Keywords

1 Introduction

Due to the high altitude and significant temperature differences in the border area of Sichuan and Tibet, the bedrock undergoes further erosion, resulting in the formation of loose rock pile [1, 2, 3]. The unstable tunnel through the rock pile is prone to instability and failure during excavation. In order to address these challenges, it is important to select a suitable construction excavation method that can effectively adapt to the geological conditions of the surrounding rock, minimize construction disturbances, and ensure the safety and progress of tunnel construction.

In order to solve the construction problems of the tunnel, scholars at home and abroad have studied the stability of the tunnel in different aspects. Deng Yongjie [4] summed up the deformation law of surrounding rock in the excavation process. Zhou Xueqing [5] studied the plastic zone of surrounding rock of loose rock pile tunnel under three construction methods, and optimized the construction method. Li Wei [6, 7] analyzed the stability of the tunnel face when the shield tunnel is tunelling along the inclined stratum. Anagnostou G [8] studied the face stability of slurry-shield-driven tunnels. Lin Qingtao [9, 10] constructs the stability model of shield tunnel in pebble stratum.

This study aims to analyze the stability of tunnel surrounding rock in rock mass under different construction methods, considering the high stability requirements for tunnel crossing rock mass in southwest China. Through point measurements and numerical simulations, the stability of surrounding rock is investigated.

2 Engineering Overview and Construction Method Analysis

Rock piles, especially loose ones, are susceptible to instability. The varying composition of sand and rock in rock piles can lead to changes in their mechanical properties [11, 12, 13]. Improper excavation methods may result in mountain collapse, posing difficulties in tunnel construction, maintenance, and use. Therefore, it is crucial to formulate the tunnel construction method based on specific engineering conditions. Given the higher mountain height and larger top load in the southwest region, this study focuses on selecting an appropriate tunnel construction method for further investigation.

2.1 Analysis of Engineering Overview

The background project of this paper is C.D. Tunnel, which is located in the east of Ya ‘an to Linzhi section. The tunnel was built through loose rock piles.

This section mainly analyzes the general situation of rock piles at the entrance and exit of the tunnel. The rock pile at the exit section of the C.D. Tunnel is located at the foot of the slope and extends to the lower part of the slope. It is continuously accumulating along the right bank of the Frozen Cuoqu, with a zonal distribution. The rock pile is approximately 100–200 m long, 10–50 m thick, and over 1.5 km wide. The average volume per meter is about 5.3 × 103 m3, making it a massive accumulation. The rock mass consists mostly of gravel, which is prone to instability when exposed to vibrations.

2.2 Analysis of Construction Method

The safety of tunnel excavation depends on the construction method used, as different methods result in different stress redistribution. Therefore, it is important to choose a suitable construction method based on the specific construction environment. Currently, there are several methods commonly used in tunnel construction, including the Tunnel Boring Machine (TBM) method, the three-step method (including the multi-step method), the CD method (Center Diaphragm method), the core soil construction method, the CRD method (tunnel cross middle wall method), and the tunnel double side wall heading excavation method. Through the analysis of these construction methods, this study focuses on the TBM method, the three-step method, and the CD method, as they are more suitable considering the construction background. A comparative research will be conducted using these three methods in this article.

The TBM method, also known as the full-face excavation method, involves excavating the entire section once and then lining the construction [14]. This method offers the advantages of a large excavation section and high efficiency. However, it is prone to causing deformation in the surrounding rock. In practice, it also has drawbacks such as a high tool wear rate [15, 16], high driving cost and easy to cause shield jamming [17, 18].

The three-step method is the specific construction method involves dividing the working face into three parts for cyclic excavation. Each time, one step is excavated and after each excavation, the initial support is implemented. The secondary lining is carried out after excavating the lower step for 16 m, with a length of 4 m in a single construction [19]. The three-step method offers advantages such as a smaller operation space and multiple processes. However, it may cause disturbances to the surrounding rock due to repeated excavation using the step method. Additionally, the multiple lining constructions may lead to stress concentration [20].

