Effects of above-crossing tunnelling on the existing shield tunnels

Tunnelling and Underground Space Technology 58 (2016) 159–176

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Effects of above-crossing tunnelling on the existing shield tunnels Rongzhu Liang a,b,⇑, Tangdai Xia a,b, Yi Hong a,b, Feng Yu c a

College of Civil Engineering and Architecture, Zhejiang University, 866 Yuhangtang Road, Hangzhou 310058, China Research Center of Coastal and Urban Geotechnical Engineering, Zhejiang University, 866 Yuhangtang Road, Hangzhou 310058, China c School of Civil Engineering and Architecture, Zhejiang Sci-Tech University, Hangzhou 310018, China b

a r t i c l e

i n f o

Article history: Received 24 June 2015 Accepted 9 May 2016

Keywords: Above-crossing tunnelling Tunnel heave Winkler model Simplified analytical method

a b s t r a c t Tunnelling in the dense urban areas frequently results in over-crossing or bypassing the existing tunnels. It is obvious that the over-crossing tunnelling will adversely affect and even damage the existing tunnels if the induced deformation exceeds the capacity of tunnel structures. Increasing concerns have been raised about the interactions between the over-crossing tunnelling and underlying tunnels. In order to obtain a better mechanical understanding of the effects of the over-crossing tunnelling on the existing tunnels and provide a quick but low cost assessment alternative method for evaluating the behavior of underlying tunnels prior to construction, a simplified analytical method is proposed in this study. In this simplified method, the tunnel is simply considered as a continuous Euler-Bernoulli beam with a certain equivalent bending stiffness. The unloading stress at the tunnel location caused by the over-crossing tunnelling is computed through Mindlin’s solution, ignoring the presence of the existing tunnel. Then, the tunnel-soil interaction due to the relief stress is analyzed based on the commonly-accepted Winkler foundation model. The applicability of the presented method is validated by three well-documented case histories. Results of these case studies show a reasonable agreement between the predictions and observations. Finally, a parametric analysis is also preformed to investigate the influences of the different factors on the behavior of the existing tunnels, including clearance distance, advancing distance and multiple tunnels construction. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Nowadays, the urban railway transit system is one of the indispensable parts of city traffic system. Due to the rapid economic developments and urbanization of China, more urban metro lines are being planned or implemented to facilitate congested urban traffic system in many big cities, such as Shanghai, Beijing, Shenzhen and Hangzhou. For the metro tunnels in the cities, such as Hangzhou and Shanghai, in which very thick layer soft clay is distributed throughout the underground space, are mainly constructed by employing the shield tunnelling method. Shield tunnelling technology, including slurry shield and Earth Pressured balanced shield tunnelling methods, is one of the most sophisticated and popular tunnelling technologies with various advantages such as high effective, low cost and minor disturbance to surrounding environment. However, construction of a new tunnel in dense urban underground space often encounters the underground pre⇑ Corresponding author at: College of Civil Engineering and Architecture, Zhejiang University, 866 Yuhangtang Road, Hangzhou 310058, China. E-mail addresses: [email protected] (R. Liang), [email protected] (T. Xia), [email protected] (Y. Hong), [email protected] (F. Yu). http://dx.doi.org/10.1016/j.tust.2016.05.002 0886-7798/Ó 2016 Elsevier Ltd. All rights reserved.

existing structures and facilities, such as pile foundations, municipal pipelines and running tunnels. Therefore, serious concerns have been increasingly raised about the influence on the existing structures, especially existing tunnels which is the focus of this paper, due to adjacent tunnelling. Fig. 1 shows the common relative locations between existing and new tunnels. According to the different relative positions between exiting and new tunnels, there are mainly five types of tunnelling conditions, namely, new tunnel down-crossing below (Fig. 1(a)), new tunnel side-by-side parallelly crossing (Fig. 1(b)), new tunnel parallelly down-crossing (Fig. 1(c)), new tunnel parallelly above-crossing (Fig. 1(d)) and new tunnel above-crossing (Fig. 1(e)). To ensure the safety and serviceability of the existing tunnels is extremely critical, as the nearby new tunnel construction will alter the already balanced ground stress field and cause free soil movements, which will inevitably induce adverse effects, such as additional loads and bending moments, on the existing tunnels. Theoretically, the responses of existing tunnel structures result from the interaction between the disturbed soil movements induced by tunnel excavation and the bearing capacity of existing tunnel.

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Ground surface

x

z0

O y

g itin Ex nel n tu

h

Exiting tunnel

Gro

und

surf

ace

0

x

y

H

l

ne

Lp

w

New tunnel

tun

Ne

Shield

z (a) New tunnel down-crossing

(c) New tunnel parallelly down-crossing

l

ne

ew

tun

N Gro Gro

und

surf

ace

und

g itin Ex nel n tu

0

x

ace

0

Shield

y

H

x

New tunnel

y

H

surf

Shield

Lp

Lp

z z (b) New tunnel side-by-side parallelly crossing

0

g itin Ex nel n tu

(d) New tunnel parallelly above-crossing Ground

surface

y x z

H

Z0

New tunnel

Existing tunnel

(e) New tunnel above-crossing Fig. 1. Relative position between new tunnel and existing tunnel.

However, the interaction mechanisms between the existing tunnel and the adjacent tunnelling are highly complex and severe construction risks and damage of integrity of tunnel structures

may occur, unless effective geotechnical protective measures are undertaken during the adjacent tunnelling. In order to provide effective geotechnical protective measures for the exiting tunnel,

