Citation: Huang, R.; Hu, J.; Pan, J.;

Wu, Y.; Ren, X.; Zeng, D.; Wang, Z.;

Wang, S. The Π-Formed Diaphragm

Wall Construction for Departure and

Reception of Shield Machine.

Sustainability 2022, 14, 7653.

https://doi.org/10.3390/su14137653

Academic Editors: Yutao Pan,

Qiujing Pan and Hui Xu

Received: 12 April 2022

Accepted: 13 June 2022

Published: 23 June 2022

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sustainability

Article

The Π-Formed Diaphragm Wall Construction for Departure andReception of Shield MachineRui Huang 1,2 , Jun Hu 3 , Jingbo Pan 4, Yuwei Wu 3,* , Xingyue Ren 3, Dongling Zeng 5, Zhixin Wang 5

and Shucheng Wang 3

1 School of Architecture and Civil Engineering, Xihua University, Chengdu 610039, China;huangrui@mail.xhu.edu.cn or dt207174@cc.utsunomiya-u.ac.jp

2 School of Regional Development and Creativity, Utsunomiya University, Utsunomiya City 321-8585, Japan3 School of Civil Engineering and Architecture, Hainan University, Haikou 570228, China;

hj7140477@hainanu.edu.cn (J.H.); renxny@126.com (X.R.); wsc15799032478@163.com (S.W.)4 Hangzhou Qianjiang Xincheng Investment Group Co., Ltd., Hangzhou 310002, China;

jingbo_smile@outlook.com5 Hainan Investigation Institute of Hydrogeology and Engineering Geology, Haikou 570206, China;

zdl13876637666@163.com (D.Z.); wzx6822235@163.com (Z.W.)* Correspondence: wuyuwei@eis.hokudai.ac.jp

Abstract: In the design of shield tunnels, it is important to determine the structure of the diaphragmwall in order to achieve the required retaining wall structure pattern. In this paper, the stabilizationeffect of a new diaphragm wall structure (Π-formed diaphragm wall) is investigated based on modelexperiments and numerical simulations. By varying the length of the wing wall and its angle to theend wall, it is possible to discuss the effect of different styles of Π-formed diaphragm wall on thesupport of the soil behind the wall during the departure and reception of the shield machine, theeffect of the wing wall on the internal force distribution of the diaphragm wall generated duringexcavation, the effect of the excavation of the shield machine on the internal force distribution of thediaphragm wall, and the ground settlement during the departure and reception of the shield machinein different construction stages. Π-formed diaphragm walls can effectively support the soil behindthe wall and reduce the major principal stresses generated during excavation. The maximum valueof the major principal stress in the wing wall of the Π-formed diaphragm wall increases with thelength of the wing wall, and the damage to the concrete of the diaphragm wall tends to occur on theoutside rim of the wing wall.

Keywords: diaphragm wall; shield tunnel crossing; departure and reception of shield machine; FEMmethod; numerical simulation

1. Introduction

Urbanization and economic development have led to a rapid increase in the devel-opment of underground space. Due to its environmental benefits, fast speed, and largetransport capacity, the subway has emerged as an important tool for urbanization. Thesafety of the tunnel is especially significant since it is the principal operating area of urbansubways. The collapse of tunnels due to insufficient stability could lead to significant,additional expenditure of public resources, money, or even cause casualties. The safeconstriction of these underground structures is always an integral part of maintainingurban sustainability. In urban areas, tunnel excavation is limited by the induced ground de-formation caused by tunnel excavation. Both indoor experiments and numerical modelinghave shown that a diaphragm wall can effectively mitigate excavation-induced deforma-tion [1–3]. Stress development in the diaphragm walls contributes to surface deformation,and Bilotta described the distribution of stress–strain within the diaphragm walls duringexcavation [4]. D. A. Mironov [5] summarized the specific features of diaphragm wall

Sustainability 2022, 14, 7653. https://doi.org/10.3390/su14137653 https://www.mdpi.com/journal/sustainability

Sustainability 2022, 14, 7653 2 of 19

construction and compared the calculated parameters of technological precipitates duringthe production of works with the actual values, demonstrating the potential for a widerange of applications in urban areas. Based on Terrestrial Laser Scanning (TLS) technology,Marek Wyjadłowski [6] proposed a method for estimating the subsequent soil pressure bydetecting different levels of roughness in underground diaphragm walls. The results of thisstudy are of great reference value for the design of retaining wall structures. Conventionalmethods for excavating tunnels include the cut and cover method, jack-in method, theNew Austrian Tunneling Method (NATM), and the mountain tunneling method. Theadvantage of mechanical tunneling over conventional methods of tunneling is that it can beemployed in a variety of environments, including those with challenging ground conditionsor those located in vulnerable, metropolitan areas [7]. It is crucial to understand how theshield departs and is received because it directly impacts the quality of the completedunderground tunnel axis, the efficacy of environmental protection around the hole, andthe success or failure of the shield tunneling construction [8]. Scholars have conductednumerous studies regarding the mechanism by which the shield departs and is received.Broms and Benermark introduced the concept of the working surface stability coefficientin 1967 [9], and they also proposed the corresponding theoretical equation. It is in thiscase that the stability of the tunnel face is determined by the load factor. N. Bakker [10]et al. and others concluded that clay and sandy soils exhibit significant differences inthe mechanisms of working face damage and that generalizations cannot be made. Themodel tests of Komiya [11] partially confirmed Bakker et al.’s [10] findings; however, thedestabilization pattern of circular tunnels in sandy soils is different from that describedby Mair et al. In addition to Mair’s theory, he extended the arch at an angle of 45◦ whileincreasing the vertical pressure on both sides. Wall panel size has a substantial effect onload transfer between panels, particularly in soft soils [12,13]. Numerical modeling is themost straightforward technique for calculating suitable panel sizes [14]. Furthermore, whenit comes to the function of the connection between the wing wall and end wall, verticaljoints in panels have an impact on load transfer. In general, the lower the joint stiffness,the more sufficiently the panels will deform. Shield crossing existing building structureswas studied by several authors [15–19]. Shield construction has become the most commonmethod for urban metro tunneling in soft soil areas due to its low environmental impact.When shield construction is performed in soft soils, the excavation surface may be unableto maintain stability on its own and may require support. To ensure construction safety, it iscritical to maintain the structural stability of the excavated surface during shield tunneling.A destabilized excavation surface may lead to excessive soil deformation or even collapse,resulting in a series of serious damages to the adjacent buildings such as the destruction ofsurrounding buildings.

