The Use Of Fiber Bragg Grating In Structural Health ...€¦ · The Use Of Fiber Bragg Grating In...
Transcript of The Use Of Fiber Bragg Grating In Structural Health ...€¦ · The Use Of Fiber Bragg Grating In...
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The Use Of Fiber Bragg Grating In Structural Health Monitoring Applications
H. Marzouk Faculty of Engineering, Architecture and Science Ryerson University, Toronto, Ontario, Canada
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Introduction to structural health monitoring (SHM).
Optical Fiber Bragg Grating (FBG) sensors.
Monitoring of existing structural members.
Experimental Creep Investigation.
NS, HS, UHPC.
Summary and Conclusions.
Presentation Outline
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Structural Health Monitoring
Definition of SHM
Structural health monitoring (SHM) is defined as the process ofimplementing a damage detection strategy for aerospace, civil, andmechanical engineering infrastructure. It consists of permanentcontinuous, periodic or periodically continuous recording of representativeparameters, over short or long terms.
Advantages/Benefits of SHM
1. Improved understanding of in-situ structural behaviour2. Early damage detection3. Assurances of a structure’s strength and serviceability4. Reduction in down time5. Improved maintenance and management strategies for better
allocation of resources6. Enables and encourages use of innovative materials
Doctor / Patient SHM Engineer / Structure
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Damage Detection
Damage Detection
In the most general terms, damage can be defined as changes introduced into a system that adversely affects its current or future performance.
Damage levels:
1. Identification that are detection of the damage, 2. Localization of the damage, 3. Quantification of damage, and 4. Decision-making.
Different types of damage
One-way shear cracksPunching shear cracksLongitudinal Flexure cracks
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Structural Health Monitoring Using Fiber Optics
SYSTEM COMPONENTS
1. Selection of Sensors
2. Sensor Installation and
Placement
3. Transfer to Data Acquisition
System
4. Data Sampling and
Collection
5. Intelligent processing and
management of DATA
6. Storage of processed DATA
7. Diagnostics
Sensors
(various types)
Monitored Structure
DA system
(on-site)
Communication System
(e.g. telephone lines)
Data processing
(automatically by computer)
Diagnostics
Data retrieval
(and decision making)
Data Storage
(hard discs or
CD archives)
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OPTICAL FIBER SENSORS
FIBRE OPTIC SENSORS
Advantages of Fibre Optic Sensors
1. Non-conductive
2. Stable
3. Convenience
4. Flexibility
Types of Fibre Optic Sensors
1. Fibre Bragg Grating (FBG)
2. Long Gauge Sensors
3. Fabry-Perot
4. Brillouin Scattering
Embeddable
Bondable
Weldable
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FBG Array
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Operating Principle
Operating Principle
Transmission and reflection spectra of a fiber Bragg grating FBG
2o n
Bragg wavelength
>8mm >8mm >25 to 40mm
Outer jacket Aramid reinforcing fibres Inner jacket Fibre buffer Optical fibre
Schematic showing the typical components of a bondable
fibre optic sensorΛ: modal index or
grating pitch
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Advantages of Optical Fiber Sensing
• High Sensitivity;
• Electrical Passiveness;
• Wide Dynamic Range;
• Multiplexing Capability.
