To further reveal the failure mechanism of the supporting structures at tunnel portal, the finite difference software FLAC3D 5.0 was used to simulate and analyze the dynamic tunnel portal excavation process.
4.2.1 Model establishment and boundary conditions
A three-dimensional numerical model was established according to the geological exploration data and the slope topography conditions of tunnel portal, as shown in Fig. 9. To eliminate the boundary effect, the distance between model boundaries and tunnel boundaries was three times the tunnel width, and the length of entire model was 100 m. The distance between lower model boundary and tunnel arch bottom was three times the tunnel height, and the upper model boundary was taken to the ground surface. According to the field investigation, the failure of supporting structures mainly occurred in YK39 + 866-YK39 + 910, so the longitudinal length of model was 60 m. In the process of numerical simulation, the normal displacement of four vertical boundaries was constrained, and the displacement in all directions of bottom boundary was constrained, and the top was a free boundary. The established numerical model included 296005 elements and 167004 nodes in total.
In the numerical simulation, the construction process and support parameters at tunnel portal were consistent with the actual situation. That is, the pipe shed was installed before the tunnel excavation, and the retaining wall was constructed on the right side of right tunnel (Fig. 9). The upper and lower bench method was adopted to excavate the right tunnel first, and the construction step length of each cycle was 1.0 m. The primary support was applied immediately after the tunnel portal excavation, while the application of secondary lining was 12 m behind the tunnel face. The excavation of the left tunnel was 8 m behind the right tunnel face.
4.2.2 Material parameters and simulation cases
In this simulation, the failure of surrounding rock followed Mohr-Coulomb yield criterion. Elastic element was used for retaining wall and concrete. The specific simulation parameters were shown in Table 1. The cable element was used to simulate the pre-grouting pipes and anchor bolts. The grouting reinforcement effect was achieved by increasing the strength of surrounding rock in the reinforcement area. The beam element was used to simulate the pipe shed. The specific simulation parameters of the pipes, anchor bolts and pipe shed were shown in Table 1–2.
Table 1
Parameters of surrounding rock, retaining wall and supporting structures
Material types | Unit weight (kN/m3) | Elastic modulus (MPa) | Poisson’s ratio | Cohesion (kPa) | Internal friction angle (°) |
Gravel soil | 18.5 | 50 | 0.42 | 20 | 18.6 |
Saturated gravel soil | 21.6 | 32.5 | 0.45 | 12.6 | 13.2 |
Slate with sandstone | 20.4 | 1560 | 0.24 | 110 | 39.2 |
Retaining wall | 25.0 | 28000 | 0.2 | | |
Primary support | 25.0 | 28000 | 0.2 | | |
Secondary lining | 25.0 | 31000 | 0.2 | | |
Advanced small pipe | 78.5 | 210000 | 0.3 | | |
Anchor bolt | 78.5 | 210000 | 0.3 | | |
Table 2
Length (m) | Elastic modulus (GPa) | Poisson’s ratio | Cross-sectional area (m2) | Polar moment of inertia (m4) | Secondary moment of Y axis (m4) | Secondary moment of Z axis (m4) |
40 | 65.6 | 0.262 | 1.88×10− 3 | 9.82×10− 6 | 4.91×10− 6 | 4.91×10− 6 |
According to the field investigation results, the rainy season came soon after the tunnel portal excavation. Atmospheric precipitation and surface water infiltrated through the cracks into the surrounding rock. Therefore, the influence of water infiltration was also taken into account in the simulation. Based on the model in Fig. 9, three excavation cases were simulated: ① only right tunnel was excavated; ② the right tunnel was excavated first, and the left tunnel was excavated 8 m behind the right tunnel face; ③ on the basis of case 2, considering the influence of surface water infiltration, the saturated gravel soil parameters were used to replace the original surrounding rock parameters. The parameters of saturated gravel soil were obtained from laboratory triaxial test, as shown in Table 1.
4.2.3 Analysis of simulation results
Two typical sections of YK39 + 871 and YK39 + 902 at right tunnel were selected to analyze the deformation and stress characteristics of surrounding rock and supporting structures.
