Keyword

1 Introduction

With the rapid growth of the economy in recent years, the transportation channels have expand rapidly, increasing the number and size of transportation tunnel projects. The shield method, as an important method of tunnel construction, is widely used in engineering [1]. Geological and engineering factors play a crucial role in determining the extent of surrounding rock disturbance caused by shield tunneling. Geological factors include stratum stress field, groundwater seepage field, stratum structure, etc., while engineering factors mainly include shield machine type, tunnel shape and size, tunnel burial depth, etc. In addition, the influence of tunneling parameters, such as palm face pressure and grouting pressure, also has a great impact on tunnel settlement. The evaluation of tunneling-induced disturbance in shield tunnel projects is of paramount importance, extensive research has been conducted. For instance, Qin [2] utilized Plaxis software to simulate the tunneling process of a shield machine under three distinct stratigraphic conditions, and studied the influence law of palm face pressure, shrinkage, and grouting pressure on the ground surface settlement and deformation. Ma et al. [3] found that increasing the excavation chamber pressure and synchronous grouting pressure for diversion tunnel engineering can reduce the maximum settlement. However, the present research often focuses on studying the influences of engineering factors, tunneling parameters and seepage process on the tunneling disturbance, research that considers the influence of strata anisotropy has not been paid enough attention.

Affected by the complex development of geological structures, natural strata often exhibit significant anisotropic characteristics. Many methods have been proposed to consider the influence of material anisotropy on its strength. Shi et al. [4] proposed a novel method for predicting the anisotropic strength of layered rocks based on the principle that weak surfaces within the rocks cause a reduction in the compressive strength. Based on the theory of a single weak surface, Bao et al. [5] derived a functional relationship between the compressive strength of slate and the inclination angle of the discontinuity. Pietruszczak et al. [6] proposed to incorporate the microstructure tensor and the relevant mixed invariants to characterize the anisotropic strength of material. Characterizing the influence of material anisotropy on strength based on microstructure tensor approach has a clear physical significance. Inspired by the work done by Pietruszczak et al. [6], the microstructure tensor theory has widely been used in material anisotropy characterization [7, 8].

In this study, a refined shield tunneling disturbance simulation method based on the microstructure tensor theory is proposed to reveal the influence of stratum strength anisotropy induced by the complex development of natural geological structures on the shield tunneling disturbance. The proposed method finely considered the process of shield shell advancement, lining installation, and shield tail grouting. The microstructure tensor theory is used to characterize the material anisotropy effects on its shear strength parameters. Based on a large shield tunnel project located in Wuhu City, Anhui Province, China, the proposed method is used to simulate the shield tunneling disturbance and verified with monitoring data, and the influence of strata strength anisotropy on the tunneling disturbance is analyzed.

2 Theoretical and Simulation Methods

In order to better simulate the shield tunneling disturbance with the consideration of stratum strength anisotropy induced by geological structures. The methods for refined shield tunneling simulation and stratum strength anisotropy characterizing are elaborated in this section.

2.1 Shield Tunneling Refined Simulation Method

The shield tunneling disturbance is simulated by a refined simulation method based on the structural dimensions and operation mode of the shield machine. The method accurately considers the influences of shield shell advancement, lining installation, and shield tail grouting, through continuously altering the attributes of the shield shell and lining elements and adjusting the positions of applied palm face pressure and grouting pressure according to the shield tunneling process in FLAC3D software.

Fig. 1.
figure 1

Schematic diagram of the refined simulation of shield tunneling

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Based on the shield tunneling process of the shield tunnel project selected in this study, the shield shell is modeled with seven rings of lining segment, as shown in Fig. 1, in which the shield is assumed to tunnel to the nth ring of lining segment. The transition zone is used to simulate the shield tail grouting, considering the size difference between the diameter of the shield and the outer ring diameter of the lining. The length of the grouting pressure acting in the transition zone at the tail of the shield is one ring of lining segment. After finely building the shield tunneling calculation model based on the tunneling size of each ring, the specific simulation of shield tunneling is divided into two stages as follows:

  1. (1)

    In the first stage, the shield shell gradually enters the stratum, there is no shield tail lining installation process. Whenever the shield tunneling forwards a ring distance, excavate stratum elements inside the tunnel, activate the shield shell elements and apply palm face pressure on the excavation face until the shield shell fully enters the stratum (the shield tunneling forwards seven-ring distance).

