# Research on Tunnel Construction Monitoring Method Based on 3D Laser Scanning Technology

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## Abstract

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## 1. Introduction

## 2. Fitting Surface

#### 2.1. Bicubic Spline Interpolation Surface Construction

_{0}, x

_{1}, ..., x

_{n}is defined as $S(x)\in C2[a,b]$; it is a cubic polynomial in each small interval $[{x}_{j},{x}_{j+1}]$, where $a={x}_{0}<{x}_{1}<\cdots <{x}_{n}=b$ defines subjected node. If the function value ${Y}_{j}=f({X}_{j})(j=0,1,\cdots ,n)$ is given on the node x

_{j}, and the cubic spline function is established as $S({x}_{j})={y}_{j}(j=0,1,\cdots ,n)$, then $S(x)$ is referred to as the cubic spline interpolation function.

#### 2.2. Greedy Projection Triangulation Algorithm

- The KD tree structure is used to determine the nearest points; this step is called nearest neighbor search.
- The plane and the surface are made roughly tangential to project the point cloud’s normal information to the plane in blocks.
- The procedure is completed by projecting the points to the plane, triangulating the points on the plane, reflecting the topological relationship into the space, and concluding the continuous cycle of surface reconstruction.

#### 2.3. Ablation Study

- The point cloud and surface are compatible with the greedy triangulation method, which can accurately express the tunnel’s local surface. When the density of the point cloud is high, the effect of the abrupt change in the normal angle can be overlooked because of the small change in the normal angle between adjacent triangles. A major surface fitting method for 3D laser scanning monitoring and measurement can be used in future research, given the high acceptance of this method in the engineering field.
- The B-spline interpolation method can restore the tunnel girdle area with minimal curvature by fitting the tunnel face with a polynomial in the whole area. At the same time, it maintains high goodness of fit. However, the fitting surface of the vault (area with large curvature) has a distorted position, and the partition fitting method is used to improve the fitting degree. The normal angle is continuously changing; the fitting surface is smooth and continuous at high orders. However, the fitting surface does not tend to overlap with the point cloud and has a tendency to disregard the local variations of the tunnel. Therefore, engineers and technicians have a low level of acceptance for this method; thus, it can be used as an auxiliary fitting method in future studies and compared to the greedy triangulation method for validation.

## 3. Deformation Hypothesis

## 4. Monitoring and Measurement Algorithm Based on Scattered Point Cloud

#### 4.1. Observation Point Arrangement of the Fitting Surface

#### 4.2. Calculation of Initial Support Deformation of Tunnel

_{0}, y

_{0}) can be given as follows:

_{n}is set to be positive when S

_{n}is inside S

_{1}, and negative when S

_{n}is outside S

_{1}. The normal vector matrix D is formed by summarizing the observation points of the displacement.

## 5. Maximum Entropy Analysis of Tunnel Deformation

#### Maximum Entropy Analysis

## 6. Example Verification

#### 6.1. 3D Laser Scanning Inspection and Deterministic Analysis of Traditional Monitoring Quantity

#### 6.2. Quantitative Comparison between 3D Laser Scanning Inspection and Traditional Monitoring Methods

#### 6.3. Exceedance Probability Characteristic Deformation Value Analysis

_{n}, was used to validate the results obtained by the greedy triangulation and the B-spline interpolation methods, as follows.

_{n}is the probability feature deformation value of the specific transcendence probability on an nth day.

_{n}of the 1% probability feature deformation value is approximately in line with that of the 5% probability feature deformation value. The result of the B-spline interpolation method showed significant inconsistency, and the greedy triangulation method’s judgment results were more stable and suited for assessing the initial support deformation in engineering.

## 7. Discussion

## 8. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 4.**Schematic diagram of the probability density function of the initial support deformation of the tunnel.

**Figure 5.**Schematic diagram of the deformation direction of the surface fitted by the B-spline interpolation method on the 14th–15th days (Note: the deformation direction of the golden part is outward, and the deformation direction of the red part is inward).

**Figure 6.**Schematic diagram of the deformation direction of the surface fitted by the B-spline interpolation method on the 15th–17th day (Note: the deformation direction of the golden part is outward, and the deformation direction of the red part is inward).

