J. Cent. South Univ. (2020) 27: 3040-3052

DOI: https://doi.org/10.1007/s11771-020-4527-3

Stability analysis of underground surrounding rock mass based on block theory

LIN Jian-yun(林健云)^{1, 2}, ZUO Yu-jun(左宇军)^{1, 2}, WANG Jian(王剑)³, ZHENG Lu-jing(郑禄璟)^{1, 2},

CHEN Bin(陈斌)¹, SUN Wen-ji-bin(孙文吉斌)^{1, 4}, LIU Hao(刘镐)^{1, 2}

1. Mining College, Guizhou University, Guiyang 550025, China;

2. School of Resource and Environmental Engineering, Guizhou University, Guiyang 550025, China;

3. School of Resources and Safety Engineering, Central South University, Changsha 410083, China;

4. Priority Research Centre for Geotechnical Science and Engineering, The University of Newcastle,Callaghan, NSW, 2308, Australia

Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2020

Abstract: Evaluation of the performance of existing support in underground tunnels is of great importance for production and interests. Based on field investigation, the shape and number of joints and fractures were investigated in the mining area. Then, the stability of each structural blocks is analyzed by 3D wedge stability analysis software (Unwedge). Moreover, a new analysis method based on critical block theory is applied to analyze the stability of excavated laneways in continuous and discontinuous rock and monitor the stress changes in a fractured tunnel rock mass. The test results indicate that the 3D wedge stability analysis software for underground excavation can evaluate deep tunnel support. Besides, there is no direct relation between the size of the block and the instability of the tunnel. The support method, on large and thick key blocks, needs to be improved. In a broken tunnel section, U-shaped steel support can effectively promote the stress state of the surrounding rock. By monitoring the surrounding rock, it is proven that the vibrating string anchor stress monitoring system is an efficient and real-time method for tunnel stability evaluation.

Key words: key block theory; Unwedge analysis software; stress monitoring system; support evaluation

Cite this article as: LIN Jian-yun, ZUO Yu-jun, WANG Jian, ZHENG Lu-jing, CHEN Bin, SUN Wen-ji-bin, LIU Hao. Stability analysis of underground surrounding rock mass based on block theory [J]. Journal of Central South University, 2020, 27(10): 3040-3052. DOI: https://doi.org/10.1007/s11771-020-4527-3.

1 Introduction

Around the world, the instability of laneways causes heavy casualties and serious economic losses each year [1-7]. To reduce or prevent instability, it is necessary to analyze the tunnel stability and gain a clear understanding and evaluation of rock mass failure mechanisms. In recent years, ZUO et al [8], LI et al [9-12], ZHU et al [13, 14], and other experts have done many scientific studies to assess the harm caused by dynamic disturbance in deep mining.

Due to the variable nature of rock masses, it is difficult to determine the tunnel stability. These rock masses mainly include faults, joints, anisotropy, bedding, discontinuities, etc. In geotechnical engineering and underground mining, the tunnel stability needs to be evaluated to ensure a stable state during construction and operation. Generally,field exploration of tunnel stability at different stages has different details due to the weak structural planes and the massive structure formed by hard discontinuous surface cutting. Analysis of such structures is of great importance to identify dangerous areas [15-20].