This paper investigates the effect of the connection between the wing wall and the endwall on the retaining effect of Π-formed diaphragm walls as a retaining structure. At thesame time, the settlement of the soil and the stresses in the diaphragm walls at the startand at arrival of the shield are investigated for different wing wall lengths and differentconstruction stages. Based on the above discussion, the relationship between differentstructural styles and settlement and major principal stresses is evaluated.

2. Methods

The effect of different styles of Π-formed diaphragm wall on the soil reinforcementat the end of the tunnel when the wing walls are connected to the end walls in differentways was assessed through model experiments. Numerical simulations were conductedusing MIDAS/GTS NX as the calculation platform to investigate the stress distribution inthe ground connection walls and the variation of their settlement for different wing walllengths and different construction stages.

Innovative technology for shield tunnel end reinforcement, the Π-formed diaphragmwalls entry and exit technology, can be directly cut with shield machine tool plates. Itis structurally more complex than traditional, plain concrete diaphragm walls, as it has

Sustainability 2022, 14, 7653 3 of 19

additional wing walls attached to it. Regarding the force performance, the new style ofground connection wall has been improved by using materials with better tensile strengthin comparison to plain concrete: GFRP glass fiber in the end wall and bamboo reinforcementin the wing wall. Figure 1 illustrates a schematic diagram of a Π-formed ground connectionwall structure. Many factors influence the mechanical properties of GFRP tendons, suchas the fibers, as well as the resin, how the fibers are arranged in space, how they arewound [20], the loading rate, and the environment in which they are used [21]. With theΠ-formed ground connection wall structure’s high tensile strength and low flexural andshear strengths, it can easily be cut. Furthermore, due to its high corrosion resistance, itmay be used in wet or other aggressive environments. In addition, its thermal conductivityis comparable to that of concrete, so it is unlikely that temperature changes will causeslippage between the two materials. This ensures a synergistic effect between GFRP barsand concrete.

Sustainability 2022, 14, x FOR PEER REVIEW 3 of 20

additional wing walls attached to it. Regarding the force performance, the new style of

ground connection wall has been improved by using materials with better tensile strength

in comparison to plain concrete: GFRP glass fiber in the end wall and bamboo reinforce-

ment in the wing wall. Figure 1 illustrates a schematic diagram of a Π-formed ground

connection wall structure. Many factors influence the mechanical properties of GFRP ten-

dons, such as the fibers, as well as the resin, how the fibers are arranged in space, how

they are wound [20], the loading rate, and the environment in which they are used [21].

With the Π-formed ground connection wall structure’s high tensile strength and low flex-

ural and shear strengths, it can easily be cut. Furthermore, due to its high corrosion re-

sistance, it may be used in wet or other aggressive environments. In addition, its thermal

conductivity is comparable to that of concrete, so it is unlikely that temperature changes

will cause slippage between the two materials. This ensures a synergistic effect between

GFRP bars and concrete.

Figure 1. Π-formed, underground, continuous wall structure.

2.1. Model Test

This test was intended to provide qualitative comparison. Fujian standard sand was

used in the test as the soil material to prevent the uncertainty of conventional soil from

introducing other variables. The model box used for the test was made of toughened glass,

measuring 900 mm in length, 500 mm in width, and 600 mm in height. It was used to limit

the displacement of the surrounding soil and to observe the changes in the soil inside the

box. The experimental diaphragm wall was made of a 3 mm thick steel plate, with the end

wall measuring 900 mm long by 500 mm wide and the wing wall measuring 200 mm long

by 500 mm wide. The wing walls were welded to the end wall, and both wing walls were

80 mm from the edge of the tunnel opening. A 100 mm diameter circular hole was

punched in the center of the end wall plate to indicate the tunnel opening.

To discuss the role of the angle of connection between the wing wall and the end wall

on the soil support, this study considered the retaining effect of four different diaphragm

wall structures for small and large displacements. In Figure 2, the diaphragm wall struc-

ture used in the model experiments is shown in four cases: wing wall outwards, wing wall

inwards, wing wall perpendicular to the end wall, and no wing wall. In the case of small

displacements, the cavity was always partially stress constrained, but the stress generated

by the diaphragm wall was less than the earth pressure behind the wall. In the case of

large displacements, there was no stress constraint at the opening, and the soil was free to

flow.

1

23

4

1- Headwall

2- Left wingwall

3- Right wingwall

4- Shield machine

Figure 1. Π-formed, underground, continuous wall structure.

2.1. Model Test

This test was intended to provide qualitative comparison. Fujian standard sand wasused in the test as the soil material to prevent the uncertainty of conventional soil fromintroducing other variables. The model box used for the test was made of toughened glass,measuring 900 mm in length, 500 mm in width, and 600 mm in height. It was used to limitthe displacement of the surrounding soil and to observe the changes in the soil inside thebox. The experimental diaphragm wall was made of a 3 mm thick steel plate, with the endwall measuring 900 mm long by 500 mm wide and the wing wall measuring 200 mm longby 500 mm wide. The wing walls were welded to the end wall, and both wing walls were80 mm from the edge of the tunnel opening. A 100 mm diameter circular hole was punchedin the center of the end wall plate to indicate the tunnel opening.

To discuss the role of the angle of connection between the wing wall and the end wallon the soil support, this study considered the retaining effect of four different diaphragmwall structures for small and large displacements. In Figure 2, the diaphragm wall structureused in the model experiments is shown in four cases: wing wall outwards, wing wallinwards, wing wall perpendicular to the end wall, and no wing wall. In the case of smalldisplacements, the cavity was always partially stress constrained, but the stress generatedby the diaphragm wall was less than the earth pressure behind the wall. In the case of largedisplacements, there was no stress constraint at the opening, and the soil was free to flow.

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(a) (b)

(c) (d)

Figure 2. Model drawing of Π-formed diaphragm wall. (a) Wing wall outward sloping structure.

(b) Wing wall vertical angle structure. (c) Inward sloping wing wall construction. (d) No wing wall

construction.

2.1.1. Small Displacement Test

The small displacement case refers to experiments where foam was installed at the

cavity door to simulate the restraining effect of the door on the soil in the cavity when the

cavity is not destroyed. The experimental setup for the small displacement case is shown

in Figure 3.

Figure 3. Schematic diagram of a model test with small displacements.

2.1.2. Large Displacement Test

The experimental setup for the large displacement case involved closing the cavity

with a steel plate. After the filling was complete, the steel plates were removed to simulate

the effect of supporting the underground diaphragm wall without the restraint of the

Figure 2. Model drawing of Π-formed diaphragm wall. (a) Wing wall outward sloping structure. (b) Wingwall vertical angle structure. (c) Inward sloping wing wall construction. (d) No wing wall construction.

