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Physical Modeling on Ground Responses to Tunneling in Sand Considering

the Existence of HDPE Pipes

Article  in  Geotechnical Testing Journal · October 2014

DOI: 10.1520/GTJ20140031

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Fei Wang,1 Yan-Jun Du,2 and Xiaoming Yang3

Physical Modeling on Ground Responsesto Tunneling in Sand Consideringthe Existence of HDPE Pipes

Reference

Wang, Fei, Du, Yan-Jun, and Yang, Xiaoming, “Physical Modeling on Ground Responses to Tunneling

in Sand Considering the Existence of HDPE Pipes,” Geotechnical Testing Journal, Vol. 38, No. 1, 2015,

pp. 85–97, doi:10.1520/GTJ20140031. ISSN 0149-6115

ABSTRACT

Ground settlement and relevant prediction methods related to underground tunneling have

been investigated extensively in previous studies. However, the effects of the existence of

service pipelines on the ground movement induced by tunneling have not been well addressed.

This study involved a series of physical modeling tests on ground responses to tunneling in sand

considering the existence of high-density polyethylene (HDPE) pipes using a custom-made

physical modeling system. The system included a model box, a pipe fixing frame, and a number

of settlement plates. The developed model box had dimensions of 2.0 m by 2.0 m by 1.5 m, and

the bottom of the box consisted of eight movable plates with dimensions of 0.25 m by 2 m by

0.1 m. The plates were lowered down at four levels of maximum vertical distance (10, 20, 30, and

40 mm) to form normal distribution curves, simulating tunneling effects in the sand stratum.

Four normal distribution curves were created with maximum lowering distances of the movable

plates of 10, 20, 30, and 40 mm to simulate different volumes of ground loss in the tunnel. We

performed the four tests one after another by successively lowering down the movable bottom

plates. Prior to filling, the required density of backfilled sand was determined using a self-

designed instrument. The HDPE pipes, with two diameters (i.e., 300 and 200 mm), were

installed in the model box at two different buried depths (i.e., 1.05 and 0.75 m from the spring

line of the pipes to the fill surface) using a custom-made fixing frame. The test results

demonstrate that the existence of the HDPE pipes resulted in a wider but shallower settlement

trough than in the greenfield (without pipe) case. The width of the settlement trough at a given

depth decreased with decreasing buried depth of the pipe, whereas it increased with decreasing

pipe diameter. The volume of the settlement trough at a given depth was approximately

constant, regardless of the existence of pipes, and the vertical displacement of the pipes

increased with decreasing diameter and buried depth of the pipe.

Manuscript received February 16, 2014;

accepted for publication October 7,

2014; published online November 3,

2014.

1

Ph.D., Lecturer, Institute of Geotechnical

Engineering, Southeast Univ., Nanjing,

Jiangsu, China, 210096 (Corresponding

author), e-mail: feiwangseu@gmail.com

(Currently Research Assistant, University

of Kansas, Lawrence, Kansas, USA).

2

Ph.D., Professor, Director, Institute of

Geotechnical Engineering, Southeast

Univ., Nanjing, Jiangsu, China, 210096,

e-mail: duyanjun@seu.edu.cn

3

Ph.D., P.E., Assistant Professor, School of

Civil and Environmental Engineering,

Oklahoma State Univ., Stillwater, OK

74074, United States of America,

e-mail: xmyang@okstate.edu

Copyright VC 2014 by ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. 85

Geotechnical Testing Journal

doi:10.1520/GTJ20140031 / Vol. 38 / No. 1 / January 2015 / available online at www.astm.org

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Keywords

buried HDPE pipe, tunneling, physical modeling, settlement trough volume

Introduction

In urban areas, tunnel designers have to face challenges regard-

ing congestion of the underground environment—for example,

pile foundations, existing tunnels, and pipelines for public serv-

ices (Mair 2008). It is essential to evaluate the effect of tunneling

on pipelines in order to maintain the serviceability of urban

facilities in urban tunneling.

