Keywords

1 Introduction

In case of sudden change of rock mass grade during the construction of tunnel and other underground projects, instability collapse, water and mud inrush and other accidents are very easy to occur due to the influence of surface water and groundwater seepage, which pose a huge threat to construction safety and the surrounding environment, and adversely affect the development of tunnel construction [1]. Therefore, it is of great significance to analyze the stability during tunnel construction. Some experts and scholars have carried out relevant research. For example, Shiau, Junping et al. studied the minimum bearing pressure required for the stability of the double circular tunnel through finite element numerical calculation [2]; Xiongyu Hu et al. studied the influence of the relative depth of the tunnel and the density of granular soil on the stability and collapse mechanism of shallow tunnels by using the discrete element method (DEM) [3]. Jinjie Zhou et al. analyzed the influence of groundwater seepage on surface settlement in the shallow underground excavation section of the north entrance of Hangzhou Zizhi Tunnel by combining on-site monitoring data analysis with numerical simulation [4]; Liyuan Wei et al. conducted model tests on Qingdao Jiaozhou Bay undersea tunnel, and obtained the variation rules of seepage field and displacement field values [5]; Kezhong Wang et al. conducted finite element analysis on the Rizhao Shushui East Diversion Tunnel Project, and obtained the surrounding rock pore water pressure and deformation law [6]; Xumei Du et al. analyzed the stability of surrounding rock excavation of the Jiangmen Tunnel from Guangzhou to ZhuHai by using 3D numerical simulation, and obtained effective reinforcement measures [7]; Fenglin Li et al. used the finite difference method to conduct numerical simulation on the SiJiaZhai small spacing tunnel project of Guizhou Panxing Expressway, and obtained the change law of the tunnel excavation displacement field under Grade V surrounding rock [8]; Yanchun Li et al. obtained the distribution characteristics of seepage field, stress field and displacement field of surrounding rock of the water rich fracture zone project of Liangshan Tunnel in Zhangzhou, Fujian Province through simulation analysis [9].

Scholars at home and abroad have summarized the laws of pore water pressure, stress and deformation of surrounding rock of underground projects in different construction strata and different calculation methods, but there is little research on the stability of surrounding rock during excavation through the sudden change area of rock mass grade under the fluid solid coupling effect of shallow tunnel. In this paper, based on the change of seepage field, stress field and displacement field of tunnel surrounding rock, COMSOL Multiphysics software is used to conduct fluid structure coupling simulation analysis on the construction process of shallow tunnel.

2 Fluid Structure Coupling Equation

2.1 Seepage Field Equation

Based on Biot’s consolidation theory, the governing differential equation corresponding to fluid structure coupling can be expressed by Darcy's law of fluid motion. We simplify the groundwater seepage mode into laminar flow, and Darcy’s law is:

$$ q_{i} = - k\frac{\partial }{\partial x}\left( {p - \rho gx} \right) $$
(1)

In the formula, \(q_{i}\) refers to seepage velocity vector, \(k\) refers to permeability coefficient of medium, \(p\) refers to pore water pressure, \(\rho\) refers to liquid density, \(g\) refers to gravity acceleration component.

For the convenience of calculation, the rock soil layer can be regarded as a porous elastic medium. According to the principle of seepage mechanics, the seepage field control equation is [10]:

$$ \nabla \cdot - \frac{{k_{m} }}{u} \cdot \left( {\nabla p - \rho g} \right) + \left( {\frac{\alpha - \phi }{{k_{s} }} + \frac{\phi }{{k_{i} }}} \right)\frac{\partial p}{{\partial t}} + \alpha \frac{\partial \varepsilon }{{\partial t}} = q_{m} $$
(2)

In the formula, \(k_{m}\) is the permeability of porous media, \(\alpha\) is the Biot coefficient, \(\phi\) is the porosity of porous media, \(\varepsilon\) is the strain component, \(q_{m}\) is the sink term of the fluid.

