fib models for modeling of chloride ion ingress and concrete carbonation: Levels of assessment of input parameters

Degradation processes affecting structural materials, such as chloride ion ingress, concrete carbonation, and the subsequent corrosion of reinforcement, are limiting factors for the service life of reinforced concrete structures and/or structural elements. The objective of a structural condition assessment is to determine the current state and estimate the future performance of a structure with a maximum degree of accuracy and a minimum of effort. There is therefore a need for advanced methodologies and predictive deterioration models for the assessment of structures/structural elements over time. In the paper, the focus is on the widely accepted models for modeling of chloride ion ingress into concrete and concrete carbonation process incorporated in the fib Model Code 2010. Three levels of assessment of input parameters are presented, starting with simple quantification based on codes/literature recommendations and progressing to higher levels of assessment using design documentation and visual inspection data, additional on‐site measurements, and/or laboratory tests.


| INTRODUCTION
The service life and durability of reinforced concrete structures and/or structural elements are affected by degradation processes which act on structural materials. Concrete carbonation, chloride ion ingress, and the subsequent corrosion of reinforcement are the most common deterioration phenomena.
Within the management of structures, due to the desire to minimize overall cost, the most common type of structural evaluation is the nonformal assessment, where the condition of a structure is evaluated on the basis of visual inspections. The objective of a structural condition assessment is to determine the current state of a structure and estimate its future performance with a maximum degree of accuracy and a minimum of effort. Data collected during visual inspections should mainly provide information about the most serious problems and suggest the most suitable scheme for the extension of the performed inspection via monitoring, additional on-site measurements, and/or laboratory tests.
In order to ensure the desired durability outcomes occur, modeling based on mathematical principles and measured material characteristics is seeing increased use in durability design. The fib Model Code 2010 1 has Discussion on this paper must be submitted within two months of the print publication. The discussion will then be published in print, along with the authors' closure, if any, approximately nine months after the print publication. incorporated a performance-based approach for such design. Here, the verification of limit states associated with the durability of structures may be performed using the following approaches: (a) the fully probabilistic format; (b) the partial safety factor format; (c) the deemedto-satisfy approach; and (d) the avoidance-of deterioration approach. In general, structural assessment is carried out using limit state principles with characteristic values and partial safety factors. However, only the fully probabilistic approach provides quantitative information about safety level and hence is increasingly supported if more refined methods are necessary.
The aim of this paper is to describe the levels of assessment of input parameter values for the prediction of deterioration due to chloride ion ingress into concrete and concrete carbonation process for existing structures. Due to inherent uncertainties in material, technological, and environmental characteristics, stochastic models, dealing with probabilistic approaches and presenting the performancerelated design of structures for durability, are recommended creating an effective tool for the assessment and prediction of time-dependent degradation processes (see fib Model Code 2010 1 and ISO 16204:2012 2 ). Hence, the focus is on the widely accepted analytical models incorporated into the fib Model Code 2010 1 and consequently in the fib Model Code 2020 for existing structures, as well as on the fully probabilistic approach, see Strauss et al. 3,4 This paper does not primarily deal with the required adaptation of models developed for new structures to existing structures, or vice versa, which would certainly be of interest to the engineering community. It deals with the survey options on construction sites and laboratory and its applicability for processing the suggested degradation models and its input parameters. Nevertheless, the proposed categorization developed for existing structures can already be transferred to the models for the verification of the quality of new concrete structures, which will be in a next step treated in the corresponding fib commissions, for example, in Chapter 27.11 of ModelCode 2020.

| MODELING OF CHLORIDE ION INGRESS AND CONCRETE CARBONATION ACCORDING TO THE FIB MODEL CODE 2010
The limit state associated with the durability of structures is described by the limit condition: where R(t D ) and A(t D ) represent the resistance capacity and the cumulative degradation of the structure/ structural component at the end of its design life, t D , and P f and P d stand for the actual and design probability of failure. For the case of chloride ion ingress into concrete, the resistance capacity is replaced by the critical concentration of dissolved Cl − leading to steel depassivation and degradation is represented by the concentration of Cl − at the depth of concrete cover. Similarly, the concrete cover is compared to the carbonation depth at time when carbonation process is considered. The widely used analytical models for modeling of chloride ion ingress into concrete are based on the error function "erf." 5 According to fib Bulletin No. 34, 6 the Cl − concentration at the depth of concrete cover at time, C(a, t) (wt%/c) is calculated as According to fib Bulletin No. 76, 7 D app (t) can be determined based on field data obtained via the chloride profiling method or the rapid chloride migration (RCM) test method. Subsequently, an aging exponent may be determined using the following approaches A or B: where the environmental variable k e [−], which takes into consideration the effect of temperature on chloride ingress into concrete, is described as For meaning of the individual model input parameters, see Table 1.
A simple approach to the calculation of carbonation depth at time, x c (t) [mm] can be defined, according to which The constant A is quantified through the evaluation of carbonation depths measured on real concrete structures. Using different forms of parameter A, it is possible to cover the whole range of carbonation situations.
Based on DuraCrete Project 9 and according to fib Bulletin No. 34, 6 the carbonation depth x c (t) (mm) at a certain point of time is defined as with the environmental function k e [−] and execution transfer parameter k c [−] assessed according to following formulas: k Meso-climatic conditions due to the re-wetting of concrete surfaces caused by rain events are taken into account using the time-dependent weather function, which is defined as with w [−] being the weather exponent. Meaning of all the model input parameters is summarized in Table 2.
Later, von Greve-Dierfeld and Gehlen 11-13 introduced an additional parameter-carbonation rate k NAC , which T A B L E 1 List of input parameters for the modeling of chloride ingress

