# Overall Instability Failure Mechanism and Monitoring Strategy Research of the Shallow Tunnel under Unsymmetrical Pressure during Operation Period

Authors: Hongyan Guo; Xinrong Liu; Ke Li; Zuliang Zhong
Journal: Advances in Materials Science and Engineering
 (2022)

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## Abstract

Aiming at the safety of tunnel operation, based on the investigation and statistical analysis of a large number of operating tunnel diseases, comprehensively considering the interaction between the surrounding rock and the structure, this paper establishes the failure criteria for surrounding rocks and lining materials by using numerical limit analysis and theoretical analysis methods, analyzes the overall stability and instability failure mechanism on the shallow tunnel under unsymmetrical pressure during the operation period by using the strength reduction method in light of the operation safety of the tunnel, proposes the reasonable monitoring strategy, and also constructs monitoring index system. The analysis and research results show that the tunnel structure is affected by bias pressure due to the asymmetry of the terrain. The probability of disease in the bias pressure tunnel under asymmetric terrain conditions is significantly higher than that of the general terrain. The shallow tunnel under unsymmetrical pressure has experienced three development stages from shear failure to overall instability, including rock mass fracture and sliding, structural damage, and overall instability, which can be divided into eight processes. During operation, the key monitoring indicators of surface deformation are the subsidence and deformation of the slope top and the horizontal displacement of the slope itself, followed by the monitoring of the uplift and deformation at the bottom of the slope. Meanwhile, close attention should be paid to the structural stress states in the sliding direction and perpendicular to the sliding direction of the lining structure, which demonstrates that the principal compressive stress in the sliding direction is more sensitive than the principal tensile stress in perpendicular to the sliding direction and should be listed as the key monitoring and early warning indicators of the structural stress.


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## Body

## 1. Introduction

With a large number of express highway tunnels put into use, the problems of defects in tunnel structure are prominent, the operation safety accidents occur frequently and the tunnel operation safety including driving and traffic safety and surrounding rock and structure safety has attracted extensive attention [1, 2]. This paper focuses on studying the surrounding rock and structure safety.In recent years, more and more experts and scholars have studied the operational safety of tunnel structures [3]. He [4] has built a risk prediction model for operating tunnels with a BP neural network and V/S analysis to evaluate the safety state of operating tunnels and predict their risk development trends. Chen [5] has established a set of two-level fuzzy comprehensive evaluation methods which combine the percentage quantitative and qualitative evaluation based on the “normal cloud model.” Zhang [6] has constructed the safety evaluation system of the operating tunnel with the safety classification based on the screening and identification of the factors affecting the operating tunnel safety, thus, realizing the safety state evaluation of the tunnel. Liu and Wu [7, 8] have comprehensively evaluated the health and safety state of operating tunnel structures by the Monte Carlo method and obtained the sensitive factors affecting the health and safety of operating tunnel structures through sensitivity analysis. Hu et al. [9–13] have established the evaluation system and classification standard of the structural safety grade state of highway tunnels by using the analytic hierarchy process and fuzzy principle. Wu [14] has proposed a method to calculate the safety factor of the lining cross-section by using cross-section ultimate load-bearing capacity curve on the basis of discussing the relationship between cross-section safety envelope and the ultimate load-bearing capacity curve and then evaluating the safety of lining. Judging from the current study results, most of the existing studies evaluate the safety of the tunnel structure based on the structure itself, without comprehensively considering the geological conditions of the surrounding rock. In this evaluation method, it is mostly necessary to establish the structural safety grade evaluation index system and classification standard by using the analytic hierarchy process, but not necessary to quantify the safety state and instability failure mechanism of the surrounding rock and supporting structure from the perspective of mechanics.The results of the study show that the asymmetry of the terrain causes the tunnel structure to bear the influence of bias pressure [15, 16]. The probability of disease in the biased tunnel with asymmetric terrain is significantly higher than that of the general terrain. This paper takes the shallow tunnel under unsymmetrical pressure (ratio of slope 1 : 1) as an example to comprehensively consider the interaction of surrounding rock and structure, and establish the failure standard of surrounding rock and lining materials by using numerical limit analysis and theoretical analysis methods. At the same time, this paper has analyzed the overall stability and instability failure mechanism during the operation period of the shallow tunnel under unsymmetrical pressure through the strength reduction method and proposed a reasonable monitoring strategy to provide certain guidance on structural safety monitoring, curing management decisions for the tunnel portal during the operation period of the shallow section under unsymmetrical pressure, and ensure the safety of tunnel operation.


