When a tunnel is excavated in the water-rich soft rock stratum, the strength of the soft rock is greatly reduced due to the seepage of groundwater. The condition may result in engineering accidents, such as large deformation, limit invasion, and even local collapse of the tunnel. Therefore, it is very important to research the stability of the surrounding rock in the water-rich soft rock tunnel. The water-rich disturbance factor considering the seepage influence of groundwater and blasting disturbance is proposed, and the generalized Hoek–Brown strength criterion is modified on the basis of the immersion softening test of soft rock. In accordance with the classical elastic–plastic mechanics theory, the stress, strain, and displacement calculation formulas of the tunnel surrounding rock are derived. The displacement of tunnel surrounding rock is analyzed using the derived formula and the modified Hoek–Brown strength criterion and then compared with the measured value. Results show that the displacement of surrounding rock, which is calculated by modified Hoek–Brown strength criterion considering water-rich disturbance factor and the displacement calculation formula, is close to the measured deformation of surrounding rock in water-rich soft rock tunnel, and the error is small. Therefore, the modified Hoek–Brown strength criterion can be applied to the water-rich soft rock tunnel, and the derived displacement calculation formula can accurately calculate the deformation of tunnel surrounding rock. It is of great significance to the study of surrounding rock stability of water-rich soft rock tunnel.

With the rapid development of highway tunnels and railway tunnels in China, more and more tunnels need to be built in water-rich soft rock strata [

In the past 30 years, many scholars have found that groundwater has a great influence on the stability of surrounding rock after tunnel excavation. Some scholars have conducted a number of studies on the softening effect of water on the soft rock strength and deformation and have made considerable achievements. For example, Yang et al. [

The above research results only analyzed the softening properties and failure modes of soft rock after immersion, which can be used to study the mechanism of large deformation of water-rich soft rock tunnel and predict the failure mode of the tunnel. However, it cannot be used to analyze the stability of tunnels. In tunnel construction, the stability of surrounding rock is often judged by monitoring the deformation of surrounding rock. If the cumulative deformation of surrounding rock is small, the surrounding rock of tunnel is considered to be stable; on the contrary, if the cumulative deformation of surrounding rock is large, it is considered that the stability of surrounding rock is poor, and corresponding measures should be taken to strengthen support, such as temporary inverted arch, biological improvement grouting reinforcement [

The existing research results can accurately calculate the deformation of the tunnel surrounding rock in the natural state. However, the softening effect of groundwater on soft rock is not considered. There is still a large error in the calculation of the surrounding rock displacement in a water-rich soft rock tunnel. Thus, the stability of the surrounding rock of the water-rich soft rock tunnel cannot be accurately analyzed. Therefore, the variation law of physical and mechanical properties of soft rock is analyzed through the immersion softening test of soft rock. On this basis, the water-rich disturbance factor considering the influence of groundwater on the mechanical properties of soft rock is proposed. It is introduced into the generalized Hoek–Brown strength criterion for modification. The modified Hoek–Brown strength criterion can be applied to the displacement calculation and stability analysis of water-rich soft rock tunnel. The applicability of the modified Hoek–Brown strength criterion is verified by monitoring data in engineering practice.

The rock samples are obtained from the face of the Xiejiapo tunnel, which is a water-rich soft rock tunnel, and the lithology is mainly carbonaceous phyllite. In accordance with the requirements of “Test method standard for engineering rock mass” (GB/T50266-2013) and on the basis of the actual test scheme and conditions, the rock specimens were made into cylindrical blocks with a diameter of 50 mm and height of 100 mm, as shown in Figure

Prepared phyllite specimens.

The surface integrity of the initially processed rock samples was examined to prevent the large discreteness of the test data. The RSM-SY5(T) nonmetallic acoustic testing instrument was used to detect the wave velocity of the rock samples. The rock samples with no evident surface defects and similar wave velocity were selected for the test.

The prepared samples were divided into five groups with three blocks in each group. Five groups of test blocks were placed in a

Phyllite specimen immersed in water.

The P-wave velocity of the samples soaked for 0, 30, 90, 180, and 270 days was tested. The test equipment was RSM-SY5(T) acoustic wave tester, as shown in Figure

P-wave velocity test.

The porosity test was carried out when the samples were soaked for 0, 30, 90, 180, and 270 days. The test equipment was MesoMR23-060 H-I nuclear magnetic resonance instrument. Prior to the nuclear magnetic test, the specimen required vacuum saturation. The porosity of material was calculated accurately by analysing the relaxation behaviour of proton in rock under a magnetic field.

