# Study on the Safety Thickness of Rock Strata for Outburst Prevention in Deep Tunnel Based on Numerical Modeling and Backpropagation Neural Network

Authors: Zhensheng Cao; Jiazhu Liu; Shaoqiang Zhang; Bowen Li; Zhenhu Zhang; Zhongjie Wang; ChenChen Jiang
Journal: Geofluids
 (2023)

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## Abstract

Water inrush and mud inrush pose a serious threat to safe construction in underground engineering, but it is very difficult to determine the safe distance of outburst prevention rock mass. Based on deep-buried tunnel engineering, this paper proposes a method to determine the safe distance from water inrush disaster between the tunnel and the fault fracture zone. This method combines numerical modeling and backpropagation (BP) neural network. By means of numerical simulation, the internal influence law of the water pressure, lateral pressure coefficient, fault fracture zone width, and tunnel burial depth on the surrounding rock is analyzed. The evolution law of the minimum safe strata thickness under a single variable and the correlation degree between minimum safe strata thickness and various disaster factors are revealed. Based on the BP neural network analysis of the simulation results and the measured data of Wulaofeng Tunnel, the calculated values of safe strata thicknesses of fault fracture zone (F10) were determined. The results show that the thickness of the safe rock strata increases with increasing water pressure, lateral pressure coefficient, fault fracture zone width, and tunnel burial depth. The minimum safe thickness of F10 of the tunnel ranges from 7.1 m to 7.4 m, and 10 m is reserved in the actual project. The calculated results are consistent with the reserved thickness value in the construction. This conclusion can provide a reference for similar projects.


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## Body

## 1. Introduction

At this stage, the network of expressways and railways in the west is advancing continuously, and there are an increasing number of mountain tunnel construction projects. With the continuous development of tunnel construction technology and the needs of operation, tunnel engineering is constantly developing toward the characteristics of large burial depth, high ground stress, high ground temperature, high water pressure, and strong karst. During tunnel excavation, the problem of water gushing appears repeatedly. Tunnels in mountainous areas have large burial depths and long tunnel lines. The tunnel site area is likely to cross the fault fracture zone. The rock mass structure in the fault fracture zone is well developed, and the rock mass is loose and broken, with poor integrity, low strength, and poor self-stability. Most of the fault fracture zones have good water richness, and the problem of the non-Darcy flow exists in the process of seepage [1–4]. Therefore, fault fracture zones become natural places for water storage and conduction and are one of the main sources of disasters in the process of tunnel construction [5–8].The surrounding rock between the tunnel face and the fault fracture zone is the antioutburst layer. Many practices have shown that preserving a certain thickness of the antioutburst layer in actual projects can effectively prevent the occurrence of water inrush disasters. For this reason, many studies have been performed on the issue of tunnel stability or safe rock stratum of water inrush disasters and can be divided into three main categories: empirical analysis [9, 10], numerical simulation [11–13], and experimental analysis [14]. Gan et al. [15] comprehensively considered the perturbation depth of the surrounding rock mass by drilling and blasting, the relaxation thickness of the surrounding rock after tunnel excavation, the expansion of water-bearing fissures under high water pressure, and the rock mass in situ stress state and magnitude. The thickness of the safe rock layer was determined, but the specific calculation formula for the thickness of the safe rock layer has not been established. Xu et al. [16] proposed a mathematical model that can simply and quickly predict the safe thickness of the water-resisting rock disk in front of the tunnel using the three-dimensional finite element method. Zhang et al. and Li et al. [17, 18] developed a model test for simulating water inrush hazards to study the minimum safe rock thickness when tunnel water inrush occurs under different ground stress, surrounding rock types and water pressure, and made a comparative analysis with the results of numerical simulation and theoretical analysis. Li et al. [19] discussed the water inrush mechanism and the minimum safe thickness of the face of a karst tunnel under drilling and blasting construction conditions based on fracture mechanics, theoretical derivation, and numerical experiments and deduced a reasonable reflection of blasting excavation disturbance and cracks under water pressure. A calculation formula for minimum safe thickness of rock mass was determined. Based on the elastic thick plate theory, Guo et al. [20] deduced the calculation formulas for the thickness of the rock wall against outbursts and the critical water pressure of the tunnel face in the two modes of fixed support and simple support.According to the existing studies, the empirical method mainly uses professional knowledge for analysis, but the results cannot reach a high accuracy and often show relatively large deviations [21]. The experimental method is also an optional way that has been used to study sudden water hazards, but the use of this method is greatly limited due to the cumbersome operation, expensive tests, and limited geological conditions considered. As the third scientific research method, numerical simulation has been increasingly used but fails to adequately consider the problems of fluid, solid, and high stress coupling.Artificial intelligence (AI) is a new technical science which is used to simulate and extend human intelligence [22, 23]. In recent years, artificial intelligence has been applied to the analysis of underground engineering problems [24–26]. Among them, BP neural network is a kind of multilayer feedforward network with error backpropagation, which can be fitted by functions to solve nonlinear problems among multiple variables. In this study, the factors of the water-rich tunnel and the thickness of the safe rock layer are nonlinear mapping, and there does not exist some specific linear relationship, so BP neural network can be considered for the exploration study of this problem.In this paper, based on the Wulaofeng Tunnel engineering of Jianyuan Expressway, the numerical simulation was combined with BP neural network, considering the flow-solid coupling under high ground stress, and the theoretical analysis was used for assist verification to determine the minimum safe strata thickness from water inrush disaster. This study is aimed at providing a proven calculation method for safe strata thickness of outburst prevention in underground engineering with faulted and broken zone structures and providing guidance for engineering practice.


## 2. Engineering Background

The Jianyuan Expressway is located in Honghe Prefecture, Yunnan. The Wulaofeng Tunnel has a total length of 8,350 m, which is a typical long mountain tunnel. The tunnel entrance axis direction is 138°, and the tunnel exit axis direction is 110°. Generally, the burial depth is 50~900 m, the minimum burial depth is 25 m, and the maximum burial depth is 929 m. The Wulaofeng Tunnel is a deep-buried extralong tunnel, and the specific geographical location is shown in Figure1. The entrance is connected to the proposed deep filling subgrade section, and the exit is connected to the Wulaofeng bridge, which is a deep-buried super long tunnel [27]. The strata that the tunnel crosses are dominated by granite sandy mudstone, slate, limestone, and dolomite.Figure 1
Space location map of the Wulaofeng Tunnel.The tunnel crosses the Yanshan-age Cretaceous granite strata (γ53(a)) of Upper Triassic Torgo Formation (T3n) and Middle Triassic Zhilao Formation (T2g). The lithology is mudstone, mud siltstone, dolomite, tuff, and granite. Mudstone and mudstone siltstone are thinly bedded to medium-thick bedded, tuff and dolomite are medium-thick bedded to massive bedded, and granite is fractured, mosaic, and subblock structure. According to geological survey and analysis, there are mainly multiple groups of IV and V structural planes in the tunnel passing section. The fault zone and joint dense zone through which the tunnel passes have poor stability of the surrounding rock. During tunnel excavation, the groundwater is mostly dripping, linear, and small effluents, and there may be rain-like or large-strand-like running water locally, such as exposing large fissures and karst areas. There is a possibility of greater water inrush hazards. There is confined water in the granite section. If the confined water layer is excavated, major water gushing will occur [28].


## 3. Numerical Model and Parameters

### 3.1. Calculation Model

The 3D numerical simulations in this paper are performed using FLAC3D, a 3D explicit finite difference program developed by Itasca, which can simulate the 3D mechanical behavior of geotechnical or other materials. The calculation is divided into several processes: model establishment, setting of initial and boundary conditions, initial ground stress balance, excavation solution, output, and plotting. According to the theory of elastoplastic mechanics, a three-dimensional model is established, as shown in Figure2, with a size of 100m×30m×90m. The section shape of the tunnel is a horseshoe shape. Taking the section of a highway tunnel IV as a grade tunnel, the section span is 12.42 m, the height is 8.77 m, the initial support thickness is 20 cm, and there is a 6 cm reserved control. The simulated excavation depth of the tunnel is 30 m. The angle between the strike line of the fault fracture zone and the tunnel axis is 15°, and the fault dip is 66°. When Y=0, the minimum distance between the fault fracture zone and the tunnel edge is 10.9 m, and when Y=30, the minimum distance between the fault fracture zone and the tunnel edge is 2.7 m.Figure 2
Three-dimensional calculation model.
(a)
Model front view(b)
Model stereogramThe bottom of the model is restrained by a fixed end, and horizontal restraints are imposed on the surroundings. The Mohr-Coulomb model was selected for the rock and soil constitutive. To simulate the deep-buried project, the S-B method was used to generate the initial ground stress. According to the survey data, the buried depth of the selected section was 610 meters, and the maximum ground stress value was 24.5 MPa. The length of the tunnel excavation is 2.5 m, and a total of 12 excavation cycles were carried out [29].


