ΑΡΙΣΤΟΤΕΛΕΙΟ ΠΑΝΕΠΙΣΤΗΜΙΟ ΘΕΣΣΑΛΟΝΙΚΗΣ
ΤΜΉΜΑ ΠΟΛΙΤΙΚΏΝ ΜΗΧΑΝΙΚΏΝ - ΕΓΚΑΤΑΣΤΆΣΕΙΣ
19 ΜΆΙΟΣ 2009
Seismic Retrofitting, Base Isolation,
Dynamical Testing and System Identification:
A Case Study in Sicily
Giuseppe Oliveto, Department of Civil and Environmental Engineering ­ University of Catania
THE TWO SOLARINO BUILDINGS BEFORE SEISMIC
REHABILITATION
Characteristic compression strength of concrete 13 N/mm² (25 N/mm²)
Periods of vibration: T1= 0.94 s – longitudinal direction (too large for building type)
T2= 0.86 s – torsion
T3= 0.71 s – transverse direction
Available Seismic Resistance: 92% of required resistance in the longitudinal direction 60% of required resistance in the transverse direction Maximum inter­story drift: 3.7610­3 >> 2.0010­3 (Allowable value)
Seismic Retrofitting
1
FOUNDATION
• Foundation soil: limestone of the Climiti Mountain formation
• Inverted beam foundation with short columns supporting first storey
• Cutting of columns and building support relatively simple
•Ideal solution: Retrofitting by base isolation
Two views of foundation system
Seismic Retrofitting
THE RETROFITTING DESIGN
Strengthening of the superstructure
First floor
Second and third storey
First storey
Fourth storey
2
FOUNDATION ENLARGEMENT
Seismic Retrofitting
LAYOUT OF THE DUAL SEISMIC ISOLATION SYSTEM
INCLUDING 12 HDRB AND 13 LFSB
Laminated rubber bearing
HDRB
Low­friction bearing
LFSB
Seismic Retrofitting – Base Isolation
3
ISOLATION BEARINGS
High Damping Rubber Bearing
Low Friction Sliding Bearing
Seismic Retrofitting – Base Isolation
ISOLATION BEARINGS
High Damping Rubber Bearing
Low Friction Sliding Bearing
Seismic Retrofitting – Base Isolation
4
TESTING APPARATUS
Data acquisition system
Electric connection cables
Reaction wall
Hydraulic
jack
Fuse
Building
Load
cell
Loading device
Measurement equipment 15 acceleration transducers
12 displacement transducers
Dynamic Testing
SCHEMATIC VIEW OF LOADING DEVICE
HYDRAULIC JACK
SUDDEN RELEASE DEVICE
LOAD CELL
REACTION WALL
Dynamic Testing
5
SUDDEN RELEASE DEVICE - BASIC IDEA
F: APPLIED LOAD, N: TRACTION FORCE IN THE FUSE
Fuse N N m 1 F Fuse Hydraulic jack Load cell F F=mN Dynamic Testing
SUDDEN RELEASE DEVICE
FUSE: CALIBRATED HS STEEL ROD
PROTOTYPE
Dynamic Testing
6
LOAD CELL AT THE HEAD OF LOADING DEVICE
NOVATECH ­ UK
MODEL F205­CFR0K0
Dynamic Testing
LOCATION OF THE MEASURING STATIONS
PENNY&GILES ­ UK
Linear Displacement Sensors
MODEL SLS320
Dynamic Testing
7
SCHEMATIC ACCELEROMETERS LAYOUT
PCB­Piezotronics
Seismic Acceleration Transducer
MODEL 393B31
Measuring stations and acquisition channels Dynamic Testing
LOAD-DISPLACEMENT CURVE (L-D)
Dynamic Testing
8
INITIAL PART OF LOAD-DISPLACEMENT CURVE
Dynamic Testing
DYNAMIC TEST N. 1 PERFORMED ON 9 JULY 2004
Dynamic Testing
9
DYNAMIC TEST N. 2 PERFORMED ON 9 JULY 2004
Dynamic Testing
DYNAMIC TEST N. 3 PERFORMED ON 9 JULY 2004
Dynamic Testing
10
PERIODS OF VIBRATION AND EQUIVALENT VISCOUS
DAMPING RATIO
TEST 1
TEST 2
