# A Novel Calculation Method of Process Load for Extra-Large Section Tunnels

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

_{0}from 0.8 to 3), and the excavation roof rise-to-span ratio on the surrounding rock pressure.

^{2}, in this study, we calculated the loosening pressure of the large-span Liantang Tunnel through traditional state calculation methods and analyzed and compared the calculated results. This paper discusses the problems existing in the application of load and surrounding rock pressure calculation methods to extra-large-section tunnels. On this basis, we proposed a concept of process design load and focused on the difference and relationship between the process load calculation method and the traditional state load calculation method. By introducing the concepts of influence coefficient and weight coefficient in combination with various excavation methods, a calculation method, considering the influence of the construction process, for the process load of extra-large-section tunnels was developed. By comparing the on-site monitored pressure data and the calculated load results, this paper demonstrates the rationality and feasibility of the process load calculation method from a practical perspective and provides a theoretical reference and a calculation basis for the design and construction of similar projects in the future.

## 2. Project Overview

^{3}/m, which is the largest section highway tunnel in the world so far. How to determine the load and surrounding rock pressure of the Liantang Tunnel is a major technical problem to be solved in the design of the supporting parameters for extra-large-section tunnels. The section size map of the Liantang Tunnel’s large-span bifurcation section and the geological section of the tunnel are shown in Figure 2 and Figure 3, respectively. All sections are symmetrical.

## 3. Application of Traditional State Calculation Methods in the Extra-Large Section of the Liantang Tunnel

#### 3.1. Analysis of the Load and Surrounding Rock Pressure of the Liantang Tunnel

#### 3.1.1. Calculation Based on the Code for the Design of Road Tunnels

^{2}); $h$ is the load equivalent height (m); $\gamma $ is the surrounding rock unit weight (kN/m

^{3}); $S$ is the surrounding rock grade; $\omega $ is the width influence coefficient; ${B}_{t}$ is the maximum excavation span of the tunnel (m); and $i$ denotes the rate of increase or decrease of surrounding rock pressure for every 1 m increase or decrease in ${B}_{t}$, which is based on the vertical uniform pressure of the surrounding rock of the tunnel, with ${B}_{t}=5\text{}\mathrm{m}$, $i$ = 0.2 when ${B}_{t}<5\text{}\mathrm{m}$, and $i$ = 0.1. Furthermore, $e$ is the average horizontal uniform surrounding rock pressure (kN/m

^{2}), and $\lambda $ is the lateral pressure coefficient, which was adopted according to the specifications given in Table 3.

#### 3.1.2. Calculation Based on the Protodyakonov’s Theory

^{2}), ${h}_{q}$ is the pressure arch height (m), ${B}_{m}$ is the pressure arch span (m), ${B}_{p}$ is the projection width of the rupture surface on both sides of the tunnel on the horizontal plane (m), ${B}_{t}$ is the tunnel excavation span (m), ${H}_{t}$ is the tunnel excavation height (m), ${\phi}_{c}$ is the calculated friction angle (°), ${f}_{kp}$ is the surrounding rock Protodyakonov coefficient, and ${R}_{b}$ is the uniaxial compression strength of rock (MPa).

#### 3.1.3. Calculation Based on the RMR System

- uniaxial compressive strength, ${R}_{c}$;
- RQD;
- spacing of joint group;
- groundwater influence coefficient;
- joint roughness coefficient;
- joint occurrence and combination relationship.

^{2}), $\gamma $ is the surrounding rock unit weight (kN/m

^{3}), and $B$ is the tunnel maximum excavation span (m).

#### 3.2. Analysis of the Load Calculation Results of the Liantang Tunnel’s Large-Span Section

## 4. State Design Method and Process Design Method

#### 4.1. Concept of Process Design Method

#### 4.2. Connections and Differences Between the State Design Method and Process Design Method

## 5. Calculation Method of Process Load for Extra-Large-Section Tunnel

#### 5.1. Proposal for Calculating Loosening Load of Extra-Large-Section Tunnel

#### 5.2. Establishment of Simplified Model for Process Load Calculation Method

#### 5.3. Derivation of the Calculation Correlation for Process Load Method

#### 5.3.1. Influence Coefficient $\eta $ and Weight Coefficient $\alpha $

#### 5.3.2. Deduction of the Calculation Correlation

#### 5.4. Comparison and Analysis of Construction Methods Based on Process Load

#### 5.5. Process Load Calculation of Large-Span Section of the Liantang Tunnel

#### 5.6. On-Site Monitoring of Surrounding Rock Pressure of the Liantang Tunnel

#### 5.7. Discussions

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 4.**Simplified models of excavation methods: (

