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ISSAEST, Fairbanks, AK, USA, August 2-5, 2015
Mechanical behavior of piled-raft foundation
for high-speed railway subjected to train
loading
Linlin Gu, Ph.D. stdnt., Geotechnical Engineering
Nagoya Institute of Technology
Guanlin Ye, Ph.D., Geotechnical Engineering
Shanghai Jiaotong University
Xiaohua Bao, Ph.D., Geotechnical Engineering
Shenzhen University
Feng Zhang, Ph.D., Geotechnical Engineering
Tongji University
August 5, 2015
ISSAEST, Fairbanks, AK, USA, August 2-5, 2015
Outline
Introduction
Description of the case history
Constitutive model for soils and foundation
Numerical simulation
Results and discussion on settlement and
EPWP of subgrade ground
Results and discussion on response of piles
Conclusion
2
ISSAEST, Fairbanks, AK, USA, August 2-5, 2015
Introduction
3
• High-speed railways (speed: 300km/h) are being constructed intensively in Yangtze
River Delta.
• The subgrade soils of the railways are mostly the so-called Shanghai soils with large
water content, high compressibility and low shear strength.
• After the operation of the trains, the ground may settle significantly when subjected to
cyclic train loading if it were not properly designed and constructed.
How to effectively control the settlement of the foundation of the high-speed railway
“Empirical methods” with fitting formula or numerical simulation based on some
primitive constitutive models were used to calculate the ground settlement and
change of EPWP during and after the train vibration. Unfortunately, were not
accurate enough and above all, lack of rationality.
Traditional methods…
EPWP: Excess pore water pressure
ISSAEST, Fairbanks, AK, USA, August 2-5, 2015
Introduction
4
This research …
Numerical simulation based on
Cyclic Mobility Model (Zhang et
al.2007, 2011)
describe properly the soils subjected to
different loadings, dynamic or static, under
different drained conditions in a unified way
investigate
Behavior of piled-raft foundation during
the train loading but also in post-loading
consolidation (simulation result)
Monitoring data within
one month
compare
Performance of this numerical simulation
(the changes of settlement and EPWP)
demonstrate
ISSAEST, Fairbanks, AK, USA, August 2-5, 2015 5
Description of the case history
60
13.2
06.8
08.2
28.7
312.4
15.7
74.0
3
6.0
0
58.1
14.8
23.6
0
F
12
A3 C3B3
A2 B2 C2
A1 B1 C1
1
2
3
4
5
6
7
8
9
10
A1 B1 C1
A2 B2 C2
A3 C3B3
Ⅰ Ⅱ Ⅲ
Artificial fillClayey soil
Silty clay
Mucky soil
Silty clay
Mucky soil
Silty clay
Silty clay
Silty clay
Silty sand
Survey points
ISSAEST, Fairbanks, AK, USA, August 2-5, 2015 6
Description of the case history
Piled-raft foundation
Plane view Sectional view
ISSAEST, Fairbanks, AK, USA, August 2-5, 2015 7
Description of the case history
60
13.2
06.8
08.2
28.7
31
2.4
15.7
74.0
3
6.0
0
58
.1
14.8
23.6
0
F
12
A3 C3B3
A2 B2 C2
A1 B1 C1
1
2
3
4
5
6
7
8
9
10
A1 B1 C1
A2 B2 C2
A3 C3B3
Ⅰ Ⅱ Ⅲ
Artificial fillClayey soil
Silty clay
Mucky soil
Silty clay
Mucky soil
Silty clay
Silty clay
Silty clay
Silty sand
a thickness of 2-3m,
crusty layer
high plasticity, the softest
stratum, a sensitivity of
about 4.5-5.5
less sensitivity (about 3-
3.5)
dense fine sandy layer,
the supporting layer of
the pile
Shanghai Soil
Horizontal distributed Grain size distribution
Undisturbed samples from No-2 and No-9 layers sampled using a
Shelby thin-walled tube sampler.
Undisturbed samples from No-4 layer at the depth of 10m were taken
with block sampling method.
ISSAEST, Fairbanks, AK, USA, August 2-5, 2015
Constitutive model for Shanghai soils
8
A kinematic hardening elastoplastic model using an associated flow rule, initially
proposed by Zhang et al. (2007, 2011)
Describe the mechanical behavior of a soil with different density, subjected to
different loading (monotonic or cyclic) under different drained condition, in a
unified way by considering the effects of stress-induced anisotropy, density, and the
structure formed during the natural deposition process.
