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文献文章-PFC和FLAC3D耦合-Numerical Examination
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详细说明：PFC和FLAC耦合的SCI文章，This study investigated earth pressure balance (EPB) shield tunneling–induced responses in terms of muck pressure, machine
parameters, and surface settlements using an efficient numerical scheme that couples PFC3D and FLAC3D software. Tunneling cases with
different discharge ratios in the chamber were conducted using PFC3D, and the surrounding ground was modeled in FLAC3D. The results
showed that the muck pressures near the bulkhead vary periodically during shield tunneling and have negative relations with the discharge
ratios. Pressure differences between the left and the right sides in the shield chamber, and at different longitudinal positions, were found to be
subject to the discharge ratio in the chamber. Furthermore, negative relations between the discharge ratio and both the thrust in the shield and
the torque in the cutterhead were observed during excavation. Finally, it was found that positive ground loss has a larger effect on surface
settlement than its negative counterpart500
Stress(kPa)
1 00kPa Experimental ---.-200kPa Experimental
20
40
300kPa experimental
400kPa Experimental
400
▲PFC
-.100kPa Numerical ---.-200kPa Numerical
×PFC
FLAC
300kPa Numerical
400kPa Numerical
◆ PFC OZ
1000
Buried depth
东200
of the pfc
2000
100
0
3000
Shear displacement(mm
Fig 4 Comparison of initial stresses between FLAC3D and PFC3D
Fig. 2. Variation of shear stress versus shear displacement(experimen-
domains
tal and numerical tests)
of shield tunneling behavior. There fore a scaled model with a diaIr
日
calibrated by DEM modeling. In reality, the sand includes particles
eter of 0.88 m was established with DEM(Fig. 3). The coupled
numerical model contained initial ground with dimensions of
of different sizes. It is impossible to simulate fine particles using
6, 120 X 4, 200 X 2, 640 mm. The DEM model was centrally post
the DEM considering current model size and available computer
tioned with a size of 1,080 X 720 X 1, 140 mm, and the remaining
resources; howcvcr, it is both reasonable and practical to usc par
part was modeled with FLAC3D, in which the real physical param
ticles with the same diameters to investigate the macroscopic shear
eters and typical Mohr-Coulomb constitutive relationships were
behavior of the soil as long as the models containing unifornly
used
sized particles exhibit the same shear behaviors as those that in
To develop a naturally coupling ground, the initial stress in the
clude particles of various sizes(Feng and Owen 2014; Coetzee
inner pfc3d domain should match those in the outer FLAC3D
2017). Therefore, in this study, particles 8 mm in radius were zones. The initial stress in the pfc3d domain was calculated
dopted for modeling in PFC, considering the practicability of
and it varied with the depth increase. It was then imposed on
the model. The linear elastic contact model without bonds was used
the PFC3D model using the servoloading approach. The generally
to characterize the sand sample because it had extremely weak co
satisfactory agreement of the stresses in the three directions (o,o
hesion Specific calibrations were performed to obtain micropara
and o2) between FLAC3D and PFC3D zones is shown in Fig. 4
meters of the sand. Numerical direct shear models were iteratively
which indicates that the initial stress of the coupling ground
conducted to calibrate microparameters based on the shear stress coincided exactly with that of the FLAC model
curves obtained experimentally(Fig. 2). The microparameters of
the sand wcre subscqucntly obtained (Table 1)
Tunneling and Soil-Conditioning Parameters
The tunneling parameters of the soil entering and discharging the
Numerical model of epb shield
shield chamber are critical to the muck pressure in the chamber
Engineering-scale discrete-element simulation is highly time
and the ground response. In this study, three types of discharging
consuning, even using the slale-Df-the-arl DEM algorithm. This ratios(greater than 1, equal to 1, and less than 1)were performed
study did not aim to supply quantitative applications for specific numerically to analyze the muck and ground responses induced by
construction sites, but paid more attention to a general investigation
tunneling
Coupled Boundary
■■■■■■■■■■■■■■■■■■■■■■■■
ELAC Zones
■■■■■■■
Shield
PFC Balls
PFC Walls
C balls
(b)
Fig 3. Coupling model: (a) sketch plan along longitudinal section; and(b) 3D model (one-half)
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Table 2. Tunneling parameters of numerical EPB shield
Rotation rate
