Introduction

Nowadays, a tunnel is designed and constructed towards large span and section to accommodate various needs1,2,3,4,5,6,7, and the lining is vital to the tunnel stability during construction8,9,10. When excavating a large-section tunnel in a weak stratum11, the temporary lining is usually employed to reduce the span with the help of various sequential excavation methods, which include the center diaphragm method12, the center cross diaphragm method13,14, the side drift method15,16, and other tunneling methods17,18,19,20. Yiouta-Mitra et al.21 used a sensitivity analysis method to assess the impact of various geotechnical parameters on the internal forces and displacements of temporary tunnel lining, and obtained the optimal parameters. Admittedly, the temporary lining stabilizes the ground and controls displacement during excavation. However, dismantling temporary linings often negatively affects primary linings because the loads sustained by temporary linings would be transferred to the surrounding bearing elements22.

Traditionally, controlling the dismantling length of the temporary lining per round is often used to mitigate these adverse effects. Zhang et al.23,24 pointed out that the risk of dismantling temporary tunnel lining can be reduced, and the structure’s safety can be ensured by using step-by-step dismantling temporary lining and installation of the secondary lining. The previous studies25,26,27,28,29 recommended the dismantling length per round using 6 ~ 12 m. Zhang et al.30 pointed out that with the increase of the one-time demolition length of temporary lining, the safety factor of tunnel would first increase and then decrease, and it was suggested that the reasonable one-time demolition length of the temporary lining should be 9 m. Wang et al.31 optimized the demolition length of the temporary lining (from 6 m to 12 m) and the amount of excavation section (from 7 excavation sections to 4 excavation sections) of the super-large section subway tunnel, which significantly shortened the construction period and cost. Zhang et al.32 pointed out that the timing of dismantling of vertical temporary linings is the main factor affecting tunnel safety, and it is in the best interest of tunnel safety to dismantle the vertical temporary linings at last. However, it has to be pointed out that this suggested dismantling length is too short to carry out the subsequent parallel installation of the final linings and therefore will seriously affect the tunneling efficiency. From the above, it is essential to analyze, without considering the three-dimensional effect, the deformation increments about the preliminary lining led by dismantling the temporary linings and optimizing the tunneling method to reduce the adverse effects.

The previous works done by our research group (Zhang et al.33) focused on the displacement increment led by the dismantling of temporary lining before the preliminary lining closed (none closed-loop preliminary lining loading). However, there is no further research on the risk assessment led by the dismantling of temporary lining after the preliminary lining closed (closed-loop preliminary lining loading). This study is based on the same four-line railway station tunnel in Zhang et al.33, and the cross-section profile is shown in Fig. 1. Two alternative tunneling methods proposed in the tunneling methods (plans) comparison and optimization stage, marked as tunneling method 1 (abbreviated as TM-1) and tunneling method 2 (abbreviated as TM-2) respectively, are presented in Fig. 2. The corresponding lining parameters are summarized in Table 1. In this paper, the comprehensive research is conducted on the displacement risk caused by dismantling temporary lining based on these two alternative methods. Besides, the following three influence factors are taken into consideration: the axial forces in temporary linings, the thickness of preliminary linings, and the deformation modulus of ground. After that, in order to reduce the risk of dismantling temporary linings, tunneling method optimization plan is proposed. All the research results can provide some important reference for the similar tunnel engineering in the future.

Figure 1
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Tunnel profile of the four-line railway tunnel.

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Figure 2
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Two alternative tunneling methods.

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Table 1 Details of the preliminary lining, temporary lining and final lining.
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Calculation model

The bedded-beam model is widely used in tunnel analyses and designs, as suggested by the International Tunnel Association Tunnel Design Working Group34, and in research relevant to tunnel engineering35,36, which is adopted in this paper.

In the numerical simulation, the tunnel section is built according to the tunnel profile in Fig. 1. The preliminary lining, as well as temporary lining, is modeled using the beam structure element (Beam 3), and the interaction between the preliminary lining and ground is realized by spring (Link 10). Note that the interaction springs around the tunnel perimeter can only bear compressive loads, and the forces of springs will be set to 0 when tension appears. The outer ends of the springs are fixed. The calibration of the bedded-beam model can be referred to the previous works conducted by our research group (namely, Zhang et al.33). The two tunneling methods involved in this study are two alternative methods based on the same background project mentioned in Zhang et al.33.

