DEVELOPMENT OF GUIDELINES FOR DURABILITY DESIGN OF REINFORCED CONCRETE STRUCTURES

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1 DEVELOPMENT OF GUIDELINES FOR DURABILITY DESIGN OF REINFORCED CONCRETE STRUCTURES Joost Gulikers Ministry of Transport, Centre for Infrastructure, Utrecht, The Netherlands Abstract Design for durability of infrastructure facilities is becoming increasingly important in view of the large economical impact of premature maintenance and repair. The deem-to-satisfy approach presented in the current standards and codes is considered too restrictive to allow a wide range of design service lives to be used and does not make any or only limited distinction between type of cement and concrete qualities. Consequently, transparent guidelines are urgently required to support durability design using performance criteria. With respect to reinforcement corrosion induced by the ingress of chlorides a simple mathematical expression has been developed based on a full probabilistic approach by identifying the major influencing model parameters. This formula employs a deterministic approach using mean values for the parameters but by introducing a scaling factor that is dependent on the type of cement and the prevailing exposure conditions, the translation to the desired probability of corrosion initiation is made. Dependent on the economical importance and the possibilities of maintenance of a structure 3 levels of probability have been distinguished. For practical applications, a number of tables have been introduced as to give guidance for concrete producers and consultants. 1. INTRODUCTION The current approach regarding design for durability of reinforced concrete structures is largely based on prescriptive requirements on maximum water to cement ratio, minimum cement content, and minimum thickness of the concrete cover. With respect to reinforcement corrosion both the quality (permeability) and the quantity (thickness) of the concrete cover are considered decisive for the level of protection afforded. In the current European codes the minimum cover depth is specified for a design working life of 50 years and 100 year, taking into account the prevailing exposure class. According to informative table provided in EN [1] for a design working life of 100 years and a given concrete quality the thickness of the cover has to be increased by 10mm compared to a working life of 50 years. In principle, such a deemed-to-satisfy approach does not make any distinction between performance related to the type of cement nor does this approach take into account the 359

2 influence of curing and compaction on the quality of the near-surface layer. However, practical experience has clearly shown that the use of supplementary cementing materials, e.g. blast furnace slag and fly ash, will result in a significantly improved resistance against chloride ingress. Hence a performance-based approach could prove to be advantageous. To this end performance criteria pertaining to relevant transport properties of the concrete material should be established. To allow a wide spread use in practice a simple, fast and reliable test method is preferred to demonstrate that the performance criteria are met. Such an approach could result into a range of combinations of thickness and quality of concrete cover as to meet the durability performance requirements put forward by the asset manager. Ideally, a performance-based approach will allow the contractor to opt for the most economical solution.. MATHEMATICAL EXPRESSION FOR CHLORIDE INGRESS In order to develop performance criteria an accepted mathematical model to describe the relevant deterioration process over time should be available. With respect to chloride ingress the analytical solution to Fick s second law diffusion is most often used to calculate chloride ingress over time. The basic mathematical expression is given by: ( ) x (1) C x,t = C s 1 erf D a t where C is chloride content expressed as a mass-% with respect to cement, [%m/m]; C s is chloride content at the exposed concrete surface, [%m/m]; x is distance to the exposed concrete surface, [mm]; D a is apparent chloride diffusion coefficient, [10-1 m /s]; t is age of a structure/duration of exposure, [yr]; erf: is error function. In the course of time this formula has been modified to a significant extent as to take into account the time-dependency of the (apparent) chloride diffusion coefficient which is reflected in an ageing exponent, n, and an initial level of chloride contamination, C i. In general, an initial contamination of the concrete mix is not taken into account, however the use of sea-dredged aggregates, mixing water contaminated with chlorides, or chloride-based accelerators may necessitate the inclusion of C i. In addition, the expression has been adapted to allow for the design of new structures by the introduction of a chloride diffusion coefficient resulting from an accelerated laboratory test as to reflect the potential quality of the concrete mix to be used on-site. The translation of this laboratory result to a practice level, i.e. the apparent chloride diffusion coefficient D a, is achieved by the introduction of a number of correction factors. In the European project DuraCrete [] this so-called factorial approach has resulted into a modified expression given by: () C = C s ( C C ) s i erf x k k D e c test n to t t where C i is initial chloride content, [%m/m]; k e is environmental factor, [-]; k c is curing factor, [-]; D test,o is result from an accelerated laboratory test, [mm /yr]; t o is reference age/concrete age at which the laboratory test has been performed, [yr]; n is ageing exponent, 0.0 n 1.0 [-]. 360

