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Carbonaceous slate is heterogeneous and anisotropic, which has a great influence on the stability of tunnel. In this paper, by means of laboratory test, field measurement, and numerical simulation, the surrounding rock stability and plastic zone distribution characteristics of the carbonaceous slate tunnel at different intersection angles are analyzed. First, combined with the Haibaluo tunnel project, Brazilian splitting and uniaxial compression tests of jointed carbonaceous slate are performed. The test results show that the tensile strength of carbonaceous slate is related to joint dip angle. When the joint angle is 0°, the tensile strength is the largest and decreases with the increase of the joint angle. The uniaxial strength of rock decreases first and then increases. Based on the discrete fracture network (DFN) technology, a calculation model is established. The calculation results show that the maximum displacement is 0.45 m, when the dip angle of the surrounding rock joint is 45°. The field measurement also shows that the dip angle of the surrounding rock joint has an important influence on the distribution of the plastic zone. When the joint dip angle is 45°, the plastic zone develops most strongly.

The stability of surrounding rock plays a decisive role in the safe excavation of tunnel. In the process of tunnel excavation, when the surrounding rock is disturbed, the stress will redistribute and plastic zone would be expansion. The strength of rock mass in the plastic zone decrease obviously, the fracture expands, and the stability of surrounding rock is weak [

Numerical analysis has become a more and more common method in the study of surrounding rock stability. In the study by Xiang and Feng [

The main methods of measuring plastic zone in engineering field include acoustic wave method, multipoint displacement meter method, geological radar method, seismic wave method, resistivity method, permeability method, borehole camera method, and radioactive element method. The acoustic method is to use the ultrasonic detector to infer the range of the plastic zone by measuring and analyzing the parameters according to the different characteristics of the ultrasonic propagation speed in the rock with different integrity [

In this paper, uniaxial and Brazilian splitting tests are used to analyze the influence of different dip angles of surrounding rock joints on rock strength at laboratory scale. At the same time, the influence of dip angles is analyzed by discrete element numerical simulation. Using the method of acoustic testing, the distribution characteristics of plastic zone of tunnel surrounding rock under different dip angles are analyzed in engineering practice.

Haibaluo tunnel is located on the line from Shangri La to Lijiang in Yunnan Province. Its length is 2262 m, and the maximum buried depth is 461 m. The maximum relative height difference of tunnel crossing is 540 m. The elevation of the tunnel located is 2455–2902 m. According to the internationally accepted altitude classification standard, it belongs to high altitude area, which is a typical carbonaceous slate tunnel. The vertical section is shown in Figure

Tunnel construction location and geological profile. (a) Tunnel location. (b) Geological section. (c) Characteristics of surrounding rock.

The tunnel is located in high altitude area with thin air, low air pressure, and poor natural conditions. The geological structure of the tunnel area is complex, and the greatest influence geological structure is Qinghai Tibet Plateau, with many active faults. Zhongdian fault and longpanqiaohou fault also have a great influence. The tunnel mainly passes through strongly and moderately weathered carbonaceous slate. The structure is mainly thin-layer and cataclastic. The joints and fissures are relatively developed with poor integrity. The local groundwater is relatively developed, and the surrounding rock is easy to soften when encountering water.

Typical carbonaceous slate samples are selected for X-ray fluorescence spectrum analysis. The main minerals in carbonaceous slate are quartz and clay minerals, and the clay minerals are mainly illite and chlorite, as shown in Table

X-ray diffraction analysis of minerals.

Mineral content (%) | ||||

Quartz | Potash feldspar | Plagioclase | Halite | Clay minerals |

37.7 | 0.7 | 7.2 | 1.9 | 52.5 |

Relative content of clay minerals (%) | ||||

I/S | It | K | C | C/S |

— | 43 | — | 52 | — |

S: smectites; I/S: illite mixed; It: illite; K: kaolinite; C: chlorite; C/S: mix of turquoise and montmorillonite.

