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MODELING OF SEISMIC SLOPE BEHAVIOR WITH SHAKING TABLE TEST
Meei-Ling Lin and Kuo-Lung WangDepartment of Civil Engineering, National Taiwan University
The Next Generation of Research on Earthquake-induced LandslidesAn International Conference in Commemoration of 10th Anniversary of the Chi-Chi Earthquake, 2009
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Outline
• Shaking table test
• Specimen preparation and law of similarity
• Test result
• Particle Image Velocimetry (PIV) analysis
• Displacement behavior
• Summary
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Objectives
The initiation of landslide and the development of slip surface for landslides induced by earthquakesRun-out distance and slope recession caused by landslideIdentification of affected area of potentially unstable slope
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4
Model Slope Shaking Table Test System calibration
100
440
120
50
177
AC7AC8
AC9
AC10
AC12,AC13
AC11
L1,L2
L3,L4
AC1,AC2
AC3,AC5
AC4,AC6
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0 5 10 15 20 25
Time(sec)
Accce
lera
tio
n(g
)
m: 39838 kgk: 551.9kN/m c: 174.3 kN.sec/m
Insignificant amplification were found from accelerometer and LVDT measurements
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Law of Similitude• Assumptions (Iai, 1989)
– soil skeleton is regarded as continuous medium– deformation is assumed to be small so that the equilibrium equation
remains the same before and after the deformation– the strain of the soil skeleton is small
• 8.9 Hz of loading frequency was applied for a scale factor of 20 based on 1-g, equivalent density, and strain conditions
Mass Density 1 Acceleration 1 Length λ
Force λ 3 Shear Wave Velocity λ 1/2 Stress λ
Stiffness λ 2 Time λ 1/2 Strain 1
Modulus λ Frequency λ -1/2 EI λ 5
Meymand(1998)
33
3
3
1
mm
pp
mm
pp
m
p
V
V
am
am
F
F
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Model Granular Slope Shaking Table Test Specimen Preparation
• Sand– Uniform, medium, poorly graded sand (SP, Unified Soil Classification
System)• Preparation method
– Compaction – Dry pluviation
Pluviation equipment attached on the model box
Sieve
Sampling container
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7
Study on boundary effects FLAC (Version 4.00)
LEGEND
11-May-04 19:53 step 20425 2.511E-01 <x< 4.498E+00 -1.576E+00 <y< 2.671E+00
Max. shear strain increment 0.00E+00 5.00E-03 1.00E-02 1.50E-02 2.00E-02 2.50E-02 3.00E-02 3.50E-02 4.00E-02 4.50E-02
Contour interval= 5.00E-03
-1.250
-0.750
-0.250
0.250
0.750
1.250
1.750
2.250
0.500 1.000 1.500 2.000 2.500 3.000 3.500 4.000
JOB TITLE : 1:1:1 ssi
Itasca Consulting Group, Inc. Minneapolis, Minnesota USA
1:1:1 FLAC (Version 4.00)
LEGEND
11-May-04 19:54 step 21011 2.511E-01 <x< 4.498E+00 -1.576E+00 <y< 2.671E+00
Max. shear strain increment 0.00E+00 5.00E-04 1.00E-03 1.50E-03 2.00E-03 2.50E-03 3.00E-03 3.50E-03 4.00E-03 4.50E-03
Contour interval= 5.00E-04
-1.250
-0.750
-0.250
0.250
0.750
1.250
1.750
2.250
0.500 1.000 1.500 2.000 2.500 3.000 3.500 4.000
JOB TITLE : 2:1:2 ssi
Itasca Consulting Group, Inc. Minneapolis, Minnesota USA
2:1:2
FLAC (Version 4.00)
LEGEND
11-May-04 19:56 step 23116 2.511E-01 <x< 4.498E+00 -1.576E+00 <y< 2.671E+00
Max. shear strain increment 0.00E+00 5.00E-04 1.00E-03 1.50E-03 2.00E-03 2.50E-03
Contour interval= 5.00E-04
-1.250
-0.750
-0.250
0.250
0.750
1.250
1.750
2.250
0.500 1.000 1.500 2.000 2.500 3.000 3.500 4.000
JOB TITLE : 3:1:3 ssi
Itasca Consulting Group, Inc. Minneapolis, Minnesota USA
3:1:3
30 cm base thickness is chosen after analysis
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8
Specimen preparation - compaction
slope modeling tool
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9
Instrumentation and loading sequence
30100
440
177
86
177
E-W Accelerometer
Z Acclerometer
AC AC8AC9
AC10AC12, AC13
AC11
L1,L2
L3,L4
AC1,AC
AC3,AC5
AC4,AC6
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
0 5 10 15 20 25 30 35
Time(sec)
Acce
lera
tio
n(g
)
First loading sequence
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10
-1.00
-0.80
-0.60
-0.40
-0.20
0.00
0.20
0.40
0.60
0.80
1.00
20.5 20.6 20.7 20.8 20.9 21.0 21.1 21.2 21.3 21.4 21.5
Time(sec)
Acc
ele
ratio
n(g
)
AC8
AC12
Input Acc.