### 3.2. Selection of Parameters

#### 3.2.1. Geotechnical Parameters

Generally, the geological profile of the water-rich fault fracture zone is complex, the lithology is relatively broken, the structural surface is complex, and the stability of the surrounding rock is poor. Water inrush and mud outburst disasters are more likely to occur in the grade IV and grade V surrounding rocks [14, 30]. Therefore, this study takes the parameters of grade IV granite as an example for simulation research. The surrounding rock is assumed to be homogeneous and isotropic. Because the excavation distance of the simulated tunnel is too small, the distance between the tunnel face and the initial excavation position is far from the distance of the second lining construction, so only the initial lining material parameters are considered. The specific material parameters are shown in Table 1.Table 1
Geotechnical parameters of the numerical model.
Geotechnical typeVolume weight (kN/m3)Cohesion (kPa)Internal friction angle (°)Bulk modulus (GPa)Shear modulus (GPa)Granite (Grade IV)24.55503215.7325Fault2065301.264.08Initial lining2336004917.111.8


#### 3.2.2. Hydraulic Parameters

According to the evaluation of the water inflow of the tunnel in the “Construction Drawing Design for the 03 Section of the Honghe Prefecture Jianshui (Gejiu)-Yuanyang Expressway,” the maximum water inflow of K28+665~K31+025 is seen to be 3218.38 m3/d; see Figure 3 for the permeation phenomenon of the surrounding rock at K28+653. The tunnel mainly crosses two large-scale faults, namely, the F10 fault and F18 fault. The F10 is located at K28+638~K28+809, which is mainly composed of broken granite and tectonic conglomerate. There is confined water in this area. According to tunnel design specification [31], the classification of water seepage and pressure head is shown in Table 2.Figure 3
Water inrush phenomenon of the heading face at K28+653.Table 2
Water seepage volume and pressure head classification.
Active statusSeepage quantityq (L/(min·m))Pressure headH0 (m)Dry-dripping waterq<2.5H0<10Linear flow2.5<q<12.510<H0<100Gushing waterq>12.5H0>100For the on-site water inrush monitoring at K28+695 and K28+756 in the Wulaofeng Tunnel, five main monitoring points were selected. The monitoring time was 24 hours, and the measured water inflows were 16.60 m3/d, 17.25 m3/d, 18.42 m3/d, 18.72 m3/d, and 19.88 m3/d, respectively, corresponding to the relationship between the above table seepage volume and the water head classification. The pressure head was 0.9 MPa, 0.99 MPa, 1.05 MPa, 1.1 MPa, and 1.15 MPa.


## 3.1. Calculation Model

The 3D numerical simulations in this paper are performed using FLAC3D, a 3D explicit finite difference program developed by Itasca, which can simulate the 3D mechanical behavior of geotechnical or other materials. The calculation is divided into several processes: model establishment, setting of initial and boundary conditions, initial ground stress balance, excavation solution, output, and plotting. According to the theory of elastoplastic mechanics, a three-dimensional model is established, as shown in Figure2, with a size of 100m×30m×90m. The section shape of the tunnel is a horseshoe shape. Taking the section of a highway tunnel IV as a grade tunnel, the section span is 12.42 m, the height is 8.77 m, the initial support thickness is 20 cm, and there is a 6 cm reserved control. The simulated excavation depth of the tunnel is 30 m. The angle between the strike line of the fault fracture zone and the tunnel axis is 15°, and the fault dip is 66°. When Y=0, the minimum distance between the fault fracture zone and the tunnel edge is 10.9 m, and when Y=30, the minimum distance between the fault fracture zone and the tunnel edge is 2.7 m.Figure 2
Three-dimensional calculation model.
(a)
Model front view(b)
Model stereogramThe bottom of the model is restrained by a fixed end, and horizontal restraints are imposed on the surroundings. The Mohr-Coulomb model was selected for the rock and soil constitutive. To simulate the deep-buried project, the S-B method was used to generate the initial ground stress. According to the survey data, the buried depth of the selected section was 610 meters, and the maximum ground stress value was 24.5 MPa. The length of the tunnel excavation is 2.5 m, and a total of 12 excavation cycles were carried out [29].


## 3.2. Selection of Parameters

### 3.2.1. Geotechnical Parameters

Generally, the geological profile of the water-rich fault fracture zone is complex, the lithology is relatively broken, the structural surface is complex, and the stability of the surrounding rock is poor. Water inrush and mud outburst disasters are more likely to occur in the grade IV and grade V surrounding rocks [14, 30]. Therefore, this study takes the parameters of grade IV granite as an example for simulation research. The surrounding rock is assumed to be homogeneous and isotropic. Because the excavation distance of the simulated tunnel is too small, the distance between the tunnel face and the initial excavation position is far from the distance of the second lining construction, so only the initial lining material parameters are considered. The specific material parameters are shown in Table 1.Table 1
Geotechnical parameters of the numerical model.
Geotechnical typeVolume weight (kN/m3)Cohesion (kPa)Internal friction angle (°)Bulk modulus (GPa)Shear modulus (GPa)Granite (Grade IV)24.55503215.7325Fault2065301.264.08Initial lining2336004917.111.8


### 3.2.2. Hydraulic Parameters

According to the evaluation of the water inflow of the tunnel in the “Construction Drawing Design for the 03 Section of the Honghe Prefecture Jianshui (Gejiu)-Yuanyang Expressway,” the maximum water inflow of K28+665~K31+025 is seen to be 3218.38 m3/d; see Figure 3 for the permeation phenomenon of the surrounding rock at K28+653. The tunnel mainly crosses two large-scale faults, namely, the F10 fault and F18 fault. The F10 is located at K28+638~K28+809, which is mainly composed of broken granite and tectonic conglomerate. There is confined water in this area. According to tunnel design specification [31], the classification of water seepage and pressure head is shown in Table 2.Figure 3
Water inrush phenomenon of the heading face at K28+653.Table 2
Water seepage volume and pressure head classification.
Active statusSeepage quantityq (L/(min·m))Pressure headH0 (m)Dry-dripping waterq<2.5H0<10Linear flow2.5<q<12.510<H0<100Gushing waterq>12.5H0>100For the on-site water inrush monitoring at K28+695 and K28+756 in the Wulaofeng Tunnel, five main monitoring points were selected. The monitoring time was 24 hours, and the measured water inflows were 16.60 m3/d, 17.25 m3/d, 18.42 m3/d, 18.72 m3/d, and 19.88 m3/d, respectively, corresponding to the relationship between the above table seepage volume and the water head classification. The pressure head was 0.9 MPa, 0.99 MPa, 1.05 MPa, 1.1 MPa, and 1.15 MPa.