From the perspective of mechanical equilibrium, removing the temporary lining will transfer to the surrounding bearing elements the loads that the temporary lining sustains (see Fig. 3). Hence, the numerical models of TM-1 and TM-2 are established, respectively, as shown in Fig. 4a,b. It can be seen from the numerical models that there are three influence factors, i.e. the axial forces in the temporary lining (AFTL), the stiffness of preliminary linings (referred to the thickness of preliminary lining in this paper, abbreviated as TPL), and the deformation modulus about ground (DMG).

Figure 3
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Calculation models of dismantling the temporary linings by TM-1 and TM-2.

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Figure 4
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Numerical calculation models of TM-1 and TM-2.

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For the magnitude of the parameters entered in the analysis, different calculation cases are assumed based on the on-site monitoring data as well as suggestions from the literatures. With regard to AFTL, the maximum value monitored by the background project is nearly 700 kN/m, while some literature27,28,37 points out that the AFTL can be up to 1026 kN/m. Besides, for the TPL, 400 mm is adopted in the background project, while it is suggested greater than 200 mm by the design experiences and guidelines. For the DMG, it is a wide range from the bad to the good ground, but it is more meaningful to focus on the sensitive range of 50 Mpa/m ~ 500 Mpa/m. Therefore, in the following numerical simulation, it is reasonable to set the AFTL in the range of 0 ~ 800 kN/m, the TPL between 200 mm and 700 mm, and the DMG from 50 Mpa/m to 500 Mpa/m.

Calculation results based on tunneling method 1 (TM-1)

Based on the numerical model in Fig. 4a, the calculation parameters are initially set as follows: the TPL is 200 mm; the DMG is 50 MPa/m; and Na and Nb are both set as 400 kN/m. The obtained result is presented in Fig. 5. Due to the curvature difference, the deformation increments about preliminary linings led by dismantling temporary linings are mainly shown as invert uplift. The maximum settlement increment (MSI) about the arch is 6.8 mm, while the MDI of the invert of the preliminary lining is 81.0 mm. Subsequently, the MDI of preliminary lining would be employed to quantify the impact of dismantling temporary linings.

Figure 5
figure 5

Deformation increment profile of preliminary linings led by the dismantling of temporary linings based on TM-1.

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Influence factor—AFTL (Na and Nb)

The DMG is set as 150 MPa/m, and TPL is set as 400 mm. Two cases are considered to investigate the AFTL (Na and Nb): keeping Na = Nb and varying Na and Nb independently.

Keeping Na = Nb

The force parameters and calculation results are shown in Table 2 and Fig. 6. A linear relationship between Na (or Nb) and MDI is displayed in the figure. The MDIs increase with AFTL. Generally, it is found that MDI increases by 5.6 mm for each 100 kN/m increasement in AFTL.

Table 2 Calculation cases and results for Na = Nb in TM-1.
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Figure 6
figure 6

MDI versus AFTL when keeping Na = Nb in TM-1.

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Varying Na and Nb independently

The force parameters and calculation results are shown in Table 3 and Fig. 7. From Fig. 7, the Nb—MDI distribution curve exhibits nonlinear behavior under a constant Na. Specifically, under a constant Na, MDI decreases with the increase of Nb before Na = Nb. After that, MDI increases with the further increase of Nb (Nb > Na). Note that the minimum MDI is achieved when Na = Nb. In other words, the most favorable situation can be achieved when the axial forces in the two vertical temporary linings keep the same Na = Nb. In addition, the MDI is mainly subject to the dominant axial force when Na and Nb are different.

Table 3 Calculation cases and results (MDI/mm) for Na and Nb independently varying in TM-1.
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Figure 7
figure 7

The relationship among the MDI, Na, and Nb when axial forces Na and Nb vary independently in TM-1.

