Field Observation and Theoretical Study on an Existing Tunnel Underpassed by New Twin Tunnels

)e 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. Short-term displacement of the existing tunnel is greatly influenced by the relative distance between the shield face and the existing tunnel and shield parameters. )e 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. )e 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. )e proposed model can be widely applicable for reinforcement design and safety check of the existing tunnel.


Introduction
e 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. [1,2] presented a good summary comparison of the studies and only studies that illustrates the shield underpassing or parallel underpassing the existing tunnel.Yamaguchi et al. [3] presented successively the numerical model and then analyzed three configurations of the twin tunnels in Japan: aligned horizontally, vertically, and inclined.e construction of the upper tunnel at first leads to both higher settlement and bending moment.
e maximum soil settlement was obtained for vertical-aligned tunnels, while horizontal-aligned tunnels caused the lowest settlement.Addenbrooke and Potts [4] analyzed the influence of tunnel position, tunnel spacing, rest period, and sequence of excavation on the interaction between the two tunnels.
It concentrated on the shape of the settlement profile and the volume loss induced by the two tunnels.e shield underpassing the existing tunnel is highly site specific.
e soil condition, the tunnel buried depth, and the relative position of the new tunnel and existing tunnel all affect the response of the existing tunnel.Field observations remain the commonly recognized approach for understanding the interaction behavior between the new tunnel and existing tunnel.Usually, the underpassing of a shield with a loss of soil often causes settlement of the existing tunnel at last [5][6][7].Chehade and Shahrour [8] used the finite element method to investigate the influence of the relative position of tunnels and the construction procedure on the soil settlement.e results showed that the settlements of the existing tunnel for the vertical parallel tunnels were larger than those for the horizontal parallel tunnels.Li and Yuan [9] studied the twin tunnels passing under a double-decked tunnel at an angle of 55 in weathered granite gneiss.Only settlements were found, and the horizontal displacement was smaller than the vertical displacement in the existing tunnel.Despite a number of studies having been carried out, current understanding of the interaction between the two tunnels is still limited.
In order to ensure the stability of the existing tunnel, local thickening is needed at the sides of the existing concrete lining.ere 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.
e effect of reinforcement on the longitudinal behavior of the tunnel is not yet clear in current analysis.
e 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. [10], (2) the Winkler model [11], and (3) the two-parameter elastic models.When variable stiffness of the existing tunnel needs to be considered, the methods are no longer applicable.Selvadurai [12] divided the beam on foundation into N elements and used the method of initial parameters to analyze the beam's displacement.In the paper, we assume the existing tunnel as a beam resting on a two-parameter foundation, combining the initial parameter method and the transfer matrix method to analyze the reinforcement effect on the longitudinal behavior of the existing tunnel.
e 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.

Project Overview
e location of the Line 4 tunnels and the upline of Line 1 are shown in Figure 1. e upline of Line 1 is the existing tunnel built in 2012.Figure 2 shows a plan view of tunnel alignment and arrangement of the monitoring points in the existing tunnel.e shield of the northbound tunnel of Line 4 starts from Guanhe Station, passes under the existing tunnel with a small angle of 23 °, and reaches East railway station at last.en, the shield machine is reassembled with tunnels in a reversed direction.e northbound tunnel with a length of 329.675 m consists of 275 rings numbered starting with zero from Guanhe Station to East railway station, while the southbound tunnel with a length of 323.834 m consists of 270 rings numbered starting with zero from East railway station to Guanhe Station.e lateral distance between the northbound tunnel and the southbound tunnel is 9.4-15.0m.
Figure 3 shows the longitudinal profile of soil and tunnels.e vertical distance between the existing tunnel and Line 4 is 2.12 m. e existing tunnel and new tunnels are all built using an articulated shield tunnelling machine with an outer diameter of 6.4 m and a length of 8.5 m. e spokes plus panel-type cutter head are used, and the aperture ratio of cutter head is 40%.Each ring of new tunnels consists of six precast concrete segments.e outer diameter, the inner diameter, and the thickness of the segment are 6.2 m, 5.5 m, and 0.35 m, respectively.