**a**) double sidewall heading method, (

**b**) center diaphragm (CD) method, and (

**c**) bench method.

Item | Applicable Conditions | Indicators of Influencing Factors Involved | Characteristics of Correlations | Weakness |
---|---|---|---|---|

Code for the Design of Road Tunnels (in Chinese) | Span less than 12 m, span ratio less than 1.7 | Span, surrounding rock grades | Empirical statistics | Neglects the effect of height |

Code for the Design of Railway Tunnels (in Chinese) | Span ratio less than 1.7 | Surrounding rock grades | Empirical statistics | Only a handful of parameters considered |

Code for the Design of Hydraulic Tunnels (in Chinese) | Span less than 12 m, span ratio less than 1.7 | Span, tunnel height | Empirical statistics | Only a handful of parameters considered |

Protodyakonov’s theory | Loose media, small span | Span, tunnel height, internal friction angle, solidity coefficient | Formula derivation | Solidity coefficient needs to be determined by experience |

Barton classification | Various formation conditions | Joints, groundwater, and other factors | Empirical statistics | Neglects the effect of geometrical dimension |

Rock mass rating (RMR) system | Various formation conditions | Span, joints, groundwater, and other factors | Empirical statistics | Neglects the effect of height |

Goel correlation | More suitable for deep-buried tunnels | Span, joints, groundwater, and other factors | Empirical statistics | Neglects the effect of height |

Singh correlation | Various formation conditions | Estimated value involves multiple factors | Empirical statistics | Neglects the effect of geometrical dimension |

**Table 2.**Surrounding rock’s mechanical parameters for the Liantang Tunnel’s large-span bifurcation section.

Item | Two-Lane Section | Three-Lane Section | Maximum Section | Gradient Section | Four-Lane Section |
---|---|---|---|---|---|

Unlined tunnel span (m) | 12.47 | 15.73 | 30.01 | 23.62 | 21.03 |

Unlined tunnel height (m) | 9.94 | 11.03 | 18.41 | 15.00 | 13.51 |

Surrounding rock grades | II | III | III | IV | V |

Bulkdensity (kN/m^{3}) | 25 | 24 | 24 | 23 | 19 |

Modulus of elasticity (GPa) | 20 | 12 | 12 | 6 | 1.5 |

Poisson’s ratio | 0.22 | 0.25 | 0.25 | 0.30 | 0.35 |

Cohesion (kPa) | 1200 | 700 | 700 | 200 | 50 |

Internal friction angle (°) | 50 | 40 | 40 | 30 | 25 |

Consistent coefficient | 6.0 | 4.5 | 4.5 | 2.3 | 1.1 |

Elastic resistance coefficient (MPa/m) | 1200 | 540 | 540 | 160 | 90 |

Surrounding Rock Grades | I, II | III | IV | V | VI |
---|---|---|---|---|---|

Lateral pressure coefficient | 0 | <0.15 | 0.15–0.3 | 0.3–0.5 | 0.5–1.0 |

Cross-Section Type | Surrounding Rock Grades | Lateral Pressure Coefficient | Height of Loose Media (m) | Vertical Uniform Pressure (kPa) | Horizontal Uniform Pressure (kPa) |
---|---|---|---|---|---|

Two-lane section | Class II and deep burial | 0 | 1.57 | 39.31 | 0 |

Three-lane section | Class III and deep burial | 0.15 | 3.73 | 89.55 | 13.43 |

Maximum section | Class III and deep burial | 0.15 | 6.30 | 151.24 | 22.69 |

Gradient section | Class IV and deep burial | 0.3 | 10.30 | 236.97 | 71.09 |

Four-lane section | Class V and deep burial | 0.5 | 18.74 | 356.09 | 178.05 |

Cross-Section Type | Surrounding Rock Grades | Consistent Coefficient | Span of Equilibrium Arch (m) | Height of Equilibrium Arch (m) | Vertical Uniform Pressure (kPa) |
---|---|---|---|---|---|