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Influence factor—TPL

In this subsection, Na and Nb are set as 400 kN/m, and the DMG is set as 150 MPa/m. The TPL changes in the range of 200 ~ 700 mm with an interval of 100 mm. The relationship between MDI and TPL can be captured by a power function (see Fig. 8). It should be pointed out that MDI reduces rapidly when TPL is small; and that with further increase of TPL, MDI decreases slowly. This finding implies that further increasing TPL will not significantly decrease the risks of dismantling temporary linings when the preliminary lining is competent (or TPL is large).

Figure 8
figure 8

MDI versus the TPL in TM-1.

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Influence factor—DMG

In this subsection, Na and Nb are set as 400 kN/m and TPL is set as 400 mm. The DMG is set to 50 MPa/m, 100 MPa/m, 150 MPa/m, 200 MPa/m, 300 MPa/m, and 500 MPa/m, respectively. The corresponding calculation results are shown in Fig. 9. In Fig. 9; the MDI decreases with the increase of DMG (from soft ground to hard ground), which can also be described by a power function. Similarly, with the increase of DMG, MDI decreases slowly. This finding implies that improving the ground condition can be an effective measure in reducing the risks of dismantling temporary linings only when the ground is weak.

Figure 9
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MDI versus the DMG in TM-1.

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Discussion

A total of 216 calculation conditions as well as the corresponding result involving all three influence factors are listed in Table 4 and Fig. 10.

Table 4 Calculation cases and results (MDI/mm) for involving all the three influence factors in TM-1.
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Figure 10
figure 10

3D surface graphs among the MDI, TPL, DMG and AFTL.

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As can be seen from Fig. 10, the peak MDI with 121.5 mm is reached when the AFTL reaches the highest value (i.e. 600 kN/m) and both the TPL and DMG are the lowest (i.e. 200 mm and 50 MPa/m, respectively). The minimum MDI of 2.0 mm is obtained under the opposite condition where the AFTL reaches the lowest value (i.e. 100 kN/m) and both the TPL and DMG are the highest (i.e. 700 mm and 500 MPa/m, respectively). All faces in Fig. 10 show convex downward. The highest gradient of the contour plot is near the peak MDI where the preliminary lining and DMG are weak, indicating that increasing the TPL and improving the DMG can be effective measures in lowering the risks of dismantling the temporary linings when the preliminary lining and ground are weak.

To better illustrate the impact of the three elements on MDI, three contour plots are extracted from Fig. 10, as shown in Figs. 11, 12 and 13.

Figure 11
figure 11

Curve about MDI concerning the TPL and the DMG.

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Figure 12
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Curve about MDI concerning the DMG and the AFTL.

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Figure 13
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Curve about MDI concerning the TPL and the AFTL.

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Figure 11 presents the influence of the TPL and DMG on MDI. The red section represents the high risks (significant value of the MDI), while the blue section refers to the low risks. The contour lines close to the red area are denser. Along the horizontal axis, increasing the TPL can make the MDI change from the red section to the blue section. Along the vertical axis, increasing the DMG can only make the MDI change from the red section to the yellow section. This indicates that increasing the TPL is more effective in reducing the MDI than increasing the DMG. Increasing the TPL and DMG simultaneously can effectively control the risks of removing the temporary linings.

Figure 12 shows the influence of the AFTL and DMG on the MDI. Along the vertical axis, decreasing the AFTL can make the MDI change from the red section to the blue section. Along the horizontal axis, increasing the DMG cannot make the MDI change from red to blue. This indicates that increasing the AFTL is more effective in reducing the MDI than increasing the DMG. When the axial force Na = Nb = 100 kN/m, the risks of dismantling temporary linings are small (the MDI is in blue), and therefore the impact of DMG on the MDI can be ignored. Note that the entire horizontal axis is blue in color.

Figure 13 displays the influence of the AFTL and TPL on the MDI. Along the horizontal and vertical axes, increasing the TPL or decreasing the AFTL can make the MDI change from the red section to the blue section. Countermeasures of increasing the TPL and decreasing the AFTL simultaneously are effective. Meanwhile, it is noted that when the axial force is small, such as Na = Nb = 100 kN/m, the influence of the TPL on the MDI is slight.