Soil Condition.
e engineering properties of the rock and the soils in this site are very complicated.Figure 4 shows geotechnical parameters of soil in this site.e soil layers from top to bottom are (1) fill, (3) silty clay, (4) clay, (6) the muddy silty clay, and (8) soft silty clay and gravel layer.e existing tunnel and new tunnels are located in the muddy silty clay layer at a depth of 20 m and 25 m, respectively.Along the metro line, an extensive geotechnical investigation is carried out.
e standard penetration test (SPT), vane shear test (VST), piezocone test (CPTU), flat plate dilatometer test (DMT), and water pumping test (WPT) are conducted along Line 1. e maximum water content of clay and muddy silty clay is about 40%, which is close to the liquid limit value.e average undrained shear strength of undisturbed clay and remolded clay which is obtained by VST is 70.5 kPa and 10.9 kPa, respectively.
e coefficient of the at-rest earth pressure (K 0 ) of soft clay is obtained by DMT.

Hydrological Geology.
e shallow ground water is pore phreatic water, mainly found in layers from (1) to (8). e elevation of the water surface is 2.232 m.
e laboratory penetration test and field steady flow test can be seen in Table 1.It can be seen that the permeability coefficient of the clay layer is very small, and the permeability coefficient of the gravel layer is 1-2 m/d.e seepage induced from water head difference might influence the stability of tunnels.Figure 6 shows the applied tunnel face pressure.In practice, the tunnel face pressure should be adjusted with the theoretical value as well as the feedback displacement of the existing tunnel.

Shield Driving Parameters
e existing tunnel redistributes the soil stress, and the applied tunnel face pressure should be adjusted by (1) as follows: where K 0 is the coefficient of earth pressure at rest; c ′ is the effective gravity of soil; h is the thickness of overburden depth (m); p w is the water pressure; Q 1 is the weight of the existing tunnel (kN); Q 2 is the weight of the soil with the same internal volume of the existing tunnel (kN); and 20 kPa is the pressure fluctuation.e applied tunnel face pressure of the southbound tunnel cannot be calculated by (1) which is due to the redistribution of the earth pressure after the construction of the northbound tunnel nearby and should be adjusted according to the displacement of the existing tunnel.
Figure 7 shows the tail void grouting volume of the shield of the northbound and southbound tunnels of Line 4. Shield parameter adjustments play an important role in the displacement controls, reducing the tail void grouting volume and applied tunnel face pressure when Line 1 heaves.Opposite measures are taken when there is a subsidence in Line 1.

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Observation Results and Discussions
4.1.Monitoring Arrangement of Line 1. Arrangement of the monitoring rings of the existing tunnel can be seen in Figure 2. e total station Topcon MS05AX xed on the tunnel sidewall arranged from rings 404 to 559 in the existing tunnel is an automatic real-time measuring system which is used to monitor vertical and horizontal displacement.One monitor section is set every two rings in the most a ected zone (from rings 447 to 499 in the existing tunnel), and one monitor section is set every ve rings in the rest part.An LECAI D5 hand-held distance nder is used to monitor the converge displacement every 5 rings from 404 to 679 in the existing tunnel.e arrangement of monitoring points at the cross section of the existing tunnel is shown in Figure 8.

Vertical Displacement of the Existing Tunnel. Figure 9
shows time-varying vertical displacement in the monitoring rings of the existing tunnel.e x-axis is the ring number of the existing tunnel.A positive value of the ordinate denotes heave, while a negative value denotes settlement of the existing tunnel.e selected monitoring rings start to heave when the shield face is 0-10 m away from the selected monitoring rings which is mainly due to large applied tunnel face pressure, bulk addictive thrust (Figure 6), and the friction force between the shield shell and soil mass.When the shield tail is far beyond the selected monitoring rings, a reduction of heave in the selected monitoring points is observed which is mainly due to the closure of the tail void.Only small settlements and heaves are measured after the construction of the northbound tunnel.During the 3-month shutdown of the shield, additional settlement ranges from 2 mm to 3 mm can be observed in rings from 430 to 520.Additional settlements ranges from 2 to 4 mm were measured in rings from 460 to 540 during the southbound tunnel's construction.e long-term additional settlements, monitored up to 140 days (from 2014/6/1 to 2014/10/19), range from 2 to 4 mm in rings from 460 to 510. e settlements of rings from 430 to 520 range from 2 mm to 12 mm, and the settlement curve of the upline of Line 1 is "U" shaped after the long-term monitoring.
e settlement curve is approximately symmetric about the dashed line C after the long-term monitoring.e maximum settlement is 12 mm which is located in ring 487.
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Horizontal Displacement of the Existing Tunnel.
e horizontal displacement of the existing tunnel with respect to the location of the shield is illustrated in Figure 10.A positive horizontal displacement denotes northward transverse tunnel movement away from the original tunnel centerline, while a negative horizontal displacement denotes southward transverse tunnel movement away from the original tunnel centerline.
ere are northward displacement on the left side of point C and southward displacement on the right side of point C. e horizontal displacement curve is approximately symmetric about point C after the long-term monitoring.
e 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 e ect.No change of horizontal displacement is observed in the long-term conditions (from 2014/5/28 to 2014/10/19).