R. Liang et al. / Tunnelling and Underground Space Technology 58 (2016) 159–176

especially for aging tunnels, during the disturbances of the nearby tunnel construction, a comprehensive understanding of the interactions is critical and essential. Moreover, because of the rapid development of urban tunnel construction, the need for quick assessment alternative method to evaluate the influences of existing tunnels due to adjacent tunnelling is extremely urgent. A variety of approaches have used to study the impacts of adjacent tunnelling on existing tunnels or pipelines, namely, physical model experiments, field observations, numerical analyses and empirical/analytical methods. Lots of researches have been focused on the interaction between the existing tunnel or pipeline and newly tunnelling by developing physical model tests, including reduced-scale model tests and centrifuge model tests. Kim et al. (1998) carried out a series of single gravity physical model tests, including close parallel tunnels and perpendicular tunnels, to investigate the effects of exiting tunnels caused by nearby tunnelling in clay. The testing results of perpendicular tunnel tests showed that interaction effects are mainly caused by the jacking forces applied to the liner and the tunnelling machine during tunnel installation. However, as for parallel tunnel tests, the existing tunnel was predominately influenced by the redistribution of stresses within the soil caused by liner deformations and ground loss. In the study by Byun et al. (2006), large-scale model tests were conducted to investigate the ground behavior during construction of a new tunnel crossing beneath the existing tunnel. The tests results showed that the longitudinal arching effect contributed considerably to the redistribution of the earth pressure and the settlement of the ground in the crossed zone by the lower tunnel excavation. Choi and Lee (2010) performed a number of physical model tests to investigate the influence of various factors, such as the size of an existing tunnel, distance between twin tunnel centers and lateral earth pressure factor, on mechanical behavior of the exiting tunnel and new tunnels by quantifying the displacement and crack propagation during the excavation of a new tunnel. Based on the tests results, it found the induced displacements decreased and stabilized as the distance between tunnel centers increased depending on the size of the existing tunnel. Marshall et al. (2010) conducted a series of centrifuge tests to study the problem of tunnelling beneath buried pipelines in sand and the relationship between soil strains and pileline bending behavior. The field observation is the most popular and straightforward method for understanding the interaction between existing and nearby crossing tunnels. Kimmance et al. (1996) described the measured results of existing cast iron lined and NATM tunnels near London Bridge Station during the excavation of new tunnel beneath them. It found that tunnel settlement generally occurred when a new tunnel was constructed beneath it. Selman (1998) described and analyzed the settlement, rotation and distortion in the existing Bakerloo and Northern Line tunnels, and District and Circle Line tunnels at Westminster during the construction of Jubilee Line Extension tunnel beneath them. Cooper et al. (2002) reported the results of short and long-term behavior of exiting Piccadilly Line tunnels during the construction of three station tunnels blow, based on an extensive instrumentation program. A series of marked asymmetry settlement curves of existing tunnel were caused by the upline and downline tunnelling after the construction of the central concourse tunnel. Mohamad et al. (2010) reported the responses of an old masonry tunnel due to newly tunnel construction below at King’s Cross, London, using a novel optical fibres distributed strain measurement system. The monitored data indicated that the cracking might have occurred and flexural behavior along the longitudinal section of the tunnel was examined during the construction of the new underlying tunnel. Fang et al. (2015) reported the monitoring settlements of twin shield tunnels associated with down-crossing excavation of two new tun-

161

nels using shallow tunnelling method and proposed a superposition technology to fit the settlement profile of existing tunnels. With the rapid development of computer techniques, the finite element numerical simulation is becoming the most efficient way to investigate the interactions between the already buried tunnels and the newly tunnelling construction. Addenbrooke and Potts (2001) carried out a series of 2D finite element analyses to study the effects of different tunnel relative position (side-by-side parallel and piggyback) and construction sequences on the existing tunnel. Ng et al. (2004) reported the results of 3D finite element analysis to consider the multiple interactions between large parallel twin tunnels constructed in stiff clay using the new Austrian tunnelling method. Hage Chehade and Shahrour (2008) conducted a 2D finite element numerical analysis to study the impacts of nearby tunnelling on preexisting tunnel with different construction procedures. Chakeri et al. (2011) conducted 3D finite element numerical analyses to analyze the changes of the ground stress distribution, the deformations and the surface settlements during the twin Tohid tunnels driving perpendicularly beneath the Line 4 metro tunnel in Tehran. Do et al. (2014a, 2014b) performed a series of 3D numerical analyses to investigate the influences of constructions process on two parallel and stacked tunnels. Comparing with the numerical simulation, the analytical and empirical approaches serve to provide a relative simple and useful way for assessing the interactions between newly tunnelling and existing tunnels in primary design stage. Many researchers have proposed various analytical or empirical approaches to compute the displacements and bending moment of overlying tunnel or pipeline due to newly tunnelling (Klar et al., 2005, 2007; Vorster et al., 2005; Zhang and Huang, 2014). Klar et al. (2005, 2007) and Vorster et al. (2005) proposed the elastic continuum solution and the closed-form Winkler model solution to compute the displacement and bending moment of preexisting pipelines when subjected to down-crossing tunnelling. Recently, by assuming existing tunnel as an elastic beam supported on Winkler type foundation, Zhang and Huang (2014) introduced a simplified analytical solution to calculate the deformation of above-existing tunnel when a new tunnel constructs obliquely beneath it. By reviewing literatures, it is found the previous researches mainly focused on the problem of interaction between existing tunnel and side-by-side parallelly crossing, parallelly downcrossing, parallelly above-crossing or perpendicular downcrossing tunnel excavation. However, minimal attention has been given to the effects of above-crossing tunnel construction on the underlying existing tunnels and the problem remains to be further understood. Ghaboussi et al. (1983) pointed out that the over passing of a new tunnels was a significant unloading process and carried out a 2D finite element analysis to investigate responses of existing subway tunnel. The simulation results matched the measurements perfectly and indicated that the vertical diameter increased and the horizontal diameter decreased associated with over-crossing tunnelling. Chen et al. (2006) and Ding and Yang (2009) carefully reported the monitoring results of the longitudinal vertical displacements of the exiting Metro Line-2 tunnels due to the over-passing of Metro line-8 twin tunnels in Shanghai. The upheaval of exiting tunnel was observed during and after abovecrossing tunnel excavation. Liao et al. (2009) found the new shield driving above would induce heave of the underlying tunnel and carried out a 3D Finite element analysis to study the interaction mechanisms. Liu et al. (2009) found if the new tunnel were driven perpendicularly above the exiting tunnel in the region like Sydney with relatively high horizontal stresses, compressive failure of the shotcrete lining of the crown would occur and the tensile forces of the rock bolts around the crown would increase significantly, based on the results of full 3D simulation. Zhu and Huang (2010) described a case study of MetroLine-13 twin tunnels passing over

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existing Metro Line-4 tunnels. The heave of tunnels was also measured and it found the displacements of tunnels could be reasonably fitted by using commonly used normal distribution curve. Huang et al. (2012) and Li et al. (2014) conducted a series of centrifuge model tests to investigate the influences of the new overlying tunnel excavation on the existing metro tunnels in service, respectively. The soil excavating process, the ground losses and grouting were simulated by discharged or injected dense solution in the model test. The heave of the exiting tunnels was also measured and it was found that the back-fill grouting could significantly reduce the heave of the underlying tunnel. However, few analytical approaches have been proposed to calculate the behaviors of existing tunnel due to above-crossing tunnelling. This paper aims to propose a simple and reliable semi-analytical method for evaluating the interactions between newly abovecrossing tunnelling and the underlying existing tunnel. In this study, the existing tunnel is simply modelled as a continuous Euler-Bernoulli beam resting on the Winkler foundation with a certain equivalent bending stiffness (Chang et al., 2001; Zhang et al., 2013; Zhang and Huang, 2014). The unloading stress at the location of existing tunnel induced by newly tunnelling is simulated through the Mindlin’s solution (Mindlin, 1936), ignoring the presence of existing tunnel. Then, the responses of tunnels induced by the unloading stress are computed by solving the governing differential equation. The applicability of the proposed method is verified by three selected cases in China. Systemic parametric analyses are also performed to explore and discuss the influences of various factors on the tunnel movements, including clearance distance, advancing distance and multiple tunnels construction. The proposed semi-analytical method gives a better mechanical understanding of the interactions between the over-crossing tunnelling and the existing tunnel and provides a quick prediction for evaluating the effects and risks on the existing tunnel for engineers in the primarily design stage. 2. Method of analysis The above-crossing tunnelling is a process of stress unloading because the weight of excavated soils in unit length is greater than that of the installed segmental lining. Therefore, the underlying tunnel will be ‘‘pulled up” inevitably by the unloading effect acting on the existing tunnel and the heave and additional bending moment will occur subsequently. If the deformation caused by the unloading stress exceeds the capacity of the tunnel structures, cracking and seepage will occur and the safety of running trains will be seriously threatened. In order to simplify the analysis, the problem of the responses of exiting tunnel caused by abovecrossing tunnelling is basically divided into two stages: firstly, estimating the above-tunnelling induced unloading stress at the tunnel level, and second, computing the responses of existing tunnels due to the imposed unloading stress. Notwithstanding the shoving forces induced by shield jacking may cause slightly horizontal movements on existing tunnel when the clearance distance between two tunnels is close enough, however, in most cases heave of tunnel dominates the tunnel deformation. Thus, the effects of shoving forces are not involved in the proposed method. 2.1. Unloading pressures on the underlying tunnel Fig. 2 shows calculation model of the responses of existing tunnel associated with above-crossing tunnelling. The removal of excavated soils in the new tunnel causes stress release in the ground. Since the new tunnel is constructed in a certain deep under the ground surface, which is a typical semi-infinite space problem. Thus, the unloading vertical stress field beneath the new tunnel can be

