# The Relationship between Concrete Strength and Classes of Resistance against Corrosion Induced by Carbonation: A Proposal for the Design of Extremely Durable Structures in Accordance with Eurocode 2

^{*}

## Abstract

**:**

## 1. Introduction

_{2}) emissions into the atmosphere affects carbonation depth, making concrete carbonation a serious problem [15]. The service life of a structure is the period of time between the construction of the structure and the moment in which its performance fails to meet the requirements of the users [16]. According to [7], service life is defined as the sum of the corrosion initiation time (or the time the pollutant takes to affect the thickness of the whole concrete cover), and the time needed for the propagation of the corrosion (which is the time between the initiation period and the moment when the level of corrosion degradation is unacceptable). However, regarding carbonation, damage usually occurs at the instant when the carbonation front comes into contact with the reinforcement [17,18]. So, when assessing service life, the period of time corresponding to the propagation of corrosion is not considered. This is supported by the fact that when the carbonation front reaches the reinforcing bar, the damage to the structure is of a significant level.

_{2}over time can be evaluated.

_{2}content, relative humidity, and temperature), exposure conditions (protection from the rain), concrete material (water/binder ratio (w/b), cement type, and content), the amount of CO

_{2}in the environment, and pore size distribution [18,19,25,26,27].

_{2}diffusion is usually modeled using Fick’s first law. So, the carbonation coefficient or carbonation rate constant, K, (mm/year

^{0,5}) is calculated using the ‘square root of time’ relationship, i.e., as the ratio between the attack penetration depth (mm) and the square root of the exposure time to CO

_{2}(year) [7,28]. The square root model has been verified both in the laboratory and in the field [29].

_{2}into concrete easier, while, for a fixed water–cement ratio, the use of a higher cement content in the concrete mix improves concrete durability [31]. Moreover, compressive strength influences the porous structure of concrete, and so it is a key factor in the diffusion of carbon dioxide through the material, which also makes it a key factor in carbonation. Generally, a high compressive strength is associated with more compact concrete mixes and with concretes with a higher clinker content. Additionally, due to the chemical reactions during carbonation, the higher the clinker content, the slower the carbonation coefficient is [15].

_{min,dur}to protect reinforcement from corrosion. These cover values depend on the different classes of exposure and are defined for 50 and 100 years of design service life [32,34,35].

_{2}(year) or the time when corrosion starts. In the Spanish Structural Code [35] the apparent carbonation coefficient, K

_{app,carb}, is obtained as a function of the mean compressive strength of concrete and other factors, such as the amount of entrained air and the type of binder.

_{min,dur}is tabulated by classifying a structure in two ways: exposure class (EC) and exposure resistance class (ERC). The minimum levels of concrete cover for durability needed that can withstand carbonation are presented in a tabular format for 50 and 100 years of design service life.

## 2. Materials and Methods

#### 2.1. Carbonation Front, a Deterministic Point of View

_{2}) formed in the hydration process of cement generates an alkaline environment as a result of the OH

^{−}ions that it generates in the presence of water [40]. Due to the porous nature of concrete, atmospheric CO

_{2}slowly penetrates through the pores of the concrete and comes into contact with calcium hydroxide, with which it reacts and forms calcium carbonate (CaCO

_{3}), which causes a drop in the concrete pH. This reaction causes the high and low pH zones to be divided by the carbonation front (see Figure 2).

_{2}concentration, humidity, etc.) and concrete characteristics (w/c ratio, type of cement, etc.) and it varies significantly from one structure to another [28]. In [28], the mean compressive strength is used to estimate K using a regression analysis.

_{2}to penetrate the concrete as it is a gas. Therefore, the maximum carbonation rate is found at levels of intermediate humidity, and the most unfavorable scenarios are the wet–dry cycles. It is interesting to note that carbonation hardly occurs in either very dry concrete (because of the absence of water) or in completely saturated concrete (as CO

_{2}cannot move through the pores that are full of water).

_{ap,carb}is the apparent carbonation coefficient in mm/year

^{0.5}so x(t) is obtained in mm, c

_{env}is a coefficient that depends on environmental conditions (see Table 1). c

_{air}is 1.0 if air-entrained concrete with less than 4.5% of entrained air (of the volume of the concrete) is used. If the amount of entrained air is greater than or equal to 4.5%, then c

_{air}= 0.7. In Equation (2), a and b are dimensionless parameters that depend on the type of binder (see Table 2).

_{env}(see Table 1) according to [35], Equation (2). In Figure 3, c

_{air}= 1 is considered.

_{env}), the influence of concrete compressive strength is greater.

_{env}= 1.0 (structure sheltered from the rain), c

_{air}= 1, Portland cement, and f

_{ck}= 50 MPa is plotted, together with the carbonation depth obtained from the Portuguese standard [28] for equivalent conditions. Figure 4 corresponds to: c = 400 ppm of the environmental carbon dioxide concentration (adopted as a value of reference in prEN 1992 [34]), f

_{ck}= 50 MPa, f

_{cm}= (f

_{ck}+ 8) MPa, k

_{0}= 3 (standard test conditions), k

_{2}= 1 (standard curing), and exposure class XC3 (moderate humidity, which corresponds to the external concrete sheltered from rain in prEN 1992 [34]). According to Eurocode 2, f

_{ck}is the characteristic concrete cylinder compressive strength and f

_{cm}is the mean concrete cylinder compressive strength.