2.1.1. Small Displacement Test

The small displacement case refers to experiments where foam was installed at thecavity door to simulate the restraining effect of the door on the soil in the cavity when thecavity is not destroyed. The experimental setup for the small displacement case is shownin Figure 3.

Sustainability 2022, 14, x FOR PEER REVIEW 4 of 20

(a) (b)

(c) (d)

Figure 2. Model drawing of Π-formed diaphragm wall. (a) Wing wall outward sloping structure.

(b) Wing wall vertical angle structure. (c) Inward sloping wing wall construction. (d) No wing wall

construction.

2.1.1. Small Displacement Test

The small displacement case refers to experiments where foam was installed at the

cavity door to simulate the restraining effect of the door on the soil in the cavity when the

cavity is not destroyed. The experimental setup for the small displacement case is shown

in Figure 3.

Figure 3. Schematic diagram of a model test with small displacements.

2.1.2. Large Displacement Test

The experimental setup for the large displacement case involved closing the cavity

with a steel plate. After the filling was complete, the steel plates were removed to simulate

the effect of supporting the underground diaphragm wall without the restraint of the

Figure 3. Schematic diagram of a model test with small displacements.

2.1.2. Large Displacement Test

The experimental setup for the large displacement case involved closing the cavitywith a steel plate. After the filling was complete, the steel plates were removed to simulatethe effect of supporting the underground diaphragm wall without the restraint of the cavitydoor. The standard sand was placed in the tray at the lower end of the hole and filled into

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the model in uniform layers. Once the specimen in the model had filled the mold, the steelplate was pressed down by hand and quickly removed so that the sand and gravel couldflow out of the hole behind the plate. The support effect of this type of diaphragm wallwas estimated by measuring the mass of the specimen flowing out of the hole. When thegravel behind the plate was stable and did not continue to slide, the collapse area wasmeasured. The width parallel to the end wall, the depth perpendicular to the end wall,and the maximum value of the width and depth of the collapsed area in the mold weremeasured. The experimental procedure is shown in Figure 4.

Sustainability 2022, 14, x FOR PEER REVIEW 5 of 20

cavity door. The standard sand was placed in the tray at the lower end of the hole and

filled into the model in uniform layers. Once the specimen in the model had filled the

mold, the steel plate was pressed down by hand and quickly removed so that the sand

and gravel could flow out of the hole behind the plate. The support effect of this type of

diaphragm wall was estimated by measuring the mass of the specimen flowing out of the

hole. When the gravel behind the plate was stable and did not continue to slide, the col-

lapse area was measured. The width parallel to the end wall, the depth perpendicular to

the end wall, and the maximum value of the width and depth of the collapsed area in the

mold were measured. The experimental procedure is shown in Figure 4.

Figure 4. Schematic diagram of a model test with large displacements.

2.2. Numerical Simulation

The numerical model and mesh division are shown in Figure 5; the model is divided

by hexahedral cells. The mesh division and geometric model of the diaphragm wall are

shown in Figure 6. The model is meshed with a 20-node hexahedral mesh, with a total of

634,135 hexahedral cells in the model.

Figure 5. MIDAS/GTS NX model diagram.

Figure 4. Schematic diagram of a model test with large displacements.

2.2. Numerical Simulation

The numerical model and mesh division are shown in Figure 5; the model is dividedby hexahedral cells. The mesh division and geometric model of the diaphragm wall areshown in Figure 6. The model is meshed with a 20-node hexahedral mesh, with a total of634,135 hexahedral cells in the model.

Sustainability 2022, 14, x FOR PEER REVIEW 5 of 20

cavity door. The standard sand was placed in the tray at the lower end of the hole and

filled into the model in uniform layers. Once the specimen in the model had filled the

mold, the steel plate was pressed down by hand and quickly removed so that the sand

and gravel could flow out of the hole behind the plate. The support effect of this type of

diaphragm wall was estimated by measuring the mass of the specimen flowing out of the

hole. When the gravel behind the plate was stable and did not continue to slide, the col-

lapse area was measured. The width parallel to the end wall, the depth perpendicular to

the end wall, and the maximum value of the width and depth of the collapsed area in the

mold were measured. The experimental procedure is shown in Figure 4.

Figure 4. Schematic diagram of a model test with large displacements.

2.2. Numerical Simulation

The numerical model and mesh division are shown in Figure 5; the model is divided

by hexahedral cells. The mesh division and geometric model of the diaphragm wall are

shown in Figure 6. The model is meshed with a 20-node hexahedral mesh, with a total of

634,135 hexahedral cells in the model.

Figure 5. MIDAS/GTS NX model diagram. Figure 5. MIDAS/GTS NX model diagram.

2.2.1. Assumptions

• It was considered that the soil behind the retaining wall was uniformly distributed ateach layer, and the loss of material due to overexcitation and voids outside the tunnelperimeter was not considered;

• Intermittences during shield construction were not considered, and it was assumedthat the shield machine advanced continuously with continuous palm pressure;

• The mechanical properties of the soil were maintained during the excavation process,regardless of regional discontinuities;

• The initial ground stress was calculated based on only the self-weight stress of the soilwithout considering the tectonic stress or vibrations of the shield machine on the soilbody during excavation;

• The soil was isotropic elastic plastic, and its intrinsic relationships were determinedby the modified Mohr–Coulomb criteria.

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Figure 6. Model of Π-formed diaphragm wall.

2.2.1. Assumptions

• It was considered that the soil behind the retaining wall was uniformly distributed

at each layer, and the loss of material due to overexcitation and voids outside the

tunnel perimeter was not considered;

• Intermittences during shield construction were not considered, and it was assumed

that the shield machine advanced continuously with continuous palm pressure;

• The mechanical properties of the soil were maintained during the excavation process,

regardless of regional discontinuities;

• The initial ground stress was calculated based on only the self-weight stress of the

soil without considering the tectonic stress or vibrations of the shield machine on the

soil body during excavation;

• The soil was isotropic elastic plastic, and its intrinsic relationships were determined

by the modified Mohr–Coulomb criteria.

2.2.2. Model Building

The numerical model in this study simulated a common geological structure with 4

m of miscellaneous fill in the upper layer and 56 m of clay in the lower layer, with the soil

parameters shown in Table 1. With the ground surface as the base and below as positive

and l as the distance from the surface, groundwater is located at l = 5 m. The excavation

surface is the XOZ plane, with the positive direction along the y-axis specified as the di-

rection of tunnel excavation. The tunnel diameter D = 6.4 m, and the distance between the

center of the tunnel and the ground surface l = 20 m.

Figure 6. Model of Π-formed diaphragm wall.

