# Multiparametric Analysis of a Gravity Retaining Wall
## 5 Conclusions  
The optimization was performed 567 times to obtain an optimal design of a gravity retaining wall for different site characteristics and project data. The results of this study will help engineers to determine the wall section in the first iteration that meets the stability requirements and minimum construction costs. During optimization, some of the geotechnical constraints were fully exploited, so this paper also discusses which geotechnical constraints govern the design. Critical geotechnical constraints also depend on the site characteristics and project data. While geotechnical engineers are not always able to determine the exact soil properties, this study is appropriate for determining what effect vague input data have on the cost of a gravity retaining wall. The following conclusions can be drawn based on the multiparametric analysis:  
* The optimal width of the front wall section \(b_{f}\) reached the highest values among all dimensions of the wall, while the optimal width of the rear wall section \(b_{b}\) was found to be 0 m at all different combinations of parameters.
* The most important parameter for the optimal cost of the gravity retaining wall is the height of the retained ground, followed by the shear angle of the soil, the soil-wall interaction coefficient, the slope angle and the variable surcharge load.
* The shear angle of the soil is most relevant to the bearing capacity and eccentricity condition, while the interaction coefficient is most relevant to the sliding condition.
* Given the unfavorable site characteristics and project data (\(\varphi_{k}=30^{\circ}\), \(k=0.5\), \(\beta=20^{\circ}\), \(q_{Qk}=0\ kPa\)), doubling the height of the retaining wall (from 2.5 to 5 m) increases the cost from 653.7 to 2510.7 EUR/m, almost four times the cost of a smaller wall.
* Gravity retaining walls are usually sloped toward the earth mass behind them to counteract the force of gravity acting against them, which is called \"setback\". Based on the parametric analysis, the optimum angle of this slope ranges from 7 to \(47^{\circ}\), with an average value of about \(18^{\circ}\) (slope ratio HD/VD = 1:3).
* The depth of the foundation for a gravity retaining wall depends on the height of the wall. Based on the parametric analysis, the optimum depth of the retaining wall is between 10 and 40% of the height of the wall, with an average value of 20% (one-fifth of its height below ground level).  
Figure 12: Influence of each input variable on the optimal cost of a gravity retaining wall and the utilization of geotechnical conditions.  
The article gives recommendations for the optimal design of gravity retaining walls. The usefulness of the developed diagrams is illustrated with examples. While European countries adopt different load, material and resistance factors, the Eurocode 7 standard defines three design approaches. Since the cost of building a gravity retaining wall depends on key parameters such as quantity of materials, unit material prices and labor costs, an economically optimal design may also change as the relative ratios among the key parameters change. The optimal designs of gravity retaining walls in this paper correspond only to design approach 1 (combination 2). Because the optimization model was developed in a general form, other design approaches and unit prices can also be considered, and their influence on the optimal design can be further investigated.  
Conceptualization, P.J.; methodology, P.J.; formal analysis, P.J. and R.V.; writing--original draft preparation, P.J., B.Z. and R.V. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Slovenian Research Agency (grant number P2-0268) and the GEOLAB project (grant number 101006512).  
Not applicable.  
The data presented in this study are available upon request from the corresponding author.  
The authors declare no conflict of interest.