# Study on a Surrounding Rock Pressure Calculation Method for Super-Large Section Highway Tunnels

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}, making it the largest highway tunnel in the world so far. Based on this project, this paper analyses the applicability of various traditional methods of calculating the surrounding rock pressure for super-large section tunnels. In addition, based on the Tunneling Quality Index (Q), the factor of span is introduced into the method of calculating the surrounding rock pressure using the numerical simulation results of super-large symmetrical tunnels with different values of Q and different spans. Additionally, calculated correlations that could quickly estimate the surrounding rock pressure of tunnels are obtained. The comparison of surrounding rock pressures between the estimated and monitoring results of Liantang tunnel and more than 30 projects around the world effectively proves the rationality and universal applicability of the proposed correlations. This method could provide engineers and designers with a quick way to predict the surrounding rock pressure of deep super-large section underground structures during their design and construction stage.

## 1. Introduction

^{2}and the super-large section tunnel is over 140 m

^{2}. According to some statistics, up till now, there are 51 highway tunnels with a maximum area of more than 200 m

^{2}excavated by drilling and blasting methods in China and abroad. The construction situation of some super-large section tunnels is shown in Table 2.

_{0}from 0.8 to 3) and excavation roof rise-to-span ratio on the surrounding rock pressure. Based on the block theory, Prasad et al. [12] proposed a calculation method for surrounding rock pressure. Scussel et al. [13] proposed a new approach to obtain tunnel support pressure for polyaxial state of stress. The proposed method incorporates the intermediate principal stress in the analysis and has a wide applicability to many available software. These research results provide abundant references for calculating the surrounding rock pressure of large section tunnels. However, due to the complexity of geological conditions and construction processes, studies focusing on the surrounding rock pressure of super-large section highway tunnels with excavation area exceeding 400 m

^{2}are scarce in literature.

## 2. Project Overview

_{c}—Uniaxial compressive strength of rocks; K

_{ν}—Integrity index of the rock mass. The Tunneling Quality Index (Q) system [15] was proposed by the Norwegian scholar Barton to estimate the surrounding rock pressure that can reflect the influence of multiple factors. The corresponding correlation is given by Equation (2):

_{n}—Joint group coefficient; J

_{r}—Joint roughness coefficient; J

_{a}—Joint alteration value; J

_{w}—Water cut reduction coefficient of joints; SRF—Initial stress reduction coefficient. The surrounding rock classification is based on the [BQ] value or the Q value. Table 3 [16] shows the simplified relationship between the two systems.

^{3}/m. It is the largest highway tunnel in the world (Figure 3). Since this excavation span is very rare and there are only a few analogous projects, reasonable calculation of the surrounding rock pressure of the super-large section deep-buried underground structure becomes the key to the structural design and safe construction of the Liantang tunnel (China).

## 3. Applicability Analysis of Various Traditional Methods of Calculating the Surrounding Rock Pressure for Super-Large Section Tunnel

- 1)
- Traditional theories: including Protodyakonov’s theory, Terzaghi theory, and the Caquot correlation.
- 2)
- Industry recommended standards: Code for Design of Railway Tunnel (TB10003-2016), Guidelines for Design of Highway Tunnel (JTG D70-2010) and Specification for design of hydraulic tunnel (DLT_5195-2004).
- 3)
- Surrounding rock pressure correlations based on rock mass classification system: including correlations based on the Q system proposed by Grimstad and Barton [15] and by Bhasin and Grimstad [19]. Geol [20] proposed a correlation based on rock mass number N, while Unal [21] proposed a correlation based on RMR classification system.

