A new model to predict ground surface settlement induced by jacked pipes with flanges

Tunnelling and Underground Space Technology 98 (2020) 103330

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A new model to predict ground surface settlement induced by jacked pipes with flanges

T

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Pengjiao Jiaa, Wen Zhaoa, , Arman Khoshghalbb, Pengpeng Nic, Baofeng Jianga, Yang Chend, ⁎ Shengang Lia, a

School of Resources and Civil Engineering, Northeastern University, Shenyang 110819, China School of Civil and Environmental Engineering, University of New South Wales, Sydney 2052, Australia c Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai), Guangdong Key Laboratory of Oceanic Civil Engineering, Guangdong Research Center for Underground Space Exploitation Technology, School of Civil Engineering, Sun Yat-sen University, Guangzhou 510275, China d School of Civil Engineering and Architecture, Xi’an University of Technology, Xi’an, China b

A R T I C LE I N FO

A B S T R A C T

Keywords: Pipe jacking Flanges Soil disturbance Ground surface settlement Mindlin’s solution Stochastic medium theory Cavity expansion theory

Ground surface settlement is one of the critical parameters that needs to be controlled strictly during pipe jacking. The calculation model for estimating the ground deformation induced by pipe jacking is scarce in the literature, especially for pipes with irregular cross-section (e.g., circular pipes with flanges). In this study, considering the pipe-soil interaction, the distribution characteristics of frictions between pipe and soil, and the support force at the tunnel face, a settlement formula is proposed for a single jacked pipe using the Mindlin’s solution and the Stochastic medium theory. Based on the cavity expansion theory, a relationship for calculating the circumferential plastic zone is developed considering the effect of flanges. The distribution of the plastic zone around the pipe and the superimposition effect due to multiple pipes are discussed. Finally, a correlation is established to estimate the ground surface settlement for three types of multiple jacked pipes with different spacing. A case study of a subway station project using the Steel Tube Slab (STS) method is presented. Comparisons of ground settlement from field measurements and theoretical calculations show that the proposed approach can reasonably predict the ground surface settlement for multiple jacked pipes.

1. Introduction The traditional pipe roofing method was originally developed to construct tunnels under a support system consisting of circular steel pipes without flanges, such as the initiative of pipe roofing project in Antwerp, Belgium (Musso, 1979; Hemerijckx, 1983). Steel pipes are jacked to the design location by a pipe jacking machine to form an initial support system. These adjacent pipes are filled with grout or concrete to construct a roofing system before the implementation of tunnel excavation (Jia et al., 2019), as shown in Fig. 1. Considering that the technology has a great advantage in controlling the propagation of ground surface settlement and reducing the associated influence of excavation on the surrounding environment, it has been subsequently used to construct underground structures in many countries, such as Japan (Yamazoyi et al., 1991; Kaneke et al., 2003), South Korea (Park et al., 2006), United States (Rhodes & Kauschinger, 1996) and China (Yao et al., 2004; Zhu et al., 2005; Zhang et al., 2016; Yang and Li,

2018). This method, with some improvements, has been recently introduced in China, e.g. Steel Tube Slab method (STS) (Zhao et al., 2016; Jiang et al., 2018b). Unlike the traditional pipe roofing method, it is proposed that the adjacent steel tubes are connected by flange plate, bolt and concrete, as shown in Fig. 2. All measures can significantly increase the lateral stiffness and bearing capacity of the pipe roofing system to better control the soil movement (Jia et al., 2018, 2019). The pipe jacking process with flanges is a crucial construction step that needs to be investigated systematically. Several scholars studied the prediction of jacking force and the pipesoil interaction through laboratory testing, numerical simulation and in-situ testing for linear jacked pipes, from which different pipe jacking force calculation models were proposed (Potyondy, 1961; Haslem, 1986; Teruhisa, 1994; Marshall, 1998; Pellet and Kastner, 2002; Marco et al., 2006; Shou and Jiang, 2010; Yen and Shou, 2015; Ciaran and Trevor, 2017). These proposed analysis methods can consider the influence of several key parameters, such as the geometry of the pipe, the

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Corresponding authors. E-mail addresses: [email protected] (P. Jia), [email protected] (W. Zhao), [email protected] (A. Khoshghalb), [email protected] (P. Ni), [email protected] (B. Jiang), [email protected] (Y. Chen), [email protected] (S. Li). https://doi.org/10.1016/j.tust.2020.103330 Received 3 December 2018; Received in revised form 8 January 2020; Accepted 1 February 2020 Available online 18 February 2020 0886-7798/ © 2020 Published by Elsevier Ltd.

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Fig. 1. Traditional pipe roofing method using circular jacked pipes.

Fig. 2. Steel Tube Slab method using jacked pipes with flanges.

pipe jacking operation; overestimation of pipe-soil frictions is associated with a higher predicted value of pipe jacking force, resulting in unsafe pipe jacking operation. The mobilized earth pressure acting on the shield face is also an important aspect, which has been studied extensively and discussed in several standards, including the German standard ATV A 161 (German ATV rules and standards, 1990), the Chinese standard GB50332 (The Ministry of Construction of China, 2002), the Japan Microtunnelling Association (JMA) standard (Japan Microtunnelling Association, 2013), and the UK Pipe Jacking Association (PJA) standard (Pipe Jacking Association, 1995). Most earth pressure models were derived based on the Terzaghi arching model (Terzaghi, 1943; Zhen et al., 2014; Jiang et al., 2018a). The Marston earth pressure model (Qin et al. 2017) is also routinely adopted for pipes in open cuts. Although the formulas for both Marston and Terzaghi models are very similar, differences exist in the kinematics of shearing bands. The Marston model is developed to account the mobilized differential settlement in upper soils, while the Terzaghi model is governed by unloading (Zhang et al., 2016). Ji et al. (2018) modified the Protodyakonov’s arch model, which can provide calculations of jacking force for deeply buried pipes. However, all existing earth pressure models can only accurately predict the behavior of steel or concrete pipes with regular cross-sections, and do not reflect the influence of flanges on the mobilized earth pressure acting on the shield face. Compared with the shear failure zone for a conventional pipe, the influencing area of the pressure arch for a jacked pipe with flanges is much larger. Hence, larger earth pressure can be expected to act on the

geological conditions, the surface roughness of the pipe, the burial depth, the deformation at pipe joints, the lubricant slurries and the construction schedule (Reilly and Orr, 2017; Namli, and Guler, 2017). With the development of pipe jacking technology, the curved pipe jacking technique has been proposed to construct underground spaces over the last decade. Compared with the linear pipe jacking technique, the curved jacking technique is much more complicated and difficult, because it requires a system providing a high pipe jacking force (Zhang et al., 2018). The eccentric pipe jacking force can produce a great bending moment, leading to instability for the initial jacked pipe segment during the construction stage (Nanno, 1996; Milligan and Norris, 1999; Broere et al., 2007; Cui et al., 2015). It could also result in pipe failure in the jacking system (Beckmann et al., 2007). Zhang et al. (2018) proposed two analysis methods for pipe-soil interaction, i.e., partial contact model and full contact model, to evaluate the curved pipe jacking force in the field and study the stability conditions for the excavation (Zhang et al., 2018). In the literature, regardless of the pipe alignment (i.e., whether linear or curved), the jacked pipe usually has a regular cross-section, e.g. circular and rectangular. It should be emphasized that all existing analytical models do not consider the influence of flanges on pipe-soil frictions. This means that all existing models cannot consider the influence of flanges on the mobilization of pipe-soil frictions during the pipe jacking process. Hence, calculations using these analytical methods could produce a conservative estimation for pipe-soil frictions. Underestimation of pipe-soil frictions could result in a lower predicted value of pipe jacking force, leading to difficulty in 2