2.2.2. Model Building

The numerical model in this study simulated a common geological structure with 4 mof miscellaneous fill in the upper layer and 56 m of clay in the lower layer, with the soilparameters shown in Table 1. With the ground surface as the base and below as positive andl as the distance from the surface, groundwater is located at l = 5 m. The excavation surfaceis the XOZ plane, with the positive direction along the y-axis specified as the direction oftunnel excavation. The tunnel diameter D = 6.4 m, and the distance between the center ofthe tunnel and the ground surface l = 20 m.

Table 1. Table of soil and concrete parameters.

Material Parameters Mixed Fill Clay C30 C50

Elastic modulus (kN/m2) 6220 16,100 3 × 107 3.45 × 107

Poisson’s ratio 0.37 0.33 0.2 0.2Weight capacity (kN/m3) 17 20.3 25 25Cohesion (kN/m2) 18 48 / /Friction angle (◦) 6 12 / /Drainage parameters Drainage Drainage / /Ontogenetic model Modified Mohr–Coulomb Modified Mohr–Coulomb Elastic Elastic

MIDAS/GTS NX generates the default boundary conditions. The bottom of the modelis parallel to the XOY plane, which is set as a fixed boundary condition; the front andback of the model are parallel to the XOZ plane, which is set as a movable hinge, and thepoints on this boundary are displaced in the Y direction to 0; the left and right sides ofthe model are parallel to the YOZ plane, which is set as a movable hinge, and the pointson this boundary are displaced in the Y direction to 0. The model is concerned with theinfluence of the length of the wing walls on the distribution of the internal forces in theΠ-formed diaphragm wall during the departure and reception of the shield machine. Themodel studies the influence of the length of the wing walls on the distribution of internalforces in the Π-formed underground diaphragm wall during the departure and receptionof the shield machine, as well as the force characteristics of the shield machine at each stageof the excavation process and the changes in the ground settlement caused by it.

Sustainability 2022, 14, 7653 7 of 19

After the excavation is carried out, the exposed soil is installed in time for the tunnelpipe sheet. This model pipe sheet is a simulated concrete slab unit, as shown in Figure 7,and its strength is taken as C50. The construction stage of tunnel excavation is 2 m forwardalong the tunnel axis in every other stage, and the location of its construction stage isshown in Figure 8. Observation path 1 is set along the tunnel axis, and observation path 2is set along the ground parallel to the x-axis at a distance of 4 m from the end wall. Thedistribution of observation points along the observation path is shown in Figure 9.

Sustainability 2022, 14, x FOR PEER REVIEW 7 of 20

Table 1. Table of soil and concrete parameters.

Material Parameters Mixed Fill Clay C30 C50

Elastic modulus (kN/m2) 6220 16,100 3 × 107 3.45 × 107

Poisson’s ratio 0.37 0.33 0.2 0.2

Weight capacity (kN/m3) 17 20.3 25 25

Cohesion (kN/m2) 18 48 / /

Friction angle (°) 6 12 / /

Drainage parameters Drainage Drainage / /

Ontogenetic model Modified Mohr–Coulomb Modified Mohr–Coulomb Elastic Elastic

MIDAS/GTS NX generates the default boundary conditions. The bottom of the model

is parallel to the XOY plane, which is set as a fixed boundary condition; the front and back

of the model are parallel to the XOZ plane, which is set as a movable hinge, and the points

on this boundary are displaced in the Y direction to 0; the left and right sides of the model

are parallel to the YOZ plane, which is set as a movable hinge, and the points on this

boundary are displaced in the Y direction to 0. The model is concerned with the influence

of the length of the wing walls on the distribution of the internal forces in the Π-formed

diaphragm wall during the departure and reception of the shield machine. The model

studies the influence of the length of the wing walls on the distribution of internal forces

in the Π-formed underground diaphragm wall during the departure and reception of the

shield machine, as well as the force characteristics of the shield machine at each stage of

the excavation process and the changes in the ground settlement caused by it.

After the excavation is carried out, the exposed soil is installed in time for the tunnel

pipe sheet. This model pipe sheet is a simulated concrete slab unit, as shown in Figure 7,

and its strength is taken as C50. The construction stage of tunnel excavation is 2 m forward

along the tunnel axis in every other stage, and the location of its construction stage is

shown in Figure 8. Observation path 1 is set along the tunnel axis, and observation path 2

is set along the ground parallel to the x-axis at a distance of 4 m from the end wall. The

distribution of observation points along the observation path is shown in Figure 9.

Figure 7. Model drawing of the tunnel tube sheet.

Figure 8. Tunnel excavation location.

Figure 7. Model drawing of the tunnel tube sheet.

Sustainability 2022, 14, x FOR PEER REVIEW 7 of 20

Table 1. Table of soil and concrete parameters.

Material Parameters Mixed Fill Clay C30 C50

Elastic modulus (kN/m2) 6220 16,100 3 × 107 3.45 × 107

Poisson’s ratio 0.37 0.33 0.2 0.2

Weight capacity (kN/m3) 17 20.3 25 25

Cohesion (kN/m2) 18 48 / /

Friction angle (°) 6 12 / /

Drainage parameters Drainage Drainage / /

Ontogenetic model Modified Mohr–Coulomb Modified Mohr–Coulomb Elastic Elastic

MIDAS/GTS NX generates the default boundary conditions. The bottom of the model

is parallel to the XOY plane, which is set as a fixed boundary condition; the front and back

of the model are parallel to the XOZ plane, which is set as a movable hinge, and the points

on this boundary are displaced in the Y direction to 0; the left and right sides of the model

are parallel to the YOZ plane, which is set as a movable hinge, and the points on this

boundary are displaced in the Y direction to 0. The model is concerned with the influence

of the length of the wing walls on the distribution of the internal forces in the Π-formed

diaphragm wall during the departure and reception of the shield machine. The model

studies the influence of the length of the wing walls on the distribution of internal forces

in the Π-formed underground diaphragm wall during the departure and reception of the

shield machine, as well as the force characteristics of the shield machine at each stage of

the excavation process and the changes in the ground settlement caused by it.

After the excavation is carried out, the exposed soil is installed in time for the tunnel

pipe sheet. This model pipe sheet is a simulated concrete slab unit, as shown in Figure 7,

and its strength is taken as C50. The construction stage of tunnel excavation is 2 m forward

along the tunnel axis in every other stage, and the location of its construction stage is

shown in Figure 8. Observation path 1 is set along the tunnel axis, and observation path 2

is set along the ground parallel to the x-axis at a distance of 4 m from the end wall. The

distribution of observation points along the observation path is shown in Figure 9.

Figure 7. Model drawing of the tunnel tube sheet.

Figure 8. Tunnel excavation location. Figure 8. Tunnel excavation location.

