Characteristics, numerical analysis and countermeasures of mud inrush geohazards of Mountain tunnel in karst region

Abstract

The excavation of tunnels in karstic rocks inevitably intersects with karst caves even with reasonable geological survey and alignment design. The filler in karst caves directly affect the harmfulness of mud inrush geohazards to tunnels. Therefore, it is essential to understand the properties and failure characteristics of the filler in karst caves before treating karst caves. Based on a tunnel mud inrush case in Guangxi Province, China, failure characteristics and mechanism of clay filler in karst cave were analyzed. Besides, geological survey and geological prospecting indicate that the clay filler was formed by the deposition of surface clay entering the karst cave from the cracks of rock mass. The failure evolution process of clay filler was demonstrated based on discrete element method. The numerical simulation results show that excavation induced sliding force and insufficient shearing strength of clay were the mainly triggering of instability of clay filler in the karst cave. Advanced grouting, construction method improving were used to prevent mud inrush from bursting again and achieved satisfactory reinforcement effect. The lessons and analysis results in this case has reference value for the prevention of tunnel mud inrush in karst area.

Keywords:

• Mountain tunnel
• mud inrush geohazards
• characteristics
• discrete element
• countermeasures

1. Introduction

Karst cave in carbonate rock area is a common unfavorable geological structure in underground engineering. And its geological identification, prediction technology, disaster causing mechanism, disaster control technology, etc. have always been the key technical problems in restricting the development of tunnel engineering construction (Gutierrez et al. 2014; Li et al. 2014b; 2017a; 2020; Elbaz et al. 2021). Tunnel excavation in rock strata in karst areas is a dangerous task, which often leads to special tunnel construction disasters, such as water inrush, mud inrush, collapse and other sudden dangerous problems (Chen et al. 2020; Peng et al. 2020; Zheng et al. 2021b; Ma et al. 2022c). Statistical analysis of mud accidents and classification of mud and water-causing structures shows that water and mud inrush caused by karst structures are the most important (Li et al. 2018b). The surface soil enters the karst cave through the long-term sedimentation of fissures and dissolution of carbonatite in the karst cave, which will form clay fillers in the karst cave (Yuan et al. 2019; Ma et al. 2022a). Moreover, due to the concealment of karst caves and the complexity of the geotechnical properties of fillings, it is difficult to accurately predict the occurrence of water and mud inrush caused by karst cave and its harmfulness in tunnel excavation (Zhang et al. 2022a; Yang et al. Ma et al. 2022b). When the karst cave structure is damaged by excavation and the fillings gush out of the cave, mud inrush disaster will occur. And the engineering structure will be damage, the construction cost will be increased and the construction period will be delayed (Wu et al. 2019; Wang et al. 2020a; Lin et al. 2021; Li et al. 2021a). In view of these problems, some research findings have been reported made about mud inrush in disaster.

However, mud inrush in tunnel is a complex engineering problem, which has significant dynamic characteristics and disaster evolution process. At present, the theory and technical system of tunnel mud burst still need continuous improvement, especially in terms of disaster evolution mechanism and disaster control (Jorda-Bordehore et al. 2016; Liu et al. 2021). Xue et al. (2017) built the potential function for tunnel mud inrush geohazard production based on cusp catastrophe model. Li et al. (2017b) found that effective geological identification is crucial for the prediction and prevention of tunnel mud inrush. Huang et al. (2023) taking the mud inrush of Qiyueshan Tunnel as an example, the identification method and treatment technology for mud inrush of the deep karst trough in tunnel is proposed. However, few research focuses on the failure characteristics and mechanism of fillings in karst caves during mud inrush (Wu et al. 2017; Liu et al. 2022b). When the tunnel passes through the karst cave, the internal force and displacement of the tunnel structure are related to the physical and mechanical properties of the fillings in the karst cave. Through the mechanical properties and the initial conditions of the fillings in the karst cave obtained from geological exploration, the stress and distribution of the fillings in the karst cave after the mud inrush can be judged, which is helpful to the prevention and treatment of the mud inrush disaster. In the process of mud inrush, the stress distribution of the fillings in the karst cave is also constantly adjusted. Physical model tests show that the stress of the fillings is an evolutionary process of gradual decline from top to bottom (Li et al. 2018a). The increasing strength of fillings will improve the mechanical state and safety of tunnel structure (Zheng et al. 2021a). Obviously, the physical and mechanical properties of the fillings in the karst cave become one of the main destructive factors of the mud inrush. Studying the failure mechanism and characteristics of the fillings in the karst cave is helpful to take reasonable countermeasures, but so far, there is little research on the failure characteristics of the clay fillings in the karst cave. Therefore, the study on the failure mechanism and characteristics of clay filler in karst caves is of great significance for the countermeasures of mud inrush.

