Neural Network-Based Prediction Model for the Stability of Unlined Elliptical Tunnels in Cohesive-Frictional Soils
Abstract
:1. Introduction
2. Problem Definition
3. Numerical Analysis
4. FELA Results and Discussion
5. Proposed Models
5.1. Multiple Linear Regression (MLP)
5.2. Artificial Neural Network (ANN)
5.3. Cross-Validation
5.4. Performance Measures
5.5. Multiple Linear Regression (MLR) Equation
5.6. Details of Proposed Artificial Neural Network (ANN) Model
6. Conclusions
- The combination of FELA solutions and the ANN is presented as a guide for geotechnical engineers. Note that the proposed predictive model for the stability factor of this problem can be evaluated based on the complex solutions that are derived from the matrices obtained in this study.
- It is notable that just one hidden layer with seven neurons can sufficiently build a reliable high-performance neural network model.
- The proposed model can be used to accurately predict the stability factor of shallow elliptical tunnels in cohesive-frictional soils based on a new dataset using the weight and bias matrices derived in this study.
- The limitation of the proposed model is that the new dataset should be within the ranges provided in this study.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Input Parameters | Values | Average |
---|---|---|
C/D | 1, 2, 3, 4 | 2.5 |
B/D | 0.5, 0.75, 1, 1.33, 2 | 1.116 |
γD/c′ | 0, 1, 2 | 1.5 |
ϕ | 0, 5, 10, 15, 20, 25 | 12.5 |
γD/c′ | B/D | ϕ | C/D = 1 | C/D = 2 | C/D = 3 | C/D = 4 |
---|---|---|---|---|---|---|
0 | 0.5 | 0 | 3.194 | 4.042 | 4.6415 | 5.112 |
5 | 3.941 | 5.2585 | 6.2735 | 7.11 | ||
10 | 5.0205 | 7.197 | 9.0535 | 10.671 | ||
15 | 6.7035 | 10.6005 | 14.3025 | 17.758 | ||
20 | 9.537 | 17.311 | 25.606 | 34.1285 | ||
25 | 14.846 | 32.5035 | 54.5715 | 80.1625 | ||
0.75 | 0 | 2.8235 | 3.766 | 4.3965 | 4.877 | |
5 | 3.449 | 4.8515 | 5.8745 | 6.698 | ||
10 | 4.3435 | 6.5475 | 8.3315 | 9.8635 | ||
15 | 5.6975 | 9.4395 | 12.83 | 15.989 | ||
20 | 7.9025 | 14.885 | 22.1915 | 29.491 | ||
25 | 11.9115 | 26.743 | 45.0285 | 65.952 | ||
1 | 0 | 2.4365 | 3.4595 | 4.131 | 4.6315 | |
5 | 2.9435 | 4.406 | 5.4625 | 6.29 | ||
10 | 3.65 | 5.875 | 7.622 | 9.1015 | ||
15 | 4.6915 | 8.2945 | 11.4835 | 14.387 | ||
20 | 6.3665 | 12.72 | 19.1735 | 25.7245 | ||
25 | 9.2615 | 21.9155 | 37.1275 | 54.594 | ||
1.33 | 0 | 1.9845 | 3.0405 | 3.7625 | 4.297 | |
5 | 2.346 | 3.827 | 4.9115 | 5.7565 | ||
10 | 2.844 | 5.006 | 6.7365 | 8.174 | ||
15 | 3.559 | 6.8775 | 9.8775 | 12.558 | ||
20 | 4.6385 | 10.23 | 15.913 | 21.5575 | ||
