Keywords

1 Introduction

The step method is widely used for grade V surrounding rock in tunnel excavation [1, 2]. Improper selection of excavation footage can lead to problems like face instability and vault collapse [3,4,5]. Therefore, selecting a suitable excavation footage is crucial for safe tunnel construction [6, 7]. Shi Xianhuo et al. [8] used silo theory to analyze the excavation footage and found that reserved core soil enhances face stability; Cai Jun et al. [9] obtained a reasonable excavation footage for the Yangjiaping tunnel considering the dilatancy angle. Li Hui et al. [10] derived a calculation formula for shallow rock tunnels’ excavation footage, showing that it is primarily determined by vault and face stability.

Drawing from the rock pressure calculation model for the Xie Jiajie tunnel, this study extends its 2D framework into a comprehensive 3D model. It establishes an excavation footage formula tailored for shallow-buried soft rock tunnels, prioritizing face stability. The adapted formula is applied in assessing the excavation progress within the north-south Yueling tunnel in Kyrgyzstan. Utilizing the step method in conjunction with numerical simulations, it aims to ascertain the most efficient excavation footage for optimal tunneling outcomes. Compare and analyze the results with existing literature's formula calculation results, verifying the rationality of the formula to calculate tunnel excavation footage.

2 Determination Method of Tunnel Excavation Footage

2.1 Calculation Model

We introduce a computation model for excavating soft rock strata in tunnels: ① The rock and soil mass exhibit an inclined plane as the fracture surface, inclined at an angle to the horizontal. ② As the overlying rock settles, compressed by surrounding rock, it induces decline in triangular masses on both sides. The sliding mass moves under resistance of undisturbed rock on both sides and the rock ahead of tunnel head. Refer to Fig. 1) and c for details.

Fig. 1.
figure 1

Calculation model of excavation footage.

Full size image

2.2 Determination of Footage Based on Vault Stability

Post-excavation, it is imperative that the upper section of the tunnel's surrounding rock remains stable within the specified loosening range, avoiding collapse. The self-weight of the surrounding rock should not exceed the four-side frictional force. To establish equilibrium in the extreme scenario, an equilibrium equation is formulated. The calculation diagram is shown in Fig. 2.

$$ W_1 - 2T_1 \sin \theta - 2T_2 \sin \theta = 0 $$
(1)

where, \(W_1\) is the self weight of the overburden rock mass ABEF on the tunnel top.

$$ W_1 = sdH\gamma $$
(2)

\(2T_1 \sin \theta\) is the friction force of the soil on both sides when the rock mass ABEF slides, and \(2T_2 \sin \theta\) is the friction force on the other two sides. The solution is shown in Fig. 3.

Fig. 2.
figure 2

Calculation model.

Full size image
Fig. 3.
figure 3

Calculation model.

Full size image

The self weight of the triangular prism is:

$$ \frac{1}{2}\gamma \times \overline{AF} \times \overline{DF} \times s = \frac{1}{2}\gamma H^2 \frac{1}{\tan \beta }d $$
(3)

According to the sine theorem:

$$ \frac{T_1 }{{\sin (\beta - \phi_0 )}} = \frac{W_2 }{{\sin [90^0 - (\beta - \phi_0 + \theta )]}} $$

Bring Eq. (3) into the above equation and simplify it to obtain:

$$ T_1 = \frac{1}{2}\gamma H^2 \frac{\lambda }{\cos \theta }d $$
(4)

Similarly:

$$ T_2 = \frac{1}{2}\gamma H^2 \frac{\lambda }{\cos \theta }s $$
(5)

Where,

$$ \tan \beta = \tan \phi_0 + \sqrt {{\frac{{\left( {\tan^2 \phi_0 + 1} \right)\tan \phi_0 }}{\tan \phi_0 - \tan \theta }}} $$
(6)
$$ \lambda = \frac{\tan \beta - \tan \phi_0 }{{\tan \beta \left[ {1 + \tan \beta \left( {\tan \phi_0 - \tan \theta } \right) + \tan \phi_0 \tan \theta } \right]}} $$
(7)

Bring Eqs. (2) (4) (5) into the Eq. (1):

$$ s = \frac{dH\lambda \tan \theta }{{d - H\lambda \tan \theta }} $$
(8)

Where, \(s\) is the excavation footage; \(d\) is the width or diameter of the tunnel; \(H\) is the covering thickness of soil layer; \(\phi_0\) is the friction angle.