Sustainability 2022, 14, x FOR PEER REVIEW 8 of 20

(a) (b)

Figure 9. Path selection. (a) Path 1. (b) Path 2.

3. Results and Analysis

In the model experiments, the influence of four distinct types of Π-formed dia-

phragm wall on the end soil was investigated, with and without constraints in the cavity.

The purpose of this numerical simulation was to investigate the effect of different wing

wall lengths on the suppression of displacement during each excavation stage, as well as

the stress distribution on the diaphragm wall. The results of the experimental study and

the numerical simulations are discussed in this section

3.1. Effect of Wing Wall Length on Stress Distribution during Departure and Reception of Shield

3.1.1. Small Displacement Model Test Results and Analysis

In the small displacement experiment, the average value of the displacement of the

foam circular cake at the start and arrival of the shield when the angle between the wing

wall and the end wall connection was different. In Figure 10, it can be seen that the deflec-

tion angle of the wing wall is not significant in supporting the end soil when small dis-

placements are experienced. However, under the same experimental conditions, the dis-

placements out of the hole are all smaller than the displacements into the hole. This indi-

cates that the overall displacement of the incoming hole is large, and the supporting struc-

ture of the hole has a supporting effect on the outflow of sand during the outgoing hole.

Three sets of control tests were set up, and the average values of the displacements of the

three control groups under the same experimental conditions were found, as shown in

Figure 11. By observing the displacement of the foam cakes, the effect of the correspond-

ing diaphragm wall style could be inferred. The analysis found that the deflection angle

of the wing wall did not significantly change the support effect of the end soil when small

displacements occurred. In the case of small displacement, the deflection angle of the wing

wall did not change the support effect of the end soil very significantly. Meanwhile, the

Π-formed ground connection wall with the same wing wall deflection angle produced

slightly larger overall displacements during shield entry. This is because the model tunnel

at the cavern entrance had a certain blocking effect on the sand exit from the cavern en-

trance.

Figure 9. Path selection. (a) Path 1. (b) Path 2.

3. Results and Analysis

In the model experiments, the influence of four distinct types of Π-formed diaphragmwall on the end soil was investigated, with and without constraints in the cavity. Thepurpose of this numerical simulation was to investigate the effect of different wing walllengths on the suppression of displacement during each excavation stage, as well as thestress distribution on the diaphragm wall. The results of the experimental study and thenumerical simulations are discussed in this section.

3.1. Effect of Wing Wall Length on Stress Distribution during Departure and Reception of Shield3.1.1. Small Displacement Model Test Results and Analysis

In the small displacement experiment, the average value of the displacement of thefoam circular cake at the start and arrival of the shield when the angle between the wingwall and the end wall connection was different. In Figure 10, it can be seen that thedeflection angle of the wing wall is not significant in supporting the end soil when small

Sustainability 2022, 14, 7653 8 of 19

displacements are experienced. However, under the same experimental conditions, thedisplacements out of the hole are all smaller than the displacements into the hole. Thisindicates that the overall displacement of the incoming hole is large, and the supportingstructure of the hole has a supporting effect on the outflow of sand during the outgoinghole. Three sets of control tests were set up, and the average values of the displacements ofthe three control groups under the same experimental conditions were found, as shown inFigure 11. By observing the displacement of the foam cakes, the effect of the correspondingdiaphragm wall style could be inferred. The analysis found that the deflection angle ofthe wing wall did not significantly change the support effect of the end soil when smalldisplacements occurred. In the case of small displacement, the deflection angle of the wingwall did not change the support effect of the end soil very significantly. Meanwhile, the Π-formed ground connection wall with the same wing wall deflection angle produced slightlylarger overall displacements during shield entry. This is because the model tunnel at thecavern entrance had a certain blocking effect on the sand exit from the cavern entrance.

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Inward Outward Verticle64

65

66

67

68

69

70

71

72

73

Reception

Departure

Dis

pla

cem

ent

aver

age

(mm

)

Inclination of wing wall to end wall connection

Figure 10. Sand output at different wing wall deflection angles for small displacements.

67

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63 66

767570 67

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Entrying the tunnel case 1 Exit the tunnel case 1

Entrying the tunnel case 2 Exit the tunnel case 2

Entrying the tunnel case 3 Exit the tunnel case 3

Average of entrying the tunnel Average of exit the tunnel

0

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)

Figure 11. The deflection direction of different wing walls influences the small displacement.

3.1.2. Large Displacement Model Test Results and Analysis

The test results for different wing wall deflection angles at large displacements are

shown in Figure 12. In terms of sand output, the sand output from the diaphragm wall

with wing walls was significantly higher than that from the diaphragm wall without wing

walls. Without the wing wall, the sand output was 17.1 kg, but, with the wing wall de-

flected inwards, the sand output was only 9.8 kg: a difference of almost twice as much. At

the same time, the angle of deflection of the wing wall in the case of having a wing wall

also had a different effect on controlling the amount of sand outflow, with the inward

deflection having a better support effect; the further the outward deflection, the more sand

outflow, as shown in Figure 12.

Figure 10. Sand output at different wing wall deflection angles for small displacements.

Sustainability 2022, 14, x FOR PEER REVIEW 9 of 20

Inward Outward Verticle64

65

66

67

68

69

70

71

72

73

Reception

Departure

Dis

pla

cem

ent

aver

age

(mm

)

Inclination of wing wall to end wall connection

Figure 10. Sand output at different wing wall deflection angles for small displacements.

67

78

6671 71 73

63 66

767570 67

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10

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(mm

)

Wing wall style

Entrying the tunnel case 1 Exit the tunnel case 1

Entrying the tunnel case 2 Exit the tunnel case 2

Entrying the tunnel case 3 Exit the tunnel case 3

Average of entrying the tunnel Average of exit the tunnel

0

10

20

30

40

50

60

70

80

90

100

Dis

pla

cem

ent

(mm

)

Figure 11. The deflection direction of different wing walls influences the small displacement.

3.1.2. Large Displacement Model Test Results and Analysis

The test results for different wing wall deflection angles at large displacements are

shown in Figure 12. In terms of sand output, the sand output from the diaphragm wall

with wing walls was significantly higher than that from the diaphragm wall without wing

walls. Without the wing wall, the sand output was 17.1 kg, but, with the wing wall de-

flected inwards, the sand output was only 9.8 kg: a difference of almost twice as much. At

the same time, the angle of deflection of the wing wall in the case of having a wing wall

also had a different effect on controlling the amount of sand outflow, with the inward

deflection having a better support effect; the further the outward deflection, the more sand

outflow, as shown in Figure 12.

Figure 11. The deflection direction of different wing walls influences the small displacement.

