The methodology of the existing displacement control is illustrated taking the shield of twin tunnels of Line 4 underpassing the upline tunnel of existing metro Line 1, for example. Vertical, horizontal, and convergence displacement of the existing tunnel is monitored and analyzed in detail in this paper. Shield parameters are predefined and adjusted based on the feedback of the displacement of Line 1. Shortterm displacement of the existing tunnel is greatly influenced by the relative distance between the shield face and the existing tunnel and shield parameters. The shapes of horizontal and convergence displacement curves are similar. Line 1 is reinforced, and a new analysis method is firstly proposed for the design of reinforcement of the existing tunnel which is verified by the analytical methods derived from prior studies. The results show that the change of reinforcement stiffness has a greater effect on the normalized bending moment and the normalized shear force of the existing tunnel, and reinforcement of 25 rings on either side of the intersection point is the best choice in this case. The proposed model can be widely applicable for reinforcement design and safety check of the existing tunnel.
The interaction between new shield construction and existing tunnel has become a common and important issue with the rapid development of underground traffic system, which has been studied in the past using a variety of approaches: field observations, model tests, analytical methods, and finite element modeling. Kim and Liu et al. [
In order to ensure the stability of the existing tunnel, local thickening is needed at the sides of the existing concrete lining. There are a plenty of research about the conventional reinforcement methods such as inner steel plate reinforcement or new reinforcement approaches such as FRC or composite concrete, but they all focus on the performance of reinforcement on the single ring. The effect of reinforcement on the longitudinal behavior of the tunnel is not yet clear in current analysis. The analytical method of longitudinal displacement of the tunnel due to adjacent excavation and multiple tunnelling is researched a lot: (1) the elastic continuum models developed by Vorster et al. [
The major objectives of this paper are (1) to investigate the influence of the tunnel driving parameters and the relative distance between the shield and the existing tunnel on the existing tunnel based on the interpretation of the field measured data and (2) to study the effects of different stiffness and ranges of reinforcement on the existing tunnel using analytical methods.
The location of the Line 4 tunnels and the upline of Line 1 are shown in Figure
Location of the new tunnels and the existing tunnel in Hangzhou. A: Guanhe Station; B: East railway station.
Plan view of tunnel alignment and location of the monitored rings.
Figure
Longitudinal profile of soils and tunnels.
The engineering properties of the rock and the soils in this site are very complicated. Figure
Soil profile and geotechnical parameters.
The shallow ground water is pore phreatic water, mainly found in layers from (1) to (8). The elevation of the water surface is 2.232 m. The laboratory penetration test and field steady flow test can be seen in Table
Laboratory penetration test and field steady flow test.
Soil layer  Laboratory penetration test (cm/s)  Field steady flow test (cm/s)  



 
3–2  4.79 × 10^{−5}  7.81 × 10^{−5}  4.21 × 10^{−3} 
3–3  2.55 × 10^{−4}  2.30 × 10^{−4}  1.57 × 10^{−3} 
3–5  9.63 × 10^{−5}  1.74 × 10^{−4}  — 
3–6  3.29 × 10^{−4}  3.01 × 10^{−4}  — 
4–3  2.39 × 10^{−7}  7.84 × 10^{−7}  / 
6–1  2.06 × 10^{−7}  3.03 × 10^{−7}  — 
6–2  2.62 × 10^{−7}  1.28 × 10^{−7}  — 
8–1  1.88 × 10^{−7}  5.11 × 10^{−7}  — 
Figure
Advancetime curve of the shield.
Figure
The applied tunnel face pressure.
The applied tunnel face pressure of the southbound tunnel cannot be calculated by (
Figure
The grouting volume.
Arrangement of the monitoring rings of the existing tunnel can be seen in Figure
Arrangement of the monitoring points at the cross section of the existing tunnel.
The location of point A as shown in Figure
Figure
Timevarying vertical displacement of the existing tunnel.
The horizontal displacement of the existing tunnel with respect to the location of the shield is illustrated in Figure
Timevarying horizontal displacement of the existing tunnel.
There are northward displacement on the left side of point C and southward displacement on the right side of point C. The horizontal displacement curve is approximately symmetric about point C after the longterm monitoring. The maximum northward displacement is 10 mm in the ring near the intersection point A, and the maximum southward displacement is −10.5 mm in the ring near the intersection point B after the completion of the two tunnels’ construction. During the construction of the northbound tunnel, rings from 453 to 471 move southward which is likely due to the additional bulkhead additive thrust and the squeezing force provided by the shield shell. When the shield tail leaves ring 459, rings from 439 to 459 move southward slowly. Only 2 to 5 mm additional southward displacement is measured in rings from 487 to 560, and nearly no displacement is observed on the left side of point B during the construction of the southbound tunnel which is mainly due to the northbound tunnel’s barrier effect. No change of horizontal displacement is observed in the longterm conditions (from 2014/5/28 to 2014/10/19).
Figure
Convergence displacement of the existing tunnel.
Figure
Reinforcement in the existing tunnel.