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top of jacked pipe with flanges than that on a conventional jacked pipe (Jia et al., 2019). Therefore, one can anticipate that all existing calculation methods underestimate the soil pressure in front of the shield face. It is essential to modify the existing arching model to accurately calculate the soil pressure for jacked pipes with flanges. It is well-known that the development of ground surface settlement is one of the most important parameters in design and construction of pipe jacking. Up to now, many investigations have been conducted to evaluate the ground surface settlement due to pipe jacking by means of laboratory tests, numerical analyses and field measurements (Chapman, 1999; Feng et al., 2003; Khazaei et al., 2006; Guo et al, 2011; Sun, et al., 2015; Yang et al., 2018; Pan, 2019; Song et al., 2019a, 2019b). For example, the empirical Gaussian curve (Peck, 1969) is used to predict the ground surface settlement (Lin, 2008; Wei et al., 2016; Shi et al., 2019a, 2019b). In practice, the STS method is used to construct underground structures with the support system formed by jacked pipes with flanges. However, up to now, all existing formulations cannot consider the influence of flanges on the mobilization of ground surface settlement. In other words, there is no calculation model that can be used to predict the ground surface settlement during the construction of jacked pipes with flanges. In this study, considering the pipe-soil interaction, the friction characteristics mobilized at the pipe-soil interface, and the support force at the tunnel face, a relationship is proposed to calculate the ground settlement induced by a single jacked pipe using the Mindlin’s solution and the Stochastic medium theory. In view of the cavity expansion theory, a correlation is developed to estimate the circumferential plastic zone developed around the pipe considering the effect of flanges. Subsequently, theoretical formulas for the development of ground surface settlement are proposed for three kinds of multiple pipe jacking processes. Finally, the in-situ ground settlements measured during the construction of the Olympic Sports Center Subway Station using jacked pipes with flanges (Jia et al., 2019) in Shenyang, China are compared with the predictions using the proposed models.

During the pipe jacking process, the average jacking force is 800 kN, and the maximum jacking force is always less than 3000 kN. The construction process of pipe jacking at the site can be seen in Fig. 6. 3. Calculation of ground settlement caused by single pipe jacking 3.1. Basic assumptions During the jacking process of steel pipes with flanges, the induced ground settlement can be attributed to three reasons: frictions mobilized at the interface between the pipe shaft and the soil, soil deformation due to insufficient support force at the tunnel face, and volume loss. To simplify the computational model, the following assumptions are made: (a) To present an analytical formulation to predict the ground surface settlement induced by jacked pipes with flanges, the surrounding soil is only defined as standard elastomer, such that a closed-form solution can be derived; (b) Since the groundwater level was lowered than the construction surface before the implementation of pipe jacking, the influence of groundwater level is neglected; (c) Given construction settlement is the main reason for the total settlement, and the post-construction settlement is generally small, especially, for sandy soil. Instantaneous ground deformation occurs at the tunnel face during tunnel excavation (no continued ground movement after tunnel excavation); (d) To use the superposition method to calculate ground surface settlement, the frictions mobilized around the pipe are divided into two components: at pipe walls and at flanges; (e) To simplify the computational model and promote the applicability of the proposed model, the friction force is evenly distributed in the contact area. The impact of frictions mobilized at pipe shafts is basically the same as the contribution from support force at the tunnel face. From the mechanical point of view, both forces, acting on an infinite body in a half space, causing the internal deformation problem. Jiang et al. (2018a) proposed a pressure arch theory to estimate earth pressures around the circumference of flanged steel jacked pipe. According to this theory, the soil around a jacked pipe with flanges is divided into seven zones as shown in Fig. 7. Since the surrounding soil is defined as standard elastomer, the superposition method can be used directly in the calculation of ground surface settlement induced by different components. The distribution characteristics of earth pressure over different zones around the pipe with flange slabs is systematically described. The Platts arch model (Yang et al., 2013) is adopted to analyze the earth pressure acting on the pipe due to soil collapse (area A and area E); the limited earth pressure model (Ma, 2015) is adopted to evaluate the earth pressure caused by the soil-plug effect (areas B, C and F); and the soil reaction force formed by self-weight (Murin et al., 2013) is assessed by the elastic beam model (area D and area G), as shown in Table 1. For different earth pressure components around the pipe, the Mindlin’s solution is used to improve the support model at the excavation face of the pipe, and to study the distribution characteristics of the circumferential friction force, based on which the induced settlement can be calculated. The pipe jacking process inevitably leads to the occurrence of volume loss, forming a cavity inside the soil. Ground settlement initiates in upper soils, after which the settlement trough is further propagated both in the transverse and longitudinal directions of the pipe (Ni and Mangalathus, 2018). It should be emphasized that the magnitude of ground settlement caused by volume loss and by frictions mobilized around the pipe is different. The mechanism of soil collapse is degenerated as a large-deformation problem. Therefore, the theory of elastic mechanics is not applicable for use in the analysis. The

2. Project overview This investigation illustrates the performance of a pipe jacking project using the Steel Tube Slab (STS) method in the Olympic Sports Center Subway Station in Shenyang, China. The cross-section view of the station is shown in Fig. 3. In this engineering project, jacked pipes with flanges are used. Steel pipes were jacked slowly into the ground over a distance of 66 m using an auger boring machine and a hydraulic jack at a rate of 3 m per working day. Each jacked pipe has an outer diameter of 0.9 m and a pipe wall thickness of 0.016 m. The thickness of the flange plate is also 0.016 m. The surfaces of both steel pipes and flange plates are not polished and coated to increase the surface roughness. The spacing between the centre of two adjacent pipes is 1.0 m. In total, 28 pipes (1# to 28#) and 12 pipes (29# to 40#) are jacked to construct the horizontal and vertical roofs, respectively, for the station using a horizontal spiral drill. At the site of the station, detailed geotechnical investigations are conducted to evaluate the geological conditions according to GB500212001 (2002). The geological profile of the construction site is depicted in Fig. 4. Above the pipe, the average cover depth is approximately 3.5 m. To investigate the development of ground surface settlement caused by pipe jacking, a total of 5 monitoring sections were arranged as shown in Fig. 5. A total of 12 points were arranged at each section to measure the profile of ground surface settlement. The total length of pipe jacking is more than 1800 m for horizontal pipes (pipe 1#–28#) within the time window from December 25th, 2015 to April 5th, 2016. Hence, the average velocity is approximately 18.6 m/d. The total length of pipe jacking is approximately 800 m for vertical pipes (pipe 29#–40#) within the time frame from May 6th, 2016 to July 14th, 2016. Hence, the average velocity is 18.6 m/d. 3

