A Comparison Study of the Radial and Non-Radial Support Schemes in the Deep Coal Mine Roadways under TBM Excavation by the 3-D Equivalent Continuum Approach

Abstract

In recent years, TBM has been widely applied in deep coal mining to lift the TBM tunneling efficiency and avoid accidents, and more flexible support schemes are expected and required. This research aims to evaluate the performance of the two different support schemes and to study the law of the support effect. A three-dimensional continuum model was established based on the available geological information, and the support effect at the three-dimensional level was studied by changing the support spacing and was assessed in term of the stress, displacement, failure zone, bolt force distributions, and axial deformation behavior of the tunnel. The results show that no matter what the geological condition was, the support of the non-radial support was a little lower than that of the radial support, and with a worse geological condition, the non-radial support had a better performance in the stabilizing tunnel. Additionally, the law of the support effect was found. The interlapping of the support influence domain was the essence of the increase in the support effect. Finally, according to the support law, the appropriate support spacing is found, which is smaller than 50% of the support influence domain length.

1. Introduction

In China, about 95% of coal mining work takes place underground [1]. With the depletion of coal resources within shallow ground, coal mining has been entering greater depths in recent years [2]. In deep coal mines, the behavior of the surrounding rock mass is quite different from that of shallow mines. This difference results in challenges for underground excavation projects, where the traditional drill and blast method cannot satisfy the demands for tunneling and support. Meanwhile, the development of rapid excavation is extremely desired in the mining industry. Therefore, deep mining demands a new alternative construction method [3].

The tunnel boring machine (TBM, as shown in Figure 1) is typified as full-face excavation equipment that combines the functions of rock breaking, support installation, mucking, and conveying into one machine [4]. It has been applied in tunnelling, hydropower, traffic, and municipal engineering for over 50 years. In recent years, because of its significant advantages, such as a high construction efficiency, low project cost, being conductive to environmental protection, and favorable stability control for surrounding rock, compared with the traditional drill and blast method, TBM has been applied to the coal mining industry [5]. In 1970, TBM was first successfully used in a drift excavation project in Minister Stein Colliery, Germany [6]. In addition, in Germany, in 1980, the application of TBM was done through an 8000 m conveyor drift excavation project in the Franz Haniel Coal Mine [7]. In China, the Methane Gas Extraction Roadway of the Zhangji Coal Mine was constructed using TBM in 2014. This was the first TBM boring line for a full-face hard rock roadway in a vertical shaft mine [8]. In the Xinjie Coal Mine Inclined Shaft Tunnel Project, the single-shield TBM with an earth pressure balance function was first used to construct a long inclined shaft tunnel coal mine with a steep slope [9].

In the process of tunneling using TBM, the mucking speed of the rock and soil in front of the face largely determines the advance rate of the machine because the accumulation of the rock and soil could cause a drop in the tunneling speed or even the capture of TBM. In order to increase the advance efficiency and avoid accidents, a conveyor belt to help transport the soil needs to be installed, which causes the position of the jumbolters to move up and the operation space to reduce, thus the supporting scheme of the blots should be changed from perpendicular to the wall (radial support) to inclined to the wall (non-radial support). Theoretically, this change could weaken the support effect for stabilizing the tunnel. With comprehensive consideration, the improvement in the tunneling efficiency could shorten the construction period and reduce the cost, and for this purpose the weaker support effect is worthy and a greater cost to stabilize the tunnel is acceptable. Understanding the law of supporting action and variation of the support effect of different schemes is critical to evaluate the security and feasibility of the preceding operation.

In rock engineering, the rock mass is usually regarded as a combination of intact rock and discontinuities. Continuum and discontinuum modeling are two commonly used numerical approaches. The discontinuum modeling approach models the rock mass with the existence of discontinuities in order to simulate the reality. There are a number of researchers using the discontinuum modeling approach (Sapigni et al. [10]; Vardakos et al. [11]; Macklin et al. [12]; Shi et al. [13]; Gao et al. [14]; Yang et al. [15]). The equivalent continuum modeling approach considers the rock mass as the continuous medium, and the minor discontinuities are considered to be a weakening of the strength, which is represented as a reduction in the parameters of the intact rock. As a common numerical method, equivalent continuum modeling has already been used by many researchers to study various geotechnical problems. Wang et al. [16] investigated the stability of a tunnel under a high in situ stress condition. Shreedharan et al. [17] used the back-analysis method to study the rock mass mechanical property values for different tunnel shapes. Huang et al. [18] studied the subsidence due to underground excavation and backfilling during open stoping operations. Xing et al. [19] investigated the stability of the tunnels under different in situ lateral stress ratios by estimating the rock mass properties using the Hoek–Brown equation. Moreover, K. Aliakbari et al. [20,21] used a numerical method.

