# Optimization of Mass Concrete Construction Using a Twofold Parallel Genetic Algorithm
## 4 Case Study
### Design Variables  
The design variables are the following:  
**The type of concrete \((Ty_{c})\):** Four typical massive concrete mixes, taken from the data bank of the Laboratory of FURNAS [27], were elected as the possible choices for the present case study. FURNAS is the company responsible for the generation and distribution of electricity in the southeastern region of Brazil. Its data bank comprises comprehensive thermo-chemo-mechanical studies of more than 260 massive concrete mixes from some of the most important hydroelectric power plants in the world [28].  
The composition of each concrete is presented in Table 1.  
The main chemical properties, which drive the hydration reaction of the several concretes are:  
(a) The activation energy \((Ea)\), which was considered as constant for all materials:  
\[Ea=(4000K)\cdot R\ \forall Ty_{c}\]  
(b) The normalized affinities, which were derived from the adiabatic temperature rise curves obtained from the data bank referenced in [28] (see Figure 4). The derivation was carried out using the equation which govern the problem in adiabatic conditions (see [14] for details).  
The thermo-mechanical properties are displayed on Table 2, where \(f_{1/00}\), \(f_{c,\infty}\) and \(E_{\infty}\) are, respectively, the tension strength, the compressive strength, and the Young's modulus for complete hydration.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \(Ty_{c}\) & **Cement** & **Fly-Ash** & **Water** & **Fine Aggregate** & **Coarse Aggregate** & **Entrained Air** & **Retardant/Plasticizer** \\ \hline
1 & 400.0 & & 180 & 610.0 & 1193.0 & 0.080 & 0.800 \\
2 & 337.6 & 56.8 & 190 & 596.9 & 1124.0 & 0.105 & 0.844 \\
3 & 229.2 & 50.3 & 187 & 629.7 & 1138.9 & 0.940 & 0.748 \\
4 & 366.4 & & 185 & 632.0 & 1204.0 & & 0.841 \\ \hline \end{tabular}
\end{table}
Table 1: Concrete composition in kg/m\({}^{3}\).  
Figure 3: Geometric characteristics and finite element mesh of the simulated foundation.  
**The placing temperature:** the set defining the placing temperatures was defined as composed by 16 possible discrete placing temperatures. The minimum possible cooling temperature was considered to be \(P_{T_{min}}=8~{}^{\circ}\)C and the highest temperature was taken as the environmental average temperature, \(P_{T_{max}}=26~{}^{\circ}\)C. Therefore, the set of possible placing temperatures can be written as:  
\[P_{T}(^{\circ}\text{C})\in\{8;9;10;\ldots;19;20;22;24;26\} \tag{15}\]  
**The height of the lifts:** the following values were adopted for the height of lifts:  
\[H_{l}(\mathfrak{m})\in\{0.25;0.50;0.75;1.00;1.25;1.50;1.75;2.00\} \tag{16}\]  
Each height implies a corresponding number of lifts, which is estimated according to Equation (5). Thus, the total number of lifts for each height is given by, respectively:  
\[N_{l}\in\{8;4;3;2;2;2;2;1\} \tag{17}\]  
**The placing frequency:** the time required for treatment of the horizontal joints and also for dissipation of the heat released by the hydration reaction determines the placing schedule for pouring the subsequent lifts. For the case study here presented the following frequencies were adopted for placing the concrete lifts:  
\[P_{f}(\text{days})\in\{6,7,8;\ldots;13\} \tag{18}\]