Discharge
Distance of one
Tunneling
Discharge
Advancing speed
of cutterhead
d of muck
tunneling cycle
Penetration
raul
(mm/s)
(rad/s)
(mm/s)
(Imrn
(mm/rad)
0.96
0.98
33333
796.23
150
10
1.0
30
887.6
150
1.02
30
981.4
150
30
1,639.2
150
Sensitivity analysis was performed at different tunneling speeds, selected carefully to characterize the improvement of the muck
and few impacts were found when the discharge ratio remained
The muck was conditioned typically by injecting an agent from
unchanged. Hence an advance speed of 30 mm/s was adopted cor
both the chamber bulkhead and the cutterhead in the epb shield
sidering the available computational resources. Corresponding
Here. in addition to the muck in the whole excavation chamber. a
enlarged muck-discharging speeds were selected considering the distance of D/8(wherc D is the excavation diameter) in front of the
suitable discharge ratios in the chamber. The actual discharge cutterhead was also assumed to be completely conditioned
speeds were hard to predetermine accurately because only the vol-
ume of particles was considered here, and the volume of porosity
Stress monitoring in DEM
amid the particles was not counted as a part of the muck. Here, the
The stress is originally derived based on a continuum assumption
actual discharge speeds were measured as 1639.2,. 4, 887.6,
and is thus not applicable for a discontinuous medium. To deter
796.2, and 680.6 mm/ s along the axis of the screw conveyor, cor-
mine the stress at certain points in the PFC domain, the approach of
responding to actual discharge ratios of 1.1, 1.02, 1.0, 0.98, and
using measurement spheres was used in the PFC3D program
0.96, respectively. Additionally, the penctration (ic, the ratio of
(Itasca Consulting Group 2003). The stress is calculated by aver
the advancing speed to the angular velocity of cutterhead rotation)
ging the contact forces on the measurement spheres. Care should
is normally in the range 6-40 mm/rad( Copur et al. 2014). Here
be taken to choose a suitable size for the measurement spheres to
penetration of 10 mm/rad was used; therefore, the rotation velocity
obtain reliable values for the stress. It was found that the radius ratio
of the cutterhead was set to 3 rad /s based on the designated
should be at least 5 to obtain a reliable stress. so the radius ratio was
advancing speed. Details of tunneling parameters are provided
determined to be 6 in this stud-
in table 2
To characterize soil conditioning during EPB shield tunneling,
particularly the incrcasing fluidity, the friction coefficient of the
Numerical results
particles was reduced. For verification, a series of slump tests
was carried ouL numerically in PFC3D. These tests are commonly
Distributions of muck pressure
adopted to evaluate soil conditioning during EPB shield tunneling
(Budach and Thewes 2015; Vinai et al. 2008; Ye et aL. 2017). Fig. 5
Muck pressure in front of chamber bulkhead
shows the variation of the slump value as a function of the friction
coefficient during 40,000 calculation steps; the slump value de
Fig. 6 shows the distribution of the muck pressure in front of
creased from 16.5 to 10.9 cm with an increase in the friction co
the chamber bulkhead before and after excavating a cycle (a width
cfficient from 0 to 3.3. This curve shows that the spccimcn with a
f 0.15 m)at different discharge ratios. Fig. 6(a) shows the stress
distribution of the muck particles directly in front of the chamber
the friction coefficient can reasonably characterize the growing flu
bulkhead prior to tunneling. The longitudinal stress of the muck
idity of the muck. In this study, a friction coefficient of 0.3 was
generally had an upward trend with increasing depth. Because of
the presence of the screw conveyor at the boton of the chanber
the longitudinal stress decreased locally around the screw conveyor
17
nlet. Similar findings were reported by Bezuijen et al. (2005)based
on their field monitoring results
The contour patterns for groups of tunneling cases were similar
to each other [Figs. 6(b-f)l, and three significant points were par
ticularly
15
Initial model Cyele ooo
1. The muck pressures in the back of the spokes were less than
Cycle 20000
014
those behind the opening of the cutterhead, because the spokes
directly bear the soil pressure roin natural ground during tun
Cycle 40000
13
neling instead of the muck behind them. The muck pressures
behind the spokes are released as the shield advances
2. The muck pressures near the screw conveyor remained small
◆ Slump value
because muck near the exiting area is continuously discharged
Fitted curve
and thus the muck remains in a loose and flowing state during
tunneling.