Uniaxial compression tests were carried out by YA-2000 digital pressure testing machine, as shown in Figure

Uniaxial compression test.

The parameters of soft rock under different immersion time are obtained by analysing the test data, as shown in Table

Parameters of soft rock under different immersion time.

Test specimen number | Immersion time (t/d) | Compressive strength ( | Poisson ratio ( | Elastic modulus (E/GPa) | P-wave velocity (V/m·s^{-1}) | Porosity ( |
---|---|---|---|---|---|---|

1-1 | 0 | 23.58 | 0.337 | 33.214 | 2650 | 0.467 |

1-2 | 0 | 23.40 | 0.348 | 33.383 | 2647 | 0.446 |

1-3 | 0 | 22.96 | 0.333 | 32.656 | 2539 | 0.421 |

2-1 | 30 | 18.12 | 0.336 | 30.007 | 2638 | 0.572 |

2-2 | 30 | 18.45 | 0.332 | 30.131 | 2609 | 0.568 |

2-3 | 30 | 18.32 | 0.337 | 29.952 | 2629 | 0.583 |

3-1 | 90 | 14.35 | 0.337 | 26.935 | 2578 | 0.762 |

3-2 | 90 | 15.13 | 0.330 | 27.917 | 2541 | 0.695 |

3-3 | 90 | 14.96 | 0.329 | 27.272 | 2558 | 0.707 |

4-1 | 180 | 10.92 | 0.336 | 25.029 | 2501 | 1.098 |

4-2 | 180 | 11.38 | 0.327 | 24.960 | 2458 | 0.974 |

4-3 | 180 | 11.10 | 0.336 | 25.510 | 2418 | 1.063 |

5-1 | 270 | 9.96 | 0.328 | 24.929 | 2449 | 1.218 |

5-2 | 270 | 9.82 | 0.334 | 24.137 | 2439 | 1.196 |

5-3 | 270 | 10.58 | 0.336 | 25.017 | 2321 | 1.101 |

Generally, the lithology of surrounding rock in the same section is similar. Table

Fitting formula and correlation coefficient comparison table.

Form of fitting function | Fitting formula | Correlation coefficient |
---|---|---|

Exponential function | 0.998 | |

0.985 | ||

0.995 | ||

0.971 | ||

Power function | 0.859 | |

0.822 | ||

0.681 | ||

0.764 | ||

Polynomial function | 0.977 | |

0.977 | ||

0.809 | ||

0.967 |

Considering the correlation coefficient and relative error, the formula with the highest fitting degree was determined, as shown in Formula (

The change in P-wave velocity and porosity can reflect the change in mechanical properties. Therefore, the P-wave velocity and rock porosity in Table

In 1980, based on the theoretical research results of Griffith, Hoek and Brown [

To apply the Hoek–Brown strength criterion to the water-rich soft rock tunnels, the softening effect of groundwater should be considered. To a certain extent, the change in the mechanical properties of soft rock after immersion can reflect the seepage influence of groundwater on the mechanical properties of surrounding rock in soft rock tunnel.

The elastic modulus of rock is an index used to describe the elastic deformation resistance of rock, so it can best reflect the change of mechanical properties of rock. According to the water immersion softening test of soft rock and the principle of damage mechanics, the change in elastic modulus under water-rich condition is used to characterise the influence of groundwater on soft rock, and the water-rich influence factor is proposed. The definition is shown in Formula (

The elastic modulus can be obtained by uniaxial compression test of rock and analysis of stress-strain curve. The porosity and P-wave velocity of rock can be obtained only by simple nondestructive test, and the test is relatively simple and fast. Therefore, the P-wave velocity and porosity are selected to calculate the damage variable of rock. According to the propagation theory of elastic wave in rock, the P-wave velocity of rock is related to elastic modulus, Poisson’s ratio, and rock density, such as Formula (

According to the results of the water immersion softening test, the Poisson’s ratio of the soft rock has no evident change after soaking and can be ignored. Substitute the equality transformation of Formula (

The relationship among P-wave velocity, porosity, and immersion time is substituted into the expression of the water-rich influence factor to accurately calculate the water-rich influence factor under different working conditions. The water-rich influence factor with timeliness is obtained, such as Formula (

According to the results of the soft rock immersion softening test, after 180 days of soft rock immersion, the changes in various parameters are small and tend to be stable. It can be assumed that in the water-rich section of the soft rock tunnel, the