Block theory is always applied in the stability analysis in rock mass engineering. The publication of GOODMAN [21] indicates that block theory has been used as an effective method for rock mass engineering analysis. Since then, block theory has been widely applied in various projects due to its distinct characteristics. KOCHARYAN et al [22- 25] proposed a method for constructing three- dimensional block structures based on jointed rock mass parameters, and the stability of the block and its influence on the tunnel were studied. Based on block theory, WANG et al [26] developed geotechnical structure and model analysis software (GeoSMA-3D) and applied it to analyze a rock slope. GREIF et al [27] carried out static analysis of 45 selected Medieval Castle Rock Slopes in Slovakia and calculated the safety factors of more than 12000 potentially unstable blocks under static conditions using key block theory. DONG et al [28] analyzed the stability of the Jiaojia rock mass and established a nonprobabilistic reliability model of the surrounding rocks in underground caverns which can be used in the absence of field data. KRASNOVSKY et al [29] proposed a method for identifying the weakening position of rock blocks and applied it to rock pillars. HATZOR et al [30] collected the block failure data of Berkeley’s two tunnel sidewalls and proposed a method of integrating block motion criteria in an empirical rock classification system. CHEN [31] used the First-order Second-moment Method (FOSM) to assess the probability of key block formation and the possibility of key block failure. GONG et al [32-35] carried out the simulation experiments using a rock true-triaxial electrohydraulic servo mutagenesis testing system, and a wireless microcamera was used to record and monitor the damage process on the sidewalls of the tunnel in real time. WANG et al [35] combined supporting technology with U-shaped steel support and proposed the anchor-grouting approach for the surrounding soft rock. The numerical simulation of the combined supporting technology and in-situ deformation monitoring results show that the soft rock surrounding the roadway has been supported effectively.

In addition, support evaluation is important for the roadway stability. Therefore, it is of great significance to develop reliable monitoring technology and predict potential roadway instability based on test results. URBANCIC et al [36] outlined the current status of seismic monitoring instruments in underground mines in Canada and identified the changes in the direction of principal stress during deep mining through seismic monitoring. DONG et al [37-40] used micro seismic monitoring technology to investigate the fracture location and stress condition characterization for the physical process of rock mass deformation and failure, which provided guidance for the evaluation of dangerous areas.

With the increase of mining depth, the tunnel stress increases correspondingly, which increases the risk of surrounding rock breaking tunnel instability, as shown in Figure 1. The main destruction forms include falling roofs caused by broken surrounding rock and collapse caused by joint fracture development (Figure 1). To understand the deep rock mass characteristics in the Jiaojia Gold Mine, a vibrating wire anchor stress monitoring system is set up, and stress monitoring tests are carried out on the working face of the fractured rock mass. In addition, the evaluation of deep tunnel support in mining areas, combined with the numerical simulation, is carried out. The proposed research method can provide useful guidance for roadway support under deep complex geological conditions, and ensure the production of mine economic benefits and safety.

2 Investigation of joints and fractures in study area

The Jiaojia gold deposit is in a tectonic fracture zone, the orebody and surrounding rock are all broken and unstable. According to rock mechanics, the rocks of the Jiaojia gold deposit are semi-hard/hard rock, with tensile strength only 1/9- 1/19 of the uniaxial compressive strength. Moreover, the tensile strength perpendicular to the surface of the structure tends to be zero. The maximum principal tectonic stress field in the mining area is horizontal with azimuth SE-NW, which is approximately perpendicular to the direction of the orebody.

Figure 1 Main factors of tunnel instability in Jiaojia Gold Mine:

The fractured rock mass is easily affected by blasting vibration. When the structural plane slip exceeds its displacement limit, the rock mass structure collapses, with obvious deformation. In the working progress of well and tunnel engineering, when the tensile stress of the roof exceeds the tensile strength of the rock mass, the roof collapses easily. This is the main manifestation of ground pressure activity in the Jiaojia Gold Mine. Therefore, the investigations of joint fissures are of great significance to understand the surrounding rock block structure.

A joint fracture is a structural plane formed in rock masses under stress. It is a structural fracture, with no or little displacement. Although the size of these joint fractures are not notable, their numbers are remarkable. The stability and destruction modes and degrees of orebodies and their surrounding rocks are controlled by different positions, quantities, sizes, and shapes of joints [41-43]. Joint fissures are mostly associated with structural stress, and the tectonic stress field and movement mode can be deduced from the joint fissures, which provides the basic data for the mechanical analysis of the regional tectonic stress field and structural system. It can be seen that the investigation and statistical analysis of joints and fractures are very valuable in geological engineering surveying. To fully reflect the stability of the deep rock mass in the Jiaojia Gold Mine, the survey line method was applied to investigate the joints and fractures in the mining area.