10
3. Left-side and right-side pressures at the same height were
0.5
3.5
ticeably different during excavation. As reported by mosar
friction coefficient
and Mooney(2015), the Snuck pressures on the left are greater
than those on the right when the cutterhead rotates counterclock
ig. 5. Slump values versus varying friction coefficients
wise facing the tunneling direction this is because the stress
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400
400
300
300
110
100
200
200
100
0
50
5050
100
6570
00
25
20
00
200
10
-300
0
300
Unit: kPa
Unit: kPa
400
-400
-400-300-200-1000100200300400
400-300-200-100010020030040C
(a)
x(mm)
(b)
x(mm)
400
40
300
300
118
200
200
100
尽
80
100
82
日0
8
-100
82E
200
200
20
-300
400
400
-400-300-200-1000100200300400
400-300-200-1000100200300400
x(mm)
400
300
300
135
180
200
125
200
105
75
会
-100
100
-200
200
115
300
Unit. kPa
Unit: kPa
-400
400
-400-300-200-1000100200300400
400-300-200-1000100200300400
(f)
x(mm)
Fig. 6. Distribution maps of longitudinal stresses for the muck in front of the chamber bulkhead with different discharge ratios: (a) prior to tunneling
(b)1.10;(c)1.02;(d)1.0;(e)0.98;and(f)0.96
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4321
Fig. 7. Arrangement of monitoring positions: (a)selected longitudinal monitoring points; and (b) arrangement of the measurement spheres in single
cross section
and density of the muck increase with an increase in depth in the excavating for a cycle, although few differences were found prior to
5四
presence of gravity: greater compression is expected when advancing. To be speci
sure difference before and
the spokes and mix arms rotate from the uppermost position to
behind the cutterhead occurs because the soils near the cutterhead
the bottommost position. In contrast, muck pressure may be re
are extruded by spokes during the tunneling of the shield. Due
leased when the spokes and mix arms rotate from the bottom
to the rotation of the cutterhead, soil particles that are originally
most position to the uppermost position, resulting in lower extruded by spokes might pass through the opening of the cutter
pressure
head; a sudden pressure difference thus occurs and pushes the soil
On the other hand, striking differences were captured among th
into the muck chamber. These passing actions make the soil con
tunneling cases with various discharge ratios. First, the muck pres
sume a large amount of potential energy and therefore are respon
sures changed inversely to the change in discharge ratios, which is
sible for decreased stress in the chamber. second. the epb shield
in line with common knowledge. Furthermore, negative correla- advances with the bulkhead of the chamber pushing the muck in the
tions were found between the discharge ratio and pressure differ
chamber forward during excavation. As a result, the pressures near
ences between the left and right sides This is because the rotation
the bulkhead are greater than those around the cutterhead, and th
of the cutterhead causes more evident disturbances for the denser pressure difference in the chamber always exists throughout the
muck. In the case of loose muck in the chamber, by contrast, the tunneling process. In addition, the muck pressure decreases with
rotation of the cutterhead affects the muck much less. Therefore, an increase in discharge ratio. Specifically, when the discharge ratio
the discharge ratio in the shield chamber has i negalive relation is 1.02 or 1. 1, the average muck pressures are less than those in the
with pressure differences between the left and right sides in th
ground prior to tunneling. This is because the muck quantity in the
chamber
chamber decreases gradually if the discharge ratio is greater than 1
and the decreasing muck quantity results in a lower pressure. I
Average Muck Pressure along Longitudinal Direction
contrast, when the discharge ratio is less than I, the muck quantit
To study the changes in pressures of both muck and ground during in the chamber increases gradually, and thus a larger pressure is
excavation, average muck pressures at selected cross sections
(Fig. 7)along the tunneling direction arc shown in Fig. 8. At first,
the pressures in front of the cutterhead were greater than those
atio in the chamber is shown in Fig. 9. Both the pressure diffe o
The relation between the pressure difference and discharge
in the chanber aller tunneling for a cycle. There were consid
ence before and after the cutterhead (Sections 4 and 3)and the
erable pressure differences at different longitudinal positions after
difference near the bulkhead and directly behind the cutterhead
140
……0.96
0.98
35
…)…1.0
2A…1.02
Section 4 and 3
●- Initial stress
30
Section 1 and 3
… Section4andl
100
Muck chamber
Cutterhead
……………3.…………◇
R2=0.9798
R2=0.907
×
-.