The change of volume strain will cause the change of fluid pore pressure, on the contrary, the fluctuation of pore pressure will also cause the occurrence of volume strain [11]. The constitutive equation of porous elastic medium is:

$$ \Delta \sigma_{ij} + \alpha \Delta p\delta_{ij} = {\rm H}_{ij} \left( {\sigma_{ij} ,\Delta \xi_{i,j} } \right) $$
(3)

In the formula, \(\Delta \sigma_{ij}\) is the stress variation, \(\Delta p\) is the change of pore water pressure; \(\delta_{ij}\) is Kronecher factor, \({\rm H}_{ij}\) is a given function, \(\Delta \xi_{i,j}\) is the total strain.

2.2 Stress Field Equation

The control equation of porous elastic material model is:

$$ - \nabla \cdot \sigma = \rho g $$
(4)

In the formula, \(\sigma\) is the stress tensor, \(\rho\) is the density of liquid, \(g\) and is the acceleration of gravity.

The displacement boundary condition is expressed as:

$$ u| = u_{l} $$
(5)

In the formula, \(u_{l}\) is the displacement at the boundary.

The stress boundary condition is expressed as:

$$ \sigma_{ij} \cdot n_{j} | = T_{i} $$
(6)

In the formula, \(n_{j}\) is the cosine of the angle between the stress and the normal of the projection plane. \(T_{i}\) is the surface force on the boundary.

The displacement and velocity of rock mass particle at the initial time (any selected time) are respectively expressed as:

$$ u|_{t = 0} = u_{i} $$
(7)
$$ \frac{\partial u}{{\partial t_{i} }}|_{t = 0} = v_{i} $$
(8)

In the formula, \(u_{i}\) is the displacement of rock mass particle when t = 0, \(v_{i}\) is the velocity of rock mass particle when t = 0.

3 Project Overview

Taking the Er-Jia-Gou Reservoir headrace tunnel in Harbin as an example, the headrace tunnel has a total length of 2410 m, a bottom width of 4.0 m, a tunnel height of 4.0 m, and a tunnel cross section in the shape of a city gate [12]. According to the actual project plan, the buried depth of the tunnel top in some tunnel sections is 15 m, and the surface passing by is partly mountain platform. The lithology of this part of rock is strong and weak coarse-grained granite, and the rock is relatively soft. The rock mass is saturated due to long-term farming and rainwater immersion [13]. According to the construction records, when the headrace tunnel was excavated to 0+628, serious water seepage occurred in the top arch, accompanied by large area of rock collapse.

4 Numerical Simulation Analysis

4.1 Model Establishment and Calculation Scheme

In this paper, COMSOL software is used to simulate and analyze the excavation section of the headrace tunnel, study the stability of surrounding rock in the sudden change area of rock mass grade during shallow tunnel construction, and find out the influence range of the sudden change area. According to the tunnel design, the width of the tunnel bottom is 4.0 m, the tunnel height is 4.0 m, the burial depth (the distance between the tunnel top and the ground) is 15 m, the portal is in the form of a city gate, and the calculation range of the model is set as 40 m × 40 m × 60 m. The tunnel simulation model is shown in Fig. 1, in which 0–60 m, 100–160 m are ordinary areas, and 60–100 m are sudden change areas of rock mass grade. The working condition settings are shown in Table 1, of which working condition 2 is the control group. See Table 2 for physical and mechanical parameters of rock mass.

Fig. 1
A 3-dimensional cubical design of a channel with its respective length, breadth, and height scales. There are patterns on the whole channel.

Simulation model of a 15 m deep tunnel

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Table 1 Working condition setting
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Table 2 Physical and mechanical parameters of rock mass
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4.2 Assumptions for Numerical Calculation

  1. (1)

    The initial pore water pressure before tunnel excavation is equal to the hydrostatic pressure in the rock mass.

  2. (2)

    Groundwater flow meets Darcy’s law before and after excavation.

  3. (3)

    Rock mass is a homogeneous and isotropic equivalent continuous permeable medium.