A number of methods have been proposed to estimate pipe-

line responses to the construction of underground tunnels; these

methods can be classified as two types. The first type is methods

based on the Winkler foundation model. Attewell et al. (1986)

simplified a pipeline and the soils beneath as an elastic beam

and springs, respectively, to predict the additional stresses and

strains in pipelines caused by tunneling. The effectiveness of

Attewell et al.’s (1986) model was verified using observation

data from both field and lab tests (O’Rourke and Trautmann

1982; Yeates 1984; Takagi et al. 1984; Bracegirdle et al. 1996).

Klar et al. (2005) proposed a novel method to estimate the coef-

ficient of subgrade reaction in Attewell et al.’s (1986) model.

Duan (2002) investigated the relationship between the ground

loss volume in tunnels and deformations of pipelines based on

the Winkler foundation model. Liao and Liu (1997) proposed

models with respect to rigid and flexible pipes on the basis of

the Winkler foundation model.

In the second type of method, models are based on the elas-

tic continuum solution. Klar et al. (2005) assumed pipes buried

in an elastic continuum media and derived the closed-form

solution for additional stress in pipes caused by tunneling using

Mindlin’s solution. Voster et al. (2005) suggested using the

equivalent linear approach to consider the soil’s nonlinearity in

the elastic continuum solution. Klar et al. (2008) extended the

elastic continuum solution to jointed pipeline cases affected by

tunnel construction underneath the pipes. Marshall et al. (2010)

introduced a new method involving an “out of plane” shear

argument into the elastic continuum solution to evaluate the

effects of soil stiffness on the pipe–soil interaction. Zhang

(2009) suggested a method based on the elastic continuum

method to predict the mechanical behaviors of pipes above tun-

nels in which the soil around pipes was treated as layered. In

the mentioned existing models, displacements of pipelines

induced by tunneling are the basis for the internal force calcula-

tion. The displacements of pipelines are typically assumed to be

equal to those in the greenfield tunneling settlement profile; in

other words, the stiffness of the pipes is assumed to be equal to

the stiffness of the surrounding soils. The existence of pipelines

would obviously alter the settlement profile caused by tunnel-

ing. However, the effects of the existence of pipes on ground

movements induced by tunneling have not been well addressed

by the above-mentioned models.

Physical modeling is an important approach to the study of

tunneling effects. Physical modeling of tunnels has been con-

ducted using different types of techniques, including trap door

models, rigid tubes with flexible or movable faces, pressurized

air bags, polystyrene foam and organic solvent, soil augering,

centrifuge tests, and miniature tunnel boring machines (Jacobsz

et al. 2004; Vorster et al. 2005; Meguid et al. 2008; Marshall

2009; Marshall and Mair 2011). Cenrifuge modeling was

adopted by the Cambridge research group to simulate the

influence of tunneling on pipelines (Vorster 2005; Vorster

et al. 2005; Mair 2008; Marshall and Mair 2011). In their

studies, three types of pipes were tested at 75 g to represent a

2.6 -m-diameter steel pipe with a wall thickness of 20mm, an

830-mm-diameter concrete pipe with a wall thickness of

200mm, and a 660-mm-diameter concrete pipe with a wall

thickness of 100mm. Ratios of the thickness of the wall (t) to

the diameter (D) of the three pipes were 0.007, 0.24, and 0.15,

respectively, which are all close to the limits of t/D required by

ASTM standards (ASTM A53M-12 and ASTM C118M-11).

However, difficulties could arise when producing proper centri-

fuge model pipes whose wall thicknesses match those of the

prototype pipes very well (e.g., corrugated high-density polyeth-

ylene [HDPE] pipe with a wall thickness of only several milli-

meters). The ring stiffness of pipes is proportional to (t/D)3, and

any difference in t/D therefore might cause misunderstanding

of the mechanical behaviors of pipes. Therefore, 1 g physical

modeling could be a reliable approach for investigating the

behaviors of HDPE pipes above tunneling.

To investigate the displacement of HDPE pipes above tun-

neling and its effects on settlement profiles, we designed a large-

scale laboratory model test equipment system. The system

includes a model box, a pipe fixing frame, and a number of set-

tlement plates. The details of the equipment system and large-

scale model test procedures are presented first in this paper.

The effects of the buried depth and the diameter of the HDPE

pipes on the settlement trough induced by tunneling in a sand

stratum were investigated. A discussion is presented to interpret

the mechanisms controlling the development of the settlement

trough during tunneling considering the existence of HDPE

pipes.