The common methods used to study the cause and mechanism of tunnel mud inrush include geological analysis, theoretical analysis, numerical simulation, model test (Hatzor et al. 2010; Li et al. 2014a; Alemdag et al. 2019; Zhang et al. 2019; Kaufmann and Romanov 2020). Among them, the discrete element method is a geotechnical analysis method that has emerged in recent years, and its reliability and advantages in analyzing geotechnical discontinuities have been confirmed by many studies (Bym et al. 2013; Ma et al. 2022d). When mud inrush occurs, it is necessary to comprehensively consider the construction conditions, economic conditions, geological structure characteristics of karst caves and the nature of internal fillings, and take effective measures to deal with mud inrush disaster (Wang et al. 2020b; Xue et al. 2021). For large-scale karst caves with mud inrush, pipe shed support can effectively support and pre reinforce the fillings in the karst cavity before excavation (Wang et al. 2019; Luo et al. 2020; Li et al. 2021b). Grouting is another common method, such as advance grouting and radial grouting (Guo et al. 2019; Liu et al. 2022a; Zhang et al. 2022b). However, the use of these methods should first understand the characteristics of the cave and the internal filling. It is also very important to improve the bearing capacity of the tunnel structure itself, such as increasing the primary support stiffness by reducing the steel arch spacing and increasing the thickness of shotcrete (Mohyla et al. 2020; Wang et al. 2021).

The research in this paper was to determine the failure mechanism and characteristics of the fillings in the mud inrush caused by the karst cave of Ganhuan Tunnel in Guangxi Province. Firstly, the characteristic parameters of karst caves and the properties of fillings were determined through geological survey and exploration. Then, the failure mechanism and characteristics of clay fillings in the process of mud inrush were studied using the discrete element method. Finally, the treatment methods and effects of mud inrush were analyzed. Therefore, this study will help similar projects to prevent and treat mud inrush more reasonably.

2. Case background

2.1. Project overview

2.1.1. Tunnel location and original support design

Baise City is located in the northwest of Guangxi Province in China, as shown in Figure 1. The Ganhuan Tunnel is a part of the Bama-Pingxiang Expressway Project, which represents a key section of the ‘Guangxi Expressway Network Plan (2018–2030)’. The Bama-Pingxiang Expressway Project is designed to achieve a running speed of 100 km/h. The starting and ending chainage of the right tunnel is K84 + 438 - K84 + 862, with a length of 424 m and a maximum buried depth of about 143 m. The lithology of the tunnel site is mainly carbonate rock, and underground karst is developed. Major karst mud inrush occurred during the construction process, which seriously threatened the safety of tunnel construction and operation.

Figure 1. Geographical location of Ganhuan tunnel.

The excavation area is more than 100 m², with a width of 13 m and height of 9.4 m. The bench cut method was employed to construct the tunnel. The height of the upper bench is 5.4 m. The primary support is closely followed by excavation face. The support materials and parameters, support design of Ganhuan Tunnel is shown in Figure 2.

Figure 2. Original supporting design scheme of the tunnel.

2.1.2. Geological characteristics

The total length of the tunnel is 424 m, and the maximum buried depth is 143 m. The upper overburden of the tunnel is Quaternary residual slope deposit clayey soil with gravel, which is thin, underlain by moderately weathered limestone, with developed rock joints and fissures, and strongly developed karst caves, karst pores and corrosion phenomena. The tunnel is excavated from the tunnel exit (K84 + 862) to the tunnel entrance (K84 + 438), and the excavation adopts the bench cut method. Geological survey methods such as exploratory drilling are used to verify that there is a large filled karst cave near K84 + 836 section along the tunnel. The height of the karst cave is about 25 m, and the karst cave is filled with clay with a thickness of nearly 20 m. The lower part of the tunnel excavation contour is slightly lower than the bottom of the karst cave. According to the geological advance prediction, the length of the karst cave along the longitudinal direction of the tunnel is about 20–25 m. The sediment in the karst cave is clay with low water content discovered through advanced drilling and excavation. There is no ponding in the karst cave, which indicates that there are cracks or corrosion channels in the karst cave that can discharge the water flowing into the karst cave. The geological longitudinal profile of Ganhuan Tunnel is shown in Figure 3.

