#
A Normal Cloud Model-Based Method for Risk Assessment of Water Inrush and Its Application **in a Super-Long Tunnel** Constructed by a Tunnel Boring Machine in the Arid Area of Northwest China

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Study Area

#### Engineering Background

## 3. Risk Assessment of Water Inrush

#### 3.1. Evaluation Index System

_{1}), geological factors (Q

_{2}), construction factors (Q

_{3}), and dynamic monitoring (Q

_{4}). In this paper, ten factors were selected to establish the assessment index system for water inrush, including landform and physiognomy (C

_{1}), unfavorable geological conditions (C

_{2}), strata inclination (C

_{3}), strength of the surrounding rock (C

_{4}), groundwater level (C

_{5}), water supply (C

_{6}), excavation disturbance (C

_{7}), supporting measures (C

_{8}), monitoring measurement (C

_{9}), and geological prediction (C

_{10}). C

_{1}~C

_{4}are geological factors, C

_{5}and C

_{6}are hydrological factors, C

_{7}and C

_{8}are construction factors, and C

_{9}and C

_{10}correspond to dynamic monitoring. In the established evaluation system, C

_{3}, C

_{4}, and C

_{5}are quantitative indices, and the index values were obtained by the measured data of the project. The other indices are qualitative indices, and the index values are determined by the expert scoring method. Combined with water inrush classification of the tunnel, the ten risk assessment indices were divided into four levels: low risk (I), medium risk (II), high risk (III), and higher risk (IV), as shown in Table 1.

#### 3.1.1. Landform and Physiognomy (C_{1})

#### 3.1.2. Unfavorable Geological Conditions (C_{2})

#### 3.1.3. Strata Inclination (C_{3})

#### 3.1.4. Strength of Surrounding Rock (C_{4})

#### 3.1.5. Groundwater Level (C_{5})

#### 3.1.6. Water Supply (C_{6})

#### 3.1.7. Excavation Disturbance (C_{7})

#### 3.1.8. Supporting Measure (C_{8})

#### 3.1.9. Monitoring Measurement (C_{9})

#### 3.1.10. Geological Prediction (C_{10})

#### 3.2. The Normal Cloud Model

#### 3.2.1. Cloud and Cloud Droplets

#### 3.2.2. Numerical Characteristics of Cloud

#### 3.2.3. Cloud Generator

- Calculate expectation ${E}_{x}$, entropy ${E}_{n}$, and hyper entropy ${H}_{e}$;
- Generate a normally distributed random number $\stackrel{\xb4}{{E}_{ni}}$ with expectation ${E}_{ni}$ and variance ${H}_{ei}$: $\stackrel{\xb4}{{E}_{ni}}~N({E}_{ni},{H}_{ei}^{2})$;
- Generate a normally distributed random number ${x}_{i}$ with expectation ${E}_{xi}$ and variance $\stackrel{\xb4}{{E}_{ni}}$: ${x}_{i}~N({E}_{xi},{\stackrel{\xb4}{{E}_{ni}}}^{2})$;
- Calculate the certainty degree of ${x}_{i}$, $\mu ({x}_{i})={e}^{-\frac{{({x}_{i}-{E}_{xi})}^{2}}{2{\stackrel{\xb4}{{E}_{ni}}}^{2}}}$;
- Generate a cloud drop (${x}_{i},\mu ({x}_{i})$), and repeat steps 1 to 5 until N cloud drops are generated.

#### 3.3. Evaluation Index Weight Calculation

#### 3.3.1. Subjective Weight Calculation

#### 3.3.2. Objective Weight Calculation

#### 3.3.3. Combination Weight Calculation

#### 3.4. Calculation of the Synthetic Certainty Degree

## 4. Results and Discussion

#### 4.1. Weight Calculation

#### 4.1.1. Subjective Weight Calculation Based on AHP

#### 4.1.2. Objective Weight Calculation Based on Entropy

_{1}~C

_{3}and C

_{5}~C

_{7}, the smaller the value, the lower the risk of water inrush. For the evaluation indices of C

_{4}and C

_{8}~C

_{10}, the larger the value, the lower the risk of water inrush. Based on the evaluation index values of water inrush in Table 4, the normalized matrix $B$ can be obtained by Formulas (11) and (12).