## 2. Investigation and Analysis of Structural Defects during the Operation Period of the Shallow Tunnel

Ding et al. [17] conducted a statistical analysis on the detection results of 232 operating tunnels in Chongqing, Yunnan, Zhejiang, Qinghai, Sichuan, etc. The statistical data comes from the regular tunnel inspection report of China Merchants Chongqing Communications Technology Research & Design Institute Co., Ltd. in the last ten years. The analysis results show that the structural defects during the operation period of the tunnel mainly occur in the tunnel portal section and that the lining cracking defects are more than the structural leakage defects, as shown in Figure 1.Figure 1
Statistical analysis on development density of operating tunnel defects.In combination with the tunnel design data involved in the statistics, this paper divides the 982 tunnel portals of the statistical tunnel into 3 categories, including shallow tunnel portal, portal of shallow tunnel under unsymmetrical pressure, and general tunnel portal according to the tunnel portal topography, where the development density of each type of tunnel portal defects is shown in Figure2 and the defect development density in different parts of the lining structure of the shallow tunnel under unsymmetrical pressure is shown in Figure 3.Figure 2
Statistical analysis on defect development density at the tunnel portal.Figure 3
Statistical analysis on defect development density at the portal of shallow tunnel under unsymmetrical pressure.It can be seen from Figures2 and 3 that the probability of defects at the portal of the shallow tunnel under unsymmetrical pressure is significantly higher than that at the tunnel portal in shallow terrain and general terrain. At the same time, the defects at the portal of the shallow tunnel under unsymmetrical pressure along the potential slip surface are significantly more than those perpendicular to the potential slip direction, and the arch crown defects are the least. The vulnerability of key parts of the structure is sorted as follows: inner arch > outer side wall > outer arch > inner side wall > arch crown.


## 3. Study on Failure Standards of Tunnel Surrounding Rock and Concrete Materials

### 3.1. Study on the Failure Standard of Surrounding Rock Mass Materials

The tunnel portal section is considered as Class V1 surrounding rock and the mechanical parameters of surrounding rock are taken according to Specifications for Design of Highway Tunnels (JTG 3370.1-2018) with the following principle: take the parameter median recommended by the specification as the input parameter for calculation and analysis, as shown in Table1 for details, and numerically analyze the ultimate strain of the equivalent rock block according to the mechanical parameters of surrounding rock to obtain the ultimate strain of the equivalent rock block through numerical analysis. FLAC3D is used to simulate the uniaxial compression test of equivalent rock blocks of Grade V1 surrounding rock. The calculation model is simulated by a cube specimen with the size of 150 mm × 150 mm × 150 mm, the bottom surface is restrained, and the top surface is subjected to a vertically downward load uniformly distributed, but the top surface friction is not considered. The calculation model is shown in Figure 4. The load is increased step by step on the upper surface of the calculation model, and the displacement of the central point is monitored. When the displacement of the central point of the rock does not converge under a certain level of load, the rock will be damaged, and the strain value corresponding to the previous level of load will be taken as the ultimate strain.Table 1
Computational mechanics parameters.
Material nameElastic ratio (GPa)Poisson’s ratioDensity (kN/m3)Friction angle (°)Cohesion (MPa)Surrounding rock1.30.391800220.12Figure 4
Numerical test analysis model.The variation law for the vertical displacement of the center point of equivalent rock block under different loads is shown in Figure5. The variation law for maximum shearing strain and maximal principal stress of equivalent rock blocks under different loads is shown in Figure 6.Figure 5
Variation law for vertical displacement of the center point of equivalent rock block under different loads.Figure 6
Variation law for ultimate strain of equivalent rock block under different loads.It can be seen from Figures5 and 6 that with the increase of load, the displacement of the center point of the equivalent rock block and the maximum shearing strain increase. When the load is 0.4961 MPa, the vertical displacement of the center point of the equivalent rock block does not converge, and the equivalent rock block has a shear failure. The strain of the upper-level load (0.4960 MPa) is taken as the ultimate strain. Therefore, the ultimate shearing strain of equivalent rock block of Grade V1 surrounding rock is 1.02‰.


### 3.2. Study on the Failure Standard of Concrete Materials

The judgment standard of concrete material failure is based on the study results of Zheng Yingren [18, 19]. The elastic compressive strain and shearing strain can be derived from the Hooke formula [20]; there is no formula to calculate the plastic compressive strain and shearing strain, but the relationship between plastic shearing strain and compressive strain is known, and the elastoplastic compressive strain and shearing strain can be calculated by numerical method. In FLAC3D, When it is assumed that the three principal strains of the material are ε1, ε2, and ε3, the shearing strain is represented by J2′.(1)J2′=ε1−ε22+ε2−ε32+ε1−ε326=ε1−ε33.The ultimate strain of concrete [21] under different strengths is shown in Table 2.Table 2
Value table of the ultimate shearing strain of concrete.
Concrete strength gradeC20C25C30C35C40J2′Calculated value1.241.461.611.86(Formula (1))1.071.241.461.611.87