3 It should be borne in mind that these modifications have rendered the expression largely empirical in nature as the quantification of both the ageing exponent, n, and the correction factors k e and k c is performed through fitting procedures in order to arrive at a reasonable agreement between observed chloride ingress in existing structures and the postdiction obtained by employing Eq. (). In this respect these fitting factors could be regarded as calibration factors, although it should be noted that in DuraCrete [] there was a significant lack of data to allow for a reliable quantification of the fitting factors, in particular for concrete made with blended cements. In DuraCrete the so-called Rapid Chloride Migration test [3] has been adopted as the laboratory test method to quantify the potential resistance against chloride ingress; most often the migration coefficient D RCM,o is determined at an age t o = 8 days. For the design of new concrete structures, end of service life is considered to be reached when the chloride content at the level of the reinforcing steel, i.e. at x = c, equals the so-called critical chloride content, C crit, upon which initiation of corrosion will ensue. By re-arranging Eq. () the mathematical relationship between cover thickness, c, and potential concrete quality, D RCM,o (or more general D test,o ), can then be derived: (3) D RCM,o c = Cs C inverf Cs C crit i 1 to ke kc t dsl n t where D RCM,o is chloride migration coefficient determined at concrete age t o, [10-1 m /s]; c is concrete cover thickness, [mm]; C crit is critical chloride content, [%m/m]; t dsl is design service life, [yr]; inverf is inverse of the error function. As an example, the mathematical relationship between chloride migration coefficient, D RCM,o, and cover depth, c, is depicted in Figure 1 for 3 levels of the ageing exponent, n. In view of the pronounced effect this factor has on the relationship, it is evident that care should be exercised in choosing it s value as in practice the ageing exponent frequently turns out to be an attractive parameter to direct the output to the desired result. migration coeff., DRCM,o [10-1 m /s] n = 0.70 t dsl = 80yr t o = 8d C s = 3.0% C i = 0.15% C crit = 0.6% k e = 1.5 n = 0.50 k c = 1.0 n = cover depth, c [mm] Figure 1: Relationship between concrete cover thickness and concrete quality 361

