# An Innovative Balanced-Yielding Support Method for Tunnel in Deep Inclined Strata

Authors: Wei Yongke; Guo Hongyan; Hu Juyi; Liu Jiaqing; Liu Limin
Journal: Geofluids
 (2022)

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## Abstract

Aiming at the problem that the uneven deformation of the tunnel surrounding rock in the deep inclined rock strata caused local instability, an innovative balanced-yielding support technology was proposed with the engineering background of the Shangping tunnel in Huafeng Mine. Based on the mechanism analysis of this technology, the specific implementing steps were proposed. It mainly included in situ stress analysis, the stress distribution of the tunnel surrounding rock with different sections, the design of the parameter of bolt-cable and yielding structure, and supporting effect evaluation. The results showed that (1) the stress concentration appeared at the top corners of the lower side and the bottom corner of the upper side of the rectangular and semicircular arched tunnel. (2) Compared with rectangle and vertical-wall semicircular arch tunnels, the trapezoidal tunnel could relieve the shearing effect of the inclined rock strata. (3) The length, prestress, spacing-row distance of the bolt, and the parameter of the yielding structure were all optimally designed to form the balanced-yielding support system. (4) In engineering application, the maximum deformations of the roof, right side and left side, were less than 80 mm. Compared with the original support system, the shallow separation of the trapezoidal tunnel supported by the balanced-yielding support system had been reduced by 147%.


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## Body

## 1. Introduction

The underground rock mass is in a state of stress balance before excavation. Manual excavation removes the constraint force in one direction of the rock mass, resulting in an unbalanced state. So, the rock mass will move to the excavated free space to reach a new stress balance state. In order to maintain the stability of the underground rock mass, a certain external force needs to be applied to make up for the original restraining stress. The methods of controlling the stability of the surrounding rock mainly include active support and passive support [1–6]. Passive support only uses the bearing capacity of the support structure itself to resist the stress of the surrounding rock, mainly including shed-type supports, single pillar, U-shaped steel support, and concrete-filled steel tube support. Active support is to reinforce the shallow surrounding rock through the support structure to improve the self-carrying capacity of the rock mass to resist the stress released by the deep rock mass. Active support mainly includes bolts, cables, anchor cables, grouting, and shotcreting.As the depth of underground engineering gradually increases, ground stress gradually increases. General passive support is difficult to meet the requirements of the controlling deep surrounding rock. Active support was widely used in deep tunnel with its concept of actively reinforcing the surrounding rocks. Among them, bolt and cable supports were the most widely used. In addition, the combined support of bolts and cables can connect the rock masses of different depths, realizing the suspension of shallow bearing arches on deep rock masses [7, 8]. It plays the role of combining the self-loading of the shallow surrounding rock with the deep surrounding rock, and is widely used in deep coal mine tunnels, deep metal mine tunnels, high stress tunnels, etc. [9–12].For special deep surrounding rock tunnels including dynamic pressurized tunnels, soft rock tunnels, asymmetric surrounding rock tunnels, and inclined rock tunnels, different bolt-cable support schemes are required. Among them, the surrounding rock controlling of the tunnel in deep inclined rock strata has always been a big problem [13–16]. There are two main reasons. On the one hand, the in situ stress of deep rock mass is relatively high. On the other hand, the inclined rock strata make the stress of the tunnel surrounding rock uneven, resulting in local stress concentration [17–20].Many scholars had investigated the support method for deep inclined rock tunnel. Liang et al. [21] proposed the two-dimensional hydraulic-mechanical calculation model and the key-strata stability analysis model to analyze the theoretical range of failure and the stability of inclined floor strata after mining. Sun et al. [22] investigated the inclination effect of mine strata on the stability of loess land slope under the condition of underground mining. Wang et al. [23] proposed DFH control strategies of the tunnel driven in deep inclined strata. Ye et al. [24] analyzed the fracture evolution characteristics of overlying strata above working face with large inclination angle and mining depth. Sun et al. [25] present an experimental study on the floor heave of tunnel excavated in deep ten degree inclined strata.Although the above research had played a role in the control of the surrounding rock of the inclined rock strata, the current research and application were both limited. There was no unified design concept. It failed to balance support costs and effects. On the one hand, the supporting parameters were too large, resulting in waste of supporting materials. On the other hand, the supporting parameters were too small, resulting in poor control effect. Due to the local stress concentration of the tunnel surrounding rock in inclined rock strata, the force of local bolts increases too fast and breaks, so the ordinary strong anchor theory is difficult to give full play to its effective role. It is necessary to adopt the yield-antibalance combination concept. The rod is protected by yielding structure to give full play to the role of the high-strength bolt. Then, the asymmetrical surrounding rock stress is balanced by the asymmetrical bolt-cable parameters to achieve the overall balance of the tunnel surrounding rock. The buried depth of the Shangping tunnel of Huafeng Mine in Tai’an, China, is more than 1000 m. The inclination angle of the rock strata is greater than 30°. It belongs to a typical deep inclined rock tunnel. The original support scheme was high-strength bolts with the type ofΦ25×2500mm and the density of 700×700mm to control the surrounding rock of the tunnel. Although the strength of the supporting structure was already great, the local surrounding rock deformation was still great, especially part of the bolt had broken.Taking the Shangping tunnel of Huafeng Mine as the engineering background, the paper innovatively proposed the balanced-yielding support technology for tunnel in the deep inclined rock. Then, the implementation steps were described in detail. This technology reinforced the tunnel surrounding rock by the yielding support structure to eliminate the local stress concentration, achieving that the deformation of the local surrounding rock was basically equal. The technology could achieve the overall balance of the deformation and stress of the tunnel surrounding rock through the asymmetrical yielding support structure.


## 2. Background

Huafeng Mine is located in Tai’an, Shandong, China. The inclination angle of the 6th coal is 31° to 33°. Figure1 shows the characteristics of the roof-floor rocks of the 6th coal seam. The elevation of the Shangping tunnel is -922 m. Above and below it are the mined 1610 working face and the unmined 1611 working face, respectively. The strike length of the Shangping tunnel is 400 m. Its average buried depth is 1020 m. The characteristics of large buried depth, large inclination angle, and high ground stress determine the difficulty of surrounding rock control. The original high-strength bolt-net support scheme with the high-strength bolt with the type of Ф25×2500mm and the density of 700×700mm, one cable with the length of 4500 mm in the middle of the roof and the metal net and steel strip laid on the surface was used to control the surrounding rock of the Shangping tunnel. However, the local surrounding rock had a large deformation, so it cannot meet the requirements of normal use. And the bolts in the top corners of the lower side and the bottom corner of the upper side of the tunnel were broken. So, only the high-strength support concept cannot effectively control the stability of the surrounding rock of the Shangping tunnel. Therefore, it is urgent to find a new support concept. Based on the yield-antibalance combination concept, this paper attempted to use prestressed yield bolts to control the surrounding rock in Shangping tunnel.Figure 1
Partial stratigraphic section of Huafeng Mine.