Material parameters
1 Cement and binder types CEM I-V -(1), 2, 3b Petrographic examination 2 Water to cement (water to binder) ratio Migration coefficient based on RCM-test method D RCM (t 0 ) or the apparent coefficient of chloride diffusion based on the field data D app (t 0 ) can be used. b The long-term behavior of the D app (t) of existing structure has to be considered by analyzing the development of chloride profiles over time; at least two different points in time for D app (t) or combination of the D app (t) obtained from the field data and the D RCM (t 0 ) of the design concrete gained from laboratory RCM tests are required in order to be able to quantify the aging exponent α.
c By measuring the corrosion current and electrode potential at different depths in the concrete cover, it is possible to predict when the chloride-based corrosion front will reach the reinforcement. The critical chloride content, C cr , can thus be assessed.
replaced the inverse carbonation resistance R NAC −1 . Here, x c (t) is defined as Furthermore, function k a [−] describes the effect of CO 2 concentration in the ambient air.
For a detailed overview of carbonation and chloride ingress parameters, and their implementation for condition assessment in existing structures, see Zambon et al. 14 Tables 1, 2) can be used based on input value precision and the accompanying uncertainties. In the case of an existing structure, three levels can be distinguished (see also Figure 1): (i) Level 1-No inspection of the structure and/or onsite measurements has been carried out and the only available information about materials, loading, and the   Tables 1, 2) where definitions of input parameters using appropriate statistical characteristics such as the probability density function, mean value, the coefficient of variation and limits if needed can be found. These are based on former measurements and/or experience. The definition of input values using only codes and other literature sources may not always be completely accurate. For a more precise analysis, it is recommended that higher levels of assessment be utilized in combination with the probabilistic approach.
(ii) Level 2-The design documentation is available, and/or a visual inspection of the structure was carried out.
When design documentation is available for the structure, and the structure is well documented, precise information about material properties can be obtained. Especially data on parameters, such as cement type, water to cement/binder ratio, carbonation resistance properties, chloride diffusion properties, period of curing, depth of concrete cover, are crucial for the realistic quantification of input variables for the modeling of the degradation processes over time. Unfortunately, in the prevailing number of cases, only basic input parameters such as the age of the structure and/or concrete cover are documented. If the required data cannot be obtained from design documentation, a visual inspection is needed. The results from a single visual inspection may be used to estimate the remaining service life, from which the timing of future inspections/maintenance can be determined based on the current level of risk, and the need to perform other tests in different areas can be assessed.
(iii) Level 3-Updated or realistic input values are available from on-site measurements (Level 3a) and/or supplementary laboratory tests (Level 3b).
If reliable data are not available from design documentation or visual inspection, additional on-site measurements and/or laboratory tests should be carried out. Tests may be carried out directly on the structure itself (in-situ testing), or on test specimens made in the laboratory or taken from the structure. Nondestructive test methods and methods of sample analysis can be employed at intervals during the structure's life. Regarding the environmental parameters, data from the nearest weather station can also be utilized. If these are not available, on-site measurements of environmental characteristics such as temperature, relative humidity, or precipitation can be employed. Some parameters can also be obtained with sufficient accuracy using calibration processes. Individual test methods for quantifying the individual parameters are mentioned in "Method" column of Tables 1, 2; for details, see also Šomodíková et al. 20 3.1 | Suitability of each level to apply a probabilistic service life analysis In general, the probabilistic methods can be used at all three levels described above.
At Level 1, it is typical that the issues to be treated are represented in models (e.g., see Equations (2)-(9)), which are accessible to a mathematical-numerical treatment. For these models, always a single value (usually a fractile value) is used for each variable. The result consequently appears in a single number. This is usually an engineering procedure used for dimensioning and evaluation problems. However, it is particularly recommended to use several different numerical values in the models presented above to test the sensitivity of the results.
It is therefore already important at Level 1 to introduce those variables with their statistical distribution forms (probability density functions, PDFs) and statistical parameters (mean, standard deviation, etc.) influencing the considered assessment problem in terms of reliability theory. The transfer of the influencing variables, which are mostly defined as fractile values in standards, into distribution forms and the associated statistical parameters can be carried out according to clear statistical relationships taking into account standard background documentation, such as the Probabilistic Model Code 21 by the Joint Committee on Structural Safety.
Level 2 tests are typical on-site tests at the structure. This level is associated with the updating of information on environmental and mechanical condition of the structure. Specialized specialist bodies are usually involved in this procedure. Rather, it is reasonable and cost-effective to use the Level 1 gained insights to set up a targeted and suitable examination program, as well as to determine what needs to be checked.
Level 2/Level 3a tests are typical for the condition assessment of concrete structures in bridge engineering. The process step is known as information updating and is performed in general by specialized departments. The additional information obtained from these testing is included in the assessment in order to finally dispel the doubts that still exist at the end of Level 1 and to demonstrate sufficient reliability. In general, the conventional probabilistic models proposed above and the updated values will be used for these procedures. In this context, Bayesian or similar methods can be used, in order to process the additional information in the characterization of the above mentioned probability density functions and its associated statistical parameters. Based on "a priori probabilities" (e.g., from the Level 1 surveys), by adding additional information, taking into account a posteriori predictor, values for the improved probability density function are determined.
If the reliability achieved is received as insufficient and the general test-specific criteria show a high assessment complexity, then a structural performance at Level 3 procedure is proposed. In Level 3 procedure, probabilistic models are predominantly used in the assessment. The probabilistic expert analyses in Level 3 consequently substitute the standards, which guarantee a balanced level of safety in the structural design phase. The acceptance of increased risks or a reduced safety should in principle be reserved for an expert panel.