  2. (2)

    In the second stage, the whole shield shell is in the stratum, and the processes of the lining installation and shield tail grouting should be considered. After the completion of the previous stage of tunneling simulation, when the shield tunneling forwards to the 8th ring, excavate stratum elements inside the tunnel, activate the shield shell elements in the 8th ring, and apply palm face pressure on the excavation face. Meanwhile considering the lining installation and shield tail grouting process, change the shield shell elements in the 1st ring as the transition zone elements, activate the lining elements in the 1st ring, and apply grouting pressure in these elements. Afterwards, the subsequent simulation of shield tunneling is conducted according to the above simulation process, by continuously-regularly activating the shield elements, applying palm face pressure on the excavation face, adjusting the shield shell element in the tail to the transition zone elements and applying grouting pressure, until the end of the simulation.

2.2 Theory of Stratum Strength Anisotropy Analysis

Affected by the dominant-orientation development of geological structures, the stratum strength may exhibit significant anisotropic characteristics [7]. In order to consider the influence of stratum strength anisotropy during shield tunneling modeling, the microstructure tensor theory proposed by Pietruszczak et al. [6] is adopted to characterize the anisotropy of the shear strength parameters cohesion c and internal friction angle φ, with the following expressions:

$$ c = c_{0} \left[ {1 + A_{ij} l_{i} l_{j} + b_{1} \left( {A_{ij} l_{i} l_{j} } \right)^{2} } \right] $$
(1)
$$ \varphi = \varphi_{0} \left[ {1 + B_{ij} l_{i} l_{j} + b_{2} \left( {B_{ij} l_{i} l_{j} } \right)^{2} } \right] $$
(2)

where Aij and Bij are traceless symmetric tensors describing the bias in the spatial distribution of cohesion and internal friction angle [4]; \(c_{0}\) \(\varphi_{0}\) b1 and b2 are material parameters; li are the components of the generalized loading vector associated with the principal triad of the microstructure tensor [8].

For the layered stratum, cut by only one set of parallel structural planes, one obtains, \(A_{ij} l_{i} l_{j} = A_{1} (1 - 3l_{3}^{2} )\) \(B_{ij} l_{i} l_{j} = B_{1} (1 - 3l_{3}^{2} )\) in which \(l_{3}^{2} = \frac{{tr({\varvec{m}} \otimes{\varvec{m\varSigma}}^{2} )}}{{tr({\varvec{\varSigma}}^{2} )}}\), m denotes the unit normal vector of the parallel structural planes, represents the stress tensor. Then Eqs. (1)– (2) 1can be simplified as:

$$ c = c_{0} \left[ {1 + A_{1} \left( {1 - 3l^{2} } \right) + b_{1} \left( {A_{1} \left( {1 - 3l_{3}^{2} } \right)} \right)^{2} } \right] $$
(3)
$$ \varphi = \varphi_{0} \left[ {1 + B_{1} \left( {1 - 3l_{3}^{2} } \right) + b_{2} \left( {B_{1} \left( {1 - 3l_{3}^{2} } \right)} \right)^{2} } \right] $$
(4)

3 Modeling Analysis of Large-Diameter Shield Tunneling Disturbance

A large-diameter shield tunnel under construction, located at the “Big Bend” of the Wanjiang section of the Yangtze River in Wuhu City, Anhui Province, China is selected as the research object in this paper. The length of the shield tunnel is about 3.9 km, starting from the Jiangbei work shaft with two mud-water balanced shields, tunneling southward crossing the Yangtze River, and then reaching the Jiangnan work shaft. The right-line shield tunneling first, with the diameter of the shield shell is 15.07 m. After tunnel excavation, a reinforced concrete lining with a thickness of 0.6 m is utilized, with a length of 2 m for each ring of the lining segment. The outer diameter of the lined tunnel is 14.5 m, while the inner diameter is 13.3 m. Taking the tunneling section of the right-line shield tunnel from 60 m to 122 m in front of the Jiangbei working shaft for study, a 3D finite element calculation model is established, as shown in Fig. 2. The actual geological strata and tunnel structure are finely considered by the calculation model, with a total of 208530 elements and 218816 nodes. The Mohr-Coulomb model in the FLAC3D software is utilized to characterize the mechanical behavior of strata.

Fig. 2.
figure 2

Schematic diagram of the 3D finite element calculation model of the tunnel

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According to the engineering geological investigation report, the material parameters for shield tunneling simulation are shown in Table 1. In order to truly reflect the weight of all components inside the shield, the equivalent weight of the shield shell elements should be converted based on its thickness [9]. The calculated parameters for the shield shell are Elastic modulus of 200 GPa, Poisson’s ratio of 0.3, and specific weight of 247 kN·m−3. The palm surface pressure is taken as 0.25 MPa, and the grouting pressure is 0.2 MPa. The assumptions for calculation are: (1) the strata are homogeneous and continuous; (2) the possible temporary loads on the ground are neglected; (3) the stiffness reduction effect of the connection between lining segments is not considered; (4) the grouting pressure is evenly distributed along the surface of the pipe segment. The initial and boundary conditions used are: Zero-displacement normal constraints are applied on the bottom and lateral boundaries of the calculation model; The initial stress field is determined by conducting strata self-weight stress calculation.