Convergence Displacement of the Existing
Tunnel. Figure 11 shows the convergence displacement of the existing tunnel with respect to the locations of the shield.
A negative value indicates the reduction horizontal diameter of the existing tunnel, while a positive value indicates the addition horizontal diameter of the existing tunnel.It can be observed that the convergence displacement is not obvious when the shield reaches ring 48 (22 rings away from the intersection point A).During the process of the shield driving from ring 64 to ring 87, a signi cantly additional increase in the negative convergence displacement in rings from 440 to 490 is observed, and the maximum displacement occurs in the intersection point A. e reason might be that the shield face squeezes one side of the existing tunnel,  The ring number of the northbound tunnel of Line 4 The corresponding ring number of the upline tunnel of Line 1 The ring number of the southbound tunnel of Line 4 The applied tunnel face pressure (MPa)

Reinforcement Scheme of the Existing Tunnel
Figure 12 shows the reinforcement in the existing tunnel.Radial reinforcement by an arc-shaped supporting steel plate connected to the tunnel segment and longitudinal reinforcement by channel section steel to provide longitudinal tensile stress are conducted in the existing tunnel.Radial steels and longitudinal steels are connected by welding, and so, the reinforcement becomes a whole one.25 rings are reinforced at rst on either side of the intersection point A before the underpassing of the northbound tunnel, and the whole reinforcement is

Theoretical Analysis of the Reinforcement Design
e 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 bene ts coming from the reinforcement method, the behavior of the tunnel is investigated.
Figure 13 shows a schematic view of the existing tunnel-soil tunnelling interaction.
e analysis method demonstrated in this paper can be divided into two steps: rstly, estimating the green eld displacement induced by the tunnelling.Secondly, calculating the responses of the existing tunnel subjected to the soil displacement.e method of analysis is based on three assumptions: (1) the above existing tunnel does not a ect the displacement of soil due to tunnelling, (2) the soil foundation is assumed as the Winkler or the Pasternak foundation, and (3) the soil displacement is calculated by superimposing the independent settlement predicted for each individual tunnelling.
In this paper, the tunnels are considered as an in nite beam on the Winkler foundation, an in nite beam on the Pasternak foundation, and a nite beam on the Pasternak foundation (the new method).Comparing the de ection, rotation angle, normalized bending moment, and shear force of the existing tunnel with constant sti ness based on the three models, the new method is veri ed.en, di erent sti ness of the reinforcement is taken into consideration, and the optimal reinforcement range of the existing tunnel is discussed.

e Subsurface Soil Displacement due to Tunnelling.
For the theoretical analysis, the alignment of the new tunnels and the existing tunnel is assumed to be straight.Figure 14 shows a schematic diagram of the new tunnels and the existing tunnel in this case.e green eld settlement s(x) due to the tunnelling can be replaced by the equivalent distributed load q(x) acting on the beam on the third assumption as follows: q(x) ks(x). ( In this study, subsurface settlement s(x) at the depth of z induced by tunnelling is calculated based on closed-form analytical solutions presented by Loganathan and Poulos [13] as follows:   Advances in Civil Engineering where s(x) subsurface settlement of the soils due to tunnelling; R tunnel radius; z depth below ground surface; H depth of the axis of the new tunnel; v Poisson's ratio; x lateral distance from tunnel centerline; and ε 0 equivalent ground loss ratio which is de ned as where g is the gap parameter (Lee et al. [14]); u * 3D is the three-dimensional elastoplastic deformation at the tunnel face; w is the workmanship factor; and G p represents the physical gap between the outer skin of the shield and the lining which is given as where Δ is the thickness of the tail piece and δ is the clearance required for erection of the tail piece.e parameter w can be neglected due to considerable experience with the equipment and good tunnelling technique of construction workers based on the study of Rowe and Lee [15].