## 3.1. Study on the Failure Standard of Surrounding Rock Mass Materials

The tunnel portal section is considered as Class V1 surrounding rock and the mechanical parameters of surrounding rock are taken according to Specifications for Design of Highway Tunnels (JTG 3370.1-2018) with the following principle: take the parameter median recommended by the specification as the input parameter for calculation and analysis, as shown in Table1 for details, and numerically analyze the ultimate strain of the equivalent rock block according to the mechanical parameters of surrounding rock to obtain the ultimate strain of the equivalent rock block through numerical analysis. FLAC3D is used to simulate the uniaxial compression test of equivalent rock blocks of Grade V1 surrounding rock. The calculation model is simulated by a cube specimen with the size of 150 mm × 150 mm × 150 mm, the bottom surface is restrained, and the top surface is subjected to a vertically downward load uniformly distributed, but the top surface friction is not considered. The calculation model is shown in Figure 4. The load is increased step by step on the upper surface of the calculation model, and the displacement of the central point is monitored. When the displacement of the central point of the rock does not converge under a certain level of load, the rock will be damaged, and the strain value corresponding to the previous level of load will be taken as the ultimate strain.Table 1
Computational mechanics parameters.
Material nameElastic ratio (GPa)Poisson’s ratioDensity (kN/m3)Friction angle (°)Cohesion (MPa)Surrounding rock1.30.391800220.12Figure 4
Numerical test analysis model.The variation law for the vertical displacement of the center point of equivalent rock block under different loads is shown in Figure5. The variation law for maximum shearing strain and maximal principal stress of equivalent rock blocks under different loads is shown in Figure 6.Figure 5
Variation law for vertical displacement of the center point of equivalent rock block under different loads.Figure 6
Variation law for ultimate strain of equivalent rock block under different loads.It can be seen from Figures5 and 6 that with the increase of load, the displacement of the center point of the equivalent rock block and the maximum shearing strain increase. When the load is 0.4961 MPa, the vertical displacement of the center point of the equivalent rock block does not converge, and the equivalent rock block has a shear failure. The strain of the upper-level load (0.4960 MPa) is taken as the ultimate strain. Therefore, the ultimate shearing strain of equivalent rock block of Grade V1 surrounding rock is 1.02‰.


## 3.2. Study on the Failure Standard of Concrete Materials

The judgment standard of concrete material failure is based on the study results of Zheng Yingren [18, 19]. The elastic compressive strain and shearing strain can be derived from the Hooke formula [20]; there is no formula to calculate the plastic compressive strain and shearing strain, but the relationship between plastic shearing strain and compressive strain is known, and the elastoplastic compressive strain and shearing strain can be calculated by numerical method. In FLAC3D, When it is assumed that the three principal strains of the material are ε1, ε2, and ε3, the shearing strain is represented by J2′.(1)J2′=ε1−ε22+ε2−ε32+ε1−ε326=ε1−ε33.The ultimate strain of concrete [21] under different strengths is shown in Table 2.Table 2
Value table of the ultimate shearing strain of concrete.
Concrete strength gradeC20C25C30C35C40J2′Calculated value1.241.461.611.86(Formula (1))1.071.241.461.611.87


## 4. Overall Instability Failure Mechanism and Monitoring Strategy of Tunnel

### 4.1. Establishment of the Calculation Model

In this numerical simulation, FLAC3D software is used to analyze the vulnerable key parts and damage characteristics of the lining structure under the condition of a slope ratio of 1 : 1. It is assumed that all soil layers except the surface are layered and uniformly distributed, that the initial stress considers the influence of initial self-weight stress, that the formation material adopts the Mohr-Coulomb yield criterion, and that the calculation adopts a small deformation mode and the stress and strain of the stratum and materials vary within the elastoplastic range. Considering the mutual coupling between the tunnel surrounding rock and the lining, the mesh division around the tunnel and the central part is densified, and the lining is simulated by solid element (for the tunnel portal section, the lining structure of the surrounding rock section is set with inverted arch, and the lining thickness is 60 cm) during the calculation and modeling. The upper part of the model is a free boundary, the bottom, left and right boundaries are fixed boundaries, and the longitudinal dimension of the model is the length of framwork 1 concrete lining (12 m). Considering the boundary effect, the left, right and bottom parameters of the model are taken according to 3 to 5 tunnel diameters. The mathematical calculation model of the tunnel is shown in Figure7.Figure 7
Numerical analysis model.


### 4.2. Parameter Selection and Analysis Method

The mechanical parameters of the surrounding rock and lining structure are taken according to specifications for design of highway tunnels (JTG 3370.1-2018), where the mechanical parameters of surrounding rock are shown in Table1 and the calculated mechanical parameters of concrete (C30) are shown in Table 3.Table 3
Mechanical parameters of C30 concrete calculation.
Material nameElastic ratio (GPa)Poisson’s ratioDensity (kN/m3)Friction angle (°)Cohesion (MPa)Secondary lining31.50.2240061.63.9In order to fully analyze the mechanical characteristics, instability failure mode, and safety evaluation of the structure, the strength parameters of the surrounding rock are continuously reduced under the condition of keeping the mechanical parameters of the lining structure unchanged in this calculation and analysis, and the surrounding rock stability state and instability failure mode are analyzed through the ultimate strain of the surrounding rock (1.02∗ 10−3). Besides, the structural safety state, vulnerable key parts, damage characteristics, and instability failure mode of the structure are analyzed through the ultimate strain (1.46 ∗ 10−3) distribution law of the lining concrete (C30). When the shearing strain of the unit reaches the ultimate shearing strain; that is, the unit has a shear failure. When multiple units have shear failure; that is, a failure area is formed, and when the failure area of a certain part is connected, it can be considered that the surrounding rock or lining structure is in a local instability state, and the displacement indexes in different states, and the mechanical characteristic indexes of typical structures are extracted for analysis.