input amplitude from 0.4g to 0.5g
-1.00
-0.80
-0.60
-0.40
-0.20
0.00
0.20
0.40
0.60
0.80
1.00
25.5 25.6 25.7 25.8 25.9 26.0 26.1 26.2 26.3 26.4 26.5
Time(sec)
Acc
ele
ratio
n(g
)
AC8
AC12
Input Acc.
Outward slope
Inward slope
input amplitude from 0.5g to 0.6g
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11
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
26.20 26.25 26.30 26.35 26.40
Time(sec)
Acc
ele
ratio
n(g
)
AC8
AC9
AC10
AC11
AC12
input acceleration amplitude of 0.6g
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12
0.8
0.9
1.0
1.1
1.2
1.3
1.4
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Peak acceleration(g)
Am
plifi
catio
n fa
ctor
Amp. AC12/AC8
Amp. AC12/AC7
linearnon linear
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Specimen Preparation - Pluviation
30cm
50cm 30°
100 cm
253.4 cm
Specimen Unit weight(kN/m3)
Preparation Method
BoundaryTreatment
A 15.3 Pulviation Grease
B 15.8 Pulviation Grease w/ plastic sheet
C 15.8 Pulviation Grease w/ plastic sheet
D 15.5 Excavation afterPulviation
Grease w/ plastic sheet
E 15.5 Excavation afterPulviation
Grease w/ plastic sheet
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Instrumentation and Measurement
Reference frame
Shaking table
Accelerometers
• Acceleration by accelerometers• Image video recordings, particle displacement, particle velocity • Mapping of slip and deposit surface, mapping of run-out and
recessional line
Video camera (CCD)
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Loading Sequences
SpecimenMaximum Loading
(H, V) in g Loading History
A 1st - (0.35, 0.00)
2nd - (0.58, 0.00)
B 1st - (0.28, 0.00)
2nd - (0.43, 0.00)
C 1st - (0.34, 0.08)
2nd - (0.41, 0.20)
D 1st - (0.26, 0.10)
2nd - (0.32, 0.19)
E 1st - (0.38, 0.12)
2nd - (0.38, 0.12)
-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0 2 4 6 8 10 12 14 16 18
Time (sec)
Acc
eler
atio
n (g
)
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0 2 4 6 8 10 12 14 16 18 20
Time (sec)
Acce
lera
tion
(g)
AchieveLat(g)AchievedVert(g)
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0 5 10 15 20 25
Time(sec)
Acc
eler
atio
n(g)
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0 5 10 15 20 25 30 35
Time (sec)
Acc
eler
atio
n (g
)
Table_achive_EW(g)
Table_achive_V(g)
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0 5 10 15 20 25 30 35 40 45
Time (sec)
Acc
eler
atio
n (g
)
AchieveLat(g)
AchievedVert(g)
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16
Specimen B
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17
Instrumentation and loading sequence
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0 2 4 6 8 10 12 14 16 18
Time (Sec)
Accele
ra
tio
n (g
)
First loading sequence
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18
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
9.5 9.55 9.6 9.65 9.7 9.75 9.8 9.85 9.9 9.95 10
Time (sec)
Acce
leration
(g
)
AC8(g)
AC9(g)
AC10(g)
AC12(g)
AC15(g)
0.80
0.85
0.90
0.95
1.00
1.05
1.10
1.15
1.20
1.25
0 0.05 0.1 0.15 0.2 0.25 0.3
Peak acceleration of AC8(g)
Am
plification
facto
r
AC12/AC8
AC10/AC8
AC15/AC8
AC9/AC8
possible sliding
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19
Specimen C
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Instrumentation and loading sequence
First loading sequence
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0 5 10 15 20 25 30 35
Time (sec)
Acce
leration
(g)
Table_h
Table_v
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-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
24.0 24.1 24.1 24.2 24.2 24.3 24.3 24.4 24.4 24.5 24.5
Time (sec)
Acce
lera
tio
n (
g)
AC7(g)
AC8(g)
AC9(g)
AC10(g)
AC12(g)
-0.60
-0.50
-0.40
-0.30
-0.20
-0.10
0.00
0.10
0.20
0.30
0.40
0.50
21.5 22.0 22.5 23.0 23.5 24.0 24.5 25.0
Time (sec)
Acce
lera
tio
n (
g)
Table_achive_EW(g)
AC7(g)
AC12(g)
0.3g