## 3. Balanced-Yielding Support Technology for Tunnel in the Deep Inclined Rock

### 3.1. Proposal

In the deep inclined rock, the component force of the rock layer in the sloping direction causes the nonuniform stresses of the tunnel surrounding rock. The stress concentration occurs in the surrounding rock locally, resulting in uneven damage to the surrounding rock. In order to alleviate the effect of the gravity component of the overlying inclined rock strata, a reasonable cross-sectional shape of the tunnel should be selected first. Then, the nonuniform supporting structure minimizes the stress concentration. That is, the interaction between the supporting structure and the surrounding rock makes the system reach a certain relative balance.The yielding structure plays a first role in the stress concentration area of the surrounding rock, relieving local excessive stress to reduce the stress concentration, which can promote the overall force of the surrounding rock to be more uniform. So, the yielding support structure can promote the balance of stress and displacement of the surrounding rock. The balanced-yielding support technology mainly controls the uneven deformation of the tunnel from the angle of stress and displacement balance through the yielding structure and the asymmetrical anchor cable. The stress balance is achieved by controlling the tensile stress of the asymmetric surrounding rock within a basically symmetrical range by forming a common bearing body between the supporting structure and the surrounding rock. The displacement balance is achieved by controlling the surface displacement of the tunnel in a basically symmetrical range by forming a common bearing body between the supporting structure and the surrounding rock.The balanced-yielding support technology is applicable to the reinforcement of mine roadways, tunnels, and other underground chambers. In the underground tunnel support system, the surrounding rock is controlled by applying prestress and installing yielding structures to the bolts (cables). The yielding structure can be deformed before the bolt-rod is stressed to the yield strength, so as to achieve controlled yielding. The supporting structure can provide constant supporting resistance for a long time and maintain the long-term stability of the surrounding rock. The layout parameters of prestressed anchor cables should be based on the stress of the tunnel surrounding rock in order to achieve differential active control.


### 3.2. Implementing Steps

In the balanced-yielding support technology, the stress distribution of the tunnel surrounding rock can be analyzed through theoretical analysis, numerical calculation, and other methods. According to the stress distribution of the surrounding rock, the cross-sectional shape of the tunnel and the bolt-cable parameters can be determined. Then, the reasonable structure of the anchor cable is designed to pave the way for the balanced-yielding support technology. The specific implementing steps are shown in Figure2.Figure 2
The specific implementing steps of the balanced-yielding support technology.According to the above implementation steps, the balanced-yielding support technology was used to control the Shangping tunnel of Huafeng Mine.


## 3.1. Proposal

In the deep inclined rock, the component force of the rock layer in the sloping direction causes the nonuniform stresses of the tunnel surrounding rock. The stress concentration occurs in the surrounding rock locally, resulting in uneven damage to the surrounding rock. In order to alleviate the effect of the gravity component of the overlying inclined rock strata, a reasonable cross-sectional shape of the tunnel should be selected first. Then, the nonuniform supporting structure minimizes the stress concentration. That is, the interaction between the supporting structure and the surrounding rock makes the system reach a certain relative balance.The yielding structure plays a first role in the stress concentration area of the surrounding rock, relieving local excessive stress to reduce the stress concentration, which can promote the overall force of the surrounding rock to be more uniform. So, the yielding support structure can promote the balance of stress and displacement of the surrounding rock. The balanced-yielding support technology mainly controls the uneven deformation of the tunnel from the angle of stress and displacement balance through the yielding structure and the asymmetrical anchor cable. The stress balance is achieved by controlling the tensile stress of the asymmetric surrounding rock within a basically symmetrical range by forming a common bearing body between the supporting structure and the surrounding rock. The displacement balance is achieved by controlling the surface displacement of the tunnel in a basically symmetrical range by forming a common bearing body between the supporting structure and the surrounding rock.The balanced-yielding support technology is applicable to the reinforcement of mine roadways, tunnels, and other underground chambers. In the underground tunnel support system, the surrounding rock is controlled by applying prestress and installing yielding structures to the bolts (cables). The yielding structure can be deformed before the bolt-rod is stressed to the yield strength, so as to achieve controlled yielding. The supporting structure can provide constant supporting resistance for a long time and maintain the long-term stability of the surrounding rock. The layout parameters of prestressed anchor cables should be based on the stress of the tunnel surrounding rock in order to achieve differential active control.


## 3.2. Implementing Steps

In the balanced-yielding support technology, the stress distribution of the tunnel surrounding rock can be analyzed through theoretical analysis, numerical calculation, and other methods. According to the stress distribution of the surrounding rock, the cross-sectional shape of the tunnel and the bolt-cable parameters can be determined. Then, the reasonable structure of the anchor cable is designed to pave the way for the balanced-yielding support technology. The specific implementing steps are shown in Figure2.Figure 2
The specific implementing steps of the balanced-yielding support technology.According to the above implementation steps, the balanced-yielding support technology was used to control the Shangping tunnel of Huafeng Mine.


## 4. Stress Distribution of the Tunnel Surrounding Rock with Different Section Shapes

### 4.1. In Situ Stress Analysis

The in situ stress was measured by the hydraulic fracturing technique. A total of 3 monitoring points were selected. The first monitoring point was located at the -1100 level, where the buried depth of the tunnel was about 1220 m. The second monitoring point was located 65 m north of the sixth Shimen, where the buried depth of the tunnel was about 1130 m. The third monitoring point was located 45 m east of Shimen in the -920 level, where the buried depth of the tunnel was about 1040 m. The measurement results of the in situ stress are shown in Table1.Table 1
The measurement results of the in situ stress.
Monitoring pointsBuried depth (m)Vertical stress (MPa)Maximum horizontal principal stress (MPa)Minimum horizontal principal stress (MPa)Direction of maximum horizontal principal stress1122030.5042.1922.80N3°E2113028.2533.1519.10N31.5°E3104026.0031.3516.20N23.5°WTable1 shows that the buried depths of the three monitoring points were all over 1000 m, especially for the deepest reaching 1220 m. The maximum horizontal principal stresses of the three monitoring points were 42.2 MPa, 36.15 MPa, and 31.35 MPa, respectively. So, the maximum horizontal principal stress was greater than 30 MPa. The direction of the maximum horizontal principal stress was mainly in N3°E~N23.5°W. The minimum horizontal principal stresses of the three monitoring points were 22.8 MPa, 19.1 MPa, and 16.2 MPa, respectively, which were all greater than 15 MPa. It showed that the vertical stress, the maximum horizontal principal stress, and the minimum horizontal principal stress gradually increased with the increase of the buried depth. The ratios of the maximum horizontal principal stress to the vertical stress at the three monitoring points were 1.305, 1.207, and 1.133, respectively, indicating that the initial rock stress field was dominated by horizontal stress. And the ratio gradually increased as the depth increases, and that was the deeper the mining depth, the more obvious the effect of tectonic stress.


### 4.2. Stress Distribution of the Surrounding Rock

#### 4.2.1. Rectangle and Vertical-Wall Semicircular Arch Tunnels

According to the mining geological conditions of Huafeng Mine, the length, width, and height of the numerical model were 220 m, 150 m, and 200 m. The inclination angle of the coal-rock strata was 33°. The mechanical parameters of the 6th coal roof and floor strata are shown in Table2. In order to simplify the force of the overlying strata, a uniform load was applied to the upper boundary of the model. The load was equal to the weight of the overlying rock. The depth was 920 m, so the stress applied on the upper boundary was 23.46 MPa. Single-directional restraints were imposed on both sides of the model, and bidirectional constraint was imposed on its bottom boundary. The model took the Mohr-Coulomb constitutive relation. According to the implementing steps of the balanced-yielding support technology, the purpose was to select a reasonable tunnel cross-sectional shape. Firstly, the common rectangle and vertical-wall semicircular arch tunnels were selected for stress analysis.Table 2
Mechanical parameters of the 6th coal roof and floor strata (average).
LithologyElastic modulus (GPa)Poisson’s ratioCohesion (MPa)Internal friction angle (°)Uniaxial tensile strength (MPa)Uniaxial compression strength (MPa)Bulk density (kg·m-3)Sandstone260.1317226.1702600Mudstone60.354.6162.3262500Coal50.374.2152.1241300Medium sandstone210.1812185.4382600Siltstone400.257.5329.0472550Figures3 and 4 show the stress distributions of the surrounding rocks of rectangular and vertical-wall semicircular arch tunnels. It could be seen from Figure 3 that the stress concentration occurred at the junction of the left side and the roof and the intersection of the right side and the floor of the rectangular tunnel. The shear failure of the tunnel roof would occur in the left half. The coal wall on the left side would be severely damaged. Figure 4 shows that the stress concentration occurred at the left half of the vertical-wall semicircular arch tunnel roof. The degree of stress concentration on the left vertical-wall was much greater than that on the right vertical-wall. The arched roof of the tunnel would cause shear failure due to extrusion. The coal wall of the left straight wall would be greatly deformed. So, in the engineering application, the support strength of the left side and floor of the tunnel should be improved, especially to ensure the support effect of the bolts in bottom corner.Figure 3
Stress distribution of the surrounding rock of rectangular tunnel.
(a)
Shear stress distribution(b)
Minimum principal stress distributionFigure 4
Stress distribution of the surrounding rock of vertical-wall semicircular arch tunnel.
(a)
Shear stress distribution(b)
Minimum principal stress distribution


