# Service Life Design of Concrete Structures Made of High-Volume Limestone Powder Concrete—Case of the Carbonation-Induced Corrosion

^{1}

^{2}

^{*}

## Abstract

**:**

_{2}emissions reduction in the concrete industry is to use low-clinker cements, providing at the same time the performance of concrete that is adequate for application in concrete structures. This paper explores the impact of the clinker replacement with high amounts of limestone powder (21–70% in the powder phase) on concrete carbonation resistance. To quantify this impact, the empirical relationship between the carbonation resistance and the compressive strength of the high-volume limestone powder concrete (HVLPC) was established. For that purpose, the regression analysis was applied on the experimental results collected from the published research. The service life analysis based on the full probabilistic approach was performed using the fib Model Code 2010 prediction model and proposed empirical relationship. The first-order reliability method (FORM) was applied to solve the limit state function of reinforcement depassivation with a reliability index equal to 1.3. The obtained minimum concrete cover depths were 40–110% higher compared to those prescribed in the current European standard EN 1992-1-1:2004 for indicative strength classes. Based on the full probabilistic analysis, recommended cover depths are given for all carbonation exposure classes, commonly applied concrete strength classes, and service lives of 50 and 100 years.

## 1. Introduction

_{2}emissions [8]. Therefore, decarburization of the concrete/cement sector plays an important role in achieving a carbon neutral future.

_{2}presents one of the viable solutions to this problem. Today we already use commercial cements with part of the clinker replaced with SCMs: CEM II/A with up to 20% fly ash (FA), ground granulated blast furnace slag (GGBS) and limestone (LS), CEM II/B with up to 35% FA, and GGBS, LS, and CEM III with up to 95% GGBS. Bearing in mind the limited global availability of commonly used SCMs (FA and GGBS) [9], alternative SCMs, abundant in nature, should be looked for. Limestone, if finely ground, can serve this purpose [10]. However, compared to FA and GGBS, it is less effective and has a higher impact on the mechanical and durability-related concrete properties due to its very low reactivity [11,12,13,14,15]. Therefore, higher clinker replacements with limestone powder (>15–20%) present a problem for the structural concrete at all performance aspects.

_{c}is the carbonation depth, k is the carbonation rate coefficient, and t is time. Unlike that for the concrete with FA and GGBS blended cements [22], very few mathematical prediction models for the limestone powder concrete have been developed so far [11,34,35]. These models are complex and require knowledge on many parameters that influence the carbonation process. For everyday engineering practice, however, simpler models are needed. One such simpler model is given in the previously mentioned fib Model Code 2010 [33], originating from the fib Model Code for service life design [36]. Although simple, this prediction model requires an experimental determination of the carbonation depth under defined conditions. Therefore, the property that reflects the concrete carbonation resistance has to be experimentally determined. Current European standards EN 12390-10:2018 [37] and EN 12390-12:2020 [38] prescribe the test conditions for determining the carbonation resistance under natural and accelerated conditions, respectively. Tests under natural conditions should last for one year, while for the tests under accelerated conditions, which are shorter (70 days), non-standard laboratory equipment—carbonation chamber—is required. To avoid this experimental test, finding an empirical relationship with concrete properties that must be tested in any case, such as concrete compressive strength, would significantly improve the feasibility of the model. For the sake of reliability, this relationship would preferably be established for carbonation resistance under natural conditions.

## 2. Objectives

- To establish the empirical relationship between the carbonation resistance and the compressive strength of the HVLPC (21–70% limestone powder content in the concrete powder phase). The relationship was obtained using the regression analysis applied to the experimental results collected from the published research.
- To propose the concrete cover depths for the HVLPC, depending on the limestone powder content and carbonation exposure class. The service life analysis based on the full probabilistic approach was performed using the fib Model Code 2010 [33] prediction model and proposed empirical relationship.

## 3. Methodology

- x
_{c} - is the carbonation depth (mm);
- k
- is the carbonation rate coefficient (mm/year
^{0.5}) defined as:

- k
_{e} - is the environmental function (-);
- k
_{c} - is the execution transfer parameter (-);
- C
_{s} - is the CO
_{2}concentration in the air (kg/m^{3}); - W(t)
- is the weather function (-);
- R
^{−1}_{NAC} - is the inverse effective carbonation resistance of concrete under natural conditions ((mm
^{2}/years)/(kg/m^{3})).