## 3.2.1. Geotechnical Parameters

Generally, the geological profile of the water-rich fault fracture zone is complex, the lithology is relatively broken, the structural surface is complex, and the stability of the surrounding rock is poor. Water inrush and mud outburst disasters are more likely to occur in the grade IV and grade V surrounding rocks [14, 30]. Therefore, this study takes the parameters of grade IV granite as an example for simulation research. The surrounding rock is assumed to be homogeneous and isotropic. Because the excavation distance of the simulated tunnel is too small, the distance between the tunnel face and the initial excavation position is far from the distance of the second lining construction, so only the initial lining material parameters are considered. The specific material parameters are shown in Table 1.Table 1
Geotechnical parameters of the numerical model.
Geotechnical typeVolume weight (kN/m3)Cohesion (kPa)Internal friction angle (°)Bulk modulus (GPa)Shear modulus (GPa)Granite (Grade IV)24.55503215.7325Fault2065301.264.08Initial lining2336004917.111.8


## 3.2.2. Hydraulic Parameters

According to the evaluation of the water inflow of the tunnel in the “Construction Drawing Design for the 03 Section of the Honghe Prefecture Jianshui (Gejiu)-Yuanyang Expressway,” the maximum water inflow of K28+665~K31+025 is seen to be 3218.38 m3/d; see Figure 3 for the permeation phenomenon of the surrounding rock at K28+653. The tunnel mainly crosses two large-scale faults, namely, the F10 fault and F18 fault. The F10 is located at K28+638~K28+809, which is mainly composed of broken granite and tectonic conglomerate. There is confined water in this area. According to tunnel design specification [31], the classification of water seepage and pressure head is shown in Table 2.Figure 3
Water inrush phenomenon of the heading face at K28+653.Table 2
Water seepage volume and pressure head classification.
Active statusSeepage quantityq (L/(min·m))Pressure headH0 (m)Dry-dripping waterq<2.5H0<10Linear flow2.5<q<12.510<H0<100Gushing waterq>12.5H0>100For the on-site water inrush monitoring at K28+695 and K28+756 in the Wulaofeng Tunnel, five main monitoring points were selected. The monitoring time was 24 hours, and the measured water inflows were 16.60 m3/d, 17.25 m3/d, 18.42 m3/d, 18.72 m3/d, and 19.88 m3/d, respectively, corresponding to the relationship between the above table seepage volume and the water head classification. The pressure head was 0.9 MPa, 0.99 MPa, 1.05 MPa, 1.1 MPa, and 1.15 MPa.


## 4. Excavation Simulation and Result Analysis

The excavation simulation was carried out according to the calculation model, and the analysis of the simulated plastic zone changes was obtained. In the simulation of different influencing factors and different parameter assignments, the connectivity of plastic zone between tunnel and fault fracture zone mostly occurred at the 8th or 9th excavation. When connectivity occurred, it was in a critically damaged state. Therefore, in order to reduce the analysis workload, the 7th excavation (Y=6 m, 8m, 10m and 12 m) was selected as the object of trend analysis. The horizontal stress changes at the arch waistX=56.1 and Z=35.3 on the right side of the tunnel above and the vertical stress changes at the vault X=53.1 and Z=40.3 were monitored.To analyze the influence of changes in water pressure, lateral pressure coefficient, width, and tunnel embedment depth in the fault fracture zone on the stress distribution of the surrounding rock and the extent of the plastic zone, the method of controlling variables was used to fix the values of other influencing factors, and the changes were studied.


### 4.1. Water Pressure

The parameters of water pressure are shown in Table3, and the stress changes at the right arch waist and the vault under different water pressures are shown in Figure 4.Table 3
Calculation parameters for water pressure variation.
ParameterValueSide pressure coefficientλ1.5Width of fault fracture zoneD (m)10Tunnel depthH (m)650Water pressureP (MPa)1.22.43.6Figure 4
Changes in horizontal stress at the right arch waist on the right side and vertical stress at the top of the vault under different water pressures.As shown in Figure4, as the excavation distance increases, the compressive stress in the XX-direction decreases. The different water pressure conditions are under the same excavation distance; as the water pressure increases, the compressive stress value in the XX-direction at the same point will slightly decrease, but there is basically no major change.As the excavation distance increases, the compressive stress in theZZ-direction first decreases, then increases, and finally decreases. The compressive stress in the ZZ-direction at the vault does not change as much as the excavation trend, possibly because the excavation cycle is 2.5 m, and the stress will be released in each excavation. The stress release causes the change to the tunnel vault where it has been excavated. From the perspective of water pressure changes, the compressive stress in the ZZ-direction at the dome is not significantly affected by water pressure.Due to the good lithology of the outer edge of the fault fracture zone, in the state of no seepage, the water pressure has little effect on the stress in theZZ-direction/right side of the tunnel vault.


### 4.2. Side Pressure Coefficient

The parameters of side pressure coefficient are shown in Table4, and the stress changes at the right arch waist and the vault under different side pressure coefficients are shown in Figure 5.Table 4
Calculation parameters for side pressure coefficient variation.
ParameterValueWater pressureP (MPa)2.4Width of fault fracture zoneD (m)10Tunnel depthH (m)650Side pressure coefficientλ1.251.51.75Figure 5
Changes in horizontal stress at the arch waist on the right side and vertical stress at the top of the vault under different side pressure coefficients.Figure5 shows that under the conditions of different lateral pressure coefficients, as the excavation distance gradually increases, the compressive stress in the XX-direction at this point gradually decreases. The larger the tunnel surface is, the greater the compressive stress that the tunnel must bear to maintain the stability of the surrounding rock. As the lateral pressure coefficient gradually increases, the horizontal compressive stress in the XX-direction gradually increases under the same excavation distance.As the excavation distance approaches, the compressive stress in theZZ-direction tends to decrease, but considering the stress release of each excavation, the compressive stress in the ZZ-direction will increase in an interval, but the overall trend remains unchanged. At the same excavation distance, the greater the lateral pressure coefficient is, the greater the compressive stress in the ZZ-direction at the dome. Since the lateral pressure coefficient is related to the vertical stress and the horizontal stress, according to the analysis of the above figure, the change in the lateral pressure coefficient has a significant influence on the stress changes in the ZZ- and XX-directions of the tunnel surface.


### 4.3. Width of Fault Fracture Zone

The parameters of width of fault fracture zone are shown in Table5, and the stress changes at the right arch waist and the vault under different side pressure coefficients are shown in Figure 6.Table 5
Calculation parameters for the width variation of fault fracture zone.
ParameterValueWater pressureP (MPa)2.4Side pressure coefficientλ1.5Tunnel depthH (m)650Width of fault fracture zoneD (m)101520Figure 6
Changes in horizontal stress at the arch waist on the right side and vertical stress at the top of the vault under different widths of fault fracture zones.Figure6 shows that there is no regular relationship between the XX-direction stress and the excavation distance. As the width of the fault increases, the stress in the XX-direction tends to increase before the excavation distance is 10 m, but between the excavation distances of 10 and 12 m, the stress in the XX-direction of D=10m increases suddenly, which is much larger than D=15. The corresponding value is 20 m. There is no obvious functional relationship between the vertical stress at the vault and the width of the fault fracture zone. Before the excavation distance is 9.6 m, the vertical stress increases with the increase in the fault fracture zone. After an excavation distance of 9.6 m, D=20m corresponds to a sharp drop in vertical stress.The above analysis shows that the correlation between the stress change in theXX-direction of the tunnel surrounding rock and the stress change in the ZZ-direction of the surrounding rock at the vault and the width of the fault fracture zone on one side of the tunnel needs further analysis and research.


### 4.4. Tunnel Embedment Depth

The parameters of tunnel depth are shown in Table6.Table 6
Calculation parameters for depth variation.
ParameterValueWater pressureP (MPa)2.4Side pressure coefficientλ1.5Width of fault fracture zoneD (m)10Tunnel depthH (m)650750850Similarly, the stress variation under different tunnel buried depth conditions was studied. The horizontal stress at the right arch waist gradually decreases. AsH continues to increase, the horizontal stress at the arch waist gradually increases, and the increase is relatively stable. With the increase in burial depth, the vertical pressure at the vault also increases, and under the same excavation distance, the increase in vertical stress is almost the same, and the growth rate is almost the same.Through the above analysis, it can be found that there is a strong correlation between the change in the surrounding rock stress at the tunnel vault and the buried depth of the tunnel, and there is a strong correlation between the horizontal stress change in the surrounding rock at the tunnel arch waist and the buried depth of the tunnel.