### 4.3. Ultimate Strain Analysis

The ultimate strain cloud diagram of the surrounding rock and lining structure under different reduction coefficients is shown in Figures8 and 9, respectively, and the cloud diagram only shows the area that reaches the ultimate strain value, as shown in Figure 8.Figure 8
Ultimate strain cloud diagram of surrounding rock under different reduction coefficients.Figure 9
Ultimate strain cloud diagram of lining structure under different reduction coefficients.It can be seen from Figure8 that when the reduction coefficient is equal to 1.50, the surrounding rock mass at the left side wall and arch crown of the tunnel first shows shear failure; when the reduction coefficient is equal to 1.65, the existing shear failure area gradually increases, and the surrounding rock mass at the right side wall begins to show shear failure. At this stage, the shear failure is distributed in a point shape along the potential slip surface; when the reduction coefficient is equal to 1.85, the shear failure area at the left and right side walls of the tunnel is gradually connected, and the shape of the potential slip surface has been shown. With the increasing reduction coefficient, the shear failure area at the potential slip surface continues to increase and gradually extends to the slope top. When the reduction coefficient is equal to 1.94, the shear failure area reaches the slope top, and the shear failure area at the potential slip surface is connected. However, the calculation results show that when the reduction coefficient is greater than 1.94, the shear failure area is separated due to the existence of a lining structure, the slope does not converge as it is not unstable, and the side slope slip risk is reduced due to the action of the lining structure. When the reduction coefficient is equal to 1.946, the shear failure area runs through the whole slope and reaches the limit state of instability; when the reduction coefficient is equal to 1.947, the calculation does not converge. Therefore, the stability state of the shallow tunnel under unsymmetrical pressure shall be comprehensively judged in combination with the ultimate strain state of the lining structure.It can be seen from Figure9 that when the reduction coefficient is equal to 1.85, the area where the outer surface of the lining structure is in contact with the shear failure area of the surrounding rock first enters the shear failure state; when the reduction coefficient is equal to 1.91, the shear failure begins to show at the left arch springing of the lining structure, and develops toward the direction of depth and width with the increase of the reduction coefficient; when the reduction coefficient is equal to 1.94, the shear failure begins to show on the inner surface of the left hance of the tunnel lining structure and develops toward the direction of depth and width with the increase of the reduction coefficient; when the reduction coefficient is equal to 1.945, the shear failure area of the lining structure continues to increase, and the shear failure area at the left arch springing is connected, resulting in a movable hinge connection; when the reduction coefficient is equal to 1.946, the shear failure areas at the 4 key parts of the tunnel lining structure, left and right hance and left and right arch springing become a movable hinge connection, and the tunnel lining structure is in an unstable critical state; and when the reduction coefficient is equal to 1.947, the calculation does not converge.Based on the above, the shallow tunnel under unsymmetrical pressure has mainly experienced 3 development stages from a stable state to instability, including rock mass fracture and slip, structural damage failure, and overall instability failure, which can be subdivided into 8 processes, as shown in Figure10. From the perspective of overall stability, the stability safety factor of the shallow tunnel under unsymmetrical pressure during the operation period is 1.945 under the condition of a slope ratio of 1 : 1. It is suggested that the key parts to be monitored are 4 key points, including the left and right arch springing and left and right hance of the tunnel.Figure 10
Progressive instability failure process of the shallow tunnel under unsymmetrical pressure.


### 4.4. Displacement Analysis of Surrounding Rock

The slope displacement cloud diagram and moving direction under different reduction coefficients are shown in Figure11; the distribution laws of surface settlement and horizontal displacement under different reduction coefficients are shown in Figures 12 and 13, respectively.Figure 11
Displacement cloud diagram of the tunnel slope and its moving direction.Figure 12
Distribution law of tunnel surface settlement.Figure 13
Distribution law of the horizontal displacement of the tunnel surface.It can be seen from Figures11 to 13 that during the operation stage of the shallow tunnel under unsymmetrical pressure, the slope slip failure is different from the conventional slope slip. Due to the anti-slip effect of the tunnel structure, the slope slip failure part moves upward and appears in the outer arch of tunnel structure, which is about 1/4 of the slope height. In terms of vertical displacement, the maximum value of surface settlement appears at the edge of slope top, the maximum ground uplift occurs at the edge of the slope toe, and the reverse bending point of surface vertical displacement occurs at 1/3H to 1/2H of the slope height; in terms of horizontal displacement, the surrounding rock moves to the outside of the slope as a whole, and the maximum horizontal displacement occurs in a certain area above the tunnel arch. In order to facilitate comparative analysis, the characteristic values of slope deformation (the maximum and minimum values of vertical displacement and the maximum value of horizontal displacement) are extracted, and their variation law with reduction coefficient is drawn, as shown in Figure 14.Figure 14
Variation law for slope deformation characteristic value with reduction coefficient.It can be seen from Figure14 that the comparison is as follows: the maximum horizontal displacement of the slope toe > the maximum surface settlement at the slope top > the maximum ground uplift of the slope toe; that is, during the operation stage of the shallow tunnel under unsymmetrical pressure, the horizontal displacement of the slope toe and the vertical settlement of the slope top caused by the outward slip of the slope body are the main ones, and the horizontal displacement of the slope toe and the vertical settlement of the slope top are much larger than the uplift of the slope toe. At the same time, with the increase of reduction coefficient, the three displacement characteristic values also increase gradually, and the growth rate is also increasing. The increase of uplift displacement at the slope toe is relatively slow; that is, the reduction of surrounding rock strength has little effect on the uplift deformation of arch springing. When the reduction coefficient is 1.94, the three displacement indexes show a certain surging sudden change. Combined with the comparative analysis of Figures 8 and 9, the shear failure area of surrounding rock is connected, and the shear failure area of the left arch springing of lining is connected; that is, the failure of the lining structure will accelerate the instability failure of surrounding rock. Therefore, for the shallow tunnel under unsymmetrical pressure, the key observation indexes of surface deformation during operation include settlement deformation of the slope top and horizontal displacement of slope toe, followed by uplift deformation monitoring of the slope toe.