In the middle of the -470 m mining area, 13# joints were selected to investigate the joints and fractures, and 65 joints were measured. The cluster analysis of joint fissures and the statistical analysis of the data are shown in Figure 2. The structural plane was discrete and the dominant position was roughly divided into 4 groups according to their tendency: The first group tended to be 0°-20°, with an average tendency of 12.9°, and mean obliquity of 75.5°. The second group tended to be 290°-310°, with an average tendency of 300.4°, and mean obliquity of 78.5°. The third group tended to be 110°-130°, with an average tendency of 112.6°, and mean obliquity of 60.5°. The fourth group tended to be 200°-230°, with an average tendency of 213.3°, and mean obliquity of 70.1°. According to the trend, the dominant position can be divided into 3 groups (Figure 2), 30°, 280° and 300°, and the inclination is mostly distributed at 30°-90°.

Figure 2 Investigation results of 13# pulse joint fracture in the middle part of -470 m:

3 Key block stability analysis

Longitudinal and transverse cutting of joints and structural planes make rock mass properties quite different from those of intact rock. The key block theory has been widely applied in the engineering field as an important method for analyzing jointed rock mass reliability [44]. To study the failure mechanism and stability of jointed rock masses in mining areas, the key block theory, combined with Unwedge software, is applied in this paper. Stability analysis was carried out on the results of the investigation of 13# joints in the middle section of the -470 m mining area, and the appropriate parameters were determined and selected in the Unwedge software for support analysis and evaluation.

In Unwedge, 3 groups of structural planes are analyzed each time, and the generated blocks are numbered automatically. Generally, the blocks formed by cutting structural planes mainly exist on the top and sides of the tunnel. As the mining work face deepens, the ground stress in the rock surrounding the roadway and mining site keeps increasing. Roof and side fall easily cause rock burst accidents. Therefore, for the development of the structure surface, emphasis should be placed on the stability of blocks formed by cutting structural planes. The following is a simulation of the 13 joints in the middle section of the -470 m mining area.

3.1 Stability analysis of a block formed by 1, 2 and 3 combined structural planes

From blocks formed in a combination of the 1, 2, and 3 structures, blocks 4 and 8 are at the top, blocks 3 and 6 are on the sides, and 5 is stable at the bottom of the tunnel as shown in Figure 3. The safety factor of each block is shown in Table 1. According to the results, the safety factors of blocks 3, 4 and 5 are larger than the critical value of 1 in the stable block formed by the combination of structural planes 1, 2 and 3. The safety coefficients of blocks 6 and 8 are all below the critical value of 1, which indicates an unstable condition.

Figure 3 Spatial distribution of blocks formed by combined cutting of 1, 2 and 3 structural planes

Table 1 Safety factor of blocks formed by 1, 2 and 3 cuts of structural planes

Accordingly, blocks 6 and 8 should be supported to ensure safety in production.

The normal and shear stress of each structural plane on the block can be obtained by software analysis and calculation, as shown in Figure 4. The maximum normal stress on each structural plane formed by the 1, 2 and 3 cuts is 2.65 MPa and the minimum is 0.16 MPa. The maximum shear stress is 1.30 MPa, and the minimum is 0.11 MPa. After determining the location of the normal stress and the maximum shear stress, attention should be paid to the stability of the site to avoid stress concentration and rock mass instability.

Since the exposed areas of blocks 6 and 8 are small, pipe bolts are installed at two locations for support. According to an actual mine condition, a 1.8 m pipe seam bolt was selected. By adjusting the row spacing between the anchor bolts and calculating the safety factor, the bolt and row spacing are set at 1.3 m. Safety factors are in Table 1. After bolting, all the block safety factors are greater than the critical value of 1, which indicates that the rock mass is in a stable state.

3.2 Stability analysis of blocks formed by 1, 3 and 4 combined structural planes

In the blocks formed by the 1, 3 and 4 structural planes, blocks 3 and 6 are at two sides of the tunnel, and block 1 is at the bottom. The distribution of each block is shown in Figure 5. The safety factor of each block is shown in Table 2. According to the results, in the blocks formed by the 1, 3 and 4 structural planes, the safety factors of blocks 1, 3 and 7 are all larger than the critical value of 1, indicating that they are stable blocks. The safety factors of blocks 6 and 8 are less than 1 and are unstable. Therefore, blocks 6 and 8 should be supported to ensure safety in production.