The CD method, which stands for tunnel middle wall excavation method, involves excavating one side first, supporting the middle wall, and then excavating the other side during the excavation process. This method has some disadvantages, such as difficult construction, complex process, small construction space, and the need to remove the middle partition wall. However, it offers the advantage of timely applying initial support to each part during construction [21, 22], allowing for the quick formation of a ring. This reduces disturbance to the surrounding rock and effectively controls settlement deformation. The CD method is widely used in engineering practice, especially when dealing with broken surrounding rock [23, 24, 25].

3 Surrounding Rock Stability Model of Rock Pile Tunnel

3.1 Computation Module Establishment

In this section, numerical simulation is used to simulate the construction process of different excavation techniques in the construction process of rock pile tunnel, and the variation law of displacement, stress and strain of lining and surrounding rock in tunnel excavation process is analyzed and compared. The tunnel excavation section is 11.6 m high (z direction) and 13.6 m wide (x direction). Because in the process of tunnel excavation, the release of load will change the stress field and strain field of surrounding rock. The stress field and strain field are about less than 5% outside 3 times the diameter of the hole, and less than 1% outside 5 times the diameter of the hole. Therefore, the excavation diameter of the soil on both sides is 4 times the excavation diameter. The bottom of the model is taken to 35 m below the tunnel excavation contour line. The longitudinal (y direction) length of the model is 100 m, of which the tunnel excavation length is about 80 m. The model is shown in Fig. 1.

The surrounding rock is assigned parameters according to the Mohr-Coulomb constitutive model. The required materials are preferentially obtained from the engineering geological survey data. For the lack of material properties, the research literature and related specifications are selected [26, 27].

Fig. 1.
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Computation module

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3.2 Measuring Point Arrangement

The data observed by the measuring point has the characteristics of high efficiency and reliability, so the layout of the measuring point needs to clarify the purpose of the layout [28]. The stability of the tunnel at the entrance section mainly includes the stability of the tunnel body, the stability of the slope and the stability of the lining structure. In order to solve these problems, the vault settlement, surrounding displacement, bottom uplift, surface subsidence and internal force of the supporting structure are mainly monitored in the numerical calculation process. The surface subsidence provides data support for slope safety analysis, and the monitoring data in the cave provides the basis for structural safety analysis. With the advance of the construction section, the buried depth of the tunnel is also increasing. Therefore, in order to facilitate the analysis, six sections of the tunnel buried depth of 5 m, 10 m, 15 m, 20 m, 25 m and 30 m were selected for monitoring.

4 Numerical Simulation Analysis of Tunnel Under Three Kinds of Tunnel Construction Methods

To analyze the stability of the tunnel, we should start from the displacement and stress of the tunnel, the change of displacement and stress of tunnel surrounding rock is closely related to the construction method. After analyzing the change trend of displacement and stress of tunnel surrounding rock, this section further links it with the construction method, and gradually analyzes the relationship between the change trend of displacement and stress of tunnel surrounding rock and the construction method.

4.1 Tunnel Settlement Analysis

Analysis of Ground Settlement

The numerical simulation of the comparison of the construction methods requires the settlement of the tunnel as the basic data. The data of the detection results of the surface settlement in the numerical simulation calculation are extracted and plotted as follows.

Fig. 2.
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Curve of ground settlement with buried depth

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According to Fig. 2, the maximum surface settlement among the three construction methods occurs directly above the tunnel vault. Therefore, the analysis focuses on the surface settlement directly above the vault. The figure shows that the TBM method results in the largest surface settlement, while the three-step method has the smallest settlement, and the CD method falls in between. This observation differs from our previous engineering experience, possibly due to the poor self-stability of the surrounding rock at the entrance of the tunnel. The direct excavation by TBM creates a large free surface, which hampers the stability of the surrounding rock after excavation. Consequently, significant displacement occurs rapidly, leading to large settlement. Although the excavation section of the CD method is smaller, the numerous construction procedures and the long closed-loop time of the lining structure result in long-term deformation of the surrounding rock, causing significant displacement as well. On the other hand, the three-step method, with a smaller excavation section than TBM and an earlier lining forming time compared to the CD method, exhibits the smallest displacement.