TEST 3
Dynamic Testing
LOAD-DISPLACEMENT CURVES FOR THE STATIC
PHASES OF DYNAMIC TESTS
TEST 1
TEST 2
TEST 3
Dynamic Testing
11
LOW FREQUENCY COMPONENT OF PEAK ACCELERATION
AND ESTIMATED BUILDING MASS
TEST 1
TEST 2
TEST 3
Dynamic Testing
FREE VIBRATION TESTS
Dynamic Testing
12
SUDDEN RELEASE DEVICE
Dynamic Testing
SUDDEN RELEASE DEVICE
Dynamic Testing
13
SUDDEN RELEASE DEVICE
Dynamic Testing
FREE VIBRATION TEST
Dynamic Testing
14
FREE VIBRATION TEST
Dynamic Testing
FREE VIBRATION TEST
Dynamic Testing
15
FREE VIBRATION TEST
Dynamic Testing
FREE VIBRATION TEST
Dynamic Testing
16
FREE VIBRATION TEST
Dynamic Testing
FREE VIBRATION TEST
Dynamic Testing
17
FREE VIBRATION TEST
Dynamic Testing
FREE VIBRATION TESTS
Dynamic Testing
18
Wavelet Decomposition (8NCEE)
• Daubechies, I., 1992. Ten Lectures on Wavelets, Society for
Applied Mathematics, Philadelphia, Pennsylvania.
• Morlet, J., Arens, G., Fourgeau, I., Giard, D., (1982). Wave
propagation and sampling theory, Geophysics, 47, pp. 203­236.
• Newland, D., E., 1993. An Introduction to Random Vibration,
Spectral & Wavelet Analysis, Longman, England.
• Walker, J., S., 1999. A Primer on Wavelets and their Scientific Applications, Chapman&Hall/CRC, London.
System Identification – Signal Treatment
Wavelet Decomposition (8NCEE, Daub30, livello 6)
Recorded Acceleration
Fourier’s Spectrum
System Identification – Signal Treatment
19
Wavelet Decomposition (8NCEE, Daub30, livello 6)
Recorded Acceleration
Fourier’s Spectrum
System Identification – Signal Treatment
Wavelet Decomposition (8NCEE, Daub30, livello 6)
Recorded Acceleration
Fourier’s Spectrum
System Identification – Signal Treatment
20
Wavelet Decomposition (8NCEE, Daub30, livello 6)
Recorded Acceleration
Fourier’s Spectrum
System Identification – Signal Treatment
Wavelet Decomposition (8NCEE, Daub30, livello 6)
Recorded Acceleration
Fourier’s Spectrum
System Identification – Signal Treatment
21
Wavelet Decomposition (8NCEE, Daub30, livello 6)
Recorded Acceleration
Fourier’s Spectrum
System Identification – Signal Treatment
Wavelet Decomposition (8NCEE, Daub30, livello 6)
Recorded Acceleration
Fourier’s Spectrum
System Identification – Signal Treatment
22
Signal Treatment
System Identification – Signal Treatment
Daub30 - level 11
Somma dei dettagli dal livello 7 al livello 11
System Identification – Signal Treatment
23
Daub30 - level 11
Somma dei dettagli dal livello 7 al livello 11
System Identification – Signal Treatment
JSSI 2004, 8NCEE 2006
2.4
2.2
T [s]
2
1.8
1.6
1.4
1.2
0
5
10
15
u [cm ]
Fundamental Period versus Displacement Amplitude
Elementary System Identification
24
Displacement [cm]
PERIOD EVALUATION
Time [s]
Elementary System Identification
EQUIVALENT DAMPING RATIOS (8NCEE 2006)
First mode damping ratios for base isolated building
25
z [%]
20
z=zv+zf
zv
15
10
zf
5
0
0
5
10
15
u [cm ]
z, total equivalent damping ratio; zv , equivalent viscous damping ratio; zf , equivalent frictional damping ratio.