#### 4.2.2. The Mechanism of Stress Concentration

Taking the vertical-wall semicircular arch tunnel as an example, the mechanism of stress concentration was analyzed. The immediate roof of the Shangping tunnel was low-strength siltstone, which would inevitably increase the damage to the surrounding rock. In addition, under the influence of the component force of the rock layer’s own weight stress in the inclined direction and the horizontal stress, the stress distribution of the surrounding rock of the tunnel was uneven, especially in the local stress concentration. However, the component force of the rock layer’s own weight stress in the inclined direction had different effects on the two sides of the tunnel. This effect is shown in Figure5. The red streamline indicated the rock layer’s own weight stress curve in the inclined direction. Figure 5 shows that the stress concentration occurred at the top corner of the right side and the bottom corner of the left side of the tunnel. In addition, the stress release occurred at the top corner of the left side and the bottom corner of the right side of the tunnel.Figure 5
The component force effect of the rock layer’s own weight stress in the inclined direction.The component force of the rock layer’s own weight stress in the inclined direction was the basic reason of the rock layer’s shear slip. The shear slip was the main reason for the shear stress between layers. The shear stress caused the stress concentration at the top corner of the right side and the bottom corner of the left side. So, in order to reduce the stress concentration here, the roof and floor could be changed to follow the direction of the rock layer as much as possible. This could reduce the degree of shear failure of the tunnel surrounding rock. In addition, considering the basic requirements of the tunnel for pedestrians, transportation, and pipelines, the tunnel floor must be level. So, the overall shape of the tunnel could be a trapezoid with an inclined roof.


#### 4.2.3. Stress Distribution of Trapezoidal Tunnel

Based on the above theoretical analysis and numerical simulation, considering the combined effect of the component force of the rock layer’s own weight stress in the inclined direction and the horizontal stress, the roof direction of the trapezoidal tunnel was designed roughly along the combined direction of the rock layer and the horizontal. The width and the height of the two sides of the tunnel were designed to be 3.8 m, 3.0 m, and 2.5 m, respectively. The stress distribution of the surrounding rock of trapezoidal tunnel is shown in Figure6.Figure 6
Nephogram of the stress distribution of the trapezoidal tunnel surrounding rock.
(a)
Shear stress distribution(b)
Maximum principal stress distributionIt could be seen from Figure6, under the combined effect of the component force of the rock layer’s own weight stress in the inclined direction and the horizontal stress, the stress concentration still occurred at the top corner of the left side and the bottom corner of the right side of the tunnel, and the stress release occurred at the other two opposite angles. The shear stress at the top corner of the left side was generally 4.5 MPa, with the maximum of 7.25 MPa. The stress concentration penetrated the surrounding rock to the rock interface. The shear stress at the bottom corner of the right side of the tunnel was 4.2 MPa, which was slightly smaller than that at the top corner of the left side. In addition, the shear stress at the two sides was about 3 MPa. It showed that the stress concentration of the surrounding rock was not large, which was consistent with the theoretical analysis results. The inclined roof of the trapezoidal tunnel effectively weakened the effect of the component force of the rock layer’s own weight stress in the inclined direction. The maximum roof tensile stress and the maximum principal stress peak of the tunnel were both located on the left half of the inclined roof. In the area of maximum roof tensile stress here, the anchor cables should be arranged perpendicular to the rock layer for reinforcement. In addition, since the stress concentration was the most serious at the top corner of the left side, an inclined anchor cable was arranged to balance the stress concentration here.


## 4.1. In Situ Stress Analysis

The in situ stress was measured by the hydraulic fracturing technique. A total of 3 monitoring points were selected. The first monitoring point was located at the -1100 level, where the buried depth of the tunnel was about 1220 m. The second monitoring point was located 65 m north of the sixth Shimen, where the buried depth of the tunnel was about 1130 m. The third monitoring point was located 45 m east of Shimen in the -920 level, where the buried depth of the tunnel was about 1040 m. The measurement results of the in situ stress are shown in Table1.Table 1
The measurement results of the in situ stress.
Monitoring pointsBuried depth (m)Vertical stress (MPa)Maximum horizontal principal stress (MPa)Minimum horizontal principal stress (MPa)Direction of maximum horizontal principal stress1122030.5042.1922.80N3°E2113028.2533.1519.10N31.5°E3104026.0031.3516.20N23.5°WTable1 shows that the buried depths of the three monitoring points were all over 1000 m, especially for the deepest reaching 1220 m. The maximum horizontal principal stresses of the three monitoring points were 42.2 MPa, 36.15 MPa, and 31.35 MPa, respectively. So, the maximum horizontal principal stress was greater than 30 MPa. The direction of the maximum horizontal principal stress was mainly in N3°E~N23.5°W. The minimum horizontal principal stresses of the three monitoring points were 22.8 MPa, 19.1 MPa, and 16.2 MPa, respectively, which were all greater than 15 MPa. It showed that the vertical stress, the maximum horizontal principal stress, and the minimum horizontal principal stress gradually increased with the increase of the buried depth. The ratios of the maximum horizontal principal stress to the vertical stress at the three monitoring points were 1.305, 1.207, and 1.133, respectively, indicating that the initial rock stress field was dominated by horizontal stress. And the ratio gradually increased as the depth increases, and that was the deeper the mining depth, the more obvious the effect of tectonic stress.


## 4.2. Stress Distribution of the Surrounding Rock

### 4.2.1. Rectangle and Vertical-Wall Semicircular Arch Tunnels

According to the mining geological conditions of Huafeng Mine, the length, width, and height of the numerical model were 220 m, 150 m, and 200 m. The inclination angle of the coal-rock strata was 33°. The mechanical parameters of the 6th coal roof and floor strata are shown in Table2. In order to simplify the force of the overlying strata, a uniform load was applied to the upper boundary of the model. The load was equal to the weight of the overlying rock. The depth was 920 m, so the stress applied on the upper boundary was 23.46 MPa. Single-directional restraints were imposed on both sides of the model, and bidirectional constraint was imposed on its bottom boundary. The model took the Mohr-Coulomb constitutive relation. According to the implementing steps of the balanced-yielding support technology, the purpose was to select a reasonable tunnel cross-sectional shape. Firstly, the common rectangle and vertical-wall semicircular arch tunnels were selected for stress analysis.Table 2
Mechanical parameters of the 6th coal roof and floor strata (average).
LithologyElastic modulus (GPa)Poisson’s ratioCohesion (MPa)Internal friction angle (°)Uniaxial tensile strength (MPa)Uniaxial compression strength (MPa)Bulk density (kg·m-3)Sandstone260.1317226.1702600Mudstone60.354.6162.3262500Coal50.374.2152.1241300Medium sandstone210.1812185.4382600Siltstone400.257.5329.0472550Figures3 and 4 show the stress distributions of the surrounding rocks of rectangular and vertical-wall semicircular arch tunnels. It could be seen from Figure 3 that the stress concentration occurred at the junction of the left side and the roof and the intersection of the right side and the floor of the rectangular tunnel. The shear failure of the tunnel roof would occur in the left half. The coal wall on the left side would be severely damaged. Figure 4 shows that the stress concentration occurred at the left half of the vertical-wall semicircular arch tunnel roof. The degree of stress concentration on the left vertical-wall was much greater than that on the right vertical-wall. The arched roof of the tunnel would cause shear failure due to extrusion. The coal wall of the left straight wall would be greatly deformed. So, in the engineering application, the support strength of the left side and floor of the tunnel should be improved, especially to ensure the support effect of the bolts in bottom corner.Figure 3
Stress distribution of the surrounding rock of rectangular tunnel.
(a)
Shear stress distribution(b)
Minimum principal stress distributionFigure 4
Stress distribution of the surrounding rock of vertical-wall semicircular arch tunnel.
(a)
Shear stress distribution(b)
Minimum principal stress distribution