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22
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0 5 10 15 20 25 30 35
Time (sec)
Acc
ele
ratio
n (
g)
Vertical acceleration response
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23
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
1.2
1.3
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
Peak acceleration of AC8 (g)
Am
plifi
catio
n fa
ctor
AC12/AC8
AC10/AC8
AC9/AC8
slipping with separation
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Test Result – the Initiation of Slip
• Surface change detection via particle image velocimetry (PIV)– Particle moving direction and
magnitude– The initiation of slope surface slip
• Identification of slip initiation from acceleration history– The initiation of subsurface slope
slip
Specimen C
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
0.4
0.5
0 5 10 15 20 25 30 35
Time (sec)
Acc
ele
ratio
n (
g)
Table_achive_EW(g)
AC12(g)
crest
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Test Result – Video Recording and PIV Analysis
Processed with PIVview2C
Note: play video files
CrestCrest
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Test Result – the Initiation of Slip
Specimen Loading amplitude (g) from PIV
Loading amplitude (g)/Time (sec) from acceleration history
A 0.11 0.35g, 11sec
B N/A 0.28g, 4.04sec
C 0.09 0.32g, 22.04sec
D 0.15 0.24g, 25.2sec
E N/A 0.24g, 9.85sec
Initiation of surface slipInitiation of subsurface slip
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Runt-out and Recessional Distances
Specimen A
Specimen B
Specimen C
CrestToe
unit: cm
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Run-out and Recessional Distances
Specimen D
Specimen E
CrestToe
unit: cm
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Relationship Between Distances and Loadings
Specimen Unit weight(kN/m3)
Maximum Loading Amplitude(H, V) in g
Loading Period(sec)
Crest Displacement
Max/Min
(cm)
Toe Displacement
Max/Min(cm)
A 15.3 1st - (0.35, 0.00)
2nd - (0.58, 0.00)
1st - 21 sec
2nd - 11 sec
43.5/22.1 28.6/19.1
B 15.8 1st - (0.28, 0.00)
2nd - (0.43, 0.00)
1st - 14 sec
2nd - 14 sec
12.7/8.6 18.5/10.3
C 15.8 1st - (0.34, 0.08)
2nd - (0.41, 0.20)
1st - 32 sec
2nd - 32 sec
26.7/21.8 45.6/22.6
D 15.5 1st - (0.26, 0.10)
2nd - (0.32, 0.19)
1st - 32 sec
2nd - 32 sec
12.6/8.0 17.2/6.3
E 15.5 1st - (0.38, 0.12)
2nd - (0.38, 0.12)
1st - 16 sec
2nd - 16 sec
11.4/7.7 15.8/5.7
Values after prolong loading sequence
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Comparing specimens (A, B) and (C, D) Recessional and run-out distance increased with increasing maximum loading amplitudeThe set of data with larger displacement were subjected to higher vertical loading coupled with higher horizontal loading
Comparing specimens (B, C)Recessional and run-out distance increased with additional vertical loading amplitude
Comparing specimens (D, E) and (C, E)Higher vertical loading resulted in higher recessional and run-out distances
0
5
10
15
20
25
30
35
40
45
50
0.3 0.35 0.4 0.45 0.5 0.55 0.6
Maximun loading amplitude (g)
Max
imum
dist
ance
(cm
)
RecessionalRun-out
0
5
10
15
20
25
0.3 0.35 0.4 0.45 0.5 0.55 0.6
Maximum loading amplitude (g)
Min
imum
dist
ance
(cm
)
RecessionalRun-out
Maximum distances
Minimum distances
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The Relationship Between Crest Recession and Toe Run-out versus Loading Amplitude
y = 15.274x2 - 11.392x + 2.3379R2 = 0.999
y = 4.8699x2 - 3.4769x + 0.9517R2 = 0.9872
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0.30 0.35 0.40 0.45 0.50 0.55 0.60Maximum loading amplitude (g)
Nor
mal
ized
to s
lope
hei
ght
RecessionalRun-outPolynomial (Recessional)Polynomial (Run-out)
y = 2.7462x2 - 1.437x + 0.294R2 = 0.9664
y = 6.3613x2 - 4.6475x + 0.9973R2 = 0.9995
0.0
0.1
0.2
0.3
0.4
0.5