4 Eq. (3) is considered a suitable basis for deriving performance criteria for durability design with respect to chloride-initiated reinforcement corrosion. 3. DERIVATION OF PERFORMANCE CRITERIA 3.1 Introduction of a probabilistic approach It is clear that when in Eq. (3) for all model parameters mean values are used this will result in a probability of corrosion initiation P i 50%, i.e. according to a deterministic approach. As this is regarded an unacceptably high level, the stochastic nature of all model parameters has to be taken into account. In this respect the adoption of a full probabilistic approach seems to be logical, however this requires that a reliable statistical quantification of all model parameters is available as well as the establishment of an acceptable criterion for the probability of corrosion initiation, P i. At present a full probabilistic approach has a number of pitfalls and disadvantages, e.g.: for most of the model parameters an insufficient amount of data is available to allow for a sound statistical characterization, i.e. mean value μ, standard deviation σ, and type of distribution, e.g. lognormal; there is no agreement on the (assumed) statistical quantification of most model parameters, especially with respect to the ageing exponent, n, and the critical chloride content. C crit, being the most influencing parameters; there is no agreement on the true physical meaning of probability of corrosion initiation, P i, in terms of nature and extent of damage; probabilistic calculations are difficult to understand as well as to check by outsiders; probabilistic calculations can easily be misused through massage or even manipulation of input values. In order to overcome some of these problems associated with a full probabilistic approach a simplified procedure would be welcomed especially by practitioners. 3. Semi-probabilistic approach according to CUR Guideline In the Netherlands a CUR Guideline [4] for durability design of concrete structures with respect to reinforcement corrosion initiated by chloride ingress was developed based on a semi-probabilistic approach. Chloride ingress was calculated by employing Eq. () and using a fixed set of values for all model parameters either according to [] or based on expert opinion. For design purposes tables for a design working life of 80, 100 and 00 years were established providing combinations of thickness of concrete cover, c, and chloride migration coefficient, D RCM,o, determined at a concrete age of 8 days. In each table a clear distinction between 4 types of cement and groups of exposure conditions was made, thus resulting in 8 design situations. In order to simplify the calculation procedure a so-called semi-probabilistic approach was adopted which essentially comprised the use of mean values for all model parameters and the introduction of an allowance for the concrete cover thickness, Δc. For such an approach, the relationship between cover depth and chloride migration coefficient is then given by: 36

5 D RCM,o c Δc = Cs C inverf Cs C crit i 1 to ke k c t dsl n t In [4] Δc = 0mm was chosen as this allowance was expected to result in a probability of corrosion initiation of less than approximately 10%. This assumption was checked by a limited number of full probabilistic calculations, yielding probability levels ranging from 6 to 16% and an average level of 10%. For practical reasons in this guideline only exposure situations were considered: XD (exposure to de-icing salts XD1-XD-XD3 and atmospheric zones in a marine environment XS1) and XS (marine environment; submerged, splash and tidal zone). Details on the statistical quantification of the model parameters can be found in [4]. Figure shows the results obtained for concrete structures exposed to a marine environment, comprising exposure classes XS and XS3. The environmental conditions were reflected in a fixed value μc s = 3.0% whereas it was assumed that the initial chloride content μc i = 0.1%; the critical chloride content was chosen μc crit = 0.60% (for all exposure environments and all types of cements). (4) mean migr. coeff., μdrcm,o [10-1 m /s] t dsl = 100yr marine environment (XS - XS3) t o = 8d mean cover depth, μc [mm] CEM II/B-V CEM I CEM III/A CEM III/B Figure : Performance criteria according to [4] for t dsl = 100yr, marine environment XS-XS3 (CEM II/B-V: 0-30% FA; CEM III/A: 5-50% slag; CEM III/B: 50-80% slag) However, the acceptance of such a semi-probabilistic approach by an asset manager will automatically imply that he also accepts probability levels that could significantly differ from the target level P i = 10%. From an owner s point of view it is anticipated that if the actual probability levels P i are significantly higher than the target level this may cause serious problems in real projects as the guideline explicitly supports a full probabilistic approach. Consequently the contractor may misuse these indirectly accepted higher probability levels for the acceptance of a concrete quality or cover depth being less than agreed upon. In order to determine the actual range of probability of corrosion initiation P i, all combinations of cover depth and migration coefficient presented in [4] for a design working life of 100 years were elaborated by a full probabilistic approach. For the input values the 363