### 4.2.2. The Mechanism of Stress Concentration

Taking the vertical-wall semicircular arch tunnel as an example, the mechanism of stress concentration was analyzed. The immediate roof of the Shangping tunnel was low-strength siltstone, which would inevitably increase the damage to the surrounding rock. In addition, under the influence of the component force of the rock layer’s own weight stress in the inclined direction and the horizontal stress, the stress distribution of the surrounding rock of the tunnel was uneven, especially in the local stress concentration. However, the component force of the rock layer’s own weight stress in the inclined direction had different effects on the two sides of the tunnel. This effect is shown in Figure5. The red streamline indicated the rock layer’s own weight stress curve in the inclined direction. Figure 5 shows that the stress concentration occurred at the top corner of the right side and the bottom corner of the left side of the tunnel. In addition, the stress release occurred at the top corner of the left side and the bottom corner of the right side of the tunnel.Figure 5
The component force effect of the rock layer’s own weight stress in the inclined direction.The component force of the rock layer’s own weight stress in the inclined direction was the basic reason of the rock layer’s shear slip. The shear slip was the main reason for the shear stress between layers. The shear stress caused the stress concentration at the top corner of the right side and the bottom corner of the left side. So, in order to reduce the stress concentration here, the roof and floor could be changed to follow the direction of the rock layer as much as possible. This could reduce the degree of shear failure of the tunnel surrounding rock. In addition, considering the basic requirements of the tunnel for pedestrians, transportation, and pipelines, the tunnel floor must be level. So, the overall shape of the tunnel could be a trapezoid with an inclined roof.


### 4.2.3. Stress Distribution of Trapezoidal Tunnel

Based on the above theoretical analysis and numerical simulation, considering the combined effect of the component force of the rock layer’s own weight stress in the inclined direction and the horizontal stress, the roof direction of the trapezoidal tunnel was designed roughly along the combined direction of the rock layer and the horizontal. The width and the height of the two sides of the tunnel were designed to be 3.8 m, 3.0 m, and 2.5 m, respectively. The stress distribution of the surrounding rock of trapezoidal tunnel is shown in Figure6.Figure 6
Nephogram of the stress distribution of the trapezoidal tunnel surrounding rock.
(a)
Shear stress distribution(b)
Maximum principal stress distributionIt could be seen from Figure6, under the combined effect of the component force of the rock layer’s own weight stress in the inclined direction and the horizontal stress, the stress concentration still occurred at the top corner of the left side and the bottom corner of the right side of the tunnel, and the stress release occurred at the other two opposite angles. The shear stress at the top corner of the left side was generally 4.5 MPa, with the maximum of 7.25 MPa. The stress concentration penetrated the surrounding rock to the rock interface. The shear stress at the bottom corner of the right side of the tunnel was 4.2 MPa, which was slightly smaller than that at the top corner of the left side. In addition, the shear stress at the two sides was about 3 MPa. It showed that the stress concentration of the surrounding rock was not large, which was consistent with the theoretical analysis results. The inclined roof of the trapezoidal tunnel effectively weakened the effect of the component force of the rock layer’s own weight stress in the inclined direction. The maximum roof tensile stress and the maximum principal stress peak of the tunnel were both located on the left half of the inclined roof. In the area of maximum roof tensile stress here, the anchor cables should be arranged perpendicular to the rock layer for reinforcement. In addition, since the stress concentration was the most serious at the top corner of the left side, an inclined anchor cable was arranged to balance the stress concentration here.


## 4.2.1. Rectangle and Vertical-Wall Semicircular Arch Tunnels

According to the mining geological conditions of Huafeng Mine, the length, width, and height of the numerical model were 220 m, 150 m, and 200 m. The inclination angle of the coal-rock strata was 33°. The mechanical parameters of the 6th coal roof and floor strata are shown in Table2. In order to simplify the force of the overlying strata, a uniform load was applied to the upper boundary of the model. The load was equal to the weight of the overlying rock. The depth was 920 m, so the stress applied on the upper boundary was 23.46 MPa. Single-directional restraints were imposed on both sides of the model, and bidirectional constraint was imposed on its bottom boundary. The model took the Mohr-Coulomb constitutive relation. According to the implementing steps of the balanced-yielding support technology, the purpose was to select a reasonable tunnel cross-sectional shape. Firstly, the common rectangle and vertical-wall semicircular arch tunnels were selected for stress analysis.Table 2
Mechanical parameters of the 6th coal roof and floor strata (average).
LithologyElastic modulus (GPa)Poisson’s ratioCohesion (MPa)Internal friction angle (°)Uniaxial tensile strength (MPa)Uniaxial compression strength (MPa)Bulk density (kg·m-3)Sandstone260.1317226.1702600Mudstone60.354.6162.3262500Coal50.374.2152.1241300Medium sandstone210.1812185.4382600Siltstone400.257.5329.0472550Figures3 and 4 show the stress distributions of the surrounding rocks of rectangular and vertical-wall semicircular arch tunnels. It could be seen from Figure 3 that the stress concentration occurred at the junction of the left side and the roof and the intersection of the right side and the floor of the rectangular tunnel. The shear failure of the tunnel roof would occur in the left half. The coal wall on the left side would be severely damaged. Figure 4 shows that the stress concentration occurred at the left half of the vertical-wall semicircular arch tunnel roof. The degree of stress concentration on the left vertical-wall was much greater than that on the right vertical-wall. The arched roof of the tunnel would cause shear failure due to extrusion. The coal wall of the left straight wall would be greatly deformed. So, in the engineering application, the support strength of the left side and floor of the tunnel should be improved, especially to ensure the support effect of the bolts in bottom corner.Figure 3
Stress distribution of the surrounding rock of rectangular tunnel.
(a)
Shear stress distribution(b)
Minimum principal stress distributionFigure 4
Stress distribution of the surrounding rock of vertical-wall semicircular arch tunnel.
(a)
Shear stress distribution(b)
Minimum principal stress distribution


## 4.2.2. The Mechanism of Stress Concentration

Taking the vertical-wall semicircular arch tunnel as an example, the mechanism of stress concentration was analyzed. The immediate roof of the Shangping tunnel was low-strength siltstone, which would inevitably increase the damage to the surrounding rock. In addition, under the influence of the component force of the rock layer’s own weight stress in the inclined direction and the horizontal stress, the stress distribution of the surrounding rock of the tunnel was uneven, especially in the local stress concentration. However, the component force of the rock layer’s own weight stress in the inclined direction had different effects on the two sides of the tunnel. This effect is shown in Figure5. The red streamline indicated the rock layer’s own weight stress curve in the inclined direction. Figure 5 shows that the stress concentration occurred at the top corner of the right side and the bottom corner of the left side of the tunnel. In addition, the stress release occurred at the top corner of the left side and the bottom corner of the right side of the tunnel.Figure 5
The component force effect of the rock layer’s own weight stress in the inclined direction.The component force of the rock layer’s own weight stress in the inclined direction was the basic reason of the rock layer’s shear slip. The shear slip was the main reason for the shear stress between layers. The shear stress caused the stress concentration at the top corner of the right side and the bottom corner of the left side. So, in order to reduce the stress concentration here, the roof and floor could be changed to follow the direction of the rock layer as much as possible. This could reduce the degree of shear failure of the tunnel surrounding rock. In addition, considering the basic requirements of the tunnel for pedestrians, transportation, and pipelines, the tunnel floor must be level. So, the overall shape of the tunnel could be a trapezoid with an inclined roof.