evaluated through the widely-used Mindlin’s solutions (Mindlin, 1936). Fig. 3 shows the calculation model of Mindlin’s solutions. The vertical stress rz at an arbitrary point (x, y, z) generated by an upward point load acting at the interior of a semi-infinite space is proposed by Mindlin (1936). It expresses: " F ð1  2lÞðz  cÞ ð1  2lÞðz  cÞ 3ðz  cÞ3  rz ¼ þ  8pð1  lÞ R51 R31 R32 # 2 3 3ð3  4lÞzðz þ cÞ  3cðz þ cÞð5z  cÞ 30czðz þ cÞ   ð1Þ R52 R72 where F is the upward unloading force; l is the Poisson’s ratio; c is qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi the depth of the upward point force; R1 is x2 þ y2 þ ðz  cÞ2 , R2 is qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi x2 þ y2 þ ðz þ cÞ2 . The unloading pressure p is generated by the difference between the weight of excavated soils and the tunnel segmental linings per unit length. That is:

p¼

cs pR2  ct ðpR2o  pR2i Þ 2Ro

ð2Þ

where cs and ct are the unit weight of the excavated soil and the segmental lining, respectively; R, Ro and Ri are the excavated radius, outer radius ant inner radius of segmental lining, respectively. Combined Eq. (2) and Eq. (1), the unloading pressure qðxÞ at the tunnel axis level along longitudinal direction of the existing tunnel can be obtained " pdkdg ð1  2lÞðz0  HÞ ð1  2lÞðz0  HÞ 3ðz0  HÞ3 qðxÞ ¼ þ   R31 R32 R51 R0 L1 8pð1  lÞ # 3ð3  4lÞz0 ðz0 þ HÞ2  3hðz0 þ HÞð5z0  HÞ 30Hz0 ðz0 þ HÞ3  ð3Þ  R72 R52 Z

R0

Z

L2

where z0 is the distance from ground surface to the axis of the existing tunnel. H is the burial depth the new tunnel (from the ground surface to the invert of the existing tunnel); L1 and L2 are the advancing distance from the start and the excavation face of tunnel to the intersection point, as illustrated in Fig. 2(b), respectively; a is the skew angle between the abscissa and the new tunnel axis, as shown in Fig. 2(b). Note that the value of a ranges from 0° to 90°, corresponding to relative positions from perpendicular to parallel. The parameters R1 and R2 are both expressed as qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 R1 ¼ ðx cos a  kÞ2 þ ðx sin a  gÞ þ ðz0  HÞ2 and qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 2 R2 ¼ ðx cos a  kÞ þ ðx sin a  gÞ þ ðz0 þ HÞ . 2.2. Soil-tunnel interaction The subsurface soils deform freely when subjected to adjacent engineering activities. The presence of tunnel with a certain bending stiffness, however, will significantly resist the underground soil movements. Chang et al. (2001) suggested that the behavior of the tunnel subjected to the adjacent excavation can be considered as a continuous beam. Furthermore, in the studies by Zhang et al. (2013) and Zhang and Huang (2014), the existing tunnel is both treated as a continuous Euler-Bernoulli beam resting on elastic foundation to estimate the movements of existing tunnel due to adjacent excavation and multiple tunnelling. In this study, the existing tunnel is simply considered as a continuous EulerBernoulli beam resting on Winkler foundation. The length of the underlying tunnel is assumed to be sufficiently long so that the each end of the beam is unaffected by the overlying tunnelling. The governing differential equation for the longitudinal displacement of the underlying tunnel subjected to above-crossing tunnelling is given:

R. Liang et al. / Tunnelling and Underground Space Technology 58 (2016) 159–176

163

Ground surface D

H

New tunnel

Z0

Unloading load p

De

Unloading pressure q(x)

Existing tunnel Coefficient of subgrade modulus k

(a)

el Tunn ng i t star L1

Advancing direction

New tunnel λ Existing tunnel x

L2

η R0

α y

e fac ld e i Sh (b) Fig. 2. Calculation model (a) profile view; (b) plan view.

4

EI

d WðxÞ þ kDe WðxÞ ¼ qðxÞDe dx4

ð4Þ

where EI is the equivalent bending stiffness of the existing tunnel; W(x) is the vertical displacement of the existing tunnel; k is the subgrade modulus coefficient; De is the outer diameter of the existing tunnel; q(x) is the additional vertical unloading pressure on the existing tunnel caused by above-crossing new tunnelling. Firstly, let q(x) is equal to zero. The Eq. (4) degenerates into a homogeneous differential equation and its general solution is

WðxÞ ¼ ebx ðA cos bx þ B sin bxÞ þ ebx ðC cos bx þ D sin bxÞ

ð5Þ

pffiffiffiffiffiffiffiffiffiffiffiffiffi where b ¼ 4 K=4EI; K ¼ kDe ; A, B, C and D are the integration constants and these constants are determined by given boundary conditions. Because the ends of infinite beam are unaffected by the tunnelling, when x ! 1, the W(x) = 0. Note that when x ! 1, ebx ! 1 and ebx ! 0. From Eq. (5), the following is obtained

1  ðA cos bx þ B sin bxÞ ¼ 0

ð6Þ

Obviously, only the integration constants A and B are both equal to zero, the Eq. (6) will be satisfied. Thus, the Eq. (5) can be expressed

WðxÞ ¼ ebx ðC cos bx þ D sin bxÞ

ð7Þ

If an infinite beam supported on a Winkler foundation is acted by a point load P at the origin of the beam, as shown in Fig. 4(a), the rotation angle h(x) and the shear force Q(x) at that position are zero and half of the acted load P, respectively. It can be expressed