Physical phenomenon to be measured
Wavelength Shift for Fiber Bragg Grating
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Types of Optical Fiber Sensors
1) Temperature sensor
2) Strain Sensor
3) Pressure sensor
4) Chemical sensor
5) Biomedical sensor (oxygen sensor)
6) Fiber-optic gyroscope
7) Electrical and magnetic sensors
8) Displacement and position sensors
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Reflection spectrum of a fiber Bragg Grating
-60
-55
-50
-45
-40
-35
-30
-25
-20
-15
-10
-5
0
1542 1544 1546 1548 1550 1552
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Calibration of FBG DATA ANALYSIS – STATIC LOAD TEST
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Electric Strain Gauge (ESG) Versus Fiber Bragg Grating (FBG)
0
2
4
6
8
10
12
14
16
0 5 10 15 20 25 30 35
Strain, microstrain
Load
, k
ips
Average Steel Stain (ESG)
Average Steel Strain (FBG)
Fig. 3 Comparison for average steel strain Using ESG and FBG
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Fiber Bragg grating wavelength sensing system
FBG 1 FBG 2 FBG 3
USB
Source of light
Wavelength detection
PC
Optic electronic
demodulation unit
Digital interface
PCMCIA card
FBG-SLI
Optical Fiber
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Placing of FBG In Concrete Slab
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Structural Health Monitoring Using Fiber Optics
Experimental Program
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1
2
6 3
7
4
8
5
FBG Demodulatio
n
unit
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Health Monitoring of Flexural Cracks
FBG and ESG sensors to monitor Flexural cracks
1900
1900
FBG1Fiber
ESG1 ESG2
ESG3 ESG4
Wires
ESG
Long
FBGFBG and ESG sensors glued
to tensile rebars
Stub column
Supporting beam
boundaries
1900
1900
Fiber
FBG
250
300
Long FBG sensor embedded in
the concrete slab (300 mm)
Long-gauge sensors allow the measurement of deformations over measurement bases that can reach tens of metres with resolutions in the micrometre range.
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Health Monitoring of New Structures
SHM for a reinforced concrete beam
Test setup and instrumentation
A
A
1500 600 1500
200 3600 200
375
650
300
2 # 15M
2 # 25M
30
40
Section A-A
A
A
1500 600 1500
200 3600 200
375
650
300
2 # 15M
2 # 25M
30
40
Section A-A
Dimensions and reinforcement of test beam
LVDTLVDT
LVDT
670 kN MTS
Front View
Top View
Concrete strain gauges
Steel strain gauges
4000
880254
32°
Long FBG sensor
Expected diagonal
shear crack path
900900 900 900
650
300
300
Long FBG sensor
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Test Results
Crack pattern for test beam
4000
900900 900 900
650
Long FBG sensor
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Test Procedure
Cyclic Load Test (ACI 437R-03)The loading process involved a serviceability limit state cycle test and a failure Cycle test. In the serviceability test, a relatively small force was imposed on the slab of approximately 0.5 Pu and then it was released after finishing the test.When using the cyclic load test method (ACI 437R-03), load is typically applied by hydraulic actuators in a stepped loading pattern that is made up of :1. At least three (3) load-sets.2. Each load-set is made up of two (2) or more identical load cycles.
Load-Time
0
50
100
150
200
250
0:00:00 0:14:24 0:28:48 0:43:12 0:57:36 1:12:00
Time (h:mm:ss)
Lo
ad
(kN
)
Loading profile for service loading test
Load Control (Slab) Displacement Control (Beam)
Displacement-Time
0
5
10
15
20
25
30
0:00:00 0:14:24 0:28:48 0:43:12 0:57:36 1:12:00 1:26:24 1:40:48 1:55:12 2:09:36 2:24:00
Time (hh:mm:ss)
Dis
pla
ce
me
nt (m
m)
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Test Results
Concrete tensile strain-time
Concrete strain-Time
0
200
400
600
800
1000
1200
1400
1600
0:00:00 0:14:24 0:28:48 0:43:12 0:57:36 1:12:00
Time (h:mm:ss)
Co
ncre
te s
tra
in (
με)
FBG Concrete strain (300 mm)
First Crack
Second Crack
The long FBG sensor was able to capture the initiation of the first and secondtransverse cracks; this is indicated by a sudden increase (shift) in the concrete tensile strain value. The first crack width could be calculated by multiplying the difference in the concrete tensile strain (340 µε) by the gauge length value (300 mm), and it is equal to 0.102 mm.
Concrete tensile strains
Flexural Cracks Detection (Slab)
Stub column
Supporting beam
boundaries
1900
1900
Fiber
FBG
250
300
Embedded Long FBG
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Steel strains
Strain response of cracked slab
under cyclic loading
Based on a calibration test, the wavelength-strain coefficient for the FBG sensor was estimated to be approximately 0.95 pm/με.