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Fig. 3. The Olympic Sports Center Subway Station: (a) Cross-section; (b) Design location of pipe jacking; (c) geometry of jacked pipe with flanges (in mm).

as follows:

w = Ψ(P , c ) (3 − 4μ)(z − c ) 6cz (z + c ) Px z−c [ = + − 16πG (1 − μ) R13 R23 R25 4(1 − μ)(1 − 2μ) ] + R2 (R2 + z + c )

(1)

R2 = and where R1 = (x − m)2 + (y − n)2 + (z − c )2 ; (x − m)2 + (y − n)2 + (z + c )2 . Subsequently, Wei et al (2002, 2005, 2007) used the Mindlin’s solution to calculate the ground surface settlement induced by the friction between pipe and soil. Liao et al. (2004) used the Mindlin’s solution to calculate the ground movement induced by the bulkhead additive thrust and lateral friction during pipe-jacking. The Mindlin’s solution to vertical and horizontal force is used to calculate the ground deformation induced by the face support pressure and the lateral friction resistance, respectively (Li et al., 2012). Subsequently, the development of ground deformation can be predicated during pipe jacking considering the effect of grouting pressure (Ren et al., 2018). All existing models in the literature are mainly applicable to analyze regular circular or rectangle pipes. The mechanism of ground settlement due to pipe jacking with flanges has not reported. Hence, the Mindlin’s solution is adapted in this study to calculate the ground surface settlement caused by pipe jacking with flanges. The distribution characteristics of earth pressure over different zones around the jacked pipe with flanges is computed using the proposed model of Jia et al. (2019). The friction force at pipe walls and flange plates is considered as a distributed force, rather than a concentrated force as adopted in the Mindlin’s solution. In order to make the calculations more universal,

Fig. 4. Geological profile of the STS pipe-jacking section (in m) (Jia et al., 2019).

development of ground settlement caused by volume loss is then studied based on the stochastic medium theory. In order to facilitate the derivation, the direction along the pipe alignment and the horizontal transverse direction are specified as the x and y directions, respectively. The vertical direction is denoted as the z direction. The origin of the coordinate system is at the ground surface above the tunnel face. 3.2. Ground settlement caused by frictions between jacked pipe with flanges and soil Based on the Galerkin’s displacement function, Mindlin (1936) deduced the displacement field caused by concentrated force acting on a half space infinite body. The displacement in the z direction is defined 4

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Fig. 5. Layout of monitoring points.

Fig. 6. Construction of pipe jacking in the field.

R × sinθ. The expression of ground settlement caused by frictions at pipe walls is written as:

based on the method proposed by Liang et al. (2015), the concentrated force is converted into a distributed force. The coordinate system of (x, y, z) for the original Mindlin’s solution moves by a vector (m, n), and the local coordinate system for the distributed force becomes (x', y', z'). The axes in the two coordinate systems are parallel to each other. The coordinate transformation is defined by:

x′ = x − m⎫ y′ = y − n ⎬ z′ = z ⎭

w = Ψ(P , H ) L

θ2

= ∫ dl ∫ 0

θ1

(3 − 4μ) Pr (x + l) z − H + r sin θ [ + 16πG (1 − μ) R13 R23

(z − H + r sin θ) 6 × z × (H − r sin θ) × (z + H − r sin θ) × − R23 R25 4(1 − μ)(1 − 2μ) ]dθ + R2 (R2 + z + H − r sin θ) (3)

(2)

Substituting Eq. (2) into Eq. (1), the ground displacement at any point (x, y, z) in the spatial coordinate system can be derived.

R2 = where R1 = (x + l)2 + (y − r cos θ)2 + (z − H + r sin θ)2 ; 2 (x + l) + (y − r cos θ)2 + (z + H − r sin θ)2 ; P is the jacking force (in kN/m2); H is the burial depth (measured from the pipe centreline to the ground surface, in m); R is the pipe radius (in m), θ represents the angle from the horizontal plane; θ1 and θ2 are the angle at the leading and ending points, respectively; and L is the jacking distance (in m). For convenience, the pipe wall is divided into three parts: area E (pipe crown), area F (pipe springline), and area G (pipe invert), as

3.2.1. Ground settlement caused by frictions at pipe walls The calculation model of ground displacement caused by soil frictions is schematically shown in Fig. 8. The interface between pipe and soil is a cylindrical surface, and the transformation relationship between the cylindrical coordinate system and the rectangular coordinate system needs to be established by m = −l, n = R × cosθ, and c = H − 5

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Fig. 9. Regions for calculating the frictions at the pipe-soil interface. Fig. 7. Earth pressure zones around an STS pipe with flange plates. Table 1 Different regions and the corresponding earth pressure theory. Area

Location

Calculation model

A E B C F D G

Above the upper flange plate Above the pipe crown Below the upper flange plate Above the lower flange plate At the pipe springline Blow the lower flange plate Below the pipe invert

Platts arch model Limited earth pressure model

Elastic beam model

Fig. 10. Regions for calculating the frictions at STS pipe flange plates.

The coordinate transformation relationship for area A1 is given as: m = −l, n = −L1, and c = L3, and the integral variable is dldy. The calculation model of ground displacement caused by frictions between flange and soil is shown in Fig. 11, which can be expressed by:

Fig. 8. Calculation model for estimating the ground displacement induced by frictions between pipe and soil.

shown in Fig. 9, and the ground deformation in each zone is obtained using Eq. (3). 3.2.2. Ground settlement caused by frictions at flange plates The frictions mobilized at flange plates play an important role in settlement control. Mobilization of frictions acting on the upper flange plates (parts A and B) and the lower flange plates (Parts C and D) can further cause ground disturbance, which can be regarded as a deformation problem for an infinite half space subjected to a distributed force. The Mindlin’s solution is also used for this calculation, as shown in Fig. 10. Taking area A as an example, both the global coordinate system and the local coordinate system are the Cartesian coordinate systems.