Two-lane section | Class II anddeep burial | 6.0 | 19.71 | 1.64 | 41.05 |

Three-lane section | Class III anddeep burial | 4.5 | 26.02 | 2.89 | 69.38 |

Maximum section | Class III anddeep burial | 4.5 | 47.18 | 5.24 | 125.81 |

Gradient section | Class IV anddeep burial | 2.3 | 40.94 | 8.90 | 204.70 |

Four-lane section | Class V anddeep burial | 1.1 | 38.24 | 17.38 | 330.29 |

Cross-Section Type | Two-Lane Section | Three-Lane Section | Maximum Section | Gradient Section | Four-Lane Section |
---|---|---|---|---|---|

Surrounding rock grades | II | III | III | IV | V |

${R}_{c}$ (MPa) | 60 | 45 | 45 | 23 | 11 |

Score | 7 | 6 | 6 | 4 | 1 |

Rock quality designation (RQD) | 90 | 75 | 75 | 50 | 25 |

Score | 18 | 15 | 15 | 13 | 4 |

Spacing of joint group | 2.9 | 1.2 | 1.2 | 0.3 | 0.05 |

Score | 25 | 20 | 20 | 12 | 3 |

Groundwater influence coefficient | 1.0 | 1.0 | 1.0 | 1.0 | 1.0 |

Score | 10 | 9 | 9 | 8 | 3 |

Joint roughness coefficient | 20 | 18 | 18 | 12 | 2 |

Joint occurrence and combination relationship | 0 | −2 | −2 | −5 | −5 |

RMR value | 80 | 66 | 66 | 44 | 8 |

P (kPa) | 62.35 | 128.36 | 244.88 | 304.23 | 367.60 |

Class III and Deep Burial | Class IV and Deep Burial | Class V and Deep Burial | ||||
---|---|---|---|---|---|---|

Maximum Section | Two-Lane Section | Gradient Section | Two-Lane Section | Four-Lane Section | Two-Lane Section | |

Code for the Design of Road Tunnels (in Chinese) (kPa) | 151.24 | 75.47 | 236.97 | 144.65 | 356.09 | 238.99 |

Protodyakonov’s theory (kPa) | 125.81 | 57.97 | 204.70 | 119.74 | 330.29 | 217.07 |

RMR system (kPa) | 244.88 | 101.76 | 304.23 | 160.61 | 367.60 | 217.98 |

Mean value (kPa) | 173.98 | 78.40 | 248.63 | 141.67 | 351.33 | 224.68 |

Surrounding Rock Grades | I, II | III | IV | V | VI |
---|---|---|---|---|---|

Horizontal uniform pressure (MPa) | 0 | <0.15 $q$ | (0.15–0.3) $q$ | (0.3–0.5) $q$ | (0.5–1.0) $q$ |

Surrounding Rock Grades | Total Height of Tunnel | Total Span of Tunnel | Bulk Density (kN/m^{3}) | Consistent Coefficient | Internal Friction Angle (°) |
---|---|---|---|---|---|

Class V and deep burial | 21.03 | 13.51 | 19 | 1.1 | 25 |

**Table 10.**Comparison of the vertical uniform load calculations for different excavation methods under deep-buried Grade V surrounding rock conditions.

Excavation Method and Excavation Sequence | Protodyakonov’s Theory (kPa) | Code for the Design of Road Tunnels (In Chinese) (kPa) | Influence Coefficient ${\mathit{\eta}}_{1}$, ${\mathit{\eta}}_{2}$, ${\mathit{\eta}}_{3}$ | Width of Guide Hole ${\mathit{b}}_{1}$, ${\mathit{b}}_{2}$, ${\mathit{b}}_{3}$ (m) | Height of Guide Hole ${\mathit{h}}_{1}$, ${\mathit{h}}_{2}$, ${\mathit{h}}_{3}$ (m) | Legend of Excavation Steps | |
---|---|---|---|---|---|---|---|

Double sidewall heading method (three guide holes) | First the side and then the middle | 210.96 | 192.57 | 1.2 | 7.3 | 10.97 | |

1.2 | 7.3 | 10.97 | |||||

1.0 | 10.0 | 12.67 | |||||

Sequential excavation | 223.52 | 203.73 | 1.2 | 7.3 | 10.97 | ||

1.2 | 10.0 | 12.67 | |||||

1.0 | 7.3 | 10.97 | |||||

First the middle and then the side | 247.47 | 225.22 | 1.2 × 1.2 | 10.0 | 12.67 | ||

