Keywords

1 Introduction

In the weak and broken surrounding rock, the inverted arch structure is often used to increase the stiffness of the tunnel support to improve the mechanical performance and control the overall deformation. It plays a very important role in the tunnel support structure. Wang et al. [1] effectively prevented the development of extreme deformation of loess tunnels by using temporary steel arch and the temporary inverted arch combination. Shreedharan et al. [2] found that the inverted arch tunnel may be more efficient in reducing roof sag and floor heave for the existing geo-mining conditions. Sung et al. [3] revealed the mechanical behavior characteristics of tunnel construction of weak rock by using finite difference software. Fang et al. [4] found that the integrity of inverted arch could effectively restrain the bottom deformation.

For tunnels excavated by the bench cut method, the invert closure distance has a great impact on the deformation and pressure of the surrounding rock. Sun et al. [5] discussed the characteristics of the influence of the closure time of the support on the stress state of the surrounding rock. Designing of the tunnel support in weak rock masses is the most time consuming task of the tunnel engineers [6]. The support design is done using the collected data. With realized optimum design, the loss of time and money is prevented [7]. C.O et al. [8] used numerical analysis to simulate the mechanical behavior of the tunnel rock mass more precisely. L. Cantieniet al. [9] evaluated the mechanical behavior of the face core through extrusion measurement. The excavation method and support system can be optimized by numerical simulation [10]. The combination of the two methods is widely used to solve the problem of extreme deformation of tunnel surrounding rock [11].

The study above put forward regular suggestions for the closure distance of the back arch, but did not propose specific values for the reasonable distance. Based on those analysis, Zhong [12] took a series of numerical analysis on the impact of disposable excavation length of loess tunnel on additional displacement around the tunnel, yielding the best disposable excavation length of loess arch. Meng [13] proposed the maximum back arch closed distance under large-section loess tunnel deformation and support force by field test measurement. Jin Baocheng [14] combined the numerical simulation of the loess tunnel to analyze the clearance convergence of the arch. However, under different surrounding rock conditions, the invert closure distance also shows greater differences in different construction methods. Therefore, the invert closure distance during tunnel excavation should be adapted to local conditions [15]. The surrounding rock has the characteristics of time-deformation. When the rheological properties are considered, the stability analysis of the tunnel will become particularly complicated, which puts forward new requirements for the distance between the excavation face and the invert closure. There are few researches on the spatial influence of rheological tunnels on excavation step and invert closure distance. Based on this, relying on the Songshan Tunnel and Shimen Gang Tunnel projects of Jiangxi-Shenzhen High-speed Railway under construction, we study the impact of tunnel elevation arch excavation on tunnel deformation under different surrounding rock conditions based on numerical analysis software, aiming to further improve the relevant specifications and technical requirements and provide basic research on large-scale mechanized operation.

2 General Situation of the Project

GSSG-2 bid for Front Station Project of Ganzhou-Shenzhen Railway from Jiangsu-Guangdong Provincial Boundary to Tangxia Section, the length of the main line is 38.777 km. The Songgangshan Tunnel and Shimengang Tunnel are the controllable works along the whole line within the benchmark section and the most difficult ones. The total length of Songgangshan Tunnel is 9881 m, the first long tunnel along Gansu-Shenzhen Railway, and the total length of Shimengang Tunnel is 5759 m. In the area, Class III surrounding rocks are constructed by two-step method and Class IV and V surrounding rocks are constructed by three-step method.

Both tunnels use large-scale mechanized operation, which makes it difficult to exert the mechanical effect during construction. Therefore, in this paper, a numerical analysis is conducted on the tunnel construction process with different closure distances and exposed distances of the inverted arch, considering the creep constitutive model of the surrounding rocks. Songgangshan Tunnel and Shimengang Tunnel Project is under construction. The results provide a technical basis for improving relevant specifications and large-scale mechanized operation.

3 Numerical Modeling Calculation

3.1 Numerical Model Establishment

Using FLAC3D6.0 software, we established a numerical calculation excavation model to investigate the influence of tunnel excavation on surrounding rocks, excavation mode, and support characteristics. The model followed the tunnel construction steps shown in Fig. 1, with dimensions of 80 m along the tunnel strike (longitudinal Y-axis) and 70 m in the horizontal direction orthogonal to the tunnel, a buried depth of 20 m, and a lower part depth of 30 m. The upper boundary of the calculation model adopted a free boundary condition, while the remaining sides and underside used normal restraint boundary conditions.