The maximum surface settlement occurs at a buried depth of 15 m, possibly due to the transition of the tunnel into the deep buried stage beyond this depth.

Analysis of Vault Settlement

During the study, it was observed that the maximum vertical displacement of the tunnel excavated using these three methods occurred at the vault. This highlights the significance of the vault in the actual project. The numerical simulation yielded the following final settlement values for the vault after the excavation using the three construction methods:

Fig. 3.
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Vault settlement curve

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The settlement of the cross-section vault at different buried depths was monitored. The results are shown in Fig. 3 above. The smallest settlement was observed in the vault excavated by the CD method, indicating the best control of the surrounding rock. On the other hand, the three-step vault exhibited the largest settlement. As the excavation progressed, the vault settlement initially increased rapidly and then gradually stabilized. The curve reached an inflection point at approximately 15 m, suggesting a change in settlement behavior between 15–20 m. The transition from shallow to deep burial resulted in the formation of a stress arch in the tunnel, leading to a less pronounced change in settlement in the second half of the curve. Overall, the excavation methods of TBM and three-step showed clear trends and inflection points. The poor geological conditions of the surrounding rock mass in shallow buried section, when subjected to the larger section of TBM excavation and the three-step method, caused significant disturbance to the original state of the surrounding rock, resulting in a sharp displacement change. In contrast, the CD method exhibited a slower rate of change, emphasizing the importance of initial support ringing. Therefore, it is crucial to pay attention to support ringing in each section during actual construction to reduce deformation rates and enhance the stability of the surrounding rock.

Through the above analysis, for the control effect of vault settlement in the construction process, the three-step method is not ideal, and the CD method has the best effect, followed by the TBM method. Therefore, as long as the excavation surface can be closed in time and quickly, the deformation control effect can be better.

Analysis of Bottom uplift of Tunnel

Under the three construction methods, the bottom uplift of the tunnel at different buried depths is analyzed, and Fig. 4 is drawn.

Fig. 4.
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Bottom uplift curve of tunnel

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The figure above illustrates that the vertical deformation of the arch bottom varies across the three construction schemes as the buried depth increases. The TBM method exhibits the largest change trend. The bottom uplift curve initially increases rapidly and then gradually stabilizes with the increase in buried depth. In general, the excavation of the TBM method causes the largest uplift value of the arch bottom, reaching a maximum of 1.81 mm. Comparatively, the three-step method and the CD method show relatively smooth change trends, with a value that increases initially and then gradually stabilizes. The vault uplift generated by the three-step method is greater than that of the CD method, with maximum values of 0.46 mm and 0.19 mm, respectively. The maximum difference between them is only about 0.25 mm, which is relatively small overall.

Horizontal Displacement Analysis of Surrounding Rock Around Tunnel

The horizontal displacement of surrounding rock in each part of the three construction methods was monitored and recorded. The final horizontal displacement deformation of each measuring point is shown in Fig. 5:

Fig. 5.
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Horizontal displacement of each part of the tunnel

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The Figure above shows that the three excavation methods result in varying degrees of horizontal displacement. The largest displacement occurs at the arch waist, attended by the side wall, while the vault experiences the least horizontal displacement, almost negligible.

