 The Author(s). Licensed under a CC-BY 4.0 licence Published by the Czech Technical University in Prague EXTENT OF CORROSION DAMAGE FOR RC STRUCTURES EXPOSED TO CHLORIDE-BEARING ENVIRONMENT Federica Lollini Politecnico di Milano, Department of Chemistry, Materials and Chemical Engineering "Giulio Natta", Piazza Leonardo da Vinci 32, Italy correspondence: federica.lollini@polimi.it Abstract. In industrialized countries, most of the reinforced concrete (RC) structures and infras- tructures have more than 40 years, since they were built around 1960 − 1980, and were designed for a service life of 50 years. Consequently, in the next years, the number of structures and infrastructures that will need to be repaired will steeply increase. Several techniques, characterized by a different durability, environmental impact and economic impact, are available for the repair of a reinforced concrete structure damaged by the corrosion of reinforcement. To help the designers in the choice of the most suitable one, a preliminary assessment of the condition of the structure is essential, aimed at diagnosing the causes of deterioration, the extent of damage, i.e. the extent of corroding reinforce- ment, and its evolution in time. An approach, with a wide consensus, for the evaluation of the extent of corroding reinforcement is available for carbonation-induced corrosion, whilst it is still lacking for chloride-induced corrosion. In this paper two approaches for the evaluation of the extent of corroding reinforcement for a RC structure subject to chloride-induced corrosion are presented and compared, showing similar results. These approaches can be useful to properly plan a restoration intervention as well as to assess the reliability of the recently proposed model for service life design. Keywords: Assessment, corrosion, chloride. 1. Introduction In industrialized countries, most of the reinforced concrete (RC) structures and infrastructures, were built around 1960 − 1980 and, in general, were de- signed to last for a period of 50 − 100 years [1]. More and more of these structures are approaching the end of their designed service life, and due to their expo- sure conditions, i.e. typical urban or rural environ- ment or marine exposure, often suffer damage due to carbonation- or chloride- induced corrosion of rein- forcement, such as concrete spalling or cracking or rust stains that may affect their serviceability. A proper maintenance and rehabilitation of reinforced concrete structures could extend their service life, by restoring the structural safety and preventing the fu- ture damage. This would avoid to demolish them and build new ones, leading to a lower social, environmen- tal and economic impact, due, for instance, to a less hindrance to traffic and waste of materials [2]. Several techniques are available for the rehabilita- tion, which vary from keeping the conditions of corro- sion and serviceability under control by some form of monitoring, when the extent of damage is limited or the remaining period of use is short, to the conven- tional repair technique, which requires the replace- ment of carbonated concrete cover or chloride con- taminated cover with a cementitious mortar, to elec- trochemical techniques or hydrophobic treatments, that can control corrosion of steel bars without requir- ing the removal of the original concrete cover, except the cracked concrete [3–5]. Each of these strategies is characterizes by a different durability, environmental impact and economic impact, and the choice of the most suitable protection system should be a compro- mise among the different requirements [4]. Hence, it appears essential to choose and plan the most suitable restoration intervention, a careful con- dition investigation that cannot be limited to a visual inspection by an expert, but should include, beside the visual inspection and the examination of design documents, field tests as well as sampling for labo- ratory tests, i.e. carbonation depth, chloride profile and cover depth. The inspection should be aimed at estimating if, both at the time of inspection and at the end of the designed lifetime, the reinforcement is still passive, i.e. corrosion has not initiated since carbonation or a critical amount of chlorides has not reached the steel surface, or the reinforcement is cor- roding but the propagation is in the early stages, e.g. concrete cover is not cracked and reduction in cross section of rebars is negligible [6]. Since concrete qual- ity, mainly the permeability, nature and intensity of cracks, and concrete cover are spatially variable over the concrete surface, due to different concrete batches