8 > <

  hðxÞ ¼ dWðxÞ dx 

  > : Q ðxÞ ¼ EI d WðxÞ  dx3

x¼0

¼0

3

x¼0

¼  P2

ð8Þ

By solving the Eq. (8), the constants C and D can be obtained

C¼D¼

Pb 2K

ð9Þ

By substituting Eq. (9) into Eq. (7), the general solution of vertical displacement for a concentrated load P acting at the origin of the infinite beam can be obtained

WðxÞ ¼

Pb bx e ðcos bx þ sin bxÞ 2K

ð10Þ

Thus, the displacement of the infinite beam caused by a concentrated load q(n)dn, as shown in Fig. 4(b), at the position n on the exiting tunnel is acquired

dWðxÞ ¼

qðnÞDe dnb bjxnj e ðcos bjx  nj þ sin bjx  njÞ 2K

ð11Þ

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R. Liang et al. / Tunnelling and Underground Space Technology 58 (2016) 159–176 3

QðxÞ ¼ EI

0

Special attention shall be paid to the determination of the related parameters, such as equivalent bending stiffness EI, subgrade modulus k and the Young’s modulus of surrounding soil Es, which have a great influence on the displacement of the elastic beam when subjected to unloading pressure on Winkler foundation. The EI is a key factor reflecting the capacity of tunnel to resist the soil movement induced by adjacent construction. In reality, shield tunnel is not a continuous tubular structure. Instead, it is a composite structure consisted of various segmental pieces bolted together by steel bolts. Due to the existence of the segmental lining joints, the bending stiffness of the tunnel is significantly smaller than that of a continuous tunnel lining structure. In order to consider the effect of joints on tunnel stiffness, many methods have been proposed to calculate the equivalent bending stiffness of tunnel, including theoretical methods (Shiba et al., 1988; Shiba and Kawashima, 1989; He, 1999) and modelling tests (Lin, 2001). Among the all suggested methods, longitudinal continuous model presented by Shiba et al. (1988) is widely used for estimating the shield tunnel bending stiffness. By taking account of various factors, including bolts stiffness, number of bolts, lining stiffness and tunnel geometry, Shiba et al. (1988) proposeda theoretical method to estimate the longitudinal equivalent bending stiffness of tunnel:

Ground surface

x c R2

F

y

R1 (x,y,z) z Fig. 3. Ground stresses caused by concentrated force acting at the subsurface of the ground (Mindlin, 1936).

By integrating the Eq. (11), the vertical displacement distribution WðxÞ of existing tunnel induced by continuous unloading pressures can be obtained

Z

þ1

1

ð14Þ

2.3. Determination of related parameters

c

WðxÞ ¼

d WðxÞ dx3

qðnÞDe b bjxnj e ðcos bjx  nj þ sin bjx  njÞdn 2K

EI ¼

ð12Þ

cos3 u Ec Ic cos u þ ðu þ p=2Þ sin u 

Based on the beam theory, the corresponding bending moment M(x) and shear force Q(x) are expressed

u þ cot u ¼ p 0:5 þ

nkb l E c Ac

ð15Þ

 ð16Þ

2

MðxÞ ¼ EI

d WðxÞ dx2

ð13Þ

-∞

kb ¼ Eb Ab =lb

ð17Þ

z Euler-Bernoulli beam

+∞

0 P

x

Winkler foundation model

(a) q(ξ)dξ

-∞

Euler-Bernoulli beam

z 0

ξ

+∞ dξ

x

Winkler foundation model

(b) Fig. 4. Euler-Bernoulli beam deformation subjected to (a) a concentrated force P; (b) a concentrated load q(n)dn.

R. Liang et al. / Tunnelling and Underground Space Technology 58 (2016) 159–176

where kb is the elastic stiffness of longitudinal joints, Eb is the Young’s modulus of bolt; Ab is the section area of bolt, Ab = pr2b, rb is the radius of bolt; lb is the length of bolt; n is the number of longitudinal bolts; l is the width of a tunnel segment; Ec is the Young’s modulus of tunnel segment; u is the angle of neutral axis; Ic is the longitudinal inertia moment of the section of a segment; Ac is the sectional area of tunnel segments. In the proposed method, the theoretical formulas suggested by Shiba et al. (1988) are adopted to estimate the tunnel longitudinal equivalent bending stiffness. The subgrade modulus coefficient k is another important parameter reflecting the interaction between the soil and the tunnel. Based on various experiments of a continuous beam supporting on ground surface, Vesic (1961) proposed an empirical formula to estimate the value of subgrade modulus coefficient k. That is given by:

0:65Es k¼ Bð1  l2 Þ

sffiffiffiffiffiffiffiffiffiffi Es B4 EI

12

ð18Þ

where B is the width of the beam. Vesic’s elastic subgrade modulus may give satisfactory prediction by allowing an infinite beam resting on the ground surface. However, for a pipeline or tunnel buried at a certain depth blow the ground surface, the soil-tunnel interaction exhibits a high sensitivity to embedment depth and the use of Vesic’s elastic subgrade modulus may lead to misleading results (Attewell et al., 1986; Klar et al., 2005; Yu et al., 2013). In order to estimate the subgrade modulus more rationally, Yu et al. (2013) derived an expression of the Winkler subgrade modulus K for a pipeline or tunnel buried at arbitrary depth:

K ¼ kB ¼

3:08

g

Es 1  l2

sffiffiffiffiffiffiffiffiffiffi 4 8 E B s EI

ð19Þ

with

(

g¼

2:18

when

1þ

when

1 1:7z0 =B

z0 B z0 B

6 0:5 > 0:5

In this study, the elastic subgrade modulus derived by Yu et al. (2013) is adopted. Note that B is equal to the diameter of existing tunnel De in the analysis (B = De). In general, the Young’s modulus Es in Eq. (19) of soft soils cannot be directly obtained from the soil laboratory experiment. Fortunately, the compression modulus Es0.1–0.2 of soils is more easily acquired from the soil investigation reports. The empirical relation between the Young’s modulus Es and the compression modulus Es0.1–0.2 of Shanghai soft soils is built up by Yang and Zhao (1992), based on the statistical analysis of pile testing experiments. It expresses

Es ¼ ð2:5 e 3:5ÞEs0:10:2

ð20Þ

Based on the back-analyses results from the FE analysis, Hashimoto et al. (1999) built up empirical relationship between the undrained Young’s modulus of soft Es and the undrained shear strength cu

Es ¼ 350 cu

ð21Þ

In practice, if the acquirement of Young’s modulus of soil is difficult, the value of Es can be roughly estimated by using Eqs. (20) or (21). By combining Eqs. (3) with (12), note that it is a typical triple integral mathematical problem and it can be calculated by means of Six-point Gauss-Legendre numerical technology (Davis and Rabinowitz, 1984).

