## 4 Design Examples of Cantilever RC-Retaining Walls  
In the study, parametrical analyses are conducted to design cantilever RC-retaining walls. The aim is to evaluate the optimum dimensions of retaining systems by taking into account the minimization of material costs for different project conditions. The HS Algorithm is utilized to perform the analyses ofotechnical and structural stability and cost evaluation. A total of 105,000 analyses are conducted due to the different fictionalized cases. The cases are divided into two stages. The first stage includes cost control of retaining systems and the second stage involves dimensional optimization. Parametrical analyses are performed with the related variants about project site properties, environmental conditions, project requirements, and economic constraints on the design process of retaining walls. The variable parameters of the analyses are assumed to be the excavation depth, the properties of backfill soil, the magnitude of surcharge load, the value of ultimate bearing pressure, and the cost of concrete. The excavation depth is assumed to be changed between 3 and 12 m. These excavation depths are defined taking into consideration the applicable upper and lower boundaries of RC cantilever retaining wall heights suggested in existing design guidelines and technical literature [59; 60; 61; 62; 63; 64]. Besides, the knowledge obtained from the previous studies of the authors for the evaluation of retaining wall heights is also considered [65; 66]. \begin{table}
\begin{tabular}{c c} \hline \hline
**Description** & **Constraints** \\ \hline Safety condition for overturning stability & \(g_{1}(\text{X})\cdot\text{FoS}_{\text{ed,design}}\geq\text{FoS}_{\text{wt}}\) \\ Safety condition for sliding & \(g_{2}(\text{X})\cdot\text{FoS}_{\text{design}}\geq\text{FoS}_{\text{s}}\) \\ Safety condition for bearing capacity & \(g_{3}(\text{X})\cdot\text{FoS}_{\text{bc,design}}\geq\text{FoS}_{\text{bc}}\) \\ \hline Minimum bearing stress (\(q_{min}\)) & \(g_{4}(\text{Q})\cdot q_{min}\geq 0\) \\ Flexural strength capacities of critical sections (\(M_{d}\)) & \(g_{5-7}(\text{X})\cdot\text{M}_{d}\geq\text{M}_{u}\) \\ Shear strength capacities of critical sections (\(V_{d}\)) & \(g_{8-10}(\text{X})\cdot\text{V}_{d}\geq\text{V}_{u}\) \\ Minimum reinforcement areas of critical sections (\(A_{smin}\)) & \(g_{11-13}(\text{X})\cdot\text{A}_{s}\geq A_{smin}\) \\ Maximum reinforcement areas of critical sections (\(A_{smax}\)) & \(g_{14-16}(\text{X})\cdot\text{A}_{s}\leq A_{smax}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The constraints of design on strength and dimensions. At the design phase of the retaining walls, it is clear that the designers required the soil parameters such as the unit weight of soil and the shear strength angle for the determination of the lateral earth pressures. Unless the backfill soil parameters are supplied by the geotechnical consultant it is proper to predict them conservatively by using empirical relationships or according to proposed values from the literature. In the study, the surrounding soil of the wall system, the foundation soil profile, and backfill are selected as the same. It is assumed that the wall embeds into a homogenous soil stratum which is formed by cohesion-less soils and the geotechnical characteristics are chosen from the literature sources staying within the allowable limits. The unit weight of the soil, the shear strength angle, and the ultimate bearing pressure is assumed to be variables and various cases are derived to compare the influences of soil properties to the design problem of retaining walls and their costs. The unit weight of soil strata is preferred to be defined based on the suggestions of [PERSON] (1988) and [PERSON] (1967). [PERSON] (1988) defined the unit weight of granular soils due to their relative density and the shear strength angle values. The unit weight values are identified as 14-18, 17-20, and 17-22 \(\mathrm{kN/m^{3}}\) for loose, medium, and dense sandy soils, respectively (1988).