## 4.2.3. Stress Distribution of Trapezoidal Tunnel

Based on the above theoretical analysis and numerical simulation, considering the combined effect of the component force of the rock layer’s own weight stress in the inclined direction and the horizontal stress, the roof direction of the trapezoidal tunnel was designed roughly along the combined direction of the rock layer and the horizontal. The width and the height of the two sides of the tunnel were designed to be 3.8 m, 3.0 m, and 2.5 m, respectively. The stress distribution of the surrounding rock of trapezoidal tunnel is shown in Figure6.Figure 6
Nephogram of the stress distribution of the trapezoidal tunnel surrounding rock.
(a)
Shear stress distribution(b)
Maximum principal stress distributionIt could be seen from Figure6, under the combined effect of the component force of the rock layer’s own weight stress in the inclined direction and the horizontal stress, the stress concentration still occurred at the top corner of the left side and the bottom corner of the right side of the tunnel, and the stress release occurred at the other two opposite angles. The shear stress at the top corner of the left side was generally 4.5 MPa, with the maximum of 7.25 MPa. The stress concentration penetrated the surrounding rock to the rock interface. The shear stress at the bottom corner of the right side of the tunnel was 4.2 MPa, which was slightly smaller than that at the top corner of the left side. In addition, the shear stress at the two sides was about 3 MPa. It showed that the stress concentration of the surrounding rock was not large, which was consistent with the theoretical analysis results. The inclined roof of the trapezoidal tunnel effectively weakened the effect of the component force of the rock layer’s own weight stress in the inclined direction. The maximum roof tensile stress and the maximum principal stress peak of the tunnel were both located on the left half of the inclined roof. In the area of maximum roof tensile stress here, the anchor cables should be arranged perpendicular to the rock layer for reinforcement. In addition, since the stress concentration was the most serious at the top corner of the left side, an inclined anchor cable was arranged to balance the stress concentration here.


## 5. Balanced-Yielding Support Scheme

Based on the trapezoidal tunnel, in order to make the surrounding rock deformation basically the same, a balanced-yielding support scheme was designed by increasing the support strength in the high stress concentration area. This scheme was based on the high-strength yielding bolt support system. Next, the bolt support parameters and yield structure were designed.


### 5.1. Bolt Length

According to Mohr-Coulomb criterion, the safety factor (SF) of rock failure can be calculated [26–29]. The area where the SF of the tunnel surrounding rock was greater than 1.5 was safe. The area with SF less than 1.5 was unstable, so the support control was needed. The distribution of the SF of the unsupported tunnel is shown in Figure 7. In order to further determine the length of bolts at different positions, three paths, Dx1, Dz1, and Ds1, were selected to analyze the stress distribution. The stress distribution path is shown in Figure 8. The maximum principal stress along each path is shown in Figure 9.Figure 7
The distribution of the SF of the unsupported tunnel.Figure 8
The stress distribution path.Figure 9
The maximum principal stress along each path.
(a)
Dx1(b)
Dz1(c)
Ds1It could be seen from Figures8 and 9 that under the influence of tunnel excavation, the maximum height of the tensile stress zone at the top corner of the left side was about 0.8 m. The maximum height of the tensile stress zone of the roof rock layer was about 1.2 m. The maximum height of the tensile stress area at the top corner of the right side was about 0.2 m. So, the maximum height of the tensile stress zone of the roof was 1.2 m. The bolt should be anchored in the rock layer outside the tensile stress zone to effectively control its damage. So, the length of the tensile section of the bolt-rod should be greater than the maximum depth of the tensile stress zone. It was assumed that the length of the bolt outside the tensile stress zone was 0.6 m, and the exposed length of the bolt in the tunnel was 0.1 m. It was calculated that the length of the roof bolt should be 1.9 m. In addition, because the immediate roof of the tunnel was 1.8 m thick siltstone with poor stability, the bolt needed to pass through the siltstone and be anchored into the stable rock stratum. So, the length of the tunnel roof bolt was designed to be 2.5 m.It could be seen from Figure7 that the safety factor at the 1.4 m and 1.8 m depth of the two sides reached 1.3 and 1.5. The bolts at the two sides should be anchored to the area where the SF was less than 1.5, so the length of the bolts should be more than 1.8 m. Due to the large burial depth, “coal burst” frequently occurred during the tunneling process. In addition, the horizontal stress was relatively high. So, the length of the roof bolt and the side bolt was determined to be 2500 mm. Due to the large stress concentration on the left side of the tunnel, the bolt support density of the left side should be increased to balance the stress of the surrounding rock.


### 5.2. Prestress of Bolt

According to the optimal bolt length of 2500 mm determined in Section5.1, the prestress of the bolt was investigated. As the roof rock layer was the most representative, this part only studied the support effect of prestressed bolts on the tunnel roof. Four bolts were arranged on the tunnel roof, and the bolts at the two corners were inclined. The prestressing force was selected as 20 kN and 40 kN, respectively. Figures 10 and 11 show the stress distributions of the tunnel roof with the prestressed bolts of 20 kN and 40 kN, respectively.Figure 10
The stress distribution of the tunnel roof with the prestressed bolts of 20 kN.Figure 11
The stress distribution of the tunnel roof with the prestressed bolts of 40 kN.It could be seen from Figure10 that when the prestress was 20 kN, the tensile stress area of the tunnel roof was relatively large. And the number of separations in the roof rock layer within 1000 mm was relatively large. It showed that the prestressed bolt with the prestress of 20 kN could not meet the requirements of tunnel support. So, it was necessary to increase the prestress of bolt. It could be seen from Figure 11 that when the prestress was 40 kN, the tensile stress area of the tunnel roof was basically eliminated. And the roof separation was basically closed. It showed that the prestressed bolt with the prestress of 40 kN could basically control the roof rock layer actively. In application, in order to ensure the supporting effect, the prestress of the bolt was designed to be 50 kN.


### 5.3. Spacing and Row Distances of Bolt

Based on the abovementioned bolt length of 2500 mm, the spacing and row distances between bolts were investigated by numerical simulation. According to the above numerical model, the deformations of tunnel with bolt spacing of 500 mm, 600 mm, 700 mm, 800 mm, 900 mm, and 1000 mm and bolt row distances of 700 mm, 800 mm, 900 mm, 1000 mm, and 1100 mm were calculated, respectively, without anchor cable. The relationships between the spacing and row distances of bolt and surrounding rock deformation are shown in Figure12.Figure 12
The relationships between the spacing and row distances of bolt and surrounding rock deformation.
(a)
The spacing distances of bolt(b)
The row distances of boltIt could be seen from Figure12(a) that when the bolt spacing on the right side was less than 800 mm, the change of surrounding rock deformation was no longer obvious. So, the optimal spacing distance between the right side bolts was 800 mm. When the bolt spacing on the left side was less than 700 mm, the change of surrounding rock deformation was no longer obvious. So, the optimal spacing distance between the left side bolts was 700 mm. When the roof bolt spacing was less than 700 mm, the change rate of surrounding rock deformation would gradually decrease as the spacing continues to decrease. When the roof bolt spacing was less than 600 mm, the surrounding rock deformation would basically no longer change. So, considering the cost and effect of support, the roof bolt spacing was selected as 650 mm. Figure 12(b) shows that when the bolt row distances on the roof and two sides were less than 900 mm, the changes of surrounding rock deformations were no longer obvious. So, the bolt row distances were selected as 900 mm. According to the above analysis, the spacing and row distances of the bolts on roof, right side and left side, were 650×900mm, 800×900mm, and 700×900mm, respectively.