#### 3.1. Comparison of the Common-Applied Calculation Methods for Surrounding Rock Pressure

- γ—Rock mass bulk density; h
_{1}= d_{1}/f; d_{1}= 0.5d + htan(45°–0.5ϕ); d—Tunnel span; h—Tunnel height; ϕ—Internal friction; f—Rigidity coefficient. - c—Cohesion; λ—Lateral pressure coefficient. The other parameters are the same as above.
- h* = h{0.45×2
^{s−}^{1}×[1+i(B−5)]}; S—Surrounding rock grade; B—Tunnel span; i—Surrounding rock pressure change rate. The other parameters are the same as above. - k
_{1}and k_{2}, calculation coefficients; r—Approximate radius. The other parameters are the same as above. - $Q=\frac{RQD}{{J}_{n}}\times \frac{{J}_{r}}{{J}_{a}}\times \frac{{J}_{w}}{SRF}$; RQD—Rock quality index; J
_{n}—Joint group coefficient; J_{r}—Joint roughness coefficient; J_{a}—Joint alteration value; J_{w}—Water cut reduction coefficient of joints; SRF—Initial stress reduction coefficient. P_{1}is the same as P_{2}when J_{n}= 9, P_{1}is greater than P_{2}when J_{n}< 9 and P_{1}is less than P_{2}when J_{n}> 9. - $N=\frac{RQD}{{J}_{n}}\times \frac{{J}_{r}}{{J}_{a}}\times {J}_{w}$. α is a correction factor, usually 0.5~2.0. The other parameters are the same as above.
- The parameters are the same as in Correlation 5
- RMR
_{76}is the hierarchical value of the RMR system.

#### 3.2. Analysis of Different Surrounding Rock Pressure Calculation Methods for the Large-Span Section of the Liantang Tunnel

#### 3.3. Influence of Span on the Calculation Methods of Surrounding Rock Pressure

## 4. Study on Surrounding Rock Pressure under Different Spans and Different Q Values

#### 4.1. Numerical Model

#### 4.2. Selection of Parameters and Calculation Conditions

#### 4.3. Analysis of the Calculated Results

- 1)
- Under the same span, the surrounding rock pressure decreases with the increase in Q value.
- 2)
- Under the same Q value, the pressure increases with the increase in tunnel span. However, as the Q value increases, the increase in pressure gradually decreases.

## 5. Estimation of the Surrounding Rock Pressure Based on Q System and Span

#### 5.1. Establishment of the Estimation Correlation

^{3}. Therefore, the estimation correlation for surrounding rock pressure based on Q value and span d is obtained as follows (see Equations (13) and (14)):

_{roof}

_{1}and P

_{roof}

_{2}in Equations (11) and (12) are kPa, while those of d are m. J

_{n}—Joint group coefficient; J

_{r}—Joint roughness coefficient. P

_{roof}

_{1}= P

_{roof}

_{2}when J

_{n}= 9; P

_{roof}

_{1}> P

_{roof}

_{2}when J < 9; P

_{roof}

_{1}< P

_{roof}

_{2}when J

_{n}> 9.

_{n}= 9 and J

_{r}= 1, the relationship between the surrounding rock pressure and Q values under different spans is calculated, and the corresponding results are shown in Figure 12.

- 1)
- Under the same span, with the increase in Q value, the quality of surrounding rock increases. Furthermore, the surrounding rock pressure of the vault gradually decreases and tends to stabilize.
- 2)
- Under the same Q value, as the span increases, the surrounding rock pressure of the vault gradually becomes larger.
- 3)
- According to the local graph, when Q value is between 0 and 1, the slope of surrounding rock pressure curve increases rapidly with the decrease in Q value for the same span. This means a worse quality of surrounding rock results in a greater increase in the surrounding rock pressure.
- 4)
- As shown in the local graph, smaller the Q value, worse is the quality of surrounding rock, and more obvious is the influence of span on the surrounding rock pressure.

- 1)
- The relationship between the slope β and Q value is based on the calculation model of lateral pressure coefficient λ = 2 and height-to-span ratio of 0.6. Therefore, the correlations are applicable to caverns, whose product of the lateral pressure coefficient and height-to-span ratio is close to 1.
- 2)
- The correlations are derived on the basis of Q system, so they are similar to the correlation based on Q system. They represent the calculation of surrounding rock pressure under deep burial conditions.
- 3)
- The surrounding rock pressure of underground structure with a span greater than 10 m is analyzed statistically in the process of deriving the correlation. Therefore, the calculation correlations for the surrounding rock pressure are more suitable for underground structures with large span.

