Hieu Toan NGUYENJean-Alain FLEURISSONRoger COJEAN

Evaluation of topographic site effect in Evaluation of topographic site effect in slope stability under dynamic loadingslope stability under dynamic loading

PLAN DE LA PRESENTATION

VEESD 2013 Page 3

1. Introduction

Topography site effect Cause: the irregularities of the morphology

(slope, ridge, cliff...) → the interference of the incident and the reflected waves

Consequence: the spatial, spectral and temporal modifications of the seismic signal

Aggravation of the earthquake damages and the slope instabilities

Las Colinas landslide triggered by the earthquake 13-01-2001 (Mw=7.6)

Amplification

De-amplification

Incident waves

AmplificationDe-amplification

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1. Introduction

Eurocode 8 (2005) Slope belong to the two-dimensional

topographic irregularities: long ridges, cliff… Slope height ≥ 30m Slope angle ≥ 15°

French paraseismic code PS-92

1.0 : I i 0.4

1 0.8 (I i 0.4) : 0.4 I i 0.9

1.4 : I i 0.9

20 Ib min H 10

4

Remarks Do not take into account the role of the geologic and seismic conditions of slope. Do not take into account the characteristic of the seismic signal.

Study purpose Identify the factors influencing the slope topographic site effect. Determine the relationships between these factors and this phenomenon. Provide a simple method to quantify this effect.

ConfigurationsAmplification

factor

Isolated cliffs and slopes ST≥1.2

Ridges with crest width significantly less than the base width

<30° ST≥1.2

≥30° ST≥1.4

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Interpretation criteria Amplifications factors

Proportion by area of the amplified zones

Dimension of the amplified zone at the slope crest: Hx, Dxc

2a. Methodology outline Mesh size

N=30÷100 Numerical error < 3% Boundary conditions

Free Field Quiet boundary

Seismic excitation SV wave, sinusoidal signal PGA=0.4g, F=0.5÷10Hz

lN

maxxaccAx

2PGA maxyacc

Ay2PGA

AA

T

SpS 100

S AS

AST

SpS 100

S

02468

101214

10 20 30 40 50 60 70 80 90 100

Erro

r (%

)

N

20m

H

5H H/tan( 15H+H/tan(

Quiet boundary

2H²

S1 U S2 U S3 U S4 S1 U S2 U S3

1 3

4

2

Dxc

Hx

pSAS

pSA

AxAy

2H

H

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2b. Impact of the dimensionless frequency

Important parameters in a site effect study Step-like slope with homogeneous, isotropic and elastic

material• Morphologic parameters: H, • Geologic parameters : E, , • Seismic characteristic parameter:

Sinusoidal seismic signal• Amplitude : PGA• Frequency : F• Shaking duration : t

Dimensionless frequency () Integrated parameters : H, E, F,

s

H H F H F

V E2(1 )

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2b. Impact of the dimensionless frequency

Parametric analyses Change the value of 2 of the 5 parameters

(H, E, F, ) each time 10 couples Change 4 times for each couple 40 cases

Results Evaluate the coefficient of variation

(standard deviation/mean) Conclusions

Ax=f(H) Ay=f(H, ) pS=f(H) Hx=f(H) Dxc=f(H, )

Couple of varying parameters [H,F] [H,E] [H,] [H,] [F,E] [F,] [F,] [E,] [E,] [,]

Numerical simulation number 1 2 3 4 5 6 7 8 9 10

0

5

10

15

20

25

1 2 3 4 5 6 7 8 9 10

CV (%

)

Cases

Ax Ay pSA, pSAS Hx/H Dxc/HpSA, pSAS

H,EH,F

1 3

4

2

Dxc

Hx

pSAS

pSA

AxAy

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2b. Impact of the dimensionless frequency

-0,2

-0,1

-0,1

0,0

0,1

0,1

0,2

0,2

0 2 4 6 8 10 12 14Acc

élér

ation

(g)

Temps (s)

Accélérogramme (Sicile-Italie)