^{−1}

_{NAC}reflects the carbonation resistance of concrete depending mostly on the water-to-cement ratio and binder type, while other parameters in Equations (2) and (3) take into account the influence of the environmental and execution conditions. It is recommended in [33,36] that R

^{−1}

_{NAC}is calculated using R

^{−1}

_{ACC}, which is experimentally determined under defined accelerated conditions (ACC):

- k
_{t} - is the regression parameter for the test effect of the ACC test (-);
- ε
_{t} - is the error term for inaccuracies that can occur when using the ACC test method ((mm
^{2}/years)/(kg/m^{3})).

^{−1}

_{NAC}and compressive strength of the limestone powder concrete, experimental results were collected from the previous research in the 1995–2023 period. Collected test results were then filtered to satisfy the following conditions: limestone powder was the only SCM in the concrete mix with more than 20% participation in the powder phase, whether it was contained in the commercial CEM II/B-L(LL) cement or added to CEM I concrete mix in a certain amount; minimal mean compressive strength of concrete f

_{cm}on the cylinder was equal to 20 MPa; measured carbonation depth was not less than 1 mm; minimum natural exposure duration was 140 days; all necessary curing and environmental conditions were reported. Since the curing conditions have a large impact on the carbonation front propagation, a minimal curing period of 7 days was adopted. Applying these filters led to 75 experimental results of carbonation depth measured under natural indoor and sheltered outdoor conditions [12,13,16,18,25,26,49,50,51,52,53,54,55,56], on which the regression analysis was performed. Those data originate from 14 different laboratories; however, from some experimental campaigns, only 2 or 3 measured data satisfied the mentioned conditions and were included. The data range is shown in Table 1.

^{−1}

_{NAC}and f

_{cm}, the service life was predicted using Equation (2). By comparing the probability of the carbonation depth reaching the nominal concrete cover depth (c

_{nom}), the limit state function of reinforcement depassivation can be written in the following form:

_{nom}), defined in EN 1992-1-1:2004 [57], represents the mean value of the concrete cover depths (see Table 2). It consists of the minimum cover necessary to protect the reinforcement from corrosion (c

_{min}

_{,dur}) increased by an absolute value of the accepted negative deviation (Δc

_{dev}), which depends on the quality of execution works. For cast-in-situ structures, the prescribed Δc

_{dev}is 10 mm. It is reasonable to assume that the concrete cover standard deviation (σ

_{c}) is controlled by the execution requirements, which are often interpreted as 5% quantile of concrete cover values [58]:

_{e}represents the environmental conditions:

_{real}is the environmental relative humidity (%), RH

_{ref}is the referent relative humidity (65%), f

_{c}is an exponent (5.0), and g

_{c}is another exponent (2.5).

_{c}) represents the curing conditions and is defined as:

_{c}is the curing period (days), and b

_{c}is the regression exponent (-).

_{c}) of 7 days was adopted assuming that this is the standard on-site curing period. It is also the time defined in the fib Model Code for service life design [36] for the accelerated carbonation test. The distribution parameters of the exponent b

_{c}were adopted according to the recommendation from the same document [36]. In addition, the distribution parameters for the CO

_{2}concentration (C

_{s}) were adopted according to values defined in [36], taking into account the constant increase in concentration in the past century. For the weather function W(t), the maximum value (1.0) was taken, given that only indoor and sheltered-from-rain samples were analyzed in this study. Finally, the distribution of predicted R

^{−1}

_{NAC}was calculated according to the procedure explained in Section 4.2. The summary of all input parameters is shown in Section 4.3.

_{f}≤ 0.10) was adopted as per the fib Model code for the service life design [36] requirement for the depassivation limit state. A service life of 50 and 100 years was used in the calculations. By solving the limit state function defined in Equation (5), it is possible to obtain the required concrete cover depth for the defined parameters, or to determine the service life for the defined concrete cover.

## 4. Results and Discussion

#### 4.1. Relationship between R^{−1}_{NAC} and Compressive Strength of the Limestone Powder Concrete

_{c}or carbonation rate coefficient k; in the latter case, carbonation depth was calculated using Equation (1).

^{−1}

_{NAC}calculated in that way and the reported compressive strengths were considered as mean values.

^{−1}

_{NAC}and f

_{cm}was best described with the power regression model. However, reducing the power regression to the linear regression model of the log-transformed variables offers a simpler mathematical tool for further application. The linear model of the log-transformed variables is:

_{0}and b

_{1}are the linear regression coefficients representing intercept and slope, respectively.