For water-rich soft rock tunnels, the effects of blasting disturbance and water-rich on tunnels should be considered simultaneously. In this regard, a water-rich disturbance factor considering blasting disturbance and groundwater effect is established. According to the principle of strain equivalence, the blasting disturbance factor is the first disturbance effect, and the water-rich disturbance factor is the second disturbance effect. Combined with the damage coupling principle in damage mechanics theory, the second disturbance effect can only affect other parts except for the first disturbance effect. Then, the expression of water-rich disturbance factor is defined in Formula (

By substituting Formula (

From the parameter solution Formula (

After substituting Formula (

By substituting time-dependent water-rich disturbance factor and time-dependent geological strength index into the parameter solving Formula (

Combined with the water-rich condition of the tunnel, the water-rich time

The problem of deep tunnel excavation can be simplified as the “thick wall cylinder” problem in elastic–plastic mechanics. The inner diameter of “cylinder” is the diameter of tunnel excavation, and the outer diameter can be ideally regarded as infinite. The deformation of the corresponding position of the tunnel surrounding rock can be obtained by calculating the displacement of the inner wall of the “thick wall cylinder.”

Prior to the elastic–plastic analysis of the deformation of tunnel surrounding rock, the rock mass is assumed to be continuous, homogeneous, and isotropic. The lithology of the surrounding rock in each part of the tunnel is consistent. At the same time, assuming the surrounding rock is an ideal linear elastic body, the plastic zone strain of the tunnel conforms to the Hoek–Brown strength criterion. The excavation mechanical model of the tunnel is shown in Figure

Mechanical model diagram of tunnel excavation.

As shown in Figure

The stress component of any point in the elastic zone of the surrounding rock is only related to the distance to the centre of the tunnel. It is independent of the position of the point. The stress of any point in the elastic zone of surrounding rock is only related to the radius and independent of the angle. The stress equilibrium equation and geometric equation at any point in the elastic zone of surrounding rock are shown in Formula (

On the boundary of the elastic zone and plastic zone of the surrounding rock, the stress of the elastic zone is the same as that of the plastic zone. Therefore, the stress expression of any point in the elastic zone of the surrounding rock can be obtained, as shown in Formula (

In polar coordinates, the expression of Hoek–Brown strength criterion is shown in Formula (

Formula (

where

On the boundary of the elastic–plastic zone of the surrounding rock, where

The radius of the plastic zone can be calculated by Formulas (

Substituting the radius of the plastic zone into Formula (

The rock mass has an initial ground stress

When the surrounding rock is in the elastic zone, Formula (

According to the stress–strain equation of the surrounding rock under polar coordinates, the stress–strain equation of surrounding rock under stress increment can be obtained using Formula (

Substituting stress increment in Formula (

when

The plastic deformation of the tunnel surrounding rock mainly considers the shape change. Assuming the tunnel surrounding rock is an incompressible material, the deformation is shown in Formula (

In Formula (

In elastic–plastic mechanics, “thick-walled cylinder” is a plane strain problem, considering

In the plastic zone and the tunnel excavation boundary, where

The displacement of the surrounding rock of the water-rich soft rock tunnel can be obtained through the displacement formula of the tunnel surrounding rock and the solution formula of each parameter.

The newly-built Xiejiapo tunnel is a typical water-rich soft rock tunnel in Ankang–Langao Expressway, located in Hanbin District, Ankang City, Shaanxi Province. The tunnel is a separate one-way two-lane tunnel. The entrance pile number of the left line of the tunnel is

Groundwater is developed in the tunnel site area; it is mainly composed of pore fissure water of quaternary loose rock and basic fissure water. The surrounding rock is under water-rich conditions for a long time. The tunnel has a net width of 11.77 m and a net height of 8.80 m. The internal radius of the arch wall is 6.05 m, and the internal radius is 17.0 m in the inverted arch. The tunnel is in the Qinling fold tectonic belt, and the Dabashan fault zone passes through it. Tunnel construction is prone to collapse and water inrush events.

The water-rich section

The surrounding rock of the tunnel is mainly carbonaceous phyllite. According to the lithology of carbonaceous phyllite observed on site,

Parameters of the generalized Hoek-Brown strength criterion.

0 | 0.4500 | 31.815 | 0.30232 | 0.000135 | 0.51977 | 23.314 |

360 | 0.4500 | 31.815 | 0.30232 | 0.000135 | 0.51977 | 7.917 |

Parameters of the modified Hoek-Brown strength criterion.