165

By using this method, the unloading effects caused by overcrossing tunnelling can be modelled and the longitudinal deflection of existing tunnel can be rapidly predicted prior to construction. 3. Case studies In order to examine the validity of the proposed simplified analytical method, a comparative analysis is conducted with the measurement of the three selected case histories, including the Bund passage over-crossing Metro Line-2 tunnels project (Huang et al., 2012), Metro line-8 tunnels above-crossing Line-2 tunnels project (Chen et al., 2006; Ding and Yang, 2009) and Metro line-13 tunnels above-crossing Line-4 tunnels project (Zhu and Huang, 2010) in Shanghai, China. 3.1. The bund passage over-crossing Metro line-2 tunnels project Huang et al. (2012) reported the measured results of the displacements of Shanghai Metro Line-2 running tunnels subjected to the above-excavation of large diameter Bund Passage tunnel. The relative position between the new and existing tunnels is shown in Fig. 5. The Bund Passage shield tunnel is 1098 m long with total 549 segmental rings (the length of each ring is 2 m), constructed by a 14.27 m-diameter shield tunnelling machine. The external and internal diameters of the Bund Passage tunnel are 13,950 mm and 12,750 mm, respectively. The buried depth of the large diameter tunnel is 15.4 m (from the ground surface to the tunnel axis). The underlying shanghai Metro line-2 is composed of two directional tunnels, namely, Up line and Down line, respectively. The spacing between the twin parallel tunnels axes is about 11.4 m. The twin 6.2-m-diameter underlying existing tunnels with 0.35 m thickness concrete linings are the typical Shanghai metro shield tunnels. Table 1 gives the typical related tunnel structure parameters about Shanghai metro line tunnels. The shield was driven across the Down line tunnel first, following by the Up line tunnel. The minimum clearance is only 1.46 m from the new tunnel invert to the crown of existing tunnel, as shown in Fig. 5(b). The underground soil conditions are also shown in Fig. 5. As shown in Fig. 5, the large diameter tunnel was mainly driven through grey muddy clay (Layer ④) and grey clay (Layer ⑤1), of which were low strength, high compressibility, high water content and sensitive to disturbance. The existing metro tunnels buried in grey clay (Layer ⑤1) and grey silty clay (Layer ⑤3). The main physical parameters of soils are summarized in Table 2. Note that in order to obtain the soft soil Young’s modulus, the in-situ vane shear test results along Shanghai metro Line-2 collected by Lee et al. (1999) are adopted in Table 2. Since the Bund Passage tunnel was driven perpendicularly above the underlying twin tunnels with close clearance in soft clay, the structures safety and the displacements of underlying twin tunnels were both under special consideration. Two monitoring arrays were installed along each tunnel to monitor the vertical movements of the existing tunnel, as shown in Fig. 5(b). A close monitoring program was performed during and after abovecrossing tunnelling. Based on the Shiba’s method (Shiba et al., 1988) the calculated longitudinal equivalent bending stiffness EI of the typical metro tunnel in Shanghai region is 7834 MN m2. The estimated Young’s modulus of grey silty clay is 28.8 MPa according to the Eq. (21). The Poisson’s ratio of the grey clay is assumed as 0.3 in the analysis. About 690 m length distance has been constructed before the shield approaching to the centerline of Down line tunnel, so the advancing distances L1 are taken as 690 m and 707.6 m for Down

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6.6

Grey muddy silty clay

1Grey

Driving direction -12.0

14.27

12

1 +3.4

The Bund Passage Tunnel

clay

6.

2

-23.6

13.4

Down Line

11.40

Up line

1

3Grey

Unite :m

silty clay

(a)

Grey muddy silty clay

-12.0

1Grey

1.46

Monitoring point

clay

6.6

The Bund Passage Tunnel

12

+3.4

-23.6

2 3Grey

1-1

Unite:m

silty

clay

13.4

Down Line

(b) Fig. 5. Layout of existing tunnels and new tunnel (a) cross-section; (b) cross-section 1-1.

Table 1 Tunnel lining parameters.

Table 2 The related physical parameters of soils.

External diameter 2Ro (mm)

Internal diameter 2Ri (mm)

Lining width l (mm)

Young’s modulus of lining Ec (MPa)

Soils

Unit weight csat (kN/m3)

Water content w (%)

In-site vane shear strength cu (kPa) ⁄

6200 Number of longitudinal bolts n 17

5500 Diameter of bolt rb (mm)

1200 Length of bolt lb (mm)

3.45  104 Young’s modulus of bolt Eb (kPa)

④ Grey muddly silty clay ⑤1 Grey clay ⑤3 Grey silty clay

16.9

49.4

23.2

17.8 17.9

36.7 34.0

50.1 82.3

30

400

2.06  108

line and Up line tunnel, respectively. The monitored results of twin tunnels were given in Huang et al. (2012) when the shield left the up line and down line tunnels 15 day later, as shown in Fig. 6. According to shield operation records, the average driving speed was approximate 6.6 m/day. Thus, the advancing distances L2 from the intersections to the tunnelling face for both two tunnels are

⁄

Adopted from Lee et al. (1999).

about 99 m and 116.6 m, respectively. According to the operation records, the advancing distances as well as the skew angle are summarized in Table 3. The presented method is applied to compute the longitudinal displacements of twin running tunnels. The predicted and observed displacements of the underlying twin tunnels are both

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Tunnel heave (mm)

Measured (Huang et al., 2012) Calculated 10

8

6

4

2

0

The Bund tunnel axis -2 0

20

40

60

80

100

Offset distance from the first monitoring point (m)

Tunnel heave(mm)

(a) Down line tunnel 12

Measured (Huang et al.,2012) Calculated

10

8

6

4

2

0

The Bund tunnel axis -2 0

20

40

60

80

100

Offset distance from the first monitoring point (m)

(b) Up line tunnel Fig. 6. Comparison between the predicted and observed tunnel movements due to the Bund Passage tunnel construction above (a) Down line tunnel; (b) Up line tunnel.

plotted in Fig. 6(a) and (b), respectively. In the entire paper, positive and negative values of tunnel displacements denote tunnel heave and settlement, respectively. From inspection of Fig. 6, it shows that the tendency and magnitudes of predicted longitudinal displacements are generally in accordance with the measured results, although the maximum heave values are slightly larger than the observations. It demonstrates that the heave of existing tunnel occurs due to above tunnelling. The presented semi-analytical method can be applied to

effectively and quickly evaluate the behavior of exiting tunnel prior to construction. 3.2. Metro Line-8 tunnels above-crossing Line 2 project in Shanghai Chen et al. (2006) and Ding and Yang (2009) reported the case history of Shanghai Metro line-8 shield tunnel crossing over the existing Metro Line 2 twin tunnels. The relative position of the Metro Line-8 tunnels and Line-2 tunnels are shown in Fig. 7.