The normal and shear stress of each structural plane on the block can be calculated, as shown in Figure 6. The maximum normal stress on each structural plane of the blocks formed by the 1, 3 and 4 cuts is 2.42 MPa, and the minimum is 0.25 MPa. The maximum and minimum shear stresses are 1.41 and 0.14 MPa, respectively.

The length of the pipe joint anchor is chosen as 1.8 m for support because of the large volume and mass of blocks 6 and 8 in the 1, 3 and 4 combinations of structural planes. In the process of adjusting the spacing, the safety factors of blocks 6 and 8 vary slightly. Even if row and column spacing are set to 0.8 m, the safety factor is still less than the critical value of 1. The effect of the pipe support is shown in Figure 7. The safety factor for each block at the spacing of 0.8 m is shown in Table 2. It is believed that even if the spacing between the rows is very small, the safety factor will never reach the critical value of 1, according to its change in the adjustment process. Furthermore, as the anchor spacing shortens, the support cost increases sharply and the economic benefits decrease. In this case, to meet the product safety requirements, U-shaped steel is recommended for support.

Figure 4 Distribution of normal stress and shear stress on structural plane of blocks formed by 1, 2 and 3 cuts of structural planes:

Figure 5 Spatial distribution of blocks formed by combined cutting of 1, 3 and 4 structural planes

Table 2 Safety factor of blocks formed by 1, 3 and 4 cuts of structural planes

3.3 Stability analysis of blocks formed by 2, 3 and 4 combined structural planes

Structure surfaces 2, 3, and 4 were cut into 4 blocks, block 1 is stable at the bottom of the tunnel, blocks 3 and 6 are at the sides, and block 8 is at the top of the tunnel. The spatial distribution of each block is shown in Figure 8. The block safety factor is calculated and provided in Table 3. It can be seen that #1 is stable, and the safety factors of blocks 3 and 6 are greater than 2, so they are safe in the production process. The safety factor of block 8 is only 0.826, less than the design safety factor, so the stability of #8 needs to be further analyzed.

Figure 6 Distribution of normal stress and shear stres s on structural plane of blocks formed by 1, 3 and 4 cuts of structural planes:

The normal and shear stress on the structural plane can be calculated, as shown in Figure 9. The normal and shear stress at different parts of the structural plane is different. The minimum and maximum values of normal stress are 0.02134 MPa and 4.767 MPa, respectively, and the minimum and maximum values of shear stress are 0.040408 MPa and 2.20982 MPa, respectively.

Figure 7 Impression drawing after installing anchor bolt support

The volume of #8 is 17.192 m³. The weight is 464.185 kN. A bolt is used for support, and the safety factor is analyzed and calculated. According to the field condition of the Jiaojia Gold Mine, a 1.8 m pipe joint anchor is used for support, by adjusting the anchor and row spacing between the bolts. A 2 m anchor spacing and 1.9 m row spacing are finally determined. The safety factor of #8 reaches 2.01, which fits with the requirements of safety production. The safety factor for each block is shown in Table 3. The specific support condition is shown in Figure 10. It can be seen that the use of 5 slotted pipe bolts can meet the requirements. Thus, in the middle 13# joint of the -470 m mining area, bolt supports can meet the requirements for roadway stability.

Figure 8 Three views of a block formed by a structural plane cutting

Table 3 Safety factor of blocks formed by 2, 3 and 4 cuts of structural planes

Figure 9 Distribution of normal stress and shear stress on structural plane of blocks formed by 2, 3 and 4 cuts of structural planes:

4 Stability analysis of surrounding rock in-field monitoring

A broken tunnel in the middle slope of the -630 m mining area is selected to conduct stress monitoring tests. The main rocks of the Jiaojia Gold Mine deposit are porphyritic biotite granite and yellow iron sericite granite. The upper and lower footwall of the orebody is sericite, and the indirect surrounding rocks are black cloud hornblende, orthoclase diorite, black cloud plagioclase gneiss and black cloud granulite. The footwall is relatively intact, and the upper part is broken. The main body of the ore is beresite. Since the position of the vibrating wire anchor stress sensor is very close to the blasting face, the effect of blasting on the tunnel is obvious, and it can be analyzed by monitoring the data.

