## 6 Conclusions  
This study investigates the corner effect, defined as the plane-strain ratio (PSR), on soil nailed walls using Plaxis v.23 software. In the initial stage, displacement analyses were conducted using 25 three-dimensional (3D) models and 25 plane-strain slice models. This stage aimed to determine the impact of excavation pit dimensions on the corner effect. In the second stage, displacement analyzes were performed on 336 3D models and 336 plane-strain slice models depending on four variable factors, and 1610 data points were obtained from the analysis results. The analysis results were evaluated to determine how and in which direction the parameters affected the PSR value. Then, a PSR estimation study was carried out using machine learning methods. The results obtained from the studies are as follows:  
* It was observed that the secondary wall had no effect on the excavation pit dimensions in the nailed retaining systems (H = 10 m) used in hard clay soils. It was observed that the primary wall exhibited a greater corner effect, especially under conditions of short wall length (20 m). However, if the primary wall length was 40 m or longer, the plane-strain ratio (PSR) increase graphs were equal. The PSR value reached its maximum level at a distance of 3H from the corner;  
Figure 16: Relative importance of PSR prediction parameters with machine learning methods.  
* The corner effect increased with the increase in slope angle (\(\beta\)) and excavation depth (H), because these factors decreased the stiffness of the nailed wall. Conversely, increasing the nail length (L/H) and wall angle (\(\alpha\)) increased the stiffness and decreased the corner effect;
* A very strong relationship was obtained between the plane-strain ratio (PSR) and the distance from the corner (xH) on the nailed wall, with a correlation coefficient of 0.83. This was followed by a negative relationship between PSR and the slope angle (\(\beta\));
* Plane-strain ratio (PSR) prediction was performed using machine learning models and extreme gradient boosting (XGBoost), and classified and regression tree (CART) achieved excellent performance results with an R\({}^{2}\) value of 0.99. The predictions were compared with the results of the finite element analysis, and compatible predictions were obtained.  
This study conducted a comprehensive parametric analysis of the corner effect on soil-nailed walls and developed machine learning (ML) models for predicting plane-strain ratio (PSR) values. In this way, designs can be realized by taking into account the corner effect under different slope angle (\(\beta\)), wall angle (\(\alpha\)), excavation depth (H), and nail length (L/H) conditions on nailed walls in hard clay soils. Consequently, in areas where corner effects may occur during the design phase, the nail length can be reduced or nail spacing can be increased. Modeling and analysis with the finite element method sometimes requires a solution process that takes days. With trained and proven reliable machine learning methods, these times have been reduced to seconds and 99% accuracy has been proven.  
Conceptualization, S.P. and I.V.; methodology, S.P. and I.V.; software, S.P.; validation, I.V.; formal analysis, S.P.; investigation, S.P.; resources, I.V.; data curation, S.P.; writing--original draft preparation, S.P.; writing--review and editing, I.V.; visualization, S.P.; supervision, I.V.; project administration, I.V.; funding acquisition, I.V. All authors have read and agreed to the published version of the manuscript.  
This work was supported by Scientific Research Project Coordination Unit of Sakarya University of Applied Sciences. Project Number: 054-2021.  
Not applicable.  
Data availability StatementData are contained within the article. The data presented in this study can be requested from the authors.  
All the pertinent data for the soil nailed wall case study presented in this paper were provided by Zetas Zemin Teknolojisi A.S.  
The authors declare no conflicts of interest.