Design of Test Instruments

MODEL BOX

Figure 1 presents a schematic diagram of the custom-made

model test box used in the current study. The box was 2m in

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length, 2m in width, and 1.5m in height. To allow observation

of the test proceedings, the front wall of the model box was built

with Plexiglas. To ensure the stability of the box after it was

filled with sand, steel frames were used to reinforce the box

walls. The bottom of the model box consisted of eight movable

plates. Existing literature shows that the settlement trough, at

both the ground surface and the subsurface induced by tunnel-

ing, can be represented by a normal distribution curve (Mair

et al. 1993; Aoyagi 1995; Moh et al. 1996; Ahmed and Iskander

2011). Therefore, the eight movable plates were lowered various

vertical distances to form a normal distribution curve, simulat-

ing the tunneling effect (see Fig. 1). Each of the plates was

0.25m wide, 2m long, and 0.10m thick. Lubricating oil was

smeared at the interfaces of neighboring plates to reduce fric-

tion. The lowering of the plates, with a designed maximum

value of 100mm, was accomplished by rotating handles beneath

the test box. Ten rounds of rotation of a given handle lowered

the movable plate 1mm. Vaseline was applied on the model

box walls to reduce the friction between the side wall and the

backfill material in order to minimize any possible soil arching

effect developing near the side walls.

LOWERING DEVICE

Figure 2 presents a schematic diagram of the lowering device.

The lowering device included three portions: (a) hinge joints

with rigid sticks, (b) the lowering system, and (c) the fixing sys-

tem. Each movable plate corresponded to a lowering device,

and these plates were connected to each other through hinge

joints and rigid sticks bonded with a screwing rod for transmit-

ting the screwing energy to lower the movable plate. The screw-

ing energy transmitting system consisted of a screwing handle,

the screwing energy transmitting box, and the screwing rod.

With screwing of the handle, the energy was transmitted to the

screwing rod through the screwing energy transmitting box,

which drove the rod forward or backward to lower or lift the

movable plates. The fixing system contained a footing plate and

two fixing rings. The fixing rings were used to connect the

FIG. 1 Schematic diagram of the model box (not to scale; unit, mm).

FIG. 2

Schematic diagram of the lowering device (not to scale;

unit, mm).

WANG ET AL. ON TUNNELING IN SAND WITH HDPE PIPES 87

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screwing rod with the footing plate to ensure the stability of the

lowering device.

BOX FILLING INSTRUMENTATION

The sand pluviation method was used to fill the model box with

sand. The instrument consisted of two parts: the uplifting device

and the raining system. Sand was lifted to a certain height using

a custom-made device that was driven by an electromotor. Sub-

sequently, sand was passed to a rigid box, namely, the raining

box, through a plastic membrane tube. The bottom of the rain-

ing box had a sieve with an opening size of 2mm, which slowed

the falling speed of the sand particles to zero. The raining box

was 300mm in height, 1000mm in width, and 1000mm in

length. The four corners of the raining box were connected

using four rubber ropes to enable manual shaking of the raining

box and even spreading of the sand to the model box during fill-

ing. After the box was filled with 100mm lift, the raining box

was moved upward by 100mm. The final thickness was

1300mm from the bottom of the model box.

TESTED PIPE FIXING FRAME

Figure 3 shows two directional views of the pipe fixing frame.

The fixing frame was made from steel and fixed at the model

box wall. Five different buried depths of the tested pipe could be

provided by the fixing frame, namely, 0.75, 0.90, 1.05, 1.20, and

1.35m from the top of the model box. Pipe plugs were made

from polyethylene and used to connect the tested pipe with the

fixing frame. Pipe plugs were bonded with the fixing frame

using bolts and nuts through their centerlines, and then the

pipes were installed. The diameter of the pipe plug was exactly

equal to the inner diameter of the pipe, and the pipe plug could

be pushed into the pipe to connect the pipe with the model box

to simulate a spigot joint in practice. To maintain tight contact

between the plugs and tested pipes, two rubber O-rings with a

thickness of 1.5mm were used to cover the plugs before the

tested pipe was installed. Two types of corrugated HDPE pipes

with outside diameters of 200 and 300mm, respectively, were

selected in this study. Accordingly, two different diameters of

pipe plugs were used.