Figure 10 presented the deformation of surrounding rock and supporting structures at YK39 + 871 under three cases. Table 3 showed the field monitoring results and numerical simulation results of surrounding rock deformation at various positions at this section under case Ⅰ, in which the vertical deformation was positive upward and the horizontal deformation was positive to the right. Combined with Fig. 10 (a) and Table 3, after the right tunnel portal excavation, the deformation of surrounding rock and supporting structures presented obvious asymmetry due to the influence of topographic bias. The maximum deformation occurred at left arch shoulder, reaching 25.181 mm. As the tunnel left side was deep buried side, the tunnel structure was shifted to lower right under the significant loose load generated by the gravel soil at left side. These deformation characteristics were consistent with the field monitoring results. The deformation of retaining wall showed the characteristics of rotating clockwise with wall corner as the center, that is, the deformation value gradually increased from wall corner to wall top. Form Table 3, it could be seen that the simulation results of surrounding rock deformation at various positions in YK39 + 871 section were in good agreement with the monitoring results. It indicated that the established numerical model and the simulation parameters were conformed to the actual project, and the calculation results were reasonable and feasible.
Table 3
Comparison between field monitoring and numerical simulation of deformation at YK39 + 871 section (unit: mm)
Positions | Field monitoring value | Numerical simulation value |
Vault | Vertical deformation | 6.0 | 4.78 |
Horizontal deformation | 9.0 | 9.75 |
Left arch waist | Vertical deformation | -16.0 | -15.36 |
Horizontal deformation | 18.5 | 19.23 |
Right arch waist | Vertical deformation | 1.5 | 1.27 |
Horizontal deformation | 6.0 | 6.42 |
From the Fig. 10 (a)-(b), the left tunnel excavation had an obvious negative influence on the stability of right tunnel. After the left tunnel portal excavation, the surrounding rock deformation at right tunnel increased significant, and the asymmetrical deformation and tendency of right tunnel to shift to right was more pronounced. The deformation at the left arch shoulder increased from 25.181 mm to 36.663 mm. It showed that under small clear-distance tunnel arrangement, the following tunnel excavation could aggravate the prior tunnel deformation, which was not conducive to the prior tunnel stability. Comparing Fig. 10 (a)-(c), after the gravel soil was immersed and deteriorated, the asymmetrical loose load on tunnel portal increased sharply. The deformation at left arch shoulder surged to 90.878 mm, and the deviation trend of tunnel structure from deep buried side to shallow buried side was further intensified.
Figure 11 presented the deformation of surrounding rock and supporting structures at YK39 + 902 under three cases. Comparing Fig. 10 and Fig. 11, the surrounding rock load borne by tunnel structures gradually increased with the thickness of overlying surrounding rock gradually increased, resulting in the deformation of surrounding rock and supporting structures also gradually increased. The deformation was still asymmetry and the maximum deformation position of surrounding rock was transferred from left arch shoulder to right side of vault (Fig. 11a-b). Comparing Fig. 11 (a) and (b), the following tunnel excavation aggravated the surrounding rock deformation of prior tunnel, and the maximum deformation at vault increased from 58.525 mm to 76.385 mm. After the gravel soil layer was immersed and deteriorated, the surrounding rock deformation at vault surged to 99.296 mm, and the maximum deformation shifted from vault to slope surface. It indicated that the slope instability was prone to occur under case Ⅲ. Thus, it was recommended to take some auxiliary measures for slope waterproofing and drainage and stabilized the stratum before excavation.
