Study on Optimization of Row Spacing Between Steel Arches in Deep Buried Fault Cave Sections

Abstract

As a widely used support form in tunnel support, the support effect of steel arch is influenced by the row distance between steel arches. In F8 fault fracture zone of the North Main Canal of Letan Reservoir in Guangxi, the support system of “steel arch + shotcrete” in this faulted cavern section was equalized with elastic modulus and yield stress by using theoretical analysis and numerical simulation, and the characteristic curves of rock support of deeply buried circular cavern under modified axisymmetric loading were obtained. The sensitivity analysis and optimization study of the spacing between steel arches were conducted by using FLAC^3D. The results show that with the increase of steel arch spacing, the cavity wall displacement increases, the support reaction force decreases nonlinearly, and the radial displacement and plastic zone around the cavity continue to increase. When the distance between steel arches >600 mm, the deformation of cavern perimeter changes abruptly and the plastic zone increases significantly. Based on comprehensive analysis, the optimization suggestions of steel arch are proposed.

1 Introduction

The construction of the supporting structure can effectively restrain the deformation of the surrounding rock and improve the overall bearing capacity of the surrounding rock. For the weak surrounding rock section, a reasonable combined support system such as grid mesh or steel arch frame is often selected according to the degree of rock fragmentation. In actual projects, to ensure the safety of the project, a tighter steel arch spacing is often used, but the reduction of the steel arch spacing will increase the engineering cost. How to use economical and reasonable steel arch spacing, which can not only limit the deformation of the surrounding rock, but also be economical and reasonable, is a technical issue that the project is concerned about.

Many experts and scholars have studied the influence of steel arches on surrounding rock support. Gao et al. [1] conducted numerical simulations on the mechanical properties of three-composite steel arches and sprayed concrete initial support systems, and gave recommended value of steel arch spacing under class IV surrounding rock. Mei Hua et al. [2] used the theory of common deformation to calculate the composite support of profiled steel arches, suspended steel mesh, and shotcrete. The deformation and stress of the three complied with the theory of common deformation. The effect of steel arch spacing on the surrounding rock of class V was analyzed, and corresponding suggestions were put forward for the actual situation of Caigu tunnel project. Li Xuefeng et al. [3] used the method of equivalent elastic modulus to calculate the supporting system formed by the steel arch and the primary shotcrete. By comparing the calculation results of different steel arch spacing, in view of reducing cave deformation, it is not so effective to reduce the steel arch spacing than by changing the thickness of the initial lining support. Liao Wei et al. [4] used numerical simulation to calculate the tensile damage of the surrounding rock, and then selected the safe arch spacing for class V surrounding rock according to the tensile damage area, and verified it by actual monitoring data. Zuo Qiankun et al. [5] used beam elements to simulate steel arches and proposed the optimal steel arch spacing of class IV surrounding rock when there is no inverted arch. Li et al. [6] used beam elements to simulate steel arches and proposed a support arch yielding criterion based on the arch section compression-bending bearing capacity equation, and embedded the modified beam elements through FISH language programming. The modified numerical simulation method is more reliable for large deformation tunnels using combined arch-bolt support, especially in supporting the bearing and damage behaviour of the arch and anchor rods. Song et al. [7] used a beam element to simulate steel arches, and the arrangement of the steel arches had a significant effect on controlling the sinking of the surrounding rock. As the spacing of the steel arches increased, the vertical displacement of the dome and floor slab increased, and the areas where larger displacements occurred tended to expand in the direction of the arches. Wang et al. [8] proposed a steel-concrete composite support system for loess tunnels, which consisted of a steel arch layer, a reinforced skeleton layer and a concrete filling layer, and found that the steel-concrete composite support system was superior to the traditional support system in terms of structural safety and load-bearing capacity. Liu et al. [9] conducted numerical analysis and field monitoring tests for shallow buried tunnels under soft surrounding rocks, proposing that under shallow buried tunnel conditions, the tunnel vault is the most unfavourable location and pre-supporting measures such as pre-emptive small tube grouting should be taken to ensure the safety of tunnel construction.

