## 5 Sustainability Analysis for the Proposed Method  
Besides the economic analysis, environmental sustainability is also an important factor nowadays to influencing retrofit planning. Carbon emission is a commonly used index relevant to the ecological environment. The carbon emission calculation for a building can be divided into four stages: material preparation, construction, building use and demolition. The carbon emission model in the life-cycle period is [52]  
\[P_{LC}=P_{1}+P_{2}+P_{3}+P_{4} \tag{7}\]  
where \(P_{LC}\) is the carbon emission in the life-cycle period; and \(P_{1}\), \(P_{2}\), \(P_{3}\), and \(P_{4}\) are the carbon emissions during material preparation, construction, building use and demolition, respectively. \(P_{1}\) positively correlates to material usages, their carbon emission factors, and their hauling distances. \(P_{2}\) positively correlates to the amount of required equipment and their carbon emission factors, and the number of workdays. In this study, the carbon emission during the building use (\(P_{3}\)) for the original frame and for the retrofitted frame is assumed to be almost the same, so \(P_{3}\) is not further discussed later in the calculation. \(P_{4}\) positively correlates to \(P_{1}+P_{2}\), and so usually 10%(\(P_{1}+P_{2}\)) is adopted in the calculation. The specific estimation process of carbon emission is as follows. \(P_{1}\) can be calculated using the following equation  
\[P_{1}=\sum_{i=1}^{n}M_{i}\times\left(EF_{cl,i}+L_{i}\times EF_{j,i}\times 10^{ -4}\right) \tag{8}\]  
where \(M_{i}\) is the total usage of \(i\)th material; \(EF_{cl,i}\) is the emission factor of \(i\)th material (about 0.2 for steel and 0.15 for concrete [52]); \(L_{i}\) is the hauling distance of the \(i\)th material; \(EF_{j,i}\) is the emission factor of \(i\)th material during hauling (about 0.07 for railway hauling, 1.65 for highway hauling, and 0.15 for waterway hauling [52]); and \(n\) is the number of used material types. Figure 15: Median values of repair times under different earthquake intensities (parallel construction): (a) 3D original frame, frequent earthquake; (b) 3D retrofitted frame, frequent earthquake; (c) 3D original frame, occasional earthquake; (d) 3D retrofitted frame, occasional earthquake; (e) 3D original frame, rare earthquake; (f) 3D retrofitted frame, rare earthquake. \(P_{2}\) can be calculated using the following equation  
\[P_{2}=\sum_{j=1}^{n}N_{j}\times EF_{sg,j}+R\times 0.012 \tag{9}\]  
where \(N_{j}\) is the amount of equipment of type \(j\); \(EF_{sg,j}\) is the emission factor of \(j\)th equipment; \(R\) is the number of workdays; 0.012 is the estimated value of carbon emission of a person per day; and \(n\) is the number of equipment types. The original frame is collapsed and the retrofitted frame is in a repairable state under a rare earthquake. Therefore, the original frame needs complete replacement, which leads to extra demolition (\(P_{4}\)) and much more material usage (\(P_{1}\)) for rebuilding than for retrofitting. According to Equation (8), if the hauling type is the same, \(P_{1}\) for original frame will be much larger than \(P_{1}\) for the retrofitted frame, because the \(M_{i}\) for the original frame (in the case of total replacement) will be much larger than that of the retrofitted frame (in the case of repair). It is a difficult thing to estimate how much equipment will be used in the replacement process without a detailed construction organization analysis. However, it is easy to see that more equipment needs to be used in the replacement process than in the repair process. As shown in Table 11, \(R\) is 482 days and 53 days for the original frame and retrofitted frame, respectively. Therefore, according to Equation (9), \(P_{2}\) for original frame will be much larger than \(P_{2}\) for the retrofitted frame. Since \(P_{3}=10\%\) (\(P_{1}+P_{2}\)) is adopted in the calculation, \(P_{3}\) for original frame is larger than \(P_{3}\) for the retrofitted frame.