Figure 10 Result of supporting block 8 with slotted bolts

The ramp consists of 4 vibrating wire anchor stress gauges, a data acquisition system and an analytical computer. A 64-channel vibrating wire anchor stress monitoring system is set up. Each vibrating wire anchor stress gauge has 4 vibrating wire stress sensors and 1 temperature sensor equally distributed in 4 parts. The plane diagram of the test ramp is shown in Figure 11. The green and red circles represent the hole and bottom of the Z-axis of the vibrating wire anchor. Vibrating wire anchor stress gauges I, III and IV are installed in a U-shaped steel section that supports the broken surrounding rock. Gauge II is installed in a no support section. The coordinates and installation angle of stress meters I to IV are shown in Table 4.

The stress meter is connected to a readout in the 1000-3600 Hz reading range and set to the stress mode, to start data measuring. The output of the vibrating string stress meter is micro strain. The unit directly displayed by the readout instrument is 0.39102×10^-3 f ². The difference between the initial reading and the current reading can be calculated by subtracting the initial reading from the current reading. Anchor rod stretching will increase (R_t-R₀=+). Conversely, anchor rod stretching will decrease (R_t-R₀=-).

After installation and debugging, a set of initial data is collected. To avoid excessive data collection, data cannot be exported. Data copy work is carried out every 3-5 d, the data collected earlier in the acquisition instrument is cleared and the collection work continues. After the data acquisition is completed, the axial force variation trend is calculated and analyzed, as shown in Figure 12. A positive value indicates that the bolt stress gauge axial force is tensile, and a negative value indicates that it is compressive.

The installation position of stress meter I is close to laneways. According to the monitoring results, the axial force of the S₁ to the S₄ sensor is tensile, which may indicate that the steel support loses contact with the surrounding rock and fails to achieve its function. Then, the axial force gradually stabilizes, and the steel support begins to take effect. Stress gauge III is installed in the middle of the tunnel, where the steel support closely contacts the tunnel roof. Therefore, the axial forces of the S₉ to the S₁₂ sensors are all compressive. Stress gauge IV is installed near the other side of the roadway. The axial forces of the S₁₃ and the S₁₄ sensors are tensile. The axial force of the S₁₅ and the S₁₆ sensors is compressive, which shows that the steel support is in close contact with the surrounding rock. From the diagram, before and after the explosion, the data of all sensors show an abrupt change. With the increase of mining depth, the influence of blasting on the test section gradually weakens, and the curve is more smooth. Based on the overall axial force, the variation of stress meter II shows nonlinear growth, while the other 3 stress meters tend to be balanced, also the surrounding rock loosening ring is less than 2 m , which shows that the steel support has made a significant improvement in the rock deformation control after excavation. It is worth nothing that, the S₇ sensor cannot receive signals due to poor contact.

Figure 11 Plane map of slanted ramp in Jiaojia Gold Mine

Table 4 Azimuth and setting angle of vibrating wire bolt stress sensor

Figure 12 Real time monitoring of vibrating wire bolt stress meter (The red dotted line represents the blasting time group):

The temperature sensor data extracted from the stress gauges are plotted in Figure 13. The temperature trends of the T₁, T₃ and T₄ sensors are the same and remain at a certain range. The increasing trend temperature anomaly of the T₂ sensor is large and related to the installation position of stress meter II. After blasting, there is a sudden change in temperature.

According to Figures 12 and 13, bolts I, III and IV are in the support section, and their axial force values first increase and then gradually stabilizes, while the temperature values change slowly and steadily. No. II bolt is in the unsupported section, and its axial force has a large fluctuation range and a straight upward trend, and its temperature shows a dramatic wave dynamic, this proves that the U-shaped steel support improves the stability of the roadway in this section.

