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

Outline

• Shaking table test

• Specimen preparation and law of similarity

• Test result

• Particle Image Velocimetry (PIV) analysis

• Displacement behavior

• Summary

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

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

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

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

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

8

Specimen preparation - compaction

slope modeling tool

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

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

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

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

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

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)

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)

16

Specimen B

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

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

19

Specimen C

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

-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

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

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

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

Test Result – Video Recording and PIV Analysis

Processed with PIVview2C

Note: play video files

CrestCrest

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

Runt-out and Recessional Distances

Specimen A

Specimen B

Specimen C

CrestToe

unit: cm

Run-out and Recessional Distances

Specimen D

Specimen E

CrestToe

unit: cm

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

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

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

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

Newmark’s analysis – specimen A

FLAC

After test

Khy=0.29

Jibson et al. (2000)

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)

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)

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

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

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

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

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

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

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.

Thank you for your attention