## 3 Results of the Parametric Study
In addition, the volume of concrete is shown in Figure 10: the trend of adjustment is parabolic, as in the case for reinforcing  
Figure 8: Relation between embodied energy and cost. Figure 7: Relation between embodied energy and cost for the wall heights of the study, in m.  
steel, with the expression of concrete volume for the embodied energy optimization being \(V_{\text{cs}}\) = 0.0433 \(H^{2}-0.3137\)\(H\) + 2.2213, with a R\({}^{2}\) = 0.9984 for the stem, and \(V_{\text{cf}}\) = 0.0881 \(H^{2}-1.294\)\(H\) + 5.8902, with a R\({}^{2}\) = 0.9969 for the footing. The expression of the global volume of concrete adjusts to \(V_{c}\) = 0.1313 \(H^{2}-1.6074\)\(H\) + 8.11, with a R\({}^{2}\) = 0.9989. You can observe that the embodied energy optimization gives a higher value of concrete volume than the cost optimization in contrast with the reinforcing steel amount, where the embodied energy gives a lower amount. Both optimizations have resulted in a concrete compressive strength of 25 MPa (C25/30) and B500 steel grade for all cases studied. This is because the cost and energy consumed increase as the resistance of the concrete increases and, therefore, varying the geometry and modifying the quantities of materials gives better results than varying the characteristic resistance of the concrete. Figure 10: Relation between volume of concrete and wall height. Figure 9: Relation between reinforcement ratio and wall height. Once the cost, energy, and the amount of materials were obtained, the geometrical variables obtained by the optimization procedures were studied to analyze the variations between cost and energy results. The largest differences between the geometrical variables were produced in the stem thickness (\(s_{t}\)) and in the buttress distance (\(b_{d}\)), while the difference between the foundation geometry obtained by the two optimization objectives is negligible, giving both optimization objectives the same values. Figure 11 shows the values obtained at the stem thickness (\(s_{t}\)). It can be observed that, from 6 to 11 m, the stem thickness obtained is 0.25 m for the two optimizations, but from 11 m of wall height upwards, the embodied energy optimization takes on a parabolic trend equal to \(s_{t}=0.0028\)\(H^{2}-0.0607\)\(H+0.5809\), with a R\({}^{2}=0.9533\). The cost optimization shows higher values of stem thickness from 9 m upwards compared with the embodied energy expression. The values obtained from the optimization take the lower limit imposed by the constructive facility of these types of structures; from this point, a greater thickness of wall is needed to resist the efforts. Figure 12 displays the results for the buttress distance, showing that the embodied energy optimization takes lower values for the buttress distances. A shorter distance allows a reduction in the flexural moments and, as a consequence, the need for reinforcing steel at the expense of increasing the concrete amount. This result shows how embodied energy optimization allows us to reduce the amount of reinforcing steel to reach a lower amount of total embodied energy. The expression of the linear trend obtained is \(b_{d}=0.0567\)\(H+2.4546\), with a R\({}^{2}=0.4435\). Furthermore, the results obtained by this optimization have been compared with the Calavera recommendations [41] in Figure 13; as can be seen, the cost optimization is inside the area defined by the geometrical limits defined as the buttresses distance by Calavera (\(H/3\) to \(H/2\)), while the energy optimization is only inside from 6 to 10 m.  
From a 10 m wall height, energy optimization takes lower values from the distance between buttresses. In addition, the comparison between the footing thickness obtained by this optimization procedure and the values provided by [PERSON] [41] were compared.