40
10
20
R2=0.984
50200
300
0.960.9811021.041061081.1
Y-coordinate(mm)
Discharge ratio
Fig. 8. Distribution of average longitudinal stresses with different Fig. 9. Pl
between specific sections against the
discharging ratios
discharge ratios
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(Sections I and 3)decreased gradually with an increase in discharge First, muck pressures at all the positions changed periodically
ratio. Particularly, the pressure difference almost disappeared when and had similar cycle periods, but the time to reach the peak muck
the discharge ratio was 1.1. On the other hand, for the pressure dif- pressure occurred at different times. Second, although the muck
ference near the bulkhead and directly behind the cutterhead, the pressures in the chamber changed periodically, their overall values
bulkhead extrudes the muck in the chamber slightly when there always remained stable during excavation due to a balanced
is only a limited muck quantity in the chamber. The pressure differ-
discharge ratio. In addilion. the pressure at Monitoring Poinls 3
ences before and behind the cutterhead remained nearly stable
and 5 exceeded the pressure at Monitoring Point 1, followed by
under various discharge ratios because this value results from ex- the pressures at Monitoring Points 2 and 4 in general, which is
trusion of spokes during tunneling and it is purely determined by the
consistent with the overall trend obtained previously
configuration of the cutterhead and penetration parameters. The dif-
Taking monitoring point 2 as an example in the numerical
ference between the right front of the cutterhead and the area near analysis, practical formulas for muck pressure were used to com
the bulkhead in the chamber has received considerable interest pare with these numerical outputs. The buried dep
pth of monitoring
(Wang 2012). When the discharge ratio is less than 1.0, this differ
Point 2 was 1, 101 mm, and the coefficient of lateral earth pressure
ence increases with a decrease in discharge ratio. Nevertheless, this
at rest(Ko) was 0.538. Thus, the lateral earth pressure at rest(Po)
pressure difference is weakly dependent on discharge ratio when the
can be calculaled as follows
discharge ratio exceeds 1.0
Po= KoPgh(1-n)
Changes of Muck Pressure in Chamber during
where p and n particle density and porosity, respectively, in
Excavation
PFC3D and h
depth of point 2
If calculated based on passive earth pressure(Pu)
To study the variation of muck pressure during shield tunneling,
several monitoring points were chosen near the bulkhead(Fig. 10)
Kp=tan2(45°+c/2)
at different heights in the chamber
Fig. 1l shows the changes in muck pressure at five selecte
Pp=kppgh(I-n
monitoring points during tunneling with a discharge ratio of 1
where K, coefficient of passive earth pressure; and a= internal
friction angle of the soil
A preparatory pressure from 10 to 20 kPa is normally added to
derive soil pressure in practice(Koizumi 1997). Because the model
MPI
MPI
is scaled 10 times, the current preparatory pressure should be
bctwccn I and 2 kPa. In this study, the preparatory prcssurc
MP2
MP2
was selected as roughly 1.2 kPa. The upper-limit earth pressure
(Pup, passive instability) and the lower limit of control pressure
MP3
置Mm3
(Plo, active instability) can thus be quantitively determined
b Adding the analytical upper and lower limit pressures to the
merical outputs in Fig. 12, some conclusions can be drawn
IMP
MP4
a linear relation was fitted to characterize the tendency in the aver-
MPS
MPS
age value of the muck pressure in the chamber. When the discharge
ratio was larger than 1, the slope of the fitted pressure curve was
Discharge area
Discharge area
negative, indicating that muck pressure in the chambcr decreased
gradually during tunneling. For the case in which the discharge ra
tio was less than l, the slope of the fitted pressure curve remained
MP: Monitoring Point
positive, meaning that the muck pressure increased as the shield
advanced. For the case in which the discharge ratio was 1, the pres
目
Fig. 10. Muck pressure monitoring points near bulkhead
sure curve remained generally horizontal. This indicates that the
discharge ratio had a negative relationship with muck pressure
Finally, under various cases of discharge ratios, the muck pressure
140
MP
----MP2
………MP3
at Monitoring Point 2 varied between the upper-and the lower-limit
MP4
MP5
pressures bascd on the stated passive and activc soil prcssurc
120
theory. However, based on the changing tendency, it can be
predicted that the muck pressure when the discharge ratio is more
than 1 or less than I will exceed these theoretically determined safe