When the buried depth is shallow, the horizontal displacement caused by the three construction methods is analogous. However, as the buried depth increases, they start to vary. The three-step method exhibits the largest horizontal displacement at the arch waist, followed by the TBM method, while the displacement caused by the CD method is the smallest. Notably, all three construction methods demonstrate a distinct change tendency around 20 m. Prior to this depth, the curve change slope increases with the burial depth, but after 20 m, the curve change stabilizes. The horizontal displacement of the side wall is described in the above diagram. Parallel to the trend at the arch waist, the three construction methods exhibit a similar change pattern. The curve slope decreases as the buried depth increases and generally stabilizes after 20 m. The largest horizontal displacement is observed with the three-step method, followed by the CD method, while the TBM method falls in between.

In order to explore the change of horizontal displacement during tunnel excavation at the same buried depth, the tunnel section when the buried depth is 20 m is selected, and the arch waist part is taken as an example for analysis, as shown in Fig. 6 below.

Fig. 6.
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Horizontal displacement of arch waist with the construction step change curve

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For the TBM method, the horizontal displacement generated by the excavation of the upper steps is large, which is due to the stress release caused by the one-time large-area excavation. Therefore, it is extremely important to control the horizontal displacement in time after the excavation of the section. If the support is not closed in time during the construction process, it will not only increase the horizontal displacement of the surrounding rock of the tunnel, but also increase the uplift of the bottom of the tunnel. For the CD method, the horizontal displacement of the arch waist caused by each step of the excavation of the left pilot tunnel is small. This is because the excavation area of the left pilot tunnel is small and the temporary middle wall will be set up in time after the excavation is completed, which effectively controls the deformation of the surrounding rock of the arch waist. However, it should be pointed out that when the excavation of the upper bench of the right pilot tunnel is carried out, the horizontal displacement tends to increase sharply. This may be because the excavation of the right pilot tunnel increases the area and changes the momentary state of the surrounding rock and the middle wall, which causes the release of the surrounding rock stress and increases the horizontal displacement. For the three-step method, the horizontal displacement change of the arch waist in each step is basically stable, and there is no dramatic displacement change, which has a good control effect on the deformation of the surrounding rock. This is explained by the fact that the three-step method divides the section into three parts, and excavates separately. The three steps are staggered between each other, and each construction step is excavated and supported separately and the excavation soil is less. Therefore, the displacement caused by a single construction step is small, so the three steps have a beneficial effect on the control of the deformation of the surrounding rock of the arch waist. However, because there are many processes and the initial support is closed into a ring time, the overall cumulative displacement is the largest of the three construction methods.

In summary, it can be seen that in the construction of the tunnel through the rock pile, the displacement change of each construction step during the excavation of the three-step method is relatively stable, but the cumulative horizontal displacement is the largest after the construction is completed. The cumulative horizontal displacement caused by CD method is the smallest, but the sudden increase of horizontal displacement should be given attention to during excavation. When TBM method is used, the initial horizontal displacement of each construction step is the largest, but the ultimate cumulative displacement is between the other two methods. During construction, attention should be paid to timely support after section excavation to avoid excessive horizontal displacement deformation.

4.2 Stress Analysis of Surrounding Rock of Tunnel

Horizontal and Vertical Stress Analysis of Tunnel

The displacement and deformation in the process of tunnel excavation are analyzed, but the stress state of surrounding rock in the process of excavation also has a great influence on the stability of surrounding rock. Therefore, the horizontal stress and vertical stress near the tunnel during the excavation of the three construction methods are monitored. The three parts of the vault, arch waist and side wall are focused on, and the horizontal stress and vertical stress are obtained respectively. The results are as follows Tables 1 and 2 show:

Table 1. Horizontal stress
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Table 2. Vertical stress
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The simulation results of the vertical stress and horizontal stress of the surrounding rock of the three construction methods are indicated above. The vertical surrounding rock stress and horizontal surrounding rock stress of the vault, hance and side wall of the CD method are the smallest. The table show that: The maximum horizontal stress of the vault of the CD method is 62% lower than that of the TBM method, and the side wall is reduced by 75%, and the stress of the surrounding rock at the excavation section of the tunnel is under pressure. Therefore, in the process of excavation, attention should be given to the phenomenon of horizontal stress concentration at the vault, and the maximum vertical stress appears at the side wall, which should also be paid attention to.