Most previous studies regarding the support effect of the rock bolt were based on small-scale analysis, such as the pullout tests of the bolts, the numerical simulations, and the corresponding theoretical analysis. Wang et al. [22] investigated the influence of the structure plane surface situation and bolt inclination on the strength and deformation characteristic of the structure plane. Kang et al. [23] studied the anchorage performances and affecting factors of resin bolts through the combination method of theoretical analysis, laboratory tests, numerical modeling, and field measurement. Because of the limitation of the small scale of study, this kind of research cannot provide direct guidance for the design of a support scheme for underground excavation. On the other hand, not much research supports this effect and the performance of the support scheme at an overall engineering scale. In 2021, based on the real engineering data, Tang et al. [24] used two-dimensional discrete element code UDEC to study the performance of two different support schemes. However, because of the limitation of the two-dimensional analysis, the numerical simulation results only referred to a cross section of the tunnel, which was not enough to obtain an overall evaluation about the change in the support schemes. Therefore, in order to guide the design of the support scheme of underground excavation project, a stability analysis at a three-dimensional level and based on the overall engineering scale to evaluate the performance of the different support schemes is important to carry out.

In this paper, a three-dimensional continuum model was established to investigate and improve the performance of different support schemes. The properties of intact rock and minor discontinuities were considered as a whole and were represented as the properties of rock mass, and the strain-softening constitutive model was employed. The different support spacings were modeled to study the influence of the axial (along the advance direction) effect of the support on the overall tunnel stability. Finally, the performance of different support schemes was evaluated through the stress, the displacement distribution, and the failure zone distribution of the rock mass. The bolt force and the law of the support effect on the tunnel stability was also investigated.

2. Numerical Model of the Tunnel and the Support Schemes

2.1. Numerical Model

The dimensions of the model established according to the actual stratigraphic information were 30 m × 140 m × 30 m (Figure 2). The length of the circular tunnel with a radius of 2.15 m was 120 m. The depth of the tunnel was assumed to be 1095 m. In order to eliminate the influence of the opening on the boundary on stability, the tunnel was excavated inside the model. The model was set up in 3DEC (Itasca), which is a discrete element method software and addresses two points: (1) allows for finite displacements and rotations of discrete bodies, including complete detachment, and (2) recognizes new contacts automatically as the calculation progresses [25]. The rock mass was assumed to be homogeneous and isotropic, and was arranged so to meet the strain-softening constitutive model suing the Mohr-Coulomb criterion. The estimation of the rock mass properties has been investigated by many researchers. Hoek and Brown used a GSI system to estimate the rock mass property values [26]. Based on the laboratory tests, Kulatilake et al. assumed that the mean rock mass modulus was 51% of that of the intact rock, and the rock mass Poisson’s ratio was 21% higher than that of the intact rock [27]. The internal friction angle of the rock mass was usually taken to be 0.83 to 0.9 times that of the intact rock (Huang et al. [18]; Hudson et al. [28]). Yang et al. used an empirical equation to estimate the rock mass cohesion [29]. According to the above research, the calculation parameters of each lithology were determined and are listed in

Table 1. Physical and mechanical parameters of the different lithologies.

Lithology	Fine Sandstone	Medium Sandstone	Siltstone
Density (kg/m³)	2550	2600	2500
Bulk modulus (GPa)	6.13	5.84	1.11
Shear modulus (GPa)	1.89	1.47	0.55
Friction angle (°)	36.7	31.1	34.7
Cohesion (MPa)	0.05	0.46	0.58
Tensile strength (MPa)	0.06	0.67	0.72

.

The bulk modulus (K) and shear modulus (G) given in Table 1 were calculated from deformation modulus (E) and Poisson’s ratio (v) of the rock mass using Equations (1) and (2).

$$K=\frac{E}{3\left(1-2v\right)}$$

(1)

$$G=\frac{E}{2\left(1+v\right)}$$

(2)

In addition, because of the lack of laboratory test data about the strain-softening behavior, some research (Hajiabdolmajid et al. [30]; Alejano et al. [31]) works were reviewed to estimate the strain-softening property values, as given in

Table 2. Strain-softening property values of the rock masses.