#### 5.2. Comparison between the Results of Correlations and the Measured Values

#### 5.3. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 4.**Comparisons between the measured values and the calculated values using different correlations.

Section Size | Excavation Area/m^{2} | Remark |
---|---|---|

Standard section | 70~80 | Two-lane highway tunnel |

Large section | 100~140 | Two-lane highway tunnel with crosswalk |

Super-large section | > 140 | Highway tunnels with three or more lanes |

Tunnel | Span/m | Tunnel Height/m | Height-Span Ratio | Excavation Area/m^{2} | Tunnel Type | Completion Time |
---|---|---|---|---|---|---|

Qingdao Jiaozhou Bay | 28.3 | 18.64 | 0.66 | 411.9 | Branch | June 2011 |

Dalian Hanjialing | 21.2 | 15.52 | 0.731 | 230 | Single Four-lane | April 2003 |

Guangzhou Longtoushan | 24.5 | 13.56 | 0.63 | 230 | Twin Eight-lane | October 2008 |

Shenzhen Henglongshan | 29.2 | - | - | 304 | Branch | October 2008 |

Shenzhen Yabao | 20.9 | 13.48 | 0.645 | 220 | Twin Eight-lane | January 2007 |

Fuzhou Jinjishan | 41.4 | 13.2 | - | 171 × 2 | Twin-arch | May 2009 |

Sang-Lim, Korea | 18.77 | 10.48 | 0.56 | 170 | Single Four-lane | 2005 |

Dongming, Japan | 16.53 | 8.4 | 0.51 | 170~200 | Single Three-lane | 1989 |

Toshikazu, Japan | 20 | 13.5 | 0.67 | 225 | Water diversion | 1989 |

The Channel, Europe | 21.2 | 15.4 | 0.73 | 252 | - | - |

Second, Japan | 24 | - | - | 240 | - | - |

Kobylish Metro, Czech | 20.35 | 13.75 | 0.68 | 220 | Single | 2006 |

Value | Class I (Very Good) | Class II (Good) | Class III (Fair) | Class IV (Poor) | Class V (Very Poor) |
---|---|---|---|---|---|

[BQ] | >550 | 451~550 | 351~450 | 251~350 | <250 |

Q | >40 | 10~40 | 4~10 | 1~4 | <1 |

Number | Section Size | Value of [BQ] | Value of Q | Evaluation of Q | Classification of Surrounding Rock |
---|---|---|---|---|---|

1 | Standard two-lane | 464.98 | 19.97 | Good | II |

2 | Maximum section | 395.91 | 5.92 | Fair | III |

3 | Gradient section | 395.91 | 5.92 | Fair | III |

4 | Gradient section | 346.92 | 2.02 | Poor | IV |

5 | Standard four-lane | 346.92 | 2.02 | Poor | IV |

6 | Standard four-lane | 243.15 | 0.86 | Very poor | V |

Number | Correlation | Proposer |
---|---|---|

1 | $P=\gamma {h}_{1}$ | Protodyakonov [22] |

2 | $P=\frac{\gamma {d}_{1}-c}{\lambda \mathrm{tan}\phi}$, ${d}_{1}=0.5d+h\mathrm{tan}({45}^{\xb0}-0.5\phi )$ | Karl Terzaghi [23] |

3 | $P=\gamma {h}^{*}$, ${h}^{*}=h\left\{0.45\times {2}^{s-1}\times \left[1+i\left(B-5\right)\right]\right\}$ | TB10003-2016 of China [14] |

4 | $P={k}_{1}\gamma r-{k}_{2}c$ | Caquot [24] |

5 | ${P}_{1}=\left(\frac{200}{{J}_{r}}\right){Q}^{-\frac{1}{3}}$, ${P}_{2}=\frac{200{J}_{n}^{\frac{1}{2}}{Q}^{-\frac{1}{3}}}{3{J}_{r}}$ | Barton [15] |