### 4.5. Displacement Analysis of the Lining Structure

The displacement cloud diagram and deformation shape of the tunnel lining structure under different reduction coefficients are shown in Figure15. The variation law for typical characteristic values of tunnel structural displacement (maximum structural settlement displacement, maximum structural uplift displacement, and maximum structural horizontal displacement) with reduction coefficient is shown in Figure 16.Figure 15
Displacement cloud diagram and deformation shape of the tunnel lining structure.Figure 16
Variation law for displacement characteristic value of tunnel lining structure with Reduction Coefficient.It can be seen from Figures15 and 16 that the deformation direction of the tunnel structure displacement is consistent with the slope slip direction. The displacement of the outer hance position is the largest, the comparison is as follows: the maximum horizontal displacement of the structure > the maximum structural settlement > the maximum structural uplift, and the horizontal displacement of the structure is much greater than the vertical displacement of the structure; that is, during the operation stage of the shallow tunnel under unsymmetrical pressure, the structure mainly moves horizontally outward, of which the horizontal displacement of the structure is mainly affected by the horizontal movement of the surrounding rock and moves together with the surrounding rock, while the vertical displacement is dominated with the deformation of the structure itself. At the same time, with the increase of the reduction coefficient, the three displacement characteristic values also gradually increase. With the increase of the reduction coefficient, the growth rate of the horizontal displacement of the structure is also increasing, while the growth rate of the vertical displacement of the structure is relatively slow. In addition, it is not difficult to find from Figure 16 that when the reduction coefficient is 1.94, the three displacement indexes show a certain surging sudden change. Combined with the comparative analysis of Figures 8 and 9, the shear failure area of surrounding rock is connected, the shear failure area of the left arch springing of the lining is connected, the structural deformation is accelerated, and the risk of structural instability failure is increased.


### 4.6. Stress Analysis of Lining Structure

The cloud diagram of the maximum vertical principal tensile stress and maximum principal compressive stress of the lining under different reduction coefficients is shown in Figure17. The variation law for typical characteristic values of tunnel structure stress (maximum principal tensile stress and maximum principal compressive stress of structure) with reduction coefficient is shown in Figure 17.Figure 17
Maximum principal stress cloud diagram of the tunnel lining structure.It can be seen from Figure17 that the maximum principal tensile stress of the tunnel structure is mainly distributed in the slip direction and concentrated in the middle of the inverted arch, the outer sidewall, and the inner hance. The principal compressive stresses of the structure are mainly distributed in the direction perpendicular to the slip direction and concentrated on the outer hance and inner sidewalls. The maximum principal stress area gradually expands with the increase of the reduction coefficient and gradually moves to the deepest part of the lining structure. It can be seen from Figure 18 that the maximum principal tensile stress of the lining structure increases slowly with the increase of reduction coefficient, while the maximum principal compressive stress of the lining structure increases with the increase of the reduction coefficient, and the growth rate is fast, which increases approximately exponentially; the maximum principal tensile stress of the tunnel is about 2.19 MPa, and the maximum principal compressive stress value is 24.2 MPa when the overall instability of the tunnel occurs. The principal compressive stress of the structure surface perpendicular to the slip direction is more sensitive than the principal tensile stress during the overall instability failure of the tunnel and can be used as the main monitoring and early warning index of structural stress.Figure 18
Variation law for the maximum principal stress of the tunnel structure with reduction coefficient.Based on the above analysis, the operation safety monitoring index system of the shallow tunnel under unsymmetrical pressure is constructed, as shown in Figure19.Figure 19
Monitoring index system.


## 4.1. Establishment of the Calculation Model

In this numerical simulation, FLAC3D software is used to analyze the vulnerable key parts and damage characteristics of the lining structure under the condition of a slope ratio of 1 : 1. It is assumed that all soil layers except the surface are layered and uniformly distributed, that the initial stress considers the influence of initial self-weight stress, that the formation material adopts the Mohr-Coulomb yield criterion, and that the calculation adopts a small deformation mode and the stress and strain of the stratum and materials vary within the elastoplastic range. Considering the mutual coupling between the tunnel surrounding rock and the lining, the mesh division around the tunnel and the central part is densified, and the lining is simulated by solid element (for the tunnel portal section, the lining structure of the surrounding rock section is set with inverted arch, and the lining thickness is 60 cm) during the calculation and modeling. The upper part of the model is a free boundary, the bottom, left and right boundaries are fixed boundaries, and the longitudinal dimension of the model is the length of framwork 1 concrete lining (12 m). Considering the boundary effect, the left, right and bottom parameters of the model are taken according to 3 to 5 tunnel diameters. The mathematical calculation model of the tunnel is shown in Figure7.Figure 7
Numerical analysis model.