^{2}for the linear regression models of log-transformed variables ranges between 0.76 and 0.80 depending on the mix (Table 3). The coefficient estimates, their standard errors, and significance are also given in Table 3. The null hypotheses that b

_{0}= 0 and b

_{1}= 0 can both be rejected for all mixes at virtually any significance level. Each regression model was also shown to have independent, homoscedastic, and normally distributed residuals. The normality of the residuals was tested by applying the Kolmogorov–Smirnov goodness-of-fit test at the 5% significance level. Figure 1, Figure 2 and Figure 3 also show the 90% confidence intervals for predicted values of R

^{−1}

_{NAC}.

^{2}between 0.76 and 0.8):

^{3}. The second problem, a low amount of carbonatable constituents, depends mainly on the clinker content: the lower the clinker content, the lower the alkaline reserve. Due to low Ca(OH)

_{2}content, the carbonation rate is faster, i.e., carbonation resistance is lower and the mix optimization methods mentioned here cannot help. For that reason, HVLPC has lower carbonation resistance compared to pure-clinker concrete for the same compressive strength. The obtained results are: the similar relationships (11) and (12) for 21–35% and 36–70% limestone powder groups, respectively, mean that the impact of porosity, which dictates CO

_{2}diffusivity, prevails over the impact of the available alkaline reserve.

^{2}equal to 0.78 can be considered strong enough for the simplified prediction model. It is important to note that the proposed equations are valid for concrete mixes that are wet-cured for at least 7 days. If shorter curing periods were included (1 and 3 days), a single relationship with a strong correlation between inverse natural carbonation resistance and compressive strength could not be obtained due to the significant impact of short periods on the carbonation resistance. This was however considered acceptable for the simplified prediction model. Moreover, curing periods shorter than 7 days are not likely in practice—they are rather an exception to the rule in special cases.

#### 4.2. Distribution of Predicted R^{−1}_{NAC} for Selected Values of Mean Compressive Strength

^{−1}

_{NAC}for a given ln f

_{cm}, as well as to compute the prediction (confidence) interval for the values of ln R

^{−1}

_{NAC}for a given ln f

_{cm}. While this procedure is straightforward for linear regression, interpretation of the results with log-transformed variables needs careful consideration. For the sake of clarity, we use the following notation: y = ln R

^{−1}

_{NAC}and x = ln f

_{cm}.

^{2}. Consequently, predicted response variable y is also normally distributed with conditional mean being the regression line and with the same variance σ

^{2}. Furthermore, the least-squares estimators of regression coefficients ${\widehat{b}}_{0}$ and ${\widehat{b}}_{1}$ are random variables by their nature. The variability of ${\widehat{b}}_{0}$ and ${\widehat{b}}_{1}$ means that the estimated regression line (10) may deviate from a true one in terms of both slope and intercept. For a fixed value of the explanatory variable x = x

_{0}, the estimated conditional mean response ${\mu}_{Y|X={x}_{0}}=\widehat{{b}_{1}}\xb7{x}_{0}+\widehat{{b}_{0}}$ is normally distributed as:

_{xx}is the sum of squares of x, b

_{1}and b

_{0}are true regression coefficients, and n is the number of observations. The variance of the estimated prediction of the response variable ${\widehat{y}}_{0}$ for the given x

_{0}is obtained by combining the variances of the estimated regression model and the variance of the residuals ε:

_{0}of the response variable:

_{n}

_{−2,1−}

_{α}

_{/2}is the Student’s t variate with n − 2 degrees of freedom and probability 1 − α/2. The confidence interval of log-transformed R

^{−1}

_{NAC}that is symmetric due to the normality assumption becomes asymmetric after exponentiation:

^{−1}

_{NAC}for the given x

_{0}is normally distributed, the predicted R

^{−1}

_{NAC}is log-normally distributed. When exponentiated, the mean value of the log-normal distribution is not equal to the mean value of the normal distribution, although it is equal to the median value of normal distribution [61]. Therefore, the power curves shown in Figure 1a, Figure 2a and Figure 3a do not represent the mean predicted response of R

^{−1}

_{NAC}, but the median predicted response. The lower and upper confidence limits of the asymmetric 90% confidence interval in Figure 1a, Figure 2a and Figure 3a represent the same probabilities (5% and 95%) of the conditional distribution as in Figure 1b, Figure 2b and Figure 3b.