3.1.2. Large Displacement Model Test Results and Analysis

The test results for different wing wall deflection angles at large displacements areshown in Figure 12. In terms of sand output, the sand output from the diaphragm wall with

Sustainability 2022, 14, 7653 9 of 19

wing walls was significantly higher than that from the diaphragm wall without wing walls.Without the wing wall, the sand output was 17.1 kg, but, with the wing wall deflectedinwards, the sand output was only 9.8 kg: a difference of almost twice as much. At thesame time, the angle of deflection of the wing wall in the case of having a wing wall alsohad a different effect on controlling the amount of sand outflow, with the inward deflectionhaving a better support effect; the further the outward deflection, the more sand outflow,as shown in Figure 12.

Sustainability 2022, 14, x FOR PEER REVIEW 10 of 20

10.811.3

14.4

17.1

9.6

10.5

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15° inwards Vertical 15° outwards No wing wall0

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18

Qual

ity o

f sa

nd c

om

ing o

ut

of

the

cave(

kg) Exit the tunnel

Entering into tunnel

Wing wall angle

Figure 12. Sand output from different wing walls for large displacements.

3.2. Influence of Wing Wall Length on the Stress Distribution within the Diaphragm Wall

during Shield Initiation and Reception

Because of the small difference in stress and displacement changes in the departure

and reception of the shield, the numerical simulations only simulated the departure situ-

ation, and the reception situation was similar to that of the departure status. The hazard-

ous working condition was the moment the shield broke through the hole door and the

palm surface acted on the soil.

This can be seen in Figure 13. When no wing wall is present to support the cavity

door, there will be a larger stress area at the center of the cavity, and the length of the wing

wall at the edge of the cavity will affect the stress distribution near the cavity door. More-

over, a longer wing wall will result in a smaller stress distribution of the soil near the

cavity door in the y-axis direction.

Figure 12. Sand output from different wing walls for large displacements.

3.2. Influence of Wing Wall Length on the Stress Distribution within the Diaphragm Wall duringShield Initiation and Reception

Because of the small difference in stress and displacement changes in the departure andreception of the shield, the numerical simulations only simulated the departure situation,and the reception situation was similar to that of the departure status. The hazardousworking condition was the moment the shield broke through the hole door and the palmsurface acted on the soil.

This can be seen in Figure 13. When no wing wall is present to support the cavity door,there will be a larger stress area at the center of the cavity, and the length of the wing wallat the edge of the cavity will affect the stress distribution near the cavity door. Moreover, alonger wing wall will result in a smaller stress distribution of the soil near the cavity doorin the y-axis direction.

The forces inside and outside the wing walls of the diaphragm wall during the de-parture of the shield are shown in Figures 14 and 15, respectively. As the length of thewing wall increased, the major principal stresses in the end wall tended to decrease. Thepresence of the wing wall played an important role in the stress redistribution in the endwall, and the major principal stress value shifted from the end wall position to the wingwall position as the length of the wing wall increased. The red areas in the stress clouddiagram, which appear mainly near the cavity, indicate the higher stresses here. Whenthe wing wall appeared, the stresses around the hole appeared to decrease, and the redareas appear on the outside of the wing wall where the stresses increased and became morepronounced on both sides of the wing wall as the length of the wing wall increased.

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(a)

(b)

(c)

(d)

Figure 13. Cont.

Sustainability 2022, 14, 7653 11 of 19Sustainability 2022, 14, x FOR PEER REVIEW 12 of 20

(e)

(f)

Figure 13. Stress distribution in the y-axis for different support structures under hazardous working

conditions. (a) Traditional method. (b) No wing wall. (c) Wing wall is 2 m. (d) Wing wall is 4 m. (e)

Wing wall is 6 m. (f) Wing wall is 8 m.

The forces inside and outside the wing walls of the diaphragm wall during the de-

parture of the shield are shown in Figures 14 and 15, respectively. As the length of the

wing wall increased, the major principal stresses in the end wall tended to decrease. The

presence of the wing wall played an important role in the stress redistribution in the end

wall, and the major principal stress value shifted from the end wall position to the wing

wall position as the length of the wing wall increased. The red areas in the stress cloud

diagram, which appear mainly near the cavity, indicate the higher stresses here. When the

wing wall appeared, the stresses around the hole appeared to decrease, and the red areas

appear on the outside of the wing wall where the stresses increased and became more

pronounced on both sides of the wing wall as the length of the wing wall increased.

Figure 13. Stress distribution in the y-axis for different support structures under hazardous workingconditions. (a) Traditional method. (b) No wing wall. (c) Wing wall is 2 m. (d) Wing wall is 4 m.(e) Wing wall is 6 m. (f) Wing wall is 8 m.

3.3. Surface Settlement and Internal Stress Distribution in Diaphragm Wall at Different Stagesof Construction

When the wing wall was 6 m long and perpendicular to the end wall, the surfacedisplacements and the stress distribution within the diaphragm wall for each constructionphase in the departure case were considered. The construction process can be divided intosix construction phases, which are:

Stage 1: The tunnel is not excavated; the model is subject to gravity only, and themodel is analyzed for ground stress equilibrium. To prevent settlement of the groundsurface by the initial displacement, this stage should zero out the displacement.

Stage 2: The cavern door is broken, and the palm face of the shield machine is placedagainst the internal structure of the tunnel, providing a palm force of 150 kN/m2 acting onthe cavern door soil.

Stages 3–5: In each stage, the shield machine advances 2 m along the y-axis to cut thesoil, applying a force of 150 kN/m2 to the excavated soil surface to simulate the shieldpalm surface thrust and promptly assembling the excavated soil with the pipe sheet untilthe cutter reaches the end of the wing wall.

Stage 6: The shield machine continues to dig forward for 2 m beyond the end of thewing wall, the force from the palm surface is applied to the soil, and the pipe sheet iscompleted in time to form the support.

Sustainability 2022, 14, 7653 12 of 19Sustainability 2022, 14, x FOR PEER REVIEW 13 of 20

(a) (b)

(c) (d)

(e)

Figure 14. External stress distribution clouds for different styles of diaphragm wall. (a) No wing

wall. (b) Wing wall is 2 m. (c) Wing wall is 4 m. (d) Wing wall is 6 m. (e) Wing wall is 8 m.

Figure 14. External stress distribution clouds for different styles of diaphragm wall. (a) No wing wall.(b) Wing wall is 2 m. (c) Wing wall is 4 m. (d) Wing wall is 6 m. (e) Wing wall is 8 m.