In general, the horizontal stress and vertical stress of TBM construction are greater than those of the other two schemes, which may be caused by the large excavation section.

Tunnel Surrounding Rock Shear Stress

The buried depth of the tunnel has a certain influence on the shear stress state of the tunnel section. Taking the TBM method as an example, the variation law of the shear stress of the surrounding rock under different buried depths is analyzed. Through the observation of the results, the shear stress in the XZ plane can more effectively reflect the stress concentration and stress. The final results are shown in Fig. 7.

Fig. 7.
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Shear stress diagram under different buried depth

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From the above shear stress diagram, it can be observed that the shear stress of the tunnel under different buried depths is mainly concentrated near the entrance of the tunnel, mainly concentrated in the arch waist and side wall of the excavation section. Comparing the shear stress concentration area, it is found that the maximum shear stress may appear at the arch waist. For the maximum shear stress under different buried depths, it is found that with the increase of buried depth, the maximum shear stress increases first, then increases first and then decreases. The maximum value of appears at a depth of 15 m, and the maximum value is approximately 90 kPa. It shows that when the buried depth is more important than a certain range, the shear stress will decrease. Therefore, attention should be paid to the concentration of shear stress near the haunch and side wall during excavation, especially near the buried depth of 15 m.

Stress Analysis of Excavation Section.

When evaluating the stability of surrounding rock, the stress state of the rock is a crucial factor. The stress cloud diagram below illustrates the maximum and minimum principal stresses under various excavation methods. Based on the previous analysis, it was observed that the maximum displacement of the surrounding rock occurred within the range of 15–20 m. Therefore, a tunnel section with a burial depth of 15 m was chosen for further analysis. The obtained results are presented in Fig. 8 below.

Fig. 8.
figure 8

The maximum principal stress and minimum principal stress under different construction methods

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This paper presents an analysis of the stress characteristics of the surrounding rock around the tunnel arch ring. The figure above illustrates that the maximum principal stress is predominantly compressive stress. During tunnel excavation, the unloading effect causes changes in the stress field of the surrounding rock, leading to a decrease in compressive stress around the tunnel. Consequently, it is crucial to pay attention to stress concentration in the range of the side wall during each step of excavation when employing the CD method or three-step excavation. This is particularly important in the tunnel passing through the southwest alpine environment, as it may create weak areas and require special attention to ensure construction safety.

According to the upper minimum principal stress diagram, the stress in the surrounding rock is predominantly compressive, with no tensile stress. Although the three-bench and CD methods have better control over surface settlement compared to the TBM method, each section excavation still leads to stress concentration. When the lining structure is not fully closed into a ring, force transmission becomes uneven, potentially causing damage to local parts of the structure. Therefore, it is important to address this issue during construction and consider reinforcing the corresponding areas if necessary.

In order to analyze the variation law of the maximum principal stress with the buried depth of the tunnel, the TBM method is selected to study the maximum principal stress when the buried depth is 5, 10, 15, 20, 25 and 30 m, as shown in Fig. 9.

Fig. 9.
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Curve of maximum principal stress changing with buried depth

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It can be seen from the above figure that the maximum principal stress of the surrounding rock is affected by the gravity field. During the excavation construction, with the continuous circulation of the excavation, the buried depth increases, and the corresponding maximum principal stress also gradually increases. With the increase of buried depth, the maximum principal stress curve increases rapidly and then tends to be gentle, and the maximum value is 1.067 MPa. The inflection point of the curve transformation slope is near the buried depth of 15 m. When the buried depth is less than 15 m, the maximum principal stress increases approximately linearly, and the rate is faster. When the buried depth is greater than 15 m, the curve area is smooth, and the variation of the maximum principal stress changes little with the increase of the buried depth. This may be that after 15 m, the tunnel enters the deep buried state from the shallow buried state, forming the stress arch effect, so the variation is very small.