^{−1}

_{NAC}for the given f

_{cm}, the relationship between the moments of the original and log-transformed normal variables was used to define the mean and variance of estimated R

^{−1}

_{NAC}prediction for the given f

_{cm}as:

^{−1}

_{NAC}prediction and ${\widehat{y}}_{0}$ denotes the estimated ln R

^{−1}

_{NAC}prediction for the given x

_{0}, i.e., for the given f

_{cm}. This allows for computing the moments of the estimated R

^{−1}

_{NAC}prediction for selected values of f

_{cm}and using them in the original space of R

^{−1}

_{NAC}for the service life analysis. Distribution parameters for R

^{−1}

_{NAC}have been determined for commonly applied concrete classes defined in EN 1992-1-1:2004 [57]. The distribution parameters, concrete classes, as well as the corresponding f

_{cm}are shown in Table 4 for the 21–70% limestone powder concrete since service life analysis was performed for this group of concrete mixes.

#### 4.3. Service Life Analysis

_{SL}) concrete cover (c

_{nom}) for all exposure classes (XC1–XC4).

_{SL}= 57 years). With a further increase in strength, the service life increased up to 79 years for the C40/50 concrete class. By solving the limit state function for the depassivation period of 50 years, the obtained concrete cover depth for strength class C20/25 was 42 mm, instead of the prescribed 25 mm [57].

_{nom}) for all carbonation exposure classes.

_{min}

_{,dur}) from the durability point of view for commonly applied concrete classes are shown in Table 6. Given that the calculation was made with the nominal cover depth (c

_{nom}), as explained in the Methodology, the minimum cover depth was calculated by reducing the nominal value by the value of the accepted negative deviation (Δc

_{dev}).

## 5. Conclusions

^{2}can be considered strong enough for the simplified prediction model. It is important to note that the proposed relationships are valid for concrete mixes wet cured for at least 7 days and indoor and outdoor sheltered natural conditions.

_{min}

_{,dur}for HVLPC were significantly larger compared to those prescribed in EN 1992-1-1:2004 for indicative strength classes. For a service life of 50 years, the calculated minimum cover depths were 32 mm for XC1, 46 mm for XC2 and XC3, and 42 mm for XC4. For a service life of 100 years, the calculated cover depths were 48 mm for XC1, 68 mm for XC2, 67 mm for XC3, and 63 mm for XC4. Altogether, the increase varied between 40 and 110%, or between 12 and 33 mm, depending on the exposure class and service life duration. These results clearly indicate that HVLPC should be used for the structures where a service life of 50 years is acceptable. Adding a safety factor of 10 mm for cast-in-situ structures according to EN 1992-1-1:2004 leads to nominal covers of 75–80 mm for a service life of 100 years, which may not be acceptable in practice.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Relationship between the natural inverse carbonation resistance and mean compressive strength of concrete for mixes with 21–35% limestone powder: (

**a**) power regression and (

**b**) linear regression of log-transformed variables.

**Figure 2.**Relationships between the natural inverse carbonation resistance and mean compressive strength of concrete for mixes with 36% to 70% limestone powder: (

**a**) power regression and (

**b**) linear regression of log-transformed variables.

**Figure 3.**Relationships between the natural inverse carbonation resistance and mean compressive strength of concrete for mixes with 21% to 70% limestone powder: (

**a**) power regression and (

**b**) linear regression of log-transformed variables.

**Figure 4.**Reliability index (β) values during time of exposure for 50-year service life concrete covers (c

_{nom}) and different exposure classes.

**Figure 5.**Reliability index (β) during time of exposure for a 100-year service life concrete cover (c

_{nom}) and different exposure classes.

Properties of concrete mix | |

Limestone powder content (% of total powder phase) | 21–70 |

Cement type | CEM I or CEM II/B-L(LL) |

Curing time (days) | 7–28 |

Mean compressive strength, 28 days, cylinder (MPa) | 20–62 |

Environmental conditions | |

RH (%) | 60–75 |

CO_{2} concentration (%) | 0.035–0.045 |

Exposure conditions | indoor and outdoor sheltered |

Exposure time (days) | >140 |

**Table 2.**The nominal concrete cover depths for service lives of 50 and 100 years according to [57].

Service Life (t_{SL}) | Exposure Class | ||||
---|---|---|---|---|---|

XC1 | XC2 | XC3 | XC4 | ||

c_{nom} (mm) | 50 years | 25 | 35 | 35 | 40 |

100 years | 35 | 45 | 45 | 50 |

**Table 3.**Linear regression of R

^{−1}

_{NAC}on ln f

_{cm}: model adequacy as measured by coefficient of determination, estimated coefficients, and their properties.