Figure 3. Longitudinal geological profile of Ganhuan tunnel.

The surrounding rock along the tunnel is moderately weathered limestone, which is prone to karst caves under long-term groundwater erosion (Parise and Lollino 2011; Wang et al. 2014; Mádl-Szőnyi and Tóth 2015). The photograph of the mud inrush of the tunnel is shown in Figure 4(a). There is a hollow on the ground above the cave that caused the mud outburst, and the rock mass at the bottom of the hollow is severely weathered with several obvious cracks (Figure 4(b)). The maximum width of the cracks is about 40 cm. The cracks are filled with silty clay, and the appearance of the clay filled in cracks is similar to the clay in karst cave leading to the mud inrush.

Figure 4. Photographs of collapsed corrosion pit: (a) location of collapsed corrosion pit; (b) surface corrosion.

2.2. Soil parameters of clay

The soil parameters of clay failed in karst cave can obtained from in-situ and laboratory tests. The shear strength of the clay filled in the karst cave directly affects the stability of the filling in the karst cave. The direct shear test is a method to determine the shear strength of the soil. After the test, collate the derived data and draw the shear stress shear displacement curve. Draw the shear strength line of soil mass direct shear test with confining pressure as the horizontal axis and shear strength as the vertical axis, and obtain the cohesion of clay shear strength c = 34.4 kPa and internal friction angle φ = 16°. The water content in clay has a significant impact on the properties of clay and the characteristics of mud inrush geohazard (Yang and Juanes 2018; Yang et al. 2019; Li et al. 2022). The test and analysis of the samples of the clay in karst cave show that the average natural water content of the clay was 12.03%, and the average natural density was 2.19 g/cm³. Mechanical properties of clay in the karst cave are shown in Table 1.

Table 1. Physical and mechanical parameters of clay.

Parameters	Density (g/cm^3)	Cohesion (kPa)	Internal friction angle (°)	Compressive modulus (MPa)	Poisson’s ratio	Unconfined compressive strength (kPa)
Value	2.19	34.4	16	5.54	0.3	84

2.3. Failure characteristics

On January 12, 2021, the excavation face of the tunnel reached K84 + 836 section. After the blasting excavation of the excavation face was completed, yellowish brown clay appeared on the upper part of the excavation face, then the clay in front of excavation face began to gush out. The constructors withdrew the construction machinery in time. The fillings were pushed forward for about 30 min until it flowed out of the tunnel, then the fillings were stable and stopped moving. The distance of mud inrush was about 27 m, and the amount of mud inrush was about 800 m³. The gushing clay were both loose clay and large pieces of intact clay, as shown in Figure 5(a). The main component of the clay was mixture of yellow clay and red clay, mixed with a small amount of block stones and gravels, and its stability was poor, as shown in Figure 5(b). The mud inrush was in dry season, and there is no obvious water inrush when the mud inrush disaster occurs.

Figure 5. Disaster site and clay sample: (a) disaster site; (b) clay sample.

3. Numerical analysis of mud inrush

The discrete element method (DEM) is a numerical simulation method specifically designed to simulate discontinuous medium (Liu et al. 2020). The theoretical basis of the DEM is Newton’s Second Law, and the constitutive relationship in elastic-plastic mechanics of the material is unnecessary (Ma et al. 2020; Su et al. 2020). As one of the discrete element methods, the Particle Flow Code in 2-Dimensions (PFC2D) is mainly used for the study of discontinuous medium problems and large deformation problems in the field of solid mechanics. The contact failure between particles can be divided into two types: shear failure and tensile failure. In a wide range of soil instability and collapse problems, the deformation of small soil particles in motion can be completely ignored (Tran et al. 2015; Cui et al. 2017). Therefore, it is reasonable to simulate actual engineering problems by assuming that unit particles are rigid bodies and do not participate in deformation in the discrete element numerical simulation software, and only defining the contact relationship between particles and between particles and wall elements. Aiming at the karst mud inrush accident in Ganhuan Tunnel, PFC2D discrete element software is used to simulate the whole process of mud inrush to analyze its characteristics and mechanism.