4.3 Comprehensive Comparative Analysis of Tunnel Construction Methods Combined with Engineering Background

The safety of the tunnel vault is of utmost importance in the southwest region due to its high mountains and susceptibility to landslides. Additionally, the accumulation of rock piles can exert a significant load on the slope’s base, necessitating control over the stability of other sections. Among the three construction methods, the CD method demonstrates the smallest settlement, maximum displacement, and surrounding rock stress, indicating its superior protection for the vault. In terms of secondary factors, the CD method exhibits the smallest displacement of the haunch side wall, as well as the lowest vertical and horizontal surrounding rock stress during construction. Conversely, the TBM method suffers from drawbacks such as a large excavation section, resulting in substantial surface settlement, tunnel bottom uplift, and increased horizontal and vertical stress. The three-step method causes more soil disturbance, leading to significant vault settlement that fails to meet the project’s stringent stability requirements.

Overall, the CD method should be prioritized when constructing tunnels traversing rock piles in the southwest region.

5 Conclusion

In this paper, the numerical simulation analysis of tunnel crossing rock mass is performed by numerical simulation. The TBM method, three-bench method and CD method are selected and set up, and the displacement and stress of surrounding rock are monitored. The stress variation law and displacement variation law of surrounding rock during tunnel excavation are analyzed, and the reasons for the different changes of stress and displacement of tunnel surrounding rock under different construction methods are analyzed, which provides a reference for the construction technology of tunnel crossing rock mass. The main contents are as follows:

  1. (1)

    During the construction of TBM method, the surface settlement is the most important thing, the surface settlement of the three-bench method is the smallest, and the CD method is in the middle. The uplift value of arch bottom caused by TBM excavation is the most important thing. Relatively speaking, the change trend of three-bench method and CD method is quite smooth, but there is still a value that increases first and then gradually stabilizes. The vault uplift produced by the three-step method is larger than that of the CD method, but it is generally smaller; the settlement of the vault excavated by the CD method is the smallest, the control of the surrounding rock is the best, and the settlement of the three-bench vault is the largest, while the TBM method is between the two.

  2. (2)

    The horizontal displacement of the arch waist obtained by using these three methods is the largest, followed by the side wall, and the horizontal displacement deformation of the vault is the smallest, and far less than the other two parts, which can be approximately regarded as no displacement. The maximum displacement of the vault of these three methods occurs at a buried depth of 15 m, and the maximum displacement of the haunch and the side wall occurs at a buried depth of 30 m. Among the three methods, the maximum displacement of the vault is the largest when the TBM method is constructed, followed by the three-bench method, and the CD method is the smallest. The displacement of the haunch and side wall is the most important thing when the three-bench method is constructed, while the displacement of the haunch side wall is the smallest when the CD method is constructed.

  3. (3)

    The vertical surrounding rock stress and horizontal surrounding rock stress of vault, haunch and side wall of CD method are the smallest. The change trend is curvilinear growth, and the slope changes from large to small. The maximum horizontal stress of the three methods occurs at the vault, and the maximum vertical stress occurs at the side wall. With the change of buried depth, the distribution law and shape of shear stress are relatively similar, and the maximum value of shear stress appears at the arch waist. For the maximum shear stress under different buried depths, it is found that with the increase of buried depth, the maximum shear stress increases first, then increases first and then decreases. During TBM excavation, the stress concentration occurs near the side wall. When the CD method is excavated, stress concentration occurs in each part of the excavation, and the range of stress concentration is larger than that of the TBM method, and the stress concentration range has a tendency to diffuse from the side wall to the arch waist.

  4. (4)

    Coupled with the numerical simulation data and engineering background, the CD method has the strongest protection for the vault, and has better safety guarantee for other parts. It is the best thing construction method for the tunnel crossing the rock pile region.