LEZIONI DAL PASSATO: LE TECNICHE DI PROTEZIONE SISMICA NELLA STORIA DELLE COSTRUZIONI

Maria GirardiIstituto di Scienza e Tecnologie dell’Informazione “A. Faedo” CNR-ISTI

Analisi strutturale e monitoraggio di costruzioni storiche

Mechanics of Materials and Structures Laboratory

Computational solids Mechanics

Mechanics of masonry structures

Structural Health Monitoring

www.isti.cnr.itwww.nosaitaca.it

The NOSA-ITACA code (freely downloadable at www.nosaitaca.it)

• NOSA-ITACA is a free software package developed by ISTI-CNR. It is a finiteelement code that combines NOSA (solver) with the open source graphic platformSALOME (pre-post processing operations), suitably modified. It has been specificallyimplemented to study the static and dynamic behavior of masonry constructions,trough the constitutive equation of masonry-like materials.

• NOSA-ITACA is distributed via the http://www.nosaitaca.it/software/ website. Thedownloadable package includes SALOME v8.3.0, and is available for Ubuntu 14.04and 16.04.

• NOSA-ITACA library: beam, truss, shell, 2D, 3D elements (35 elements)

• Static analysis• Dynamic analysis• Thermal loads

• Stress and displacement fields• Collapse load• Elastic, cracking and crushing strain• Time-histories

• Modal analysis • Natural frequencies, mode shapesNOSA-ITACA

• Model updating• Optimization procedures based on model reduction and the thrust region method

masonry-like

The NOSA-ITACA code – some example applicationsLucca – Safety assessment of some reinforcement operations on the South wall of the San Francesco Church

Crack patterns in the longitudinal walls via NOSA-ITACA

Southern wall

Northern wall

Detected cracks in the Southern wall

Crack strains E11

The dome of the San Cerbone Cathedral (Massa Marittima)

NOSA-ITACA – some example applications

brick arch travertinearch

Principal fracture strains in the dome

Finite-element modelof the dome

Thrust line in the brick arch

NOSA-ITACA – some example applications

Undeformed and deformed shape of the vault

a) b)

Finite-element modelof the valut

Crack pattern in the vault: a) NOSA-ITACA; b)existing

Pisa – A vault in Palazzo Franchetti

NOSA-ITACA – some example applications

Livorno – The “Voltone” under Piazza della Repubblica

2

0( )(1 )

2m m

RdM h σ σσ

= −

M/MRd

Structural Health Monitoring Finite-element model

Model updating (optimization procedures)

Finite-element analysis and vulnerability assessment

Measured quantitiesdisplacements, natural frequencies,

damping ratios

Model parametersmechanical properties, boundary

conditions, ect.

In collaboration with R.M.Azzara (INGV)

Structural Health Monitoring of the San Frediano bell tower in Lucca

• Continuous, long-term (from October 2015 to September 2017)• Dependence of measurements on the environmental factors• Damage detection

The façade of the Basilica

The San Frediano bell tower

R.M. Azzara, G. De Roeck, M. Girardi, C. Padovani, D. Pellegrini and E. Reynders. “The influence of environmental parameters on the dynamic behaviour of the San Frediano belltower in Lucca”, Engineering Structures 156(2018): 175-187.

In collaboration with:INGV-Seismic Observatory of ArezzoKU Leuven, Department of Civil Engineering

Instruments: 4 SARA seismic stations (electrodynamicvelocity transducer SS20, digitizer SL06 – 24 bit), samplingfrequency = 100Hz.

• 1° phase: 29 May (L1) -> 3 June 2015

• 2° phase: October 2015 (L2) ->July 2016

• 3° phase: July 2016 (L3) -> September 2017

Monitoring scheme

Amatrice earthquake on the San Frediano bell tower

24/08/2016

14

Data Analysis: Operational Modal Analysis

kkk

kkk

vCxywAxx

+

++

=

=1

Covariance Driven Stochastic Subspace Identification method (MACEC code):

kx

ky

kk ,vw

, state of the system

, measured output;

, process and output noise

Estimate of matrices A e C

Natural frequenciesDamping ratios Mode shapesStabilization diagram

Dependence of frequencies on temperatureDaily variations

1.07

1.08

1.09

1.10

1.11

1.12

1.13

1.14

1.15

29/5

/15

13:0

0

30/5

/15

0:00

30/5

/15

11:0

0

30/5

/15

22:0

0

31/5

/15

9:00

31/5

/15

20:0

0

1/6/

15 7

:00

1/6/

15 1

8:00

2/6/

15 5

:00

2/6/

15 1

6:00

3/6/

15 3

:00

Freq

uenc

y f 1

[Hz]

1.35

1.36

1.37

1.38

1.39

1.40

1.41

1.42

29/5

/15

13:0

0

30/5

/15

0:00

30/5

/15

11:0

0

30/5

/15

22:0

0

31/5

/15

9:00

31/5

/15

20:0

0

1/6/

15 7

:00

1/6/

15 1

8:00

2/6/

15 5

:00

2/6/

15 1

6:00

3/6/

15 3

:00

Freq

uenc

y f 2

[Hz]

