Integrating modal analysis and seismic interferometry for structural dynamic response: The case study of giotto's bell tower in Florence (Italy)

Integra)ng  Modal  Analysis  and  Seismic  

Interferometry  for  full  structural  dynamic  

response:  Gio:o’s  Bell  Tower.

Giorgio  Lacanna

_{,  Renato  Lancello:a}

_{,  Maurizio  Ripepe}

1  _{Università  di  Firenze}   2  _{Politecnico  di  Torino}  

Ambient  Vibra)on  Test  

Classic  Method  Opera)onal  Modal  Analysis:    

Ø  OMA   is   passive   seismic   tool   for   Structural   frequencies,   Modal   shapes   and   Damping   iden)fica)on.   We   applied   the   Enhanced   Frequency   Domain   Decomposi)on  (EFDD)  

Ø  Calibrate  Numerical  Model  

Ø  Structural  Health  Monitoring  (SHM)  purposes.  

Ambient  Vibra)on  Test  is  commonly  used    to  iden)fy  the  dynamic  response   of  the  Building.  

Seismic  Interferometry  is  performed  on  the  same  seismic  data:    

Ø  IRFs  (Impulsive  Response  Func)on)  allow  to  es)mate  seismic  wave  velocity  (V_s   and  V_p).  

Ø  V_s  a  new  parameter  for  SHM  (Velocity  is  less  affect  by  SSI  than  frequency).  

Ø  Seismic   Wave   analysis   integrated   with   the   structural   frequencies   gives  

Dynamic  Monitoring  

_{10  Seismic  Sta)ons  equipped:}  

• 

Broadband   3-­‐component  

seismometrs   (Lennartz   5s,  

Guralp  10s,  Guralp30s)  

• 

_{Digi)zer  24  bit  (Guralp,  CMG-­‐}

DM24)  sampling  at  100Hz  

• 

_{Synchroniza)on  using  GPS}  

Automa)c  Iden)fica)on  Modal  Parameters  –  EFDD    

Assump)on  -­‐-­‐>  Modal  Shapes  are  sta)onary  for  3  hours    

!(!_!!_!(! !), !!!!!!!!(!!)) = [!! !_! !! ][!!!!!!!! !! ]! ! ([!_!!! _! ! ][!!!! !! ])([!!!!!!!! !! ][!!!!!!!! !! ])

MODAL  

COHERENCE  

Rainieri  &  Fabrocino,  2010   Lacanna  et  al,  2016  

Mean  

C  

C  

6  Modal  Frequencies  Iden)fied  

0.623  

0.647  

2.543  

3.081  

3.156  

5.731  

First  and  Second  Modal  Shapes  

+  

₌  

1°+2°  Shapes  Mode    

51°N  

_141°N  

1°  and  2°  Shapes  Mode  moves    together  along  the  diagonal  of  the  square   plan  of  Gio:o’s  Bell  Tower  

The  two  first  Shapes  Mode  are  coupled  and  resul)ng  in  circular  movement   slightly  eccentric  in  North-­‐South  direc)on    

III°  -­‐IV°  -­‐V  °-­‐  VI°  Modal  Shapes  

4°  and  5°  Shapes  Mode  as  the  first  two  modes  moves    approximately  

to  the  diagonal  of  the  square  plan  of  Gio:o’s  Bell  Tower    

Automa)c  Tracking  of  Modal  frequencies

Frequency (Hz)

Mean Frequency (Hz) Min (%) Frequency (Hz) Max (%)

0.623 0.618 (0.76) 0.628 (0.80)

0.647 0.642 (0.81) 0.652 (0.73)

2.543 2.520 (0.90) 2.573 (1.18)

3.081 3.052 (0.93) 3.105 (0.79)

3.156 3.134 (0.68) 3.174 (0.57)

A  posi)ve  correla)on  is  found   between  the  6  modal  frequencies  

and  temperature.  

Frequency  changes  ≤  1.1  %  

The   Modal   frequencies   are   detected   automa)cally   for   36   hours   and   compared  with  temperature  

Flexible  structure

  The  building  horizontal  displacement  is  a  sum  of  three  terms  

Transla=on     Rota=on    

Soil  founda=on     Deforma=on  of  Building    

(Luco  1987,  Todorovska  2008)  

The   modal   frequencies   extracted   with   OMA   (f₀)   is   related   to   the   mechanical  

proper)es  of  the  building  but  is  also  affected  by  the  soil-­‐structure  interac)on     For  Flexible  structure  f_fixed    is  given  by  basic  equa)on:    

    _{=4.26  m  Iner=a  radius  cross-­‐sec=on}    

=84  m  Eleva=on  of  the  building     Compressional  P-­‐wave  velocity  

the  seismic  velocity

is  es)mated  by  interferomety  

Seismic  Interferometry

Evaluates  the  IRFs  through  the  deconvolu)on  of  the  signals:  

! ! = !!(!)!!"#

∗ _(!)

!!"#(!)

!

+ !

u_refà  _{Sta=on  locate  to  the  Top}  

Sneider  &  Safak,     BSSA  2006  

2040  m/s  

North  

Sta=ons   _Sta=ons  South  

2040  m/s  

R

_=0.99  

=0.70  Hz  

The  velocity  is  es)mated  from   the  slope  of  the  travel  )me  

Using  least  square  fit      

Rocking  Frequency

ROCKING  FREQUENCY:  

Vs  =380  m/s  

The  soil  structure  interac)on  reduces  the  fixed-­‐base  frequency  by  8%  and  it   is  expected  by  considering  the  high  Vs=380  m/s  of  the  soil  founda)on  

Rocking  S)ffnnes  

Results  

AutomaLc  idenLficaLon  EFDD  technique  on  GioRo’  Bell  Tower:  

Ø  The  1°  -­‐  2°  modes  move  to  the  diagonal  of  the  square  plan  

Seismic  Interferometry  technique  on  GioRo’  Bell  Tower:  

Ø  Seismic  velocity  V_p=2040  m/s  à  Fixed  base  frequency      

IntegraLng  results  of  the  two  techniques  

Ø  Provides  detail  informa=on  on  the  degree  of  soil-­‐structure  interac=on.  

Ø  The   rocking   frequency   is   consistent   with   the   geotechnical   proper=es   and   it   reduces  the  fixed  base  frequency  of  10%  

Ø  The  value  f_R=1.36  Hz  can  be  used  to  validate  analy=cal  rela=onship  to  compute  

the  rocking  s=ffness  for  advanced  seismic  analysis  

Conclusions  

The  full  structural  dynamic  iden)fica)on  (OMA-­‐  Interferometry)  shows  a   Weak  contribu)on  of  soil-­‐structure  interac)on