3.1. Establishing of the numerical model

As shown in Figure 6, a two-dimensional discrete element numerical simulation model of tunnel mud inrush was established by PFC2D. In the model, the wall element was used to establish a model box to simulate the structure of the karst cave. The tunnel was formed by wall elements. The tunnel face was set as a retaining wall, and the tunnel excavation damage inrush prevention layer was simulated by deleting the retaining wall. The side wall of the karst cave was simplified as a vertical wall, and the size of the karst cave was 20 m × 20 m. When mud inrush disaster occurs, only the upper bench of the tunnel was excavated. Therefore, the excavation height of the upper bench was 4.5 m in the model. In order to observe the characteristics of filling material gushing out, the tunnel length was set as 40 m in the model. The parallel-bond model was used to simulate the contact between particles, which can effectively simulate the cohesion of clay. The particle radius of the model was from the minimum radius R_min to the maximum radius R_max to simulate clay in the karst cave. There was a total of 20618 particles used in the discrete element model. The process of model establishment and numerical calculation is as follows: Firstly, the wall of the karst cave was generated, and particles were generated in the cave enclosed by the wall. Then, the acceleration was applied to the wall through the servo function to eliminate the excessive contact force caused by particle overlap when generating particles, so that the particles quickly reached the equilibrium state. Next, applying gravitational acceleration to particles, and the balance was performed on particles under gravity. Finally, the wall simulating the tunnel was generated and the contact parameters were set. The wall at the tunnel face was deleted to realize the karst cave damage caused by tunnel excavation.

Figure 6. Schematic illustration of the numerical model.

3.2. Microscopic material parameters

The calibration of microscopic material parameters is an important step in discrete element numerical simulation. The microscopic parameters between particles should be continuously adjusted to ensure that the macroscopic mechanical characteristics of the materials obtained from the discrete element method and laboratory test are consistent. To clarify the macroscopic mechanical characteristics of the soil in the karst cave, a direct shear test on soil samples taken from the site of mud inrush geohazards was undertaken. The equipment in this direct shear test was strain controlled direct shear apparatus, produced by Nanjing Ningxi Soil Instrument Co., Ltd. The photographs of samples are shown in Figure 7.

Figure 7. Photographs of samples for direct shear test: (a) before shear failure; (b) after shear failure.

The shear rate was set to 0.8 mm/min. When the pointer of the dial indicator stopped moving forward or the shear displacement reached 4 mm, stopped shearing and recorded shearing displacement. The shearing stress-shearing displacement curves are shown in Figure 8(a). The experimental results were analyzed using the elastic–plastic intrinsic model with the Mohr–Coulomb strength criterion. The shear strength curve obtained from direct shear test is shown in Figure 8(b). According to the shear strength curve obtained from the direct shear test, it can be obtained that the cohesion of the soil sample is 34.4 kPa and the angle of internal friction is 16°.

Figure 8. Direct shear test results of soil samples: (a) stress-strain curves; (b) shear strength curve.

The comparison between discrete element numerical simulation results and direct shear test results are shown in Figure 9(a). It can be seen that the discrete element numerical simulation results were basically consistent with the direct shear test results. The uniaxial compression numerical test was conducted to verify the accuracy of microscopic parameters obtained through calibration. As shown in Figure 9(b), the unconfined compressive strength of soil obtained through numerical simulation was 91 kPa, which was slightly higher than the actual unconfined compressive strength of 84 kPa. The simulation results of experiments indicated that the parameters obtained from parameter calibration can be used in the discrete element simulation of mud inrush. The calibrated microscopic parameters in this discrete element numerical simulation model were shown in Table 2.

Figure 9. The calibration results: (a) comparison between direct shear test results and numerical simulation; (b) test results of unconfined compressive strength.

Table 2. Microscopic parameters of the model.