In this paper, the theoretical analysis method is applied to equate the elastic modulus and yield stress of the “steel arch + shotcrete” support system of the Letan Reservoir TBM diversion tunnel, establishing an equivalent calculation model of the joint support considering the steel arch. The influence of the steel arch on the surrounding rock displacement and surrounding rock reaction force of the deeply buried circular cavern is quantitatively evaluated under axisymmetric loading by using modified Fenner formula and elastic thin shell theory.

The finite difference software “FLAC^3D” is used to establish a three-dimensional model to simulate the stress-strain characteristics of the surrounding rock and the force characteristics of the support structure, and to carry out parametric sensitivity analysis on different steel arch spacing under three-dimensional conditions. The comparison verifies the results of the theoretical analysis and provides reference for engineering support design and construction.

2 Project Overview

The first phase of the Guangxi Guizhong Drought Control Letan Reservoir Diversion and Irrigation District Project consists of two parts: the main trunk canal and the northern trunk canal. The former section of the North Main Canal starts from the village of Nengrong and goes eastwards for about 1.5 km to the village of Yaowa. From the village of Yaowa, it passes through Chencun and Beisi to Liulang, with a total length of about 25.47 km, mainly in the form of tunnels.

The TBM in the Yaowa-Lulang Tunnel (5.94 m diameter) in the North Main Canal encountered the F8 fault zone near 17 + 833.2 m (Fig. 1). The F8 fault has the following attitude: N11°E, SE∠85°, tilting downstream and intersecting the axis of the tunnel at a large angle, with the fault zone partially twisted. The parent rock is mainly muddy siltstone with a small amount of muddy tuff. The nature of the filling is not homogeneous, and the upper part of the filling has collapsed many times under self-weight and mechanical vibration, forming pits of different sizes, so it is necessary to take reasonable support measures to ensure construction safety and overall stability of the surrounding rock.

Fig. 1.

F8 fault geological map.

3 Basic Theory

3.1 Equivalent Model of the Support System

Due to the intermittent arrangement of the steel arches in the actual project, it is difficult to obtain the analytical solution for each steel arch. To simplify the calculation, for the support system of “steel arch + shotcrete” shown in Fig. 2(a), the modulus of elasticity and yield strength of the steel arch are converted into concrete according to the principle of equal modulus of elasticity and yield stress. And the concrete parameters are modified to replace the steel arch for the equivalent of the support system.

Fig. 2.

Schematic diagram of equivalent model of “steel arch + shotcrete”.

As shown in Fig. 2(b), the steel arch is intercepted in section 1-1, the modulus of elasticity of the H-shaped steel arch is E_g, the yield stress is σ_g, the height and width of the steel arch are B. The flange width is t₁, the web thickness is t₂, the area is A₁, the modulus of elasticity of plain concrete is E_c, the yield stress is σ_c, the area is A₂, the total area of section 1-1 is A, and the lining thickness is H. The equivalent modulus of elasticity E_h and the equivalent yield stress σ_sh of the 1-1 profile are:

$$E_{h} = E_{g} \cdot \frac{{A_{1} }}{A} + E_{{\text{c}}} \cdot \frac{{A_{2} }}{A}$$

(1)

$$\sigma_{sh} = \sigma_{g} \cdot \frac{{A_{1} }}{A} + \sigma_{{\text{c}}} \cdot \frac{{A_{2} }}{A}$$

(2)

As shown in Fig. 2(c), the equivalent elastic modulus E₁and equivalent yield stress σ_s1 of the surrounding rock support system for profile 2-2 with steel arch spacing T are:

$$E_{1} = E_{h} \cdot \frac{B}{B + T} + E_{c} \cdot \frac{T}{B + T}$$

(3)

$$\sigma_{s1} = \sigma_{sh} \cdot \frac{B}{B + T} + \sigma_{c} \cdot \frac{T}{B + T}$$

(4)

3.2 Enclosure Support Characteristic Curves

Previous studies have shown [10] that when a tunnel is in a deep burial situation (burial depth Z ≥ 20R, R being the excavated hole diameter), a deeply buried tunnel can be simplified to an axisymmetric plane strain problem [11].