| DISCUSSION ON THE RELEVANCE OF THE CORROSION PROPAGATION TIME
When observing the duration of service life, a rate and type of corrosion propagation is to be taken into account. In the carbonation environment, the rate of corrosion propagation after the point of initiation is expected to be very slow. Accordingly, there would be only negligible material and mechanical changes of the concrete member concerned, even at the point in time when the first cracks appear.
However, there is an obvious contrast of carbonation caused corrosion in comparison with the situation where chloride induced corrosion involving pitting occurs. The process is followed with very limited amounts of corrosion products being produced, and possibly little of no cracking, depending upon the nature of the exposure environment. Furthermore, pitting corrosion can rapidly induce significant local loss of rebar area causing significant losses of member carrying capacity. The effects of pitting corrosion include a reduction of material properties such as yield strain and elongation at failure, changes in bond and anchorage, as well as associated effects such as the reduction in the confinement of the main reinforcement due to corrosion damage to stirrup reinforcement.
When a possible propagation allowance is observed, it is important to mention that it would not be appropriate in cases where prestressing wires or tendons could be affected by carbonation or chloride induced corrosion, as there is a likelihood that hydrogen embrittlement of the steel could arise. Furthermore, there are similar considerations for circumstances where fatigue or fretting occur, for both reinforced and prestressed concrete members.
When observing future development of codes and regulations, there is an obvious need to define how to take in account corrosion propagation development in service life design (SLD). It is necessary to recognize and differentiate a full account of different design situations where various actions and environmental effects could arise, singularly, or perhaps in conjunction. In summary, all accompanying circumstances of the corrosion propagation process have to be clarified, to define in which cases the corrosion propagation time could be implemented in SLD and within which limits, as well as under which constraints.

| CONCLUSIONS
In the paper, levels of assessment of input parameter values for modeling of chloride ion ingress into concrete and concrete carbonation process were briefly presented with the focus on the widely accepted models incorporated into the fib Model Code 2010. 1 Based on input value precision and the accompanying uncertainties, three levels can be distinguished. For the first estimation in degradation modeling, input parameters can be quantified using appropriate statistical characteristics, such as the probability density function, mean value, the coefficient of variation and limits if needed, according to codes and/or other literature sources. For many of the input parameters, these values may not be entirely accurate and realistic, and consequently their use may lead to very uncertain (and sometimes even unsafe) modeling results. Hence, higher levels of assessment using additional onsite measurements and/or laboratory tests are recommended.