_{real}), the average number of rainy days per year with a volume of precipitation water that is over 25 mm (h

_{Nd}), and the probability of driving rain obtained from the average distribution of the wind direction during rain events (p

_{sR}). The two last parameters should be obtained from weather station data. In Figure 4 (shaded area), the range of values of the carbonation depth according to [36] when HR

_{real}varies between 0 and 100% has also been represented for h

_{Nd}= 182 days (half a year) and p

_{sR}= 0 (horizontal structural element).

#### 2.2. Minimum Cover Required for Protection against Carbonation in prEN 1992

_{min,dur}) for protection of the reinforcement against corrosion induced by carbonation depends on the design service life, the exposure class, and the exposure resistance class (ERC). Each ERC is identified as XRC followed by a number that corresponds to the carbonation rate (see Equation (1)) related to the 90% fractile of the depth of the carbonation front (in mm) after 50 years and under the following reference conditions: 400 ppm CO

_{2}in a constant 65%-RH environment and at 20 °C.

_{min,dur}are presented in a tabular format. The values given by prEN 1992 are shown in Figure 5, where XC is the exposure class for carbonation and XRC is the resistance class against corrosion caused by carbonation. To facilitate the identification of the different exposure classes and service design lives, discrete values given by prEN 1992 [34] have been connected with lines in Figure 5.

## 3. Results

#### 3.1. Continuous Formulation of the Carbonation front Based on Eurocode 2

_{ck}in [35] as the characteristic concrete strength, which corresponds to a confidence level of 95%. Equation (4) is also proposed by the European standard [33,41,42]. So, the first change to make in the new expression Equation (3) to fit prEN 1992 [34], is to obtain the compressive concrete strength corresponding to the 90% fractile. Assuming that the compressive strength of concrete follows a standard normal distribution, this value can be obtained by using basic statistical concepts from the following system of equations:

_{ck}+ 1.8, which is the value in brackets in Equation (3).

_{ck}in Equation (3) have been adjusted so that they match the values given by prEN 1992 [34], Figure 5. In this work, it has been assumed that each resistance class against corrosion induced by carbonation (XRC) corresponds to a value of the characteristic concrete cylinder compressive strength (f

_{ck}) for each type of binder and entrained air content. By using this approach, the corrected environmental coefficient (c

^{*}

_{env}, see Table 1) in Equation (3) has been obtained from a least square regression for the case corresponding to the most common type of cement and with no entrained air (i.e.,: Portland cement and air-entrained concrete with less than 4.5% of entrained air, in volume of the concrete). So, according to [35] the following values for the parameters in Equation (3) are considered as: c

_{air}= 1.0, a = 1800, and b = −1.7; see Table 3.

^{*}

_{env}for each exposure class in prEN 1992 [34] (XC) are summarized in Table 3.

_{ck}). The corresponding values of characteristic concrete strength (f

_{ck}), which are the unknown of the adjustment, are adjusted for each type of binder (i.e.,: Portland, Portland +28% fly ash, and Portland + 9% silica fume, see Table 2), and for the two cases related to the entrained air content (under or over 4.5% of entrained air of the volume of the concrete) in [35]. A least square regression has been used for the adjustment.

_{min,dur}) for the four exposure classes, XC1 to XC4, given by prEN 1992 [34] (see Figure 5) are also represented, and they are linked by dashed straight lines in Figure 6, where the term “approx” identifies the adjusted curves. Figure 6a,b represents the design service lives of 50 and 100 years, respectively.

_{ck}could be suitable for obtaining a first approximation of the XRC class, as proposed in Table 4.

#### 3.2. Case Studies

#### 3.2.1. The Green Tunnel on the London–Birmingham High Speed Railway Line

_{air}= 1.0 and c

^{*}

_{env}= 0.90 for XC3 class and c

^{*}

_{env}= 0.95 for XC4 (see Table 3).

_{ck}= 50 MPa and for these two exposure classes. Figure 7 shows that, as a first approximation, the life expectancy of the Green Tunnel is about 500 years. This result is based on the continuous approximation proposed in this work (Equation (3)), which is based on prEN1992 [34].

#### 3.2.2. Camino de Ronda Street Buildings (Granada, Spain)

## 4. Limitations of the Study

## 5. Conclusions

- The presented study proposes a new continuous formulation for the carbonation front.
- The formulation is based on the ‘square root of time’ expression given by the relevant literature and is in accordance with the minimum cover proposed by prEN 1992.
- The minimum cover required to protect against carbonation can be determined from the proposed expression, which is formulated as a function of the compressive strength of concrete.
- The proposed expression allows for the indicative strength classes against corrosion induced by carbonation proposed by prEN 1992 to be considered.
- The new expression is shown to be a useful tool for the design of extremely durable structures.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Conceptual scheme of a reinforcement corrosion process as a function of time, adapted from [7].