3.2.1 Surrounding Rock Characteristic Curves

(1) Elastic state of the surrounding rock. The excavation of a circular cavern chamber of diameter R in the case of deep burial can be equated to a thick-walled cylinder, where the external pressure is p₀ (mountain rock pressure) and the internal pressure is p₁(support reaction force).

According to the axial symmetry problem in elastic mechanics and the constitutive equation of plane strain, when there is a support reaction force p₁ acting on the surrounding rock, the elastic radial displacement around the cavern chamber is:

$$u_{o} = \frac{{1{ + }\mu }}{E}\frac{{R^{2} }}{r}(p_{0} - p_{1} )$$

(5)

• E -- modulus of deformation of the surrounding rock.

• μ -- poisson's ratio of the surrounding rock.

The inverse relationship between the radial displacement and the support reaction force is obtained from Eq. (5), and the characteristic curve of the surrounding rock in the fully elastic state is:

$$p_{1} = p_{0} - \frac{{u_{o} E}}{(1 + \mu )R}$$

(6)

(2) Plasticity state of the surrounding rock

When the surrounding rock enters the plastic zone, assuming that the surrounding rock is an ideal elastic-plastic body, the radius of the plastic zone is R_p, the support reaction force provided by the lining is p₁, and the mountain rock pressure is p₀, it is known from the modified Fenner equation [11] that:

The radius of the plastic zone of the enclosing rock is:

$$R_{p} = R\left[ {\frac{{\left( {p_{0} + c\cot \varphi } \right)\left( {1 - \sin \varphi } \right)}}{{\left( {p_{1} + c\cot \varphi } \right)}}} \right]^{{\frac{1 - \sin \varphi }{{2\sin \varphi }}}}$$

(7)

• c -- the cohesive force of the surrounding rock.

• φ-- the angle of internal friction of the surrounding rock.

The support reaction forces are:

$$p_{1} = \left( {p_{0} + c\cot \varphi } \right)\left( {1 - \sin \varphi } \right)\left( {\frac{R}{{R_{p} }}} \right)^{{\frac{2\sin \varphi }{{1 - \sin \varphi }}}} - c\cot \varphi$$

(8)

Radial displacement in the plastic zone:

$$u_{o} = \frac{\sin \varphi }{{2G}}(p_{0} + c\cot \varphi )R[\frac{{(p_{0} + c\cot \varphi )(1 - \sin \varphi )}}{{p_{1} { + }c\cot \varphi }}]^{{\frac{1 - \sin \varphi }{{\sin \varphi }}}}$$

(9)

• G -- the shear deformation modulus of the surrounding rock.

The inverse relationship between the radial displacement and the support reaction force is obtained from Eq. (9), and the characteristic curve of the surrounding rock in the plastic state is:

$$p_{1} = (p_{0} + c\cot \varphi )(1 - \sin \varphi )[\frac{{\sin \varphi (p_{0} + c\cot \varphi )R}}{{2Gu_{o} }}]^{{\frac{\sin \varphi }{{1 - \sin \varphi }}}} - c\cot \varphi$$

(10)

3.2.2 Support Characteristic Curves

• (1) Initial displacement of the surrounding rock

  In the relationship of the surrounding rock-support structure, u_oc is defined as the radial displacement of the cavern wall before the support is set, which is the main unknown quantity and can be calculated by actual field measurements or by the empirical formula proposed by Hoek [12].

  $$\frac{{u_{oc} }}{{u_{m} }} = [1 + \exp (\frac{ - x/R}{{1.10}})]^{ - 1.7}$$

  (11)

  • x -- the distance of the applied support from the palm face.