In order to comprehensively analyze the influence of joint angle of surrounding rock on rock strength, the compressive strength and splitting strength under different inclination angles are analyzed. Figure

Influence of rock joint dip angle on uniaxial strength. (a) Uniaxial strength curve of different dip angles. (b) Rock strength under different dip angles.

As a special slate, carbonaceous slate has a low sample rate due to the development of fractures and joints, so there are a few studies on its tensile properties in the current literature. Therefore, it is necessary to carry out in-depth experimental research on Brazilian splitting of carbonaceous slate.

The sample preparation of Brazilian splitting test is divided into two steps: ① select a 50 mm diameter sleeve to core and cut the disc according to the predetermined inclination angle; ② smooth the sample with a grinder. The plane along the thickness direction shall be flat to 0.01 mm, and the concave deviation shall not be greater than 0.5°, so that the processed samples can meet the requirements of relevant specifications of rock mechanics test. The experimental results are shown in Figure

Influence of rock joint dip angle on tensile strength. (a) Strength curve of different dip angles. (b) Tensile strength under different dip angles.

Through the calculation and processing of the test data, the average tensile strength is 1.49 MPa, 1.21 MPa, 1.09 MPa, 0.88 MPa, and 0.56 MPa, respectively, at 0°, 30°, 45°, 60°, and 90° inclination. The test results show that the maximum tensile strength of carbonaceous slate is when the joint dip angle is horizontal. The horizontal angle of joint angle represents that the joint inclination angle is 0°, and the strength decreases with the increase of the angle between the joint and the horizontal plane. The variance coefficient

For the numerical simulation of jointed surrounding rock, there are two kinds of analysis modes: finite element and discrete element. From the simulation principle, the 3D discrete element software is more suitable for practical engineering. The purpose of this study is finding out the relative magnitude of the influence of joint on tunnel stability under different dip angles. So, it is feasible to use 3DEC discrete element software to simulate the joint plane. In order to study the stability and plastic zone distribution characteristics of tunnels with different dip angles, five models were established in this study, which were 0° dip angle, 30° dip angle, 45° dip angle, 60° dip angle, and 90° dip angle.

In the process of establishing the numerical model, the plane model is used to simulate, and the size of the analysis area has a great influence on the study of tunnel surrounding rock. The model size is 50 m × 50 m, which is five times the tunnel diameter. In the numerical simulation, Mohr Columb criterion and Coulomb slip model are adopted for rock mass discontinuities. The beam element is used to simulate the initial support, and the thickness of the initial support is 350 mm. Referring to the GSI rock classification standard, combined with the numerical inversion analysis in the simulation process, the parameter values of the strength model of carbonaceous slate rock are shown in Table

Mechanical parameters of carbonaceous slate.

Lithology | Rock mass parameters | Structural plane parameters | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

Density (kg/m^{3}) | K (GPa) | G (GPa) | ^{b} (MPa) | ^{b} | K^{n} (GPa) | k^{s} (GPa) | ^{j} (MPa) | ^{j} | |||

Carbonaceous slate | 2423 | 0.49 | 0.26 | 1.58 | 27 | 0.56 | 28.99 | 11.98 | 3.69 | 28 | 3.32 |

Numerical calculation model of different surrounding rock inclination. (a) The dominant joint angle 0 degrees. (b) The dominant joint angle 30 degrees. (c) The dominant joint angle 45 degrees. (d) The dominant joint angle 60 degrees. (e) The dominant joint angle 90 degrees.

The displacement of surrounding rock under different dip angles is shown in Figure

Different dip angles and deformation characteristics of surrounding rock. (a) The dominant joint angle 0 degrees. (b) The dominant joint angle 30 degrees. (c) The dominant joint angle 45 degrees. (d) The dominant joint angle 60 degrees. (e) The dominant joint angle 60 degrees. (f) Relationship between dip angle deformations of different surrounding rocks.