### 4.5. Determination of Safe Rock Thickness

During tunnel excavation, due to the 15° included angle between the direction of the fault fracture zone and the direction of the tunnel excavation axis, as the excavation cycle continues to expand, the distance between the tunnel face and the lower edge of the fault fracture zone decreases. The expansion of the plastic zone between the tunnel and the lower boundary of the fracture zone is getting closer; when the plastic zone between the tunnel and the lower boundary of the fault fracture zone is close to pass through, the rock formation between the tunnel and the fault fracture zone is in a state of near failure. If you continue to excavate forward, as the plastic zone around the tunnel and the lower edge of the fault fracture zone continue to expand and overlap, under the action of the high ground stress and high head pressure of the deep-buried tunnel, the deeply buried brittle rock will gradually crack, and the cracks will gradually expand and merge. Through the tunnel, a complex and dense runoff channel will be formed between the tunnel and the fault fracture zone, and the tunnel is very prone to water and mud disasters [32, 33]. Therefore, the distance between the plastic zone through the tunnel and the fault fracture zone at the current moment is generally taken as the minimum safe strata distance.To analyze the influence of different factors in the fault fracture zone on the stress distribution of the surrounding rock and the extent of the plastic zone, the method of controlling variables was adopted, the values of other influencing factors were fixed, and the values of the influencing factors to be studied were changed. Taking water pressure as an example, the influence of pressure on the safe thickness, horizontal stress, vertical stress, horizontal displacement, vertical displacement, and limit penetration of the plastic zone is analyzed, as shown in Figure7.Figure 7
Calculation cloud diagram of the tunnel section under different water pressures. (a) Horizontal stress. (b) Vertical stress. (c) Horizontal displacement. (d) Vertical displacement. (e) Plastic zone limit penetration.
(a)(b)(c)(d)(e)According to the excavation simulation calculation results, when the water pressureP is 1.2 MPa, 2.4 MPa, and 3.6 MPa, the minimum safe rock thickness is calculated to be 7.40 m, 8.24 m, and 8.67 m; the lateral pressure coefficient λ is 1.25. At 1.5 and 1.75, the corresponding minimum safe rock thicknesses are 6.97 m, 8.24 m, and 9.17 m, respectively; when the fault fracture zone width D is 10, 15, and 20 m, the minimum safe rock thickness should be 6.84 m, 7.00 m, and 7.37 m, respectively. When the buried depth H of the tunnel is 650, 750, and 850 m, the corresponding minimum safe rock thickness is 8.24, 8.26, and 9.44 m, respectively.


## 4.1. Water Pressure

The parameters of water pressure are shown in Table3, and the stress changes at the right arch waist and the vault under different water pressures are shown in Figure 4.Table 3
Calculation parameters for water pressure variation.
ParameterValueSide pressure coefficientλ1.5Width of fault fracture zoneD (m)10Tunnel depthH (m)650Water pressureP (MPa)1.22.43.6Figure 4
Changes in horizontal stress at the right arch waist on the right side and vertical stress at the top of the vault under different water pressures.As shown in Figure4, as the excavation distance increases, the compressive stress in the XX-direction decreases. The different water pressure conditions are under the same excavation distance; as the water pressure increases, the compressive stress value in the XX-direction at the same point will slightly decrease, but there is basically no major change.As the excavation distance increases, the compressive stress in theZZ-direction first decreases, then increases, and finally decreases. The compressive stress in the ZZ-direction at the vault does not change as much as the excavation trend, possibly because the excavation cycle is 2.5 m, and the stress will be released in each excavation. The stress release causes the change to the tunnel vault where it has been excavated. From the perspective of water pressure changes, the compressive stress in the ZZ-direction at the dome is not significantly affected by water pressure.Due to the good lithology of the outer edge of the fault fracture zone, in the state of no seepage, the water pressure has little effect on the stress in theZZ-direction/right side of the tunnel vault.


## 4.2. Side Pressure Coefficient

The parameters of side pressure coefficient are shown in Table4, and the stress changes at the right arch waist and the vault under different side pressure coefficients are shown in Figure 5.Table 4
Calculation parameters for side pressure coefficient variation.
ParameterValueWater pressureP (MPa)2.4Width of fault fracture zoneD (m)10Tunnel depthH (m)650Side pressure coefficientλ1.251.51.75Figure 5
Changes in horizontal stress at the arch waist on the right side and vertical stress at the top of the vault under different side pressure coefficients.Figure5 shows that under the conditions of different lateral pressure coefficients, as the excavation distance gradually increases, the compressive stress in the XX-direction at this point gradually decreases. The larger the tunnel surface is, the greater the compressive stress that the tunnel must bear to maintain the stability of the surrounding rock. As the lateral pressure coefficient gradually increases, the horizontal compressive stress in the XX-direction gradually increases under the same excavation distance.As the excavation distance approaches, the compressive stress in theZZ-direction tends to decrease, but considering the stress release of each excavation, the compressive stress in the ZZ-direction will increase in an interval, but the overall trend remains unchanged. At the same excavation distance, the greater the lateral pressure coefficient is, the greater the compressive stress in the ZZ-direction at the dome. Since the lateral pressure coefficient is related to the vertical stress and the horizontal stress, according to the analysis of the above figure, the change in the lateral pressure coefficient has a significant influence on the stress changes in the ZZ- and XX-directions of the tunnel surface.


## 4.3. Width of Fault Fracture Zone

The parameters of width of fault fracture zone are shown in Table5, and the stress changes at the right arch waist and the vault under different side pressure coefficients are shown in Figure 6.Table 5
Calculation parameters for the width variation of fault fracture zone.
ParameterValueWater pressureP (MPa)2.4Side pressure coefficientλ1.5Tunnel depthH (m)650Width of fault fracture zoneD (m)101520Figure 6
Changes in horizontal stress at the arch waist on the right side and vertical stress at the top of the vault under different widths of fault fracture zones.Figure6 shows that there is no regular relationship between the XX-direction stress and the excavation distance. As the width of the fault increases, the stress in the XX-direction tends to increase before the excavation distance is 10 m, but between the excavation distances of 10 and 12 m, the stress in the XX-direction of D=10m increases suddenly, which is much larger than D=15. The corresponding value is 20 m. There is no obvious functional relationship between the vertical stress at the vault and the width of the fault fracture zone. Before the excavation distance is 9.6 m, the vertical stress increases with the increase in the fault fracture zone. After an excavation distance of 9.6 m, D=20m corresponds to a sharp drop in vertical stress.The above analysis shows that the correlation between the stress change in theXX-direction of the tunnel surrounding rock and the stress change in the ZZ-direction of the surrounding rock at the vault and the width of the fault fracture zone on one side of the tunnel needs further analysis and research.


## 4.4. Tunnel Embedment Depth

The parameters of tunnel depth are shown in Table6.Table 6
Calculation parameters for depth variation.
ParameterValueWater pressureP (MPa)2.4Side pressure coefficientλ1.5Width of fault fracture zoneD (m)10Tunnel depthH (m)650750850Similarly, the stress variation under different tunnel buried depth conditions was studied. The horizontal stress at the right arch waist gradually decreases. AsH continues to increase, the horizontal stress at the arch waist gradually increases, and the increase is relatively stable. With the increase in burial depth, the vertical pressure at the vault also increases, and under the same excavation distance, the increase in vertical stress is almost the same, and the growth rate is almost the same.Through the above analysis, it can be found that there is a strong correlation between the change in the surrounding rock stress at the tunnel vault and the buried depth of the tunnel, and there is a strong correlation between the horizontal stress change in the surrounding rock at the tunnel arch waist and the buried depth of the tunnel.


## 4.5. Determination of Safe Rock Thickness

During tunnel excavation, due to the 15° included angle between the direction of the fault fracture zone and the direction of the tunnel excavation axis, as the excavation cycle continues to expand, the distance between the tunnel face and the lower edge of the fault fracture zone decreases. The expansion of the plastic zone between the tunnel and the lower boundary of the fracture zone is getting closer; when the plastic zone between the tunnel and the lower boundary of the fault fracture zone is close to pass through, the rock formation between the tunnel and the fault fracture zone is in a state of near failure. If you continue to excavate forward, as the plastic zone around the tunnel and the lower edge of the fault fracture zone continue to expand and overlap, under the action of the high ground stress and high head pressure of the deep-buried tunnel, the deeply buried brittle rock will gradually crack, and the cracks will gradually expand and merge. Through the tunnel, a complex and dense runoff channel will be formed between the tunnel and the fault fracture zone, and the tunnel is very prone to water and mud disasters [32, 33]. Therefore, the distance between the plastic zone through the tunnel and the fault fracture zone at the current moment is generally taken as the minimum safe strata distance.To analyze the influence of different factors in the fault fracture zone on the stress distribution of the surrounding rock and the extent of the plastic zone, the method of controlling variables was adopted, the values of other influencing factors were fixed, and the values of the influencing factors to be studied were changed. Taking water pressure as an example, the influence of pressure on the safe thickness, horizontal stress, vertical stress, horizontal displacement, vertical displacement, and limit penetration of the plastic zone is analyzed, as shown in Figure7.Figure 7
Calculation cloud diagram of the tunnel section under different water pressures. (a) Horizontal stress. (b) Vertical stress. (c) Horizontal displacement. (d) Vertical displacement. (e) Plastic zone limit penetration.
(a)(b)(c)(d)(e)According to the excavation simulation calculation results, when the water pressureP is 1.2 MPa, 2.4 MPa, and 3.6 MPa, the minimum safe rock thickness is calculated to be 7.40 m, 8.24 m, and 8.67 m; the lateral pressure coefficient λ is 1.25. At 1.5 and 1.75, the corresponding minimum safe rock thicknesses are 6.97 m, 8.24 m, and 9.17 m, respectively; when the fault fracture zone width D is 10, 15, and 20 m, the minimum safe rock thickness should be 6.84 m, 7.00 m, and 7.37 m, respectively. When the buried depth H of the tunnel is 650, 750, and 850 m, the corresponding minimum safe rock thickness is 8.24, 8.26, and 9.44 m, respectively.