Analytical Methods
Derived from Prior Studies.Attewell et al. [16] proposed a tunnel-soil interaction model and solved the analytical solution of the longitudinal displacement of an in nite tunnel: where q(x) is the concentrated load acting on the origin point of the beam; EI is the exural sti ness of a tunnel, which is recommended by Ye et al. [17]; and k is the subgrade modulus that represents the pipe-soil interaction.
If the soil foundation is assumed as the Winkler foundation, the foundation counterforce p(x) can be expressed as p(x) kw(x) (8) e two-parameter 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 y-direction is neglected.If the soil foundation is assumed as the Pasternak foundation, the foundation counterforce p(x) can be expressed as where G is the coe cient of the shear element in the Pasternak's model with the dimension of force per unit length.
Attewell et al. [16] presented a solution for the concentrated load q on an in nite beam resting on the Winkler foundation and computed the de ection as It can be concluded that each of the concentrated load ks(τ) at point τ contributes the following amount to the de ection of the existing tunnel on the Winkler foundation: where L 1 is the distance between the coordinate origin of the existing tunnel and the intersection point between the new tunnel and the existing tunnel and α is the intersection angle between the new tunnel and existing tunnel.e de ection, rotational angle, bending moment, and shear force of the existing tunnel which is assumed as an in nite beam on the Winkler foundation and the Pasternak foundation are illustrated in Appendix A.

A Brief Description of the New Method.
In this study, we want to gure out the e ects of the reinforcement on the existing tunnel, the sti ness varies in this case and the existing tunnel assumed as an in nite beam is not suitable.
Assuming the existing tunnel with nite length and introducing (7) to ( 9), the basic di erential equation governing the exure of the beam resting on the Pasternak foundation can be written in the form with an assumption of Gλ 2 /k < 1: where b 1i b i (1 +( G i /k i /b i )), subscript i represents the ith element of the beam, b i is the width of the beam, and b 1i is the modi ed width of the beam.Assuming a solution of (12) in the form of w(x) e λx , the general solution of vertical displacement of the beam is as follows: x' x''  Figure 14: A schematic diagram of tunnels for the analytical methods.

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Advances in Civil Engineering where C i (i 1, 2, 3, 4) are undetermined parameters, which are dependent on the boundary conditions, and F i (x) (i 1, 2, 3, 4) are the basic functions of the general solution, which are given as follows: where e relationship of the de ection, rotational angle, bending moment, and shear force of the beam proposed by Lancaster and Mitchell [18] is as follows: where θ i (x), M i (x), and Q i (x) are the amplitudes of rotational angle, bending moment, and shear force of the section area, respectively.Figure 15 shows that di erent sti ness is replaced by equivalent stepped sti ness.According to di erent sti ness and distributed load, the local coordinate system is established as illustrated in Figure 16.Selvadurai [12] suggests an initial parameter method to solve the parameters of the beam.e four parameters at the origin of the coordinates are w i (0 i ), θ i (0 i ), M i (0 i ), and Q i (0 i ), and four parameters at the end of the element are w i (x i ), θ i (x i ), M i (x i ), and Q i (x i ).C 1 , C 2 , C 3 , and C 4 can be expressed by w i (0 i ), θ i (0 i ), M i (0 i ), and Q i (0 i ) by introducing x i 0 to (13) and (18).
w i (x i ), θ i (x i ), M i (x i ), and Q i (x i ) can be rewritten in the matrix-array form as where [k ij ] is a sti ness submatrix with 5 × 5 order; i, j 1, 2, . .., 5. M and V are, respectively, the bending moment and the generalized shear force.Formula ( 19) can be simpli ed as where Figure 17 shows that curved distributed load is replaced by equivalent triangular and square distributed load which can be expressed as where q i−1 and q i are, respectively, the load of the starting point and the ending point of the ith element and ξ is the position of arbitrary load.From (19), we can obtain (22) In order to avoid numerical errors in the calculation process, the integration of k i5 is shown in Appendix B. e rest of k ij can be referred in the work by Selvadurai [12].
Figure 18 shows the tunnel matrix transfer diagram.Assuming that the tunnel is composed of N elements, the x-coordinate of beginning points of the ith element is x i (i 0, 1, 2, . . .n) and the length of each element is L i , where Figure 16: Forces and local coordinate system.