Table 3 The advancing distances L1 and L2 and skew angle a in different projects. Projects The Bund Passage over-crossing Metro Line-2 tunnels project Metro Line-8 tunnels above-crossing Line-2 project

Metro Line-13 tunnels above-crossing Line-4 tunnels project

Existing tunnels Down line tunnel Up line tunnel North line tunnel (first crossing) South line tunnel (first crossing) North line tunnel (second crossing) South line tunnel (second crossing) South line tunnel (first crossing) South line tunnel (second crossing) North line tunnel (first crossing) North line tunnel (second crossing)

Advancing distance L1 (m)

Advancing distance L2 (m)

a (°)

690 707.6 849.6 867.6 40.8 22.8 272.4 270 284.4 282

99 116.6 39.4 21.4 130 93 82.8 48 70.8 48

0 0 14 14 14 14 13 13 13 13

Skew angle

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The total 889 m long Metro Line-8 tunnel section running from Qu-hu station to People’s Square station consists of two parallel running tunnels, namely, Up line tunnel and Down line tunnel, respectively. A 6.34 m–diameter advanced shield machine was employed in this project and muddy silty clay and muddy clay were encountered during the crossing. The external and internal diameter of the twin tunnels are 6.2 m and 5.5 m, respectively. The thickness of the tunnel segmental lining is 0.35 m and the width of each segmental lining is 1.2 m. The shield obliquely crossed over the Line-2 twin tunnels with the skew angle of 76°, as illustrated in Fig. 7(b). The metro Line-2 consists of two running

tunnels, North line and South line, respectively. The distance between the centerlines of the North and South tube is as close as 18 m. The length of segmental lining is 1 m and the adjacent segmental concrete pieces are bolted together with high strength bolts. The minimum clearances between new shield tunnel and underlying tunnel are as close as 1.33 m and 1.35 m for South and North line tunnel, respectively, as shown in Fig. 7(a), which means the disturbance of the construction of new shield may cause unforeseen adverse impacts on the operating tunnel linings. The soil profile revealed by site investigation is also illustrated in Fig. 7(a) and the mechanical parameters of soils are summarized

Muddy clay

8.3

Silty clay

6.8

1.33

1.35

13.09

Shield driving direction

Φ6.2

Φ 6.2 North line tunnel of Metro Line2

14

South line tunnel Metro Line 2

(a) Sectional view

Qu-hu Station Upline tunnel of Metro Line8 Down line tunnel of Metro Line 8

° 76

North line tunnel of No.708Ring Metro Line2

No.34Ring

40.8

No.19 Ring

22.8

21.4

39.4

No.723Ring

South line tunnel of Metro Line2

3.8

Fill Muddy silty clay

6.2

8.59

Up line/Down line tunnel of Metro Line 8

1.2

Unite:m

Monitoring Points 2

Shield driving direction Unite:m

People s square station

(b) Plan view Fig. 7. Layout of the relative position between Metro line-8 and line-2 and the instrumentation section.

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in Table 4. The 6.2-diameter existing Line-2 twin tunnels were buried in silty clay and muddy clay, which are typical Shanghai soft ground condition with low strength, high water content and high compressibility. Detailed description of the construction process and the ground responses of Metro Line-2 during shield tunnelling can be referred to Lee et al. (1999). Since the Metro Line-2 tunnels being crossed over were the most heavily traveled ones in the Shanghai transit system, the train service was not allowed to be interrupted and the safety and structural integrity must be guaranteed and perfectly controlled during the crossing construction. In order to investigate the responses and potential excessive displacements of underlying existing tunnel during construction of the new tunnels, a comprehensive program of instrumentation and full-time monitoring were undertaken. Numerous of monitoring points positioned at 2 m spacing were installed along the twin tunnel alignments, as shown in Fig. 7(b), to ensure that any adverse developments during crossing would be recognized. Furthermore, an average 2.5 tons/m ballast of steel sand had been applied in the tunnel to reduce the excessive heave of the running tunnels. The vertical displacements of the underlying tunnels were continuously monitored during and after each individual shield advancing. In construction of Up line tunnel, the shield firstly passed over the North line, following by the South line tunnel of Line-2. The intersection points between the alignments of Up line and twin existing tunnels are at No. 708 ring and No. 723 ring, respectively, as shown in Fig. 7(b). When the shield arrived at the People’s Square station, the shield machine was reassembled and restarted to advance towards the Qu-hu station. At this time, on the contrary, the South line of Metro line-2 was first crossed over, following by the North line. The intersection points between the Down line alignment and underlying twin tunnels are No. 19 ring and No. 34 ring, respectively, as illustrated in Fig. 7(b). According to the construction process, the advancing distances L1 and L2 as well as the skew angles a for the two individual crossing are all summarized in Table 3. The longitudinal equivalent bending stiffness of Line-2 tunnels is taken the exact value as that of Case 1. The Young’s modulus of silty clay is taken as 13.8 MPa, which is 3.5 Es0.1–0.2 according to the Eq. (20). The Poisson’s ratio is assumed to be 0.3. The predicted as well as the measured tunnel displacements, including first and second crossing, are all plotted in Fig. 8. It found that the vertical displacements were slightly overestimated using the proposed method. The reason for these less satisfactory agreements may be attributed to the ballast applied on the running tunnels at the part of crossing prior to above-crossing construction, which effectively reduced the heave movements of the running tunnels caused by the stress relief. However, in general, the trends of the vertical tunnel displacements predicted using the proposed simplified method are in reasonable agreement with the observed values. 3.3. Metro Line-13 tunnels above- crossing Line-4 tunnels project Zhu and Huang (2010) reported the field monitoring results of the responses of Shanghai Metro Line-4 twin tunnels due to the

overlapped construction of Metro Line-13 tunnels. The plan and sectional views of the position relationship between the Metro Line-4 and Line-13 tunnels are shown in Fig. 9(a) and (b), respectively. Line-13 tunnel section between Lupu Bridge Station and Madang Road Station consists of two running tunnels, Up line and Down line, respectively, as shown in Fig. 9(a). All tunnels of Line-13 were constructed by employing EPB tunnelling technology. As shown in Fig. 9(a), the Metro Line-13 tunnels obliquely passed over the Line-4 and there is a skew angle of 77° between the intersected alignments. The axes of Line-13 and Line-4 tunnels are about 11.6 m and 20.8 m below the ground surface, respectively. The clearance between Line-13 and Line-4 tunnels was so close (about 3 m) that concern about the impacts on the underlying running tunnels was raised during overlapped crossing construction. Each tunnel of Line-13 and Line-4 is 6.2 m in outer diameter and 5.5 m in inner diameter. The length of segmental lining of Line-4 tunnels is 1.2 m. Each lining consists of several segmental pieces bolted by steel bolts. Subsoils in the construction filed are mainly soft soil, including alluvial and marine sediments, deposited during the Quaternary geologic period. As for Line-4, the tunnels are mainly buried in the typical Shanghai soft muddy clay (Layer ④), which is low strength and sensitive to disturbance. The shields mainly encountered the Layer ④ muddy clay and Layer ⑤1 silty clay. Unfortunately, the ground profile and mechanics parameters of soils are both not given by Zhu and Huang (2010). Thus, a roughly simple soil profile is drawn, as shown Fig. 9(b), according to the underground condition description of Zhu and Huang (2010). A similar overlapped crossing project (Line-11 tunnels down-crossing Line4 tunnels) reported by Zhang and Huang (2014) is very close to the studying site of this paper. Comparisons have been made between the two projects and it is found that the subsurface ground condition given by Zhang and Huang (2014) is general consistent with the subsoil description in Zhu and Huang (2010). Therefore, the related soil parameters given by Zhang and Huang (2014) are used in this analysis to predict the tunnel displacements due to the over-crossing construction. The related soils parameters are summarized in Table 5. The Young’s modulus of muddy clay is taken as 7.35 MPa, which is 3.5 times of compression modulus Es0.1–0.2 of muddy clay according to the Eq. (20). The Poisson’s ratio is assumed to be 0.29. The shield of Down Line tunnel of Metro Line-13 started from Lupu Bridge Station and advanced towards the Madang Station. During the over-crossing construction, the shield was carefully operated and moved in a low speed (approximately 4.5 m/day) in order to minimize the adverse impacts on the existing tunnels. It arrived at the No. 242 ring at 11th January, 2008. About two months later, after completely assembling, another shield started at the Lupu station and it moved towards the same direction as the first shield. However, with the accumulated experiences the crew became more confident and the average advancing speed increased as high as 7.2 m/d when Up line tunnel shield crossed over the existing tunnels. The shield tail left the No. 224 ring at 15th March, 2008. The advancing distances L1 and L2 as well as the skew angles a for the two individual crossing are all summarized in Table 3.