## 5. Network Model Construction

### 5.1. BP Neural Network

The BP neural network is a multilayer feedforward neural network, and the structure is shown in Figure8. Its basic idea is the gradient descent method, which uses gradient search technology to minimize the error mean square error between the actual output value of the network and the expected output value [34, 35]. The characteristic of the BP algorithm is that the input data are propagated forward, the network output is obtained through the hidden layer, and the error of the actual output is backpropagated. In each round trip process, the network parameters are adjusted to make the network output close to the actual output, and the error is minimized. At this time, the trained neural network can process the nonlinearly transformed information with the smallest output error on the input information of similar samples [36].Figure 8
BP neural network structure diagram.


### 5.2. Example Analysis of the BP Neural Network Model

#### 5.2.1. Selection of Model Parameters

For the determination of the minimum safe rock thickness for crossing the fault fracture zone, the data simulated by FLAC3D are used as the output combination of the sample, and after the neural network is generated, the measured input values of the F10 and F18 faults of the Wulaofeng Tunnel are brought into the generated network to obtain the output combination under the measured input conditions [37].According to the engineering situation in this paper, there are 4 hazard factors that affect the thickness of the safe rock layer. These factors are the water pressure, lateral pressure coefficient, fault fracture zone width, and tunnel embedding depth. That is, the number of neurons in the input layer of the network is 4, and the output is the smallest. For a safe rock thickness, the number of neurons in the output layer is 1. The number of neurons in the hidden layer of the designed 3-layer BP neural networkl and the number of neurons in the input layer n have the following approximate relationship: l=2n+1, so in the BP neural network, the number of neurons in the hidden layer is 9. The BP neural network structure set in this paper is 4-9-1; that is, the input layer has 4 nodes, the hidden layer has 9 nodes, and the output layer has 2 nodes. Relevant parameters of neural network are shown in Table 7.Table 7
Relevant parameters of neural network.
BP neural network parametersInput layerHidden layerInput layerTransfer function 1Transfer function 2491tansiglogsig


#### 5.2.2. Construction of Training Samples

The input layer data of the sample are based on the geological survey report of the Wulaofeng Tunnel and the physical and mechanical parameters of the deep-buried tunnel rock involved in numerous studies. The single-variable method is used to study the water pressure, lateral pressure coefficient, fault width, and tunnel. The impact of the changes in the 4 hazard factors of the embedding depth on the minimum safe rock thickness of the fault fracture zone to calculate and simulate the minimum safe rock thickness under the influence of different hazard factors was investigated [38]. The linear relationship between the single uniform hazard factor and the minimum safe rock thickness was further fitted, and the independent variable and the corresponding dependent variable were randomly selected within a certain range. The simulated value and the randomly selected value as the input value (ip) of the training sample and the output value (op) were combined. The training sample data is shown in Table 8.Table 8
Training sample data.
Serial numberSample input layerSample output layerWater pressure (MPa) ASide pressure coefficient BFault width (m) CBuried depth (m) DSafe rock thickness (m) E12.41.5106508.2421.21.5106507.433.61.5106508.6744.81.5106509.0552.41.25106506.9762.41.75106509.1772.421065011.1782.41.5206508.7992.41.5256509.2102.41.5107508.75112.41.5108509.44122.41.5109509.891331.5106508.42141.81.5106507.81152.11.5106508.08161.51.5106507.56173.31.5106508.551811.5106507.221921.5106508.012041.5106508.78212.41.3106507.22222.41.35106507.48232.41.4106507.7242.41.45106507.98252.41.55106508.49262.41.606508.72272.41.65106508.89282.41.7106509.03292.41.8106509.39302.41.5126508.34312.41.5146508.4322.41.5166508.5332.41.5186508.58342.41.5226508.9352.41.5246509.12362.41.5266509.22372.41.5286509.29382.41.5107608.79392.41.5107708.85402.41.5107808.92412.41.5107909.02422.41.5108109.15432.41.5108209.18442.41.5108309.26452.41.5108409.36462.41.5108609.42472.41.5108709.46482.41.5108809.51492.41.5108909.53502.41.5109009.58512.41.5109109.63


#### 5.2.3. Training Result Analysis

Figure9 shows that the mean square error is divided into training set, validation set, and test set. The mean square error continues to decrease with the increase in training algebra and tends to be stable in 5 generations of training. Among these sets, the validation set and training set converge during the 4th generation training, and the best mean square error value of the validation set is 0.0013455, indicating that the mean square error of this training is small, and the actual output value is seen to be closer to the expected output value.Figure 9
Mean square error of training samples.By analyzing the trained network in this paper, the goodness-of-fitR of training, validation, and testing is above 0.9. The regression linearity shows that R2 is the goodness of fit. The larger the R2 is, the better the fit. Therefore, the network has reached the simulation purpose.Sensitivity analysis is an uncertainty analysis method that analyzes the degree of influence of input parameters on the uncertainty of output parameters [39]. In this study, a series of analyses were performed based on numerical simulation-artificial intelligence method, but the sensitivity of the influence of each factor is not yet clear, so the cosine amplitude approach was chosen to perform sensitivity analysis for each input parameter [40]. The results of the statistical analysis are shown in Figure 10, where Rij represents the correlation strength, and WP, LPC, TD, and FFZW represent the input parameters, including water pressure, lateral pressure coefficient, tunnel depth, and fault fragmentation zone width, respectively. The analysis shows that water pressure has the greatest influence on the results, followed by lateral pressure coefficient and burial depth, and width has the least influence.Figure 10
Influence analysis of different input parameters.


#### 5.2.4. Mechanical Criterion Analysis

Under the condition of plate-like failure in the fault fracture zone, the safe rock layer is regarded as a plate-like structure, and the thickness of the safe rock layer is calculated by using structural mechanics. Based on the allowable bending strength of the rock mass and the allowable shear strength of the rock mass, the minimum safe rock layer thickness is calculated from Equations (1)–(3) [41].Let the weight of the mixture of filling medium and rock-soil mass except water in the fault fracture zone beW, and the pressure generated by the mixture of rock-soil mass and filling medium on the rock layer of the lower wall of the fault is W′, which can be obtained from
(1)W′=W∗cosα.Under the condition of allowable bending strength,(2)T≥n3ρgh3+5W′h2+5qh210σ.Under allowable shear strength conditions,(3)T≥n21ρgh2+30W′h+30qh40τ,whereT is the safe rock thickness (m); n is the correction factor, generally 0~1; ρ is the density of fissure water in fault fracture zone (kg/m3); h is the maximum span of the section under the fault dip direction (m); σ is the allowable bending strength (kPa); and τ is the allowable shear strength (kPa).The geological exploration report of the Wulaofeng Tunnel and the right geophysical prospecting map are shown in Figure11. According to the experimental results, the compressive strength of the granite at K28+750 of the tunnel is 80 MPa~200 MPa. The compressive strength of the granite at K28+750 in the Wulaofeng Tunnel is between 80 and 200 MPa. Therefore, when calculating the minimum safe rock thickness, the default rock strength is low, which is prone to water inrush disasters. Therefore, the compressive strength of the granite is 100 MPa. Thus, the shear strength of granite is 7.06 MPa, and the bending strength is 8.4. According to the allowable stress calculation formula, we calculate σ=6MPa and τ=5.76MPa (see Table 9 for other data).Figure 11
Part of the right geophysical map of the Wulaofeng Tunnel.Table 9
Other data of Wulaofeng Tunnel (K28+750).
TypenαρhστActual value0.56610009.6465.76The corresponding minimum safe rock layer thickness was obtained, and the error relationship with the neural network simulation value was analyzed. The error relationship is shown in Tables10 and 11.Table 10
Simulated and theoretical values of minimum safe thickness under the condition of shear strength.
y1y2y3y4y5Simulated safe thickness (m)7.146.876.846.847.10Theoretical safe thickness (m)7.557.647.697.817.73Error (%)5.7411.2112.4314.188.87Table 11
Simulated and theoretical values of minimum safe thickness under the condition of flexural strength.
y1y2y3y4y5Simulated safe thickness (m)7.146.876.846.847.10Theoretical safe thickness (m)6.836.866.886.946.91Error (%)4.540.150.581.462.75From the analysis of Tables10 and 11, we can conclude that compared with the calculation of the minimum safe thickness under the condition of shear strength, the error between the minimum safe rock layer thickness obtained by the calculation formula under the condition of bending resistance and the simulated value obtained by the neural network is smaller, and the error range from small to large is 0.15%, 0.58%, 1.46%, 2.75%, and 4.54%, respectively; the calculated safe rock thickness error under shear conditions is large, but the minimum safe thickness value is conservative. From the perspective of reducing the possibility of risk disasters, the calculated value of the minimum safe rock layer thickness under the condition of shear strength should be selected.