**Figure 9.**Comparison of positive feature deformation between greedy triangulation and B-spline interpolation.

**Figure 10.**Comparison of negative feature deformation between greedy triangulation and B-spline interpolation.

Compare Dates | 14–15 | 15–16 | 16–18 | 18–19 | 19–21 | 21–22 | |
---|---|---|---|---|---|---|---|

Section 01 | Vault sinks | 17.2 | −17.2 | 10.5 | 6.0 | −7.3 | −3.5 |

Deformation of the left arch | 16.2 | −12.0 | −7.8 | 1.7 | 2.9 | 2.9 | |

Deformation of the right arch | −9.5 | 9.0 | −5.6 | −4.2 | −1.9 | −1.8 | |

Section 02 | Vault sinks | −24.5 | −18.3 | −10.2 | 5.1 | −1.7 | 2.6 |

Deformation of the left arch | 24.4 | −24.4 | 20.3 | −7.2 | 7.7 | 2.1 | |

Deformation of the right arch | −22.8 | 24.1 | −14.5 | −3.6 | −4.0 | −3.1 | |

Maximum forward deformation | 24.4 | 24.1 | 20.3 | 6.0 | 7.7 | 2.9 | |

Negative deformation maximum | −24.5 | −24.4 | −14.5 | −7.2 | −7.3 | −3.5 |

Compare Dates | 14–15 | 15–17 | 17–18 | 18–19 | 19–20 | 20–21 | 21–22 | 22–23 | |
---|---|---|---|---|---|---|---|---|---|

Greedy Triangulation | Positive 1% probability feature deformation value | 13.50 | 12.58 | 11.70 | 14.64 | 13.77 | 9.12 | 8.38 | - |

Negative 1% probability feature deformation value | −13.51 | −12.60 | −11.70 | −14.63 | −13.82 | −9.12 | −8.38 | - | |

B-spline Interpolation | Positive 1% probability feature deformation value | 13.50 | 19.85 | 11.69 | 15.48 | 11.30 | 3.41 | 4.35 | - |

Negative 1% probability feature deformation value | −13.49 | −15.39 | −10.92 | −14.28 | −14.50 | −7.85 | −5.38 | - | |

Greedy Triangulation | Positive 5% probability feature deformation value | 9.50 | 8.86 | 8.18 | 10.18 | 9.69 | 6.43 | 5.91 | - |

Negative 5% probability feature deformation value | −9.50 | −8.72 | −8.17 | −10.20 | −9.55 | −6.43 | −5.91 | - | |

B-spline Interpolation | Positive 5% probability feature deformation value | 9.50 | 12.91 | 8.11 | 10.69 | 8.33 | 1.93 | 3.04 | - |

Negative 5% probability feature deformation value | −9.50 | −11.35 | −7.82 | −10.24 | −9.46 | −6.00 | −3.82 | - |

Compare Dates | 14–15–17 | 15–17–18 | 17–18–19 | 18–19–20 | 19–20–21 | 20–21–22 | |
---|---|---|---|---|---|---|---|

Greedy Triangulation | Negative 1% probability feature deformation value | −7.31% | −7.52% | 20.08% | −6.32% | −50.99% | −8.83% |

Positive 1% probability feature deformation value | −7.22% | −7.69% | 20.03% | −5.86% | −51.54% | −8.83% | |

B-spline interpolation | Negative 1% probability feature deformation value | 31.99% | −69.80% | 24.48% | −36.99% | −231.38% | 21.61% |

Positive 1% probability feature deformation value | 12.35% | −40.93% | 23.53% | 1.52% | −84.71% | −45.91% | |

Greedy Triangulation | Negative 5% probability feature deformation value | −7.22% | −8.31% | 19.65% | −5.06% | −50.70% | −8.80% |

Positive 5% probability feature deformation value | −8.94% | −6.73% | 19.90% | −6.81% | −48.52% | −8.80% | |

B-spline interpolation | Negative 5% probability feature deformation value | 26.41% | −59.19% | 24.13% | −28.33% | −331.61% | 36.51% |

Positive 5% probability feature deformation value | 16.30% | −45.14% | 23.63% | −8.25% | −57.67% | −57.07% |

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**MDPI and ACS Style**

Wei, Z.; Wang, Y.; Weng, W.; Zhou, Z.; Li, Z. Research on Tunnel Construction Monitoring Method Based on 3D Laser Scanning Technology. *Symmetry* **2022**, *14*, 2065.
https://doi.org/10.3390/sym14102065

**AMA Style**

Wei Z, Wang Y, Weng W, Zhou Z, Li Z. Research on Tunnel Construction Monitoring Method Based on 3D Laser Scanning Technology. *Symmetry*. 2022; 14(10):2065.
https://doi.org/10.3390/sym14102065

**Chicago/Turabian Style**

Wei, Zheng, Yinze Wang, Wenlin Weng, Zhen Zhou, and Zhenguo Li. 2022. "Research on Tunnel Construction Monitoring Method Based on 3D Laser Scanning Technology" *Symmetry* 14, no. 10: 2065.
https://doi.org/10.3390/sym14102065