0 | 0.4500 | 31.815 | 0.30223 | 0.000135 | 0.51977 | 23.314 |

360 | 0.5616 | 27.790 | 0.19400 | 0.000052 | 0.52592 | 7.917 |

The initial vertical ground stress of the tunnel only considers the self-weight of the surrounding rock in Formula (

In Formula (

According to the provisions of “Specification for design of highway tunnels” (JTG 3370.1-2018), the formula for calculating the vertical surrounding rock pressure at the arch of deep-buried tunnels is shown in Formula (

According to the vertical initial stress and vertical support resistance, the parameters in Tables

Calculation results of tunnel vault surrounding rock deformation.

Immersion time (d) | The displacement using generalized Hoek-Brown strength criterion (mm) | Displacement using Hoek-Brown strength criterion considering water-rich disturbance factor (mm) |
---|---|---|

0 | 43.51 | 43.51 |

360 | 44.33 | 54.53 |

Table

According to the requirements of the “Technical specification for monitoring and measuring highway tunnels” (DB13/T 2177-2015), combined with the construction of the Xiejiapo tunnel,

Temporal curve of vault subsidence monitoring section.

The figure shows that the vault subsidence values of the four sections are 53.6, 55.1, 44.3, and 42.3 mm. The deformation of surrounding rock in the natural section is obviously smaller than that in the water-rich section, and the stability time of surrounding rock in the natural section is obviously earlier than that in the water-rich section.

The field monitoring measurement results are compared with the theoretical calculation results, and the error is shown in Table

Displacement of surrounding rock under different strength criterion.

Section number | Section | The deformation value of tunnel vault (mm) | The displacement using generalized Hoek-Brown strength criterion | Displacement using modified Hoek-Brown strength criterion | ||
---|---|---|---|---|---|---|

Theoretical value (mm) | Relative error (%) | Theoretical value (mm) | Relative error (%) | |||

1 | 53.6 mm | 44.33 mm | -20.91% | 54.53 mm | 1.71% | |

2 | 55.1 mm | 44.33 mm | -24.30% | 54.53 mm | -1.05% | |

3 | 44.3 mm | 43.51 mm | -1.81% | 43.51 mm | -1.81% | |

4 | 42.3 mm | 43.51 mm | 2.78% | 43.51 mm | 2.78% |

It can be seen from Table

Through the immersion softening test, the softening law of the mechanical properties of soft rock under the groundwater seepage influence is obtained, and on this basis, the water-rich influencing factor is established. Combined with the disturbance characteristics when the water-rich soft rock tunnel excavated, the water-rich disturbance factor is introduced to modify the generalized Hoek-Brown strength criterion. Using the “thick wall cylinder” problem in elastic-plastic mechanics theory, the calculation formula of tunnel surrounding rock displacement is obtained. By comparing the monitoring value and theoretical calculation value of surrounding rock displacement in practical engineering, the applicability of the modified Hoek-Brown strength criterion is verified. The main conclusions are as follows:

Through the immersion softening test of soft rock, it was found that the Poisson’s ratio of soft rock did not change significantly with the extension of immersion time. The uniaxial compressive strength, elastic modulus, and P-wave velocity of soft rock decreased rapidly at the beginning of immersion and then gradually stabilized. On the contrary, the porosity of soft rock changes little at the beginning of immersion and then increases rapidly. On this basis, the variation formula of physical and mechanical indexes of soft rock with immersion time is fitted

According to the damage of elastic modulus of soft rock after immersion, the concept of water-rich influence factor is proposed. Combined with the disturbance characteristics of water-rich soft rock tunnel excavation, the water-rich disturbance factor considering both blasting disturbance and groundwater softening is established. Based on this, the generalized Hoek-Brown strength criterion is modified

In the water-rich section of Xiejiapo tunnel, the relative error between the vault subsidence displacement obtained by the modified Hoek-Brown strength criterion and the field monitoring measurement is small, so the modified Hoek-Brown strength criterion can be applied to the displacement calculation and the stability analysis of water-rich soft rock tunnel

The raw/processed data required to reproduce these findings cannot be shared at this time as the data also form part of an ongoing study.

The authors declare that they have no conflicts of interest.

This research was financially supported by the National Natural Science Foundation of China (Grant No. 51408054 sponsored) and the Natural Science Foundation of Shaanxi Provincial Department of Science and Technology (2017JM5136).