Table 1. Material parameters for shield tunneling simulation
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4 Results Analysis for the Shield Tunneling Disturbance

To verify the effectiveness of the refined shield tunneling simulation method, the simulation analysis of the shield tunneling disturbance is first conducted and compared with monitoring data. Figure 3 presents the vertical displacement distribution on the A-A profile (location shown in Fig. 2) induced by shield tunneling forward to different lining rings. When tunneling to the 7th ring, the whole shield shell just enters into the stratum, the induced longitudinal settlement range is about 38 m, and the maximum surface settlement is 7.5 mm located right above the excavation surface. As the shield tunnels forward, the settlement at the top of the tunnel increases. When tunneling to the 25th ring, the maximum surface settlement increases to 14.4 mm, which is about 92% higher than the result obtained when tunneling to the 7th ring. After shield tunneling, there are locally large settlement areas at the top and excavated surface of the tunnel, while a significant uplift occurred at the bottom, which is mainly caused by the unloading effect of tunnel excavation.

Fig. 3.
figure 3

Vertical displacement distribution on A-A profile after tunneling to different ring numbers (m)

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Figure 4 shows the vertical displacement distribution on the C-C profile (location shown in Fig. 2) induced by shield tunneling forward to different lining ring numbers. After shield tunneling, the ground surface settlement on the transverse profile is symmetrically distributed along the tunnel’s central axis, and the range of the settlement area is about 3 times the diameter of the tunnel. The induced settlement above the tunnel on the C-C profile increases with the forward tunneling of the shield. When tunneling to the 7th ring, the maximum settlement on the surface is 6.7 mm, and obviously increases to 12.2 mm after tunneling to the 25th ring, with an increment of 82%.

Fig. 4.
figure 4

Vertical displacement distribution on C-C profile after tunneling to different ring numbers (m)

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The comparisons between the simulated and measured settlement values on the A-A and C-C profiles after tunneling to the 7th ring, 11th ring, 13th ring and 25th ring are respectively shown in Figs. 5 and 6. With the forward tunneling of the shield, the ground surface settlement gradually increases. The surface settlement in front of the excavation surface decreases with the increasing distance from the excavation surface. The simulated surface settlements after tunneling to different lining ring numbers agree well with the monitoring data on the A-A and C-C profiles, demonstrating the effectiveness and reliability of the refined shield tunneling simulation method considering the process of shield shell advancement, lining installation, and shield tail grouting.

Fig. 5.
figure 5

Comparison of simulated and monitored surface settlements on A-A profile after tunneling to different ring numbers

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Fig. 6.
figure 6

Comparison of simulated and monitored surface settlements on C-C profile after tunneling to different ring numbers

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5 Influence of Stratum Strength Anisotropy on the Tunneling Disturbance

To analyze the influence of stratum strength anisotropy on the shield tunneling disturbance, the experimental data of anisotropy compression strength on layered stratum in other sections of the large-diameter shield tunnel projects is used to characterize the anisotropy of the stratum where the shield located. By best fitting the triaxial compression strengths under the confining pressure of 0.5 MPa, 1.5 MPa and 3.0 MPa with different dip angles of the layered structures, the anisotropic expressions for cohesion and internal friction angle can be obtained as.

$$ c = 5.33\left[ {1 + 0.6\left( {1 - 3l_{2}^{2} } \right) + 1.81\left( {0.6\left( {1 - 3l_{2}^{2} } \right)} \right)^{2} } \right] $$
(5)
$$ \varphi = 15.65\left[ {1 + 0.172\left( {1 - 3l_{3}^{2} } \right) + 3.7\left( {0.172\left( {1 - 3l_{3}^{2} } \right)} \right)^{2} } \right] $$
(6)

Based on Eqs. (5)–(6), the comparison of the predicted and experimented strengths for layered stratum with different dip angles of layered structures are shown in Fig. 7. One can find from Fig. 7 that the strength of layered stratum is closely related to the dip angle of the layered structures, and the predicted anisotropic strengths for layered stratum based on the microstructure tensor theory agree well with the experimental results. By applying the expressions for the anisotropy of cohesion and internal friction angle in the refined shield tunneling simulation, the influence of stratum strength anisotropic can be studied.