Fig. 11. Calculation model of ground displacement induced by frictions between flanges and soil. 6

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w1 = Ψ(P , H ) =

P (x + l) z − L3 [ 16πG (1 − μ) R13 (3 − 4μ) × (z − L3) 6 × z × L3 × (z + L3) + − R25 R23 4(1 − μ)(1 − 2μ) ]dy + R2 (R2 + z + L3)

∫0

L

dl

∫0

L1

(4)

R2 = and where R1 = (x + l)2 + (y + L1)2 + (z − L3)2 ; (x + l)2 + (y + L1)2 + (z + L3)2 . The coordinate transformation relationship for area A2 area is defined by: m = −l, n = −L2, and c = L3, and the integral variable is dldy. The calculation model of ground displacement due to frictions between flange and soil is then written as: w2 = Ψ(P , H ) =

P (x + l) z − L3 [ 16πG (1 − μ) R13 (3 − 4μ) × (z − L3) 6 × z × L3 × (z + L3) + − R23 R25 4(1 − μ)(1 − 2μ) ]dy + R2 (R2 + z + L3)

∫0

L

dl

∫0

L2

Fig. 12. The convergence of a circular section.

circle is R and the coordinates of the circle centre are (0, H), the equation for the circle is expressed by:

(5)

R2 = R1 = (x + l)2 + (y + L2)2 + (z − L3)2 ; and where (x + l)2 + (y + L2)2 + (z + L3)2 . By superimposing Eqs. (4) and (5), the ground settlement caused by soils in zone A can be obtained:

Y 2 + (Z − H )2 = R2

If the circular section collapses completely, it results in the maximum displacement on the ground surface after a certain period of time. The terms of Y, Z and X in Eq. (7) are successively integrated to obtain the integral equation for the circular section:

(6)

w = w1 + w 2

where L1 is the length of left flange plate (in m); L2 is the length of right flange plate (in m); and L3 is the distance measured from the upper flange plate to the ground surface (in m). The integral form of zone B and zone A is the same, and the corresponding calculation of friction force can be substituted. For zones C and D, the integral variable in Eq. (4) should be replaced by: m = -l, n = -L1 and L2, and c = L4, respectively, where L4 is the distance measured from the lower flange plate to the ground surface (in m).

We (X , Y , Z ) =

H+R

dη

R2 − (η − H )2

∫−

2

R − (η − H )

2

tan2 β (η − Z )2 (9)

In the normal jacking stage, the leading section of steel pipe presents uniform shrinkage following the circular section. However, the soil around the leading pipe is usually excavated manually. The shrinkage area can be obtained by superimposing the semicircle section and the rectangular section. Taking the left semicircle as an example, the pipe radius is denoted as R, and the pipe centre coordinates are (0, H), such that the terms of Y, Z and X in Eq. (7) are successively integrated to obtain the integral equation for the semicircle section.

During the pipe jacking process, the excavation section cannot collapse completely, but volume loss occurs inevitably (Rowe et al., 1992a, 1992b; Lee et al., 1992). The initial jacking section is denoted as Ω0, and it contracts from Ω0 to Ω1 due to volume loss. The magnitude of ground settlement above the section should be equivalent to the settlement caused by soil loss from Ω0 to Ω1. Based on this, the stochastic medium theory is first used to compute the ground surface settlement induced by tunnel excavation.

We (X , Y , Z ) = × exp{ −

0

H+R

∫−L dε ∫H−R

dη

∫−

0 R2 − (η − H )2

tan2 β (η − Z )2

π tan2 β × [(X − ε )2 + (Y − ς )2]}dζ (η − Z )2

(10)

Similarly, the integral equation for the rectangular section can be obtained as:

2

β ∭ (ηtan − Z )2

Ω0 - Ω1

π tan2 β × exp{ − × [(X − ε )2 + (Y − ς )2]} (η − Z )2

0

∫−L dε ∫H−R

π tan2 β × exp{ − × [(X − ε )2 + (Y − ς )2]}dζ (η − Z )2

3.3. Ground settlement caused by volume loss

We (X , Y , Z ) =

(8)

We (X , Y , Z ) = (7)

× exp{ −

It should be noted that the calculation method is widely used for predication of settlement during shield tunnel construction (Shi et al., 2003; Shi et al., 2010; Zhang et al., 2013; Liu et al., 2018), deep excavation, metro station excavation (Meng et al., 2012) and rectangular pipe jacking (Xu et al., 2018; Yin et al., 2018). However, the ground surface settlement induced by jacking circular steel pipes has not been investigated as reported in the literature, especially for jacked pipes with flanges. Based on the Stochastic medium theory (Liu and Zhang, 1995), the problem of ground settlement due to volume loss is transformed into problems for different integral regions. The cross-section under the jacking operation is shown in Fig. 12. Assuming that the radius of the

0

∫−L dε ∫a

b

dη

∫c

d

tan2 β (η − Z )2

π tan2 β × [(X − ε )2 + (Y − ς )2]}dζ (η − Z )2

(11)

It is noted that the above equations are not integrable, and as such an analytical solution to the original function cannot be obtained. Eqs. (7)–(11) can be solved by the Legendre-Gauss numerical integration method. 3.4. Ground surface settlement caused by support force at the tunnel face The silo-wedge model was initially introduced by Horn (1961), and was subsequently improved by different researchers (Anagnostou and Kovári, 1996; Broere, 2001; Kirsch and Kolymbas, 2005; Anagnostou, 7

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2012; Ji et al., 2018). Anagnostou and Kovári (1996) investigated the problem of face instability during the tunneling process with an earth pressure balance shield machine with a modified silo-wedge model. Broere (2001) explored the working face limit support pressure of a slurry balance shield tunnel in heterogeneous soil, where the impact of seepage force was considered. The contributions of the horizontal frictional force and the cohesive force between the silo and the wedge were taken into account by Kirsch and Kolymbas (2005). Anagnostou (2012) revised the classical silo-wedge model, where the friction force acting on the vertical slip surface of the wedge was directly considered. Ji et al. (2018) modified the Protodyakonov’s arch model for jacked pipe at a deep burial depth, and the classical silo-wedge model was improved to evaluate the limit face support pressure during pipe jacking. All previous investigations mainly focused on the analysis of circular tunnel, and there is a lack of study to evaluate the performance of jacked pipe with flanges using the silo-wedge model. Hence, the conventional silo-wedge model needs to be further improved to consider the contribution from flanges.

Fig. 14. Force equilibrium for the silo.

3.4.1. Calculation of support force at the tunnel face Under ideal conditions, the support force at the tunnel face and the earth pressure in front of the pipe should be balanced. In this part, the silo-wedge model is used in the analysis, in which the soil in front of the pipe is distinguished into two parts: a ‘silo’ and a ‘wedge’ as shown in Fig. 13. The wedge-shaped body is considered as a rigid plastic body, and the irregular failure plane is assumed to satisfy the Mohr-Coulomb failure criterion. Inside the rigid plastic body, no failure planes are formed. The silo contains the soil prism above the wedge-shaped body. Relevant research (Lee et al. 2003; Lee et al. 2004) show that the soil in the excavation disturbance zone is “grooved” and the maximum ground deformation occurs above the excavation section. When the support force at the excavation face is insufficient, the soil has a tendency to move towards the nearby spaces, such that the relative displacement between soils results in friction resistance. The Terzaghi pressure model for loose soils is generally used for calculation. When the upper soil prism above the excavation face moves downward, the motion is also hindered by the sliding force mobilized along the failure planes. The influence of groundwater level is neglected, since drainage

measures are often conducted during pipe jacking to minimize the detrimental effect of groundwater. Hence, the contribution of water pressure is omitted in this investigation, and the force equilibrium for the silo is established as shown in Fig. 14. The force equilibrium for the silo can be written as

σv (z )·B1·h2·cot α + γ ·B1·h2·cot α dz = (σv (z ) + dσv (z ))·B1·h2 ·cot α + 2(c + σh·tan φ) × (B1 + h2 ·cot α ) dz (12) Eq. (12) is simplified as a linear ordinary differential equation by:

σv (z ) =

A (1 − e−B × z ) + P0 × e−B × z B 2(B1 + h2 cot α ) c; B1 × h2 × cot α

(13) 2(B1 + h2 cot α ) B1 × h2 × cot α

× K 0 × tan φ . where A = γ − and B = where h1 is the height of the silo (in m); h2 is the height of the wedge (in m); B1 is the width of the wedge (in m); α is the angle measured from the sliding surface in front of the wedge to the horizontal; γ is the unit weight of the soil (kN/m3); φ is the angle of internal friction of the soil; C is the soil cohesion; Gp is the prismatic dead weight; K0 is the lateral earth pressure coefficient; P0 is the traffic load; Z is the cover depth; σh is the horizontal stress; and σv is the vertical stress. In the following, the silo-wedge model is simplified by considering that only rigid deformation occurs in the wedge. The force equilibrium for the wedge is established in Fig. 15. In most cases, the superposition method is adopted to consider the dead weight for the wedge (Gw). In this investigation, the isolated body derivation is expressed as follows:

Fig. 13. Silo-wedge model for calculating the support pressure at the tunnel face (Cheng et al., 2019).

Fig. 15. Force equilibrium for the wedge. 8

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Gw = γ ·B1·cot α·

∫0

h2

(h2 − z1) dz1 =

h22 γ ·B1·cot α 2

(14)

For frictions mobilized at the lateral sides of the wedge, the derivation is similar to that for the silo. Researchers pointed out that the lateral earth pressure coefficient for soils in the wedge should be different from that in the silo (Broere, 2001; Perazzelli et al., 2014). In subsequent discussions, Kw is used to represent the lateral earth pressure coefficient, and the calculation model for T2 can be obtained as follows:

T2 =

=

Kw tan φN1 tan α

h2

∫ (h2 − z1) dz1 + 0

Kw γ tan φ tan α

∫0

h2

(h2 z1 − z12) dz1

h2 h3 Kw × tan φ × N1 K tan φ × γ × 2 + w × 2 tan α 2 tan α 6

(15) Fig. 16. Calculation model for estimating the support force at the tunnel face.

The force equilibrium is established for the isolated body:

P + 2(T2 + C2) × cos α + (T3 + C3) × cos α = N3 × sin α

(16)

N1 + Gw = N3 × cos α + (T3 + C3) × sin α + 2(T2 + C2) sin α

(17)

Fig. 16, and given as follows:

w = Ψ(P , H )

The mobilized friction force by lateral wall pressures is written as

T3 = N3 × tan φ

=

(18)

Combining Eqs. (14), (15) and (16), the calculation formula for the support force P before pipe excavation is obtained.

P = ζ1 N1 + ζ2 G + ζ3 T2 + ζ 4 (2C2 + C3) sin α − tan φ cos α sin α − tan φ cos α ζ1 = cos α + tan φ sin α ; ζ2 = cos α + tan φ sin α ; −1 ; N1 is the vertical force acting on cos α + tan φ sin α

where

R

dr

∫0

2π

4(1 − μ)(1 − 2μ) 6 × (H − r sin θ) × z × (z + H − r sin θ) ]dθ + R25 R2 (R2 + z + H − r sin θ)

(19)

ζ3 =

P×x×r z − H + r sin θ [ 16πG (1 − μ) R13 (3 − 4μ) × (z − H + r sin θ) + − R23

∫0

−2 ; cos α + tan φ sin α

(20)

ζ4 = the wedge from the silo; N3 is the normal force acting at the inclined sliding surface; P is the support force at the tunnel face; Gw is the dead weight of the wedge; T2 is the lateral shear force; T3 is the friction mobilized at the inclined sliding surface; C2 is the cohesion of lateral soil; and C3 is the cohesive force of soil along the sliding plane. Considering the area equivalent to the excavation face of the circular jacked pipe or the tunnel is required before the derivation. Several commonly used area equivalent methods were reported in existing literature (Broere, 2001; Anagnostou and Kovári, 1996; Anagnostou, 2012). However, all the previous studies do not consider the influence of flanges on the support force. Compared with the support force for a conventional pipe, the value of for a jacked pipe with flanges is much larger. Hence, in this investigation, the pipe with irregular cross-section (e.g., circular pipes with flanges) is firstly equivalent to the regular circular pipe based on area equivalent. Subsequently, the circular section is simplified to the rectangular section referred to the proposed method of Broere (2001).

x2

r cos θ)2

r sin θ)2 ;

R2 = and where R1 = + (y − + (z − H + x 2 + (y − r cos θ)2 + (z + H − r sin θ)2 . 4 Calculation of disturbance and influence zone around the circular tube with flanges 3.5. Degree of ground disturbance Xu and Sun (1999) showed that the ground disturbance can result in changes in physical and mechanical parameters of soil. The degree of ground disturbance Dd can be expressed by Eq. (21).

Dd = 1 −

Md M0

(21)

where Md is the mechanical parameter after disturbance; and M0 is the mechanical parameter of undisturbed soil. Xu and Sun (1999) adopted the soil stress state to characterize the degree of ground disturbance based on the laboratory test results.

Dd = 1 −

3.4.2. Calculation of support force at the tunnel face Pipe jacking can be achieved either using a pipe jacking machine or using manual excavation. The jacking force from the pipe jacking machine is usually greater than the static earth pressure of the soil, which is defined as the “additional jacking force”. On the contrary, the tunnel face in manual excavation is in an open state, where no lateral support can be applied at the tunnel face. The soil at the tunnel face can then move towards the pipe, along with the occurrence of soil relaxation. The effect of excessive or insufficient support force at the tunnel face can be analyzed by evaluating the displacement field in a half space infinite body subjected to a concentrated force. The Mindlin’s solution can also be used for the problem. The integral domain of the tunnel face is circular. The global coordinate system is the orthogonal coordinate system, whereas the local coordinate system follows the polar coordinate system. At this point, the coordinate transformation relationship is defined as m = 0, n = r × cosθ, and c = H − r × sinθ, and the integral variable is rdrdθ. The calculation model for ground displacement caused by support force at the tunnel face is shown in

σd′ σ0′

(22)

where σ’d is the effective stress of soil influenced by pipe jacking; σ’0 is the effective stress of undisturbed soil. The index for evaluating the degree of ground disturbance must be easy to obtain, with a low variation and a high sensitivity, which should also take into account the geological characteristics of coarse sand with interbedded silty clay at the shallow ground of Shenyang. Although the concept of defining the degree of ground disturbance through stress index is clear, the stresses of undisturbed and disturbed soil generally need to be determined in the laboratory, and as such boring samples at the site becomes demanding. Therefore, it is feasible to define the degree of ground disturbance using deformation index, which can be easily obtained by in situ tests. For typical soils in Shenyang, the results from preliminary studies show that the changes in deformation modulus of soil before and after disturbance can be used to estimate the degree of ground disturbance as follows: 9