  4. (4)

    The initial stress field of rock mass is calculated according to the dead weight of rock mass.

  5. (5)

    The influence of support is not considered.

4.3 Boundary Condition

  1. (1)

    The horizontal displacement is limited around the tunnel model, which is set as roller support constraint, and fixed constraint is set at the bottom.

  2. (2)

    The upper surface of the model is the ground, which is set as the free boundary together with the excavation section.

  3. (3)

    The upper surface of the model and the face of the tunnel are in direct contact with the air, and the pore water pressure is set to zero.

  4. (4)

    To prevent groundwater from flowing around, the model is set with water storage mode and no flow boundary around and at the bottom.

5 Result Analysis

The tunnel is excavated in full section. In order to facilitate analysis, a monitoring section is set up at 5 m behind the tunnel face to study the pore water pressure, stress and vertical displacement variation of the monitoring section during the construction of the tunnel with a buried depth of 15 m. The COMSOL steady state mode is selected for numerical calculation.

5.1 Change of Seepage Field

Pore water pressure data is measured at 5 m from the monitoring section of the tunnel to the left arch waist. This location is selected as the research object to calculate the distribution law of pore water pressure under different working conditions. It can be seen from Fig. 2 that the distribution law of pore water pressure curve under working condition 1 and 3 is basically consistent. At a distance of 20 m from the abrupt change area, the pore water pressure under working condition 1 and 3 has a sudden change, which is greatly reduced after entering the abrupt change area of rock mass grade. It can be seen from the comparison of data under working conditions 1 and 3 that the higher the rock mass grade in the abrupt change area, the greater the amplitude of pore water pressure fluctuation during construction.

Fig. 2
A graph of pore water pressure at 5 meters of left arch waist versus propulsion distance. Beginning at about 75 kilopascals, 3 decreasing curves form an erratic pattern until they cross each other at a position of 120 meters. All data is approximated.

Distribution of pore water pressure at the research location of the monitoring section with a buried depth of 15 m

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Figure 3 shows the dynamic distribution of the pore water pressure of Y–Z monitoring section under different driving distances under working condition 3. The initial pore water pressure of surrounding rock before excavation is layered and increases with the depth from top to bottom. After excavation, the pore water pressure inside the tunnel is zero, forming a certain pressure difference with the pore water pressure outside the tunnel, causing the balance of the original seepage field to be broken, and finally forming a low pressure area similar to a funnel around the tunnel.

Fig. 3
4 color saturation maps for undrilled, excavation advancement at 40, 60, and 80 meters, respectively. A small dome-shaped point is at the center of each excavation advancement map.

Dynamic change of pore water pressure of monitoring section under working condition 3

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When the tunnel excavation is advanced to the sudden change area, the maximum pore water pressure at the research location of the monitoring section is reduced from 74.7 to 56.2 kPa, a decrease of 24.8%. Under the effect of pressure difference, groundwater is easy to penetrate into the tunnel, causing softening of surrounding rock and stress reduction. Therefore, in the actual construction process, grouting and plugging shall be carried out in time at the leakage location to prevent water inrush and mud leakage. For micropores that cannot be grouted, two layers of waterproof coating can be applied for plugging.

5.2 Change of Stress Field

It can be seen from Fig. 4 that the distribution law of stress curve under working condition 1 and 3 is similar, and the stress of surrounding rock is affected and gradually concentrated at the place 20 m away from the fracture zone when the tunnel is excavated. With the sudden change of rock mass grade, the first principal stress of the tunnel surrounding rock monitoring section under working condition 1 and 3 decreases by 47% and 24% respectively. It can be seen from the data analysis under working conditions 1 and 3 that the higher the rock mass grade in the mutation area, the more frequent the stress mutation.

Fig. 4
A graph of the maximum value of the first principal stress versus propulsion distance. The line for project situation 2 is parallel to the x-axis. The line for project situations 1 and 3 dips at 60 meters, increases quickly at 100 meters, and then crosses over with other lines.