#### 5.2.5. Field Measurement Analysis and Verification

Based on the comprehensive survey of the Wulaofeng geological survey report and the excavation section, the F10 fault is located in the K28+638~K28+809 section of the right tunnel. The fault is close to the tunnel exit number K28+720, and the embedment depth is between 605 and 625 m. This interval is granite, the rock formation is relatively hard and brittle, there is a confined water section, the groundwater state is rain-like, and there may be water gushing. The lateral pressure coefficients obtained from the measured in situ stress are 1.12, 1.1, 1.15, 1.13, and 1.18. The width of the broken zone is 10-20 m. The F18 fault is located in the K24+820~K25+0060 section of the right cave. The fault is close to the tunnel exit number K24+956, and the embedment depth is between 203 and 218 m. The rock in this section is mainly fractured rock and filling medium, but there is little groundwater, there is no sufficient water supply in the rock formations, and the permeable state of the fault near the tunnel is dripping.As seen from the output groups in Tables12 and 13, the minimum safe thickness of the tunnel crossing the F10 fault fracture zone is between 6.8 m and 7.2 m, and the minimum safety thickness of the tunnel crossing the F18 fault fracture zone is between 7.1 m and 7.4 m. In the actual excavation process of the tunnel, the safety distance was taken as 10 m, and corresponding support and reinforcement measures were taken. The tunnel safely passed the F10 fault fracture zone.Table 12
Measured input group (F10).
Serial numberABCD10.91.121262020.991.11661831.11.151561041.151.131861551.051.1815620Table 13
Measured output group (F10).
y1y2y3y4y57.146.876.846.847.10In tunnel construction under drilling and blasting conditions, the calculation of the safety distance often needs to be multiplied by a safety factor greater than 1 on the basis of the theoretical value. The safety factor is 1.2, and the minimum safe rock thickness of F10 is obtained by replacing the above theoretical value with the actual value 8.5~8.9 m, which is closer to the reserved thickness of 10 m in the actual project.


## 5.1. BP Neural Network

The BP neural network is a multilayer feedforward neural network, and the structure is shown in Figure8. Its basic idea is the gradient descent method, which uses gradient search technology to minimize the error mean square error between the actual output value of the network and the expected output value [34, 35]. The characteristic of the BP algorithm is that the input data are propagated forward, the network output is obtained through the hidden layer, and the error of the actual output is backpropagated. In each round trip process, the network parameters are adjusted to make the network output close to the actual output, and the error is minimized. At this time, the trained neural network can process the nonlinearly transformed information with the smallest output error on the input information of similar samples [36].Figure 8
BP neural network structure diagram.


## 5.2. Example Analysis of the BP Neural Network Model

### 5.2.1. Selection of Model Parameters

For the determination of the minimum safe rock thickness for crossing the fault fracture zone, the data simulated by FLAC3D are used as the output combination of the sample, and after the neural network is generated, the measured input values of the F10 and F18 faults of the Wulaofeng Tunnel are brought into the generated network to obtain the output combination under the measured input conditions [37].According to the engineering situation in this paper, there are 4 hazard factors that affect the thickness of the safe rock layer. These factors are the water pressure, lateral pressure coefficient, fault fracture zone width, and tunnel embedding depth. That is, the number of neurons in the input layer of the network is 4, and the output is the smallest. For a safe rock thickness, the number of neurons in the output layer is 1. The number of neurons in the hidden layer of the designed 3-layer BP neural networkl and the number of neurons in the input layer n have the following approximate relationship: l=2n+1, so in the BP neural network, the number of neurons in the hidden layer is 9. The BP neural network structure set in this paper is 4-9-1; that is, the input layer has 4 nodes, the hidden layer has 9 nodes, and the output layer has 2 nodes. Relevant parameters of neural network are shown in Table 7.Table 7
Relevant parameters of neural network.
BP neural network parametersInput layerHidden layerInput layerTransfer function 1Transfer function 2491tansiglogsig


### 5.2.2. Construction of Training Samples

The input layer data of the sample are based on the geological survey report of the Wulaofeng Tunnel and the physical and mechanical parameters of the deep-buried tunnel rock involved in numerous studies. The single-variable method is used to study the water pressure, lateral pressure coefficient, fault width, and tunnel. The impact of the changes in the 4 hazard factors of the embedding depth on the minimum safe rock thickness of the fault fracture zone to calculate and simulate the minimum safe rock thickness under the influence of different hazard factors was investigated [38]. The linear relationship between the single uniform hazard factor and the minimum safe rock thickness was further fitted, and the independent variable and the corresponding dependent variable were randomly selected within a certain range. The simulated value and the randomly selected value as the input value (ip) of the training sample and the output value (op) were combined. The training sample data is shown in Table 8.Table 8
Training sample data.
Serial numberSample input layerSample output layerWater pressure (MPa) ASide pressure coefficient BFault width (m) CBuried depth (m) DSafe rock thickness (m) E12.41.5106508.2421.21.5106507.433.61.5106508.6744.81.5106509.0552.41.25106506.9762.41.75106509.1772.421065011.1782.41.5206508.7992.41.5256509.2102.41.5107508.75112.41.5108509.44122.41.5109509.891331.5106508.42141.81.5106507.81152.11.5106508.08161.51.5106507.56173.31.5106508.551811.5106507.221921.5106508.012041.5106508.78212.41.3106507.22222.41.35106507.48232.41.4106507.7242.41.45106507.98252.41.55106508.49262.41.606508.72272.41.65106508.89282.41.7106509.03292.41.8106509.39302.41.5126508.34312.41.5146508.4322.41.5166508.5332.41.5186508.58342.41.5226508.9352.41.5246509.12362.41.5266509.22372.41.5286509.29382.41.5107608.79392.41.5107708.85402.41.5107808.92412.41.5107909.02422.41.5108109.15432.41.5108209.18442.41.5108309.26452.41.5108409.36462.41.5108609.42472.41.5108709.46482.41.5108809.51492.41.5108909.53502.41.5109009.58512.41.5109109.63


### 5.2.3. Training Result Analysis

Figure9 shows that the mean square error is divided into training set, validation set, and test set. The mean square error continues to decrease with the increase in training algebra and tends to be stable in 5 generations of training. Among these sets, the validation set and training set converge during the 4th generation training, and the best mean square error value of the validation set is 0.0013455, indicating that the mean square error of this training is small, and the actual output value is seen to be closer to the expected output value.Figure 9
Mean square error of training samples.By analyzing the trained network in this paper, the goodness-of-fitR of training, validation, and testing is above 0.9. The regression linearity shows that R2 is the goodness of fit. The larger the R2 is, the better the fit. Therefore, the network has reached the simulation purpose.Sensitivity analysis is an uncertainty analysis method that analyzes the degree of influence of input parameters on the uncertainty of output parameters [39]. In this study, a series of analyses were performed based on numerical simulation-artificial intelligence method, but the sensitivity of the influence of each factor is not yet clear, so the cosine amplitude approach was chosen to perform sensitivity analysis for each input parameter [40]. The results of the statistical analysis are shown in Figure 10, where Rij represents the correlation strength, and WP, LPC, TD, and FFZW represent the input parameters, including water pressure, lateral pressure coefficient, tunnel depth, and fault fragmentation zone width, respectively. The analysis shows that water pressure has the greatest influence on the results, followed by lateral pressure coefficient and burial depth, and width has the least influence.Figure 10
Influence analysis of different input parameters.