Load-Steel strain
0
50
100
150
200
250
0 200 400 600 800 1000 1200
Steel strain (με)
Lo
ad
(kN
)
Load-Steel Strain
0
50
100
150
200
250
0 200 400 600 800 1000 1200 1400
Steel strain (με)
Lo
ad
(kN
)
FBG Steel Strain Gauge (20 mm)
Electrical Strain Gauge
Test ResultsFlexural Cracks Detection (Slab)
Typical behaviour
Load-steel strain
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Shear strains
Test ResultsBeam Shear Sensor
Shear strain-Time
Long FBG sensor was able to measure the shear strain and to capture the initiation of two Flexural cracks. The first shear crack occurred at a shear strain of 214 micro strain and a load 145 kN. The max. recorded shear strain Of 1186 micro strain at a failure load of 226 kN.
Shear strain-Time
0
50
100
150
200
250
300
350
400
450
0:00:00 0:28:48 0:57:36 1:26:24 1:55:12 2:24:00
Time (hh:mm:ss)
Sh
ea
r str
ain
(µ
ε)
Shear strain
Flexural crack
Flexural crack
Load - Shear strain
Load-Shear strain
0
50
100
150
200
250
300
350
400
450
0 50 100 150 200 250 300 350 400 450
Shearl strain (µε)
Lo
ad
(kN
) Long FBG sensor
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Dispacement - Time
0
1
2
3
4
5
6
7
8
0:00:00 0:14:24 0:28:48 0:43:12 0:57:36 1:12:00 1:26:24 1:40:48 1:55:12
Time (hh:mm:ss)
Dis
pla
ce
me
nt (m
m)
Loading Profile
Test ResultsOne-Way Shear (Beam)
Displacement - Time
The test was carried out using a closed-loop (MTS) testing machine with a maximum capacity of 670 kN. The load was applied by means of a hydraulic actuator in displacement control mode.
Displacement-Time
0
5
10
15
20
25
30
35
40
45
0:00:00 0:14:24 0:28:48 0:43:12 0:57:36 1:12:00 1:26:24
Time (hh:mm:ss)
Dis
pla
ce
me
nt (m
m)
Service test Failure test
Load-Time
0
50
100
150
200
250
300
350
400
450
500
0:00:00 0:14:24 0:28:48 0:43:12 0:57:36 1:12:00 1:26:24
Time (hh:mm:ss)
Lo
ad
(kN
)
Load - Time
Service test Failure test
Load - Time
0
50
100
150
200
250
0:00:00 0:14:24 0:28:48 0:43:12 0:57:36 1:12:00 1:26:24 1:40:48 1:55:12
Time (hh:mm:ss)
Lo
ad
(kN
)
Flexural cracksFlexural cracks
Concrete CrushingFlexural + Shear cracks
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Steel strains
Test ResultsOne-Way Shear (Beam)
Steel strain-Time
Steel strain-Time
0
200
400
600
800
1000
1200
1400
0:00:00 0:28:48 0:57:36 1:26:24 1:55:12 2:24:00
Time (hh:mm:ss)
Ste
el str
ain
(µ
ε)
Steel strain
Flexural crack
Flexural crack
Electrical strain gauges (ESG) sensors were able to capture the initiation of two Flexural cracks as well as m.
Load-Steel strain
0
50
100
150
200
250
300
350
400
450
0 200 400 600 800 1000 1200 1400 1600 1800
Steel strain (µε)
Lo
ad
(kN
)
Steel gauge 1
Load - Steel strain
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(FBG) sensors are the most common types of fiber optic sensors used for structural applications
FBG system includes:• Optical fiber with prewritten grating sensors
• A broadband source
(light emission device)
• Coupler
• Optical spectrum
analyzers (OSA)
Fiber Bragg Grating sensors (FBG)
FBG 1 FBG 2 FBG 3
USB
Source of light
Wavelength detection
PC
Optic electronic
demodulation unit
Digital interface
PCMCIA card
FBG-SLI
Optical Fiber
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Fiber Bragg GratingASSMEBLEING
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Fiber Bragg Grating Packaging
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I-MON 512-USB2 Evaluation software
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FBG installation for Beam
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CIVIL ENGINEERING DEPARTMENT
DR. H. Marzouk
E-MAIL: [email protected]
Definition of SHMStructural health monitoring (SHM) is defined as the process of implementing
a damage detection strategy for aerospace, civil, and mechanical engineering
infrastructure. It consists of permanent continuous, periodic or periodically
continuous recording of representative parameters, over short or long terms.
