## 4 Design Examples of Cantilever RC-Retaining Walls
### Numerical Analysis with GeoS Software  
To validate the design procedure arranged with the use of Harmony Search Algorithm for reinforced concrete retaining walls, numerical analyses were conducted using the commercial software Geo5 that is an effective software package depending on both analytical and finite element methods and developed for solving geotechnical problems like slope stability, foundations, retaining walls, and so on. The analytical method allows the users not only to design but also to check structure stability situations quickly and efficiently. The analytically designed structure is transferred to the finite element model for the overall analysis of the whole structure. This transmission process saves the computational time of designers and compares two independent solutions, so it increases the safety of the design [72; 73; 74; 75; 76; 77]. Within the software context, there are 28 different moduli (like abutment, anti-slide pile, beam, cantilever wall, gabion, spread footing, and so on.) which include different geotechnical design structures individually. However, all moduli can transfer or communicate with each other and form an integrated total package. Besides, worldwide usage is ensured with the existence of design conditions proposed by various geotechnicalIn the study, depending on the previously mentioned properties of the software, Geo5 version 2021 is preferred to be used to validate the suggested design dimensions. The free version of the software has been used without restrictions of the program, to analyze the selected specific cases. The shear strength angle and the unit weight of the foundation and backfill soil are assumed to be 30\({}^{\circ}\) and 18 kN/m\({}^{3}\), respectively, and no surcharge loading is considered. All the envisaged cases that are analyzed with HS optimization logic have been also solved with Geo5 software, but the details of the analysis for the 3-m excavation depth only have been illustrated. The geotechnical and structural design standards are selected in the first step of the analyses conducted with Geo5 (Figure 25). The structural design requirements are modeled depending on the limitation of ACI 318, and AASHTO is used to model geotechnical standards. The active and passive earth pressure calculations are arranged to be performed with the use of Rankine theory. Besides, the foreseen geometry of the wall system, the properties of the soil formation, and the stratification situation of the foundation soil medium are defined at the first stage. The second stage of the analyses includes additional situations like the existence of the water table or external forces. In the context of the analyses considered for this section, there is not any necessary condition to define. The third step includes the verification of overturning and sliding safety, bearing capacity adequateness, structural dimensioning control, and overall stability research with slope analyses. The HS optimization results for 3-m excavation depth is given in Figure 26. The total height of the wall is determined as 3.3-m by the sum of the excavation depth and the thickness of the foundation base. The L-shaped section is obtained without the toe length, and the heel length is suggested to be 1.85 m. The thickness of the stem at the top and bottom is calculated 0.2 and 0.3 m, respectively. Figure 26 reflects the bearing capacity adequateness for the envisaged dimensioning of the design. The eccentricity and foundation soil situations are found to be satisfactory. The next step of the verification process is the control of structural dimensioning in terms of shear and bending conditions of wall stem and wall heel. In this context, Figure 27 shows that the front and back reinforcement and heel reinforcement are found to be adequate in terms of shear and bending moment. The last step of the verification process is the control of overall stability (FoS\({}_{\text{0s}}\)) in terms of slope stability.