Calculation results based on tunneling method 2 (TM-2)

In TM-2, two more transverse temporary linings are added compared with TM-1. According to Fig. 4b, the AFTLs are marked as Na, Nb, Nc, and Nd. There are still the same three influence factors: AFTL, TPL, and DMG. Since the AFTL in TM-2 is more complicated, calculation cases are divided into three groups in the following analyses: keeping Na = Nb = Nc = Nd, keeping Na = Nb and Nc = Nd, keeping Na = Nb and fixing Nc = 400 kN/m with varying Nd, named as Group A, Group B, and Group C, respectively.

Group A – keeping Na = Nb = Nc = Nd

It is assumed that the axial forces in the transverse-vertical temporary linings are the same, that is, Na = Nb = Nc = Nd. The corresponding calculation cases and results, as well as the comparisons with TM-1 (only vertical temporary linings), are shown in Table 5 and Fig. 14.

  1. (1)

    From the data of each row in Table 5, when the AFTL increases from 200 to 400 kN/m or from 300 to 600 kN/m in TM-2, the MDI just doubled. In other words, the MDI is linearly related to the AFTL when Na, Nb, Nc, and Nd increase simultaneously, as shown in Fig. 14a. However, the values of the MDI in TM-2 are smaller than in TM-1. It implies that dismantling the temporary transverse linings can suppress the MDI led by dismantling the vertical temporary linings. Moreover, when TPL and DMG are fixed, the ratio of MDI in TM-2 to that in TM-1 is the same under the same magnitude of axial force.

  2. (2)

    As shown in Fig. 14b, when Na, Nb, Nc, and Nd are fixed to the same value, the MDI decreases with the TPL and shows a power function relationship. That is consistent with the findings from TM-1. The discrepancy between the solid and dashed curves under the same axial forces increases with the TPL, for example. With the DMG equal to 200 MPa/m, the ratios of the MDIs in TM-2 to those in TM-1 are 0.96, 0.94, 0.92, 0.85, and 0.81 respectively, corresponding to the TPL are 200 mm, 300 mm, 400 mm, 500 mm, and 600 mm. It implies that although the MDI decreases with the TPL, the difference in the MDI between the two tunneling methods increases.

  3. (3)

    As shown in Fig. 14c, when Na, Nb, Nc, and Nd are fixed to the same value, the MDI reduces with DMG and shows a power function relationship. That is consistent with the findings from TM-1. The differences between the solid and dashed curves under the same axial forces decrease with the DMG before they converge at the same point. It indicates that the absolute values of MDI and the differences in MDI between the two tunneling methods decrease with the DMG.

Table 5 Calculation cases and results (MDI/mm) for Na = Nb = Nc = Nd in TM-2 and comparison with TM-1.
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Figure 14
figure 14

Calculation results of TM-2 (Na = Nb = Nc = Nd) and the comparison with TM-1 (Na = Nb).

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Group B – keeping Na = Nb and Nc = Nd

This subsection assumes that the axial force in the two transverse temporary linings varies simultaneously (Nc = Nd), as well as those in the two vertical temporary linings (Na = Nb). However, the axial force in the transverse and vertical temporary lining varies independently. The calculation result is displayed in Table 6 and Fig. 15 under the following conditions: the DMG is set as 200 MPa/m, and TPL is set as 400 mm.

Table 6 MDI location under different AFTL in group B.
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Figure 15
figure 15

Contour chart about MDI concerning the vertical forces (Na = Nb) and the transverse forces (Nc = Nd).

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It should be noted first that the MDI location may change when axial force in the transverse temporary lining is more significant than that in the temporary vertical lining, compared with TM-1. Table 6 summarizes the MDI results and locations. Please assume that the axial force in the temporary vertical lining is small (Na = Nb = 200 kN/m) to explain the evolution of MDI and its location. When the axial force in the transverse temporary lining (Nc and Nd) increases from 200 to 300 kN/m, the MDI location is still at the invert, but the value of MDI decreases. It means that the MDI and its location are mainly dominated by the vertical forces Na and Nb, whereas the transverse forces Nc and Nd only have a suppression effect on the MDI. When Nc and Nd continue to increase from 300 to 500 kN/m, the MDI location changes from the invert to the sidewall. At this stage, it means the MDI is mainly caused by the transverse forces Nc and Nd. When Nc and Nd change from 500 to 600 kN/m, the MDI location is still at the sidewall and the value of MDI increases. With the vertical forces Na = Nb = 400 kN/m and the transverse forces Nc and Nd varying from 200 to 600 kN/m, the MDI location is always at the invert, but the deformation increment at the sidewall becomes from low to high progressively. In addition, the value of MDI continuously decreases due to the suppression effect by Nc and Nd.