  • u_m -- the maximum value of the radial displacement of the cave wall.

• (2) Maximum support force

  The maximum support force can be calculated according to the theory of a circular tube under external pressure, and since lining thickness H > 0.04R, the maximum support resistance p_max that can be provided by the “steel arch + shotcrete” support system is [13]:

  $$p_{\max } = \frac{1}{2}\sigma_{s1} [1 - \frac{{R^{2} }}{{\left( {R + H} \right)^{2} }}]$$

  (12)

• (3) Radial displacement

  Before the support structure reaches the maximum support force, it can be regarded as a thick-walled cylinder subjected to uniform external pressure p₀. According to the thick-walled cylinder formula, the radial displacement of the support structure is:

  $$u_{o} = \frac{{p_{0} R^{3} (1 + \mu_{1} )}}{{E_{1} [R^{2} - (R{ - }H)^{2} ]}}[1 - 2\mu_{1} + \frac{{(R{ - }H)^{2} }}{{R^{2} }}]$$

  (13)

  • μ₁ -- poisson's ratio of the support structure.

  From Eqs. (12) and (13), the minimum displacement of the support structure u_omin can obtained when support structure reach the maximum support force, at this time the cave displacement is u_om, u_om = u_oc + u_omin.

  Then the support curve considering the support timing consists of two sections:

  When u_oc < u < u_om:

  $$p_{1} = \frac{{(u - u_{oc} )E_{1} [R^{2} - \left( {R{ - }H} \right)^{2} ]}}{{[1 - 2\mu_{1} + \frac{{\left( {R{ - }H} \right)^{2} }}{{R^{2} }}]R^{3} (1 + \mu_{1} )}}$$

  (14)

  When u>u_om:

  $$p_{1} = p_{\max } = \frac{1}{2}\sigma_{s1} [1 - \frac{{R^{2} }}{{\left( {R + H} \right)^{2} }}]$$

  (15)

3.3 Study on the Influence of F8 Fault Support Parameters on the Stability of the Surrounding Rock

3.3.1 F8 Fault Calculation Parameters

F8 fault fracture zone is encountered during tunnel boring of Letan TBM construction. The tunnel was excavated at a depth of 215 m, with a radius of R = 2.97 m. The tunnel was supported by a full section of HW150 × 150 steel, with a wet sprayed C25 concrete thickness of H = 200 mm and a steel arch spacing of T = 300 mm.

The surrounding rock parameters of the F8 fault zone tunnel are shown in Table 1 and the support parameters in Table 2.

Table 1. Surrounding rock parameters of tunnel in F8 section.

Table 2. Supporting parameters of “section steel + concrete”.

3.3.2 Analysis of Support Reaction Forces and Deformation Characteristics of the Surrounding Rock

Take the burial depth of F8 section h = 215 m, the pressure of surrounding rock is calculated by self-weight stress:

$$p_{0} = \rho gh = 4.85\;{\text{MPa}}$$

In calculating the shotcrete characteristic curve, a 3-day strength can generally be used [13]:

$$E_{c3} = 0.67E_{c} = 18.76\;{\text{GPa}}$$

$$\sigma_{c3} = 0.5\sigma_{c} = 14\;{\text{MPa}}$$

The equivalent modulus of elasticity and equivalent yield stress of the steel section + concrete can be calculated as:

$$E_{1} = \left( {E_{g} \cdot \frac{{A_{1} }}{A} + E_{c3} \cdot \frac{{A_{2} }}{A}} \right) \cdot \frac{B}{B + T} + E_{c3} \cdot \frac{T}{B + T} = 25.87\;{\text{GPa}}$$

$$\sigma_{s1} = \left( {\sigma_{g} \cdot \frac{{A_{1} }}{A} + \sigma_{c3} \frac{{A_{2} }}{A}} \right) \cdot \frac{B}{B + T} + \sigma_{c3} \cdot \frac{T}{B + T} = 21.73\;{\text{MPa}}$$