and the heterogeneity of workmanship, the corrosion conditions will vary accordingly [7–9]. An evaluation of the extent of corroding reinforcement, i.e. of the amount of steel bars that are no more longer pas- sive, and its evolution in time, is, then, needed. For carbonation-induced corrosion the extent of corrod- ing reinforcement can be assessed by comparing mea- sured carbonation depth with measured cover depths 344 https://doi.org/10.14311/APP.2022.33.0344 https://creativecommons.org/licenses/by/4.0/ https://www.cvut.cz/en vol. 33/2022 Corrosion Damage for RC Structures D�� E�� � ��� � ��� � ��� � ��� ����������������������������� C l WK �� �P DV V� RI �F HP HQ W� 3UREDELOLW\ pFRUU � ��� � ��� � ��� � ��� � �� �� �� �� �� �� �� C & O �� �P DV V� RI �F HP HQ W� 'HSWK��PP� 3URILOH�� 3URILOH�� 3URILOH�� 3URILOH�� 3URILOH�� Figure 1. Cumulative distribution function of the critical chloride content (a) and imaginary chloride profiles measured on a RC structure (b). in the structure and in the literature a statistical ap- proach with a wide consensus was proposed for its evaluation [10]. For chloride-induced corrosion, to evaluate the extent of corroding reinforcement, the chloride content at the depth of the bars needs to be compared to the critical chloride content, since corro- sion occurs when at the bar depth a chloride content equal to the critical chloride content is reached. The variability of these parameters makes it difficult to assess the extent of corroding reinforcement and, un- fortunately, an approach with a wide consensus is still lacking. This paper presents two mathematical approaches for the evaluation of the extent of corroding reinforce- ment for a reinforced concrete structure subjected to chloride-induced corrosion. A fictitious example is provided to compare the results of the two approaches and to discuss their real application. 2. Mathematical approaches for the evaluation of the extent of corroding reinforcement 2.1. Statistical approach In order to assess the extent of corroding reinforce- ment, Rdep, of an existing structure, the critical chlo- ride content, Clth, the chloride content, CCl, and the depth of the bars, c, need to be known. The critical chloride content depends on several factors, and, due to its stochastic nature, can be properly defined only through a probability density function. According to the Model Code for Service Life Design, proposed in 2006 by the International Federation of Concrete, fib [11], Clth for ordinary carbon steel bars, can be described by a Beta Distribution, lower and upper limited. Figure 1a shows the cumulative distribu- tion function of the critical chloride content, assum- ing that the average value and the standard deviation are respectively 0.6 % and 0.15 % vs mass of cement (values of 0.2 and 2 % vs mass of cement have been assumed for the lower and upper limits). The chloride content at the different depths and the concrete cover thickness can be determined dur- ing the inspection of the RC structure, through field and laboratory tests. In order to assess Rdep, and to increase its reliability and accuracy, a significant number of measurements of these parameters is re- quired. As an example, Figure 1b shows imaginary chloride profiles measured on five concrete samples taken from the structure after 10 years from the con- struction. In the example the total chloride content was evaluated at depth intervals, ∆c, of 5 mm. From the concrete cover depth measurements, carried out in situ, a frequency analysis can be performed (the depth intervals should be equal to those of the chlo- ride profiles) (Figure 2). � � � � � � �� �� �� �� �� �� )U HT XH QF \� �� � &RQFUHWH�FRYHU�WKLFNQHVV��PP� Figure 2. Imaginary frequency analysis (grey sym- bols) and probability density function (black line) of the concrete cover thickness. In order to evaluate the extent of the depassivated bars, initially the variability of the concrete cover 345 Federica Lollini Acta Polytechnica CTU Proceedings Profile Ccl (% mass of cement) pcorr, i 1 0.44 0.14 2 0.98 0.99 3 1.33 1 4 1.41 1 5 1.44 1 Table 1. Chloride contents at the depth c = 22.5 mm and calculated values of pcorr, i. ∆c [mm] 0 − 5 5 − 10 10 − 15 15 − 20 20 − 25 25 − 30 30 − 35 35 − . . . fc [%] 10.2 5.6 6.5 4.6 13 15.7 17.6 26.9 pcorr [%] 100 100 99.9 97 82.5 73.2 55 41 Rdep [%] 10.2 5.6 6.5 4.5 10.7 11.5 9.6 3.2 Table 2. Proportion, fc, of imaginary cover depth measurements falling within the range ∆c, probability of occurrence of corrosion, pcorr, and extent of corroding reinforcement, Rdep, in each depth ∆c. thickness, c, is neglected and it is considered that the bars have the same concrete