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D=1−

Eafter Ebefore

surrounding soil does not uplift. The minimum grouting pressure can be calculated as follows:

(23)

σa = Hγ tan2 (45o − φ /2) − 2c tan(45o − φ /2)

where Eafter is the deformation modulus of soil after disturbance; and Ebefore is the deformation modulus of soil before disturbance.

where H is the buried depth of pipe, and γ is the unit weight of soil. By substituting Eq. (26) into Eq. (25), the radius for the plastic zone due to stress relaxation is obtained as follows:

3.6. Calculation of the disturbance zone and plastic zone Based on the Fenner formula, Talobre (1967) initially derived the relationship between the yield zone d around a circular tunnel and the shear strength τ of soil, and the correlation between the initial earth stress σ and the uniform load p around the hole, which were used to calculate the soil disturbance zone during tunnel excavation. It should be pointed out that there is no analytical theory to calculate the disturbance zone induced by a flanged steel pipe. The use of pipe jacking with flanges is a novel concept, which is firstly adopted in the Olympic Sports Center Subway Station project in Shenyang, China. Few papers have been published to explain different mechanisms regarding the analysis of pipe jacking with flanges (e.g., Ji et al. 2018; Ji et al. 2019a, 2019b). These studies include the analysis of pipe jacking force and the calculation of earth pressure acting on the excavation face. However, the analysis of ground settlement induced by pipe jacking with flanges has never been systematically investigated. Hence, the Fenner formula is adopted in this investigation to study the disturbance zone around the flanged tube during pipe jacking. Considering the circular tube with flanges has an axisymmetric cross-section, which contradicts the centrally symmetric assumption for the cross-section in the Fenner formula. Besides, one can expect that the disturbance zone induced by a flanged steel pipe during pipe jacking is larger than the disturbance zone caused by a circular pipe. Thereby, in this investigation, The approaches of similar studies have been developed to simplify the flanged pipe into a circular pipe with an equivalent area (Wei et al., 2016). The radius of equivalent circular pipe can be evaluated, as shown in Fig. 17.

Re =

S = 0.51 m π

Rp = a [(1 − sin φ)(

−

1 − sin φ σ0 + c × cot φ )] 2 sin φ φ ° − 2c tan(45 − 2 ) + c × cot φ

φ ) 2

Taking silty clay at a depth of 3.75 m as an example (Jia et al., 2019), Eq. (26) can be employed to calculate the minimum grouting pressure as follows:

σa = 3.75 × 18.5 × tan2 (45° − 13. 1° /2) − 2 × 25.5 × tan(45° − 13. 1° /2) = 3.24 kPa

σ0 = γH = 3.75 × 18.5 = 69.375 kPa From Eq. (27), the equivalent radius of the plastic zone (Rp)is calculated by °

Rp = 0.51 × [(1 − sin 13. 1° ) ×

69.375 + 25.5 × cot 13. 1° 1 − sin 13.1° ] 2 × sin 13.1 = 3.24 + 25.5 × cot 13. 1°

0.722 m It should be noted that the concept of plastic zone and disturbance zone is not exactly the same. The plastic zone is mobilized in the soil when the shear stress τ at a certain point is less than the shear strength defined by the Mohr–Coulomb failure criterion, which is shown as:

τ < τf = c + σ × tan φ

(28)

The concept of disturbance zone is defined due to the changes in deformation modulus of soil before and after disturbance. Using the cavity expansion theory, Liu & Yang (2003) pointed out that the disturbance zone should cover the elastic region in which the mobilized stress is greater than 0.7 times the plastic stress and the plastic zone.

(24)

σ0 + c × cot φ 1 − sin φ )] 2 sin φ σa + c × cot φ

Hγ tan2 (45°

(27)

where S is the equivalent area, and Re is the equivalent radius. According to the Fenner formula, the force around the jacked pipe is assumed to distribute symmetrically, and the radius of the plastic zone Rp caused by pipe jacking can be estimated by:

Rp = a [(1 − sin φ)(

(26)

Rd =

Rp 0.7

= 1.2Rp

(29)

where Rd is the radius of the disturbance zone. According to Eq. (29), the radius of the disturbance zone is calculated as:

(25)

where σ0 is the initial earth stress, σa is the support force, a is the radius of the inner plastic zone, c is the cohesion and φ is the internal friction angle. Li and Miao (2016) proposed a solution for the minimum grouting pressure to prevent the surrounding soil from collapsing. Furthermore, the maximum grouting pressure should be controlled to ensure that the

Rd = 1.2Rp = 1.2 × 0.722 = 0.87 m

(30)

Combining Eqs. (24) and (30), the disturbance radius R measured from the axis of the pipe is:

R = R e + Rd = 1.38 m

(31)

To calibrate the proposed formulation in the plastic zone, cone penetration tests (CPTs) are conducted as illustrated in Fig. 18 to investigate the influence of pipe jacking on the compressive modulus of the surrounding soil, through the correlation between penetration resistance and compressive modulus. The in-situ test site is next to the pipe alignment of Olympic Sports Center Subway Station to measure representative soil properties. A total of 11 monitoring points (1#–11#) are arranged along the direction perpendicular to the pipe alignment. Point 1# is located right on the centreline of the pipe alignment, and other points are evenly distributed on both sides with a distance of 0.5 m. It should be emphasized that point 12# is defined as a reference point without the influence of ground disturbance as shown in Fig. 19. The penetration resistance (Ps) at each monitoring point can be measured from CPTs. Considering the soil properties in Shenyang, Eq. (32) can be used to calculate the compressive modulus of soil

Fig. 17. Simplification of the cross-section for the pipe with flanges. 10

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where the correlation coefficient (R2) obtained by nonlinear fitting is more than 95%. The measured compressive modulus at each monitoring point is compared against the value obtained at the reference point (i.e., point 12#) to calculate the degree of disturbance (Dd) according to Eq. (23). Moreover, the correlation between the degree of ground disturbance (Dd) and the coordinate along the pipe axis (x axis) is derived following a polynomial pattern, as shown in Fig. 20b. The expression is as follows:

Dd = 0.003x 4 - 0.038x 2 + 0.005x + 0.117

(34)

where the correlation coefficient (R ) obtained by nonlinear fitting is more than 95%. Based on previous engineering experience, when the degree of ground disturbance is below 5%, the soil is considered as undisturbed soil (Zhao et al., 2019). From Fig. 20b, the soil layer has a Dd = 0.05 at a distance of 1.51 m from the pipe axis, whereas the radius of the disturbance zone can be determined as 1.38 m theoretically. The difference between theoretical calculation and experimental measurement is 8.6%, which demonstrates the effectiveness of the proposed analysis model. 2

Fig. 18. Implementation of cone penetration test at a monitoring point.