Particle materials				Wall		Parallel bonding model
Rmax (m)	Rmin (m)	Friction coefficient (Pa)	Normal stiffness (N/m)	Friction coefficient	Tangential stiffness (N/m)	Effective modulus (Pa)	Normal tensile strength (kN)	Tangential shear strength (kN)
0.18	0.09	0.2	2.0 × 10^7	0.2	1 × 10^10	1 × 10^7	120	120

3.3. Analysis of simulation results

3.3.1. Evolution process of mud inrush

Figure 10 illustrates the displacement of particles at different time steps during mud inrush. At 360270 time-steps, the process of mud inrush stopped, and the front end of the clay gushing from the karst cave was 25.22 m away from the tunnel face. This was similar to the length of the clay body gushing from the karst cave observed at the site. In addition, there were several obvious displacement boundaries in the clay soil in the karst cave, and they gradually evolved into sliding surfaces, dividing the clay soil in the karst cave into several parts. The sliding part of the clay soil in the karst cave was located on the side close to the tunnel face, while the soil far away from the tunnel face has hardly moved.

Figure 10. Displacement of particles and force chain at different time steps during mud inrush: (a) time steps 41676; (b) time steps 89009; (c) time steps 158983; (d) time steps 360270.

At 41676 time-steps, the displacement of particles is shown in Figure 10(a). After the rock mass between the tunnel face and the karst cave was destroyed, the clay in karst cave close to the tunnel face lost lateral displacement limit. Affected by pressure of the clay and its own gravity, the clay close to the tunnel face is deformed in the direction of the tunnel. At that time, the force chains near the tunnel face were obviously sparser than that in other places, which indicated that the soil near the tunnel face was looser. When the numerical simulation reached 89009-time steps (Figure 10(b)), the soil mass on the side close to the tunnel face in karst cave settled down while the soil mass on the side far away from the tunnel face didn’t deform. A settlement groove appeared on the top surface of the soil mass in the karst cave due to the uneven settlement. The groove wall was nearly 90° and the settlement amount of the soil mass was close to 5 m. Besides, potential sliding surface was formed in the soil mass in karst cave (Cai et al. 2021; Zhou et al. 2021). At the bottom of the potential sliding surface, there is an arc surface with a radius of nearly 4.5 m. At 158983-time steps, the force chains above the potential sliding surface became more sparsely distributed because the soil in karst cave continued to pour out into the tunnel. When the shear stress of clay at the potential sliding surface exceeded the shearing strength of clay, shear failure occurred and a penetrating sliding surface was formed inside the soil mass. The clay on the sliding surface slid downward and the clay from karst cave kept pouring into the tunnel (Figure 10(c)). Moreover, due to the continuous gush of soil in the karst cave, new tensile cracks are generated on tops of soil in stable areas of karst cave. This indicates that the destruction scope of the soil is also expanding.

At 360270 time-steps (Figure 10(d)), a new sliding surface occurred in the soil body without sliding. This sliding surface extended to the tunnel face along the tensile crack at the top of the soil body that appeared at the 158983 time-steps. The soil body in the karst cave basically reached a stable state and the mud inrush stopped. Compared with other time steps, the force chains near the tunnel face were denser at this time step and several arched force chains (stress arch) appeared above the tunnel face, indicating that the soil body near the tunnel face has been basically stable at that time. Finally, soil body in karst cave was divided into two regions: the sliding region and the non-sliding region. The inclination angle of the dividing line is about 50°.

3.3.2. Factor analysis

3.3.2.1. Over excavation

During the tunnel excavation before mud inrush, the tunnel face gradually approached the karst cave, and the thickness of the rock between the tunnel face and the wall of the karst cave gradually decreased. As a result, the support force provided by the surrounding rock of the tunnel face to the sediment in the karst cave was getting smaller and smaller. Before the occurrence of mud inrush, the rock mass between the excavation face and the karst cave can provide sufficient support force to prevent the occurrence of mud inrush. However, until clay appeared on the excavation face, effective disaster prevention measures such as early grouting were not taken. The numerical simulation results indicated that when the clay at the excavation face in the karst cave lost its support, the clay immediately flowed outward.

3.3.2.2. Excavation method

In addition to over excavation, unreasonable excavation methods are also the cause of the mud inrush geohazard. Research and engineering experience have shown that the reserved core soil method is more conducive to ensuring the stability of the surrounding rock in front of the tunnel face compared to the bench cut method. The bench cut method was used for the tunnel excavation before the mud inrush geohazard occurred, and the clay in the karst cave gushed out from the tunnel face of the upper bench. This indicated that the surrounding rock in front of the tunnel face of the upper bench lacked sufficient support and couldn’t maintain stability. Moreover, the excavation area of the upper bench of the bench cut method was larger than that of the reserved core soil method, which also increased the outlet area of clay in the karst cave.

