## 3 Materials and Methods
### Model of Accounting for Carbon Footprint in the Materialization Stage of Prefabricated Housing  
CO\({}_{2}\) emissions make up the majority of the carbon footprint associated with the assembly phase of prefabricated structures. For this research, the carbon dioxide footprint is characterized as the amount of CO\({}_{2}\) emissions. Using the carbon emission coefficient approach and system boundary setup, the carbon dioxide and greenhouse gas emissions of the prefabricated building assembly phase were calculated. \[E_{c}=E_{c1}+E_{c2}+E_{c3}+E_{c4}+E_{c5} \tag{1}\]  
In Equation (1), \(E_{c}\) is the total carbon footprint, and \(E_{c1}\), \(E_{c2}\), \(E_{c3}\), \(E_{c4}\), \(E_{c5}\) are the carbon emissions of the building material production phase, conveyance of building materials phase, component manufacturing phase, component phase of transportation, and the building phase, respectively. \[E_{c1}=\sum_{i=1}^{n}Q_{i}\bullet F_{i} \tag{2}\]  
Figure 2: Cause-and-effect diagram for a carbon footprint. In Equation (2), \(Q_{i}\) represents the total mass of the \(i\) material and \(F_{i}\) represents the emission factor of the \(i\) material. \[E_{c2}=\sum_{j=1}^{m}\left(\sum_{i=1}^{n}D_{i,j}\times Q_{i}\right)\times F_{j} \tag{3}\]  
In Equation (3), The number of ways to carry construction supplies is represented by the symbol \(m\), and \(D_{i,j}\) denotes the transportation distance of transporting material \(i\) using transportation mode \(j\). \(F_{j}\) represents the factor of carbon dioxide emissions for transportation mode \(j\). \[E_{c3}=\sum_{h=1}^{s}\sum_{g=1}^{r}\left(E_{g,h}^{1}\times V_{g}\right)\times F _{h}+\sum_{g=1}^{r}\left(L_{g}^{1}\times V_{g}\right)\times F_{L} \tag{4}\]  
In Equation (4), \(r\) is the number of types of prefabricated components produced, \(S\) is the number of types of energy consumed, \(E_{g,h}^{1}\) is the consumption of energy \(h\) for the production of prefabricated components \(g\) per unit volume, \(V_{g}\) is the volume of prefabricated components \(g\), \(F_{h}\) is the carbon emission factor for energy \(h\), \(L_{g}^{1}\) is the consumption of labor for the production of prefabricated components \(g\), and \(F_{L}\) is the carbon emission factor for the activities of personnel. \[E_{c4}=\sum_{j=1}^{p}\left(\sum_{g=1}^{r}D_{g,j}\times Q_{g}\right)\times F_{j} \tag{5}\]  
In Equation (5), \(p\) is the number of types of modes of transportation used to transport the component to the construction site, \(D_{g,j}\) is the distance transported by transporting the component \(g\) by mode \(j\), and \(Q_{g}\) is the total mass of the \(g\) component. \[E_{c5}=\sum_{h=1}^{w}\sum_{g=1}^{r}\left(E_{g,h}^{2}\times V_{g}\right)\times F _{h}+\sum_{g=1}^{r}\left(L_{g}^{2}\times V_{k}\right)\times F_{L} \tag{6}\]  
In Equation (6), \(w\) is the number of energy types consumed, \(E_{g,h}^{2}\) is the consumption of energy \(h\) for the construction of a unit volume of prefabricated \(g\) components, \(V_{g}\) is the volume of prefabricated \(g\) components, and \(L_{g}^{2}\) is the labor consumption for the construction of prefabricated \(g\) components. A Model for Assessing the Impact Factors of Carbon Footprint Accounting in the Materialization Phase of Prefabricated Housing  
In order to make clear the connections between the elements that influence the carbon footprint of prefabricated housing during the materialization stage, as well as the extent to which each component influences the carbon footprint of assembled houses during this stage, in this study, we propose to use the DEMATEL-ISM-MICMAC approach to build a model of the factors impacting the carbon footprint during this stage of prefabricated housing. First, we asked 12 experts from colleges and universities, design institutes, prefabricated component factories, and construction companies to screen the initial influencing factors and derive the indicator system based on the data and indicator system required by the DEMATEL-ISM-MICMAC method.