# The Use of Volcanic Powder as a Cement Replacement for the Development of Sustainable Mortars
## 2 Materials and Methods
### Evaluation of Greenhouse Gas (GHG) Emissions  
Equation (4) has been proposed to calculate the total greenhouse gas emissions (GHG\({}_{\text{tot}}\) in kgCO\({}_{2}\)/ton) in relation to the production and transport of the mortars studied:  
\[\text{GHG}_{\text{tot}}\;=\;\text{GHG}_{\text{raw}}+\text{GHG}_{\text{sub}} \tag{4}\]  
where: GHG\({}_{\text{raw}}\)(kgCO\({}_{2}\)/ton) is the greenhouse gases emitted by the original materials and is calculated according to Equation (5):  
\[\text{GH}_{\text{raw}}=\sum_{\text{f}\in\text{CV}\;\text{k}}\sum_{\text{ = 1}}^{\text{n}}\text{P}_{\text{k}}\cdot(1-\text{R}_{\text{k}})\cdot\theta_{\text {k}}^{\text{f}} \tag{5}\]  
GHG\({}_{\text{sub}}\)(kgCO\({}_{2}\)/ton) is the greenhouse gases of the replacement materials and is calculated according to Equation (6):  
\[\text{GH}_{\text{sub}}=\sum_{\text{f}\in\text{CV}\;\text{k}}\sum_{\text{ = 1}}^{\text{m}}\text{P}_{\text{k}}\cdot\text{R}_{\text{k}}\cdot\theta_{\text {k}}^{\text{f}} \tag{6}\]  
where n represents the total original raw materials (in the control mortar), m represents the total replacement raw materials, f represents the life cycle stages (CV) to be analyzed, and P\({}_{\text{k}}\) is the relation between the raw material k and the total mass of the material (kg/kg). In the case of the replacement raw materials, it is the relation of the original raw materials and total mass of the material. R\({}_{\text{k}}\) is the replacement ratio (where replaced) or added ratio (where a replacement) of the raw material k. \(\theta_{\text{k}}^{\text{f}}\) is the CO\({}_{2}\) generation ratio of the raw material k in the f phase of the life cycle (kgCO\({}_{2}\)/ton), in whichis the amount of emissions associated with the production phase of the raw material k and \(\theta_{\rm k}^{\rm t}\) is the amount of emissions associated with the transport of the raw material k, which is calculated as follows:  
\[\theta_{\rm k}^{\rm t}=d_{\rm k}\text{-G} \tag{7}\]  
where \(d_{\rm k}\) represents the distance thatthe raw material is transported (km) and G represents the emissions associated with transporting one ton per kilometer (kgCO2/(ton\(\cdot\)km)).  
The factors and results related to the CO2 emissions (in kgCO2 per ton of mortar) and the embodied energy for the mortars analyzed, derived from the previously explained procedure, are shown in Table 2. The factors corresponding to the cement were taken from the \"Inventory of Carbon and Energy\" Carbon and Energy (2018). For the sand and volcanic powder, the energy consumed in the sifting process and the associated emissions were estimated (2018). In order to calculate the emissions emitted when transporting the raw materials, the database for Conversion Factors for Greenhouse Gases from the UK government was considered (2018).  
Then, to compare the sustainability of the material used (volcanic powder) and the original one (cement), the SUB-RAW Index was applied (2018), which is defined as follows:  
\[\text{SUB}-\text{RAW index}=\left[\log(\text{EE}_{\text{raw}})-\log(\text{ EE}_{\text{sub}})+\log\!\left(\theta_{\rm c}^{\rm P}\right)-\log\!\left(\theta_{\rm VP }^{\rm P}\right)\right]/2 \tag{8}\]  
where EE\({}_{\text{raw}}\) is the embodied energy of the cement (replaced material) (MJ/kg) and EE\({}_{\text{sub}}\) is the embodied energy of the replacement material (MJ/kg).  
For this index, which can take values between \(-9\) and \(9\), the more positive the value, the greater is the relative sustainability of the analyzed material.