## 2 Materials and Methods
### Sustainability Indicator  
Sustainability can be evaluated using the sustainability indicator \(k_{\mathrm{SB}}\), which has already been described in details, and the cost of the concrete mixture has been considered (material and production) to obtain a modified indicator, i.e., \(k_{\mathrm{SB,C}}\)[34; 36; 47]. The methodology used was based on previous published findings [35]. It should be noted that the cost of the material is mostly dependent on the region or country. The present analysis focused on the values for the USA. As the design of the concrete structure ensures structural safety and serviceability, along with durability, robustness, sustainability, and resilience, the sustainability indicator \(k_{\mathrm{SB,C}}\) can be incorporated to create a rank of concrete mixtures. The main advantage of \(k_{\mathrm{SB,C}}\) is its complexity, which includes all aspects, namely, strength, resilience, ecology, and economy. Equation (1) [34] was used for the computation of \(k_{\mathrm{SB}}\):  
\[k_{\mathrm{SB}}=\frac{\frac{R}{L_{\mathrm{ref}}}\times\frac{L}{L_{\mathrm{ref} }}}{\frac{E}{E_{\mathrm{ref}}}} \tag{1}\]  
where:  
* \(R\) is the performance--suitable for the mechanical characteristics of concrete, namely, compressive strength [MPa]  
Figure 1: Composition of the cementitious materials of concrete mixtures.  
* \(L\) is the service life--using a suitable analytical model (see e.g., [6; 7]), the service life of \(L\) [years] is then determined. Instead of the model, alternatively, a quantity characterizing the service life related to a certain degradation phenomenon can be used for \(L\)--in the present case, it is a diffusion parameter used to calculate the resistance of concrete to chloride ions and in connection with corrosion of reinforcement [9; 10]
* \(E\) is the eco-cost, i.e., the amount that could be spent to reduce the environmental impact to a sustainable level. It includes the impact of mining and processing of materials
* \(R_{\text{ref}}\), \(L_{\text{ref}}\), and \(E_{\text{ref}}\) are optional values, in this case, relevant to the reference concrete mixture (OPC).  
The extension of the sustainability indicator by the cost of the material can be considered in Equation (2) [36] to obtain \(k_{\text{SB,C}}\):  
\[k_{\text{SB}}=\frac{\frac{R}{L_{\text{ref}}}\times\frac{L}{L_{\text{ref}}}}{ \frac{E}{L_{\text{ref}}}\times\frac{C}{C_{\text{ref}}}} \tag{2}\]  
The description of the parameters is listed below:  
* \(C\) is the cost, i.e., the price of all materials according to the specific composition of concrete, depending mainly on the region or country
* \(C_{\text{ref}}\) is a cost related to the reference concrete. Considering these parameters, it is possible to categorize concrete mixtures based on data obtained from previous research studies. The highest values of \(k_{\text{SB}}\) and \(k_{\text{SB,C}}\) show the most advantageous concrete mixture in the studied group in terms of sustainability. Details of the entire methodology for evaluating the sustainability indicator are described comprehensively in a published study [36].  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \(D_{\text{c}}\) & \(D_{\text{c}}\) & \(D_{\text{c}}\) & \(D_{\text{c}}\) & \multicolumn{2}{c}{**Strength**} & \multicolumn{2}{c}{**Strength**} & \multicolumn{2}{c}{**Strength**} & \multicolumn{2}{c}{**Eco-Costs**} & \multicolumn{1}{c}{**Costs**} \\
**Mix ID** & **(28 Days)** & **(56 Days)** & **(91 Days)** & **(28 Days)** & **(56 Days)** & **(91 Days)** & **(56 Days)** & **(91 Days)** & **(6/m\({}^{3}\))** & **[6/m\({}^{3}\)]** \\  & \(\times 1