#### 4.1.3. Combination Weight Calculation

#### 4.2. Cloud Model of Water Inrush

#### 4.3. Risk Level Assessment

## 5. Excavation Verification

^{3}/h. Moreover, large-scale water inrush also appears on the right wall of SD52+090 and SD51+265, as seen in Figure 10b,c, and the measured maximum water inrush volume is 587 m

^{3}/h and 950 m

^{3}/h, respectively. Several outflow points of water inrush occur at the TBM shield of SD50+660, as seen in Figure 10d, and the measured maximum water inrush volume is 220 m

^{3}/h. Therefore, the evaluation results calculated by the proposed cloud model method show high consistency with the actual excavation situations, which demonstrates that this risk assessment method is of high accuracy and reliability for practical engineering.

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**The geological profile of the SS (Shuang-san) tunnel from SD52+500 to SD50+300. TBM, tunnel boring machine.

**Figure 3.**The measured data of the TBM monthly tunneling length and monthly pumping volume of the SS (Shuang-san) tunnel during the 19 months from August 2017 to February 2019.

**Figure 6.**Two different types of cloud generators. (

**a**) forward cloud generator; (

**b**) backward cloud generator.

**Figure 7.**Cloud of each assessment index generated by the forward cloud generator. (

**a**) landform and physiognomy (C

_{1}), unfavorable geological conditions (C

_{2}), water supply (C

_{6}), and excavation disturbance (C

_{7}); (

**b**) strata inclination (C

_{3}); (

**c**) strength of the surrounding rock (C

_{4}); (

**d**) groundwater level (C

_{5}); (

**e**) supporting measures (C

_{8}), monitoring measurement (C

_{9}), and geological prediction (C

_{10}).

**Figure 8.**The measured maximum water inrush volume of the ten samples in the SS (Shuang-san) tunnel.

**Figure 9.**The advanced geological prediction result of the complex frequency conductivity method at SD52+160.

**Figure 10.**Practical situation of water inrush in the SS (Shuang-san) tunnel. (

**a**) water inrush at SD52+160; (

**b**) water inrush at SD52+090; (

**c**) water inrush at SD51+265; (

**d**) water inrush at SD50+660.

Assessment Indices | I (Low Risk) | II (Medium Risk) | III (High Risk) | IV (Higher Risk) |
---|---|---|---|---|

Landform and physiognomy (C_{1}) | <25 | 25~50 | 50~75 | 75~100 |

Unfavorable geological conditions (C_{2}) | <25 | 25~50 | 50~75 | 75~100 |

Strata inclination (C_{3}) | <10 | 10~35 | 35~75 | 75~90 |

Strength of surrounding rock (C_{4}) | (BQ) > 450 | 350 < (BQ) ≤ 450 | 250 < (BQ) ≤ 350 | (BQ) ≤ 250 |

Groundwater level (C_{5}) | <10 | 10~30 | 30~60 | >60 |

Water supply (C_{6}) | <25 | 25~50 | 50~75 | 75~100 |

Excavation disturbance (C_{7}) | <25 | 25~50 | 50~75 | 75~100 |

Supporting measures (C_{8}) | 85~100 | 70~85 | 60~70 | <60 |

Monitoring measurement (C_{9}) | 85~100 | 70~85 | 60~70 | <60 |

Geological prediction (C_{10}) | 85~100 | 70~85 | 60~70 | <60 |

_{5}refers to the height difference between the tunnel floor and the groundwater level, and C

_{3}and C

_{5}are measured in meters and degrees, respectively. BQ refers to the basic quality of surrounding rock.

$\mathbf{Value}\mathbf{of}{\mathit{M}}_{\mathit{i}\mathit{j}}$ | Two-by-Two Comparison |
---|---|

1 | ${M}_{i}$ and ${M}_{j}$ are equally important |

3 | ${M}_{i}$ is slightly more important than ${M}_{j}$ |

5 | ${M}_{i}$ is more important than ${M}_{j}$ |

7 | ${M}_{i}$ is substantially more important than ${M}_{j}$ |

9 | ${M}_{i}$ is absolutely more important than ${M}_{j}$ |

2, 4, 6, 8 | the middle value of two adjacent judgements |

Explanation | When ${M}_{j}$ and ${M}_{i}$ are compared, the value is the reciprocal of ${M}_{i}$ and ${M}_{j}$ scalar. |

n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|

$RI$ | 0 | 0 | 0.58 | 0.90 | 1.12 | 1.24 | 1.32 | 1.41 | 1.45 | 1.49 |

Sample | C_{1} | C_{2} | C_{3} | C_{4} | C_{5} | C_{6} | C_{7} | C_{8} | C_{9} | C_{10} |
---|---|---|---|---|---|---|---|---|---|---|