Figure 12 presented the tensile stress of the retaining wall at YK39 + 871, and Fig. 12 (a) was the tensile stress nephogram of the retaining wall under case Ⅲ. After the tunnel portal were excavated, the right tunnel tended to shift to right under the loose rock load on deep buried side, and the retaining wall built on the shallow buried side could effectively limit the tunnel deviation. However, the significant deformation of tunnel could cause obvious tensile stress on the retaining wall body, especially at points A and B in Fig. 12 (a). Figure 12 (b) showed the tensile stress at points A and B under various cases. When only right tunnel was excavated, the maximum tensile stress on the retaining wall appeared at point B, reaching 0.358 MPa. After the left tunnel was excavated, the maximum tensile stress was transferred to point A, reaching 1.071 MPa. After the gravel soil was immersed and deteriorated, the tensile stress at point A increased sharply to 2.031 MPa, which had exceeded the ultimate tensile strength of C25 concrete (JTG 3370.1–2018). At the same time, the tensile stress at point B also increased to 1.847 MPa. Comparing Fig. 12 (a) with Fig. 5, the tensile stress concentration position of the retaining wall obtained by numerical simulation was consistent with the cracking position of the retaining wall in actual project. It indicated that the retaining wall body cracked due to excessive tensile stress in the process of limiting the tunnel deviation.
Figure 13–14 presented the tensile stress and shear stress of primary support concrete at two typical sections, respectively. From Fig. 13 (a) and Fig. 14 (a), affected by the loose rock load on the deep buried side, the maximum tensile stress and shear stress at YK39 + 871 appeared between left arch shoulder and waist under case Ⅲ, that is, the position with the maximum deformation of tunnel. After the left tunnel was excavated, the maximum tensile stress increased from 1.703 MPa to 1.952 MPa (Fig. 13c), which was very close to the ultimate tensile strength of C25 concrete (JTG 3370.1–2018). The maximum shear stress also increased from 1.501 MPa to 2.328 MPa (Fig. 14c). The concrete at arch shoulder and waist was prone to cracked due to obvious tensile stress and shear stress. As the excavation progresses, the thickness of overlying soil increased, and the position subjected to the maximum tensile stress and shear stress on the primary support concrete shifted to right shoulder (Fig. 13b and 14b), that is, the position with the maximum deformation of tunnel at YK39 + 902. After the left tunnel excavation, the maximum tensile stress and shear stress increased from 1.387 MPa and 1.042 MPa to 1.826 MPa and 1.728 MPa, respectively (Fig. 13c and 14c). And then the maximum tensile stress and shear stress increased rapidly to 2.555 MPa and 2.881 MPa when the surrounding rock was immersed and deteriorated. Under such significant tensile stress and shear stress, the primary support concrete was easily cracked, peeled and even collapsed. The stress concentration position was also consistent with the position of cracking and falling blocks of the primary support concrete in actual project (Fig. 6).
Figure 15–16 presented the tensile stress and shear stress of secondary lining concrete at two typical sections, respectively. According to the Fig. 15 (a) and 16 (a), the maximum tensile stress and shear stress of secondary lining concrete at YK39 + 871 appeared between left arch shoulder and waist in case Ⅲ, which was consistent with the stress concentration position of primary support concrete. From the Fig. 15 (c) and 16 (c), after the excavation of left tunnel and the water immersion deterioration of surrounding rock, the tensile stress and shear stress increased rapidly, and the tensile stress reached 2.107 MPa in case Ⅲ, which was very close to the ultimate tensile strength of C30 concrete (JTG 3370.1–2018). Therefore, the secondary lining concrete at left arch shoulder and waist was most likely to crack due to excessive tensile stress (Fig. 15a and 16a). It was also consistent with the crack distribution characteristics in actual project, that is, the number of secondary lining cracks at left arch shoulder and waist at tunnel portal was significantly more than that in other positions in Fig. 8 (a). As the excavation progresses, the maximum tensile stress shifted to between vault and right shoulder (Fig. 15b). The maximum tensile stress increased to 2.292 MPa in case Ⅲ (Fig. 15b-c), which had exceeded the ultimate tensile strength of C30 concrete. The secondary lining concrete at YK39 + 902 had shear stress concentration at right arch shoulder and waist (Fig. 16b). The maximum shear stress could reach 2.48 MPa in case Ⅲ (Fig. 16b-c), and the concrete at these positions was prone to crack due to excessive shear stress. From Fig. 15 (b) and 16 (b), the tensile stress and shear stress concentration positions coincided with the concentrated distribution positions of secondary lining cracks at this section in Fig. 8 (a).