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Damage evaluation of RC building with SSI by seismic
interferometry: A numerical case study
Fernando Lopez-Caballero1
E. Diego Mercerat2
1Lab. MSS-Mat - CentraleSupelecfernando.lopez-caballero@centralesupelec.fr
2CEREMA Mediterrannee, MouvGSdiego.mercerat@cerema.fr
16th ECEE
June 18, 2018
Lopez-Caballero and Mercerat (CentraleSupelec) 16ECEE June 18, 2018 1 / 13
Context
Objectives
The aim of this work :
To assess numerically the role of the non-linear soil behaviour on both theseismic response of structure and on its seismic damage assessment (⇒ SSI);
To track the evolution of induced structural damage using seismicinterferometry by deconvolution;
interesting characteristics of the dynamic response of the building can beestimated, e.g. frequencies and damping.
Lopez-Caballero and Mercerat (CentraleSupelec) 16ECEE June 18, 2018 2 / 13
Context
Fully Non linear approach - GEFDyn Code
Tiedboundaries
paraxial approximation :incident waves andabsorbing boundaries
x y
z
e1
e2
e3 Σ
uΣ = uPSV ek + uSH(
e3 ∧ ek)
ECP’s elastoplastic multi-mechanism model
10−6
10−5
10−4
10−3
10−2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
γ [−]
G/G
max
[−]
p0’=0.1[MPa]
p0’=0.5[MPa]
p0’=1.0[MPa]
soil-foundationinterface :
σt
σ.n
σnn
n
Σbs
plastic hingebeam-column elements :
mJtmI
tθJt
θIt
θJ,pt
θI ,pt
αJt
αIt
elastic - plasticcomposant
elasticcomposant
[Saez09]
Lopez-Caballero and Mercerat (CentraleSupelec) 16ECEE June 18, 2018 3 / 13
Context
Effect of non linear soil behaviour on SSI
Structural model
100 101
f [Hz]
0
5
10
15
20
25
30
35
|TF
| [1]
FF-BedTop-FF SSITop-Base SSITop-Base RB
Transfer function - Elastic Soil behaviour
b
b b
bBed
FFBase
Top
8-story structure - 28m height - fstr = 1Hz - fsoil = 1.7Hz
Lopez-Caballero and Mercerat (CentraleSupelec) 16ECEE June 18, 2018 4 / 13
Context
Seismic Hazard
10-2 10-1 100
T [s]
10-4
10-3
10-2
10-1
100
101
PS
A [g
]
= 5%
Data
40 Real signals
Lopez-Caballero and Mercerat (CentraleSupelec) 16ECEE June 18, 2018 5 / 13
Context
Seismic Hazard
10-2 10-1 100
T [s]
10-4
10-3
10-2
10-1
100
101
PS
A [g
]
= 5%
Data
40 Real signals
0 0.1 0.2 0.3 0.4 0.5a
max out [g]
0
0.1
0.2
0.3
0.4
0.5
0.6
a max
[g] 1:2
1:1
FFBase Str.Idriss (1990)Dickenson-Seed (1996)
Soil response
Lopez-Caballero and Mercerat (CentraleSupelec) 16ECEE June 18, 2018 5 / 13
Context
Effect of non linear soil behaviour on SSI
Structural response - Overall damage index DIov
Overall damage index Park and Ang(1985):
DIloc,i =θpm,i
θpu
+ λp1
Mpy,i
θpu
∫
tM
pi dθ
pi
DIov =∑
iλi DIloc,i
with λi =∫
t Mpidθ
pi
∑
i
∫
t Mpidθ
pi
Maximum Interstory drift ISDmax :
ISDmax = maxi,t
{
|ui+1y (t)−uiy (t)|z i+1
−z i
}
10-2 10-1 100 101
ISD [%]
10-2
10-1
100
DI ov
[1]
RB
Overall damage index - inter-story drift
Lopez-Caballero and Mercerat (CentraleSupelec) 16ECEE June 18, 2018 6 / 13
Context
Effect of non linear soil behaviour on SSI
Structural response - Overall damage index DIov
10-2 10-1 100
DIov RB
[1]
10-2
10-1
100
DI ov
SS
I [1]