## 4.2. Parameter Selection and Analysis Method

The mechanical parameters of the surrounding rock and lining structure are taken according to specifications for design of highway tunnels (JTG 3370.1-2018), where the mechanical parameters of surrounding rock are shown in Table1 and the calculated mechanical parameters of concrete (C30) are shown in Table 3.Table 3
Mechanical parameters of C30 concrete calculation.
Material nameElastic ratio (GPa)Poisson’s ratioDensity (kN/m3)Friction angle (°)Cohesion (MPa)Secondary lining31.50.2240061.63.9In order to fully analyze the mechanical characteristics, instability failure mode, and safety evaluation of the structure, the strength parameters of the surrounding rock are continuously reduced under the condition of keeping the mechanical parameters of the lining structure unchanged in this calculation and analysis, and the surrounding rock stability state and instability failure mode are analyzed through the ultimate strain of the surrounding rock (1.02∗ 10−3). Besides, the structural safety state, vulnerable key parts, damage characteristics, and instability failure mode of the structure are analyzed through the ultimate strain (1.46 ∗ 10−3) distribution law of the lining concrete (C30). When the shearing strain of the unit reaches the ultimate shearing strain; that is, the unit has a shear failure. When multiple units have shear failure; that is, a failure area is formed, and when the failure area of a certain part is connected, it can be considered that the surrounding rock or lining structure is in a local instability state, and the displacement indexes in different states, and the mechanical characteristic indexes of typical structures are extracted for analysis.


## 4.3. Ultimate Strain Analysis

The ultimate strain cloud diagram of the surrounding rock and lining structure under different reduction coefficients is shown in Figures8 and 9, respectively, and the cloud diagram only shows the area that reaches the ultimate strain value, as shown in Figure 8.Figure 8
Ultimate strain cloud diagram of surrounding rock under different reduction coefficients.Figure 9
Ultimate strain cloud diagram of lining structure under different reduction coefficients.It can be seen from Figure8 that when the reduction coefficient is equal to 1.50, the surrounding rock mass at the left side wall and arch crown of the tunnel first shows shear failure; when the reduction coefficient is equal to 1.65, the existing shear failure area gradually increases, and the surrounding rock mass at the right side wall begins to show shear failure. At this stage, the shear failure is distributed in a point shape along the potential slip surface; when the reduction coefficient is equal to 1.85, the shear failure area at the left and right side walls of the tunnel is gradually connected, and the shape of the potential slip surface has been shown. With the increasing reduction coefficient, the shear failure area at the potential slip surface continues to increase and gradually extends to the slope top. When the reduction coefficient is equal to 1.94, the shear failure area reaches the slope top, and the shear failure area at the potential slip surface is connected. However, the calculation results show that when the reduction coefficient is greater than 1.94, the shear failure area is separated due to the existence of a lining structure, the slope does not converge as it is not unstable, and the side slope slip risk is reduced due to the action of the lining structure. When the reduction coefficient is equal to 1.946, the shear failure area runs through the whole slope and reaches the limit state of instability; when the reduction coefficient is equal to 1.947, the calculation does not converge. Therefore, the stability state of the shallow tunnel under unsymmetrical pressure shall be comprehensively judged in combination with the ultimate strain state of the lining structure.It can be seen from Figure9 that when the reduction coefficient is equal to 1.85, the area where the outer surface of the lining structure is in contact with the shear failure area of the surrounding rock first enters the shear failure state; when the reduction coefficient is equal to 1.91, the shear failure begins to show at the left arch springing of the lining structure, and develops toward the direction of depth and width with the increase of the reduction coefficient; when the reduction coefficient is equal to 1.94, the shear failure begins to show on the inner surface of the left hance of the tunnel lining structure and develops toward the direction of depth and width with the increase of the reduction coefficient; when the reduction coefficient is equal to 1.945, the shear failure area of the lining structure continues to increase, and the shear failure area at the left arch springing is connected, resulting in a movable hinge connection; when the reduction coefficient is equal to 1.946, the shear failure areas at the 4 key parts of the tunnel lining structure, left and right hance and left and right arch springing become a movable hinge connection, and the tunnel lining structure is in an unstable critical state; and when the reduction coefficient is equal to 1.947, the calculation does not converge.Based on the above, the shallow tunnel under unsymmetrical pressure has mainly experienced 3 development stages from a stable state to instability, including rock mass fracture and slip, structural damage failure, and overall instability failure, which can be subdivided into 8 processes, as shown in Figure10. From the perspective of overall stability, the stability safety factor of the shallow tunnel under unsymmetrical pressure during the operation period is 1.945 under the condition of a slope ratio of 1 : 1. It is suggested that the key parts to be monitored are 4 key points, including the left and right arch springing and left and right hance of the tunnel.Figure 10
Progressive instability failure process of the shallow tunnel under unsymmetrical pressure.