6 | $P=\left(\frac{\alpha}{30}\right){10}^{\frac{{H}^{0.6}{r}^{0.1}}{50{N}^{0.33}}+3}$ | Bhasin and Grimstad [19] |

7 | $P=\frac{40}{{J}_{r}}d{Q}^{-\frac{1}{3}}$ | Geol [20] |

8 | $P=\frac{100-RM{R}_{76}}{100}\rho d$ | Unal [21] |

Item | Q | ρ (kg/m^{3}) | ϕ | c(kPa) | λ | h(m) | d(m) |

Value | 5.92 | 2500 | 45° | 700 | 2 | 18.4 | 30 |

Item | H(m) | J_{n} | J_{r} | RMR | k_{1} | k_{2} | |

Value | 0 | 9 | 1 | 60.01 | 0.249 | 0.261 |

Correlation Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |

Result/kPa | 503.31 | 194.97 | 157.52 | 52.37 | 155.78 | 50.20 | 756 | 326.10 |

Number | Value of Q | E(GPa) | ρ(kg/m^{3}) | ν | ϕ | c (kPa) |
---|---|---|---|---|---|---|

1 | 0.86 | 1.3 | 2500 | 0.3 | 22 | 100 |

2 | 2.02 | 3 | 2500 | 0.3 | 33 | 500 |

3 | 5.92 | 10 | 2500 | 0.3 | 45 | 700 |

4 | 19.97 | 27 | 2500 | 0.3 | 50 | 2100 |

Span/m | Q = 0.86 | Q = 2.02 | Q = 5.92 | Q = 19.97 |
---|---|---|---|---|

5 | Two-bench excavation | Two-bench excavation | Full face excavation | Full face excavation |

10 | Two-bench excavation | Two-bench excavation | Two-bench excavation | Two-bench excavation |

15 | Three-bench seven-step excavation | Three-bench excavation | Three-bench excavation | Three-bench excavation |

20 | Three-bench seven-step excavation | Three-bench excavation | Three-bench excavation | Three-bench excavation |

25 | Three-bench seven-step excavation | Three-bench seven-step excavation | Three-bench seven-step excavation | Three-bench seven-step excavation |

30 | Oneside-wallheading excavation | Oneside-wall headingexcavation | One side-wall heading excavation | Three-bench seven-Step excavation |

35 | Doubleside-wall headingexcavation | Double side-wall heading excavation | Doubleside-wallheading excavation | One side-wall heading excavation |

40 | Doubleside-wallheading excavation | Doubleside-wallheading excavation | Doubleside-wallheading excavation | Double side-wall heading excavation |

Value of Q | Slope | Fitted Equations | Correlative Coefficients R^{2} |
---|---|---|---|

0.86 | 3.763 | $P=3.763d+106.10$ | 0.9477 |

2.02 | 3.223 | $P=3.223d+93.68$ | 0.9717 |

5.92 | 1.974 | $P=1.974d+86.04$ | 0.7976 |

19.97 | 1.425 | $P=1.425d+63.54$ | 0.8394 |

Number | Engineering Name | Span/m | Measured Value (kPa) | Estimated Value(kPa) | Value of Q | J_{n} | J_{r} |
---|---|---|---|---|---|---|---|