These six stages are divided into two categories: the initial stage and the excavationstage. Stage 1 is the initial stage and stages 2–6 are the excavation stage, where the tunnel isexcavated in one piece every 2 m, and the location map is shown in Figure 8. This sectiondiscusses the stress distribution state of the diaphragm wall and the surface settlementover time.

During the tunnel boring process, the maximum settlement of the ground surface isgenerally distributed along the axis of the tunnel; therefore, two typical paths of the groundsurface were selected, as shown in Figure 9. Observation points were set at 2 m intervalsalong the observation path, with a total of 31 observation points along the tunnel axis,numbered in sequence. A total of 41 observation points were set up on the observation path4 m away from the end wall and were numbered sequentially. Settlement was specifiedto be positive along the negative z-axis. As the displacement at stage 1 was specified aszero, Figure 16 shows the distribution of surface settlement along the axial direction of the

Sustainability 2022, 14, 7653 13 of 19

tunnel at stages 2–6. Figure 17 shows the distribution of surface settlement parallel to theend wall at 4 m at stages 2–6.

Sustainability 2022, 14, x FOR PEER REVIEW 14 of 20

(a) (b)

(c) (d)

(e)

Figure 15. Internal stress distribution clouds for different styles of diaphragm wall. (a) No wing

wall. (b) Wing wall is 2 m. (c) Wing wall is 4 m. (d) Wing wall is 6 m. (e) Wing wall is 8 m.

3.3. Surface Settlement and Internal Stress Distribution in Diaphragm Wall at Different Stages

of Construction

When the wing wall was 6 m long and perpendicular to the end wall, the surface

displacements and the stress distribution within the diaphragm wall for each construction

phase in the departure case were considered. The construction process can be divided into

six construction phases, which are:

Stage 1: The tunnel is not excavated; the model is subject to gravity only, and the

model is analyzed for ground stress equilibrium. To prevent settlement of the ground

surface by the initial displacement, this stage should zero out the displacement.

Stage 2: The cavern door is broken, and the palm face of the shield machine is placed

against the internal structure of the tunnel, providing a palm force of 150 kN/m2 acting on

the cavern door soil.

Stages 3–5: In each stage, the shield machine advances 2 m along the y-axis to cut the

soil, applying a force of 150 kN/m2 to the excavated soil surface to simulate the shield palm

surface thrust and promptly assembling the excavated soil with the pipe sheet until the

cutter reaches the end of the wing wall.

Figure 15. Internal stress distribution clouds for different styles of diaphragm wall. (a) No wing wall.(b) Wing wall is 2 m. (c) Wing wall is 4 m. (d) Wing wall is 6 m. (e) Wing wall is 8 m.

Sustainability 2022, 14, 7653 14 of 19

Sustainability 2022, 14, x FOR PEER REVIEW 15 of 20

Stage 6: The shield machine continues to dig forward for 2 m beyond the end of the

wing wall, the force from the palm surface is applied to the soil, and the pipe sheet is

completed in time to form the support.

These six stages are divided into two categories: the initial stage and the excavation

stage. Stage 1 is the initial stage and stages 2–6 are the excavation stage, where the tunnel

is excavated in one piece every 2 m, and the location map is shown in Figure 8. This section

discusses the stress distribution state of the diaphragm wall and the surface settlement

over time.

During the tunnel boring process, the maximum settlement of the ground surface is

generally distributed along the axis of the tunnel; therefore, two typical paths of the

ground surface were selected, as shown in Figure 9. Observation points were set at 2 m

intervals along the observation path, with a total of 31 observation points along the tunnel

axis, numbered in sequence. A total of 41 observation points were set up on the observa-

tion path 4 m away from the end wall and were numbered sequentially. Settlement was

specified to be positive along the negative z-axis. As the displacement at stage 1 was spec-

ified as zero, Figure 16 shows the distribution of surface settlement along the axial direc-

tion of the tunnel at stages 2–6. Figure 17 shows the distribution of surface settlement

parallel to the end wall at 4 m at stages 2–6.

(a) (b)

(c) (d)

(e)

Figure 16. Schematic diagram of path 1 settlement at different stages of construction. (a) Stage 2. (b)

Stage 3. (c) Stage 4. (d) Stage 5. (e) Stage 6. Figure 16. Schematic diagram of path 1 settlement at different stages of construction. (a) Stage 2.(b) Stage 3. (c) Stage 4. (d) Stage 5. (e) Stage 6.

Settlement at each observation point on path 1 at different stages of constructionis shown in Figure 18. As shown in Figure 18, settlement of the ground surface mainlyoccurred near the Π-formed diaphragm wall as the shield entered the tunnel, with pro-gressively less settlement as the distance increased. During the course of stages 2–3, thesettlement on the tunnel axis was insignificant, and, as the shield continued to advance, themaximum settlement appeared to increase, with the maximum settlement occurring at alocation approximately 10 m from the end wall.

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(a) (b)

(c) (d)

(e)

Figure 17. Schematic diagram of path 2 settlement at different stages of construction. (a) Stage 2.

(b) Stage 3. (c) Stage 4. (d) Stage 5. (e) Stage 6.

Settlement at each observation point on path 1 at different stages of construction is

shown in Figure 18. As shown in Figure 18, settlement of the ground surface mainly oc-

curred near the Π-formed diaphragm wall as the shield entered the tunnel, with progres-

sively less settlement as the distance increased. During the course of stages 2–3, the settle-

ment on the tunnel axis was insignificant, and, as the shield continued to advance, the

maximum settlement appeared to increase, with the maximum settlement occurring at a

location approximately 10 m from the end wall.

Figure 17. Schematic diagram of path 2 settlement at different stages of construction. (a) Stage 2.(b) Stage 3. (c) Stage 4. (d) Stage 5. (e) Stage 6.

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0 5 10 15 20 25 30 35 40 45 50 55 60 65-3.5

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ent

(mm

)

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stage 2

stage 3

stage 4

stage 5

stage 6

Figure 18. Settlement curve of the observation points in path 1.

Figure 19 depicts the amount of settlement at each observation point on path 2 at

different stages of construction. In the horizontal direction, the surface settlement showed

a symmetrical distribution, with the maximum settlement occurring mainly at the axial

position of the tunnel and becoming larger as the shield machine progresses. The wing

walls impeded the development of surface displacements in the horizontal direction, and

the soil settlement immediately adjacent to the wing walls was very small.

Figure 18. Settlement curve of the observation points in path 1.

Figure 19 depicts the amount of settlement at each observation point on path 2 atdifferent stages of construction. In the horizontal direction, the surface settlement showeda symmetrical distribution, with the maximum settlement occurring mainly at the axialposition of the tunnel and becoming larger as the shield machine progresses. The wingwalls impeded the development of surface displacements in the horizontal direction, andthe soil settlement immediately adjacent to the wing walls was very small.