cover (i.e. the concrete cover of all the bars falls within the same cover depth interval, ∆c). Moreover, it is initially supposed that, at the bars depth, c, a unique value of the chloride content, Ccl, is available. The probability that corro- sion initiated, pcorr , corresponds to the probability of occurrence that the variable Clth is equal to the con- sidered value of chloride content, Ccl. The probability that corrosion occurred is an estimation of the extent of corroding reinforcement. This means that, if at the bars depth a chloride content lower of 0.2 % mass of cement is measured (that corresponds to the lower limit of the Beta distribution), pcorr should be null and hence all the bars would be passive, conversely, if the chloride content were higher than 2 % mass of cement (that corresponds to the upper limit of the Beta distribution), pcorr would be equal to 100 % and, hence, all the bars would be actively corroding. As an example, a concrete cover thickness equal to 22.5 mm (as indicated by the vertical dotted line in Figure 1b) and the first profile, i.e. profile 1, can be considered; at this depth a chloride content of about 0.44 % mass of cement can be evaluated (horizontal dotted line in Figure 1b). At this chloride content corresponds a probability pcorr (= Rdep) equal to 14 %, given by the intersection between the horizontal dotted line and the Clth cumulative distribution function, as shown in Figure 1a. Considering that more measurements of chloride content at the bars depth, c, are available (as in the example of Figure 1b), pcorr can be evaluated through the equation: pcorr = n! i=1 pcorr, i n (1) Where n is the number of chloride profiles and i represents the i−th profile. Table 1 reports the chloride contents at the con- crete cover c = 22.5 mm, shown in Figure 1b, and pcorr, i evaluated for each profile. Applying equation 1 it can be evaluated that, for this depth interval, pcorr is about 83 %. However, in a real structure, it has to be taken into account also the variability of the concrete cover thickness, as shown for instance in Figure 2 and re- ported in Table 2 in terms of percentage of mea- surements, fc, falling within different depth intervals. Hence, pcorr has to be calculated, through equation (1), for all the concrete cover depth intervals, ∆c, as shown in Table 2. Rdep, j can be, then, evaluated, for each ∆c, as: Rdep, j = pcorr, j · fc (2) Where fc is the proportion of cover depth measure- ments falling within the range ∆c and j is equal to the given interval depth, ∆c. Hence, the extent of corroding reinforcement can be calculated by summing up corrosion proportions over all the depth intervals: Rdep = m! j=1 " #fc, j · $ n! i=1 pcorr, i n % j & ' (3) Where n is the number of chloride profiles and i represents the i−th profile, m is the number of cover depth intervals, ∆c, and j represents the j−th depth. By applying equation 3 to the given example, a value of Rdep about 62 % can be evaluated. 2.2. Probabilistic approach To evaluate the extent of corroding reinforcement, a probabilistic approach, similar to that used for the design of new RC structures, can be also used. In the probabilistic approach for the design of new struc- tures, the extent of corroding reinforcement corre- sponds to the probability, pdep, that the limit state 346 vol. 33/2022 Corrosion Damage for RC Structures Profile 1 2 3 4 5 Dapp [10 − 12 m2/s] 0.4 0.7 1 1.2 1.6 Cs [% mass of cement] 2.8 3.45 3.6 3.4 3 Table 3. Diffusion Coefficient, Dapp, and surface chloride concentration, Cs, of imaginary chloride profiles. Parameter Unit Type of distribution Value m σ Dapp [10 − 12 m2/s] normal 0.98 0.46 Cs [% mass of cement] normal 3.25 0.33 C [mm] normal 27.9 14.3 Clth [% mass of cement] beta 0.6 0.15 T [year] - 10 - Table 4. Values of the parameters and types of statistical distribution used as inputs in the probabilistic approach (m = mean value, σ = standard deviation). equation for the initiation of corrosion, G, is not sat- isfied, i.e. that pdep{G} < 0. For chloride-induced corrosion, the limit state equation for the initiation of corrosion can be described by means the solution of Fick’s second law: pdep = {Clth − Ccl (x, t)} = p ( Clth − Cs ) 1 − erf c 2 * Dapp t +, < 0 (4) where: Clth is the critical chloride threshold, Cs is the surface chloride concentration, c is the concrete cover depth, Dapp is the diffusion coefficient and t is the time. The variables Clth, Cs, c and Dapp are stochastic variables, whilst the time, t, is a determin- istic variable. To evaluate the actual corrosion conditions of an existing structure, reliable values for the input pa- rameters need to be provided. As