Strain-Softening Parameter	Fine Sandstone	Medium Sandstone	Siltstone
Residual friction angle, ${\varnothing }_r$, (°)	29.38	24.91	27.79
Residual cohesion, $C_r$, (MPa)	0.02	0.18	0.23
Residual tensile strength, ${\sigma }_{tr}$, (MPa)	0.03	0.27	0.29
Plastic shear strain, $e^{ps}$	4 × 10−3	4 × 10−3	4 × 10−3
Plastic tensile strain, $e^{pt}$	6 × 10−3	6 × 10−3	6 × 10−3

. The top boundary of the model was located at a depth of 1080 m. A stress boundary of vertical stress of 27.54 MPa was applied based on the average weight of 2550 kg/m³ of the overburden strata. The roller boundary condition (no vertical or displacement) was applied at the bottom. For lateral boundaries, the stress boundary conditions with consideration of the gravity gradient were applied on the corresponding sides in both x- and y-directions. The gravity gradient was also applied to the entire model to simulate real in situ stress. The horizontal stress was calculated by a lateral stress ratio of $K_x=1.35\left({\sigma }_x/{\sigma }_z\right)$ and $K_y=0.9\left({\sigma }_y/{\sigma }_z\right)$. In this study, the initial stress field was obtained by equilibrating the in situ stress with the applied boundary conditions.

2.2. Support Schemes

Different from the delayed support of the traditional drill and blast method, TBM support is carried out synchronously with the advancing, thus the deformation of the rock mass after the excavation was considered to be non-existent. In general, the support effect is correlated to the support spacing, thus shortening the support spacing is considered for compensating the reduction in the support effect. Moreover, in the TBM advancing project, the tunnel axial deformation should be roughly equal to avoid the TBM being captured. Hence, tests on different support spacings were carried out. The tested spacings were 0.5 m, 1 m, 1.5 m, 2 m, 2.5 m, 3 m, 3.5 m, 4 m, 4.5 m, 5 m, 6 m, 7 m, and 8 m, respectively. The influence of the bolt type on the support effect was not considered, and the properties of the applied bolt (length of 2.4 m) are given in

Table 3. Material property values used for rock bolt [16].

Young’s Modulus of Bolt (GPa)	Cross-Sectional Area of Bolt (m2)	Tensile Yield Strength of Bolt (MN)	Bond Shear Stiffness (MN/m/m)	Bond Strength (MN/m)
210	2.55 × 10−4	240	2000	100

[16].

In this paper, two support schemes were studied, i.e., the radial support and the non-radial support, as shown in Figure 3. As with the literal meaning, the radial support was that all bolts were oriented on the extension of the radius, which is considered to be the best support scheme without the consideration of other factors. In this paper, the non-radial support was that the anchorage points of the bolts were the same as the radial support, but all of the bolts turned downwards by 30°, which could leave sufficient space for the conveyor belt installation and would increase the advance rate greatly.

2.3. Sensitive Study of the Paramters

To investigate the application and practice potential of the support scheme under different geological conditions, three geology conditions with the consideration of different properties of the rock, were proposed with the terminology of stiff, medium, and soft. The properties of the rock mass were softened by 10% from the stiff condition to the medium condition, as well as from the medium condition to the soft condition. The residual parameters of the strain-softening model also varied with the rock mass parameters.

Table 4. Material property values used for rock bolt.

System	Rock Mass Properties	Strain-Softening Parameter
stiff	110% of rock mass properties	${\varnothing }_r$ = 80% of friction angle $C_r$ = 40% of cohesion ${\sigma }_{tr}$ = 40% of tensile strength $e^{ps}$ = 0.004, $e^{pt}$ = 0.006
medium	100% of rock mass properties
soft	90% of rock mass properties

summarizes the detailed descriptions of each condition.

3. Analysis of the Results

It was difficult to analyze the deformation of the entire tunnel because of the huge amount of data. To simplify the analysis process, a simple analysis unit that could represent the behavior of the entire tunnel is needed. Figure 4 shows a schematic diagram of the analysis unit. Under the homogeneous geological condition, every part of the tunnel between every two supports could be considered to be stressed equally and deformed in the same way, thus the behavior of this part was sufficient to represent the entire tunnel. The two cross sections were selected to evaluate the tunnel stability. One cross section was located at the support anchorage, which is where the best support effect works, termed as the support face. The other cross section was located at the middle of the two support faces, namely middle face. Assuming that the axial deformation of the tunnel was continuous, these two faces could typically characterize the axial deformation of the entire tunnel. The selected support face and middle face were located at Y = −15 and Y = −16, respectively.