## 4.4. Displacement Analysis of Surrounding Rock

The slope displacement cloud diagram and moving direction under different reduction coefficients are shown in Figure11; the distribution laws of surface settlement and horizontal displacement under different reduction coefficients are shown in Figures 12 and 13, respectively.Figure 11
Displacement cloud diagram of the tunnel slope and its moving direction.Figure 12
Distribution law of tunnel surface settlement.Figure 13
Distribution law of the horizontal displacement of the tunnel surface.It can be seen from Figures11 to 13 that during the operation stage of the shallow tunnel under unsymmetrical pressure, the slope slip failure is different from the conventional slope slip. Due to the anti-slip effect of the tunnel structure, the slope slip failure part moves upward and appears in the outer arch of tunnel structure, which is about 1/4 of the slope height. In terms of vertical displacement, the maximum value of surface settlement appears at the edge of slope top, the maximum ground uplift occurs at the edge of the slope toe, and the reverse bending point of surface vertical displacement occurs at 1/3H to 1/2H of the slope height; in terms of horizontal displacement, the surrounding rock moves to the outside of the slope as a whole, and the maximum horizontal displacement occurs in a certain area above the tunnel arch. In order to facilitate comparative analysis, the characteristic values of slope deformation (the maximum and minimum values of vertical displacement and the maximum value of horizontal displacement) are extracted, and their variation law with reduction coefficient is drawn, as shown in Figure 14.Figure 14
Variation law for slope deformation characteristic value with reduction coefficient.It can be seen from Figure14 that the comparison is as follows: the maximum horizontal displacement of the slope toe > the maximum surface settlement at the slope top > the maximum ground uplift of the slope toe; that is, during the operation stage of the shallow tunnel under unsymmetrical pressure, the horizontal displacement of the slope toe and the vertical settlement of the slope top caused by the outward slip of the slope body are the main ones, and the horizontal displacement of the slope toe and the vertical settlement of the slope top are much larger than the uplift of the slope toe. At the same time, with the increase of reduction coefficient, the three displacement characteristic values also increase gradually, and the growth rate is also increasing. The increase of uplift displacement at the slope toe is relatively slow; that is, the reduction of surrounding rock strength has little effect on the uplift deformation of arch springing. When the reduction coefficient is 1.94, the three displacement indexes show a certain surging sudden change. Combined with the comparative analysis of Figures 8 and 9, the shear failure area of surrounding rock is connected, and the shear failure area of the left arch springing of lining is connected; that is, the failure of the lining structure will accelerate the instability failure of surrounding rock. Therefore, for the shallow tunnel under unsymmetrical pressure, the key observation indexes of surface deformation during operation include settlement deformation of the slope top and horizontal displacement of slope toe, followed by uplift deformation monitoring of the slope toe.


## 4.5. Displacement Analysis of the Lining Structure

The displacement cloud diagram and deformation shape of the tunnel lining structure under different reduction coefficients are shown in Figure15. The variation law for typical characteristic values of tunnel structural displacement (maximum structural settlement displacement, maximum structural uplift displacement, and maximum structural horizontal displacement) with reduction coefficient is shown in Figure 16.Figure 15
Displacement cloud diagram and deformation shape of the tunnel lining structure.Figure 16
Variation law for displacement characteristic value of tunnel lining structure with Reduction Coefficient.It can be seen from Figures15 and 16 that the deformation direction of the tunnel structure displacement is consistent with the slope slip direction. The displacement of the outer hance position is the largest, the comparison is as follows: the maximum horizontal displacement of the structure > the maximum structural settlement > the maximum structural uplift, and the horizontal displacement of the structure is much greater than the vertical displacement of the structure; that is, during the operation stage of the shallow tunnel under unsymmetrical pressure, the structure mainly moves horizontally outward, of which the horizontal displacement of the structure is mainly affected by the horizontal movement of the surrounding rock and moves together with the surrounding rock, while the vertical displacement is dominated with the deformation of the structure itself. At the same time, with the increase of the reduction coefficient, the three displacement characteristic values also gradually increase. With the increase of the reduction coefficient, the growth rate of the horizontal displacement of the structure is also increasing, while the growth rate of the vertical displacement of the structure is relatively slow. In addition, it is not difficult to find from Figure 16 that when the reduction coefficient is 1.94, the three displacement indexes show a certain surging sudden change. Combined with the comparative analysis of Figures 8 and 9, the shear failure area of surrounding rock is connected, the shear failure area of the left arch springing of the lining is connected, the structural deformation is accelerated, and the risk of structural instability failure is increased.