6 statistical quantification of the model parameters as provided in [4] was employed. The results of this calculation exercise are presented in Figure 3. Based on these results it was concluded that the actual probabilities implied by the semi-probabilistic approach varied from 0.5 to 0.6% (t dsl = 100yr), i.e. in a very wide range around the target level P i = 10%. In addition, it was concluded that the results obtained for a design working life of 00 years were unrealistic in particular for concrete made from cement with fly ash (CEM II/B- V). In comparison to a service life of 50 years less than 3.5mm extra cover depth would be required to achieve a design service life t dsl = 00yr. This unrealistic outcome is due to the high value for the ageing exponent (for exposure environment XD it has been assumed that n =0.80) and the implicitly made assumption that this ageing effect, i.e. the decrease of the diffusion coefficient over time, will go on until infinity. The results obtained for CEM II/B-V for a design service life years and exposure to an XD-environment are presented in Figure 4 for 3 realistic levels of concrete quality: D RCM,o = m /s, m /s) and m /s). probability, Pi [%] t dsl = 100yr target level CEM II/B-V; XD CEM III/B; XD CEM III/A; XD CEM I; XD CEM II/B-V; XS CEM III/B; XS CEM III/A; XS CEM I; XS mean cover depth, μc [mm] Figure 3: Calculated probabilities of corrosion initiation corresponding to [4] (XD = de-icing salt environment; XS = marine environment) mean cover depth, μc [mm] CEM II/B-V XD n = design service life, t dsl [yr] m /s m /s m /s Figure 4: Required mean cover depth according to [4] for CEM II/B-V 364

7 These findings provided a strong incentive to develop an alternative practical approach to achieve a simple calculation procedure for service life design with respect to chloride-induced reinforcement corrosion. 3.3 Alternative semi-probabilistic approach: the scaling factor method In view of the need for a simple calculation procedure and the preference for an unambiguous criterion on probability of corrosion initiation, an alternative and more versatile approach was developed [5]. For practical reasons the approach is based on a deterministic calculation using mean values as an input for the model parameters. In stead of an allowance for cover depth, a scaling factor, α, is introduced defined by: D (5) RCM,o det μ D RCM,o ( Pi ) = α where D RCM,odet is migration coefficient resulting from a deterministic calculation using mean values, [10-1 m /s]; μd RCM,o (P i ) is mean migration coefficient for which a probability P i is achieved, [10-1 m /s]. Thus, the magnitude of α should be regarded as a weighted reflection of the stochastic nature of all model parameters as to achieve the target probability P i. The scaling factor was determined for all combinations of type of cement and exposure conditions identified in [4]. For each combination a reference situation t dsl = 100yr and μc = 40mm was used. The statistical characteristics of all model parameters were kept constant except for the mean migration coefficient, μd RCM,o, which was varied in a stepwise fashion as to result into a wide range of probabilities P i. Thereupon, the scaling factor α was calculated according to: D (6) RCM,o det α ( Pi ) = μd P RCM,o ( ) i Through interpolation the value of α for any desired target probability can then be derived. Table 1 provides the results for P i = 5, 10, and 0% for exposure environment XD (de-icing salt) and Table for XS (splash, spray and submerged) according to the statistical input used in [4]. Table 1: scaling factor α for exposure XD (input according to [4]) P i CEM I CEM III/A CEM III/B CEM II/B-V 5% 4,64 5,01 5,46 6,78 10% 3,3 3,49 3,69 4,16 0%,18,4,9,35 365

8 Table : scaling factor α for exposure XS (input according to [4]) P i CEM I CEM III/A CEM III/B CEM II/B-V 5%,90 3,09 3,30 4,63 10%,30,41,53 3, 0% 1,73 1,78 1,83,08 It should be noted that the values for the scaling factor α provided in Tables 1 and pertain to the statistical characteristics, i.e. essentially the standard deviation σ, of all model parameters as given in [4]. If the statistical characteristics are modified, in particular those of the dominating model parameters e.g. the ageing exponent n and the critical chloride content, C crit, this may have a serious impact on the magnitude of α. In this respect reference is made to [6] in which the coefficient of variation for the ageing exponent amounts to COVn = 0.40, whereas in [4] on arbitrary grounds COVn = 0.15 has been adopted. As an example Figure 5 demonstrates the effect of COVn on the magnitude of α for the combinations CEM I XD and CEM III/B XS (quantification of model parameters according to [4]). scaling factor, α [-] CEM I - XD μn = 0.60 CEM III/B - XS μn = ,0 0,1 0, 0,3 0,4 0,5 coefficient of variation ageing exponent, COVn [-] Figure 5: Influencing of the coefficient of variation of the ageing exponent, COVn, on the scaling factor, α. The α -approach was validated by performing full probabilistic calculations for cover depths ranging from 35 to 60mm, using the migration coefficient quantified according to Eq. (3). The relationship between mean cover depth μc and mean migration coefficient μd RCM,o is shown in Figure 6 for CEM I - XS according to the semi-probabilistic α -approach, the CUR Guideline and the full probabilistic approach with the latter giving the correct relationship. It is clear that the scaling factor approach provides a very good agreement with the full probabilistic approach, in contrast to the semi-probabilistic approach adopted in [4]. 366