FIG. 3

Schematic diagram of tested pipe fixing frame (not to scale;

unit, mm).

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SAND PLUVIATION TEST DEVICE

The sand pluviation method was used to fill the model box with

sand. Before filling, a pluviation test was conducted to quantify

the relationship between the falling height and the correspond-

ing sand density of the sand using a custom-made device as

shown in Fig. 4. A steel funnel was fixed to a rigid frame

(1000mm in length, 200mm in width, and 1500mm in height)

at a specific height (that is, the height of the sand’s fall). The

air-dried sand, with a volume of 0.03375 m3, fell down from

the funnel into the cubic box placed on the ground [Fig. 4(a)].

The height of the sand’s fall was adjusted using a length-

adjustable tube below the funnel. The density of the sand that

fell into the cubic box was estimated by dividing the measured

weight of the sand by the measured volume of the cubic box.

SETTLEMENT PLATES

In this study, settlement plates were used to measure the vertical

settlement during tunneling. Figure 5 presents a schematic

diagram of the locations of the settlement plates, which were

0.20, 0.40, and 0.60m from the fill surface. Five settlement plates

were placed at each depth [see Fig. 5(a)]. To minimize the mea-

surement error caused by their self-weight, the settlement plates

were made of Plexiglas. Each plate was square with a width of

50mm and a thickness of 5mm. A rod with a 10-mm diameter

was used to connect two plates. The rod was enclosed in a polyvi-

nyl chloride tube to avoid friction at the interface of the rod and

the fill, which ensured the accuracy of the settlement measurement.

The vertical displacements of pipes were also measured by attach-

ing settlement plates at the crown of the installed pipes at different

horizontal distances from the centerline of the model box.

Model Testing Methodology

FILLING MATERIAL

Yangtze River sand was used to fill the model box. The sand

was first air-dried and then passed through a sieve with an opening

size of 2mm. Figure 6 shows the particle size distribution curve of

the sieved sand used in the tests; the uniformity coefficient and the

coefficient of gradation were calculated as 2.0 and 1.39, respec-

tively. According to the Unified Soil Classification System (ASTM

D2487), the sand was classified as poorly graded sand.

PROPERTIES OF CORRUGATED HIGH-DENSITY

POLYETHYLENE PIPES TESTED

Two types of corrugated HDPE pipes, with diameters of 200

and 300mm and corresponding wall thicknesses of 3 and

5mm, respectively, were used in the tests. A parallel-plate load-

ing test was conducted as per ASTM D2412-11 to obtain the

pipe stiffness, and the results are presented in Fig. 7. The pipe

stiffness was calculated via the following equation:

PS ¼ FDy¼ 53:6

EID3

(1)

where:

PS¼ pipe stiffness, kPa,

F¼ load,

Dy¼ vertical deflection, m,

E¼modulus of elasticity, kPa,

I¼moment of inertia of wall cross-section per unit length

(I ¼ t3=12), m3,

t¼ thickness of pipes, m, and

D¼mean diameter of pipes, m.

Based on Eq 1 and Fig. 7, the stiffness of the pipe with a

diameter of 200mm at 5 % vertical deflection was computed as

177.5 kPa, and the stiffness of the 300-mm pipe was calculated

as 127.9 kPa. Therefore, the ring stiffness (RS) for the pipes with

diameters of 200 and 300mm was 26.5 kPa and 19.1 kPa,

respectively, according to the following equation:

RS ¼ 8EID3

(2)

FIG. 4 Schematic diagram of the custom-made sand pluviation test

equipment (not to scale; unit, mm).

WANG ET AL. ON TUNNELING IN SAND WITH HDPE PIPES 89

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It is worth noting the stress-strain relationship for HDPE

pipes as shown in Fig. 7. This nonlinear characteristic of

HDPE material has also been reported by several other investi-

gators (Moore and Hu 1996; Zhang and Moore 1997; Moore

and Zhang 1998). Further study is needed to consider the

effect of the nonlinear behavior of flexible pipes on the settle-

ment trough characteristics and, consequently, the mechanical

behaviors of HDPE pipe.

FIG. 5 Locations of settlement plates: (a) front view; (b) side view. (Unit, mm; not to scale.)