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For the rst element, For the end point of the rst element, For the end point of the ith element, For x at the ith element section, where x is a global coordinate, en, (20) can be expressed as us, the relation between the vector N n (x n ) at the point x n and the vector N 1 (0 1 ) at the start point x 0 is where e boundary condition of the existing tunnel assumed as an in nite long tunnel considering the shear stress of soil can be written as By applying the boundary conditions to (19), the deection, rotational angle, bending moment, and shear force of the overall beam can be obtained.e grouting process is regarded as the inverse process of soil loss due to tunnelling, and g can be expressed as g (2Δ + δ)(1 − η), where η is the injection ratio.
For the Pasternak foundation, as the thickness of the elastic layer is assumed to be 2.5 B, the subgrade elastic modulus k and shear sti ness G are suggested by Xu [19] as follows: where β is a modi ed parameter (β 1.29) and E 0 and v 0 are, respectively, the elastic modulus and Poisson's ratio for elastic foundation, which are given as follows: where the empirical relation between the Young's modulus E s and the compression modulus E s0.1−0.2 of soft soils is built up by Yang and Zhao [20].
As illustrated in Figure 14, points O 1 and O 2 are, respectively, the intersection points A and B; in practical, coordinate transformation expressions of the axis x ′ and x ″ are, respectively, where L 1 and L 2 are the distance from the beginning point of the existing tunnel to points O 1 and O 2 , respectively.e length of the existing tunnel is assumed as 250 m, and the ring spacing is 1.2 m.So, the tunnel is divided into 209 sections, and each section is 1.2 m in length.Advances in Civil Engineering

Discussions
e normalized bending moment and shear force are dened as where M i and Q i are, respectively, the normalized bending moment and shear force; M i and Q i are, respectively, the calculated bending moment and shear force; and L 0 is the length of the existing tunnel.
Figure 19 shows the comparison of the de ection, rotational angle, bending moment, and shear force of the existing tunnel with a constant sti ness which is based on three kinds of models: an in nite tunnel on the Winkler foundation, an in nite tunnel on the Pasternak foundation, and a nite tunnel on the Winkler foundation.Note that the Advances in Civil Engineering existing tunnel is only subject to soil deformation force in this case.e displacement and the de ection of beam are particular similar concepts owing to the fact that the existing tunnel is securely attached to the foundation, generally without rigid body motion.Fairly good agreement can be observed between the in nite tunnel on the Pasternak foundation and the nite tunnel on the Pasternak foundation, which shows that the method proposed in this paper is correct and can be used to analyze similar problems.Because of considering soil shear stress, vertical stress and deformation are a ected and weakened; the displacement of the existing tunnel on the Pasternak foundation is smaller than that on the Winkler foundation without considering the shear stress of soil.Using the Winkler foundation model is in good agreement with the observed data.It can be seen from ( 3) that the displacement of the existing tunnel is proportional to the grouting e ciency (i.e., η).Due to the uncertainty of η, it cannot be decided which one is the best analytical method.It is clear that the maximum normalized bending moment occurs at the points O 1 and O 2 , which are the nearest points between the existing tunnel and the new tunnels.Advances in Civil Engineering e reinforce range of the existing tunnel is assumed as 25 rings on either side of the intersection point A and the various sti ness is taken into consideration using the method proposed in this paper.Figure 20 shows the inuence of di erent sti ness of the reinforcement on the existing tunnel (i.e., 4 EI, EI, and 1/4 EI).It is evident that the reinforcement can reduce the displacement, rotational angle, normalized bending moment, and shear force of the existing tunnel, while tunnel damage (reduce the sti ness of reinforcement) has the opposite e ect.It is evident that the change of reinforcement sti ness has greater e ect on the normalized bending moment and the normalized shear force of the existing tunnel, particularly at the in ection points of the normalized bending moment and normalized shear force curve.
e reinforce sti ness of the reinforcement range is assumed as 4 EI and the various reinforcement ranges is taken into consideration using the method proposed in this paper.Figure 21 shows the in uence of di erent reinforcement ranges on the existing tunnel when the northbound tunnel of Line 4 underpasses.e normalized bending moment on either side of the intersection point is too large when the reinforcement range is 69-89.2m, and the normalized shear force on either side of the intersection point is relatively too large when the reinforcement range is less than 59.2-99.2m.So, it is necessary to reinforce larger than the range of 49.2-109.2m in the existing tunnel in this case, that is, larger than 30 m (25 rings) on either side of the intersection point.ere is no big difference in the bending moment and shear force of the existing tunnel when the reinforcement ranges are 49.2-109.2m, 39.2-119.2m, and 29.2-129.2m.In order to reduce the costs of reinforcement, reinforcement in the 30 m range (i.e., 25 rings) on either side of the intersection point is the best choice which verifies the actual design.

