damage evaluation of rc building with ssi by seismic ...€¦ · damage evaluation of rc building...

Damage evaluation of RC building with SSI by seismic

interferometry: A numerical case study

Fernando Lopez-Caballero1

E. Diego Mercerat2

1Lab. MSS-Mat - [email protected]

2CEREMA Mediterrannee, [email protected]

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.


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]


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


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


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


Context


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


Context



10-2 10-1 100

DIov RB

[1]

10-2

10-1

100

DI ov

SS

I [1]

Overall damage index - SSI/Rigid Base


Context



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)


Context


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


Context


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


Context



Structural modelbuilding impulse response (IRF)

b

b

DIov = 0.04

DIov = 0.54

Base

Top


Context



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


Context



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%


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


Thank you for your attentionσαζ ενχαριστω


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