Fig. 1.
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Numerical analysis and calculation model

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To simulate different conditions, we proposed various levels of surrounding rock conditions, using a two-step method in Class III surrounding rocks, with advance support and initial support in accordance with the construction conditions. To investigate the influence of different excavation steps and the length of the first excavation of the inverted arch on tunnel deformation, we varied the excavation steps at 30 m, 40 m, 45 m, 50 m, 55 m, and 60 m, and the length of the first excavation of the inverted arch at 3 m, 4 m, 5 m, and 6 m.

3.2 Numerical Simulation Steps

The three-dimensional simulation considers the three step excavation method under various levels of surrounding rock conditions, and the excavation diagram is shown in Fig. 2:

Fig. 2.
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Diagram of three-step excavation

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To conduct the calculation, the model followed the following steps: (1) advanced support by increasing the mechanical strength parameters of rock and soil within the advanced support range; (2) excavation of upper steps; (3) first support of the upper steps; (4) excavation of 10 steps (24.0 m) on the upper bench followed by excavation of the middle bench; (5) primary support for the middle step; (6) construction of two excavation steps (7.2 m) for the middle step, followed by excavation of the lower step; (7) initial support provided for the lower steps; (8) excavation of the inverted arch after three excavation steps (10.8 m) of the lower step without initial support. The creep model calculation had an excavation cycle time of 36000 s (10 h) for each step. The excavation duration was 17 days for a 30 m closed distance, 22 days for a 40 m closed distance, 25 days for a 45 m closed distance, 29 days for a 50 m closed distance, 35 days for a 55 m closed distance, and 38 days for a 60 m closed distance.

3.3 Material Parameter Determination

In the modeling of tunnel excavation process, based on the experiment, the basic physical parameters of surrounding rock, initial support and secondary support materials, soil and support materials are mainly involved in Table 1.

Table 1. Basic parameters of simulated materials.
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3.4 Creep Constitutive Law and Its Parameters

The classic Burgers creep model only considers rock viscoelasticity and cannot accurately depict the creep behavior of soft rocks, which typically exhibit instantaneous plasticity, elasticity, viscoplasticity, and viscoelasticity in Fig. 3.

Fig. 3.
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Typical burgers creep model and characteristic curve.

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Under constant axial stress σ0, the axial strain ε(t) is:

$$ \varepsilon \left( t \right) = \frac{{\sigma_{0} }}{9K} + \frac{{\sigma_{0} }}{{3G_{1} }} + \frac{{\sigma_{0} }}{{3G_{2} }} + \frac{{\sigma_{0} }}{{3G_{2} }}e^{{ - E_{2} /\eta_{2} t}} + \frac{{\sigma_{0} }}{{3\eta_{1} }}t $$
(1)

In Eq. (1), K represents the bulk modulus of the rock sample, G1 represents the elastic shear modulus of the model, and G2 represents the modulus of control delay elasticity, η1 and η2 determine the rate of viscous flow and delayed elasticity in the model, respectively.

Fig. 4.
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Modified burgers creep model.

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However, weak rocks often exhibit simultaneous properties of instantaneous plasticity, instantaneous elasticity, viscoplasticity, and viscoelasticity. To address this issue, using creep tests, we establish a new creep model that simulates the viscoelastic plastic properties of various rock samplesy. A new plastic element based on the Mohr Coulomb criterion, is added to the Burgers creep model as the basic model. Before the stress reaches the yield stress determined by the Mohr Coulomb criterion, the element's strain is 0. Once the stress is greater than or equal to the yield stress, it fully follows the Mohr Coulomb plastic flow law, in Fig. 4.

Table 2 presents the rheological parameters of the Kelvin and Maxwell bodies in the modified Burgers model for different levels of surrounding rock, which were determined based on on-site sampling and indoor experiments.

Table 2. Creep parameters of surrounding rocks of different grades.
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3.5 Numerical Simulation Based Analysis of Arch Settlement of V-Class Surrounding Rock Tunnel

Numerical simulations used the ideal elastic-plastic model based on the Mohr Coulomb criterion. The inverted arch had a closed distance of 30 m, and a one-time excavation of 6 m was conducted for the inverted arch. The three-dimensional simulation results can be observed in Fig. 5.

Fig. 5.
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Settlement curve with Mohr-Coulomb model

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Fig. 6.
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Deformation nephogram of three-step excavation tunnel with Mohr-Coulomb criterion

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The maximum settlement curve of the arch crown is presented in Fig. 6, with a maximum settlement deformation of only 2.5 mm.

Fig. 7.
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Deformation nephogram of three-step excavation tunnel with modified Burgers model

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The modified Burgers creep model was employed to numerically calculate the excavation model of a V-level surrounding rock three-step tunnel, with a 30 m closed distance for the inverted arch and a one-time excavation of 6 m for the inverted arch. The simulation results in three dimensions are presented in Fig. 7.