0.30 0.35 0.40 0.45 0.50 0.55 0.60Maximum loading amplitude (g)
Nor
mal
ized
to s
lope
hei
ght
Recessional
Run-out
Polynomial (Run-out)
Polynomial (Recessional)
Maximum distances
Minimum distances
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Potentially Affected Zone
Restricted exploitation area
Sand, gravel
The 0.58g loading amplitude of specimen A resulted in highest recessional distance
The vertical acceleration for specimen C could result in larger run-out and recessional distances at the crest
Toe Crest
Slope height, H=50 cm
1/2H1/2H
H H
AABBCCDDEE
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Newmark’s analysis – specimen A
FLAC
After test
Khy=0.29
Jibson et al. (2000)
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Input acceleration history – specimen 2
-400
-300
-200
-100
0
100
200
300
400
0 5 10 15 20 25
Time (sec)
Acc
eler
atio
n (c
m/s
ec/s
ec)
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Exceeding acceleration and integrated velocity
0
10
20
30
40
50
60
70
0 5 10 15 20 25
Time (sec)
Accele
ratio
n (cm
/sec/sec)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 5 10 15 20 25
Time (sec)
Velo
city (cm
/sec)
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Integrated displacement
0
0.1
0.2
0.3
0.4
0.5
0.6
0 5 10 15 20 25
Time (sec)
Dis
plac
emen
t (cm
)
0.532 cm
10.64 cm forprototype
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37
Parameters and boundary conditions
Unit weight
(kN/m3)
Cohesion
(kPa)
Friction angle
( )
Loading
Frequency
(Hz)
Peak
acceleration
(g)
16.7 1 33.5 8.9 0.4
FLAC (Version 4.00)
LEGEND
9-May-04 1:54 step 149416 -3.274E-02 <x< 4.787E+00 -2.010E+00 <y< 2.810E+00
Grid plot
0 1E 0
-1.750
-1.250
-0.750
-0.250
0.250
0.750
1.250
1.750
2.250
0.250 0.750 1.250 1.750 2.250 2.750 3.250 3.750 4.250 4.750
JOB TITLE : Boundary condition
Itasca Consulting Group, Inc. Minneapolis, Minnesota USA
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Numerical Analysis of Slope Responses
• Hardin & Drnevich (1972)
• Assimaki et al. (2000)
• Shear wave velocity
Km OCR
e
eG
5.0'2
0 1
973.23230
4426.00max 107700G
2sVG
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Amplification factor from base to the crest
Model used for modulus Shear Modulus
(MPa) Amplification factor
Hardin & Drnevich(1972) 23.9 1.05
Assimaki et al. (2000) 98.6 1.01
Shear wave velocity 293.6 1.00
Measured: 1.1
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Modulus adjustment – amplification factor at 0.4g
1.00
1.05
1.10
1.15
1.20
1.25
1.30
1.35
1.40
1.45
4 8 12 16 20 24
G(MPa)
Am
plifi
catio
n fa
ctor
Modulus by H&D(1972)
1/2 Modulus by H&D(1972)
1/3 Modulus by H&D(1972)
Variations of amplification factor with degradation of shear modulus under amplitude of 0.4g
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Amplification factors
0.8
0.9
1.0
1.1
1.2
1.3
1.4
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Peak acceleration(g)
Am
plifi
catio
n fa
ctor
Amp. AC12/AC8
H-D
1/3 H-D
1/2 H-DNonlinear
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Summary• The initiations of slope slip took place from the surface of slope, and then
the subsurface slip initiated with increasing loading amplitude.• Larger loading amplitude resulted in larger recessional and run-out
distances.• Additional vertical loading amplitude resulted in larger recessional and
run-out distances than without vertical loading condition.• The maximum recessional and run-out distances could reach as far as the
height of slope.• The initiation of slips measured from PIV analysis are smaller than those
measured from accelerometers buried in the specimens.• The potentially affected zone caused by earthquake can be estimated
using loading amplitude versus normalized slope height regression equation.
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Thank you for your attention