### 5.2.4. Mechanical Criterion Analysis

Under the condition of plate-like failure in the fault fracture zone, the safe rock layer is regarded as a plate-like structure, and the thickness of the safe rock layer is calculated by using structural mechanics. Based on the allowable bending strength of the rock mass and the allowable shear strength of the rock mass, the minimum safe rock layer thickness is calculated from Equations (1)–(3) [41].Let the weight of the mixture of filling medium and rock-soil mass except water in the fault fracture zone beW, and the pressure generated by the mixture of rock-soil mass and filling medium on the rock layer of the lower wall of the fault is W′, which can be obtained from
(1)W′=W∗cosα.Under the condition of allowable bending strength,(2)T≥n3ρgh3+5W′h2+5qh210σ.Under allowable shear strength conditions,(3)T≥n21ρgh2+30W′h+30qh40τ,whereT is the safe rock thickness (m); n is the correction factor, generally 0~1; ρ is the density of fissure water in fault fracture zone (kg/m3); h is the maximum span of the section under the fault dip direction (m); σ is the allowable bending strength (kPa); and τ is the allowable shear strength (kPa).The geological exploration report of the Wulaofeng Tunnel and the right geophysical prospecting map are shown in Figure11. According to the experimental results, the compressive strength of the granite at K28+750 of the tunnel is 80 MPa~200 MPa. The compressive strength of the granite at K28+750 in the Wulaofeng Tunnel is between 80 and 200 MPa. Therefore, when calculating the minimum safe rock thickness, the default rock strength is low, which is prone to water inrush disasters. Therefore, the compressive strength of the granite is 100 MPa. Thus, the shear strength of granite is 7.06 MPa, and the bending strength is 8.4. According to the allowable stress calculation formula, we calculate σ=6MPa and τ=5.76MPa (see Table 9 for other data).Figure 11
Part of the right geophysical map of the Wulaofeng Tunnel.Table 9
Other data of Wulaofeng Tunnel (K28+750).
TypenαρhστActual value0.56610009.6465.76The corresponding minimum safe rock layer thickness was obtained, and the error relationship with the neural network simulation value was analyzed. The error relationship is shown in Tables10 and 11.Table 10
Simulated and theoretical values of minimum safe thickness under the condition of shear strength.
y1y2y3y4y5Simulated safe thickness (m)7.146.876.846.847.10Theoretical safe thickness (m)7.557.647.697.817.73Error (%)5.7411.2112.4314.188.87Table 11
Simulated and theoretical values of minimum safe thickness under the condition of flexural strength.
y1y2y3y4y5Simulated safe thickness (m)7.146.876.846.847.10Theoretical safe thickness (m)6.836.866.886.946.91Error (%)4.540.150.581.462.75From the analysis of Tables10 and 11, we can conclude that compared with the calculation of the minimum safe thickness under the condition of shear strength, the error between the minimum safe rock layer thickness obtained by the calculation formula under the condition of bending resistance and the simulated value obtained by the neural network is smaller, and the error range from small to large is 0.15%, 0.58%, 1.46%, 2.75%, and 4.54%, respectively; the calculated safe rock thickness error under shear conditions is large, but the minimum safe thickness value is conservative. From the perspective of reducing the possibility of risk disasters, the calculated value of the minimum safe rock layer thickness under the condition of shear strength should be selected.


### 5.2.5. Field Measurement Analysis and Verification

Based on the comprehensive survey of the Wulaofeng geological survey report and the excavation section, the F10 fault is located in the K28+638~K28+809 section of the right tunnel. The fault is close to the tunnel exit number K28+720, and the embedment depth is between 605 and 625 m. This interval is granite, the rock formation is relatively hard and brittle, there is a confined water section, the groundwater state is rain-like, and there may be water gushing. The lateral pressure coefficients obtained from the measured in situ stress are 1.12, 1.1, 1.15, 1.13, and 1.18. The width of the broken zone is 10-20 m. The F18 fault is located in the K24+820~K25+0060 section of the right cave. The fault is close to the tunnel exit number K24+956, and the embedment depth is between 203 and 218 m. The rock in this section is mainly fractured rock and filling medium, but there is little groundwater, there is no sufficient water supply in the rock formations, and the permeable state of the fault near the tunnel is dripping.As seen from the output groups in Tables12 and 13, the minimum safe thickness of the tunnel crossing the F10 fault fracture zone is between 6.8 m and 7.2 m, and the minimum safety thickness of the tunnel crossing the F18 fault fracture zone is between 7.1 m and 7.4 m. In the actual excavation process of the tunnel, the safety distance was taken as 10 m, and corresponding support and reinforcement measures were taken. The tunnel safely passed the F10 fault fracture zone.Table 12
Measured input group (F10).
Serial numberABCD10.91.121262020.991.11661831.11.151561041.151.131861551.051.1815620Table 13
Measured output group (F10).
y1y2y3y4y57.146.876.846.847.10In tunnel construction under drilling and blasting conditions, the calculation of the safety distance often needs to be multiplied by a safety factor greater than 1 on the basis of the theoretical value. The safety factor is 1.2, and the minimum safe rock thickness of F10 is obtained by replacing the above theoretical value with the actual value 8.5~8.9 m, which is closer to the reserved thickness of 10 m in the actual project.


## 5.2.1. Selection of Model Parameters

For the determination of the minimum safe rock thickness for crossing the fault fracture zone, the data simulated by FLAC3D are used as the output combination of the sample, and after the neural network is generated, the measured input values of the F10 and F18 faults of the Wulaofeng Tunnel are brought into the generated network to obtain the output combination under the measured input conditions [37].According to the engineering situation in this paper, there are 4 hazard factors that affect the thickness of the safe rock layer. These factors are the water pressure, lateral pressure coefficient, fault fracture zone width, and tunnel embedding depth. That is, the number of neurons in the input layer of the network is 4, and the output is the smallest. For a safe rock thickness, the number of neurons in the output layer is 1. The number of neurons in the hidden layer of the designed 3-layer BP neural networkl and the number of neurons in the input layer n have the following approximate relationship: l=2n+1, so in the BP neural network, the number of neurons in the hidden layer is 9. The BP neural network structure set in this paper is 4-9-1; that is, the input layer has 4 nodes, the hidden layer has 9 nodes, and the output layer has 2 nodes. Relevant parameters of neural network are shown in Table 7.Table 7
Relevant parameters of neural network.
BP neural network parametersInput layerHidden layerInput layerTransfer function 1Transfer function 2491tansiglogsig


## 5.2.2. Construction of Training Samples

The input layer data of the sample are based on the geological survey report of the Wulaofeng Tunnel and the physical and mechanical parameters of the deep-buried tunnel rock involved in numerous studies. The single-variable method is used to study the water pressure, lateral pressure coefficient, fault width, and tunnel. The impact of the changes in the 4 hazard factors of the embedding depth on the minimum safe rock thickness of the fault fracture zone to calculate and simulate the minimum safe rock thickness under the influence of different hazard factors was investigated [38]. The linear relationship between the single uniform hazard factor and the minimum safe rock thickness was further fitted, and the independent variable and the corresponding dependent variable were randomly selected within a certain range. The simulated value and the randomly selected value as the input value (ip) of the training sample and the output value (op) were combined. The training sample data is shown in Table 8.Table 8
Training sample data.
Serial numberSample input layerSample output layerWater pressure (MPa) ASide pressure coefficient BFault width (m) CBuried depth (m) DSafe rock thickness (m) E12.41.5106508.2421.21.5106507.433.61.5106508.6744.81.5106509.0552.41.25106506.9762.41.75106509.1772.421065011.1782.41.5206508.7992.41.5256509.2102.41.5107508.75112.41.5108509.44122.41.5109509.891331.5106508.42141.81.5106507.81152.11.5106508.08161.51.5106507.56173.31.5106508.551811.5106507.221921.5106508.012041.5106508.78212.41.3106507.22222.41.35106507.48232.41.4106507.7242.41.45106507.98252.41.55106508.49262.41.606508.72272.41.65106508.89282.41.7106509.03292.41.8106509.39302.41.5126508.34312.41.5146508.4322.41.5166508.5332.41.5186508.58342.41.5226508.9352.41.5246509.12362.41.5266509.22372.41.5286509.29382.41.5107608.79392.41.5107708.85402.41.5107808.92412.41.5107909.02422.41.5108109.15432.41.5108209.18442.41.5108309.26452.41.5108409.36462.41.5108609.42472.41.5108709.46482.41.5108809.51492.41.5108909.53502.41.5109009.58512.41.5109109.63