### 5.4. Structural Design of Prestressed Yield Bolt

Based on the abovementioned bolt supporting parameters, a yielding structure was installed on the high-strength prestressed bolt to improve its supporting effect. On the one hand, the yielding structure could protect the bolt-rod from breaking. On the other hand, the bolts in the stress concentration area were first deformed, which could relieve the excessive force of the bolt-rod, reduce the stress concentration, and maintain the overall force balance of the surrounding rock.According to the geology and mining conditions of Huafeng Mine, high-strength yield bolts were selected. The yield strength of the bolt-rod was greater than 500 MPa. The yield load and tensile load of the high-strength bolt with the diameter of 25 mm were greater than 170 kN and 240 kN, respectively [30, 31]. According to the tensile test result of the bolt-rod in laboratory, the actual yield load of the bolt was about 220 kN. So, the start-up load of the yielding structure should be designed to be 170-200 kN. According to the characteristics of in situ stress and the surrounding rock, it was determined that the maximum yielding distance was not less than 20 mm. The stability of the yielding structure was measured by the yielding stability coefficient. It should not be greater than 2 kN/mm. The yielding stability coefficient is as follows:
(1)W=Rt−R0D,where W is the yielding stability coefficient, T/mm. Rt is the terminal load of yielding structure, kN. R0 is the start-up load of the yielding structure, kN. D is the maximum yielding distance, mm.Several groups of laboratory tests were carried out on the yielding pipe. The yielding pipe before and after work is shown in Figure13. According to the scattered points of the experiment, the regression curve was obtained. The regression curve equation of the yielding pipe is as follows:
(2)y=−0.0004x4+0.0305x3−0.8661x2+10.164x−23.624,R2=0.9125,where R2 was 0.91245, indicating that the parameters and performance of the yielding pipe were reliable. Therefore, the start-up load of the yielding pipe was 190 kN, the maximum yielding distance of the yielding pipe was 25 mm, the yielding stability coefficient was 1.6kN/mm<2kN/mm. So, the yielding pipe can meet the yielding requirement.Figure 13
The yielding pipe before and after work.


### 5.5. Balanced-Yielding Support Scheme

Based on the above research results, a balanced-yielding support scheme for Shangping tunnel was proposed. The shape of the tunnel section was trapezoidal. The width and heights of the tunnel were 3.8 m, 3.0 m, and 2.5 m, respectively. The high-strength prestressed yield bolt (as shown in Figure14) with diameter of Ф25×2500mm was selected. The spacing and row distances of the bolts on roof, right side and left side, were 650×900mm, 800×900mm, 700×900mm, respectively. The prestress of the bolts was not less than 50 kN. Each bolt matched two resins of Z2850. The start-up load of the yielding pipe was 190 kN, the maximum yielding distance of the yielding pipe was 25 mm, and the yielding stability coefficient was 1.6 kN/mm. The prestress of the high-strength anchor cable with the model of Ф17.8×4500mm was 100-150 kN. Each anchor cable matched two resins of Z2350. The metal mesh of 100~80×100~80×6~8mm and the W steel belt of 2.75×270mm were laid on the tunnel surface. Figure 15 is a schematic diagram of the tunnel support scheme.Figure 14
The high-strength prestressed yield bolt.Figure 15
The schematic diagram of the tunnel support scheme.


## 5.1. Bolt Length

According to Mohr-Coulomb criterion, the safety factor (SF) of rock failure can be calculated [26–29]. The area where the SF of the tunnel surrounding rock was greater than 1.5 was safe. The area with SF less than 1.5 was unstable, so the support control was needed. The distribution of the SF of the unsupported tunnel is shown in Figure 7. In order to further determine the length of bolts at different positions, three paths, Dx1, Dz1, and Ds1, were selected to analyze the stress distribution. The stress distribution path is shown in Figure 8. The maximum principal stress along each path is shown in Figure 9.Figure 7
The distribution of the SF of the unsupported tunnel.Figure 8
The stress distribution path.Figure 9
The maximum principal stress along each path.
(a)
Dx1(b)
Dz1(c)
Ds1It could be seen from Figures8 and 9 that under the influence of tunnel excavation, the maximum height of the tensile stress zone at the top corner of the left side was about 0.8 m. The maximum height of the tensile stress zone of the roof rock layer was about 1.2 m. The maximum height of the tensile stress area at the top corner of the right side was about 0.2 m. So, the maximum height of the tensile stress zone of the roof was 1.2 m. The bolt should be anchored in the rock layer outside the tensile stress zone to effectively control its damage. So, the length of the tensile section of the bolt-rod should be greater than the maximum depth of the tensile stress zone. It was assumed that the length of the bolt outside the tensile stress zone was 0.6 m, and the exposed length of the bolt in the tunnel was 0.1 m. It was calculated that the length of the roof bolt should be 1.9 m. In addition, because the immediate roof of the tunnel was 1.8 m thick siltstone with poor stability, the bolt needed to pass through the siltstone and be anchored into the stable rock stratum. So, the length of the tunnel roof bolt was designed to be 2.5 m.It could be seen from Figure7 that the safety factor at the 1.4 m and 1.8 m depth of the two sides reached 1.3 and 1.5. The bolts at the two sides should be anchored to the area where the SF was less than 1.5, so the length of the bolts should be more than 1.8 m. Due to the large burial depth, “coal burst” frequently occurred during the tunneling process. In addition, the horizontal stress was relatively high. So, the length of the roof bolt and the side bolt was determined to be 2500 mm. Due to the large stress concentration on the left side of the tunnel, the bolt support density of the left side should be increased to balance the stress of the surrounding rock.


## 5.2. Prestress of Bolt

According to the optimal bolt length of 2500 mm determined in Section5.1, the prestress of the bolt was investigated. As the roof rock layer was the most representative, this part only studied the support effect of prestressed bolts on the tunnel roof. Four bolts were arranged on the tunnel roof, and the bolts at the two corners were inclined. The prestressing force was selected as 20 kN and 40 kN, respectively. Figures 10 and 11 show the stress distributions of the tunnel roof with the prestressed bolts of 20 kN and 40 kN, respectively.Figure 10
The stress distribution of the tunnel roof with the prestressed bolts of 20 kN.Figure 11
The stress distribution of the tunnel roof with the prestressed bolts of 40 kN.It could be seen from Figure10 that when the prestress was 20 kN, the tensile stress area of the tunnel roof was relatively large. And the number of separations in the roof rock layer within 1000 mm was relatively large. It showed that the prestressed bolt with the prestress of 20 kN could not meet the requirements of tunnel support. So, it was necessary to increase the prestress of bolt. It could be seen from Figure 11 that when the prestress was 40 kN, the tensile stress area of the tunnel roof was basically eliminated. And the roof separation was basically closed. It showed that the prestressed bolt with the prestress of 40 kN could basically control the roof rock layer actively. In application, in order to ensure the supporting effect, the prestress of the bolt was designed to be 50 kN.


## 5.3. Spacing and Row Distances of Bolt

Based on the abovementioned bolt length of 2500 mm, the spacing and row distances between bolts were investigated by numerical simulation. According to the above numerical model, the deformations of tunnel with bolt spacing of 500 mm, 600 mm, 700 mm, 800 mm, 900 mm, and 1000 mm and bolt row distances of 700 mm, 800 mm, 900 mm, 1000 mm, and 1100 mm were calculated, respectively, without anchor cable. The relationships between the spacing and row distances of bolt and surrounding rock deformation are shown in Figure12.Figure 12
The relationships between the spacing and row distances of bolt and surrounding rock deformation.
(a)
The spacing distances of bolt(b)
The row distances of boltIt could be seen from Figure12(a) that when the bolt spacing on the right side was less than 800 mm, the change of surrounding rock deformation was no longer obvious. So, the optimal spacing distance between the right side bolts was 800 mm. When the bolt spacing on the left side was less than 700 mm, the change of surrounding rock deformation was no longer obvious. So, the optimal spacing distance between the left side bolts was 700 mm. When the roof bolt spacing was less than 700 mm, the change rate of surrounding rock deformation would gradually decrease as the spacing continues to decrease. When the roof bolt spacing was less than 600 mm, the surrounding rock deformation would basically no longer change. So, considering the cost and effect of support, the roof bolt spacing was selected as 650 mm. Figure 12(b) shows that when the bolt row distances on the roof and two sides were less than 900 mm, the changes of surrounding rock deformations were no longer obvious. So, the bolt row distances were selected as 900 mm. According to the above analysis, the spacing and row distances of the bolts on roof, right side and left side, were 650×900mm, 800×900mm, and 700×900mm, respectively.