Geotechnical Testing Journal90

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TEST CASES

Four cases were tested to evaluate the effects of the diameter

and buried depth of pipe on the mechanical behavior. Table 1

shows the details of these four cases. In each case, four tests

were conducted one after another by successively lowering the

bottom movable plates to form four different normal distribu-

tion curves as shown in Fig. 8. The maximum vertical lowering

distances for the four tests were 10, 20, 30, and 40mm, respec-

tively. The lowering distances, presented in Fig. 8, were obtained

from the readings of the data points located in the centers of the

movable plates.

Test Results and Discussion

HEIGHT OF SAND FALL AND CORRESPONDING

DRY DENSITY

Figure 9 presents the relationship between the height of the

sand’s fall and the sand density. It is shown that the density of

the sand sharply increased with an increase in the height of the

sand’s fall when the height was less than 0.80m and then tended

to reach an approximate constant when the height of the fall

exceeded 0.80m. Because of the limited testing space and the

dimensions of the model box, the height of the sand’s fall

adopted in this study was 0.70m, and the corresponding dry

density of the sand was estimated as 1.46Mg/m3 from Fig. 10.

Cresswell et al. (1999) investigated the maximum density of

sand during pluvation. Based on their method, the maximum

density of the sand in the current study was 1.47Mg/m3, and

the minimum density should be the density of sand at the

height of fall as 25.4m based on ASTM D4253. The minimum

density was determined as 1.43Mg/m3. The value of the selected

dry density is close to the ones reported in previous studies

(Moh et al. 1996; Longanathan and Poulos 1998). The internal

friction angle of sand with a density of 1.46Mg/m3 was deter-

mined as 32.5� from the results of direct shear tests conducted

as per ASTM D3080, as shown in Fig. 10.

CHARACTERISTICS OF THE SETTLEMENT TROUGH AT

DIFFERENT DEPTHS

Figure 11 shows the settlement troughs above the pipes at differ-

ent maximum lowering distances for the tested cases. The meas-

ured depths were 0.20, 0.40, and 0.60m from the ground

surface. The solid lines in Fig. 11 represent the settlement

troughs with the existence of pipes, and the dashed lines are set-

tlement troughs in the greenfield case. It is clear that the settle-

ment trough in the cases with pipes was wider and the

maximum value of the settlement trough was less relative to the

FIG. 6 Particle size distribution curve of Yangtze River sand used in the

model test.

FIG. 7 Load-deflection curves for pipes of different diameters obtained

using the parallel-plate loading test.

TABLE 1. Summary of test cases.

CaseNumber

PipeDiameter

D,mm

Buried Depthof the Springline

of PipeH, m

Maximum LoweringDistance of

Movable Plates,mm

MeasuredSettlementDepth,ma

1 300 1.05 10, 20, 30, 40 0.20, 0.40, 0.60

2 300 0.75 10, 20, 30, 40 0.20, 0.40, 0.60

3 200 0.75 10, 20, 30, 40 0.20, 0.40, 0.60

4 Greenfield(no pipe)

Greenfield 10, 20, 30, 40 0.20, 0.40, 0.60

aThe depth refers to the distance from the fill surface to the measuredplace.

FIG. 8 Plan for lowering the movable plates in different tests.

WANG ET AL. ON TUNNELING IN SAND WITH HDPE PIPES 91

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greenfield case. For example, when the maximum lowering dis-

tance of the movable plates was 10m, the maximum settlement

values at a depth of 0.20m were approximately 65 and 80mm

in case 1 and the greenfield case, respectively; however, the

widths of the settlement troughs were 280 and 255 cm for case 1

and the greenfield case, respectively. This observation suggests

that the existence of the pipe spread the settlement propagation

to a wider range and reduced the maximum settlement to a cer-

tain degree. Figure 12 presents a summary of the observed

widths of the settlement troughs for all cases. It is evident from

this figure that (1) the width of the settlement trough in the

greenfield case was narrower than in the three cases where pipes

were installed; (2) the width of the settlement trough decreased

with decreasing buried pipe depth (noted by comparing cases 1

and 2); (3) the width of the settlement trough increased when

the diameter of the pipes decreased (noted by comparing cases

2 and 3); (4) increasing the lowering distance of the movable

plates caused only a minor change in the width of the settlement

trough; and (5) the width of the settlement trough decreased

with depth. However, the average decreasing slope for the

greenfield case (7.96m/m) was approximately two times the

values of the other three cases (4.03, 4.02, and 3.71m/m for

cases 1, 2, and 3, respectively).