Cyclic Mobility Model
-60
-40
-20
0
20
40
60 -0.1
-0.05
0
0.05
0.10 0.1 0.2 0.3 0.4
q-simulationq-test
v-simulation
v-test
Volu
metric
strain
v
Devia
tor
stre
ss q
(kP
a)
Shear strain s
-200
-100
0
100
200 -0.06
-0.03
0
0.03
0.060 0.03 0.06 0.09 0.12
q-simulationq-test
v-simulation
v-test
Shear strain s
Volu
metric strain
v
Dev
iato
r st
ress
q (
kP
a)
-1500
-1000
-500
0
500
1000
1500 -0.03
-0.02
-0.01
0
0.01
0.02
0.030 0.05 0.1 0.15 0.2 0.25
q-simulationq-test
v-simulation
v-test
Shear strain s
Volu
metric strain
v
Dev
iato
r st
ress
q (
kP
a)
Clayey soil (No-2 layer) Clayey soil (No-4 layer) Sandy soil (No-9 layer)
Test: Drained monotonic triaxial test
Verify
ISSAEST, Fairbanks, AK, USA, August 2-5, 2015
Constitutive model for piled-raft foundation
9
Parameters piles Raft
Young’s modulus E (kPa) 3.25×107 3.25×107
Cross sectional area A (m2) 0.0784 -
Inertia moment I (m4) 1.23×10-3 -
Density ρ(t/m3) 2.42 2.42
Poisson’s ratio ν 0.200 0.200
Material parameters of piles and raft
Read-made
concrete
Raft is described by isoparametric solid elements with a linear elasticity.
Pile is modeled with beam element, described by a trilinear model
considering the hysteresis effect of cyclic loading, the first, second and
ultimate yielding moments of the pile, Mc, My and Mu are 150, 190 and 200
kN·m, respectively.
ISSAEST, Fairbanks, AK, USA, August 2-5, 2015
Numerical simulation
10
Code: DBLEAVES (Ye, 2007; Ye, 2011; Jin et al. 2010; Xia et al. 2010; Bao et al.
2012; Morikawa et al. 2011)
drainage boundary200 m 200 m30 m 30 m
imp
erv
iou
s
imp
ervio
us
equal displacement condition equal displacement condition
Node:1113
Element:1040
train
impervious
FEM mesh used in the numerical calculation
CRH2 type with a speed of 300 km/h,
length is 201.4m
ISSAEST, Fairbanks, AK, USA, August 2-5, 2015
Numerical simulation
11
Excitation force F is expressed with a function superimposed by a
series of sine functions. (Liang et al. 1999)
Duration: 2.42s
Maximum value: 97.6 kN (compression)
-100
-80
-60
-40
-20
0
0 0.5 1 1.5 2 2.5
t (sec)
Exci
tati
on f
orc
e F
(kN
)
ISSAEST, Fairbanks, AK, USA, August 2-5, 2015
Numerical simulation
12
Scenario of the calculation in one day
Calculating stage number
1 2 3 4 5 6 7 8 9 10
The type of loading D C D C D C D C D C
Duration time at one
stage (sec) 2.42 5400. 2.42 5400. 2.42 5400. 2.42 5400. 2.42 5400.
Time interval of each
integration step (sec) 0.01 1.0 0.01 1.0 0.01 1.0 0.01 1.0 0.01 1.0
Integration steps 24200 5400 24200 5400 24200 5400 24200 5400 24200 5400
Calculating stage number
11 12 13 14 15 16 17 18 19 20
The type of loading D C D C D C D C D C
Duration time at one
stage (sec) 2.42 5400. 2.42 5400. 2.42 5400. 2.42 5400. 2.42 37776.
