# Investigation of Transfer Learning for Tunnel Support Design

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## Abstract

**:**

## 1. Introduction

- First, a brief review of the relevant background information for tunnel support analysis and ML is provided.
- Second, the methodology and implementation of transfer learning for the simulation of the first scenario of a change in ground conditions is presented.
- Third, following the same methodology as the first scenario, the implementation of transfer learning from simple to complex tunnel support analysis is presented.
- Fourth, the results of both investigations are presented and discussed.
- Finally, the conclusions and limitations of the current work are summarized.

## 2. Background Information

#### 2.1. Tunnel Support Analysis

- The ground convergence curve
- The support curve (confinement)
- Initial displacement prior to the support

#### 2.2. Machine-Learning

## 3. Transfer Learning for Change in Ground Conditions

- DS1—represents a soil where a significant amount of data has been collected and consists of 200 rows of input parameters.
- DS2—represents a new soil formation with only 25 rows of input parameters. This soil is slightly weaker than DS1, with a significant overlap of parameter range compared to DS1.
- DS3—represents a new soil with a small dataset, similar to DS2. In contrast to DS2, DS3 has very little overlap with DS1 parameters.

## 4. Transfer Learning for Simple to Complex Analysis

## 5. Results

- The accuracy of N1 predictions on the small datasets DS2 and DS3
- The accuracy of a new ML model for predicting DS2 and DS3

## 6. Summary and Conclusions

## 7. Limitations

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Illustration of the potential of the current study for future application to real-world settings.

**Figure 4.**Stress distribution and tunnel deformation for (

**a**) hydrostatic loading, and (

**b**) non-hydrostatic loading.

**Figure 5.**Illustration of (

**a**) original ANN (NN1) and (

**b**) NN1 transferred and modified to a new ANN (NNT). The red and blue nodes represent the network components of the large and small datasets, correspondingly.

**Figure 7.**Prediction vs. actual tunnel displacements for DS3 with NSD = 5% computed with (

**a**) NN1, i.e., no transfer learning, and (

**b**) NNT, i.e., with transfer learning.

**Figure 8.**Prediction vs. actual tunnel displacements for DS3 with NSD = 10% computed with (

**a**) NN1, i.e., no transfer learning, and (

**b**) NNT, i.e., with transfer learning.

**Table 1.**Dataset #1 (DS1), #2 (DS2), and #3 (DS3) input parameter range and tunnel displacements computed via the CC method.

Friction Angle | Cohesion | In-Situ Stress | Uniaxial Strength | Young’s Modulus | Tunnel Displacement | ||
---|---|---|---|---|---|---|---|

Units: | Degrees | MPa | MPa | Mpa | Mpa | mm | |

DS1 (n = 200) | Min. | 22.5 | 0.35 | 8 | 1.05 | 524 | 34 |

Mean | 30 | 0.5 | 10 | 1.73 | 1053 | 122 | |

Max. | 37.5 | 0.65 | 12 | 2.64 | 1582 | 504 | |

DS2 (n = 25) | Min. | 20 | 0.3 | 8 | 0.86 | 383 | 124 |

Mean | 25 | 0.35 | 9 | 1.08 | 510 | 308 | |

Max. | 30 | 0.4 | 10 | 1.37 | 660 | 627 | |

DS3 (n = 25) | Min. | 40 | 0.1 | 6 | 0.43 | 339 | 43 |

Mean | 45 | 0.15 | 7 | 0.72 | 574 | 97 | |

Max. | 50 | 0.2 | 8 | 1.10 | 809 | 190 |

Friction Angle | Cohesion | Young’s Modulus | Tunnel Displacement | ||
---|---|---|---|---|---|

Units: | Degrees | MPa | MPa | mm | |

DS1 (n = 200) DS2 (n = 25) | Min. | 20 | 0.35 | 500 | 35 |

Mean | 30 | 0.5 | 1000 | 64 | |

Max. | 40 | 0.65 | 1500 | 139 | |

DS3 (n = 25) | Min. | 20 | 0.15 | 1000 | 37 |

Mean | 30 | 0.3 | 1500 | 71 | |

Max. | 40 | 0.45 | 2000 | 140 |

RMSE [mm] | ||||
---|---|---|---|---|

ML-Model | Dataset | NSD = 0% | NSD = 5% | NSD = 10% |

NN1 | DS1 | 14 | 16 | 19 |

NN1 | DS2 | 102 | 95 | 106 |

NNT | DS2 | 41 | 56 | 65 |

NN1 | DS3 | 37 | 40 | 39 |

NNT | DS3 | 21 | 22 | 24 |

RMSE [mm] | ||||
---|---|---|---|---|

ML-Model | Dataset | NSD = 0% | NSD = 5% | NSD = 10% |

NN1 | DS1 | 2 | 3 | 7 |

NN1 | DS2 | 40 | 51 | 59 |

NNT | DS2 | 26 | 29 | 33 |

NN1 | DS3 | 41 | 37 | 54 |

NNT | DS3 | 14 | 18 | 20 |

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**MDPI and ACS Style**

Mitelman, A.; Urlainis, A. Investigation of Transfer Learning for Tunnel Support Design. *Mathematics* **2023**, *11*, 1623.
https://doi.org/10.3390/math11071623

**AMA Style**

Mitelman A, Urlainis A. Investigation of Transfer Learning for Tunnel Support Design. *Mathematics*. 2023; 11(7):1623.
https://doi.org/10.3390/math11071623

**Chicago/Turabian Style**

Mitelman, Amichai, and Alon Urlainis. 2023. "Investigation of Transfer Learning for Tunnel Support Design" *Mathematics* 11, no. 7: 1623.
https://doi.org/10.3390/math11071623