far as the time, t, is concerned, it corresponds to the time between the year of construction and the considered time (in the example, 10 years). The critical chloride threshold, as previously observed, can be described for carbon steel bars through a Beta distribution, with a mean value of 0.6 % mass of cement. The other parameters are related to the considered existing structure and to its exposure conditions and can be determined, if results of a detailed inspection are available, from the experimental measurements. The concrete cover dis- tribution can be evaluated by interpolating the exper- imental measurements and determining the distribu- tion parameters, i.e. the mean value and the standard deviation. From the imaginary concrete cover thick- ness shown in Figure 2, a normal distribution, with a mean value of 27.9 mm and a standard deviation of 14.3 mm can be determined (black line in Figure 2). The interpolation of the chloride content at differ- ent depths, at time, t, by means of the second Fick’s Law, allows to calculate, for each profile, a value of Dapp and Cs. From the chloride profiles shown in Figure 1b, data summarised in Table 3 can be eval- uated. From these values, both for the diffusion co- efficient and the surface chloride concentration, the probability density function, with its characterizing parameters, can be determined. Assuming for both parameters a normal distribution, for the diffusion coefficient a mean value and a standard deviation re- spectively equal to 0.98 and 0.46 × 10−12 m2/s can be calculated, whilst for the surface chloride concentra- tion a mean value and a standard deviation equal to 3.25 % and 0.33 % mass of cement can be determined. Table 4 summarizes the values of the parameters in- volved in equation 4, to be applied for the evaluation of the extent of corroding reinforcement of the ex- ample. Solving equation 4 through a probabilistic technique, as the Montecarlo method, with the val- ues presented in Table 4, a pdep equal to 61 % can be evaluated. 3. Discussion Both mathematical approaches allow to evaluate the extent of corroding reinforcement i.e. the percent- age of reinforcement likely to be non-passive, for a reinforced concrete structure subjected to chloride- induced corrosion, by comparing the chloride content at the depth of the reinforcement, measured during an inspection, with the critical chloride threshold, taking into account the variability of each involved parameter. The extent of corroding reinforcement could be evaluated both at the time of the inspection and in the future, by estimating the evolution in time of the chloride content at different depths. The ap- proaches provide only indications on the amount of actively corroding bars, but do not give any indica- tion on their localization. Furthermore they might overestimate the percentage of bars where initiation of corrosion really occurred. Because of the mecha- nism of chloride-induced corrosion, in fact, in the sur- rounding zones of corroding bars that usually have a chloride content higher than the chloride threshold, 347 Federica Lollini Acta Polytechnica CTU Proceedings the steel benefits of the formation of macrocell that provides cathodic polarization, preventing the initia- tion of corrosion [3]. The statistical approach appears to be easily ap- plicable since the punctual value of the chloride con- tent is directly compared with the critical chloride threshold, whilst the probabilistic approach requires the elaboration of the data obtained through exper- imental measurements, i.e. the concrete cover thick- ness and the chloride profile, to determine the proba- bility density function of the input parameters. How- ever, in principle, the probabilistic method could be used for a preliminary estimation of the extent of cor- roding reinforcement even in absence of any experi- mental data derived from an inspection. Indeed, the input parameters involved in equation 4 could be de- termined from the design data and the environmen- tal exposure conditions. As concrete cover thickness, the design concrete cover could be considered, whilst from the information related to the construction ma- terials, i.e. the w/b ratio and the type of cement, and the exposure condition, the diffusion coefficient and the surface chloride concentration could be estimated. Of course, in this case, the reliability of outcomes will depend on the uncertainty in the parameters chosen for the calculations. From their application, values of 62 and 61 % of extent of corroding reinforcement were respectively obtained with the statistical approach and the proba- bilistic approach, suggesting that the