Elementary System Identification
25
Frictional Damping
Friction force
4 fd
cf 
fd
 u0
Displacement
­uo
uo
f 
­f d
fdT 2
f T2
 d3 D ( 1   2 )
3
2 m u0 2 m u0
Elementary System Identification
ONE DEGREE OF FREEDOM SYSTEM
Test N°5
4
0
3
1
3
4
1
­2]
Treated floor
accelerations
2
2
Acceleration [ms
floor
0
Same trend at
all floors
­1
­2
Differences on
high frequency
details
­3
­4
­5
­6 0
2
4
6
8
10
Time [s]
System Identification
26
ONE DEGREE OF FREEDOM SYSTEM
System Identification
ONE DEGREE OF FREEDOM SYSTEM
System Identification
27
ONE DEGREE OF FREEDOM SYSTEM
System Identification
ONE DEGREE OF FREEDOM SYSTEM
System Identification
28
MECHANICAL MODEL
uo
BS
fo
m
LD
FD
Spring force
Friction force
k1
fd
k0
­u
Displacement
uy
u
Displacement
mu  cu  f s u,u   f d signu   0
u t 0   u 0
­uo
uo
­f d
u t 0   0
System Identification
SYSTEM PARAMETER VECTOR

S  0 ,1,u d ,u y , 0

Friction force
Spring force
k1
fd
k0
­u
Displacement
uy
Displacement
u
­uo
uo
­f d
12 
k1
m
 02 
k0
m
ud 
0 
System S0 S1  0 (Hz) 0.50 0.55 fd
k0
c
2 m 0
1 (Hz) u d (m) u y (m) 0 0.40 0.35 0.005 0.004 0.02 0.03 0.05 0.03 System Identification
29
IDENTIFICATION PROCEDURE
e2 
~
~
~
~
 A0  A , A0  A t0  t ,t 0  t 

 A0 , A0 
t0 ,t 0 
AS 0   A0
S0
~
S
N
 A,B   Ai Bi
i 1
~ ~
~
  Ai ,A j   ~
ti , t j  
Cij  


  A0 ,A0  t 0 ,t 0  
Bi 
C ij X j  Bi

~
SSX
t ~
~
tj 
S
S j
State parameter vector
Trial state parameter vector
~
~ ~
~
~~
 Ai ,A0    Ai ,A  ti ,t 0    ti , t 

 A0 ,A0 
t 0 ,t 0 

A ~
~
Aj 
S
S j

~
~
AS  A
~
X j  Sj Sj
System Identification
IDENTIFICATION OF TEST FUNCTIONS
System S 0 S 1 Branches Error 1 9.9081 10 ­17 1­2 9.4827  10 ­10 1­2­3 5.4252 10 ­5 1­2­3­4 2.4896  10 ­4  0 (Hz) 0.50 0.55 1 (Hz) 0.40 0.35 0.5500 0.5500 0.5503 0.5509 0.3500 0.3500 0.3520 0.3534 u d (m) u y (m) 0.005 0.004 Identified parameters 0.0040 0.0040 0.0038 0.0037 0.02 0.03 0 0.05 0.03 0.0300 0.0300 0.0296 0.0294 0.0300 0.0300 0.0338 0.0372 System Identification
30
DATA FROM SOLARINO TESTS
Test N. 3
Untreated signal
Treated signal
(a) Original acceleration signal recorded on the 2nd floor of the Solarino building; (b) Same signal after removal of high frequency components.
System Identification
DATA FROM SOLARINO TESTS
Recorded and identified signals for test number 3
System Identification
31
DATA FROM SOLARINO TESTS
Identified system parameters, estimate of initial displacement and final quadratic error for model including viscous damping.
Test 3 5 6 7 8 Nominal u0 [m] 0.1148 0.1329 0.1308 0. 0967 0.1075 Estimated u0 [m] 0.1108 0.1169 0.1228 0.0927 0.0965 ud [m] 0.0034 0.0034 0.0035 0.0033 0.0025 uy [m] 0.0181 0.0167 0.0179 0.0173 0.0118  0 0.000000045 0.0127 0.000000036 0.000387 0.0306 0 [Hz] 0.5235 0.5117 0.5269 0.5222 0.5402 1 [Hz] e2 0.3947 0.4070 0.3909 0.3964 0.4242 0.0114 0.0040 0.0077 0.0088 0.0021 System Identification
DATA FROM SOLARINO TESTS
Identified system parameters, estimate of initial displacement and final quadratic error for model excluding viscous damping.