Concrete Mix (Limestone Content) | 21–35% | 36–70% | 21–70% |
---|---|---|---|

Number of data | 33 | 42 | 75 |

Coefficient of determination, R^{2} | 0.80 | 0.76 | 0.78 |

Slope coefficient, b_{1} | |||

estimate | −3.050 | −2.9534 | −2.9839 |

standard error | 0.2739 | 0.2640 | 0.1877 |

significance (p-value) | <<0.001 | <<0.001 | <<0.001 |

Intercept, b_{0} | |||

estimate | 20.801 | 20.489 | 20.585 |

standard error | 0.9627 | 0.9473 | 0.6674 |

significance (p-value) | <<0.001 | <<0.001 | <<0.001 |

**Table 4.**Moments of conditional log-normal distribution of predicted natural inverse carbonation resistance R

^{−1}

_{NAC}for the selected values of the mean compressive strength f

_{cm}.

Concrete Mix (Limestone Content) | Concrete Class | f_{cm}[MPa] | Prediction of R^{−1}_{NAC} ((mm^{2}/Years)/(kg/m^{3})) | ||
---|---|---|---|---|---|

Mean | Standard Deviation | CV (−) | |||

21–70% | C20/25 | 28 | 46,342 | 22,034 | 0.475 |

C25/30 | 33 | 28,362 | 13,433 | 0.474 | |

C30/37 | 38 | 18,620 | 8826 | 0.474 | |

C35/45 | 43 | 12,885 | 6131 | 0.476 | |

C40/50 | 48 | 9290 | 4445 | 0.479 |

Parameter | Distribution | μ | σ | Unit | |
---|---|---|---|---|---|

c_{nom} | Lognormal | Table 2 | 6 | mm | |

RH_{real} | XC1 | Beta | 92 (40 *) | 6 (100 *) | % |

XC2 | Beta | 79 (40 *) | 9 (100 *) | % | |

XC3 | Beta | 65 (40 *) | 10 (100 *) | % | |

XC4 | Beta | 75 (40 *) | 16 (100 *) | % | |

RH_{ref} | Constant | 65 | – | % | |

f_{c} | Constant | 5.0 | – | – | |

g_{c} | Constant | 2.5 | – | – | |

t_{c} | Constant | 7 | – | days | |

b_{c} | Normal | −0.567 | 0.024 | – | |

C_{s} | Normal | 0.0008 | 0.0001 | kg/m^{3} | |

t | Constant | 1 ÷ 100 | – | year | |

R^{−1}_{NAC} | Normal | Table 4 | (mm^{2}/year)/(kg/m^{3}) |

**Table 6.**Recommended values of minimum concrete cover depths (c

_{min,dur}) for 21% to 70% limestone powder concrete and different exposure classes.

Concrete | Exposure Class | ||||
---|---|---|---|---|---|

Service Life | Class | XC1 | XC2 | XC3 | XC4 |

50 years | C20/25 | 32 (15 *) | 61 | 75 | 71 |

C25/30 | 23 | 46 (25 *) | 57 | 54 | |

C30/37 | 18 | 36 | 46 (25 *) | 42 (30 *) | |

C35/45 | 14 | 29 | 37 | 34 | |

C40/50 | 11 | 24 | 30 | 28 | |

100 years | C20/25 | 48 (25 *) | 89 | 110 | 103 |

C25/30 | 36 | 68 (35 *) | 84 | 79 | |

C30/37 | 28 | 54 | 67 (35 *) | 63 (40 *) | |

C35/45 | 22 | 44 | 55 | 51 | |

C40/50 | 18 | 36 | 45 | 42 |

_{min}

_{,dur}for indicative minimum concrete strength class according to [57].

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## Share and Cite

**MDPI and ACS Style**

Carević, V.; Marinković, S.; Plavšić, J.; Radović, A.
Service Life Design of Concrete Structures Made of High-Volume Limestone Powder Concrete—Case of the Carbonation-Induced Corrosion. *Buildings* **2023**, *13*, 3112.
https://doi.org/10.3390/buildings13123112

**AMA Style**

Carević V, Marinković S, Plavšić J, Radović A.
Service Life Design of Concrete Structures Made of High-Volume Limestone Powder Concrete—Case of the Carbonation-Induced Corrosion. *Buildings*. 2023; 13(12):3112.
https://doi.org/10.3390/buildings13123112

**Chicago/Turabian Style**

Carević, Vedran, Snežana Marinković, Jasna Plavšić, and Andrija Radović.
2023. "Service Life Design of Concrete Structures Made of High-Volume Limestone Powder Concrete—Case of the Carbonation-Induced Corrosion" *Buildings* 13, no. 12: 3112.
https://doi.org/10.3390/buildings13123112