two approaches are comparable. The accuracy and reliability of the outcomes of both approaches depends on the avail- able number of experimental measurements of con- crete cover thickness and chloride content at differ- ent depths and their representativeness of the whole structure. The reliability of these methods could be validated by comparing their results with a careful corrosion potential mapping that allows to detect the depassivated area. The availability of a methodology that allows to evaluate the percentage of corroding reinforcement, provided that it is representative of the corrosion con- ditions of the whole structure, could help the designer in the choice of the most suitable repair technique. The percentage of depassivated area and its evolu- tion in time will represent the amount of concrete, even that sound, that must be removed in the con- ventional repair, since the concrete must be removed in all areas where the chloride threshold is reached at the depth of the reinforcement or it is expected to be reached during the design life of the repair. This re- pair technique, that also requires the careful cleaning of the surface of the reinforcement to remove all chlo- ride contaminated rust, appears to be suitable when the amount of concrete to be removed and replaced is limited. Conversely when large amount of sound concrete should be removed, i.e. when the damage is extensive, other repair methods, such as cathodic protection or electrochemical chloride removal, that require the removal of the only cracked concrete, may be considered. Finally such kind of approaches can be also useful in validating the outcome of the recently proposed probabilistic models for service life design as, for in- stance, the fib Model Code for Service life design. In these models the probability of failure, i.e. the probability of occurrence of corrosion, is evaluated as the probability that the initiation limit state func- tion reaches negative values and, in case of chloride- induced corrosion, it is defined as the difference be- tween the critical chloride threshold and the chloride content at the depth of the bars. The probability of failure has the same meaning of the percentage of cor- roding reinforcement. Hence, the application of the models for service life design to existing structures and the comparison of the results to the real corro- sion conditions of these structures might allow a pre- liminary understanding of their reliability. Usually in these models the concrete performances in relation to the resistance to chloride penetration are evaluated through accelerated tests. The results of accelerated tests are then modified through a series of correc- tive factors that are directly provided by the models themselves. These accelerated tests were usually not carried out for structures built in the past and, hence, to apply these models to an existing structure, atten- tion should be paid in their definition. An inaccurate estimation of the parameters chosen for the calcula- tion could compromise the comparison with inspec- tion results. 4. Conclusive remarks This paper presented two approaches to evaluate the extent of corroding reinforcement i.e. the percentage of reinforcement likely to be non-passive, of a rein- forced concrete structure exposed to chloride-induced corrosion, from the results of an inspection, provided that its results are representative of the whole struc- ture. In the statistical approach the extent of cor- roding reinforcement is calculated by summing up corrosion proportions that correspond to the prob- ability that the critical chloride content is equal to the chloride content at a certain depth interval, over all the considered depth intervals. In the probabilis- tic approach the extent of corroding reinforcement, corresponds to the probability that the difference be- tween the critical chloride threshold and the chloride content at the depth of the bars, both considered as stochastic parameters, reaches negative values. Their application to a fictitious example showed similar re- sults, suggesting that the two approaches are compa- rable. These approaches can be useful to properly plan a restoration intervention, since the outcomes represent the amount of concrete, even sound, that must be removed in the conventional repair, providing then indications on the suitability of such kind of repair technique rather than other treatments, such as the 348 vol. 33/2022 Corrosion Damage for RC Structures cathodic protection or the electrochemical removal of chlorides, that require the removal of the only cracked concrete. 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