Time interval of each
integration step (sec) 0.01 1.0 0.01 1.0 0.01 1.0 0.01 1.0 0.01 1.0
Integration steps 24200 5400 24200 5400 24200 5400 24200 5400 24200 37776
dynamic loading = D
consolidation = C
ISSAEST, Fairbanks, AK, USA, August 2-5, 2015
Numerical simulation
13
Parameter 1 2 3 4 5 6 7 8 9 10
Compression index λ 0.235 0.0600 0.132 0.140 0.135 0.135 0.130 0.130 0.0500 0.130
Swelling index κ 0.066 0.0050 0.066 0.066 0.066 0.0064 0.066 0.064 0.012 0.066
Stress ratio at critical state Μ
1.20 1.20 1.30 1.30 1.40 1.40 1.18 1.30 1.45 1.24
Void ratio N (p’=98 kPa on N.C.L.) 0.94 0.68 1.0 0.86 0.84 0.86 0.70 0.79 0.69 0.86
Poisson’s ratio ν 0.35 0.32 0.38 0.38 0.35 0.35 0.35 0.28 0.25 0.28
Parameter of overconsolidation m 2.0 1.0 4.0 5.0 1.5 1.5 1.5 1.2 0.020 1.5
Parameter of structure a 0.010 0.010 0.10 0.10 0.10 0.10 0.10 0.050 1.5 0.10
Parameter of anisotropy br
0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.5 0.00
Material parameters of soils
Initial values of state variables of soils Parameter 1 2 3 4 5 6 7 8 9 10
Void ratio e0 1.10 0.757 1.08 0.860 0.815 0.825 0.630 0.750 0.650 0.800
Mean effective stress
p’(kPa) 20.9 32.7 59.9 98.8 111 190 242 249 284 355
Degree of structure R0* 0.50 0.70 0.30 0.20 0.60 0.60 0.80 0.80 0.80 0.60
Overconsolidation OCR
(1/R0) 1.00 6.50 1.20 1.20 1.25 1.20 3.00 2.00 10.0 1.20
Anisotropy ζ0 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
ISSAEST, Fairbanks, AK, USA, August 2-5, 2015
Numerical simulation
14
Element behavior of soils
-6
-3
0
3
6
0 5 10 15 20 25
Effective stress p' (kPa)
Dev
iato
r st
ress
q (
kP
a)
No 2 layer
-15
-10
-5
0
5
10
15
30 45 60 75 90
Effective stress p' (kPa)
Dev
iato
r st
ress
q (
kP
a)
No 4 layer
-100
-50
0
50
100
0 100 200 300 400 500 600
Effective stress p' (kPa)
Dev
iato
r st
ress
q (
kP
a)
No 9 layer
Effective stress path
-6
-3
0
3
6
-0.1 -0.05 0 0.05 0.1
Shear strain s
Dev
iato
r st
ress
q (
kP
a)
No 2 layer-15
-10
-5
0
5
10
15
-0.02 -0.01 0 0.01 0.02
Shear strain s
Dev
iato
r st
ress
q (
kP
a)
No 4 layer
-100
-50
0
50
100
-0.02 -0.01 0 0.01 0.02
Shear strain s
Dev
iato
r st
ress
q (
kP
a)
No 9 layer
Stress-strain relations
ISSAEST, Fairbanks, AK, USA, August 2-5, 2015
Numerical simulation
15
-0.1
-0.08
-0.06
-0.04
-0.02
0
0 10 20 30 40
SimulationSurvey
t (d)
Set
tlem
ent
(m)
A1
-0.1
-0.08
-0.06
-0.04
-0.02
0
0 10 20 30 40
SimulationSurvey
t (d)S
ettl
emen
t (m
)
B1
-0.1
-0.08
-0.06
-0.04
-0.02
0
0 10 20 30 40
SimulationSurvey
t (d)
Sett
lem
en
t (m
)
C1
0.057
0.040
0.089
0.052
0.087
0.050
largest settlement
Excitation force in calculation is assigned to be the commuter trains passing at the
same time,while,it is rare that two trains in different directions passed through the
monitoring section at the same time.
Changes in settlements at prescribed points within one month
ISSAEST, Fairbanks, AK, USA, August 2-5, 2015
Numerical simulation
16
-0.1
-0.08
-0.06
-0.04
-0.02
0
0 10 20 30 40
t (d)
Sett
lem
en
t (m
)
A2
-0.1
-0.08
-0.06
-0.04
-0.02
0
0 10 20 30 40
t (d)
Sett
lem
en
t (m
)
B2
-0.1
-0.08
-0.06
-0.04
-0.02
0
0 10 20 30 40
t (d)
Sett
lem
ent
(m)
C2
0.088 0.089 0.089
-0.1
-0.08
-0.06
-0.04
-0.02
0
0 10 20 30 40
t (d)
Set
tlem
ent
(m)
A3
-0.1
-0.08
-0.06
-0.04
-0.02
0
0 10 20 30 40
t (d)
Set
tlem
ent
(m)
B3
-0.1
-0.08
-0.06
-0.04
-0.02
0
0 10 20 30 40
t (d)
Set
tlem
ent
(m)
C3
0.089 0.089 0.087
Changes in settlements at prescribed points within one month
Settlement: A2≈B2≈C2, A3≈B3≈C3
Relative deformation of the soils within the piles is also very tiny due to the
interaction of the piles and the soils.
ISSAEST, Fairbanks, AK, USA, August 2-5, 2015
Results and discussion on EPWP of subgrade ground
17
-1
0
1
2
3
0 10 20 30 40t (d)
EP
WP
(kP
a)
A1
-1
0
1
2
3
0 10 20 30 40
t (d)
EP
WP
(kP
a)
B1
-1
0
1
2
3
0 10 20 30 40
t (d)
EP
WP
(kP
a)
C1
No-2 layer (clayey soil)
Changes in EPWP within one month
Turned negative
A cyclic process of growth and dissipation, but mainly in zero level.
Even if the raft has a much larger stiffness than those of piles, the
responses at different places may be quite different.