3 Determination of Excavation Footage of Tunnel Portal Section of North South Road in Kyrgyzstan

3.1 Determination of Excavation Footage Based on Arch Crown Stability

The North-South ridge crossing tunnel in Kyrgyzstan is 3750 m long, and the main tunnel of tunnel section 3-A is 1850 m long. The service pilot tunnel spans from the initial chainage of K431+90 to the final chainage of K450+40, covering a length of 1850 m. The construction of the primary tunnel involves the upper and lower bench method, facilitating an excavation width of 12.6 m. The long pipe shed section at the portal of the service pilot tunnel is constructed by the bench method, and the full section method is adopted in other places, with the excavation width of 5.2 m. When calculating excavation footage, select physical and mechanical parameters for rock mass corresponding to grade V, as shown in Table 1, and use them for calculation.

Table 1. Calculation parameters.
Full size table

According to the requirements of highway tunnel code, the equivalent load height is 7.5 m. From Eq. (6) the excavation footage of the main tunnel under the two sets of parameters is S = 1.5 m.

3.2 Numerical Simulation Analysis Based on Excavation Footage Optimization

To determine the optimal excavation footage, three values of s (1.0 m, 1.2 m, and 1.5 m) were simulated numerically, and the displacement fields were compared and analyzed. Based on prior tunnel mechanics experience, the model's total width is 96.2 m, with a left boundary-to-main tunnel distance of 36 m, a clear distance between the two tunnels of 9 m, a right boundary-to-pilot tunnel distance of 33 m, and a height direction 20 m below the inverted arch. The tunnel's rock is homogenous, behaving elastically and plastically by Mohr-Coulomb criterion. Shotcrete and anchor bolts also follow homogeneous, elastic principles. The finite element model is shown in Fig. 4.

Fig. 4.
figure 4

Finite element model diagram.

Full size image

Surface Subsidence.

Through numerical simulation, it is found that the surface settlement under the conditions of surrounding rock ①, surrounding rock ② and surrounding rock ③ is consistent with the vertical displacement nephogram, and the maximum settlement occurs above the arch crown of the main tunnel. The maximum settlement under the three surrounding rock conditions is 2.5 mm, 4.3 mm and 5.3 mm respectively. The surface subsidence results are shown in Fig. 5.

Fig. 5.
figure 5

The max surface settlement and displacement nephogram under three kinds of surrounding rock.

Full size image

Vault Settlement and Peripheral Convergence.

The maximum vault subsidence under the three surrounding rock conditions is respectively 3.4 mm, 5.5 mm, 6.4 mm. The maximum peripheral convergence under the three surrounding rock conditions is 4.8 mm, 10.8 mm and 15.7 mm respectively. According to the above analysis, under the same surrounding rock, the surface settlement, vault settlement and peripheral convergence increase with the increase of excavation footage. Therefore, it is recommended to set the excavation footage to s = 1.5 m. The vault settlement and peripheral convergence are shown in Figs. 6 and 7.

Fig. 6.
figure 6

Crown settlement.

Full size image
Fig. 7.
figure 7

Peripheral convergence.

Full size image

4 Conclusion

The formula for calculating the excavation footage of a shallow buried tunnel with eccentric pressure is established. This formula is applied to the North-South crossing tunnel in Kyrgyzstan using the bench method, and the optimal excavation footage is obtained through numerical simulation analysis.

  1. (1)

    The analysis indicates that the excavation footage of the tunnel is influenced by both the stability of the vault and face. Outcomes highlight sensitivity to cohesion and friction angle. Emphasize precise determination in engineering computations.

  2. (2)

    The excavation footage of shallow tunnels in soft rock strata is directly related to the action of the tunnel face, increasing linearly with it.

  3. (3)

    According to the construction characteristics of North-South mountain crossing tunnel in Kyrgyzstan, the optimal excavation footage is s = 1.5 m through numerical simulation analysis.