Advantages/Benefits of SHM1. Improved understanding of in-situ structural
behaviour
2. Early damage detection
3. Assurances of a structure’s serviceability
4. Reduction in down time
5. Improved maintenance and management
strategies for better allocation of resources
6. Enables and encourages use of innovative
materials and Extended bridge service life
Advantages of Fibre Optic Sensors1. Non-conductive, Stable, Convenience and Flexibility.
2. High Sensitivity and Electrical Passiveness
3. Wide Dynamic Range and Multiplexing Capability.
Physical phenomenon to be measured
Wavelength Shift for Fiber Bragg Grating
Types of Fiber Optic Sensors1. Fibre Bragg Grating (FBG)
2. Long Gauge Sensors
3. Fabry-Perot
4. Brillouin Scattering
Analytical Model For Crack Spacing
RESEARCH OUTCOME R
RESEARCH OUTCOME
The presented work describes a structural health monitoring technique to detect,
localize and quantify damage for in existing and new structural members.
Long FBG sensor embedded in concrete slab was successfully used to detect the
width and location of first crack.
CIVIL ENGINEERING DEPARTMENT
DR. H. Marzouk
E-MAIL: hmarzouk @ryerson.ca
Doctor / Patient SHM Engineer / Structure
PROBLEMS AND CHALLENGES
The maximum effective strain, εmax, for HSC is reported to be around 16 times εp, strain at ultimate load
(Marzouk & Chen, 1995). However, when using UHPFRC it is observed that εmax is 4-6 times greater
than εp. The fracture energy can then be claculated using the load-deformation response using Eq1
(Japan Concrete Institute Standard, 2003). Table 2 summarizes the mechanical properties of the test
specimens.
GF= (0.75W0+W1)/Alig
Where,
GF = fracture energy (N/mm)
W1= 0.75(Sm1/L +2m2)*g*CMODc
W0 = area below CMOD curve up to rupture of specimen (N.mm)
W1 = work done by deadweight of specimen and loading jig (N.mm)
Alig = area of broken ligament (b*(h-a0) (mm2)
m1 = mass of specimen (kg)
S = loading span (mm)
L = total length of specimen (mm)
m2 = mass of jig not attached to testing machine but placed on specimen until rupture (kg)
g = gravitational acceleration (9.807 m/s2)
CMODc = crack mouth opening displacement at the time of rupture (mm)
RESEARCH FINDINGS
UHPFRC, exhibits superior qualities compared
to normal and high strength concrete. The
introduction of fiber reinforcement proves to
increase, significantly, the ductility of the mix;
resulting in a concrete material that behaves
rather different than conventional concrete.
High strength concrete has a more brittle
behavior to that of normal strength concrete,
demonstrated by the sharp descends in the
stress-strain curve. UHPFRC exhibits a far
more ductile behavior when compared to
normal and high strength concrete. This ductile
behavior and the increased strength ultimately
result in concrete with significantly higher
fracture energy, consequently a higher
characteristic length.