Figure 13 Temperature sensor data extracted from stress gauges (The curves of orange, black, red and green indicate the change of temperature of stress gauge I, II, III and IV with time. The blue dotted line represents the blasting time group)

As previously described, through the real-time vibrating wire anchor stress monitoring system, stress redistribution will occur in the form of tensile or compressive stress in the surrounding rock after excavation. With the application of the U-shaped steel support, the surrounding rock stress tends to be stable, whereas the stress increases without the U-shaped steel support. Since the rock surrounding the tunnel is relatively broken, without proper support after excavation, the change and redistribution of surrounding rock stress will easily cause roof collapse and wall caving accidents. The adoption of U-shaped steel supports for broken surrounding rock proves to be effective.

5 Conclusions

The evaluation of the existing support is important for mine safety, production, and benefits. In response to this critical issue, through field layout and measurement, the joints and cracks in the mining area are investigated, and the surrounding rock characteristics of the 13# joints in the middle of the -470 m mining area are obtained. A new analysis method based on key block theory is applied to analyze the surrounding rock. As the data show, bolt support can meet the stability requirements of crossing tunnels. For large and thick key blocks, steel support can be selected, but it will cause difficulties in support and increase cost. Considering the stress state and support of the rock mass, the vibrating string stress monitoring system is applied. When blasting occurs, the U-shaped steel support could improve the stability of the surrounding rock mass. However, without the U-shaped steel support, stress in the surrounding rock increases continuously. If the support is not carried out in time, the change and redistribution of surrounding rock stress will cause accidents such as roof fall and spalling. Through data analysis and practical application, it is proven that the vibrating string stress monitoring system is an efficient and real-time method for tunnel stability evaluation. This study could provide some reference value for the safety evaluation of deep tunnels.

Contributions

LIN Jian-yun, ZUO Yu-jun and WANG Jian analyzed the calculation results and wrote the article; ZHENG Lu-jing collected the construction site information; WANG Jian and CHEN Bin carried out the numerical simulation; SUN Wen-ji-bin and LIU Hao processed the data; and ZUO Yu-jun offered useful suggestions for the preparation and writing of the paper. All authors replied to reviewers’ comments and revised the final version.

Conflicts of interest

LIN Jian-yun, ZUO Yu-jun, WANG Jian, ZHENG Lu-jing, CHEN Bin, SUN Wen-ji-bin and LIU Hao declare that they have no conflict of interest.

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(Edited by HE Yun-bin)

中文导读

基于块体理论的地下围岩稳定性分析

摘要：在深部巷道支护中对现有支护的评价至关重要，对安全生产具有重要意义。通过现场布置与测量，对矿区的节理裂隙进行了调查，确定了岩体中节理的形态和数量。然后，利用三维楔块稳定分析软件(Unwedge)对地下开挖的各个结构面块体进行稳定性分析。应用关键块体理论对连续和不连续岩体中开挖巷道的稳定性进行了分析，并对裂隙围岩的应力变化进行了监测。结果表明：三维楔形体稳定性分析软件可以对深部巷道支护进行评价；块体大小与巷道失稳没有直接关系，大厚度关键块的支护方法有待改进；在巷道软弱破碎段，U型钢支护能有效改善围岩应力状态。通过对巷道围岩的监测，证明了振动弦锚应力监测系统是一种高效、实时的地下围岩稳定性评价方法。

关键词：关键块体理论；Unwedge；应力监测系统；支护评价

Foundation item: Projects(51964007, 51774101) supported by the National Natural Science Foundation of China; Project(2016-4011) supported by the High-level Innovative Talents Training Project in Guizhou Province, China; Project(2019-5619) supported by the Guizhou Mining Power Disaster Early Warning and Control Technology Innovation Team, China

Received date: 2020-05-19; Accepted date: 2020-09-20

Corresponding author: ZUO Yu-jun, PhD, Professor; Tel: +86-18798082655; E-mail: zuo_yujun@163.com; ORCID: https://orcid.org/ 0000-0001-7131-7193