3.7. Interaction between multiple pipes Wei (2005) proposed that a shear disturbance zone occurs around the pipe wall during pipe jacking, above which there is an unloading disturbance zone. The unloading disturbance zone results in ground settlement due to pipe jacking. As illustrated in Fig. 21, the failure plane of the unloading disturbance zone is tangent to the shearing disturbance zone, which inclines by an angle of 45°+φ/2 (φ is the soil friction angle) from the horizontal based on the limit equilibrium principle in the soil. The unloading disturbance zones from two adjacent jacked pipes can interact with each other. Following the work of Coring and Hansmire (1975), Wei (2005) proposed that the horizontal distance measured from the edge of the ground settlement trough to the pipe centreline is H + r, where r is the radius of the pipe. Hence, the total width of the disturbance zone L1 is obtained as follows:

Fig. 19. Layout of monitoring points perpendicular to jacked pipe.

empirically (Zhao et al., 2019).

E0 = 1.16Ps + 3.45

0.5 ⩽ Ps ⩽ 6

(32)

For example, at a distance of 1 m from the pipe alignment (i.e., point 4#), the penetration resistance (Ps) is measured as 0.69 MPa, which can be used to derive the compressive modulus of 4.25 MPa. The variation of soil deformation index (E0 is the compressive modulus) with distance is plotted with markers in Fig. 20a, along with the fitted curve using a solid line, showing a polynomial pattern after pipe jacking. The mathematical expression of the polynomial pattern is written as follows:

y = −0.013x 4 + 0.005x 3 + 0.177x 2 − 0.026x + 4.06

L1 = 2H + 2r + B

(35)

The overlapped disturbance zone from two densely spaced jacked pipes is:

L′ = 2(H + r − B ) + B = 2H + 2r − B

(36)

The influence of flanges is taken into account by calculating the equivalent area for the jacked pipe. The schematics of the problem for a flanged pipe is depicted in Fig. 22. The disturbance zone has an inclined shear plane in an angle of 45°+φ/2 from the horizontal, which is also

(33)

Fig. 20. Profile of (a) compressive modulus, (b) degree of disturbance along the pipe axis after pipe jacking. 11

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interaction. The ground surface settlements induced by the postjacked pipe and the pre-jacked pipe are calculated separately, after which the superposition method is used in the overlapped zone to calculate the final settlement. (c) The small spacing case is defined when the pipe spacing is less than 1.51 m. In this case, after pre-jacking the pipe, the ground disturbance (the plastic zone) occurs in the surrounding soil. The postjacked pipe is actual in the disturbance zone. The mechanical parameters of soil after ground disturbance should be used to calculated the settlement according to Fig. 20a. The ground surface settlements induced by the post-jacked pipe and the pre-jacked pipe are firstly calculated, and the ground disturbance effect and the interaction between adjacent pipes are considered simultaneously.

Fig. 21. Interaction of unloading disturbance zone between multiple pipes.

4.1. Ground settlement analysis in the large spacing case During the construction of the Olympic Sports Center Subway Station using the STS method, the H12 pipe is jacked into the ground without interaction with adjacent pipes, which follows the large spacing case. Using the proposed settlement calculation method for single pipe jacking, the settlement can be induced by frictions at pipe walls (areas E, F, and G) and flange plates (areas A, B, C, and D), soil deformation at the tunnel face and volume loss. The ground surface settlement induced by different components (in different zones) is depicted in Fig. 23. The ground surface settlement curve induced by soil loss has a ‘deep and narrow’ settlement trough, and other curves follow a ‘shallow and wide’ pattern. The peak ground surface settlement induced by soil loss, support force and pipe-soil friction is calculated as 3.57 mm, 0.27 mm and 2.18 mm, respectively, accounting for 59.3%, 4.5%, and 36.2% of the final settlement. Hence, the influence of soil loss is considered as the main factor that contributes to the ground surface settlement, following by the pipe-soil friction and the support force. The ground surface settlement due to pipe-soil frictions mobilized at flange plates (areas A, B, C and D) and pipe walls (areas E, F and G) accounts for 50% of the induced settlement, respectively. Moreover, areas A, B, C and D of flange plates account for 3.1%, 0, 1.41% and 13.6%, respectively. Therefore, the pipesoil friction in area D is the main factor that controls the ground surface settlement for pipe jacking with flange plates. Comparisons of settlement measured in the field and calculated using the proposed approach for the H12 pipe are presented in Fig. 24. It can be seen that the theoretically calculated settlement curve is basically consistent with the experimental measurement. The maximum calculated settlement is 6.02 mm, which is very close to the measured

Fig. 22. Disturbance zone for a circular pipe with flanges.

tangent to the shear disturbance zone. In Fig. 22, O is the centre coordinate of the disturbance zone, and OB corresponds to the burial depth measured from the pipe centreline to the ground surface, which is denoted by H. The angles in the schematic figure are defined as ∠ACD = α, ∠OAC = ω, and ∠OAB = β, and the geometric relationship between these angles is defined as:

∠ACD = ∠OAC + ∠OAB

(37)

The half width of the influence zone is assumed as AB = x. Based on the trigonometric relations, Eq. (37) can be rewritten as:

arctan(

φ H R ) + arcsin( ) = 45o + x 2 x2 + H 2

(38)

The geological parameters of silty clay are used in the analysis. The measured radius of the disturbance plastic zone and the soil parameters are substituted into Eq. (38), which gives x = 4.55 m Hence, the width of the influence zone is calculated as L = 2x = 9.1 m. 4. Case study During pipe jacking, the spacing between two adjacent steel pipes is categorized into three cases according to the size of the plastic zone and the influence zone: the large spacing case, the medium spacing case, and the small spacing case. (a) The large spacing case is adopted to characterize the condition when the spacing between adjacent steel pipes is greater than 9.1 m. At present, the influence and the disturbance zones introduced by the post-jacked pipe do not result in interference with those induced by the pre-jacked pipe. Thereby, the ground surface settlement induced by the post-jacked pipe can be defined as the final settlement. (b) The medium spacing case is used to analyze the condition when the pipe spacing falls between 1.51 m and 9.1 m. The influence zone caused by the post-jacked pipe overlaps with that induced by the pre-jacked pipe, but both disturbance zones still have no

Fig. 23. Ground surface settlement induced by each factor. 12

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Fig. 25. Ground surface settlement induced by jacking H1 and H6 pipes in the medium spacing case. Fig. 24. Ground surface settlement induced by jacking H12 pipe in the large spacing case.

value of 5.33 mm. The higher calculated settlement can be probably attributed to the assumption of elastic mechanics, where the ground deformation induced by frictions is resulted by applying a concentrated force to the pipe in a half space infinite body. In practice, frictions mobilized at the pipe springline (areas B, C, and F) and at the pipe invert (areas D, and G) should be affected by the pipe body, such that free ground deformation cannot occur. The pipe crown can be considered to deform freely, and the pipe springline and invert cannot fully contribute to deform, leading to a slightly higher theoretical settlement than the experimental measurement. 4.2. Ground settlement analysis in the medium spacing case When multiple pipes are jacked with a spacing of 1.51–9.1 m, the superposition method can be used to calculate the settlement. In this case, the pipe roof consists of 28 steel pipes. According to the construction sequence for pre-jacking and post-jacking pipes, they can be divided into unilateral jacking (i.e., the post-jacking pipe locates on one side of the pre-jacking pipe) and bilateral jacking (i.e., the post-jacking pipe is located between pre-jacking pipes). This section examines the propagation of ground settlement induced by medium densely spaced jacked pipes.