Fig. 8.
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Calculating the settlement curve of vault with modified Burgers creep model

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Figure 8 presents the maximum settlement curve of the arch crown for various closure distances. The maximum settlement of the arch crown reaches 24 mm when the closure distance is 60 m. The settlement distribution is more realistic compared to the Mohr Coulomb criterion based three-step excavation model. The failure to consider the effect of stress release and timeliness on the mechanical and deformation properties of surrounding rocks and deformation of the arch crown during excavation. During excavation, the deformation at the arch waist of the unclosed section increases with excavation steps. However, the deformation at the arch waist of the unclosed section of the inverted arch remains stable, which differs significantly from the actual monitoring situation. It is essential to consider the decrease in rock strength due to stress release after excavation and the time-dependent nature of excavation steps.

4 Analysis of the Influence of Tunnel Arch Subsidence

4.1 Impact of Invert Step Distance on Arch Crown Subsidence in V-Class Surrounding Rock Tunnel

Based on the above method, we calculated the settlement of the arch crown caused by different closure distances for V-grade surrounding rock in Table 3. As the closure distance increases from 30 m to 60 m, the maximum displacement of the arch crown increases from 13.33 mm to 25.1 mm.

Table 3. Maximum displacement of vault under different closure distances of inverted arch in V-grade surrounding rock
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4.2 Influence of Excavation Length of inverted arch of Class V Surrounding Rock Tunnel on Vault Settlement

The settlement of the arch crown caused by different lengths of the exposed inverted arch in V-grade surrounding rock was calculated.

Fig. 9.
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Variation curve of vault settlement

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The results are presented in Fig. 9 and Table 4. The calculation results show that as the exposed distance of the inverted arch decreases, the maximum settlement of the arch decreases, indicating that a smaller exposed distance of the inverted arch leads to stronger initial support stability and a more pronounced initial support force ring effect. However, the settlement curve shows that the maximum settlement of the arch is not sensitive to the exposed distance of the inverted arch, indicating that the effect of the exposed distance of the inverted arch on stability is not significant.

Table 4. Maximum displacement of inverted arch without closure of 3-6m in V grade rockmass
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4.3 Influence of Surrounding Rock Class on Arch Settlement

The stability of a tunnel is primarily influenced by the nature of the surrounding rocks. Therefore, investigating the relationship between the closure distance of the inverted arch and the maximum settlement of the initial support arch under different surrounding rock classes, the strength of the surrounding rocks was varied based on the aforementioned model.

The results obtained using the Burgers creep model are shown in Fig. 10 and Table 5. The maximum settlement value of a V-grade surrounding rock vault is larger than that of III and IV surrounding rocks, and the maximum settlement of a IV surrounding rock vault is slightly higher than that of a III surrounding rock vault at each closure distance. With an increase in the closure distance, the maximum settlement value of the vault also increases. An increase in the grade of surrounding rocks results in a significant reduction of the displacement of the tunnel vault. The stability of initial support is closely linked to the grade of surrounding rocks. When the surrounding rock conditions are good, the inverted arch closure distance can be increased, and the exposed distance can also be increased to facilitate the operation of large machinery. Conversely, when the surrounding rock conditions are poor, the inverted arch closure distance should be shortened, and the exposed distance of the inverted arch reduced, while initial support should be promptly applied to ensure the stability of the surrounding rock. Additionally, increasing the length of circular footage and reducing the time under good surrounding rock conditions can significantly enhance the stability of the tunnel.

Fig. 10.
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Tunnel vault settlement curves caused by different levels of surrounding rock and different excavation methods

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Table 5. Numerical results
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5 Conclusion

  1. (1)

    A decrease in the closure distance of the inverted arch results in a reduction of the maximum settlement of the vault. The stability of the initial support is stronger with a smaller closure distance. The maximum settlement of the vault is not sensitive to the exposed distance of the inverted arch. So the influence of the distance of the inverted arch on the stability of the initial support is not significant. After mechanized operation, the sealing distance of V-grade surrounding rock inverted arch can be controlled within a range of 55 m, while that of IV-grade surrounding rock inverted arch can be controlled within a range of 70 m. For III-grade surrounding rock, the sealing distance can be controlled depending on the specific situation.

  2. (2)

    The excavation length of V-grade surrounding rock inverted arch can be controlled within a range of 5 m at one time.

  3. (3)

    The step method is suitable for excavation in Grade III, IV, and V surrounding rocks, and the length can be controlled based on the settlement of the vault caused by the excavation.