Theoretically, in this research, the floor deformation was not directly correlated to the support action due to the nonexistence of the bolt on the floor, and the deformation of the left wall was equal to that of the right wall due to the symmetry of the model. Therefore, in the following analysis, the analysis of the floor deformation was not given, and the lateral deformation (is equal to the 50% of the sum of the left and right wall deformations) was given to express the deformations of the left and right wall. Finally, to eliminate the calculation error, the displacement reduction was used to evaluate the support effect instead of the displacement.

3.1. Performance on the Support Schemes in the Tunnel Cross Section

The support spacing should be determined first before analyzing the support effect, as the support spacing affects the support effect. As mentioned above, appropriate support spacing should be one that results in equal overall tunnel deformation, which means that the support effect of the support face is close to that of the middle face, i.e., the best support effect is close to the weakest one in the entire tunnel. We assumed this “close” criteria was whether the sum of the displacement reduction of the roof and the lateral wall was less than 2 cm. The plots in Figure 5 and Figure 6 show the support effect of the support face and the middle face under different spacings of the radial support and non-radial support, respectively. Apparently, as one would intuitively expect, with the increase in support spacing, the difference between the displacement reduction of the two faces became bigger, which demonstrates that the support effect on the middle face weakened as the support spacing increased. The ranges of the support spacing that satisfied the “close” criteria (supposing the displacement reduction varies linearly) are presented in Figure 5 and Figure 6. The range of the radial support was 3.24 m and of the non-radial support was 3.49 m. Therefore, 3 m was considered to be an appropriate support spacing to study the stability on the tunnel cross section. The distributions of stress, displacement, failure zone, and bolt force were investigated as follows.

The underground excavation resulted in a redistribution of the surrounding rock. The analysis of the stress distribution was beneficial in order to study the behavior and stability of the rock mass and to check the authenticity of the numerical simulation results. Figure 7 and Figure 8 show the stress distributions of the rock mass around the tunnel. The vertical and horizontal stresses approached zero at locations close to the roof and floor, and the lateral walls, respectively, and the far filed stresses agreed with the applied stresses on the model boundary, which indicate that inputs were applied correctly to simulate the tunnel excavation. The maximum vertical and horizontal stresses were 81.1 MPa and 62.1 MPa, respectively, under the unsupported condition. Under the radial and the non-radial support conditions, the vertical stresses increased to 92.8 MPa and 91 MPa, respectively, and the horizontal stresses increased to 67.5 MPa and 67.4 MPa, respectively. Note that the peak stress was observed a slight distance away from the boundary. The results describe that the change from one support scheme to the other had little influence on the stress distribution.

The displacement distributions of the surrounding rock are presented in Figure 9 and Figure 10. In general, the displacement distribution is a major concern because it shows the direct performance of the tunnel stability. Figure 9 shows the maximum vertical displacement at the boundary on the roof and the floor. Under an unsupported condition, the vertical displacement of the roof was 22 cm. Under the radial and the non-radial support conditions, the roof vertical displacements decreased to 13.99 cm and 15 cm, respectively. Figure 10 shows the maximum horizontal displacement at the boundary on the left and the right wall. Under the unsupported condition, the horizontal displacements of the left and the right wall were 21.88 cm and 24.54 cm, respectively. Under the radial and the non-radial support conditions, the left wall horizontal displacements decreased to 14.63 cm and 15.73 cm, respectively, and the right wall horizontal displacements decreased to 15.80 cm and 17.13 cm, respectively. The results describe that the displacement of the roadway was effectively reduced by the support installation. The radial support was obviously better than the non-radial support.

The failure zone is usually analyzed in tunnel stability studies because it directly characterizes the behavior of the surrounding rock. Figure 11 presents the failure zone distributions of the rock mass around the roadway. ImageJ image processing software is used to measure the area of the failure zone. The failure zone areas under unsupported, radial, and non-radial support conditions were 139.96 m², 104.72 m², and 113.45 m² respectively. The radial and the non-radial support reduced the failure zone areas by 25.18% and 18.94%, respectively, which demonstrates that the existence of the support was beneficial to the stability of the surrounding rock, and the radial support had a greater influence on stabilizing the surrounding rock than the non-radial support.