## 4.6. Stress Analysis of Lining Structure

The cloud diagram of the maximum vertical principal tensile stress and maximum principal compressive stress of the lining under different reduction coefficients is shown in Figure17. The variation law for typical characteristic values of tunnel structure stress (maximum principal tensile stress and maximum principal compressive stress of structure) with reduction coefficient is shown in Figure 17.Figure 17
Maximum principal stress cloud diagram of the tunnel lining structure.It can be seen from Figure17 that the maximum principal tensile stress of the tunnel structure is mainly distributed in the slip direction and concentrated in the middle of the inverted arch, the outer sidewall, and the inner hance. The principal compressive stresses of the structure are mainly distributed in the direction perpendicular to the slip direction and concentrated on the outer hance and inner sidewalls. The maximum principal stress area gradually expands with the increase of the reduction coefficient and gradually moves to the deepest part of the lining structure. It can be seen from Figure 18 that the maximum principal tensile stress of the lining structure increases slowly with the increase of reduction coefficient, while the maximum principal compressive stress of the lining structure increases with the increase of the reduction coefficient, and the growth rate is fast, which increases approximately exponentially; the maximum principal tensile stress of the tunnel is about 2.19 MPa, and the maximum principal compressive stress value is 24.2 MPa when the overall instability of the tunnel occurs. The principal compressive stress of the structure surface perpendicular to the slip direction is more sensitive than the principal tensile stress during the overall instability failure of the tunnel and can be used as the main monitoring and early warning index of structural stress.Figure 18
Variation law for the maximum principal stress of the tunnel structure with reduction coefficient.Based on the above analysis, the operation safety monitoring index system of the shallow tunnel under unsymmetrical pressure is constructed, as shown in Figure19.Figure 19
Monitoring index system.


## 5. Analysis of Typical Engineering Cases

In order to verify the reliability of this study’s conclusion, this paper investigates and analyzes the operation instability case of the shallow tunnel under unsymmetrical pressure in Fengjie County, Chongqing. The tunnel portal is in a typical shallow and unsymmetrical pressure terrain, and the side slope rate is about 1 : 1. At about 11 : 50 p.m. on July 2, 2016, a sudden rainstorm caused a landslide at the tunnel portal, as shown in Figure20.Figure 20
Overall instability failure case of a tunnel portal in Chongqing.The monitoring data of this section before and after the rainstorm are extracted from the tunnel health monitoring system, there are monitoring points for surface settlement deformation at the side slope top of the tunnel portal. The monitoring data of slope surface settlement deformation before and after the rainstorm are collected for analysis. The vertical deformation of the slope with time at different measuring points is shown in the figure below.It can be seen from Figure21 that under the action of rainstorm infiltration, the surface settlement deformation of the slope at the tunnel portal has experienced 3 stages, including slow and steady growth of deformation (about 12 hours), false stability of deformation (about 6 hours), and sharp increase of deformation, which indirectly reflects the 3 stages of instability failure at the portal of the shallow tunnel under unsymmetrical pressure: ① rock mass fracture and slip; ② structural damage failure; ③ overall instability failures. This is consistent with the previous argument. After analyzing the reason, it can be found that the strength of the overlying rock mass of the tunnel is further reduced due to the infiltration of rainstorm surface water; that is, the cohesion and angle of internal friction of the rock mass are reduced (equivalent to the strength reduction process in the theoretical analysis). When the strength is reduced to the failure limit state, the rock mass will have instability failure; that is, the rock mass fracture and slip stage; with the slip of the rock mass, the external load acting on the tunnel lining structure gradually increases. When the slip force of the rock mass exceeds the load-bearing capacity of the structure, the structure will have instability failure, that is, the structural failure stage. At this stage, because the failure of the lining structure is a brittle failure, the displacement generated in this process is small, and there will be an illusion of deformation stability; with the complete loss of structural load-bearing capacity, the overall instability failure of the surrounding rock and structure will be finally formed. The failure phenomenon and mechanism of the engineering case are basically consistent with the above analysis results, which further verifies the reliability and rationality of the above analysis.Figure 21
Observation of surface settlement deformation of tunnel portal slope.


## 6. Conclusion

Through the statistical analysis of tunnel defect data, numerical limit analysis, and comparative analysis of engineering cases, this paper analyzes the instability failure mechanism, stability evaluation, key vulnerable parts of the structure, damage development law, and key monitoring indexes of the shallow tunnel under unsymmetrical pressure during the operation period, and mainly obtains the following conclusions.(1)
During the tunnel operation period, structural defects mainly occur at the tunnel portal section. The probability of defects at the portal of the shallow tunnel under unsymmetrical pressure is significantly higher than that at the tunnel portal in general terrain. At the same time, the defects at the portal of the shallow tunnel under unsymmetrical pressure along the potential slip surface are significantly more than those perpendicular to the potential slip direction. The vulnerability of key parts of the structure is sorted as follows: inner arch > outer side wall > outer arch > inner side wall > arch crown.(2)
The shallow tunnel under unsymmetrical pressure has mainly experienced 3 development stages from stable state to instability, including rock mass fracture and slip, structural damage failure, and overall instability failure, which can be subdivided into 8 processes.(3)
The key observation indexes for surface deformation of the shallow tunnel under unsymmetrical pressures during operation include slope top settlement deformation and horizontal displacement of the slope, followed by monitoring of the uplift deformation of the slope toe. At the same time, the stress state of lining structure in the slip direction and perpendicular to the slip direction should be paid more attention. As the principal compressive stress in the slip direction is more sensitive to the principal tensile stress perpendicular to the slip direction, it shall be used as the key monitoring and early warning index of the structural stress.(4)
The study conclusion of this paper has been verified in some engineering cases, so the conclusion has certain reliability and rationality and can be used for similar projects for reference. However, due to the complexity of engineering geologic conditions, the conclusion cannot include all the actual engineering conditions but requires the verification and optimization of a large number of similar projects before being used to further guide the followup engineering practice.



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*Source: 3105787-2022-05-16.xml*