As the F8 cave section is a fault zone, the pre-emptive strengthening measure of grouting is adopted, taking x = −2.94 m, the displacement before support is:

$$u_{oc} = u_{m} [1 + \exp (\frac{ - x/R}{{1.10}})]^{ - 1.7} = 43.19\;{\text{mm}}$$

Maximum support force is:

$$p_{\max } = \frac{1}{2}\sigma_{s1} [1 - \frac{{R^{2} }}{{\left( {R + H} \right)^{2} }}] = 1.33\;{\text{MPa}}$$

From the Eq. (12), (13) joint solution can obtain u_omin, and u_oc = 43.19 mm, so the cave wall displacement u_om when the support structure reaches the maximum support force is 45.26 mm.

According to the parameters of the surrounding rock and the above calculation results, the characteristic curve of the support structure and the characteristic curve of the surrounding rock are shown in Fig. 3.

Fig. 3.

Supporting structure and surrounding rock characteristic curve with T = 300 mm, E = 0.3 GPa.

From Fig. 3: u₀ = 51.75 mm, p₁ = 1.33 MPa.

The radius of the plastic zone is:

$$R_{p} = R\left[ {\frac{{\left( {p_{0} + c\cot \varphi } \right)\left( {1 - \sin \varphi } \right)}}{{\left( {p_{1} + c\cot \varphi } \right)}}} \right]^{{\frac{1 - \sin \varphi }{{2\sin \varphi }}}} = 3.43\;{\text{m}}$$

It can be seen that when the deformation of the support structure and the deformation of the surrounding rock are equal, the displacement of the cave wall is 51.75 mm, at which time the surrounding rock and the support structure reach a state of coordinated deformation.

3.4 Sensitivity Analysis of Row Spacing Between Steel Arches

When the spacing between steel arches is between 300 and 1200 mm, the cave wall displacement and support reaction force changes as shown in Fig. 4:

Fig. 4.

Sensitivity analysis of steel arch frame spacing.

Figure 4 shows the variation curves of steel arch spacing and cavern wall displacement u_o and support reaction force p₁ at E = 0.3 GPa. It can be seen that:

• (1) With the increase of steel arch spacing, the cave wall displacement increases non-linearly, when T < 600 mm, the cave wall displacement grows faster, when T > 600 mm, the cave wall displacement grows gradually, and tends to level off.

• (2) With the increase of steel arch spacing, the support reaction force decreases non-linearly, when T < 600 mm, the support reaction force decreases rapidly, and when T > 600 mm, the support reaction force decreases slowly and finally converges.

4 Numerical Simulation Studies

4.1 Computational Models and Research Scheme

4.1.1 3D Calculation Range for the F8 Fault

The geological map of the F8 fault is shown in the Fig. 1. As seen in Table 3, for 17+757 m of fault F8, the horizontal direction of the section is taken as the X-axis direction, the interception length is 36 m. The tunnel axis is the Y-axis direction, the interception length is 20 m. The vertical direction Z is taken from 92 m elevation to 128 m elevation.

Table 3. F8 fault section 3D model calculation range table.

Self-weight stress is taken as the initial geo-stress. The self-weight of the mountain above an elevation of 128 m is applied to the top surface of the calculation model in the form of a top surface force.

4.1.2 Reinforcement Parameters for Hole Section F8

In order to facilitate the sensitivity analysis of the row spacing between steel arches, it is advisable to ignore the sprayed layer of concrete and design a support scheme that only considers the effect of steel arch support: top arch with drainage holes (top arch centre angle 120° range) Φ50@3 × 3 m, L = 3 m arranged in intervals, top arch 120° backfill grouting, full section HW150 × 150 section @300.