3.343.363.383.403.423.443.463.483.503.523.54

29/5

/15

13:0

0

30/5

/15

0:00

30/5

/15

11:0

0

30/5

/15

22:0

0

31/5

/15

9:00

31/5

/15

20:0

0

1/6/

15 7

:00

1/6/

15 1

8:00

2/6/

15 5

:00

2/6/

15 1

6:00

3/6/

15 3

:00Fr

eque

ncy

f 3[H

z]

4.40

4.45

4.50

4.55

4.60

4.65

4.70

4.75

4.80

29/5

/15

13:0

0

30/5

/15

0:00

30/5

/15

11:0

0

30/5

/15

22:0

0

31/5

/15

9:00

31/5

/15

20:0

0

1/6/

15 7

:00

1/6/

15 1

8:00

2/6/

15 5

:00

2/6/

15 1

6:00

3/6/

15 3

:00Fr

eque

ncy

f 4[H

z]

5.15

5.20

5.25

5.30

5.35

5.40

5.45

5.50

29/5

/15

13:0

0

30/5

/15

0:00

30/5

/15

11:0

0

30/5

/15

22:0

0

31/5

/15

9:00

31/5

/15

20:0

0

1/6/

15 7

:00

1/6/

15 1

8:00

2/6/

15 5

:00

2/6/

15 1

6:00

3/6/

15 3

:00Fr

eque

ncy

f 5[H

z]

The first natural frequency vs. timeStandard deviation: 0.019 Hz (maximum)

The second natural frequency vs. timeStandard deviation: 0.034 Hz (maximum)

The fourthnatural

frequency vs. time

Standard deviation: 0.107 Hz (maximum)

The fifthnatural

frequency vs. time

Standard deviation: 0.07 Hz (maximum)

The thirdnatural

frequency vs. time

Standard deviation: 0.036 Hz (maximum)

Dependence of frequencies on temperatureYearly variations

ARX modelsBlue dots: mesured valuesRed dots: simulated values

1°fr

eque

ncy

2°fr

eque

ncy

3°fr

eque

ncy

Output-only procedures Principal Component Analysis

Training period Post-earthquake

Amatrice earthquake

95° percentile

95° percentile

Linear PCA

Kernel PCA

Damage Detection

Simulated damage scenarioFirst frequency -2%Second frequency -1%

Third frequency -0.5 %

95° percentile

95° percentile

Linear PCA

Kernel PCA

Training period Post-earthquake

earthquakeDamage Detection

Finite-element model

Parameters vector x(mechanical characteristics, boundary conditions, etc.)

Numerical frequencies f(x) andmode shapes v(x) of the model

Measurement of q natural frequencies f and mode shapes v

Minimize (x)

Optimal values of the parameters

Model updating

( )( )

( )( )

|v (x) v |(x)|| v (x) || ||v ||

ii

i iiγ ⋅

=$

$1...i q=

,

An ad hoc algorithm has been implemented in NOSA-ITACA for solving thisoptimization problem

M. Girardi, C. Padovani, D. Pellegrini, M. Porcelli and L. Robol. “Finite element model updating forstructural applications”, arXiv:1801.09122 (2018).

µ( )2 2

1

(x) [ (x)] [1 (x)]q

i i i q i ii

w f f wφ γ+=

= − + −∑

.

Maddalena bridge in Borgo a Mozzano: experimental results

R.M. Azzara, A. De Falco, M. Girardi, D. Pellegrini. “Ambient vibration recordings on the Maddalenabridge in borgo a Mozzano (Italy): Data analysis”. Annals of Geophysics, 60(4), 2017.

Exp. freq. [Hz]

Mode shape 1 3.37

Mode shape 2 5.06

Mode shape 3 5.40

Mode shape 4 7.06

Mode shape 5 8.80

Mode shape 6 9.19

Maddalena bridge in Borgo a Mozzano: model updating

N.D.O.F. = 155312Computation time for model updating = 534 s

, ,

Optimal parametersE = 6889 MPa Ks = 1.929 10 N/m

10 3

Objective function

Ks (soil stiffness)

E, = 1850 kg/m

Homogeneous model3

Num. Freq Error[%]3.108 7.85.179 2.45.391 1.77.223 2.38.507 3.39.596 4.4

Maddalena bridge in Borgo a Mozzano: model updating

,

Objective function

Heterogenous modelExternal layer: 1= 2000 kg/m3 , E1Inner material: 2, E2Piers: 3 = 1900, E3 = 7000 MPa

Optimal parametersE1 =10380 Mpa, E2 =4700 Mpa, 2 = 1960 kg/m

3

Num. Freq Error[%]3.2879 2.75.2355 3.35.4239 0.46.8517 2.98.6394 1.99.7365 5.9

Mechanics of Materials and Structures Laboratory

Vincenzo BinanteSKYBOX EngineeringAerospace Engineer

Maria GirardiCivil Engineer

Cristina PadovaniMathematician

Giuseppe PasquinelliPhysicist

Daniele PellegriniCivil Engineer

Margherita Porcelli University of FlorenceMathematician

Stefano PozzaCharles University - PragueMathematician

Leonardo RobolMathematician