3.3.2.3. Mechanical properties of filler

Physical and mechanical properties of clay fillings in karst cave are fundamental reasons for the occurrence of mud inrush. The advanced horizontal drilling of the tunnel revealed that the karst cave in front of the excavation face is filled with clay. Moreover, the water content of the filled clay measured from the soil samples obtained from the drilling is about 9%. The tunnel construction personnel mistakenly judged mechanical properties and the stability of clay filling in karst cave. As a result, they misjudged the occurrence of the mud inrush geohazard when the tunnel face reached the karst cave. In fact, when the tunnel face reached karst cave, mud inrush occurred immediately. The numerical simulation results indicated that shear planes run through the clay in the karst cave during the mud inrush process. The shear failure range of clay in the karst cave continued to increase with the progress of the mud inrush. Therefore, the shear stress of the clay in karst cave exceeded its shear strength is the cause of the mud inrush.

4. Countermeasures

4.1. Pre-grouting reinforcement

4.1.1. Parametric analysis of grouting

The method to reinforce surrounding rock by grouting has achieved good application effects in cases for controlling tunnel geological hazard (Wang et al. 2016; Li et al. 2019). Mud inrush section of Ganhuan Tunnel was featured by loosely-structured karst cave filling and poor self-stability. Therefore, full-face curtain grouting method and advanced small pipe grouting method were used to reinforce surrounding rocks.

Many grouting parameters can affect the grouting reinforcement effect of tunnel surrounding rock, including grouting material type, grouting pressure, grouting amount, grouting range, grouting liquid diffusion radius, etc. Among them, the diffusion radius of grouting liquid is an important parameter affecting the grouting reinforcement effect because it can directly affect the stability of surrounding rock. On the premise that other parameters remain consistent, the discrete element numerical calculation model can be established to analyze the influence of different grouting diffusion radius on the grouting reinforcement effect.

The discrete element numerical simulation model of tunnel grouting reinforcement is shown in Figure 11. The upper boundary of the numerical model is the upper surface of clay in karst cave. According to elastic-plastic theory and existing research experience (Yu et al. 2017; Frough et al. 2019), the simulation model was 50 m in width and its vertical height was 38 m. The filling height of the karst cave was 20 m and the height of surrounding rock below the tunnel invert was 18 m. The initial stress adopted the way of self-weight balance and the upper boundaries were free boundaries. All remaining boundaries were fixed by wall element. The radius of particles ranged from 0.06 m to 0.09 m were generated.

Figure 11. The discrete element model for simulating grouting reinforcement.

The materials microscopic parameters outside the grouting area for the model were consistent with the mesoscopic parameters in Table 2. Full-face curtain grouting reinforcement was realized by enhancing the contact parameters between particles in the grouting circle (grouting circle 1). In the model, the advanced small pipe grouting area (grouting circle 2) was equivalent to the ring reinforcement area with a thickness of 1 m within the range of 140° of vault. The grouting reinforcement was simulated by increasing bond strength of particles. The mesoscopic parameters were calibrated by biaxial compression experiment and the mesoscopic parameters of grouting area and primary lining were obtained as shown in Table 3.

Table 3. Microscopic parameters of grouting area and primary lining.

Materials	Effective modulus (Pa)	Stiffness ratio	Normal bond strength (kPa)	Tangential bond strength (kPa)	Friction angle (°)	Friction coefficient
Grouting circle 1	1 × 10^7	1.6	1 × 10^3	1 × 10^3	45	0.7
Grouting circle 2	1 × 10^8	1.5	5 × 10^3	5 × 10^3	55	0.9
Primary lining	1 × 10^9	1.0	45.5 × 10^3	51.5 × 10^3	55	0.9

When it came to the establishment of the simulation model, particles of the model were generated first and they were balanced under the action of self-weight. Subsequently, the contact parameters of particles in the reinforcement area were assigned according to the calibrated mesoscopic parameters shown in Table 3 so as to simulate the grouting reinforcement. During the parameters of grouting area assignment, changes of particle contact parameters in the reinforcement area led to relative displacement between particles. The relative displacement and velocity between particles were zeroed out at the end of the grouting reinforcement. Tunnel excavation was simulated by deleting particles in the tunnel face. The thickness of full-face curtain grouting circle includes four kinds: 3, 4, 5 and 6 m. Figure 12 shows the displacement of surrounding rock after tunneling.