Fig. 26. Ground surface settlement induced by jacking H1, H3 and H6 pipes in the medium spacing case.

and the spacing between H3 and H6 is 3 m. Fig. 26 shows the comparison of ground settlement induced by pipe jacking between field measurements and theoretical calculations. The interaction between three steel pipes is significant, and the ground subsidence induced by three pipes is highly overlapped. The overlapped part accounts for 67% of the settlement trough induced by the H1 pipe. Due to the interaction, the superimposed settlement curve does not show a ‘double-peaks’ profile any more. In general, the measured settlement value is slightly higher than the theoretical calculation. For example, the measured settlement at the distance of −5.2 m is 12.89 mm, whereas the theoretical calculated value is 11.5 mm. It is inferred that the theoretically calculated curve for bilateral jacking is consistent with the field observation.

4.2.1. Unilateral jacking In this section, the H1 and H6 jacked pipes are analyzed, where the spacing between these two pipes is 5 m (clear distance is 3.89 m). The measured and calculated ground settlements caused by jacking these two pipes are compared in Fig. 25. The ground subsidence propagates to a distance of 4.55 m for the pipe with flange plates, such that the area affected by both H1 and H6 pipes is from −5 m to 5 m. It should be noted that the ground settlement induced by pipe jacking with flange plates is ‘deep and narrow’ (i.e., a high maximum settlement and a narrow settlement trough). The inflection point for the settlement trough induced by jacking the H6 pipe is at 3.3 m. Although jacking the H1 and H6 pipes conforms to the medium spacing case, the spacing between the two pipes is relatively large, and the overlap is limited. The superimposed settlement curve is “W”-shaped, having a ‘double-peaks’ profile. It can be seen that the proposed calculation in this investigation can provide comparable predictions to experimental measurements.

4.3. Ground settlement analysis in the small spacing case The effect of superposition and ground disturbance should be taken into account in the analysis in the small spacing case. After pre-jacking pipes, the ground disturbance (the plastic zone) occurs in the surrounding soil. During the post-jacking process, the jacked pipe is actually in the disturbance zone. The mechanical parameters of soil after ground disturbance should be used to calculated the settlement trough induced by post-jacking pipes. Therefore, for the calculation of ground settlement caused by small-spaced pipe jacking, the ground disturbance effect and the interaction between adjacent pipes are considered simultaneously.

4.2.2. Bilateral jacking After the construction of the H1 and H6 pipes, the H3 pipe is jacked in the middle of the two pipes. The spacing between H1 and H3 is 2 m, 13

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Fig. 28. Ground surface settlement induced by jacking H17, H18 and H19 pipes in the small spacing case.

Fig. 27. Ground surface settlement induced by jacking H24 and H25 pipes in the small spacing case.

settlement reaches 20.94 mm, whereas the monitored data has a peak value of 21.5 mm. The trends obtained from field measurements and theoretical calculations are consistent. It can be inferred that the proposed formula is effective in predicting the ground response during jacking closely spaced pipes with flange plates.

4.3.1. Unilateral jacking The H25 pipe is jacked prior to the H24 pipe. At the time of jacking the H25 pipe, the site is undisturbed. The physical and mechanical parameters of undisturbed soil are then used to calculate the ground settlement caused by jacking the H25 pipe. The proposed method can be used to calculate the ground disturbance zone around the H25 pipe. The physical and mechanical parameters of disturbed soil can be estimated (e.g., changes in deformation modulus E0). Due to the close spacing between these two pipes, the ground disturbance influences the settlement trough caused by jacking the H24 pipe. The superposition of the ground settlement induced by H25 and H24 pipes can be derived by coordinate transformation as shown in Fig. 21. Fig. 27 presents the comparison of ground settlement obtained from field tests and theoretical calculations. Due to the influence of ground disturbance, the settlement trough of H24 is no longer a strictly axisymmetric curve (exhibiting a slightly larger settlement on the right side than the left side). The maximum settlement for the theoretical calculation of the H25 pipe is 6.11 mm, while the largest settlement for the theoretical calculation of the H24 pipe is 7.08 mm. This demonstrates the influence of ground disturbance, since the maximum settlement is increased. The spacing between H24 and H25 pipes is only 1 m, and the interaction between the two pipes is significant. The settlement trough induced by the two pipes is highly overlapped, and as such the superposed settlement trough presents a ‘single-peak’ profile. The maximum settlement obtained from theoretical calculations is about 13.1 mm, and the in-situ monitored value is 13.9 mm. The difference between calculations and measurements is 6%. This indicates that the proposed calculation model can capture the ground settlement induced by multiple jacked pipes with flange plates in the small spacing case.

5. Conclusion This investigation proposes a set of calculation models to estimate the ground settlement induced by pipe jacking with flange plates. A case study is presented for a pipe jacking project in the Olympic Sports Center Subway Station using the Steel Tube Slab (STS) method. The following conclusions can be drawn: (1) Based on the Mindlin’s solution, a formula for calculating the ground surface settlement caused by frictions mobilized at pipe walls and flange plates and insufficient support force in front of the pipe is proposed. Based on the stochastic medium theory, a formula for calculating the ground settlement caused by volume loss is obtained. (2) A calculation method for estimating the degree of soil disturbance for soils in Shenyang is proposed, which can characterize the ratio of soil deformation modulus before and after jacking. (3) Based on the cavity expansion theory, a theoretical calculation formula for the plastic zone around a jacked pipe with flange plates is proposed. (4) Considering the plasticity distribution around the pipe and the superposition effect of ground settlement induced by multiple jacked pipes, criteria are established to consider the influence of spacing between pipes in three situations: large spacing, medium spacing, and small spacing. Theoretical models for three cases are proposed to calculate the ground surface settlement during multiple pipe jacking. Comparisons of ground settlement between field measurements and theoretical calculations demonstrate the effectiveness of the proposed approach.

4.3.2. Bilateral jacking After jacking the H17 and H19 pipes, the H18 pipe is jacked between these two pipes, with a spacing of 1 m measured from both H17 and H19 pipes. The ground disturbance zones can be formed during jacking the H17 and H19 pipes. The analysis involves calculations of soil deformation modulus E0 inside and outside the disturbance zone. Different soil deformation modulus is used as shown in Fig. 21. The ground settlement caused by jacking closely spaced pipes is given in Fig. 28. The primary and the secondary disturbance zones are formed in the surrounding soil by pre-jacking the H17 and H19 pipes. During the jacking of the H18 pipe, the surrounding soil is subjected to a third disturbance. The interaction among the three disturbance zones is significant (highly overlapped). Hence, the settlement curve presents the characteristics of a ‘single-peak’ profile. The calculated maximum

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgement The research described in this paper was supported by the National Science Foundation of China (No. 51578116, No. 51878127), the Fundamental Research Funds for the Central Universities (No. 14

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N180104013) and the China Scholarship Council. Finally, we deeply appreciate for the warm and efficient work by editors and reviewers.

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