## 4 Design Examples of Cantilever RC-Retaining Walls
### Numerical Dimension Analyses of Cantilever RC-Retaining Walls (Case 2)
#### 4.2.2 Investigation of the Influence of Soil Property Change (Case 2B)  
The effects of the soil properties in the design of the wall are investigated by the use of different internal friction angles, unit weights, and ultimate bearing pressure values of the foundation with medium soil. Optimization analyses are conducted to acquire the width of the foundation base and integrated evaluations are shown in Figures 20-22. In Figures 20 and 21, the differentiation of foundation width is investigated by the use of twelve (12) internal friction angles (27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, and 38\({}^{\circ}\)) and seven (7) different soil unit weights (14, 15, 16, 17, 18, 19, and 20 kN/m\({}^{3}\)). The excavation depth is selected 6 and 10 m for Figures 20 and 21, respectively. The surcharge load is assumed not to be applied and the ultimate bearing pressure of the foundation soil is supposed 300 kPa for the cases analyzed. In Figures 20 and 21, it can be seen that the increase of the soil strength causes foundation base width to become narrow as is expected. The increase of the unit weight of the soil causes to raise the lateral active pressures acting on the wall sections. Therefore, the stability of the wall tried to be ensured by the enlargement of the wall foundation. Besides, the influence rate of the soil unit weight on the dimensions of the wall system is smaller than that of the soil strength when comparisons are conducted for a unit increase of related parameters. Figure 19: Change of retaining wall design against the change of excavation depth (\(\gamma=18\) kN/m\({}^{3}\)) (**a**) \(\Phi=30^{\circ}\); (**b**) \(\Phi=32^{\circ}\); (**c**) \(\Phi=34^{\circ}\). Figure 20: The change of foundation width against friction angle and soil unit weight (H = 6 m). Especially for Figure 20, the decrease of wall foundation base width against the increase of internal friction angle has exhibited irregularities for specific cases. These cases are shown with rectangular boundaries in Figure 20. The comparison of the traditional pre-design method and optimization approach of reinforced concrete retaining walls is explained with this situation. In the traditional pre-design method of retaining walls, the designer approximately selects the base and stem dimensions, checks them against stability. If the design is not safe, a trial and error procedure is applied. Then the allowable limits of the bearing pressure are computed, base shear and moment are evaluated. Provided that the largeness of base shear, it can be preferred to increase the embedment depth until the case satisfies. It will be proper to reduce the stem height to procure constant wall height. On the other hand, if the foundation base thickness is adequate, the toe and heel steel requirements are computed. Consequently, the traditional pre-design of reinforced concrete retaining walls primarily searches for the geotechnical stability criteria and structural design requirements for the second stage. It can be shown that this pre-design process involves much busywork and seems not to be convenient concerning  
Figure 21: The change of foundation width against friction angle and soil unit weight (H = 10 m). economy, sizing, and duration [48]. Compared to the conventional design method, the optimization techniques enable an integrated loop considering both geotechnical stability and structural requirements simultaneously and ensure security and economy together. Two different structural materials with dissimilar mechanical properties and costs are used at the generation stage of structural calculations of optimization analysis. For the attainment of the stability conditions, it is necessary to use the concrete material that is relatively more cost-effective than the steel material. On the contrary, if the design needs to extend the boundaries of the wall too large and/or thick to ensure stability conditions, the cost of whole concrete sections will have been over the expected limits.