The blot force is given in Figure 12. Studying the bolt force could be used to evaluate the possibility of the local failure of the bolts. The plots show the maximum bolt forces of the radial and the non-radial support were 3.41 MN and 3.14 MN, respectively, which demonstrates that the blot failure possibility of the radial support was slightly higher than that of the non-radial support. Moreover, note that the maximum bolt force was a slight distance away from the bottom of the bolt, where the stress concentration took place.

3.2. Axial Deformation Behavior of the Tunnel under the Two Support Schemes

In Section 3.1, the support effect was analyzed at a two-dimensional level under the 3 m support spacing condition. However, at the three-dimensional level, the performance of the support schemes was unknown, i.e., we did not know whether the performance of the radial support was still better than that of the non-radial support, and this advantage remained unchanged when the support spacing was changed. Moreover, how the support affects tunnel deformation in the axial direction is also our concern. Therefore, to further evaluate the performance of the support schemes, it is necessary to study the influence of the support schemes in the third direction.

Figure 13 shows the tunnel support effect of the support face of the two support schemes. Apparently, the deformation reduction increased with the decrease in the support spacing, which demonstrates that the better supporting effect was correlated with the more intensive blot installation. On the other hand, under any of the same support spacings, the displacement reduction of the non-radial support was always less than that of the radial support, which illustrates that the radial support maintained a better effect than the non-radial support when the support spacing changed. To further compare this advantage, the support effect ratio of the support face (the sum of roof and lateral displacement of the non-radial support/that of the radial support) was defined to measure the variation between the effect of the two support schemes with the support spacing, and the results are given in Figure 14. The support effect ratio did not change much and was close to constant when the support spacing was larger than 3 m, and in a range of smaller than 3 m, the effect ratio continued increasing with the decrease in the support spacing. This reveals that the ratio of the effect of the non-radial support to that of the radial support was not fixed, particularly in the support spacing of smaller than 3 m, the effect of the non-radial support became better and better relative to the radial support.

Figure 15 presents the growth rate of the support effect of the support face—the support spacing curve. The support effect growth rate is the change rate of the displacement reduction (the sum of the roof and lateral) as the support spacing decreases, which represents the growth of the support effect caused by each support spacing reduction. Note that, in general, the curve was rising with the decrease in the support spacing, and no matter what kind of support scheme, the support effect growth rate increased suddenly in the sections of 6 m to 5 m, 3.5 m to 2.5 m, and 2 m to 0.5 m, which demonstrates that in these sections, the decrease in the support spacing could bring more benefits to the support effect. This point was unexpected. To further to analyze this phenomenon, the growth rate of the support effect of the middle face (similar to that of the support face) was defined. Thus, under the assumption that the tunnel axial deformation was continuous, the overall tunnel behavior was clearly characterized. The result is shown in Figure 16. In contrast with Figure 15, the curve of Figure 16 moved down with the smaller support spacing, and there were two distinct dips in the curve, which occurred in the section of 4.5 m to 3.5 m and 2.5 m to 2 m. This difference was understandable because the curves in Figure 15 and Figure 16 represent the best and weakest support effect, respectively. As a result, there is a conjecture to account for the above phenomenon.

Theoretically, the existence of support could stabilize the surrounding rock, which not only exists in the tunnel cross section, but also in the axial direction. Under a homogeneous geological condition, the axial influence could be the same for every set support, i.e., the influence domain was the same size. Here, a schematic diagram of the influence domain and three typical situations are given in Figure 17. When the support spacing was very large, the length of the support influence domain was much less than the support spacing and the middle face was not in either domain. Thus, the displacement reduction in the middle face was much less that of the support face, as shown in Figure 5 and Figure 6. When the support spacing was equal to the support influence domain length, as shown in Figure 17b, the two domains started to make contact and interplay, and thus the support effect growth rate of the support face suddenly increased. When the support spacing was equal to 50% of the length of the support influence domain, as shown in Figure 17c, the effect of the domain acted directly on the anchorage instead of the indirect action (shown in Figure 17b), thus the support effect rate of the support face increased greatly the second time. Then, the third increase in the support effect rate of the support face occurred when the support spacing was equal to the 25% of the support influence domain length (as shown in Figure 17d), because the number of the direct action increased. Finally, when the support spacing was smaller, more domains inter lapped, and the support effect rate of the support face was higher and higher. It was obvious that the length of the support influence domain was about 6 m, as shown in Figure 15. Then, the second increase was at about 3 m and the third was 1.5 m, which is in accordance with the conjecture.