Conclusions
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: (1) e 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.e 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.
(2) e 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. (3) e 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.e 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.e analytical method can be applied for the reinforcement design and safety check of the built tunnel.

Figure 5
Figure 5 presents advance-time curve of the shield.Before underpassing the existing tunnel, the shield advances with a very slow rate.e tunnel advancing rate is 7-8 rings/day, and the penetration rate of the shield ranges from 20 to 25 mm•min −1 .Figure6shows the applied tunnel face pressure.In practice, the tunnel face pressure should be adjusted with the theoretical value as well as the feedback displacement of the existing tunnel.eexisting tunnel redistributes the soil stress, and the applied tunnel face pressure should be adjusted by (1) as follows:

Figure 1 :
Figure 1: Location of the new tunnels and the existing tunnel in Hangzhou.A: Guanhe Station; B: East railway station.
bo un d tu nn el of Li ne 4 e sou thb ou nd tun ne l of Lin e 4 Rein force men t of the exist ing tunn el Zha-nong-kou Station e upli ne tun nel of exis ting Lin e 1 Da-ju-yuan Station A B C e auto monitoring point of vertical and horizontal displacement e manual monitoring point of horizontal displacement e manual monitoring point of vertical displacment e manual monitoring point of convergence displacement

Figure 2 :
Figure 2: Plan view of tunnel alignment and location of the monitored rings.

2 .
Displacement of the Existing Tunnel.e location of point A as shown in Figure 2 is corresponding to the intersection point of a plan view of the existing tunnel and northbound tunnel of Line 4. e location of point B is corresponding to the intersection point of the plan view of the existing tunnel and southbound tunnel of Line 4. e middle point of points A and B is point C.

Figure 4 :
Figure 4: Soil pro le and geotechnical parameters.
face of the northbound tunnel e tunnel face of the southbound tunnel Tunnel chainage (m) of the southbound tunnel 2013/12/

Figure 8 :
Figure 8: Arrangement of the monitoring points at the cross section of the existing tunnel.

Figure 9 :Figure 10 :
Figure 9: Time-varying vertical displacement of the existing tunnel.

Figure 11 :
Figure 11: Convergence displacement of the existing tunnel.

Figure 12 :
Figure 12: Reinforcement in the existing tunnel.

Figure 13 :
Figure 13: A schematic view of the existing tunnel-soil tunnelling interaction.

Figure 17 :
Figure 17: Replacement of variable load with trapezoid load.

6. 4 .
Case Study 6.4.1.Parameter Selection.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.

Figure 19 :
Figure 19: (a) Comparison of the de ection of the existing tunnel using di erent models.(b) Comparison of the rotational angle of the existing tunnel using di erent models.(c) Comparison of the normalized bending moment of the existing tunnel using di erent models.(d) Comparison of the normalized shear force of the existing tunnel using di erent models.

Figure 20 :
Figure 20: (a) e e ects of di erent reinforcement sti ness on the de ection of the existing tunnel.(b) e e ects of di erent reinforcement sti ness on the slope of the existing tunnel.(c) e e ects of di erent reinforcement sti ness on the normalized moment of the existing tunnel.(d) e e ects of di erent reinforcement sti ness on the normalized shear force of the existing tunnel.

Table 1 :
Laboratory penetration test and eld steady ow test.