Deep Learning Method on Deformation Prediction for Large-Section Tunnels
Abstract
:1. Introduction
2. Proposed Methodology
3. Project Overview and Construction Plan
3.1. Project Overview
3.2. Construction Plan
4. Determination of Construction Scheme Based on Numerical Simulation
4.1. Choice of Construction Parameters
4.2. The Establishment of Three-Dimensional Numerical Model
4.3. Steps of Numerical Simulation
4.4. Results Discussion
4.4.1. Different Excavation Sequence
4.4.2. Different Excavation Step Length
5. Tunnel Deformation Prediction Based on LSTM Algorithm
5.1. Long Short-Term Memory (LSTM)
- (1)
- The calculation formulas for the input gate, forget gate, and output gate are:
- (2)
- The update status in the neural unit cell is:
- (3)
- The output value of the LSTM unit is:
5.2. Tunnel Deformation Prediction
5.2.1. Data Preparation
5.2.2. Model Training
5.2.3. Model Prediction
5.2.4. Baseline Model
5.3. Results Discussion
5.3.1. Performance of LSTM Algorithm
5.3.2. Prediction Performance of LSTM Algorithm
5.3.3. Multi-Step Prediction Result
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Excavation Schemes | Excavation Sequence |
---|---|
1 | Ⅰ → Ⅱ→ Ⅲ→ Ⅵ→ Ⅶ→ Ⅳ→ Ⅴ |
2 | Ⅳ→ Ⅵ→ Ⅴ→ Ⅶ→ Ⅰ → Ⅱ→ Ⅲ |
3 | Ⅳ→ Ⅴ→ Ⅵ→ Ⅶ→ Ⅰ → Ⅱ→ Ⅲ |
Excavation Schemes | Excavation Step Length |
---|---|
1 | 1 m |
2 | 2 m |
3 | 3 m |
Layer | Name | ρ/(kg/m−3) | c/(kPa) | ϕ/° | E/(GPa) | υ |
---|---|---|---|---|---|---|
1 | Silty clay | 19.8 | 25 | 20 | 2.1 | 0.38 |
2 | Fully weathered granite | 20 | 10 | 32 | 4.2 | 0.25 |
3 | Strongly weathered granite | 21 | 30 | 32 | 6.4 | 0.28 |
4 | Medium weathered granite | 23 | 100 | 39 | 7.6 | 0.31 |
5 | Micro-weathered granite | 24 | 200 | 44 | 8.1 | 0.34 |
6 | Fully weathered quartz diorite | 23 | 26 | 28 | 4.8 | 0.35 |
7 | Strong weathered quartz diorite | 27.7 | 28 | 30 | 7 | 0.32 |
8 | Medium weathered quartz diorite | 28.9 | 5.5 × 103 | 41 | 4 | 0.30 |
9 | Breeze quartz diorite | 30.0 | 7.0 × 103 | 42 | 6.5 | 0.23 |
Structural Unit | ρ/(kg/m−3) | Thickness/(m) | E/(GPa) | υ | Normal Coupling Stiffness/(Gpa) | Tangential Coupling Stiffness/(Gpa) |
---|---|---|---|---|---|---|
Liner | 2000 | 1 | 30 | 0.25 | 9.77 | 9.77 |
Structural Unit | ρ/(kg/m−3) | Cross-Sectional Area/(cm2) | E/(GPa) | c/(kPa) | Grouting Perimeter/(m) | ϕ/° |
---|---|---|---|---|---|---|
Cable | 2000 | 5.9 | 200 | 50 | 0.157 | 35 |
Excavation Schemes | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|
1 | 0.13 | 0.29 | 0.45 | 0.59 | 0.74 | 0.91 | 1.1 |
2 | 0.1 | 0.17 | 0.28 | 0.37 | 0.54 | 0.62 | 0.78 |
3 | 0.16 | 0.31 | 0.62 | 0.89 | 1.15 | 1.28 | 1.56 |
Excavation Schemes | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|---|---|
1 | 0.07 | 0.11 | 0.15 | 0.21 | 0.29 | 0.36 | 0.46 |
2 | 0.1 | 0.17 | 0.28 | 0.37 | 0.54 | 0.62 | 0.78 |
3 | 0.21 | 0.89 | 2.43 | 3.69 | 4.74 | 5.42 | 6.85 |
Input Parameters | Output Parameters |
---|---|
rock uniaxial compressive strength | the deformation of the tunnel vault and bottom |
confining pressure | |
in situ stress | |
rock humidity | |
joint spacing | |
joint dip |
Parameters | Notes |
---|---|
Operation system | windows 10 |
CPU | IntelI CoITM) i7-10710U CPU @ 1.10 GHz |
GPU | GeForce MX350 |
Python | 3.9 |
PyTorch | 1.9.1 |
The Model Parameters | LSTM Layers | Units | Dense | Batch_size | Epoch | Activate Function | Optimizer | Loss |
---|---|---|---|---|---|---|---|---|
Number/Type | 3 | 64 | 1 | 100 | 150 | Relu | Adam | Mse |
Algorithms | Hyperparameters |
---|---|
RF | Max_Features = 400, Max_Depth = 6, N_Estimators = 70, Min_Sample_Leaf = 2, Min_Sample_Split = 2, Random_State = 10 |
RNN | RNN layer = 3, Number of the RNN units = 64, Each batch = 64, Iteration = 200, Dense = 1, Dropout rate = 0.1, Optimizer = Adam, Loss function = MSE, Activation function = ReLu |
Algorithms | Dataset | MAE | RMSE | R2 |
---|---|---|---|---|
LSTM | Train | 0.104 | 0.171 | 0.946 |
Test | 0.225 | 0.238 | 0.928 | |
RF | Train | 0.321 | 0.472 | 0.801 |
Test | 0.346 | 0.498 | 0.784 | |
RNN | Train | 0.256 | 0.386 | 0.843 |
Test | 0.286 | 0.402 | 0.822 |
Algorithms | Dataset | MAE | RMSE | R2 |
---|---|---|---|---|
LSTM | Train | 0.111 | 0.178 | 0.958 |
Test | 0.246 | 0.231 | 0.931 | |
RF | Train | 0.335 | 0.480 | 0.793 |
Test | 0.363 | 0.503 | 0.762 | |
RNN | Train | 0.267 | 0.391 | 0.836 |
Test | 0.291 | 0.433 | 0.817 |
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Xu, W.; Cheng, M.; Xu, X.; Chen, C.; Liu, W. Deep Learning Method on Deformation Prediction for Large-Section Tunnels. Symmetry 2022, 14, 2019. https://doi.org/10.3390/sym14102019
Xu W, Cheng M, Xu X, Chen C, Liu W. Deep Learning Method on Deformation Prediction for Large-Section Tunnels. Symmetry. 2022; 14(10):2019. https://doi.org/10.3390/sym14102019
Chicago/Turabian StyleXu, Wei, Ming Cheng, Xiangyang Xu, Cheng Chen, and Wei Liu. 2022. "Deep Learning Method on Deformation Prediction for Large-Section Tunnels" Symmetry 14, no. 10: 2019. https://doi.org/10.3390/sym14102019
APA StyleXu, W., Cheng, M., Xu, X., Chen, C., & Liu, W. (2022). Deep Learning Method on Deformation Prediction for Large-Section Tunnels. Symmetry, 14(10), 2019. https://doi.org/10.3390/sym14102019