SD52+160–SD52+135 | 45 | 85 | 66 | 320 | 104 | 30 | 70 | 55 | 65 | 50 |

SD52+135–SD52+060 | 40 | 80 | 62 | 320 | 102 | 20 | 65 | 60 | 70 | 50 |

SD52+060–SD51+980 | 20 | 45 | 60 | 400 | 115 | 10 | 40 | 85 | 80 | 85 |

SD51+980–SD51+917 | 10 | 35 | 63 | 330 | 112 | 10 | 45 | 80 | 80 | 80 |

SD51+917–SD51+280 | 10 | 20 | 62 | 380 | 115 | 10 | 30 | 90 | 85 | 90 |

SD51+280–SD51+264 | 15 | 85 | 60 | 300 | 118 | 10 | 80 | 65 | 75 | 40 |

SD51+264–SD51+212 | 20 | 50 | 55 | 280 | 113 | 10 | 60 | 70 | 75 | 65 |

SD51+212–SD51+170 | 10 | 60 | 54 | 340 | 108 | 10 | 65 | 75 | 75 | 70 |

SD51+170–SD50+660 | 10 | 15 | 65 | 380 | 117 | 10 | 35 | 90 | 80 | 90 |

SD50+660–SD50+617 | 10 | 35 | 62 | 420 | 120 | 10 | 40 | 80 | 80 | 80 |

Index | C_{1} | C_{2} | C_{3} | C_{4} | C_{5} |

AHP-based Weight | 0.1084 | 0.2672 | 0.0320 | 0.0541 | 0.2043 |

Entropy-based Weight | 0.1029 | 0.1287 | 0.1005 | 0.0985 | 0.1074 |

Combination Weight | 0.1062 | 0.2118 | 0.0594 | 0.0719 | 0.1655 |

Index | C_{6} | C_{7} | C_{8} | C_{9} | C_{10} |

AHP-based Weight | 0.1591 | 0.0290 | 0.0210 | 0.0180 | 0.1067 |

Entropy-based Weight | 0.0771 | 0.1010 | 0.1037 | 0.0720 | 0.1082 |

Combination Weight | 0.1263 | 0.0578 | 0.0541 | 0.0396 | 0.1073 |

Index | I | II | III | IV |
---|---|---|---|---|

C_{1} | (12.5, 4.1667, 0.01) | (37.5, 4.1667, 0.01) | (62.5, 4.1667, 0.01) | (87.5, 4.1667, 0.01) |

C_{2} | (12.5, 4.1667, 0.01) | (37.5, 4.1667, 0.01) | (62.5, 4.1667, 0.01) | (87.5, 4.1667, 0.01) |

C_{3} | (5, 1.6667, 0.01) | (22.5, 4.1667, 0.01) | (55, 6.6667, 0.01) | (82.5, 2.5, 0.01) |

C_{4} | (550, 33.3333, 0.01) | (400, 16.6667, 0.01) | (300, 16.6667, 0.01) | (125, 41.6667, 0.01) |

C_{5} | (5, 1.6667, 0.01) | (20, 3.3333, 0.01) | (45, 5, 0.01) | (90, 10, 0.01) |

C_{6} | (12.5, 4.1667, 0.01) | (37.5, 4.1667, 0.01) | (62.5, 4.1667, 0.01) | (87.5, 4.1667, 0.01) |

C_{7} | (12.5, 4.1667, 0.01) | (37.5, 4.1667, 0.01) | (62.5, 4.1667, 0.01) | (87.5, 4.1667, 0.01) |

C_{8} | (92.5, 2.5, 0.01) | (77.5, 2.5, 0.01) | (65, 1.6667, 0.01) | (30, 10, 0.01) |

C_{9} | (92.5, 2.5, 0.01) | (77.5, 2.5, 0.01) | (65, 1.6667, 0.01) | (30, 10, 0.01) |

C_{10} | (92.5, 2.5, 0.01) | (77.5, 2.5, 0.01) | (65, 1.6667, 0.01) | (30, 10, 0.01) |

Sample | C_{1} | C_{2} | C_{3} | C_{4} | C_{5} |

SD52+160–SD52+135 | 0.1987 | 0.8350 | 0.2579 | 0.4864 | 0.3761 |

SD52+135–SD52+060 | 0.8366 | 0.1959 | 0.5776 | 0.4864 | 0.4871 |

SD52+060–SD51+980 | 0.1944 | 0.1987 | 0.7557 | 1.0000 | 0.0441 |

SD51+980–SD51+917 | 0.8359 | 0.8355 | 0.4875 | 0.1985 | 0.0888 |

SD51+917–SD51+280 | 0.8359 | 0.1944 | 0.5776 | 0.4869 | 0.0441 |

SD51+280–SD51+264 | 0.8355 | 0.8350 | 0.7557 | 1.0000 | 0.0199 |

SD51+264–SD51+212 | 0.1944 | 0.0112 | 1.0000 | 0.4873 | 0.0707 |

SD51+212–SD51+170 | 0.8359 | 0.8352 | 0.9888 | 0.0562 | 0.1985 |

SD51+170–SD50+660 | 0.8359 | 0.8355 | 0.3264 | 0.4869 | 0.0259 |