Figure 12. Variation curves of the maximum displacement of surrounding rock varying with the thickness of grouting circle.

As shown in Figure 12, the maximum vertical displacement and maximum horizontal displacement of surrounding rock decreased with the increased of the thickness of grouting reinforcement circle. However, with the increase of grouting reinforcement circle, displacement reduction had different decrease amplitudes. The maximum displacement of surrounding rock increased with the increase of grouting reinforcement circle, which was divided into two stages: rapid decline stage and slow decline stage. When the thickness of the grouting circle increased from 3 m to 5 m, the maximum displacement decreased rapidly. When the thickness of reinforcement circle increased from 5 m to 6 m, the maximum displacement decreased reduced significantly.

Figure 13 shows the distribution of vertical displacement of surrounding rock under different thicknesses of grouting reinforcement circle. When the thickness of reinforcement circle was 3 m, the vertical displacement of surrounding rock was mainly manifested as arch settlement and inverted arch uplift. The maximum settlement of arch was 0.21 m and the maximum inverted arch uplift was 0.26 m. Therefore, tunnel grouting is vital to strengthen surrounding rock. At that time, the settlement and inverted arch uplift of the surrounding rock were still large. With the thickness increase of reinforcement circle, both the decreasing amplitudes of settlement and inverted arch uplift decreased gradually. Therefore, the thickness of full-face curtain grouting reinforcement circle of the tunnel in mud inrush section was set to be 5 m.

Figure 13. Vertical displacement of surrounding rock under different thickness of grouting circle: (a) d = 3 m; (b) d = 4 m; (c) d = 5 m; (d) d = 6 m.

4.1.2. Grouting scheme

In order to ensure the safety of construction and prevent the occurrence of secondary mud inrush disasters, the advanced small pipe grouting method and full-face curtain grouting method were adopted. If advance grouting was not carried out, the tunnel excavation can induce the instability and sliding of the filling in karst cave, causing mud inrush again. After the advance grouting was applied, the fillings were divided into upper and lower parts by the grouting ring. When the soil under the grouting circle was excavated, the grouting circle played the role of a beam structure and beard the gravity of the upper clay, which can prevent the soil above the grouting circle from sliding (She et al. 2020; Wang and Cheng 2021).

Advance grouting reinforcement was carried out for the karst filled clay about 30 m in front of the tunnel face. A single cement paste was used for advanced grouting, with a water cement ratio of 0.6:1. The preliminary design grouting pressure was 0.5–1.0 MPa and the grouting pressure changed from low to high. The circumferential space of the advanced small pipe was 0.3 m and the single-hole diffusion radius of the full-face curtain grouting was 3 m.

4.2. Improvement of construction method

After the completion of advanced small pipe grouting and full-face curtain grouting, manual excavation shall be carried out. The excavation method was changed from bench cut method before mud inrush to reserved core soil method. Also, the primary lining of the tunnel was also strengthened: the steel arch was made of I22a I-steel, the longitudinal spacing of the steel arch was reduced to 0.5 m, the steel mesh was double-layer, and the thickness of shotcrete was increased to 0.28 m.

Under the condition of advance small pipe grouting and full-face curtain grouting reinforcement, the full section excavation method was used in the numerical simulation of tunnel excavation. The distribution of vertical and horizontal deformation of surrounding rock is shown in Figure 14.

Figure 14. Displacement distribution of surrounding rock excavated with full section method: (a) vertical displacement; (b) horizontal displacement.

As shown in Figure 14, the maximum settlement of surrounding rock was mainly occurred in the vault. The maximum settlement of vault was reduced by 69.7% from 16.6 cm when full-face curtain grouting was used only to 5.03 cm. The inverted arch heaving also decreased by 28.3% from 18.1 cm to 12.97 cm. Besides, the maximum horizontal displacement was reduced by 27.14% from 4.2 cm to 3.06 cm. The maximum vertical and horizontal displacements of surrounding rock all decreased significantly after advanced small pipe grouting was implemented, which indicated that the advanced small pipe grouting was effective in controlling the surrounding rock deformation.

