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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
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
VEESD 2013 Page 4
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
VEESD 2013 Page 5
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
VEESD 2013 Page 6
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 )
VEESD 2013 Page 7
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
VEESD 2013 Page 8
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
VEESD 2013 Page 9
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
VEESD 2013 Page 10
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)
VEESD 2013 Page 11
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