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• Beam (200x300x1000 mm)
• Two point load
• 150mm gage length of FBG
• Normal strength concrete:35 Mpa
• specimens were loaded at a displacement rate
0.003 mm/s
0.002 mm/s
0.0002 mm/s
TEST SET UP FOR CONCRETE BEAMS
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Mix Properties Normal-Strength High-Strength* Ultra-High Strength
fcm28, MPa 30 70 140
Water Content 0.40-0.45 0.27-0.3 0.17-0.20
Cement Content kg/m3
(silica fume)
350 440
SF(5% of cement content)
883
SF(24% of cement
content)
Coarse aggregate kg/m3 1200 1100 -
Air entrainment agent(ml/m3) 300 325 -
Water reducing agent (ml/m3) 1400 825 4% of cement content
Superplasticizers(ml/m3) 1500 7500 Na
Relative Humidity,% 95 95 95
Type of Cement ASTM (I) ASTM (I) ASTM (I)
t 0 (time of curing, days) 28 28 28
t (time of loading, days) 28 28 28
Type of curing Moist Moist Moist
Mix Properties of three graded concrete
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SPECIMENS PREPARATION FOR CREEP AND SHRINKAGE MEASUREMNT
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Creep testing
Experimental set up for creep test
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• Civil Lab, Ryerson university
Testing procedure
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Creep testing
cylinders under constant load with
a) FBG embedded b) ESG on surface
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Compressive Strength
0
20
40
60
80
100
120
140
160
180
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014
0
5
10
15
20
25
Axi
al C
om
pre
ssiv
e St
ress
(M
Pa)
Axial Strain (mm/mm [in./in.])
Axi
al C
om
pre
ssiv
e St
ress
(ks
i)HSC HPFC1
HPFC2 UHP-FRC
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Modulus of Elasticity test with embedded FBG sensor
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Creep and shrinkage strain from FBG sensors
0
50
100
150
200
250
300
350
400
450
500
0 5 10 15 20 25 30
Cre
ep
an
d s
hri
nka
ge S
trai
n (
µε)
Days of loading
UHPC
HPC
NC
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Shrinkage from FBG sensors
0
10
20
30
40
50
60
70
28 33 38 43 48 53 58
shri
nka
ge s
trai
n (
µε)
Days after casting
UHPC HPC NC
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Long –Term creep prediction base on experimental result
y = 1.5642ln(x) + 1.1233
y = 3.783ln(x) + 2.5453
y = 19.172ln(x) + 5.2603
0
10
20
30
40
50
60
70
80
0 5 10 15 20 25 30
Cre
ep S
trai
n (
µε/
MPa
)
DAYS
UHPC
HPC
Normal
Log. (UHPC)
Log. (HPC)
Log. (Normal)
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SHM Methodology
55
Structure Health Monitoring
Data Collection
System Integration
F.E Model
Visual Inspection
Inspection Reports
Feild Mesurments
Fiber Optic Sensors
Data Acquisition
Database Station
RD Signature
Lifecycle Mangement
and Assessment
Decision Making
Risk and Reliablitiy Assesment
Reliability Index
Lifecycle Algorithm
Detoriation Model
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Management Strategy
• Assessment Results
Assumption of a generic degradation model.
Stiffness, crack width, settlement, deflection.
Visual inspection, damage detection methodologies.
Dynamic monitoring methodologies.
• Life cycle analysis, durability, the real degradation process and residual lifetime considerations
Estimation of the design life of the existing structure.
Assessment criteria in order to take corrective measure;o Dynamic bridge monitoring
o Visual inspections
o Material tests.
Maintenance instructions to preserve the original design life.
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SHM Performance IndicatorSHM Performance Indicator
Random Decrement
Integrity
Mode Shapes
Operability
Half cell Potiential
Corrosion
MultiChannel Random
Decrement
Damage Locatization
Trend (Time)
Life-Cycle-Curve
Crack Width (piezo-ceramic
sensors)
Stiffness Mapping
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Design life using probability density functions
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Bridge Condition Index (BCI)
BCI Range Condition Recommended Action
70 – 100 Good Maintenance work is usually not
required within the next five years.
60 – 70 Fair
Maintenance work is usually
scheduled within the next five year.
This is the ideal time to schedule
major bridge repairs from an
economic perspective.
Less than
60
Poor Maintenance work is usually
scheduled within one year from
inspection date.