When the attention shifted to the support effect rate of the middle face, the result was equally satisfactory. With the smaller support spacing, the support effect rate of the middle face was higher and higher, except for the section in 4.5 m to 3.5 m and 2.5 m to 2 m. The support effect rate of the middle face decreased suddenly, because then the domains were in the state of interlap and direct action, respectively, but there was no further qualitative change. This is why there were two dips in the curve in Figure 16.

Finally, this conjecture explains that why the appropriate support spacing was about 3 m. Here, 3 m is 50% of the length of the support influence domain, where the anchorage was located at one end of the domain. Therefore, under the assumption that the support effect decreased linearly, every point in the tunnel had the same support effect. Therefore, the appropriate support spacing was close to 50% of the support influence domain length.

3.3. Sensitive Study under the Different Geological Conditions

To study the effect of the two support schemes under different geological conditions, sensitive studies were carried out, and the results were expressed by some typical dates that have been analyzed in Section 3.1 and Section 3.2. In the two-dimensional tunnel cross section analysis, the support spacing was set to 3 m, as in Section 3.1. The maximum stress, the displacement, and the failure zone area were given. In the axial analysis, the support effect ratio of the non-radial to the radial support of the support face were given. Thus, the variation of the support effect under different geological conditions could be evaluated accurately. The results are shown in Figure 18, Figure 19, Figure 20 and Figure 21.

Figure 18 presents the maximum stresses and their variations under the three geological conditions. Figure 18a shows the maximum vertical and horizontal stress without the support around the tunnel. Apparently, the vertical stress remained almost constant (about 82 MPa) under different geological conditions. The maximum horizontal stress was constant (about 61 MPa) with a good rock mass quality, but it increased greatly (about 10 MPa) under the soft geological condition. Figure 18b,c shows the stress growth rate caused by the support. When the rock mass became softer, the vertical stress grew greatly, and the horizontal stress also increased, but only by a small amount, which demonstrates that the support effect on the vertical stress was more obvious than that of the horizontal stress with the change in the geological conditions. Finally, the difference between the radial and non-radial support was very small.

Figure 19 shows the displacement reductions and their variations under the three geological conditions. As expected, as shown in Figure 19a, the displacement was reduced with the rock mass of a better quality, and the displacement difference between the roof and the lateral was small. Figure 19b,c shows the roof and lateral displacement reduction rate. Apparently, the reduction rate of the radial support was always higher than that of the non-radial support, which demonstrates that the support effect of the radial was always better than that of the non-radial support. Moreover, the difference in the curve was close to a constant, which reveals that the support effect ratio remained almost constant under different geological conditions.

Figure 20 describes the failure zone area variation. Figure 20a shows that under the unsupported condition, the failure zone area was reduced with the better rock mass quality, as one would intuitively expect. In Figure 20b, the failure zone area reduction rate was the highest for the medium geological condition and the lowest rate was found at the Stiff geological condition and well below the other. The reason for this could be that in the Stiff geological condition, the tunnel had better stability, so that the support did not have much of an effect. In contrast, the effect of the support on the soft geological condition was not enough to stabilize the tunnel, which resulted in a lower reduction rate.

Figure 21 shows the support effect ratio of the non-radial to the radial support. The higher ratio shows that the support effect of the non-radial was closer to the radial. Apparently, this rate was higher for the softer rock mass. This result shows that in the rock mass of a poor quality, where accidents were more likely to happen, the non-radial support effect was increased and was closer to the radial support, which is a positive conclusion for the application of non-radial support.

4. Conclusions

In this paper, under different geological conditions, the support effect of the two support schemes was investigated by changing the support spacing. The following main conclusions were drawn:

• The numerical simulation results show that no matter what the geological condition, the support installation could effectively reduce the tunnel wall deformation and stabilize the tunnel structure. This effect largely depended on the support spacing.
• Under the same support spacing, the performance of the two support schemes was evaluated. The results showed that the effect of the non-radial support was lower than that of the radial support. This comparison was also carried out in the other two geological conditions, and the results suggest that the non-radial support scheme had a better performance for controlling the surrounding rock deformation with a worse geological condition.
• By analyzing the variation of the growth rate of the support effect with the changing support spacings, the law of the interaction of the support was found. The enhancement of the support effect originated from the interlapping of the support influence domain. According to this law, the appropriate support spacing was specified to be smaller than 50% of the support influence domain length.