Fig. 7.
figure 7

Predicted and experimented strengths for layered stratum with different dip angles of layered structures

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Previous studies have shown that the anisotropic strength characteristic of layered strata plays a significant impact on the excavation disturbance of underground engineering [10]. In this section, the layered stratum with anisotropic strength characterized by Eqs. (5)–(6) is used to simulate the stratum where the tunnel located in the calculation model (shown in Fig. 2), and the dip angle of layered structural planes is set to be 45°. The simulation cases for studying the influences of shear strength parameters anisotropy on the shield tunneling disturbance are described in Table 2, in which case 1 and case 2 respectively only consider the cohesion and internal friction angle anisotropy, case 3 considers the anisotropy of cohesion and internal friction angle, case 4 does not consider the anisotropy influence.

Table 2. Calculation parameters for different considerations of stratum anisotropy
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After shield forward tunneling to the 25th ring, the distributions of vertical displacement on profiles of A-A and C-C under different considerations of shear strength parameters anisotropy are shown in Figs. 8–9. The settlement above the tunnel increases obviously with the consideration of cohesion and internal friction angle anisotropy, and the surface settlement caused by the anisotropy of internal friction angle is obviously bigger than that of cohesion anisotropy.

Fig. 8.
figure 8

Vertical displacement distribution on A-A profile under different considerations of strength anisotropy after tunneling to the 25th ring (m): (a) cohesion anisotropy (b) internal friction angle anisotropy (c) anisotropy of cohesion and internal friction angle

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Fig. 9.
figure 9

Vertical displacement distribution on C-C profile under different considerations of strength anisotropy after tunneling to the 25th ring (m): (a) cohesion anisotropy (b) internal friction angle anisotropy (c) anisotropy of cohesion and internal friction angle

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Figure 10 shows the surface settlement curves on C-C profile under different considerations of strength anisotropy after tunneling to the 25th ring. The surface settlement curves caused by shield tunneling all show a “U-shaped” curve, and the maximum settlement is basically on the central axis of the excavation tunnel. The difference between the surface settlement curves calculated by only considering cohesion anisotropy and the case without considering strength anisotropy is small. The surface settlement calculated by considering the anisotropy of the internal friction angle is obviously larger than that without considering strength anisotropy, with the maximum surface settlement increasing from 10.2 mm to 24.1 mm. When considering the anisotropy of both cohesion and internal friction angle, the shield tunneling-induced surface settlement increases further, the maximum settlement value is 38.0 mm. Therefore, the anisotropic strength characteristics of the stratum can play a significant effect on the shield tunneling disturbance. It’s dangerous to ignore the effect of stratum strength anisotropy, and its impact should be accurately considered in the design and construction of shield tunnels based on the actual anisotropy characteristics of the stratum.

Fig. 10.
figure 10

Surface settlement curves on C-C profile under different considerations of strength anisotropy after tunneling to the 25th ring

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6 Conclusions

In this study, a shield tunneling refined simulation method considering stratum strength anisotropy is established and utilized to simulate the tunneling disturbance in a certain section of a large shield tunnel project, and the influence of shear strength parameters’ anisotropy is analyzed. Following conclusions are drawn:

  1. (1)

    The processes of shield shell advancement, lining installation, and shield tail grouting are effectively considered by the refined shield tunneling simulation method, which has successfully modeled the tunneling disturbance in a certain section of a super-large-diameter shield tunnel in Wuhu City, Anhui Province, China. The “U-shaped” distribution of surface settlement induced by shield tunneling is in a range of about three times the diameter of the tunnel, with the maximum value located on the central axis of the excavated tunnel and increases as the shield tunneling forward. The simulated surface settlements on the axial and transverse profiles of the excavated tunnel after tunneling to different lining-ring numbers agree well with the monitoring data.

  2. (2)

    The shield tunneling disturbance is greatly influenced by the anisotropy of stratum shear strength caused by the dominant-orientation development of geological structures. The shield tunneling-induced surface settlement under the case considering the anisotropy of layered stratum material’s cohesion and internal friction angle is much larger than the result under the case of isotropic shear strength. Compared to the influence of stratum cohesion anisotropy, the effect of internal friction angle anisotropy has a greater impact on the shield tunneling disturbance. Therefore, attention should be paid to considering the influence of shear strength anisotropy on the shield tunneling disturbance in actual anisotropic strata, and it’s dangerous to ignore its effect.

It is worth noting that in the simulation studies of this paper, only the influence of anisotropy caused by the development of structures in a single direction on shield tunneling is considered, and the anisotropic characteristics of actual strata may be more complex, it will be considered in our future research.