scopes after multiple tunneling cycles with the same tunneling
parameters
Torque and Thrust during Tunneling
Changes in Thrust of Shield
Fig. 13 shows the changes in thrust during EPB shield tunneling for
12131415
groups of discharge ratios. Normally, a larger shield thrust occurs
Tunneling d stance(cm)
for the smaller discharge ratio. For specific tunneling cases, the
Fig. 11. Pressure changes in selected monitoring points during
thrust increases gradually when the discharge ratio is less than 1
tunnelin
during tunneling. In contrast, the thrust decreases when the dis
charge ratio exceeds 1 during excavation. In fact, the thrust mainly
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100
1.10
→)0.96
Upper limit of control pressure in chamber(passive instability)
8
千=
60c
38
0+8
o++ o
Lower limit of control pressure in chamber(active instability)
8910112131415
Tunneling distance (cm)
Fig. 12. Changes in muck pressure during tunneling with groups of discharge ratios
460
1.1
0.98
420
1.02
0.96
400
4
38
360
098
340
1.02
0.96
320
0
15
300
Tunneling distance(cm)
12
15
Tunneling distance(cm)
Fig. 14. Changes in torque of cutterhead caused by tunneling with
groups of discharge ratios
Fig. 13. Changes in shield thrust induced by tunneling with groups of
discharge ratios.
cutterhead also experiences a generally periodic change during the
excavation of the EPB shield. As previously discussed, the muck
arises from the resistance of the cutterhead, resistance of the bulk- pressure changes periodically hecause of the rotation of the cutter
head, and the friction force between the shield and the ground. head and the flow of the muck in the chamber. The changes of the
These resistances on both the cutterhead and the bulkhead increase muck pressure lead to measurable variations in the torque of the
as the muck pressure grows. Conversely, a decrease in muck pres
cutterhead, which reasonably explains the fluctuations of torque
sure gives rise to a decrease in shield thrust. In general, the dis-
charge ratio changes the thrust of the shield by ch
muck pressure during tunnelin
Surface Settlement by Shield Tunnelling
The discharge ratio is a key factor for various responses in the
Changes in Torque of Cutterhead
ground. Fig. 15 shows the cross-section surface settlement induced
Apart from the variation of thrust in the EPb shield, the discharge by numerically tunneling for a cycle with groups of discharge ra-
ratio has a close relation to the torque of the cutterhead. Fig. 14 lios. The surface heaved up slightly for the cases with discharge
shows the changes in the torque of the cutterhead during tunneling ratios of 0.98 and 0.96, and there was a negative relation between
for a series of discharge ratios. Basically, a larger torque of the cut
the uplift volume and the discharge ratio for these cases. The set
terhead occurs at a smaller discharge ratio. The torque of the cutter
tlement was quite small for the case with a discharge ratio of 1.0
head arises from the stirring arms, cutting torque, and frictional
and thus this part of result is not further discussed. In contrast. the
torque between the shield shell and the muck or the ground When settlements for cases with discharge ratios of 1.02 and 1.10
the muck pressures increase because of a continuous low discharge had relatively higher values. Based on the previous discussion,
ratio during excavation, the stirring arms in rotation are forced to was concluded that the discharge ratio determines the variation
bear an increasing load. Furthermore, the increasing muck pressure trend for surface settlement by changing the muck pressure in
gives rise to an increase in the friction-induced torque of the cutler
the chanber lo a great extent
head. Both of these changes are responsible for the growth in
It is well-known that the ground loss induced by tunneling can
the torque of the cutterhead. On the other hand, the torque of the
be obtained by using the actual excavation volume minus the
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0.2
x-coordinate(mm)
Discussion
-4000-3000-200000
200030004000
0.2
As mentioned previously, the soil in front of the cutterhead is inevi
tably extruded by the spokes and panel of the cutterhead during
◆041芒
the epb shield excavation Therefore. the soil in front of the cutter
0.6
▲1.02
head always bears greater pressure regardless of the muck pressure
This prcssurc can be roughly calculated based on the type of
-0.8
x1.0
Letterhead
◆1.0
×098
Specifically, the current cutterhead can be approximately divided
2苏
0.96
into lwo areas during rolation (Fig. 16). The inner area(r< r1)
is the panel with fishtail cutters, and the outer area(rI
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