With the above analysis, understanding Fig. 15 would be quite straightforward. When the vertical forces are large, for example, Na = Nb = 400 kN/m, the transverse forces (Nc and Nd) make the MDI decrease when it changes from 100 to 600 kN/m, and the decreasing rate of MDI increases. When Na and Nb are small (i.e. 200 kN/m), the MDI will go through light blue—blue—light blue areas with Nc and Nd evolving from 100 to 600 kN/m. This means that Nc and Nd suppress the MDI when the MDI locates at the invert (from light blue to blue area), but Nc and Nd help increase the MDI after the MDI location moves to the sidewall (from blue to light blue area).

Group C – keeping Na = Nb and fixing Nc = 400 kN/m

It is assumed that the axial force in the two vertical temporary linings varies simultaneously (Na = Nb); and that one of the axial forces in the transverse temporary lining Nc is set as 400 kN/m, while the other transverse force Nd varies independently. The calculation result is displayed in Table 7 and Fig. 16 under the following conditions: DMG is set as 200 MPa/m, and TPL is set as 400 mm.

Table 7 MDI location under different AFTLs in group C.
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Figure 16
figure 16

Contour chart of MDI with respect to the vertical forces (Na = Nb) and the transverse force Nd (Nc = 400 kN/m).

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As shown in Table 7, when Na = Nb = 200 kN/m, Nc = 400 kN/m, and Nd = 200 kN/m, the MDI location is near the Nc action point. This is because the dominant force dominates the MDI and its location. In this example, Nc = 400 kN/m is the dominant force. Increasing Nd from 200 to 300 kN/m makes the MDI slightly increase, but the MDI location is still near the Nc action point. When further increasing Nd from 300 to 500 kN/m, the MDI increases, and the MDI location moves to near the Nd action point because of the same reason that the dominant force dominates the MDI and its location. When Nd increases from 500 to 600 kN/m, the MDI increase rate is more appreciable, and the MDI location gets closer to the Nd action point.

Moreover, the difference in MDI caused by increasing Nd from 200 to 300 kN/m is much smaller than that caused by increasing Nd from 500 to 600 kN/m. It implies that when Nd is smaller than Nc, the MDI location is near the Nc action point, and Nd has little effect on the MDI. On the contrary, when Nd is more significant than Nc, the MDI location is near the Nd action point, and Nd directly affects the MDI. On the other hand, when Na = Nb = 400 kN/m, Nc = 400 kN/m, and Nd = 200 kN/m, the MDI is located at the invert. With Nd increasing from 200 to 600 kN/m, the MDI location is always at the invert, but the MDI decreases. This is because the dominant force dominates the MDI and its location and because the forces in vertical and transverse linings are suppressing each other.

Moreover, the difference in MDI caused by increasing Nd from 200 to 300 kN/m is much smaller than that caused by increasing Nd from 500 to 600 kN/m. It implies that when Nd is smaller than Nc, Nc is dominant in the suppression effect on the MDI; Otherwise, Nd is dominant in comparison with Table 6 where Nc = Nd, a sudden increase or decrease in the MDI is not observed in the current case where Nc ≠ Nd.

Figure 16 presents the relationship among the MDI, the vertical forces (Na = Nb), and one of the transverse force Nd under condition of Nc fixing to 400 kN/m. When the vertical forces Na and Nb are greater than 400 kN/m, varying Nd from 100 to 600 kN/m makes the MDI decrease, but the MDI decrease rate is lower than that in Fig. 15. When Na = Nb = 250 kN/m, the MDI will decrease then increase with Nd varying from 100 to 600 kN/m. This is because of the change of the MDI location. When Na and Nb are smaller than 200 kN/m, increasing Nd from 100 to 600 kN/m makes the MDI increase, since the MDI location is always at the sidewall.

