Parametric Investigation of Corner Effect on Soil Nailed Walls and Prediction Using Machine Learning Methods
Abstract
:1. Introduction
2. Machine Learning Methods
2.1. Artificial Neural Networks (ANNs)
2.2. Classifical and Regression Tree (CART)
2.3. XGBoost
2.4. SVR
3. Materials and Methods
3.1. Database of Soil Nailed Wall
3.2. Finite Element Model Presentation and Verification of the Model with Field Measurement Results
3.3. Method
3.4. Corner Effect (PSR)
4. Results and Discussion
4.1. Parametric Investigation
4.2. Effect of Excavation Pit Dimensions on PSR
4.3. Effects of Slope Angle (β), Wall Angle (α), Excavation Depth (H), Nail Length (L/H), and Distance from Corner (xH) on PSR
4.4. Correlation Analysis
5. Machine Learning Models
5.1. Hyperparameters Configuration
5.2. Performance Metrics
5.3. Evaluation of Machine Learning Model Prediction Performances
6. Conclusions
- 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;
- The corner effect increased with the increase in slope angle (β) and excavation depth (H), because these factors decreased the stiffness of the nailed wall. Conversely, increasing the nail length (L/H) and wall angle (α) 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 (β);
- Plane–strain ratio (PSR) prediction was performed using machine learning models and extreme gradient boosting (XGBoost), and classifical and regression tree (CART) achieved excellent performance results with an R2 value of 0.99. The predictions were compared with the results of the finite element analysis, and compatible predictions were obtained.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Soil Nailed Wall H (m) | Soil Nail Impact Area Sh × Sv (m2) | Soil Nailed Wall Angle α (°) | Soil Nail Angle ω (°) | Soil Nail Length L (m) | Nail Diameter D (mm) |
---|---|---|---|---|---|
10.0 | 1.5 × 1.5 | 85 | 15 | 12 | 105 |
Soil | Soil Model | Unit Volume Weight (kN/m3) | Friction Angle φ′ ° | Cohesion c (kPa) | E50ref kN/m2 | Eoedref kN/m2 | Eurref kN/m2 | vur | Rinter |
---|---|---|---|---|---|---|---|---|---|
Soil 1 | Hardening soil | 19 | 25 | 15 | 53,000 | 53,000 | 159,000 | 0.25 | 0.67 |
FE | Soil Nail | E (kN/m2) | γ (kN/m3) | D (m) | Bond Strength (kPa) | Axial Skin Resistance | Tskin, Start, Max | Tskin, End, Max | Material |
---|---|---|---|---|---|---|---|---|---|
Plaxis 2D | Embedded Beam | 93.00 × 106 | 1 | 0.105 | 150 | Linear | 98.96 | 98.96 | Rock bolt, Rigid |
Plaxis 3D | Embedded Beam | 93.00 × 106 | 1 | 0.105 | 150 | Linear | 98.96 | 98.96 | Rock bolt, Rigid |
FE | Shotcrete | Material Type | γ (kN/m3) | d (m) | EA1 (kN/m) | E1 (kN/m2) | EI (kNm2/m) | V12 | Interface |
Plaxis 2D | Plate | Elastic | 1.2 | 0.200 | 4.200 × 106 | 21.00 × 106 | 14.00 × 103 | 0.2 | Defined |
Plaxis 3D | Plate | Elastic | 1.2 | 0.200 | - | 21.00 × 106 | - | 0.2 | Defined |
Group 1 | Group 2 | Group 3 | Group 4 | Group 5 | |
---|---|---|---|---|---|
B1 = 2H | B2 = 4H | B3 = 6H | B4 = 8H | B5 = 10H | |
L-1 | 2H | 2H | 2H | 2H | 2H |
L-2 | 4H | 4H | 4H | 4H | 4H |
L-3 | 6H | 6H | 6H | 6H | 6H |
L-4 | 8H | 8H | 8H | 8H | 8H |
L-5 | 10H | 10H | 10H | 10H | 10H |
Correlation Coefficient | Description | Parameters |
---|---|---|
0.80–1.00 | Very strong | PSR vs. xH |
0.60–0.79 | Strong | - |
0.40–0.59 | Moderate | - |
0.20–0.39 | Weak | PSR vs. β, β vs. H, β vs. L/H, |
0.00–0.19 | Very weak | L/H vs. xH, H vs. xH, α vs. L/H, α vs. H, β vs. α, PSR vs. α, H vs. L/H, PSR vs. H, PSR vs. L/H, β vs. xH, α vs. xH |
ML | Parameters | Value |
---|---|---|
XGBoost | Number of estimator | 200 |
Maximum depth | 5 | |
Minimum child weight | 1 | |
Learning rate | 0.1 | |
Support vectors | 117 | |
SVR | Cost | 100 |
Epsilon | 0.1 | |
Gamma | 0.01 | |
Kernel | Radial basis functions | |
CART | Max. depth | None |
Min. samples leaf | 2 | |
Min. samples split | 5 | |
ANN | Hidden layer size | 2 |
Neurons | 20 + 20 |
No | Parameter | Equation |
---|---|---|
1 | Coefficient of determination (R2) | |
2 | Mean absolute error (MAE) | |
3 | Root-mean-square error (RMSE) |
Indicator Models Used | MAE | RMSE | ||||
---|---|---|---|---|---|---|
Training | Test | Training | Test | Training | Test | |
ANN | 0.95 | 0.91 | 0.05 | 0.05 | 0.06 | 0.07 |
SVR | 0.92 | 0.91 | 0.05 | 0.06 | 0.06 | 0.07 |
CART | 0.99 | 0.98 | 0.00 | 0.01 | 0.01 | 0.02 |
XGBoost | 0.99 | 0.99 | 0.00 | 0.01 | 0.00 | 0.01 |
Features | A | B | C | D | E | F | G | H | I | J |
---|---|---|---|---|---|---|---|---|---|---|
Slope angle | 0 | 0 | 0 | 10 | 34 | 0 | 0 | 10 | 10 | 20 |
Nailed wall angle | 0 | 0 | 10 | 10 | 5 | 10 | 5 | 0 | 5 | 0 |
Excavation depth | 16 | 28 | 25 | 28 | 13 | 19 | 16 | 22 | 28 | 13 |
Nail length | 1.00 | 1.25 | 0.75 | 0.75 | 1.25 | 0.50 | 0.75 | 1.25 | 1.25 | 1.25 |
Distance from the corner | 0.5 | 2.0 | 0.5 | 0.5 | 1.5 | 0.0 | 1.0 | 0.0 | 1.0 | 2.5 |
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Poyraz, S.; Vural, İ. Parametric Investigation of Corner Effect on Soil Nailed Walls and Prediction Using Machine Learning Methods. Appl. Sci. 2024, 14, 7331. https://doi.org/10.3390/app14167331
Poyraz S, Vural İ. Parametric Investigation of Corner Effect on Soil Nailed Walls and Prediction Using Machine Learning Methods. Applied Sciences. 2024; 14(16):7331. https://doi.org/10.3390/app14167331
Chicago/Turabian StylePoyraz, Semiha, and İsa Vural. 2024. "Parametric Investigation of Corner Effect on Soil Nailed Walls and Prediction Using Machine Learning Methods" Applied Sciences 14, no. 16: 7331. https://doi.org/10.3390/app14167331