The deformed tunnel lining reinforced by inner bonding steel plates has been partially or entirely used in many built tunnels or currently under construction. To better understand the benefits coming from the reinforcement method, the behavior of the tunnel is investigated.
Figure
A schematic view of the existing tunnelsoil tunnelling interaction.
In this paper, the tunnels are considered as an infinite beam on the Winkler foundation, an infinite beam on the Pasternak foundation, and a finite beam on the Pasternak foundation (the new method). Comparing the deflection, rotation angle, normalized bending moment, and shear force of the existing tunnel with constant stiffness based on the three models, the new method is verified. Then, different stiffness of the reinforcement is taken into consideration, and the optimal reinforcement range of the existing tunnel is discussed.
For the theoretical analysis, the alignment of the new tunnels and the existing tunnel is assumed to be straight. Figure
A schematic diagram of tunnels for the analytical methods.
In this study, subsurface settlement
Attewell et al. [
If the soil foundation is assumed as the Winkler foundation, the foundation counterforce
The twoparameter model of foundation can capture the shear resistance of soil. Based on the assumption of the plane strain condition, the displacement of ground in the
Attewell et al. [
It can be concluded that each of the concentrated load
In this study, we want to figure out the effects of the reinforcement on the existing tunnel, the stiffness varies in this case and the existing tunnel assumed as an infinite beam is not suitable. Assuming the existing tunnel with finite length and introducing (
The relationship of the deflection, rotational angle, bending moment, and shear force of the beam proposed by Lancaster and Mitchell [
Figure
Sketch of equivalent stepped stiffness.
Forces and local coordinate system.
Figure
Replacement of variable load with trapezoid load.
In order to avoid numerical errors in the calculation process, the integration of
Figure
The matrix transfer diagram.
For the first element,
For the end point of the first element,
For the end point of the
For
Suppose
Then, (
Thus, the relation between the vector
The boundary condition of the existing tunnel assumed as an infinite long tunnel considering the shear stress of soil can be written as
By applying the boundary conditions to (
To enable a direct comparison, assumed parameters of the soil and existing tunnel are selected in this study. Poisson’s ratio of the soil is 0.388. The grouting process is regarded as the inverse process of soil loss due to tunnelling, and
For the Pasternak foundation, as the thickness of the elastic layer is assumed to be 2.5
As illustrated in Figure
The normalized bending moment and shear force are defined as
Figure
(a) Comparison of the deflection of the existing tunnel using different models. (b) Comparison of the rotational angle of the existing tunnel using different models. (c) Comparison of the normalized bending moment of the existing tunnel using different models. (d) Comparison of the normalized shear force of the existing tunnel using different models.
The reinforce range of the existing tunnel is assumed as 25 rings on either side of the intersection point A and the various stiffness is taken into consideration using the method proposed in this paper. Figure
(a) The effects of different reinforcement stiffness on the deflection of the existing tunnel. (b) The effects of different reinforcement stiffness on the slope of the existing tunnel. (c) The effects of different reinforcement stiffness on the normalized moment of the existing tunnel. (d) The effects of different reinforcement stiffness on the normalized shear force of the existing tunnel.
The reinforce stiffness of the reinforcement range is assumed as 4
(a) The effects of different reinforcement ranges on the deflection of the existing tunnel. (b) The effects of different reinforcement ranges on the slope of the existing tunnel. (c) The effects of different reinforcement ranges on the normalized moment of the existing tunnel. (d) The effects of different reinforcement ranges on the normalized shear force of the existing tunnel.
Based on the abovementioned statements, the response of the existing tunnel is analyzed, and analytical methods are proposed for verification and the reinforcement design. Main conclusions derived from the analysis are as follows:
The displacement of the existing tunnel changes with the relative position of the shield and the existing tunnel. Shield parameters have a major impact on the existing tunnel. The heaves of the existing tunnel might be caused by the large applied face pressure and bulkhead addictive thrust. When the shield tail is driving beyond the selected monitoring rings, the selected monitoring rings settle rapidly due to the closure of the shield tail void.
The southbound tunnel of Line 4 has less effect on the left side of the intersection point A on the existing tunnel because of the northbound tunnel’s barrier effect. A variety of measures of displacement prevention of Line 1 such as the control of shield parameters, reinforcement of the existing tunnel can ensure the normal operation of metro Line 1.
The analytical method proposed in the paper is verified by the methods derived from prior studies. It is possible to take the different stiffness and curved loads into account by applying the stepped stiffness and trapezoidal load while using a local coordinate system in the derivation of the new method. The change of reinforcement stiffness has greater effect on the normalized bending moment and the normalized shear force of the existing tunnel, particularly at the inflection points of the normalized bending moment and normalized shear force curve. The analytical method can be applied for the reinforcement design and safety check of the built tunnel.
The author declares that there are no conflicts of interest regarding the publication of this paper.
The author appreciates the help from the staff of Hangzhou and Hong Kong Tunnel Company Ltd. during instrumentation setup and data acquisition. This study is supported by the National Natural Science Foundation of China (no. 41702313).