Distribution of the first principal stress in the monitoring section of the 15 m deep tunnel

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Figure 5 is the dynamic diagram of the first principal stress of the monitoring section under condition 3. During construction, the initial stress balance is broken and the stress is redistributed. With the advance of excavation, the stress is gradually concentrated. The maximum compressive stress is concentrated at the bottom corner of the tunnel, the stress distribution at the vault and around is small, and the maximum tensile stress is concentrated at the bottom plate of the tunnel. During the excavation of the tunnel, the compressive stress increases to a certain value and then decreases suddenly. This is because at the bottom of the soft rock strength, when the stress level exceeds the bearing range of the surrounding rock, the surrounding rock presents a yield state, resulting in a stress drop. Therefore, in the process of tunnel excavation, stress monitoring and reinforcement measures should be taken in the stress concentration area to prevent the surrounding rock from reaching the stress limit and causing instability and damage.

Fig. 5
4 color saturation maps for undrilled, excavation advancement at 40, 60, and 80 meters, respectively. A small dome-shaped point is at the center of each excavation advancement map.

Dynamic change of the first principal stress of the monitoring section under working condition 3

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5.3 Change of Displacement Field

As shown in Fig. 6, during the construction of shallow tunnel, the vertical displacement at the top of the tunnel is greater than that at the bottom, and the distribution law of the displacement curve under working condition 1 and 3 is similar. At a distance of 20 m from the abrupt change area, the vertical displacement of combination mode 1 and 3 is affected and gradually increases. It can be seen from the Fig. 6a that the vertical displacement and settlement of the vault in combination mode 1 increased by 1.487 mm before and after entering the sudden change area, and the vertical displacement and settlement of the vault in combination mode 3 increased by 2.31 mm. In the Fig. 6b, the vertical displacement and settlement of the arch bottom in combination mode 1 increased by 0.97 mm after entering the sudden change area, and the vertical displacement and settlement of the arch bottom in combination mode 3 increased by 0.93 mm. According to the comparative analysis of the data under working condition 1 and 2, when the rock mass grade in the mutation area is the same, the lower the rock mass grade in the ordinary area, the smaller the vertical displacement. It can be seen from the comparison of data under working conditions 2 and 3 that when the rock mass grade in the general area is the same, the higher the rock mass grade in the mutation area, the greater the vertical displacement.

Fig. 6
2 graphs on vault displacement versus propulsion distance and arch bottom displacement versus propulsion distance, respectively. The line for project situation 1 and project situation 3 has a concave downward curve and the line for project situation 2 has a straight line parallel to the x-axis.

Vertical displacement change of monitoring section of 15 m deep tunnel

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6 Conclusion

In this paper, the construction process of the diversion tunnel of Er-Jia-Gou Reservoir in Harbin is simulated by fluid structure coupling simulation. Combined with the change data of pore water pressure, the first principal stress and vertical displacement, the following three conclusions are drawn:

  1. (1)

    During the construction of the tunnel, the original seepage balance is destroyed, and a funnel like low pressure area is formed around the tunnel, and the stress will be redistributed and gradually concentrated.

  2. (2)

    When the tunnel construction enters the sudden change area of the rock stratum, the pore water pressure and the first principal stress around the tunnel under working condition 3 decrease by 24.8% and 24% respectively, and the vertical displacement of the vault and arch bottom of the tunnel increase by 2.31 mm and 0.93 mm respectively. The higher the grade of rock mass in the abrupt change area, the greater the fluctuation amplitude of pore water pressure during construction, and the more frequent the sudden change of stress.

  3. (3)

    When the rock mass grades of ordinary area and sudden change area are different, the pore water pressure, stress and vertical displacement at 20 m away from the sudden change area will be affected. Therefore, in the actual construction process, it is necessary to avoid areas with large changes in rock mass grade as far as possible, and focus on support and reinforcement within 20 m from the sudden change area to ensure the safety of tunnel construction.