25 | 6.4805 | 16.798 | 29.2085 | 43.145 | ||
2 | 0 | 1.369 | 2.3015 | 3.0505 | 3.637 | |
5 | 1.5485 | 2.8055 | 3.878 | 4.7595 | ||
10 | 1.7905 | 3.533 | 5.148 | 6.533 | ||
15 | 2.5705 | 4.6475 | 7.226 | 9.6325 | ||
20 | 2.1125 | 6.473 | 10.9655 | 15.5125 | ||
25 | 3.293 | 9.714 | 18.507 | 28.4055 | ||
1 | 0.5 | 0 | 1.846 | 1.6285 | 1.206 | 0.6655 |
5 | 2.501 | 2.6405 | 2.508 | 2.202 | ||
10 | 3.451 | 4.2855 | 4.785 | 5.032 | ||
15 | 4.9415 | 7.2425 | 9.2465 | 10.9705 | ||
20 | 7.482 | 13.205 | 19.229 | 25.3425 | ||
25 | 12.383 | 27.1315 | 45.591 | 67.3385 | ||
0.75 | 0 | 1.5695 | 1.4205 | 1.011 | 0.471 | |
5 | 2.1085 | 2.3035 | 2.163 | 1.8355 | ||
10 | 2.877 | 3.7025 | 4.126 | 4.287 | ||
15 | 4.0515 | 6.1475 | 7.8615 | 9.28 | ||
20 | 6.004 | 10.8555 | 15.9195 | 20.9795 | ||
25 | 9.5875 | 21.4915 | 36.3595 | 53.6445 | ||
1 | 0 | 1.2515 | 1.1815 | 0.8005 | 0.2685 | |
5 | 1.6745 | 1.9235 | 1.8025 | 1.4675 | ||
10 | 2.266 | 3.098 | 3.4675 | 3.562 | ||
15 | 3.15 | 5.0775 | 6.55 | 7.7195 | ||
20 | 4.574 | 8.803 | 12.9935 | 17.166 | ||
25 | 7.0895 | 16.763 | 28.6415 | 42.36 | ||
1.33 | 0 | 0.85 | 0.832 | 0.5025 | −0.003 | |
5 | 1.1365 | 1.413 | 1.3145 | 0.9875 | ||
10 | 1.5315 | 2.2985 | 2.6275 | 2.6665 | ||
15 | 2.1005 | 3.7575 | 4.979 | 5.903 | ||
20 | 2.9985 | 6.3965 | 9.72 | 12.9735 | ||
25 | 4.4975 | 11.7655 | 20.696 | 30.9425 | ||
2 | 0 | 0.2685 | 0.1605 | −0.1195 | −0.5595 | |
5 | 0.397 | 0.4785 | 0.37 | 0.065 | ||
10 | 0.562 | 0.9475 | 1.134 | 1.0765 | ||
15 | 0.793 | 1.682 | 2.431 | 2.947 | ||
20 | 1.117 | 2.9245 | 4.892 | 6.805 | ||
25 | 1.6395 | 5.223 | 10.1485 | 15.953 | ||
2 | 0.5 | 0 | 0.43 | −0.834 | −2.277 | −3.8305 |
5 | 1.016 | −0.0105 | −1.304 | −2.778 | ||
10 | 1.8475 | 1.3195 | 0.4135 | −0.811 | ||
15 | 3.1475 | 3.777 | 3.9625 | 3.726 | ||
20 | 5.3945 | 8.93 | 12.4105 | 15.7345 | ||
25 | 9.826 | 21.3065 | 35.934 | 53.1345 | ||
0.75 | 0 | 0.244 | −0.99 | −2.4375 | −3.9995 | |
5 | 0.727 | −0.28 | −1.589 | −3.0845 | ||
10 | 1.388 | 0.8205 | −0.171 | −1.476 | ||
15 | 2.39 | 2.7845 | 2.6755 | 2.145 | ||
20 | 4.066 | 6.749 | 9.256 | 11.528 | ||
25 | 7.2225 | 15.9395 | 26.8835 | 39.7155 | ||
1 | 0 | 0.0105 | −1.1685 | −2.605 | −4.1705 | |
5 | 0.3795 | −0.5795 | −1.89 | −3.4055 | ||
10 | 0.866 | 0.2925 | −0.7695 | −2.1495 | ||
15 | 1.583 | 1.792 | 1.413 | 0.607 | ||
20 | 2.7585 | 4.7355 | 6.351 | 7.706 | ||
25 | 4.8905 | 11.302 | 19.2535 | 28.498 | ||
1.33 | 0 | −0.3225 | −1.4325 | −2.8375 | −4.395 | |
5 | −0.0875 | −1.02 | −2.308 | −3.8255 | ||
10 | 0.2075 | −0.431 | −1.5525 | −3.017 | ||
15 | 0.645 | 0.5505 | −0.1295 | −1.268 | ||