## 5.4. Structural Design of Prestressed Yield Bolt

Based on the abovementioned bolt supporting parameters, a yielding structure was installed on the high-strength prestressed bolt to improve its supporting effect. On the one hand, the yielding structure could protect the bolt-rod from breaking. On the other hand, the bolts in the stress concentration area were first deformed, which could relieve the excessive force of the bolt-rod, reduce the stress concentration, and maintain the overall force balance of the surrounding rock.According to the geology and mining conditions of Huafeng Mine, high-strength yield bolts were selected. The yield strength of the bolt-rod was greater than 500 MPa. The yield load and tensile load of the high-strength bolt with the diameter of 25 mm were greater than 170 kN and 240 kN, respectively [30, 31]. According to the tensile test result of the bolt-rod in laboratory, the actual yield load of the bolt was about 220 kN. So, the start-up load of the yielding structure should be designed to be 170-200 kN. According to the characteristics of in situ stress and the surrounding rock, it was determined that the maximum yielding distance was not less than 20 mm. The stability of the yielding structure was measured by the yielding stability coefficient. It should not be greater than 2 kN/mm. The yielding stability coefficient is as follows:
(1)W=Rt−R0D,where W is the yielding stability coefficient, T/mm. Rt is the terminal load of yielding structure, kN. R0 is the start-up load of the yielding structure, kN. D is the maximum yielding distance, mm.Several groups of laboratory tests were carried out on the yielding pipe. The yielding pipe before and after work is shown in Figure13. According to the scattered points of the experiment, the regression curve was obtained. The regression curve equation of the yielding pipe is as follows:
(2)y=−0.0004x4+0.0305x3−0.8661x2+10.164x−23.624,R2=0.9125,where R2 was 0.91245, indicating that the parameters and performance of the yielding pipe were reliable. Therefore, the start-up load of the yielding pipe was 190 kN, the maximum yielding distance of the yielding pipe was 25 mm, the yielding stability coefficient was 1.6kN/mm<2kN/mm. So, the yielding pipe can meet the yielding requirement.Figure 13
The yielding pipe before and after work.


## 5.5. Balanced-Yielding Support Scheme

Based on the above research results, a balanced-yielding support scheme for Shangping tunnel was proposed. The shape of the tunnel section was trapezoidal. The width and heights of the tunnel were 3.8 m, 3.0 m, and 2.5 m, respectively. The high-strength prestressed yield bolt (as shown in Figure14) with diameter of Ф25×2500mm was selected. The spacing and row distances of the bolts on roof, right side and left side, were 650×900mm, 800×900mm, 700×900mm, respectively. The prestress of the bolts was not less than 50 kN. Each bolt matched two resins of Z2850. The start-up load of the yielding pipe was 190 kN, the maximum yielding distance of the yielding pipe was 25 mm, and the yielding stability coefficient was 1.6 kN/mm. The prestress of the high-strength anchor cable with the model of Ф17.8×4500mm was 100-150 kN. Each anchor cable matched two resins of Z2350. The metal mesh of 100~80×100~80×6~8mm and the W steel belt of 2.75×270mm were laid on the tunnel surface. Figure 15 is a schematic diagram of the tunnel support scheme.Figure 14
The high-strength prestressed yield bolt.Figure 15
The schematic diagram of the tunnel support scheme.


## 6. Engineering Application and Evaluation

In order to evaluate the control effect of the balanced-yielding support scheme on the surrounding rock of the Shangping tunnel, a 100 m test tunnel was selected. There were 5 observation stations. The third observation station was selected for comparative analysis with the tunnel supported by the original scheme. It mainly included deformation and separation observation.


### 6.1. Deformation Observation

#### 6.1.1. Tunnel Supported by the Original Scheme

The tunnel was a vertical-wall semicircular arch. The deformation of the tunnel surrounding rock supported by the original scheme is shown in Figure16.Figure 16
Deformation of the tunnel surrounding rock supported by the original scheme.
(a)
Deformation(b)
Deformation rateFigure16 shows that the surrounding rock deformed severely within 14 days after excavation. During this period, the deformation rate of the tunnel surface was relatively large, which led to large deformation. The maximum deformation rates of the roof, left side and right side, were 5.5 mm/d, 12.5 mm/d, and 9.5 mm/d, respectively. After 14 days of excavation, the deformation rate was lower than 5 mm/d and gradually decreased with time. The surrounding rock gradually stabilized. The maximum deformation of the roof, left side and right side, was 63 mm, 118 mm, and 82 mm. That is, the total deformation of the two sides of the tunnel was 201 mm. It showed that the deformation of the two sides of the tunnel supported by the original scheme was too large, especially for the asymmetrical deformation of the two sides. The maximum deformation of the left side was 1.44 times that of the right side. This was consistent with the results of the previous numerical simulations. So, the system did not fully exert its support effect. It was necessary to adjust the shape of the tunnel and optimize the support scheme.


#### 6.1.2. Tunnel Supported by the Balanced-Yielding Support Scheme

The tunnel was trapezoidal. The deformation of the tunnel surrounding rock supported by the balanced-yielding support scheme is shown in Figure17.Figure 17
Deformation of the tunnel surrounding rock supported by the balanced-yielding support scheme.
(a)
Deformation(b)
Deformation rateIt could be seen from Figure17 that during the excavation period, the deformation of the tunnel surrounding rock was also mainly divided into two stages. Within 15 days after excavation, the surrounding rock deformation was relatively serious. The maximum deformation rates of the roof, left side and right side, were 3 mm/d, 2.5 mm/d, and 2.5 mm/d, respectively. This was far less than the maximum deformation rate of the tunnel supported by the original scheme. After 15 days of excavation, the deformation rate was lower than 2 mm/d. The surrounding rock gradually stabilized. The maximum deformation of the roof, left side and right side, was 26 mm, 30 mm, and 28 mm. Not only the maximum deformation of the surrounding rock was much lower than that of the tunnel supported by the original scheme, but also the deformations of the roof, left and right sides, were basically the same. This showed that the balanced-yielding support system had successfully realized the deformation balance of the asymmetric surrounding rock of the tunnel in the inclined rock formation, thereby controlling its overall stability.


### 6.2. Separation Observation

The roof separations of tunnels supported by the original scheme (vertical-wall semicircular arch tunnel) and the balanced-yielding support scheme (trapezoidal tunnel) are shown in Figure18.Figure 18
The roof separations of tunnels supported by the original scheme and the balanced-yielding support scheme.Figure18 shows that the number of shallow separations stabilized at about 16 days. The development period of deep separation was relatively long and tended to be stable until about 20 days. The maximum amounts of the shallow and deep separations of tunnels supported by the original scheme were 47 mm and 12 mm. Its total roof separation was 59 mm. The shallow separation accounted for 79.7% of the total roof separation. This indicated that the separation was mainly concentrated in the shallow bolt support range, which further showed that the support system could not effectively control the early separation of the roof strata.The maximum amounts of the shallow and deep separations of tunnels supported by the balanced-yielding support scheme were 19 mm and 8 mm. Its total roof separation was 27 mm. Compared with the tunnel supported by the original scheme, the amount of shallow separation was reduced by 147%. It showed that the balanced-yielding support scheme had a better effect in controlling the roof separation of the trapezoidal tunnel than the original scheme in controlling the vertical-wall semicircular arch tunnel. The performance of the support system had been better utilized. This was consistent with the monitoring results of surrounding rock deformation.