## 5.2.3. Training Result Analysis

Figure9 shows that the mean square error is divided into training set, validation set, and test set. The mean square error continues to decrease with the increase in training algebra and tends to be stable in 5 generations of training. Among these sets, the validation set and training set converge during the 4th generation training, and the best mean square error value of the validation set is 0.0013455, indicating that the mean square error of this training is small, and the actual output value is seen to be closer to the expected output value.Figure 9
Mean square error of training samples.By analyzing the trained network in this paper, the goodness-of-fitR of training, validation, and testing is above 0.9. The regression linearity shows that R2 is the goodness of fit. The larger the R2 is, the better the fit. Therefore, the network has reached the simulation purpose.Sensitivity analysis is an uncertainty analysis method that analyzes the degree of influence of input parameters on the uncertainty of output parameters [39]. In this study, a series of analyses were performed based on numerical simulation-artificial intelligence method, but the sensitivity of the influence of each factor is not yet clear, so the cosine amplitude approach was chosen to perform sensitivity analysis for each input parameter [40]. The results of the statistical analysis are shown in Figure 10, where Rij represents the correlation strength, and WP, LPC, TD, and FFZW represent the input parameters, including water pressure, lateral pressure coefficient, tunnel depth, and fault fragmentation zone width, respectively. The analysis shows that water pressure has the greatest influence on the results, followed by lateral pressure coefficient and burial depth, and width has the least influence.Figure 10
Influence analysis of different input parameters.


## 5.2.4. Mechanical Criterion Analysis

Under the condition of plate-like failure in the fault fracture zone, the safe rock layer is regarded as a plate-like structure, and the thickness of the safe rock layer is calculated by using structural mechanics. Based on the allowable bending strength of the rock mass and the allowable shear strength of the rock mass, the minimum safe rock layer thickness is calculated from Equations (1)–(3) [41].Let the weight of the mixture of filling medium and rock-soil mass except water in the fault fracture zone beW, and the pressure generated by the mixture of rock-soil mass and filling medium on the rock layer of the lower wall of the fault is W′, which can be obtained from
(1)W′=W∗cosα.Under the condition of allowable bending strength,(2)T≥n3ρgh3+5W′h2+5qh210σ.Under allowable shear strength conditions,(3)T≥n21ρgh2+30W′h+30qh40τ,whereT is the safe rock thickness (m); n is the correction factor, generally 0~1; ρ is the density of fissure water in fault fracture zone (kg/m3); h is the maximum span of the section under the fault dip direction (m); σ is the allowable bending strength (kPa); and τ is the allowable shear strength (kPa).The geological exploration report of the Wulaofeng Tunnel and the right geophysical prospecting map are shown in Figure11. According to the experimental results, the compressive strength of the granite at K28+750 of the tunnel is 80 MPa~200 MPa. The compressive strength of the granite at K28+750 in the Wulaofeng Tunnel is between 80 and 200 MPa. Therefore, when calculating the minimum safe rock thickness, the default rock strength is low, which is prone to water inrush disasters. Therefore, the compressive strength of the granite is 100 MPa. Thus, the shear strength of granite is 7.06 MPa, and the bending strength is 8.4. According to the allowable stress calculation formula, we calculate σ=6MPa and τ=5.76MPa (see Table 9 for other data).Figure 11
Part of the right geophysical map of the Wulaofeng Tunnel.Table 9
Other data of Wulaofeng Tunnel (K28+750).
TypenαρhστActual value0.56610009.6465.76The corresponding minimum safe rock layer thickness was obtained, and the error relationship with the neural network simulation value was analyzed. The error relationship is shown in Tables10 and 11.Table 10
Simulated and theoretical values of minimum safe thickness under the condition of shear strength.
y1y2y3y4y5Simulated safe thickness (m)7.146.876.846.847.10Theoretical safe thickness (m)7.557.647.697.817.73Error (%)5.7411.2112.4314.188.87Table 11
Simulated and theoretical values of minimum safe thickness under the condition of flexural strength.
y1y2y3y4y5Simulated safe thickness (m)7.146.876.846.847.10Theoretical safe thickness (m)6.836.866.886.946.91Error (%)4.540.150.581.462.75From the analysis of Tables10 and 11, we can conclude that compared with the calculation of the minimum safe thickness under the condition of shear strength, the error between the minimum safe rock layer thickness obtained by the calculation formula under the condition of bending resistance and the simulated value obtained by the neural network is smaller, and the error range from small to large is 0.15%, 0.58%, 1.46%, 2.75%, and 4.54%, respectively; the calculated safe rock thickness error under shear conditions is large, but the minimum safe thickness value is conservative. From the perspective of reducing the possibility of risk disasters, the calculated value of the minimum safe rock layer thickness under the condition of shear strength should be selected.


## 5.2.5. Field Measurement Analysis and Verification

Based on the comprehensive survey of the Wulaofeng geological survey report and the excavation section, the F10 fault is located in the K28+638~K28+809 section of the right tunnel. The fault is close to the tunnel exit number K28+720, and the embedment depth is between 605 and 625 m. This interval is granite, the rock formation is relatively hard and brittle, there is a confined water section, the groundwater state is rain-like, and there may be water gushing. The lateral pressure coefficients obtained from the measured in situ stress are 1.12, 1.1, 1.15, 1.13, and 1.18. The width of the broken zone is 10-20 m. The F18 fault is located in the K24+820~K25+0060 section of the right cave. The fault is close to the tunnel exit number K24+956, and the embedment depth is between 203 and 218 m. The rock in this section is mainly fractured rock and filling medium, but there is little groundwater, there is no sufficient water supply in the rock formations, and the permeable state of the fault near the tunnel is dripping.As seen from the output groups in Tables12 and 13, the minimum safe thickness of the tunnel crossing the F10 fault fracture zone is between 6.8 m and 7.2 m, and the minimum safety thickness of the tunnel crossing the F18 fault fracture zone is between 7.1 m and 7.4 m. In the actual excavation process of the tunnel, the safety distance was taken as 10 m, and corresponding support and reinforcement measures were taken. The tunnel safely passed the F10 fault fracture zone.Table 12
Measured input group (F10).
Serial numberABCD10.91.121262020.991.11661831.11.151561041.151.131861551.051.1815620Table 13
Measured output group (F10).
y1y2y3y4y57.146.876.846.847.10In tunnel construction under drilling and blasting conditions, the calculation of the safety distance often needs to be multiplied by a safety factor greater than 1 on the basis of the theoretical value. The safety factor is 1.2, and the minimum safe rock thickness of F10 is obtained by replacing the above theoretical value with the actual value 8.5~8.9 m, which is closer to the reserved thickness of 10 m in the actual project.


## 6. Conclusions

(1)
This paper uses numerical simulation and BP neural network to obtain the minimum safe rock thickness, which provides a new idea and method for predicting the safe barrier thickness against water inrush disaster in tunnel with fault fracture zone(2)
The variation rule of minimum thickness of outburst prevention rock mass under different variables was revealed, and the influence degree of each disaster causing factor was obtained, from strong to weak, as follows: water pressure > lateral pressure coefficient > tunnel depth > width of fault fracture zone(3)
The research results are applied to the Wulaofeng Tunnel engineering, and the theoretical calculation results have a good consistency with the actual engineering results, which proves the reasonableness and feasibility of the calculation method used in the article



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