Overall damage index - SSI/Rigid Base
Lopez-Caballero and Mercerat (CentraleSupelec) 16ECEE June 18, 2018 7 / 13
Context
Effect of non linear soil behaviour on SSI
Structural response - Overall damage index DIov
10-2 10-1 100
DIov RB
[1]
10-2
10-1
100
DI ov
SS
I [1]
Overall damage index - SSI/Rigid Base
10-3 10-2 10-1 100
PSA (T=1s) [g]
10-2
10-1
100
DI ov
[1]
RBSSI
Overall damage index - PSA(T = 1s)
Lopez-Caballero and Mercerat (CentraleSupelec) 16ECEE June 18, 2018 7 / 13
Context
Effect of non linear soil behaviour on SSI
Structural response - Induced Damage effect
Structural model
100 101
f [Hz]
0
5
10
15
20
25
30
|TF
| [1]
DIov
=0.02
DIov
=0.41
DIov
=0.54
Transfer function - NL Soil behaviour
b
b
Lopez-Caballero and Mercerat (CentraleSupelec) 16ECEE June 18, 2018 8 / 13
Context
Effect of non linear soil behaviour on SSI
Structural response - Seismic interferometry by deconvolution
Structural modelbuilding impulse response (IRF)
b
b
D(x , ω) = U(x,ω)U∗(xref ,ω)
U(xref ,ω)2+e
Lopez-Caballero and Mercerat (CentraleSupelec) 16ECEE June 18, 2018 9 / 13
Context
Effect of non linear soil behaviour on SSI
Structural response - Seismic interferometry by deconvolution
Structural modelbuilding impulse response (IRF)
b
b
DIov = 0.04
DIov = 0.54
Base
Top
Lopez-Caballero and Mercerat (CentraleSupelec) 16ECEE June 18, 2018 10 / 13
Context
Effect of non linear soil behaviour on SSI
Structural response - Seismic interferometry by deconvolution
10-2 10-1 100
DIov
[1]
-2
-1.5
-1
-0.5
0
0.5
ln(A
mp-
up/A
mp-
dow
n) [1
]
SSIRB
Relative amplitudes(upgoing/downgoing)
ln(A/A0) = −π · fstr · h/(Q · C ) → Q = 0.5β
Lopez-Caballero and Mercerat (CentraleSupelec) 16ECEE June 18, 2018 11 / 13
Context
Effect of non linear soil behaviour on SSI
Structural response - Seismic interferometry by deconvolution
10-2 10-1 100
DIov
[1]
-2
-1.5
-1
-0.5
0
0.5
ln(A
mp-
up/A
mp-
dow
n) [1
]
SSIRB
Relative amplitudes(upgoing/downgoing)
10-2 10-1 100
DIov
[1]
10-3
10-2
10-1
[1]
RBSSI
Estimated damage buildingusing relative amplitudes
ln(A/A0) = −π · fstr · h/(Q · C ) → Q = 0.5β
β ≈ 10%
Lopez-Caballero and Mercerat (CentraleSupelec) 16ECEE June 18, 2018 11 / 13
Context
Conclusions
some key points :
Apparent wave velocities in the building estimated from the deconvolvedsignals are consistent with the input model parameters and the hypothesis ofshear behaviour of the building (No shown today);
Measurement of relative amplitudes between upgoing/downgoing waves(as a proxy for attenuation) in the structure is highly correlated withdamage index independently of soil-structure or rigid-base boundaryconditions.
Acknowledgements
AO RAP 2017 French project: Caracterisation de l’ISS a partir de donnees
accelerometriques et de mesures de vibrations ambiantes and SEISM Paris SaclayResearch Institute
Lopez-Caballero and Mercerat (CentraleSupelec) 16ECEE June 18, 2018 12 / 13
Thank you for your attentionσαζ ενχαριστω
Lopez-Caballero and Mercerat (CentraleSupelec) 16ECEE June 18, 2018 13 / 13
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