## 6.1. Deformation Observation

### 6.1.1. Tunnel Supported by the Original Scheme

The tunnel was a vertical-wall semicircular arch. The deformation of the tunnel surrounding rock supported by the original scheme is shown in Figure16.Figure 16
Deformation of the tunnel surrounding rock supported by the original scheme.
(a)
Deformation(b)
Deformation rateFigure16 shows that the surrounding rock deformed severely within 14 days after excavation. During this period, the deformation rate of the tunnel surface was relatively large, which led to large deformation. The maximum deformation rates of the roof, left side and right side, were 5.5 mm/d, 12.5 mm/d, and 9.5 mm/d, respectively. After 14 days of excavation, the deformation rate was lower than 5 mm/d and gradually decreased with time. The surrounding rock gradually stabilized. The maximum deformation of the roof, left side and right side, was 63 mm, 118 mm, and 82 mm. That is, the total deformation of the two sides of the tunnel was 201 mm. It showed that the deformation of the two sides of the tunnel supported by the original scheme was too large, especially for the asymmetrical deformation of the two sides. The maximum deformation of the left side was 1.44 times that of the right side. This was consistent with the results of the previous numerical simulations. So, the system did not fully exert its support effect. It was necessary to adjust the shape of the tunnel and optimize the support scheme.


### 6.1.2. Tunnel Supported by the Balanced-Yielding Support Scheme

The tunnel was trapezoidal. The deformation of the tunnel surrounding rock supported by the balanced-yielding support scheme is shown in Figure17.Figure 17
Deformation of the tunnel surrounding rock supported by the balanced-yielding support scheme.
(a)
Deformation(b)
Deformation rateIt could be seen from Figure17 that during the excavation period, the deformation of the tunnel surrounding rock was also mainly divided into two stages. Within 15 days after excavation, the surrounding rock deformation was relatively serious. The maximum deformation rates of the roof, left side and right side, were 3 mm/d, 2.5 mm/d, and 2.5 mm/d, respectively. This was far less than the maximum deformation rate of the tunnel supported by the original scheme. After 15 days of excavation, the deformation rate was lower than 2 mm/d. The surrounding rock gradually stabilized. The maximum deformation of the roof, left side and right side, was 26 mm, 30 mm, and 28 mm. Not only the maximum deformation of the surrounding rock was much lower than that of the tunnel supported by the original scheme, but also the deformations of the roof, left and right sides, were basically the same. This showed that the balanced-yielding support system had successfully realized the deformation balance of the asymmetric surrounding rock of the tunnel in the inclined rock formation, thereby controlling its overall stability.


## 6.1.1. Tunnel Supported by the Original Scheme

The tunnel was a vertical-wall semicircular arch. The deformation of the tunnel surrounding rock supported by the original scheme is shown in Figure16.Figure 16
Deformation of the tunnel surrounding rock supported by the original scheme.
(a)
Deformation(b)
Deformation rateFigure16 shows that the surrounding rock deformed severely within 14 days after excavation. During this period, the deformation rate of the tunnel surface was relatively large, which led to large deformation. The maximum deformation rates of the roof, left side and right side, were 5.5 mm/d, 12.5 mm/d, and 9.5 mm/d, respectively. After 14 days of excavation, the deformation rate was lower than 5 mm/d and gradually decreased with time. The surrounding rock gradually stabilized. The maximum deformation of the roof, left side and right side, was 63 mm, 118 mm, and 82 mm. That is, the total deformation of the two sides of the tunnel was 201 mm. It showed that the deformation of the two sides of the tunnel supported by the original scheme was too large, especially for the asymmetrical deformation of the two sides. The maximum deformation of the left side was 1.44 times that of the right side. This was consistent with the results of the previous numerical simulations. So, the system did not fully exert its support effect. It was necessary to adjust the shape of the tunnel and optimize the support scheme.


## 6.1.2. Tunnel Supported by the Balanced-Yielding Support Scheme

The tunnel was trapezoidal. The deformation of the tunnel surrounding rock supported by the balanced-yielding support scheme is shown in Figure17.Figure 17
Deformation of the tunnel surrounding rock supported by the balanced-yielding support scheme.
(a)
Deformation(b)
Deformation rateIt could be seen from Figure17 that during the excavation period, the deformation of the tunnel surrounding rock was also mainly divided into two stages. Within 15 days after excavation, the surrounding rock deformation was relatively serious. The maximum deformation rates of the roof, left side and right side, were 3 mm/d, 2.5 mm/d, and 2.5 mm/d, respectively. This was far less than the maximum deformation rate of the tunnel supported by the original scheme. After 15 days of excavation, the deformation rate was lower than 2 mm/d. The surrounding rock gradually stabilized. The maximum deformation of the roof, left side and right side, was 26 mm, 30 mm, and 28 mm. Not only the maximum deformation of the surrounding rock was much lower than that of the tunnel supported by the original scheme, but also the deformations of the roof, left and right sides, were basically the same. This showed that the balanced-yielding support system had successfully realized the deformation balance of the asymmetric surrounding rock of the tunnel in the inclined rock formation, thereby controlling its overall stability.


## 6.2. Separation Observation

The roof separations of tunnels supported by the original scheme (vertical-wall semicircular arch tunnel) and the balanced-yielding support scheme (trapezoidal tunnel) are shown in Figure18.Figure 18
The roof separations of tunnels supported by the original scheme and the balanced-yielding support scheme.Figure18 shows that the number of shallow separations stabilized at about 16 days. The development period of deep separation was relatively long and tended to be stable until about 20 days. The maximum amounts of the shallow and deep separations of tunnels supported by the original scheme were 47 mm and 12 mm. Its total roof separation was 59 mm. The shallow separation accounted for 79.7% of the total roof separation. This indicated that the separation was mainly concentrated in the shallow bolt support range, which further showed that the support system could not effectively control the early separation of the roof strata.The maximum amounts of the shallow and deep separations of tunnels supported by the balanced-yielding support scheme were 19 mm and 8 mm. Its total roof separation was 27 mm. Compared with the tunnel supported by the original scheme, the amount of shallow separation was reduced by 147%. It showed that the balanced-yielding support scheme had a better effect in controlling the roof separation of the trapezoidal tunnel than the original scheme in controlling the vertical-wall semicircular arch tunnel. The performance of the support system had been better utilized. This was consistent with the monitoring results of surrounding rock deformation.


## 7. Conclusion

(1)
An innovative balanced-yielding support technology was proposed with the engineering background. Its implementing steps mainly included in situ stress analysis, the stress distribution of the tunnel surrounding rock with different sections, the design of the support parameter for bolt-cable and yielding structure, and supporting effect evaluation(2)
The maximum horizontal principal stresses of the three monitoring points in Huafeng Mine were greater than 30 MPa. Under the influence of the component force of the rock layer’s own weight stress in the inclined direction, the stress concentration occurred at the top corner of lower side and the bottom corner of the upper side of the tunnel. To reduce the stress concentration, the overall shape of the tunnel could be trapezoidal(3)
In the balanced-yielding support scheme, the high-strength prestressed yield bolt with diameter ofФ25×2500mm was selected. The spacing and row distances of the bolts on roof, right side and left side, were 650×900mm, 800×900mm, and 700×900mm, respectively. The start-up load of the yielding pipe was 190 kN, the maximum yielding distance of the yielding pipe was 25 mm, and the yielding stability coefficient was 1.6 kN/mm(4)
In engineering application, not only the maximum deformation of the tunnel supported by the balanced-yielding support scheme was much lower than that of the tunnel supported by the original scheme, but also the deformations of the roof, left and right sides, were basically the same. Compared with the original support system, the shallow separation of the trapezoidal tunnel supported by the balanced-yielding support system had been reduced by 147%



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*Source: 1874331-2022-08-17.xml*