4.1.3 Calculated Working Conditions and Parameters

Table 4 shows the four working conditions in the sensitivity analysis of the steel arch spacing. Varying the spacing of the steel arches (300 mm, 600 mm, 900 mm and 1200 mm) to analyse the support effect of the steel arches provides a direct response to the effect of the spacing between the steel arches on the support effect.

Table 4. Sensitivity analysis condition of row spacing between steel arches.

4.1.4 F8 Holesection Gridding

Figure 5 shows the grid diagram of the computational model.

The rock interface, steel arch and grouting area were simulated in detail in the 3D model.

• 1. Tunnel surrounding rock: the boundary range of the model section is about 6 times the diameter of the tunnel. 36 × 36 × 20 m was chosen for the tunnel surrounding rock, with a reserved excavation diameter of 5.94 m. The model was set up using Extrusion in FLAC^3D 6.0.

• 2. Steel arch: the steel arch model was drawn by 'Rhino3D', then imported into '.dxf' using FLAC^3D6.0 import command, 'beam ' structural unit is used to simulate the steel arch.

• 3. Grouting zone: the solid unit was used to simulate a grouting zone of 2.94 m in depth within 120° above the top arch.

Fig. 5.

Computational model grid.

The rock mass parameters are provided by test result of the design institute, and the support structure parameters are selected from Hydraulic Tunnel Design Code SL279-2016, shown as Table 5.

Table 5. Model parameters.

4.2 Geo-Stress Regression Calculation Results and Discussion

Self-weight load was applied to calculate the three-dimensional geo-stress field in the tunnel surrounding rock. Due to the depth of the tunnel, the top of the calculation area is not taken to the free surface of the ground. The gravity load is applied with an equivalent surface force load of the overlying rock pressure at the top boundary of the model. The geo-stress relief factor around the hole is taken to be 0.5. The initial geo-stress at the centre of the tunnel in the F8 fault was obtained as follows: σ_xx = 3.3417 MPa, σ_yy = 3.3411 MPa, σ_zz = 4.8091 MPa, τ_xy = 1.81 × 10⁻⁴ MPa, τ_yz = −0.2692 MPa, τ_zx = 1.52 × 10⁻⁵ MPa, the principal stresses are known to be:σ₁ = 4.8096 MPa, σ₂ = 3.3413 MPa, σ₃ = 3.3410 MPa.

According to the results of the geo-stress regression calculation, it can be concluded that.

• (1) For the F8 fault, the calculated burial depth at the left boundary is 226 m and at the right boundary is 209 m. Therefore, under the action of self-weight, the initial geo-stress is larger and there is a weak bias pressure phenomenon.

• (2) Under self-weight action, the regional stress field is to some extent influenced by the structure, and the vertical stress is slightly larger than the horizontal stress, and the value of the shear stress component τ_yz is small.

• (3) The major and minor principal stresses are roughly distributed along the vertical and horizontal directions respectively, and the stress magnitude is directly related to the depth of burial.

4.3 Sensitivity Analysis of Row Spacing Between Steel Arches

4.3.1 Sensitivity Analysis of the Inter-Row Spacing Between Steel Arches on the Deformation of the Surrounding Rock

The deformation of the surrounding rock after excavation shows significant symmetry. Due to the limited space, Fig. 6 gives the cloud diagram of the vertical displacement along the Z direction in the Y-Z section under GK0.6 and GK1.2 working conditions. Fig. 7 shows the cavern perimeter displacements for each working condition, Fig. 8 shows the maximum displacements for each working condition, and Table 6 lists the maximum displacements for each working condition.

Fig. 6.

Uz/m contour map of the displacement around the hole along the Z direction.

Fig. 7.

Displacement contour map of the center section around the hole with different steel arch spacing/mm.

Fig. 8.

Trend chart of maximum displacement and total plastic zone volume change under various working conditions.

Table 6. Maximum displacement and plastic zone volume under various working conditions.