The variation of surrounding rock displacement under different dip angles is shown in Figure

Acoustic testing method is to judge the integrity of rock mass according to the internal relationship between the physical and mechanical indexes (strength, density, dynamic elastic modulus, etc.) of geotechnical medium and propagation speed of ultrasonic wave in geotechnical medium. If the force (stress) of rock mass is large, the density is large, the integrity of rock mass is good, and the acoustic wave velocity will be correspondingly large.

On the contrary, when the rock mass density is small, the structural plane is developed, the lithology is poor, the groundwater exists, and the acoustic wave velocity will decrease. Therefore, in the same nature of the surrounding rock, the higher the acoustic wave velocity, the better the integrity of the rock mass; the lower the wave velocity, the more broken the rock mass, the higher the existence of cracks, and even the more likely the failure. Through testing the longitudinal wave velocity of rock mass at different depths of surrounding rock, according to the change of rock mass wave velocity, the thickness of loose zone of tunnel surrounding rock can be obtained. Figure

Schematic diagram of acoustic double-hole test method.

According to the wave theory in elastic-plastic medium, the wave velocity of stress wave is as follows [

In the field test of the project, the rock mass integrity is evaluated by the ratio of the longitudinal wave velocity of the rock mass and longitudinal wave velocity of the undisturbed rock mass. The square of the value is the rock mass integrity coefficient, and the calculation formula is as follows:^{3}),

Five sections are selected to test the loose circle of the surrounding rock, and four pilot sites are arranged at the left and right side walls and spandrels of each section. No. 1 and No. 2 measuring points are symmetrically arranged 1.5 m above the upper bench excavation line of the left and right side walls. No. 3 and No. 4 measuring points are symmetrically arranged at the spandrel of the upper and lower steps. The down-the-hole drilling is adopted, the hole depth is 8.0 m, and the hole diameter is 40 mm. The dip angles of the surrounding rocks of the five sections are 0°, 30°, 45°, 60°, and 90° respectively, and the layout of the acoustic measuring holes is shown in Figure

Layout of acoustic measuring hole.

The thickness distribution of surrounding rock loose zone is shown in Figure

Distribution characteristics of plastic zone of surrounding rock.

After the tunnel excavation in layered rock mass, the depth of plastic zone in the area perpendicular to the joint angle is larger, and the stability of surrounding rock is poor. In view of the large deformation above the arch waist of the tunnel and the characteristics of the surrounding rock when the joint angle is 45°, the length and ring distance of the bolt are optimized on the basis of the original support scheme. The support arrangement is shown in Figure

Support design optimization.

The measured data show that the optimized bolt length can control the deformation of surrounding rock (Figure

Tunnel surrounding rock deformation by optimized support.

In this paper, uniaxial compression and Brazilian splitting tests are used to analyze the strength characteristics of laboratory scale rock under different joint dip angles. Discrete element numerical simulation method is used to fully consider the distribution characteristics of joints and fissures, and the influence of different joint dip angles on the stability of surrounding rock is analyzed. The distribution characteristics of plastic zone in practical engineering are analyzed by using acoustic wave testing instrument.

The maximum tensile strength of carbonaceous slate appears when the joint angle is 0° and decreases with the increase of joint angle. With the increase of joint dip angle, the uniaxial strength of rock first decreases and then increases, and the strength of rock joint is weak in the range of 40° to 60°.

According to the simulation results, the stable displacement of tunnel surrounding rock with different dip angles is analyzed, and the maximum displacement under the condition of 45° dip angle joint is obtained.

The results show that the dip angle of surrounding rock has a great influence on the depth and distribution of plastic zone. When the joint dip angle is 45 degrees, the boundary between the plastic zone and the intact rock is the deepest.

The data used to support the findings of this study are included within the article.

The authors declare no conflicts of interest.

All authors approved the manuscript for publication.

This research was supported by the National Natural Science Foundation of China Youth Fund Project (41702320).