Figure 15 shows the displacement distribution of surrounding rock during tunneling with reserved core soil method. In the process of tunnel excavation, the vault settlement increased constantly and the horizontal displacement on both sides of the tunnel was basically symmetrical. After tunnel excavation, the maximum vertical displacement was 3.06 cm, but the maximum vertical displacement was 1.01 cm when the core soil was not excavated. After the excavation of the core soil and the lower half part of the tunnel, the maximum vertical displacement increase was 2.05 cm. Therefore, the excavation of core soil and the soil in the lower half part of the tunnel is a key construction procedure of reserved core soil method.

Figure 15. Displacement distribution of surrounding rock excavated with reservation core soil method: (a) vertical displacement without excavation of core soil; (b) vertical displacement after excavation; (c) horizontal displacement without excavation of core soil; (d) horizontal displacement after excavation.

Compared with the full section excavation method, the reserved core soil method can effectively reduce the displacement of surrounding rock caused by tunnel excavation. The inverted arch heaving decreased by 80.1% from 12.97 cm to 2.58 cm and the maximum settlement decreased by 39.2% from 5.03 cm to 3.06 cm. Therefore, the reserved core soil method can obviously control surrounding rock deformation. After the surrounding rock reinforcement of Ganhuan Tunnel was completed, the reserved core soil method was used for tunneling.

4.3. Treatment effect analysis

In order to judge the effect of the treatment scheme of tunnel mud inrush, the surrounding rock deformation of the tunnel was monitored in the section where the karst cave was located. Specific monitoring items included vault settlement monitoring and convergence monitoring. The longitudinal spacing of adjacent monitoring sections was 5 m. A total of 5 monitoring sections were set in the karst zone, and the first monitoring section was located at K84 + 862. The early monitoring frequency at the beginning of monitoring was 2 times/day. When the displacement tended to be stable, it will be reduced to be 1 time/day. Because the monitoring data of the five monitoring sections showed similar laws, the monitoring sections at K84 + 862 and K84 + 857 were selected to analyze and judge the effect of mud inrush treatment. Figure 16 shows the variation curves of the displacement of surrounding rock with the monitoring time after excavation.

Figure 16. Variation curve of surrounding rock deformation with time in Crossing karst cave section. (a) Variation curve of peripheral convergence, (b) Variation curve of vault settlement.

According to the variation curves of surrounding rock deformation, the values of vault settlement and peripheral convergence increased immediately after excavation. After the 12th day of excavation, the deformation of the surrounding rock no longer significantly increased. In addition, when the two sections were stable, the peripheral convergence values were 15.31 mm and 16.03 mm respectively and the vault settlement values were 17.46 mm and 18.80 mm respectively. These values were within the normal range.

Based on the analysis of the monitoring results of surrounding rock deformation, it has been proven that grouting reinforcement, improving support strength, and improving excavation methods can effectively control the deformation of surrounding rock, and have significant effects on the treatment of mud inrush disasters.

5. Conclusions

In this paper, a discrete element case study was carried out to investigate the failure characteristics and mechanism of clay filler in a karst cave during mud inrush geohazards, which can provide a theoretical foundation into the prevention and treatment of tunnel mud inrush geohazards. The main conclusions can be summarized as follows:

1. For tunnel construction in carbonate rock area, special attention should be paid to karst caves. The karst cave filled with unstable clay is a type of hazard-causing structure of mud inrush. A large amount of clay is filled in the karst cave, which is related to the cracks above the karst cave.

2. The main reason for the mud inrush was that the shear stress exceeded the shearing strength of clay. The distribution characteristics of force chains indicate that the stress arch prevents the continuous sliding of the clay in karst cave.

3. After the mud inrush, the clay in the karst cave was divided into two parts: the damaged zone and the non-damaged zone. This failure characteristic contributed to the rational design of mud inrush geohazards treatment measures.

4. In order to prevent the secondary mud inrush geohazards, it was recommended to conduct advance grouting for advance support, and increase the support stiffness. The monitoring results indicated that these mud inrush treatment measures were effective.

Data availability statement

Data supporting this research article are available from the corresponding author on request.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research work described herein was funded by the National Key R&D Program of China (No. 2021YFF0501101), the National Natural Science Foundation of China (No. 52178310 & 52278392), and the Fundamental Research Funds for the Central Universities CHD (Grant No. 300102212202). These financial supports are gratefully acknowledged, and the authors would like to thank reviewers for useful comments and editors for improving the manuscript.