BCI Ratings Used by MTO
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Bridge Condition Index (BCI)
Performance
Measure
Weight Factor Deterioration Type Weight Factor
Accuracy 0.25 Delamination 0.42
Precision 0.30 Corrosion 0.35
Speed 0.25 Cracking 0.10
Ease of Use 0.10 Concrete
Degradation
0.13
Cost 0.10
Deterioration Type Delamination Corrosion Cracking Concrete
Deterioration
Overall
Value
Impact Echo 4.7 1.0 2.5 3.1 3.0
Ultrasonic Pulse Echo 3.6 1.0 2.6 3.4 2.6
Half-Cell Potential 1.0 4.9 0.0 1.0 2.3
Impulse Response 3.6 1.0 0.0 2.6 2.2
Ultrasonic Surface Waves 2.5 1.0 3.0 3.4 2.2
Ground Penetrating Radar 3.0 1.0 1.0 3.1 2.1
Chain Drag/ Hammer
Sounding
3.7 1.0 0.0 1.0 2.1
Electrical Resistivity 1.0 3.9 0.0 1.0 1.9
Infrared Thermography 3.2 1.0 0.0 1.0 1.8
Galvanostatic Pulse
Measurement
1.0 3.0 0.0 1.0 1.6
Table 5.4.3.1 – Performance Measure and Deterioration Type Vs. Weight Factor (Gucunski et al, 2010)
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Equipment:
• Impact hammer (type Kistler 9728A)
• 10g accelerometer (type Kistler 8704B500)
• Data acquisition system (NI cDAQ-9184 (NI) compact DAQ)
Experimental investigation
61
Accelerometer
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The initiation of the flexural crack was achieved where the
beam was loaded using concentrated three point load setup.
Experimental investigation
62
Accelerometer 1
Load cell
Crack gauge
Accelerometer 2
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Theoretical investigation
63
𝑋𝑅𝑖 𝜏 =1
𝑁 𝑖=1
𝑁 𝑥𝑖 (𝑡𝑖 + 𝜏)
𝑋𝑅𝑖 𝜏 is the estimate of the RD interpreted in terms of correlation function
𝑡𝑖 is the time past the triggering
N is the number of triggering points
𝜏 is time lag
Brincker, R. 2005
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Theoretical investigation
64
Locating damage using differences of the normalized mode shape
𝑥𝑖(𝑡) = 𝐴𝑖 𝑒−2 𝜀 𝜔𝑡 cos 𝜔𝑖 𝑡 − 𝜑𝑖 , 𝑖 = 1,2,3… . , 𝑁
λ𝑖 = 𝐴1 , 𝐴2 , … . , 𝐴𝑚𝑇
λ𝑖∗ = 𝐴1
∗, 𝐴2∗, … . , 𝐴𝑚
∗ 𝑇
∆λ𝑖 = 𝐴1𝑛−𝐴1
∗𝑛, 𝐴2𝑛−𝐴2
∗𝑛, … . , 𝐴𝑚𝑛−𝐴𝑚
∗𝑛 𝑇
𝑥𝑖(𝑡) is the random decrement for certain channel 𝜀 is the
damping coefficient
𝜔𝑖 is the natural frequency and 𝜑𝑖 is the phase angle λ𝑖 is the mode shape
𝐴𝑖 is the displacement amplitude
n is superscript indicates the normalized value ∆λ𝑖 is the modal
vector difference
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Data analysis
• Logarithmic Decrement
65
ni
i
A
Aln
n
1
22
2
4
Tfr
1
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Methodology
Theoretical investigation
• It reduces the response to equivalent free decay of the structure.
𝜇1 + 2𝜉𝜔𝑜 𝜇1 + 𝜔02𝜇1 = 0
• It is an approach to identify the dynamic parameters using logarithmic
decrement from the free decay curve.