20 | 1.327 | 2.413 | 3.06 | 3.3055 | ||
25 | 2.5005 | 6.4225 | 11.193 | 16.616 | ||
2 | 0 | −0.845 | −2.001 | −3.329 | −4.831 | |
5 | −0.766 | −1.855 | −3.1525 | −4.6615 | ||
10 | −0.668 | −1.657 | −2.9515 | −4.5875 | ||
15 | −0.5315 | −1.344 | −2.6155 | −3.644 | ||
20 | −0.3435 | −0.7905 | −1.8125 | −2.648 | ||
25 | −0.0305 | 0.3445 | 0.49 | 0.2425 |
Methodology | R2 | Mean Absolute Error (MAE) | Root Mean Squared Error (RMSE) |
---|---|---|---|
Multiple Linear Regression (MLR) | 0.7536 | 5.1777 | 7.7086 |
Artificial Neural Network (ANN) | 0.9967 | 0.6774 | 0.9666 |
Hidden Layer Neurons (i) | Hidden Layer Bias (b1) | Hidden Weight IW1 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
B/D (j = 1) | ϕ (j = 2) | γD/σci (j = 3) | C/D (j = 4) | |||||||
1 | −1.8972 | 0.4966 | 0.3791 | −0.4916 | 0.2817 | |||||
2 | −1.4926 | 0.5715 | −0.2262 | 0.1143 | 0.7693 | |||||
3 | −5.1539 | 1.0019 | −1.0584 | 0.2803 | 2.9550 | |||||
4 | −0.5608 | −0.0674 | 0.1779 | 0.0326 | 0.3379 | |||||
5 | −0.8563 | 1.1308 | −0.3793 | −0.0940 | 0.8034 | |||||
6 | −0.6919 | 0.0469 | −0.0108 | −0.0048 | 0.3094 | |||||
7 | −3.2286 | 0.5069 | −0.1487 | −0.4482 | 1.5636 | |||||
8 | −1.4544 | −0.7200 | 1.1056 | 0.4755 | 0.8460 | |||||
9 | −1.9549 | 1.6058 | −0.0265 | 0.9068 | −0.1308 | |||||
Output layer node (k) | Output layer bias (b2) | Output weight IW2 | ||||||||
i = 1 | i = 2 | i = 3 | i = 4 | i = 5 | i = 6 | i = 7 | i =8 | i = 9 | ||
1 | 2.6100 | −0.8506 | −0.7820 | −3.5971 | −0.0863 | −0.8197 | −0.0514 | −1.6245 | 0.6988 | 1.8593 |
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Sirimontree, S.; Keawsawasvong, S.; Ngamkhanong, C.; Seehavong, S.; Sangjinda, K.; Jearsiripongkul, T.; Thongchom, C.; Nuaklong, P. Neural Network-Based Prediction Model for the Stability of Unlined Elliptical Tunnels in Cohesive-Frictional Soils. Buildings 2022, 12, 444. https://doi.org/10.3390/buildings12040444
Sirimontree S, Keawsawasvong S, Ngamkhanong C, Seehavong S, Sangjinda K, Jearsiripongkul T, Thongchom C, Nuaklong P. Neural Network-Based Prediction Model for the Stability of Unlined Elliptical Tunnels in Cohesive-Frictional Soils. Buildings. 2022; 12(4):444. https://doi.org/10.3390/buildings12040444
Chicago/Turabian StyleSirimontree, Sayan, Suraparb Keawsawasvong, Chayut Ngamkhanong, Sorawit Seehavong, Kongtawan Sangjinda, Thira Jearsiripongkul, Chanachai Thongchom, and Peem Nuaklong. 2022. "Neural Network-Based Prediction Model for the Stability of Unlined Elliptical Tunnels in Cohesive-Frictional Soils" Buildings 12, no. 4: 444. https://doi.org/10.3390/buildings12040444