Test 3 5 6 7 8 Nominal u0 [m] 0.1148 0.1329 0.1308 0.0967 0.1075 Estimated u0 [m] 0.1108 0.1159 0.1168 0.0867 0.0905 ud [m] 0.0033 0.0048 0.0033 0.0030 0.0036 uy [m] 0.0179 0.0199 0.0162 0.0141 0.0148  0 0 0 0 0 0 0 [Hz] 0.5266 0.4982 0.5377 0.5423 0.5284 1 [Hz] e2 0.3931 0.4043 0.3989 0.4086 0.4154 0.0114 0.0049 0.0073 0.0077 0.0028 System Identification
32
IDENTIFIED PHYSICAL PARAMETERS
Identified physical parameters for model including viscous damping;
f aS  100 kN
Test f 0 [kN] u0 [m] 0 [rad/s] 1 [rad/s] m [kN s2/m] k 0 [kN/m] k 1 [kN/m] uy [m] ud [m] f d [kN] 3 1027.04 0.1108 3.2892 2.4800 1210 13094 7444 0.0181 0.0034 45 5 1139.76 0.1169 3.2151 2.5573 1256 12982 8213 0.0167 0.0034 44 6 1177.17 0.1228 3.3106 2.4561 1299 14241 7838 0.0179 0.0035 50 7 828.48 0.0927 3.2811 2.4907 1114 11992 6910 0.0173 0.0033 40 8 927.04 0.0965 3.3942 2.6653 1121 12917 7965 0.0118 0.0025 32 mean 3.2980 2.5299 1200 13045 7674 0.0164 0.0032 42 st.dev. 0.0645 0.0845 82 801 510 0.0026 0.0004 7 c.o.v (%) 2 3 7 6 7 16 13 16 System Identification
IDENTIFIED PHYSICAL PARAMETERS
Identified physical parameters for model including viscous damping;
Test f 0 [kN] u0 [m] 0 [rad/s] 1 [rad/s] m [kN s2/m] k 0 [kN/m] k 1 [kN/m] uy [m] ud [m] f d [kN] 3 1027,04 0,1108 3,2892 2,4800 1184 12812 7283 0,0181 0,0034 44 5 1139,76 0,1169 3,2151 2,5573 1232 12733 8055 0,0167 0,0034 43 6 1177,17 0,1228 3,3106 2,4561 1275 13977 7693 0,0179 0,0035 49 7 828,48 0,0927 3,2811 2,4907 1083 11663 6720 0,0173 0,0033 38 8 927,04 0,0965 3,3942 2,6653 1094 12604 7772 0,0118 0,0025 32 mean 3,2980 2,5299 1174 12758 7505 0,0164 0,0032 41 st.dev. 0,0645 0,0845 84 824 518 0,0026 0,0004 7 c.o.v (%) 2 3 7 6 7 16 13 16 System Identification
33
IDENTIFIED PHYSICAL PARAMETERS
Identified physical parameters for model excluding viscous damping; f aS  100 kN
Test f 0 [kN] u0 [m] 0 [rad/s] 1 [rad/s] m [kN s2/m] k 0 [kN/m] k 1 [kN/m] uy [m] ud [m] f d [kN] 3 1027.04 0.1108 3.3087 2.4699 1215 13307 7415 0.0179 0.0033 44 5 1139.76 0.1159 3.1303 2.5403 1277 12509 8238 0.0199 0.0048 60 6 1177.17 0.1168 3.3785 2.5064 1319 15051 8284 0.0162 0.0033 50 7 828.48 0.0867 3.4074 2.5673 1134 13170 7476 0.0141 0.0030 40 8 927.04 0.0905 3.3200 2.6100 1218 13429 8300 0.0148 0.0036 48 mean 3.3090 2.5388 1233 13493 7943 0.0166 0.0036 48 st.dev. 0.1079 0.0541 70 941 455 0.0024 0.0007 8 c.o.v (%) 3 2 6 7 6 14 20 16 System Identification
IDENTIFIED PHYSICAL PARAMETERS
Identified physical parameters for model excluding viscous damping;