66
ω𝑜 is the natural frequency
𝜉 is the damping ratio
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Theoretical investigation
𝑀 𝑥(𝑡) + 𝐶 𝑥(𝑡) + 𝐾 𝑥(𝑡) = 𝑓(𝑡)
𝑥(𝑡) + 2𝜔𝑜𝜉 𝑥(𝑡) + 𝜔𝑜2 𝑥(𝑡) = 𝑓(𝑡)
Let 𝑦1 = 𝑥 and 𝑦2 = 𝑥
𝑦1 = 𝑦2
𝑦2 = −2𝜔𝑜𝜉𝑦2 − 𝜔𝑜 𝑦1 + 𝑓(𝑡)
𝜕𝑃
𝜕𝑡=
𝜕
𝜕𝑦1𝑦2𝑃 +
𝜕
𝜕𝑦2−2𝜔𝑜𝜉𝑦2 − 𝜔𝑜
2 𝑦1 𝑃 +𝜓𝑜
2
𝜕2
𝜕𝑦22
𝑃 𝑌, 𝑡 + 𝑑𝑡 𝑌𝑜 − 𝑃 𝑌, 𝑡 𝑌𝑜
=𝜕
𝜕𝑦1𝑦2𝑃 +
𝜕
𝜕𝑦2−2𝜔𝑜𝜉𝑦2 − 𝜔𝑜
2 𝑦1 𝑃 +𝜓𝑜
2
𝜕2
𝜕𝑦22
67
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Theoretical investigation
−∞
∞
𝑦2(𝜕
𝜕𝑦22𝜔𝑜𝜉𝑦2 − 𝜔𝑜
2 𝑦1 𝑃) 𝑑𝑦1𝑑𝑦2 = −(2𝜔𝑜𝜉𝑦2 + 𝜔𝑜2 𝑦1)
μ1 = μ2 = −(2𝜔𝑜𝜉𝑦2 + 𝜔𝑜2 𝑦1)
−∞
∞
𝑦1 𝑌, 𝑡 + 𝑑𝑡 𝑌𝑜 𝑑𝑦1𝑑𝑦2 = 𝜇1(𝑡 + 𝑑𝑡)
−∞
∞
𝑦2(𝜕
𝜕𝑦22𝜔𝑜𝜉𝑦2 − 𝜔𝑜
2 𝑦1 𝑃) 𝑑𝑦1𝑑𝑦2 = −(2𝜔𝑜𝜉𝑦2 + 𝜔𝑜2 𝑦1)
𝜇1 + 2𝜉𝜔𝑜 𝜇 + 𝜔02𝜇1 = 0
68
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Results
• Figures show the RD signatures at different damage.
Acc. (1) Acc. (2)
69
-1.1
-0.6
-0.1
0.4
0.9
0 0.01 0.02 0.03
Nor
mal
ized
RD
Time lag
Intact
Cracking load
Yeild Load
Ultimate load
-1.1
-0.6
-0.1
0.4
0.9
0 0.01 0.02 0.03N
orm
aliz
ed R
D
Time Lag
Intact
Cracking Load
Yeild load
Ultimate Load
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Results
70
• Concrete Beam
Load Natural frequency (Hz) Damping
ratio (%)
Intact 63.83 0.70
Cracking 62.50 1.18
Yeild 61.22 2.28
Ultimate 60.00 5.33
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Results
Normalizing the difference between the mode shapes of intact
and damaged cases
Mode (2)
71
-4
-3
-2
-1
0
1
2
3
4
1 2 3 4 5 6 7 8 9 10
Nor
mal
ized
def
lect
ion
Node Number
Intact
Damaged
0
0.2
0.4
0.6
0.8
1
1.2
1 2 3 4 5 6 7 8 9 10
Nor
mal
ized
diff
eren
ce
Node Number
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Conclusion
RD technique showed a similarity in detecting the damage in
concrete, as the technique showed significant results for detecting the
damage applied on steel structures.
RD technique can be used for structural health monitoring of
important mega structures, especially the structures subjected to
ambient vibration loads.
Damage location was determined by the normalized difference
between the intact and damaged mode shape, which was shown that
it is an effective to locate the damage.72
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T
ThanksQuestions & Comments
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Creep strain from FBG sensors
0
50
100
150
200
250
300
350
400
0 5 10 15 20 25 30
Cre
ep
str
ain
(µε)
Days
UHPC
HPC
NC
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Result for UHPC cylinders
0
20
40
60
80
100
120
140
160
0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004
Axi
al s
tres
s(M
Pa)
strain
Compressive strength (MPa) Modulus of elasticity Strain at Peak
145 49.9 0.00315