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0 10 20 30 40 50 60 70-2.2

-2.0

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stage 2

stage 3

stage 4

stage 5

stage 6

Distance from end wall (m)

Set

tlem

ent

(mm

)

Figure 19. Settlement curve of the observation points in path 2.

The data of the maximum values of the major principal stresses in the Π-formed di-

aphragm walls under different stages were compiled and analyzed, as shown in Figure

20. It was found that the maximum value of the major principal stress became larger con-

cerning the initial ground stress when the shield passed through the wing wall of the Π-

formed diaphragm walls. As the shield advanced, the maximum value of the major prin-

cipal stress tended to increase and then decrease, and the maximum value of the major

principal stress was large in stages 2–3, which means that this process is the dangerous

stage.

The maximum values of the major principal stresses in the Π-formed diaphragm

walls under different working conditions are shown in Figure 20, which shows that the

tendency of the major principal stresses in the Π-formed diaphragm walls increased and

then decreased when the shield machine was exiting the hole, with a peak value of 3505.60

kN/m2 in stage 4, i.e., when the shield blade was 4 m from the end wall.

I II III IV V VI

2600

2800

3000

3200

3400

3600

3800

4000

Max

imu

m p

rin

cip

al s

tres

s(K

N/m

2)

stages

Figure 19. Settlement curve of the observation points in path 2.

The data of the maximum values of the major principal stresses in the Π-formeddiaphragm walls under different stages were compiled and analyzed, as shown in Figure 20.It was found that the maximum value of the major principal stress became larger concerning

Sustainability 2022, 14, 7653 17 of 19

the initial ground stress when the shield passed through the wing wall of the Π-formeddiaphragm walls. As the shield advanced, the maximum value of the major principal stresstended to increase and then decrease, and the maximum value of the major principal stresswas large in stages 2–3, which means that this process is the dangerous stage.

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0 10 20 30 40 50 60 70-2.2

-2.0

-1.8

-1.6

-1.4

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stage 2

stage 3

stage 4

stage 5

stage 6

Distance from end wall (m)

Set

tlem

ent

(mm

)

Figure 19. Settlement curve of the observation points in path 2.

The data of the maximum values of the major principal stresses in the Π-formed di-

aphragm walls under different stages were compiled and analyzed, as shown in Figure

20. It was found that the maximum value of the major principal stress became larger con-

cerning the initial ground stress when the shield passed through the wing wall of the Π-

formed diaphragm walls. As the shield advanced, the maximum value of the major prin-

cipal stress tended to increase and then decrease, and the maximum value of the major

principal stress was large in stages 2–3, which means that this process is the dangerous

stage.

The maximum values of the major principal stresses in the Π-formed diaphragm

walls under different working conditions are shown in Figure 20, which shows that the

tendency of the major principal stresses in the Π-formed diaphragm walls increased and

then decreased when the shield machine was exiting the hole, with a peak value of 3505.60

kN/m2 in stage 4, i.e., when the shield blade was 4 m from the end wall.

I II III IV V VI

2600

2800

3000

3200

3400

3600

3800

4000M

axim

um

pri

nci

pal

str

ess(

KN

/m2)

stages

Figure 20. Distribution of the major principal stress in the diaphragm wall for the different stages inthe cavern.

The maximum values of the major principal stresses in the Π-formed diaphragmwalls under different working conditions are shown in Figure 20, which shows that thetendency of the major principal stresses in the Π-formed diaphragm walls increasedand then decreased when the shield machine was exiting the hole, with a peak value of3505.60 kN/m2 in stage 4, i.e., when the shield blade was 4 m from the end wall.

The objective of this study was to investigate the effects of different geometries on thestrength of the diaphragm wall through model experiments and numerical simulations.This document provides a reference and guidance for the design of diaphragm walls inpractical applications. In particular, inward-deflected wing walls and longer wing wallshave better support effects.

4. Conclusions

In this study, the influence of the shape of the diaphragm wall on the amount ofground settlement during the arrival and initiation of the shield was discussed usingexperimental and numerical simulations. At the same time, the internal force distributionof the diaphragm wall at different stages of construction was discussed, and the specificfindings are summarized as follows:

(1) During small displacements, the deflection angle of the wing wall (small angledeflection) does not differ much in the effect of supporting the underground diaphragmshield inside and outside the cavity. In the case of large displacements, wing walls withinward deflection are more effective than those with outward deflection;

(2) A shield with a diaphragm wall exiting at the bottom is the most likely place forsoil eruption. The longer the wing wall, the lower the stress in the soil around the entrance;

(3) As the length of the wing wall increases, the major principal stress in the wing wall atthe shield entry increases, and the change becomes more apparent later; the damage to theconcrete tends to occur on the outside of the wing wall. When the shield is received, the stressin the soil around the hole along the y-axis decreases as the length of the wings increases;

(4) If the wing wall is less than 4 m in length, it is most likely to be damaged on theinner side; if it is between 4 m and 8 m in length, it is most likely to be damaged on theouter side; the maximum value of the principal stress rises as the wing wall lengthens;

Sustainability 2022, 14, 7653 18 of 19

(5) In stage 2, ground settlement is mainly between wing walls; outside the wing walls,there is no soil settlement. As the shield tunnels forward, the significant settlement of theground surface appears above the front of the cutter. During tunneling, the major principalstress value first increases and then decreases, with the Π-formed diaphragm wall mostlikely to fail during stage 2.

Author Contributions: Conceptualization: J.H. and S.W.; methodology, S.W.; software, S.W.; valida-tion, S.W.; writing—original draft preparation, Y.W.; writing—review and editing, Y.W.; visualization,Y.W.; supervision, X.R. and J.P.; project administration, J.H. and Z.W.; funding acquisition, R.H. andD.Z. All authors have read and agreed to the published version of the manuscript.

Funding: This research was funded by the National Natural Science Foundation of China (grantno. 51968019), the Natural Science Foundation of Hainan Province Youth Fund Project (519QN333),the Natural Science Foundation of Hainan Province (No.519MS024), the High Technology DirectionProject of the Key Research & Development Science and Technology of Hainan Province, China(grant no. ZDYF2021GXJS020), the High-Level Talent Project of Hainan Basic and Applied BasicResearch Plan (2019RC148, 2019RC351), and the characteristic innovation (Natural Science) projects ofscientific research platforms and scientific research projects of Guangdong Universities in 2021 (grantno. 2021KTSCX139). The authors also acknowledge support from the China Scholarship Council.

Institutional Review Board Statement: Not applicable.

Data Availability Statement: Not applicable.

Conflicts of Interest: The authors declare no conflict of interest.

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