Test f 0 [kN] u0 [m] 0 [rad/s] 1 [rad/s] m [kN s2/m] k 0 [kN/m] k 1 [kN/m] uy [m] ud [m] f d [kN] 3 1027.04 0.1108 3.3087 2.4699 1189 13019 7255 0.0179 0.0033 43 5 1139.76 0.1159 3.1303 2.5403 1252 12268 8079 0.0199 0.0048 59 6 1177.17 0.1168 3.3785 2.5064 1294 14772 8130 0.0162 0.0033 49 7 828.48 0.0867 3.4074 2.5673 1103 12808 7271 0.0141 0.0030 38 8 927.04 0.0905 3.3200 2.6100 1189 13105 8099 0.0148 0.0036 47 mean 3.3090 2.5388 1206 13194 7767 0.0166 0.0036 47 st.dev. 0.1079 0.0541 73 940 460 0.0024 0.0007 8 c.o.v (%) 3 2 6 7 6 14 20 16 System Identification
34
STATIC AND DYNAMIC FRICTION COEFFICIENTS
Identification of static and dynamic friction coefficients for LFSB
Test 3 5 6 7 8 mean st.dev. c.o.v (%) Model including viscous damping f aS  100 kN f aS  120 kN s (%) 1.65 1.59 1.54 1.79 1.78 1.67 0.11 7 d (%) 0.74 0.70 0.77 0.71 0.58 0.70 0.07 10 s (%) 2.03 1.95 1.88 2.21 2.19 2.05 0.15 7 d (%) 0.74 0.70 0.77 0.71 0.58 0.70 0.07 10 Model excluding viscous damping f aS  100 kN f aS  120 kN s (%) 1.64 1.57 1.52 1.76 1.64 1.63 0.09 6 d (%) 0.72 0.94 0.75 0.70 0.79 0.78 0.10 12 s (%) 2.02 1.92 1.85 2.17 2.02 2.00 0.12 6 d (%) 0.72 0.94 0.75 0.70 0.79 0.78 0.10 12 System Identification
RESULTS IN LITERATURE
•
•
•
•
•
•
•
Oliveto, G. , Caliò, I., Marletta, M., (2004). Retrofitting of reinforced concrete
buildings not designed to withstand seismic action: a case study using base isolation,
13th WCEE, Paper No 954, Vancouver, Canada.
Oliveto, G. , Granata, M., Buda, G. , and Sciacca, P., (2004). Preliminary results from
full­scale free vibration tests on a four story reinforced concrete building after
seismic rehabilitation by base isolation, JSSI 10th Anniversary Symposium on
Performance of Response Controlled Buildings, Yokohama, Japan.
Oliveto, G. , Marletta, M., (2005). Seismic retrofitting of reinforced concrete buildings
using traditional and innovative techniques, ISET Journal of Earthquake
Technology, vol. 42 June­September 2005, pp. 21­46, ISSN: 0972­0405. Paper No 454.
Oliveto, G. , Scalia, G., (2006). Free­Vibration Tests Following Seismic Retrofitting
by Base Isolation on the Solarino Buildings. 8th US National Conference on
Earthquake Engineering (8NCEE).
Oliveto, G., Scalia, G., (2007). Wavelet analysis in dynamic identification of base
isolated buildings: application to the Solarino buildings. ANIDIS XII Convegno
Nazionale l’Ingegneria Sismica in Italia – Pisa.
Oliveto, N., D., Scalia, G., Oliveto, G., (2008). Dynamic identification of structural
systems with viscous and friction damping. Journal of Sound and Vibration 318 ­
911–926
Oliveto, N., D., Scalia, G., Oliveto, G., (2009). Time Domain Identification of Hybrid
Base Isolation Systems using Free Vibration Tests. Earthquake Engineering and
Structural Dynamics, to appear.
System Identification
35