The measured maximum settlements at different depths for

the four test cases are summarized in Table 2. It is shown that

the maximum settlement at a given depth for the greenfield case

was greater than in the other three cases. This is because the

existence of the pipes restrained the propagation of the ground

movement from the bottom of the box to the filling surface.

Nevertheless, pipes with two edges fixed to pipe plugs are likely

to transmit the subsidence energy induced by tunneling to a

wider spatial range as compensation for the limited vertical

settlement.

FIG. 9 Relationship between the falling height and the density of sand used

in model tests.

FIG. 10 Determination of shear strength parameters for the filled sand using

the results of direct shear tests.

FIG. 11 Settlement troughs at different maximum lowering distances of

movable plates compared with the greenfield case.

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VOLUME OF THE SETTLEMENT TROUGH

The volume of the settlement trough is an important parameter

used to calculate the settlement at different horizontal distances

from the centerline of the settlement trough in most of the

existing methods (Peck 1969; Mair et al. 1993; and O’Reilly and

New 1982). Therefore, the determination of the volume of the

settlement trough is essential for estimating the settlement

caused by tunneling. Generally, the volume of the settlement

trough is recognized as constant with depth and equal to the

volume of the ground loss in a tunnel constructed in clay (Mair

et al. 1993). However, the aforementioned studies correspond to

the greenfield case (i.e., without pipes). To our knowledge, no

existing method has been proposed to estimate the characteris-

tics of settlement troughs considering the existence of pipes.

Figure 13 presents the volume of the settlement trough at

different depths for four cases. In this study, the volume of the

settlement trough per unit length of the tunnel was recognized

as equal to the area of the settlement trough. It is evident that

that the volume of the settlement trough, at a given depth and

maximum lowering distance of the movable plate, was approxi-

mately constant regardless of the existence of pipes. The exis-

tence of the pipes reduced the maximum vertical settlement

value but increased the width of the settlement trough, and

thereby led to a constant volume of the settlement trough. This

FIG. 11 (Continued). FIG. 11 (Continued).

WANG ET AL. ON TUNNELING IN SAND WITH HDPE PIPES 93

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finding is consistent with the findings of Marshall et al. (2010),

who presented a series of centrifuge test results on the settle-

ment of sand induced by tunneling with the existence of pipes

above the tunnel. The volume of the settlement trough at the

ground surface (only settlement at the ground surface was pre-

sented by Marshall et al. [2010]) was calculated and is presented

in Fig. 14. It is evident that the volume of the ground trough at a

given volume of ground loss was approximately constant (see

Fig. 14). We also found that the volume of the settlement trough

increased with the maximum lowering distance of the movable

plates, which can be attributed to the soil arching effect that

developed in the ground.

Based on the results of this study and those obtained from

Marshall et al. (2010), it can be concluded that the volume of a

settlement trough in the presence of pipes can be estimated

from the greenfield case. Further study needs to be conducted

on the settlement prediction method in cases of tunneling con-

sidering the existence of pipes.

VERTICAL DISPLACEMENT OF PIPES

Figure 15 presents the vertical displacement of the pipes in three

cases with pipes. The displacement of the pipes increased with

increasing maximum lowering distance of the movable plates.

The pipes in cases 1 and 3 displayed the minimum and maxi-

mum vertical displacements, respectively, regardless of the max-

imum lowering distance of the movable plates. For instance,

when the maximum lowering distance of the movable plate was

40mm, the maximum vertical displacements in these three

cases were 19.1, 23.2, and 27.6mm, respectively. The results

FIG. 12 Widths of settlement troughs at different maximum lowering

distances of movable plates for four cases.

TABLE 2. Summary of maximum values of settlement troughs for

different cases.

