# A Durability Prediction Method for Historical Square Rebar Reinforced Concrete Buildings
## 4 The Durability Prediction Calculation Methods for Square Rebar Components
### The Time before Rebar Corrosion  
The time elapsed before corrosion for rebar depends on the carbonization life of the concrete. The calculation method for the time before rebar corrosion provided by GB/T 51,355 standard is positively related to the cover depth, which can also be considered as the carbonization depth before rebar corrosion, and negatively to the carbonization-resistant ability of the concrete, and is called as carbonization coefficient, \(k\). Since, in many cases, the rebar begins to corrode before or after the total carbonization of cover concrete, a carbonation residue parameter, \(x_{0}\), is induced to improve accuracy [18]. The calculation methods of GB/T 51,355 for the time before rebar corrosion are as follows:  
\[t_{i}=\left(\frac{c-x_{0}}{k}\right)^{2} \tag{3}\]  
\[x_{0}=\left(1.2-0.35k^{0.5}\right)\cdot\lambda_{c}-\frac{6.0}{m+1.6}(1.5+0.84k) \tag{4}\]  
\[k=3K_{kl}K_{co_{2}}K_{kl}K_{ks}T^{1/4}(1-RH)\times RH^{1.5}\left(\frac{58}{f_{ cu,e}}-0.76\right) \tag{5a}\] \[k=\frac{x_{c}}{\sqrt{t_{0}}} \tag{5b}\]  
where \(t_{i}\) is the time before steel rebar corrosion (years); \(c\) is the cover depth (mm); \(k\) is the carbonation coefficient; \(\lambda_{c}\) is an influencing factor due to cover depth and carbonization; m is a local environmental factor; \(K_{kl}\), \(K_{co_{2}}\), \(K_{kl}\) and \(K_{ks}\), are respectively the location factor, the CO\({}_{2}\) density factor, the construction factor and the working factor; RH is the environment humidity (%); \(T\) is the averaged environment temperature (\"C); \(f_{cu,e}\) is the estimated value of concrete compressive strength (MPa); \(x_{c}\) is the measured carbonation depth (mm); \(t_{0}\) is the time from the completion of the structure to the assessment. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Element Ranking** & **\(\phi\geq 95\%\)** & **95\% \textEquation (3) defines the time before rebar corrosion, relating to the cover depth, carbonation residue parameter and carbonization coefficient. Equation (4) states the carbonation residue parameter is dependent on empirical factors and the carbonization coefficient. The GB/T 51,355 standard provides two calculation procedures for carbonation coefficient: Equation (5a) is an empirical equation from extensive experiments and tests, while Equation (5b) is the definition of the carbonation coefficient, which is more accurate than the empirical equation. However, Equation (5b) requires small-invasive tests on structures. Many historical buildings are forbidden to use any invasive test method. In addition, the small-invasive test method is sometimes inappropriate for some critical structural components; thus, Equation (5a) is necessary for some projects. Although the factors contributing to concrete carbonization are the same for the historical concrete and the current concrete, the carbonization-resistant ability due to quality of the cement, the mix proportion for the concrete, the curing condition for the concrete and some more are different. Therefore, the factors and form of the empirical equations should be the same, but the constant factor should not be the same so that the variable situations can be reflected. Thus, Equations (3) and (4) can be kept for the historical concrete component cases, while Equation (5a) can be corrected through an introduction of a correction constant factor. In this study, the carbonation coefficient calculated by the Equation (5b) is taken as the target value, and a correction constant factor is introduced into the Equation (5a) for the corrected equation of carbonization coefficient for the historical concrete structure. The corrected equation is shown in Equation (6a). \[k^{\prime}=\alpha k \tag{6a}\]  
The data for correction constant factor is based on 12 historical concrete structures, including completion time of the structure, compressive strength of the concrete, thickness of concrete cover and measured carbonation depth.