1.0 | 7.3 | 10.97 | |||||

1.0 | 7.3 | 10.97 | |||||

Median septum excavation (two guide holes) | Sequential excavation | 241.32 | 222.07 | 1.2 | 0.5 × 21.03 | 12.67 | |

1.0 | 0.5 × 21.03 | 12.67 | |||||

Four guide holes | Sequential excavation | 202.15 | 153.18 | 1.2 | 0.25 × 21.03 | 12.67 | |

1.2 | 0.25 × 21.03 | 12.67 | |||||

1.2 | 0.25 × 21.03 | 12.67 | |||||

1.0 | 0.25 × 21.03 | 12.67 | |||||

A single excavation | - | 330.29 | 356.09 | - | 20.87 | 13.56 |

Section Size | Surrounding Rock Grades | Buried Depth (m) | Total Span (m) | Total Height (m) | Bulk Density (kN/m^{3}) | Consistent Coefficient | c (kPa) | $\mathit{\phi}$ (°) | Width of Guide Hole ${\mathit{b}}_{1}$, ${\mathit{b}}_{2}$, ${\mathit{b}}_{3}$ (m) | Height of Guide Hole ${\mathit{h}}_{1}$, ${\mathit{h}}_{2}$, ${\mathit{h}}_{3}$ (m) | Influence Coefficient ${\mathit{\eta}}_{1}$, ${\mathit{\eta}}_{2}$, ${\mathit{\eta}}_{3}$ |
---|---|---|---|---|---|---|---|---|---|---|---|

Maximum section | Class III and deep burial | 70 | 30.01 | 18.41 | 24 | 4.5 | 700 | 40 | 15 | 17.49 | 1.2 |

15 | 17.49 | 1.0 | |||||||||

Gradient section | Class IV and deep burial | 61 | 23.62 | 15.00 | 23 | 2.3 | 200 | 30 | 11.81 | 14.25 | 1.2 |

11.81 | 14.25 | 1.0 | |||||||||

Four-lane section | Class V and deep burial | 59 | 21.03 | 13.51 | 19 | 1.1 | 50 | 25 | 7.3 | 10.97 | 1.2 |

7.3 | 10.97 | 1.2 | |||||||||

10.0 | 12.67 | 1.0 |

**Table 12.**Loosening load of the Liantang Tunnel’s large-span section based on process design methods.

Section Size | Surrounding Rock Grades | Vertical Uniform Pressure (kPa) | |
---|---|---|---|

Protodyakonov’s Theory | Code for the Design of Road Tunnels (In Chinese) | ||

Maximum section | Class III and deep burial | 107.35 | 115.83 |

Gradient section | Class IV and deep burial | 162.52 | 154.37 |

Four-lane section | Class V and deep burial | 210.96 | 192.57 |

Section Size | Measured Value (kPa) | Calculated Value of Process Design Load (kPa) | Calculated Value of State Design Load (kPa) | ||
---|---|---|---|---|---|

Protodyakonov’s Theory | Code for the Design of Road Tunnels (In Chinese) | Protodyakonov’s Theory | Code for the Design of Road Tunnels (In Chinese) | ||

Maximum section | 94.34 | 107.35 | 115.83 | 125.81 | 151.24 |

Gradient section | 146.73 | 162.52 | 154.37 | 204.70 | 236.97 |

Four-lane section | 178.01 | 210.96 | 192.57 | 330.29 | 356.09 |

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## Share and Cite

**MDPI and ACS Style**

Gao, H.; He, P.; Chen, Z.; Li, X.
A Novel Calculation Method of Process Load for Extra-Large Section Tunnels. *Symmetry* **2019**, *11*, 1228.
https://doi.org/10.3390/sym11101228

**AMA Style**

Gao H, He P, Chen Z, Li X.
A Novel Calculation Method of Process Load for Extra-Large Section Tunnels. *Symmetry*. 2019; 11(10):1228.
https://doi.org/10.3390/sym11101228

**Chicago/Turabian Style**

Gao, Hongjie, Ping He, Zheng Chen, and Xinyu Li.
2019. "A Novel Calculation Method of Process Load for Extra-Large Section Tunnels" *Symmetry* 11, no. 10: 1228.
https://doi.org/10.3390/sym11101228