H=25m H=50m H=200mH=100m

H=25m H=50m H=200mH=100m

=0.2 =0.25 =0.35=0.3

H=40m H=80m

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0.15

2b. Impact of the dimensionless frequency

Parametric analyses Same geomorphologic condition =0.05÷1.0 (=0.05)

Conclusions Horizontal amplification

o ≤0.5 : amplification zones along the free surface• ≤0.15 : one amplified zone, at crest• >0.15 : many amplified zones, at crest and behind the crest

o >0.5 : additional amplification zones inside the slope mass Vertical amplification

o ≤0.5 : highest amplified zone located along the slopeo >0.5 : highest amplified zone located at the crest

0.0

0.5

1.0

1.5

2.0

0 0.2 0.4 0.6 0.8 1

Ax,

Ay

Ax Ay

0

20

40

60

80

100

0 0.2 0.4 0.6 0.8 1

pSA,

pS A

S(%

)

pSA pSASpSA pSAS

0

4

8

12

16

0.0

0.2

0.4

0.6

0.8

0 0.2 0.4 0.6 0.8 1

Dxc

/H

Hx/

H

Hx/H Dxc/H

=0.05 =0.4=0.2=0.1 =0.60.5

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Parametric analyses Slope angle =30÷80

Results

Conclusions The amplification factors (Ax, Ay) increase with an increase of the slope angle Dxc is not dependent on the slope angle Other criteria (pSA, pSAS, Hx), the interaction between and should be considered

2c. Impact of the slope angle

1.0

1.1

1.2

1.3

1.4

0 0.1 0.2 0.3 0.4

Ax

30 40 50 60 70 80

0.0

0.3

0.6

0.9

1.2

0 0.1 0.2 0.3 0.4A

y

30 40 50 60 70 80

0

20

40

60

80

100

0 0.1 0.2 0.3 0.4

pSA,

pS A

S(%

)

30 40 50 60 70 80

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3 0.4

Hx/

H

30 40 50 60 70 80

0

3

6

9

12

15

0 0.1 0.2 0.3 0.4

Dxc

/H

30 40 50 60 70 80

1 3

4

2

Dxc

Hx

pSAS

pSA

AxAy

Tendency of the given criterion when increases

Increase (I)

Decrease (D)

Non dependent (ND)

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3. Conclusions and perspectives

H

Ax D ND I I

AyI (≤0.3)D (>0.3)

D II

≤0.5: highest amplified zone located along the slope>0.5: highest amplified zone located at the crest

pSA

pSAS

D (≤0.15)ND (>0.15)

NDI (≤0.15)D (>0.15)

D≤0.5: amplification zones along the free surface

* ≤0.15: one amplified zone, at crest* >0.15: many amplified zones behind the

crest>0.5: additional amplification zones inside the slope mass

HxD (≤0.2)

ND (>0.2)ND

I (≤0.35)ND (>0.35)

D

Dxc D I ND D

Conclusions Important role of the dimensionless

frequency parameter Summary table of the relationships

between the affecting factors and the interpretation criteria

Graphs to estimate Ax, Ay, pSA, pSAS, Hx, Dxc as a function of (=0.05÷0.4) and (=30÷80°)

1.0

1.1

1.2

1.3

1.4

0 0.1 0.2 0.3 0.4

Ax

30 40 50 60 70 80

0.0

0.3

0.6

0.9

1.2

0 0.1 0.2 0.3 0.4

Ay

30 40 50 60 70 80

0

20

40

60

80

100

0 0.1 0.2 0.3 0.4

pSA,

pS A

S(%

)

30 40 50 60 70 80

0

0.2

0.4

0.6

0.8

1

0 0.1 0.2 0.3 0.4

Hx/

H

30 40 50 60 70 80

0

3

6

9

12

15

0 0.1 0.2 0.3 0.4

Dxc

/H

30 40 50 60 70 80

Perspectives Improve the graphs by extending the value range of and by integrating

H and Develop a calculation method applicable to a real seismic signal with a

large frequency band. Extend the study to the cases of the slopes with the more complex and

more realistic geomorphologic conditions

Thank you for Thank you for your attentionyour attention