9 migration coeff., μdrcm,o [10-1 m /s] P i = 10% α CUR Guideline mean cover depth, μc [mm] CEM I t dsl = 100yr XS P i = 10% Figure 6: Comparison between full probabilistic and scaling factor approach and CUR Guideline [4]. The calculation procedure using the scaling factor method is best demonstrated by a calculation example. Consider a situation characterized by exposure environment XD and CEM III/B (cement which contains more than 50% blast furnace slag). For a target probability P i = 10% it follows from Table 1 that α (10%) = Exposure environment XD is defined by a surface chloride content μc s = 1.5%; furthermore it is assumed that µc crit = 0.6% and, µc i = 0.15%. According to [4] for concrete with CEM III/B an ageing exponent µn = 0.70, a curing factor µk c = 1.5 and an environmental factor µk e = 1.97 apply. For a chosen (nominal) cover depth c = 40mm and a design service life t dsl = 100yr a deterministic calculation using Eq. (3) yields D RCM,odet = m /s. Employing Eq. (5) results into a requirement for the concrete quality given by μd RCM,o = m /s. In fact, for any arbitrarily chosen set of statistical characteristics for all parameters involved in the mathematical model the corresponding scaling factor can be quantified. To this end a realistic reference situation (i.e. cover depth and design service life) has to be defined and thereupon the required level of the chloride migration coefficient, or the result of any other test method, is calculated as to achieve the target probability of corrosion initiation. By employing Eq. (6) the required value of α is calculated which can then be used for a wide range of cover depths as to calculate the maximal allowable migration coefficient, D RCM,o 4. CONCLUDING REMARKS A simple and versatile procedure has been developed to calculate the required concrete quality in terms of a migration coefficient obtained from laboratory tests as a function of the design concrete cover thickness providing a satisfactory alternative to full probabilistic calculations. The procedure distinguishes three probability levels as to allow it s application on a wide variety of structures and structural components taking into account the structural and economical importance. Furthermore, the procedure can easily accommodate the use of blended cements for a wide range of cement replacement levels, different curing times, as well as different levels of initial contamination by chlorides, e.g. sea-dredged sand. The scaling factor approach is implemented in a pilot project of the Ministry of Transport, using modified values for the ageing exponent aimed at a design service life t dsl = 100yr only. In 367

10 order to simplify the procedure for contractors and concrete producers tables have been provided and in addition a correction factor has been introduced to account for the initial chloride content At present a procedure is developed to check the actually achieved concrete quality as to allow for quality control on site. REFERENCES [1] EN , Eurocode : Design of concrete structures - Part 1-1 (CEN, Brussels, 005). [] DuraCrete, Final Technical Report, Doc. BE /R17 (CUR, Gouda, 000). [3] NT Build 49, Chloride migration coefficient from non-steady-state migration experiments, (nordtest, Espoo, 1999). [4] CUR, Guideline 1 Durability of structural concrete with respect to chloride-induced reinforcement corrosion (CUR, Gouda, 009) (in Dutch). [5] Gulikers, J., Development of a practical guideline for durability design (Rijkswaterstaat, Utrecht, 010). [6] fib, Model Code for Service Life Design, bulletin 34 (fib, Lausanne, 006). 368