SD50+660–SD50+617 | 0.8359 | 0.8355 | 0.5776 | 0.4860 | 0.0110 |

Sample | C_{6} | C_{7} | C_{8} | C_{9} | C_{10} |

SD52+160–SD52+135 | 0.2022 | 0.1975 | 0.0442 | 1.0000 | 0.1355 |

SD52+135–SD52+060 | 0.1944 | 0.8352 | 0.0113 | 0.0111 | 0.1355 |

SD52+060–SD51+980 | 0.8359 | 0.8355 | 0.0111 | 0.6036 | 0.0111 |

SD51+980–SD51+917 | 0.8359 | 0.1984 | 0.6036 | 0.6036 | 0.6036 |

SD51+917–SD51+280 | 0.8359 | 0.1966 | 0.6038 | 0.0111 | 0.6038 |

SD51+280–SD51+264 | 0.8359 | 0.1979 | 1.0000 | 0.6047 | 0.6064 |

SD51+264–SD51+212 | 0.8359 | 0.8352 | 0.0111 | 0.6047 | 1.0000 |

SD51+212–SD51+170 | 0.8359 | 0.8357 | 0.6047 | 0.6047 | 0.0118 |

SD51+170–SD50+660 | 0.8359 | 0.8361 | 0.6038 | 0.6036 | 0.6038 |

SD50+660–SD50+617 | 0.8359 | 0.8355 | 0.6036 | 0.6036 | 0.6036 |

**Table 8.**Calculation results of the different evaluation methods applied to the SS (Shuang-san) tunnel.

Sample | Synthetic Certainty Degree | The Cloud Model Method | Ideal Point Method | Gray Relation Projection Method | |||
---|---|---|---|---|---|---|---|

U(I) | U(II) | U(III) | U(IV) | ||||

SD52+160–SD52+135 | 0 | 0.0466 | 0.1013 | 0.2561 | IV | IV | IV |

SD52+135–SD52+060 | 0.0245 | 0.0889 | 0.1180 | 0.1373 | IV | III | IV |

SD52+060–SD51+980 | 0.1260 | 0.1880 | 0.0449 | 0.0073 | II | II | III |

SD51+980–SD51+917 | 0.1943 | 0.3098 | 0.0432 | 0.0147 | II | II | II |

SD51+917–SD51+280 | 0.3334 | 0.0464 | 0.0343 | 0.0073 | I | II | II |

SD51+280–SD51+264 | 0.1943 | 0.0240 | 0.1709 | 0.2567 | IV | IV | IV |

SD51+264–SD51+212 | 0.1262 | 0.0240 | 0.2530 | 0.0117 | III | III | III |

SD51+212–SD51+170 | 0.1943 | 0.0567 | 0.2893 | 0.0329 | III | III | III |

SD51+170–SD50+660 | 0.4688 | 0.1072 | 0.0194 | 0.0043 | I | II | II |

SD50+660–SD50+617 | 0.1943 | 0.3816 | 0.0343 | 0.0018 | II | II | II |

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Wang, X.; Shi, K.; Shi, Q.; Dong, H.; Chen, M. A Normal Cloud Model-Based Method for Risk Assessment of Water Inrush and Its Application **in a Super-Long Tunnel** Constructed by a Tunnel Boring Machine in the Arid Area of Northwest China. *Water* **2020**, *12*, 644.
https://doi.org/10.3390/w12030644

**AMA Style**

Wang X, Shi K, Shi Q, Dong H, Chen M. A Normal Cloud Model-Based Method for Risk Assessment of Water Inrush and Its Application **in a Super-Long Tunnel** Constructed by a Tunnel Boring Machine in the Arid Area of Northwest China. *Water*. 2020; 12(3):644.
https://doi.org/10.3390/w12030644

**Chicago/Turabian Style**

Wang, Xin, Kebin Shi, Quan Shi, Hanwei Dong, and Ming Chen. 2020. "A Normal Cloud Model-Based Method for Risk Assessment of Water Inrush and Its Application **in a Super-Long Tunnel** Constructed by a Tunnel Boring Machine in the Arid Area of Northwest China" *Water* 12, no. 3: 644.
https://doi.org/10.3390/w12030644