## 4 Design Examples of Cantilever RC-Retaining Walls
### Numerical Dimension Analyses of Cantilever RC-Retaining Walls (Case 2)
#### 4.2.4 Investigation of the Influence of Concrete Cost Change (Case 2D)  
Concrete and steel are the main components of retaining wall construction which can be defined as two different structural materials that have various costs according to the related region. Due to this reason, the unit cost of these materials plays a significant role in the optimum design. To evaluate this situation, dual effect comparisons are conducted, and the unit cost of the concrete is set to be USD 50, USD 75, USD 100, USD 125, and USD 150, respectively. Firstly, the concrete cost effect is acquired with the change of excavation depths (Figure 24a-c). The ultimate base pressure 200 kPa, internal friction angle 30\({}^{\circ}\), unit weight of the soil 18 kN/m\({}^{3}\), and the surcharge load 0 kPa are assumed and shown for 7-, 9-, and 11-meter's excavation depths in Figure 24a-c. In general, the increase of the excavation depth leads to an increase of foundation dimensions, but the rates of increase are differentiated according to the change of unit cost of concrete material. This means that the influence of the increase of concrete cost is especially significant for relatively smaller excavation depths for the cases. In Figure 24a, the excavation depth is assumed 7 m. The minimum charge of the unit cost of concrete leads the designs to be constructed predominantly with a further volume of concrete. The dimension differentiation ratio between the prices that are used as the upper and lower limits of the concrete unit cost is calculated approximately 15% for this specific case. The increment of the excavation width reduces this ratio nearly to 6%. Furthermore, after a specific limit cost of concrete, the design is not changed (for H = 7 m the limit cost is USD 125, for H = 9 m the limit cost is USD 125 and for H = 11 m the limit cost is nearly USD 75). The effect of soil unit weight change against the cost of concrete influence is shown in Figure 24d-f. The depth of excavation is assumed 9 m, the ultimate soil pressure is taken as 200 kN/m\({}^{2}\), the internal friction angle is 30\({}^{\circ}\), and no surcharge load is applied. Overall, 14, 16, 40 kN/m\({}^{3}\) values are taken as the soil unit weight values, respectively. The increase of the unit weight of the soil causes to rise of the unbalanced forces of the system, and it leads to an increase in the width of the foundation as expected. This means that the increment of the unit cost of concrete contributes the dimensions to be the same after a limit cost value. The maximum dimension change occurs 10% for the condition that the dual effects of unit weight of soil and the cost of concrete are taken into account. In Figure 24g,h,j, the influence of internal friction angle change against the unit cost of concrete is investigated. Constant parameters are selected as the same as the previous case, but the internal friction angles are assumed to be 28, 32, 36\({}^{\circ}\), respectively. Maximum dimension change has occurred for the loosest soil conditions, and the influence ratio of the change is calculated maximum of 7%. The improvement of the soil properties leads to lessening the effect of concrete cost and striatens the effective rate on the total cost. Consequently, a similar behavior trend is exhibited for all the selected cases. The rise of concrete cost leads to an increase in steel amount through the design process to reduce the wall costs with the achievement of minimum sizing.