Countermeasure and tunneling method optimization

In this paper, displacement risks associated with dismantling the two conventional types of temporary linings have been evaluated using the bedded-beam model. From the results above, some countermeasures to control the risks can be proposed:

  1. (1)

    Replacing temporary linings with pre-tensioned anchor cable or bolt in order to avoid the adverse effects of forces in temporary linings during temporary lining dismantling stages.

  2. (2)

    Involving multi-layered preliminary linings to enhance the TPL.

  3. (3)

    Adopting grouting to improve the ground. From the sensitivity of these three factors, the first countermeasure would be efficient in controlling the risks in tunnel.

According to the risk-control countermeasures above, the tunneling method can be progressively optimized with the help of the pre-tensioned anchor cables in the following way (see Fig. 17):

  1. (1)

    Excavating tunnel in the sequence according to the original method shown in Fig. 17a; and replacing temporary linings with pre-tensioned anchor cables as shown in Fig. 17b. The preliminary lining as well as temporary lining is constructed immediately after every construction round. Before dismantling the temporary linings, installing pre-tensioned anchor cable to reduce the AFTL (see in Fig. 17b).

  2. (2)

    The role of transverse temporary lining would be replaced by that of pre-tensioned anchor cables, and thereafter, the temporary transverse linings can be removed after the installation of pre-tensioned anchor cables (in Fig. 17c).

  3. (3)

    The vertical temporary linings can be cut short, and the drifts would be adjusted correspondingly, as shown in Fig. 17d.

Figure 17
figure 17

The optimization route about the tunneling method.

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Optimized tunneling method application

Through optimizations on-site, the final adopted tunneling method is presented in Fig. 18. The longitudinal and transverse spacing of the anchor cables are both 1.2 m. For each cable, the free length and bonding length are both 10 m; and the pre-tension force is initially set as 500 kN, later adjusted to 300 kN. The pre-tensioned anchor cables are vital to controlling the risk of dismantling temporary linings. From the plan view of the tunneling method in Fig. 18b, a long section (more than 62 m) can be constructed without temporary linings between the upper bench and final lining. In this way, project construction period and costs can be greatly reduced by removing the limited working space restraints resulting from the installation of temporary linings, and hence by accommodating the functions of heavy duty machines/equipment in this long section. Figure 19 presents the on-site photos about adopting the pre-tensioned anchor cable to replace temporary linings. There is no sudden increase in monitoring data during the period of dismantling the temporary linings.

Figure 18
figure 18

Final adopted tunneling method.

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Figure 19
figure 19

On-site photos of the temporary linings replaced by pre-tensioned anchor cables.

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Conclusions

  1. (1)

    Based on the three influence factors, several countermeasures to decrease the risks of dismantling the temporary linings are put forward. By using the pre-tensioned anchor cables, most of the temporary linings in TM-2 are removed, and the axial force in the remained temporary lining is transferred to cables before removing the temporary linings. The optimized tunneling method is verified on site and shown to effectively control the risk of removing the temporary linings.

  2. (2)

    TM-1 always induces invert uplift, whereas TM-2 mainly brings about invert uplift or sidewall bulging depending on which linings, transverse or vertical, are dominant in terms of axial force values. When the axial forces in the vertical temporary linings are dominant, the deformation increment about preliminary linings caused by removing the temporary lining is mainly manifested as the uplift at the invert. If the axial forces in the temporary transverse linings are significantly greater than that in the temporary vertical lining, the MDI location about the preliminary linings will occur at the sidewall.

  3. (3)

    In TM-1 (double vertical temporary lining), if the axial force in double vertical temporary linings simultaneously increases (Na = Nb), the relationship between the MDI and the axial forces is linear. Otherwise (Na ≠ Nb), the MDI will significantly increase compared with the case of Na = Nb. In TM-2 (double vertical and double transverse temporary linings), the MDI is also linearly related to the AFTL when Na, Nb, Nc, and Nd simultaneously increase (i.e. Na = Nb = Nc = Nd). The axial force in the transverse temporary lining (Nc and Nd) suppresses the MDI when the MDI is located at the invert, while Nc and Nd enhance the MDI after the MDI location moves to the sidewall.

  4. (4)

    The TPL affects the MDI in the way that can be expressed using a power function. MDI reduces with the TPL, while the trend weakens with the increase of TPL. Similarly, MDI shows a power function relationship with DMG.