**Figure 3.**Evolution of the carbonation front for Portland cement according to [35].

**Figure 4.**Comparison of the evolution of the carbonation front for Portland cement according to the Spanish Structural Code [35] and the Portuguese standard LNEC E-465 [28] for XC3 exposure class, c

_{air}= 1.0, and f

_{ck}= 50 MPa. The range of values of the carbonation depth according to Annex C of CEB Bulletin 34 [36] for h

_{Nd}= 182 days, p

_{sR}= 0 for HR

_{real}ranging between 0 and 100% is shown as a shaded area.

**Figure 5.**Minimum concrete cover for protection against oxidation induced by carbonation (XC1 = dry, XC2 = wet, or permanent high humidity, XC3 = moderate humidity, XC4 = cyclic wet and dry).

**Figure 6.**Relationship between the XRC class and the characteristic concrete strength for Portland cement with a volume of entrained air of under 4.5% of the volume of the concrete. Design service lives of (

**a**) 50 and (

**b**) 100 years.

Environment | c_{env} |
---|---|

Sheltered from the rain | 1.0 |

Exposed to rain | 0.5 |

Buried elements, above the water table | 0.3 |

Buried elements, below the water table | 0.2 |

Binder | a | b |
---|---|---|

Portland cement | 1800 | −1.7 |

Portland cement +28% fly ash | 360 | −1.2 |

Portland cement + 9% silica fume | 400 | −1.2 |

**Table 3.**Environmental coefficients adjusted (${\mathrm{c}}_{\mathrm{env}}^{*}$) to fit the minimum cover for carbonation in prEN 1992 [34].

Adjusted Exposure Classes for Carbonation | XC1 | XC2 | XC3 | XC4 |
---|---|---|---|---|

${\mathrm{c}}_{\mathrm{env}}^{*}$ | 0.45 | 0.60 | 0.90 | 0.95 |

**Table 4.**Relationship between the resistance class against corrosion induced by carbonation (XRC) and the characteristic concrete cylinder compressive strength (f

_{ck}[MPa]) for each type of binder and volume of entrained air content.

Type of Binder | Portland | Portland + 28% Fly Ash | Portland + 9% Silica Fume | ||||
---|---|---|---|---|---|---|---|

Entrained Air | >4.5% | <4.5% | >4.5% | <4.5% | >4.5% | <4.5% | |

ERC in prEN 1992 [34] | XRC 0.5 | 63 | 80 | 94 | 128 | 103 | 139 |

XRC 1 | 49 | 60 | 66 | 90 | 73 | 98 | |

XRC 2 | 36 | 45 | 44 | 59 | 48 | 65 | |

XRC 3 | 32 | 40 | 36 | 49 | 39 | 54 | |

XRC 4 | 28 | 35 | 30 | 41 | 33 | 45 | |

XRC 5 | 25 | 31 | 26 | 35 | 28 | 38 | |

XRC 6 | 22 | 27 | 21 | 29 | 23 | 32 | |

XRC 7 | 21 | 26 | 20 | 27 | 21 | 29 |

**Table 5.**Indicative strength class for corrosion induced by carbonation for each exposure class according to EN 206 [41].

Exposure Class | XC1 | XC2 | XC3/XC4 |
---|---|---|---|

Strength class | ≥C20/25 | ≥C25/30 | ≥C30/37 |

Element | Precast/Cast In Situ | Nominal Cover * | |
---|---|---|---|

Inner Face | Outer Face | ||

Arch, Arch wall, Side Wall, Footing | Precast (C50/60) | 45 mm | 55 mm |

Central Wall | Precast (C50/60) | 45 mm | 45 mm |

Invert/Base Slab | Cast-in situ (C50/60) | 60 mm | 70 mm |

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**MDPI and ACS Style**

Gil-Martín, L.M.; Hdz-Gil, L.; Molero, E.; Hernández-Montes, E.
The Relationship between Concrete Strength and Classes of Resistance against Corrosion Induced by Carbonation: A Proposal for the Design of Extremely Durable Structures in Accordance with Eurocode 2. *Sustainability* **2023**, *15*, 7976.
https://doi.org/10.3390/su15107976

**AMA Style**

Gil-Martín LM, Hdz-Gil L, Molero E, Hernández-Montes E.
The Relationship between Concrete Strength and Classes of Resistance against Corrosion Induced by Carbonation: A Proposal for the Design of Extremely Durable Structures in Accordance with Eurocode 2. *Sustainability*. 2023; 15(10):7976.
https://doi.org/10.3390/su15107976

**Chicago/Turabian Style**

Gil-Martín, Luisa María, Luisa Hdz-Gil, Emilio Molero, and Enrique Hernández-Montes.
2023. "The Relationship between Concrete Strength and Classes of Resistance against Corrosion Induced by Carbonation: A Proposal for the Design of Extremely Durable Structures in Accordance with Eurocode 2" *Sustainability* 15, no. 10: 7976.
https://doi.org/10.3390/su15107976