Table 4 Soil parameters of the site. Soils

Water content w (%)

Unit weight csat (kN/m3)

Void ratio e

Cohesion c (kPa)

Friction angle u (°)

Compression modulus Es0.1–0.2 (MPa)

Fill Muddy silty clay Muddy clay Silty clay

– 56.0 65.1 33.5

– 17.4 17.6 17.2

– 1.54 1.81 0.97

– 14 13 10

– 13.5 11.5 27.0

– 1.71 1.68 3.98

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8

First crossing-measured (Chen et al., 2006) Second crossing-measured (Chen et al., 2006) First crossing-calculated Second crossing-calculated

Heave of tunnel (mm)

6

Axis of Down line tunnel

Axis of Up line tunnel 4

2

0

0

10

20

30

40

50

60

Offset from first monitor point (m)

(a) North line tunnel

Heave of tunnel(mm)

8

First crossing-measured (Chen et al., 2006) Second crossing-measured (Chen et al., 2006) First crossing-calculated Second crossing-calculated

6

Axis of Down line tunnel

Axis of Up line tunnel

4

2

0

0

10

20

30

40

50

60

Offset from the first monitoring point(m)

(b) South line tunnel Fig. 8. Comparison of the observations and predictions of both first and second over crossing construction (a) North line tunnel; (b) South line tunnel.

In order to recognize any adverse development of existing tunnels, an extensive instrumentation program was carried out to monitor displacements of underlying tunnels during overcrossing tunnelling. The developments of longitudinal displacements of the twin running tunnels associated with the two over-crossing construction are both shown in Fig. 10. The predicted longitudinal tunnel displacements using the presented simplified model are also plotted in Fig. 10. As shown in Fig. 10, as for the first crossing, the predicted vertical displacements of underlying tunnels are in good agreements with the measured results, though the maximum value is slightly larger than the measured value in South line tunnel. In general, the proposed method gives satisfactory results. When the shield crossed over

the underlying running tunnels secondly, a superimposed effect of the responses of the tunnel is also observed and the final vertical displacements of the tunnels are basically the accumulation of tunnel displacements induced by each individual crossing. The predicted peak heave values locate exactly at the middle position between the two tunnel axes. However, the proposed method slightly underestimated the maximum values for the two tunnels. Moreover, the positions of measured peak values slightly offset towards the first crossing tunnel axis. It may due to creep behavior of soft clay and the tunnel displacements continued to increase with a slow speed before the arrival of the another shield. Nevertheless, very consistent trends are obtained using the proposed simplified approach and the predicted results are all in acceptable accuracy.

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Fig. 9. Relative position between Line-13 and Line-4 tunnels.

Table 5 Geotechnical parameter for in situ soil. Soils

Water content w (%)

Unit weight csat (kN/m3)

Void ratio e

Cohesion c (kPa)

Friction angle u (°)

Compression modulus Es0.1–0.2 (MPa)

Poisson’s ratio l

④ Muddy clay ⑤1 Silty clay

55.7 32.7

16.7 18.1

1.55 0.95

11 16.0

12.5 22.5

2.09 4.66

0.33 0.29

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First crossing-measured (Zhu and Huang, 2010) Second crossing-measured (Zhu and Huang, 2010) First crossing-calculated Second crossing-calculated

Heave of tunnels (mm)

8

6

Aixs of Up line tunnel Aixs of Down line tunnel 4

2

0

0

20

40

60

80

100

Offset from the first monitoring point (m)

(a) South line tunnel First crossing-measured (Zhu and Huang, 2010) Second crossing-measured (Zhu and Huang, 2010) First crossing-calculated Second crossing-calculated

Heave of tunnel (mm)

8

6

Aixs of Down line tunnel

Aixs of Up line tunnel 4

2

0

0

20

40

60

80

100

Offset from the first monitoring point (m)

(b) North line tunnel Fig. 10. Comparison between the measured and calculated longitudinal tunnel displacements: (a) South line tunnel; (b) North line tunnel.

From the three selected case histories, it is indicated that the proposed simplified analytical method can be used to reasonably predict the deformation of existing tunnels when subjected to above-crossing tunnelling in the primary design stage. 4. Parametric analyses In the previous section, the feasibility of the proposed simplified approach has been validated by comparison with three selected case reports for the problem of over-crossing tunnelling effects on existing underlying running tunnel. In this section, a parametric analysis is carried out to gain a greater understanding of the influences of various factors on the underlying tunnel, including clearance distance, advancing distance and number of new tunnels.

In general, the new shield tunnel is supposed to pass over the running tunnel perpendicularly; the underlying tunnel is assumed as a typical Shanghai metro tunnel with an equivalent longitudinal bending stiffness EI of 7834 MN m2 and the dimensions of tunnel can be referred to Table 1. The existing tunnel is assumed to be sufficient long. The new tunnel is driven by using a 6.34-m diameter shield machine, which is commonly employed in China. The dimensions of new shield tunnel are exactly the same as existing tunnel. Besides, the following parameters are used in analysis: the unit weight of the excavated soil cs is 19 kN/m3; the Poisson’s ratio l and the compression modulus Es0:10:2 are taken as 0.3 and 3.5 MPa, respectively; The advancing distances L1 and L2 of the new tunnel are assumed symmetric over the centerline of the running tunnel and the length of each side is 100 m.