Maximum Settlement at Different MaximumLowering Distances of Movable Plates, mm

CaseNumber

MeasuredDepth, m 1 2 3 4

1 0.20 62 110 175 230

0.40 68 130 200 250

0.60 72 150 198 275

2 0.20 55 98 150 187

0.40 68 116 171 201

0.60 76 128 180 235

3 0.20 66 128 175 208

0.40 77.4 140.1 201.9 2527

0.60 76.2 154.6 211.4 2669

4 0.20 82 160 225 265

0.40 82 165 225 265

0.60 96 156 225 320

FIG. 13 Volume of the settlement trough at different depths.

Geotechnical Testing Journal94

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demonstrate that the vertical displacements of the pipes

increased with a decrease in the diameter of the pipe at a given

buried depth. This is because a pipe with a smaller diameter

possesses a lower bending stiffness, which in turn leads to

greater vertical settlement, based on beam theory. The vertical

displacement of a pipe with a given diameter also increased

with a decrease in the buried depth. The ground movement

caused unbalanced forces acting on the sides below and above

the pipes, resulting in a net loading on the pipes. Based on

beam theory, the loading area depends on the width of the set-

tlement trough at the same elevation as the pipes. A wider set-

tlement trough would lead to a larger loading area and

subsequent greater vertical displacement of the pipes.

In summary, the aforementioned results reveal that the

existence of HDPE pipes widened the settlement trough but

reduced the maximum vertical settlement of the sand. This find-

ing implies that wider range reinforcement is necessary to

maintain the stability of the structures in the vicinity when a

pipeline is buried above a construction tunnel. The results also

demonstrate that the responses of the ground (i.e., characteris-

tics and volume of settlement trough) and pipe (i.e., vertical

displacement) to tunneling are significantly controlled by the

diameter, buried depth, and stiffness of the pipes. Further

research is suggested on the influence of sand density and pipe

stiffness on ground movement and pipe displacement during

tunneling.

Discussion

The pipe plugs were used as connectors between the pipe and

the model box. They were designed to simulate the spigot joints

in real projects. However, because of the complexity of the joint

behaviors when the pipe is located above a cavity, it is hard to

quantify whether the pipe plugs had exactly the same effect as

joints on the pipe’s mechanical behavior. Further study is

needed to investigate the joint effect on the pipe deformation

above cavities and the relationships among the geometry (i.e.,

width, depth, and shape) of the cavity, the length of the pipe

between joints, and the pipe deformation.

Conclusions

A 1g physical modeling system was designed and used to inves-

tigate the ground response to tunneling below existing HDPE

pipes. This system included a model box, a pipe fixing frame,

and settlement plates. The HDPE pipes were installed in the

model box to evaluate the effects of the diameter of the pipes on

the ground movement. The vertical displacement of the HDPE

pipes and the settlement profiles of the sand induced by tunnel-

ing were monitored using self-designed settlement plates. The

characteristics of the ground response and pipe displacement

were presented. Based on the results of this study, the following

conclusions can be drawn:

(1) The existence of HDPE pipes results in a wider but shal-lower settlement trough than in the greenfield case. Thewidth of the settlement trough at a given depth abovepipes decreases with the buried depth of the pipes andincreases with a decrease in the diameter of the pipes.The decreasing rate of the width of the settlement troughwith respect to the ground depth for the greenfield casewas greater than that for the three cases with HDPEpipes.

(2) The volume of the settlement trough at a given depth inthe ground is constant regardless of the existence ofpipes, which is consistent with the centrifuge model testdata reported by Marshall et al. (2010).

(3) The vertical displacement of the pipes increased withdecreasing diameter of the pipes. However, it decreasedwith the buried depth because a narrower settlementtrough occurred at a deeper place, resulting in a smallerloading area of the pipes based on beam theory.

ACKNOWLEDGMENTS

The writers are grateful for the financial support from the

National Natural Science Foundation of China (Grant Nos.

FIG. 14 Volume of the settlement trough at different volumes of ground loss

(data from Marshall et al. 2010).

FIG. 15 Vertical displacements of pipes in different cases.

WANG ET AL. ON TUNNELING IN SAND WITH HDPE PIPES 95

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51108078, 51310105030, and 51278100) and the Natural

Science Foundation of Jiangsu Province (Grant Nos.

BK2013294 and BK2012022). The writers also express their

gratitude to Mr. Z.-X. Wang, Mr. R.-R. Wang, and Mr. Y.-X.

Zhou for their assistance in accomplishing part of the

laboratory tests.

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