1 | Liantang Tunnel | 30 | 197.12 | 183.19 | 5.92 | 1 | 9 |

2 | Jiaozhou Bay Tunnel | 28.3 | 245.12 | 224.47 | 0.83 | 1 | 8 |

3 | Longtoushan Tunnel | 18 | 143.7 | 123.40 | 0.89 | 1.5 | 9 |

4 | Xiangshan Tunne | 9.1 | 320 | 293.95 | 0.19 | 1 | 9 |

5 | Zhongnanshan Tunnel | 12.5 | 148 | 149.22 | 2.18 | 1 | 12 |

6 | Huangyanzi Tunnel | 15.8 | 56 | 74.54 | 7.39 | 1.2 | 9 |

7 | Maozhan Ridge Tunnel | 16.82 | 160 | 140.39 | 0.89 | 1.5 | 12 |

8 | Heluoshan Tunnel | 19.65 | 70 | 60.25 | 31.33 | 1 | 9 |

9 | Wushaoling tunnel | 7.95 | 373 | 481.19 | 0.11 | 1 | 15 |

10 | Bajiaoqing Tunnel | 11 | 150 | 164.18 | 0.51 | 1.2 | 9 |

11 | Banzhulin Tunne | 12.5 | 277 | 295.88 | 0.26 | 1.2 | 15 |

12 | Zhengyang Tunnel | 12 | 41 | 38.10 | 7.39 | 1.5 | 6 |

13 | Alatan Tunnel | 10 | 110 | 63.88 | 2.43 | 1 | 4 |

14 | Chhibro-Khodri | 3 | 310 | 335.97 | 0.05 | 1.5 | 12 |

15 | Chhibro-Khodri | 3 | 320 | 308.48 | 0.02 | 1.2 | 4 |

16 | Giri-Bata | 4.6 | 200 | 156.55 | 0.37 | 1 | 6 |

17 | Giri-Bata | 4.6 | 170 | 194.89 | 0.12 | 1 | 4 |

18 | Maneri Stage-I | 5.8 | 200 | 232.59 | 0.17 | 1.2 | 9 |

19 | Maneri Stage-III | 7 | 290 | 226.96 | 0.19 | 1.2 | 9 |

20 | Noonidih Colliery | 7 | 150 | 137.21 | 0.57 | 1 | 6 |

21 | Tala Hydro | 6.9 | 940 | 1203.33 | 0.01 | 1 | 15 |

22 | Tala HRT | 7.2 | 800 | 1204.65 | 0.01 | 1 | 15 |

23 | Kaligandaki | 9.7 | 900 | 791.00 | 0.03 | 1 | 15 |

24 | Kaligandaki | 9.7 | 1270 | 855.89 | 0.02 | 1 | 15 |

25 | Kaligandaki | 9.7 | 1000 | 791.00 | 0.03 | 1 | 15 |

26 | Kaligandaki | 9.7 | 1020 | 925.78 | 0.02 | 1 | 15 |

27 | Nathpa Jhakri | 11 | 260 | 224.21 | 0.41 | 1 | 9 |

28 | Nathpa Jhakri | 11 | 320 | 244.23 | 0.33 | 1 | 9 |

29 | Nathpa Jhakri | 11 | 350 | 244.23 | 0.33 | 1 | 9 |

30 | Nathpa Jhakri | 11 | 380 | 265.96 | 0.26 | 1 | 9 |

31 | Nathpa Jhakri | 11 | 990 | 582.53 | 0.03 | 1 | 9 |

32 | Udhampur rail | 6.5 | 300 | 321.45 | 0.06 | 1.5 | 12 |

33 | Chenani-Nashri | 6 | 100 | 70.00 | 2.18 | 1.5 | 12 |

34 | Chenani-Nashri | 6 | 100 | 67.47 | 2.43 | 1.5 | 12 |

35 | Chenani-Nashri | 6 | 100 | 63.07 | 3.04 | 1.5 | 12 |

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**MDPI and ACS Style**

Gao, H.; He, P.; Chen, Z.; Li, X.
Study on a Surrounding Rock Pressure Calculation Method for Super-Large Section Highway Tunnels. *Symmetry* **2019**, *11*, 1133.
https://doi.org/10.3390/sym11091133

**AMA Style**

Gao H, He P, Chen Z, Li X.
Study on a Surrounding Rock Pressure Calculation Method for Super-Large Section Highway Tunnels. *Symmetry*. 2019; 11(9):1133.
https://doi.org/10.3390/sym11091133

**Chicago/Turabian Style**

Gao, Hongjie, Ping He, Zheng Chen, and Xinyu Li.
2019. "Study on a Surrounding Rock Pressure Calculation Method for Super-Large Section Highway Tunnels" *Symmetry* 11, no. 9: 1133.
https://doi.org/10.3390/sym11091133