Soil beneath the loading point (C1) should settle more severely than the
other places, however, due to the condition that the soil and the raft are
connected, the soil could not settle, resulting in a negative EPWP.
ISSAEST, Fairbanks, AK, USA, August 2-5, 2015
Results and discussion on EPWP of subgrade ground
18
No-6 layer (mucky soil)
Changes in EPWP within one month
-2
0
2
4
6
8
10
0 10 20 30 40
t (d)
EP
WP
(kP
a)
A2
-2
0
2
4
6
8
10
0 10 20 30 40
t (d)E
PW
P (
kP
a)
B2
-2
0
2
4
6
8
10
0 10 20 30 40
t (d)
EP
WP
(kP
a)
C2
up
No-9 layer (silty fine-grained sand)
Changes in EPWP within one month
-0.5
0
0.5
1
1.5
2
2.5
0 10 20 30 40t (d)
EP
WP
(kP
a)
A3
-0.5
0
0.5
1
1.5
2
2.5
0 10 20 30 40
t (d)
EP
WP
(kP
a)
B3
-0.5
0
0.5
1
1.5
2
2.5
0 10 20 30 40
t (d)
EP
WP
(kP
a)
C3
Poor
drainage
capacity
Limited drainage
ability during the
vibration, EPWP
accumulated easily,
but it could dissipate
completely after a
period time.
ISSAEST, Fairbanks, AK, USA, August 2-5, 2015 19
Results and discussion on EPWP of subgrade ground
3.75 kPa 6.50 kPa 9.60 kPa
EPWP distribution at different times (Unit=kPa)
EPWP mainly concentrated in the two sides of group pile within No-4,
No-5 and No-6 layers, so the soils within the group piles were less
deformed.
(10 days) (20 days) (30 days)
ISSAEST, Fairbanks, AK, USA, August 2-5, 2015 20
Results and discussion on response of piles
Length of the pile l=39.35m, diameter D=0.5m, frictional pile
0
30
60
90
120
0 10 20 30 40
Pile 1
tipmiddlehead
Ax
ial
stre
ss (
kN
)
t (d)
-40
0
40
80
120
0 10 20 30 40
Pile 2
tipmiddlehead
t (d)
Ax
ial
stre
ss (
kN
)
-80
-40
0
40
80
0 10 20 30 40
Pile 3
tipmiddlehead
t (d)
Axia
l st
ress
(kN
)
Changes of axial stress of the piles within one month
upward downward transition
Relative movement to soil:
EPWP at C1 (right beneath the loading point) vibrated mostly and negative EPWP
occurred, resulting in tensile axial force at the head of pile 3.
For pile 2, the axial forces at the head and the middle part were almost equal to
zero, taking an even value of pile 1 and pile 3.
At pile tip, the values of the compressive axial forces of the piles were in the
order of pile 1, 2 and 3.
ISSAEST, Fairbanks, AK, USA, August 2-5, 2015 21
Results and discussion on response of piles
-40
-30
-20
-10
0
-20 -10 0 10 20 30
Pile 1Pile 2Pile 3
Bending moment (kN·m)
Dep
th o
f th
e pil
es (
m)
-40
-30
-20
-10
0
-20 -10 0 10 20 30
Pile 1Pile 2Pile 3
Shear force (kN)D
epth
of
the
pil
es (
m)
-40
-30
-20
-10
0
-100 0 100 200 300
Pile 1Pile 2Pile 3
Axial force (kN)
Dep
th o
f th
e pil
es (
m)
Free end
symmetrically central line
Increase dramatically
Pile 1> Pile 2
Uneven settlement of the soils due to the interaction between the piles
and the soils resulted in relative large bending moment.
Change of shear force followed the change of bending moment.
Distribution of sectional forces after one-month trial operation
ISSAEST, Fairbanks, AK, USA, August 2-5, 2015 22
Conclusion
1. High-speed railway is constructed in Shanghai soils, a
very soft diluvial ground, considerable settlement and
EPWP happened due to the cyclic train loading. Both
field observation and calculation give the same
tendency.
2. In the calculation, the mechanical behavior of the
foundation and surround soils is considered not only
during the train loading but also in post-loading
consolidation. The calculation is conducted with a
series of dynamic/static analyses in unified sequential
way strictly coincident with the field history.
ISSAEST, Fairbanks, AK, USA, August 2-5, 2015 23
Conclusion
3. The accuracy of the calculation is assured with the
fact that the FE-FD analysis is based on a
constitutive model that can describe properly the soils
subjected to different loadings, dynamic or static,
under different drained conditions in a unified way.
4. The mechanical behaviors of the piled-raft and the
soils, e.g., the accumulation of settlement and EPWP,
the distributions of EPWP, the sectional forces of
piles, are on the whole well described by the
calculation.
ISSAEST, Fairbanks, AK, USA, August 2-5, 2015