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3.0

Fig. 11 shows the relative position between the new and existing tunnel. The invert of the existing tunnel is 33.1 m below the ground surface; A series of different clearance distances are involved in the analysis, including d = 0.1D, 0.5D, D, 1.5D, 2D and 2.5D. The variation of tunnel heave distribution with different clearance distances is illustrated in Fig. 12. It is shown that the maximum heaves of tunnel occur at the intersection point and the tunnelling-induced heave sharply decreases within the range of 20 m to 20 m, which is the most significant influencing zone. Moreover, the tunnel displacements decrease with an increase in the clearance distances, as expected. The influencing region of over-crossing construction is nearly unaffected with the changes of clearance distances. It implies that the reinforced region along the existing tunnel cannot be reduced, though the clearance distances increase. The variations of the maximum tunnel displacements with different clearance distances are plotted in Fig. 13. In Fig. 13, it shows that the maximum displacements decrease smoothly with the increasing clearance distances. The decreasing trend is not as rapid as expected, which means increasing clearance distance may be not the most effective way to reduce the disturbance of overcrossing construction in practical engineering.

2.5

Heave of tunnel/mm

4.1. Influence of the clearance distance

1.5 1.0 0.5

-0.5 -50

-40

-30

-20

-10

0

10

20

30

40

50

x/m Fig. 12. The changes of tunnel heave with different clearance distances.

3.0

2.5

Ground surface

New tunnel D d

Fig. 11. Relationship between the new and existing tunnel.

Maximum heave/mm

As the shield advancing, the heave of tunnel is continuously developing and it is a typical dynamic procedure. It is necessary to study rules of the development of the tunnel heave during the over-tunnelling. Fig. 14 shows the sketch of problem focused on in this section. The advancing distance Li, shown in Fig. 14, is a basic parameter reflecting the shield driving procedure. The value of Li ranges from 100 m to 100 m. It is noted that negative value of advancing distance Li means the shield is lagged behind the centerline of existing tunnel and the positive value illustrates that the shield face is beyond existing tunnel centerline. In the section, the centerlines of new and existing tunnel are 10 and 15 m below the ground surface, respectively. Fig. 15 shows the longitudinal tunnel heave due to various advancing distances. Fig. 16 shows the development of maximum tunnel heave with the advancing distance. Combining Figs. 15 and 16, it is found that the tunnel is nearly unaffected by the shield excavation when the shield is 3D ahead or away from the centerline. However, it is worth noting that in the crossing section from 3D to 3D, defined as influencing region shown in Fig. 16, the tunnel displacement is relatively sensitive to the advancing of shield and the peak heaves of tunnel increase sharply during over-crossing the influencing region. It suggests that, in practices, more attentions should be given when the

Existing tunnel De

2.0

0.0

4.2. Influence of the advancing distance

H

0.1D 0.5D 1D 1.5D 2D 2.5D

2.0

1.5

1.0

0.5

0.0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

h/D Fig. 13. The changes of the maximum heave of existing with different distances.

shield is driven exactly over the influencing region and effective protective measures, such as applying ballast and jet-grouting, should be implemented in order to control the heave of tunnel within the acceptable magnitude. 4.3. Influence of multiple new tunnels Multiple shield tunnels over-crossing the existing tunnel is commonly encountered in congested urban areas. As mentioned in the previous case studies, the superimposed effect of the displacement of existing tunnel is often observed during the construction of multiple shield tunnels. Fig. 17 shows the plan view of three side-by-side tunnels passing over the existing tunnel. The three tunnels share the same dimensions and the spacing between the adjacent tunnels axes is 12 m. The centerlines of multiple new tunnels and existing tunnel are buried at 10 m and 15 m below the ground surface, respectively. For clarity of nomenclature, the new construction tunnels are termed as ‘left’, ‘middle’ and ‘right’ tunnel, respectively, as illustrated in Fig. 17. The responses of the existing tunnel are analyzed on basis of the proposed approach. Fig. 18 shows the results of

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L2=100 m

New tunnel

Shield driving direction

x

0

L1 =100 m

Li

Existing tunnel

y

Maximum heave/mm

Fig. 14. The sketch of influence of advancing distance on existing tunnel.

2.5

-3D -1.5D 0 1.5D 3D

Heave of tunnel/mm

2.0

1.5

3.0

2.5

2.0

1.5 Influencing region

1.0

0.5

1.0

0.0

0.5

0.0

-0.5 -50

-40

-30

-20

-10

0

10

20

30

40

50

-15

-12

tunnel movement of both the individual and multiple tunnelling. From inspection of this figure, it is evident that both the maximum tunnel heaves and influencing region resulted from constructing of two tunnels (middle and left tunnels or middle and right tunnels) or three tunnels are significantly greater than only each single tunnel construction. The maximum values of two and three tunnel are 1.6 and 1.8 times larger than that of each single tunnel. In practice, multiple tunnels are always constructed one by another. During the construction interval, the displacements of the first constructed tunnel will continue to develop due to the creep effect of soft clay, and it will lead to the fact that the final displacements will be slightly greater than the predicted values and the displacement will be generally displaced towards the axis of first constructed tunnel. Unfortunately, the proposed method cannot consider the time-dependent developments of the tunnel heave in the soft clay.

-6

-3

0

3

6

9

12

15

Li / D

x/m Fig. 15. Changes of tunnel heave due to different advancing distances.

-9

Fig. 16. Changes of maximum heaves with different advancing distances.

5. Conclusions Previous researches primarily focused on the influences of downcrossing or parallel crossing tunnelling on the existing tunnel. However, few studies consider the interaction mechanisms between existing tunnel and over-crossing tunnelling. In this paper, a simplified semi-analytical approach for evaluating the heave of underlying tunnel induced by above-crossing tunnelling is presented. In this analysis, the underlying existing tunnel is treated as a continuous Euler-Bernoulli beam resting on Winkler foundation model. The unloading stress on the existing tunnel induced by the overcrossing tunnelling is considered by using Mindlin’s solution. The responses of the existing tunnel due to the unloading pressure are computed by solving the governing differential equation numerically. The applicability of proposed method is examined against three published case reports. The estimated results proposed by

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Right tunnel

Midddle tunnel

L2=100 m

Left tunnel

Shield driving direction 0 12 m

12 m

L1=100 m

Existng tunnel

x

y Fig. 17. Related position between the new multiple tunnels and existing tunnel.

The axis of middle tunnel

5

Middle tunnel Left tunnel Right tunnel Middle +left tunnels Middle +right tunnels Three tunnels

The axis of left tunnel

Heave of tunnel/mm

4

The axis of right tunnel

3

2

1

0

-50

-40

-30

-20

-10

0

10

20

30

40

50

x/m Fig. 18. Changes of tunnels heave due to multiple tunnels passing over.

the simplified approach are in reasonable agreement with the field measurements. The parametric studies are also performed to gain a greater understanding of the behavior of the existing tunnel due to above-crossing tunnelling. The proposed analytical approach provides a quick but low cost alternative method for evaluating the tunnel responses due to over-crossing tunnel in the design stage.

Acknowledgements The authors acknowledge the financial support provided by National Natural Science Foundation of China (No.41472284 and No.U1234204) and Natural Science Foundation of Ningbo City (No. 2016A610090).

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