It can be seen that the excavation deformation has the following characteristics:

• (1) Under all working conditions, the cavern shows an overall inward deformation trend, and the horizontal and vertical displacements are basically symmetrical. When the row distance between steel arches is 300 mm, the top arch sinks by 15.00 mm, when the spacing between steel arches is 600 mm, the top arch sinks by 37.41 mm, and when the spacing is 900 mm and 1200 mm, the top arch sinks by 185.11 mm and 320.00 mm respectively, resulting in danger of cave collapse.

• (2) With the increase of the spacing between steel arches, the displacement of the cavern perimeter gradually increases. When the spacing is greater than 600 mm, the maximum displacement of the steel arches increases significantly.

4.3.2 Sensitivity Analysis of Inter-Row Spacing Between Steel Arches on Surrounding Rock Stresses

Due to space limitations, the main stress cloud diagramin the Y-Z profile of GK0.6 is given in Fig. 9.

Fig. 9.

GK0.6 (steel arch spacing 600 mm) stress diagram.

Fig. 10.

Maximum principal stress σ₁ diagram of characteristic nodes of surrounding rock under various working conditions/MPa.

Figure 10 plots the relationship between the variation of the Maximum principal stresses at each characteristic node under different working conditions. It can be seen that the distribution of the principal stresses in the F8 cavern section has the following characteristics.

• (1) The stress distribution pattern is consistent under different working conditions, with the left and right waists slightly larger than the top and bottom of the arch.

• (2) As the spacing of steel arch increases, the surrounding rock enters the plastic state from the elastic state, and the stress around the hole gradually increases. When the surrounding rock enters the failure state, the stress around the hole rapidly decreases. Study shows that when the spacing of steel arch is 900 mm and 1200 mm, the rock around the hole failed, and the stress around the hole is close to the level of complete unloading.

4.3.3 Sensitivity Analysis of Inter-Row Spacing Between Steel Arches on the Distribution of Damage Zones of The Surrounding Rock

Table 6 lists the plastic zone volumes for each working condition and Fig. 8 demonstrates the trend in plastic zone volume for each working condition. It can be seen:

With the increase of steel arch spacing, the plastic zone around the cavern increases non-linearly. When the spacing between steel arches is small, the volume of plastic zone grows slowly. But when the spacing is large, the volume of plastic zone increases rapidly, till the surrounding rock enters the failure state, indicating that the steel arches can no longer sustain the stability of the rock around the cave. For example, when the spacing is 600 mm, the volume of the plastic zone is 66.95 m³, but when the spacing is 1200 mm, the volume of the plastic zone reaches 1404.21 m³, at which point the cavern is already in danger of collapse.

5 Conclusion

Sensitivity analysis of the stability of the surrounding rock with different steel arch spacing in the F8 fault zone was carried out by means of theoretical analysis and numerical simulation, and the main results are as follows.

• (1) With the increase of steel arch spacing, the cave wall displacement increases and the support reaction force decreases non-linearly.

• (2) Under all working conditions, the cavern shows an overall inward deformation trend, the horizontal and vertical displacements are basically symmetrical, and the uplift of the bottom of the arch is slightly larger than the sinking of the top of the arch. With the increase of the spacing between steel arches, the deformation around the cavern gradually increases, and the non-linearity of the plastic zone around the cavern increases.

• (3) The stress distribution pattern of the surrounding rock under different working conditions is consistent, with the left and right waists slightly larger than the top and bottom of the arch. With the increase of steel arch spacing, the surrounding rock enters the plastic state from the elastic state, and the stress around the cavern gradually increases. When the spacing of steel arch is 900 mm and 1200 mm, the rock around the cave entered into failure state and the stress around the cave is close to the level of complete unloading.

• (4) From the analysis results of the support characteristic curve of the surrounding rock and the sensitivity analysis of the steel arch spacing, it can be obtained that for the F8 fault, the steel arch spacing should be less than 600 mm, and the spacing of 300 mm used in the actual construction is safe and feasible.