Embed Size (px)
Citation preview
IDENTIFICATION OF PRESTRESS
FORCE IN PRESTRESSED CONCRETE BOX
GIRDER BRIDGES USING ULTRASONIC
TECHNOLOGY
Manal Kamil Hussin
Bachelor Degree in Civil Engineering University of Baghdad
Master Degree in Civil Engineering University of Southern Queensland
Submitted in fulfillment of the requirements for the degree of
Doctor of Philosophy
School of Civil Engineering and Built Environment
Science & Engineering Faculty
Queensland University of Technology
2018
i
Keywords
nondestructive technology, piezoelectric transducers, prestressed concrete bridges,
structure health monitoring, ultrasonic waves, fast Fourier transform, destructive
methods, box-girder, unbonded tendons, amplitude, attenuation, resonance frequency
ii
Abstract
Prestressed concrete box-girder bridges are gaining popularity in bridge engineering
systems because of their better stability, serviceability and structural efficiency. These
advantages can be achieved by using the prestressing technique, which involves
applying a prestress force (PF) to the reinforced concrete structure to improve the
weakness of concrete to tension.
Monitoring the PF in prestressed concrete box-girder bridges without affecting
serviceability has been known as one of the most suitable approaches to achieve a
timely decision-making process concerning the health status of the bridges, including
emergency cases such as bridge collapse. However, there are currently no accepted
nondestructive technologies (NDTs) to evaluate the PF of these bridges, because
implementing such a technology in practice is not always feasible due to various
difficulties such as the large scale of the bridge, tight budget and uncertainties of new
sensing technologies.
To overcome these problems altogether, this research program aims to develop
a practical and simple, yet more comprehensive and reliable method to identify the PF
of new and existing prestressed concrete bridges using ultrasonic technology. Towards
this objective, parametric studies were carried out using a finite element method
(FEM) to identify the effect of the PF on the ultrasonic wave behaviour. The simulation
results showed that there is a relationship between the relative change in the wave
velocity and the PF applied to the tendons. The results demonstrated that it is possible
to relate the relative change in the wave velocity to the applied PF according to
acoustoelastic theory.
Prestressed concrete with a box-girder cross-section and unbonded embedded
tendons is one of the most popular bridges. However, most of the available methods
found in the literature were designed to identify the PF directly from attaching the
ultrasonic transducers on the ends of accessible prestressing tendons. To overcome this
drawback, a number of laboratory tests have been carried out on a simply supported
prestressed concrete box-girder bridge with a uniform cross section model. This was
used to determine whether it is possible to identify the PF from the inverse calculation
iii
of the compressive stress developed on the concrete surface due to applying the PF to
the tendons.
The effectiveness of the PF on ultrasonic wave parameters has been tested
experimentally and linear and nonlinear acoustic parameters of the ultrasonic wave
have been examined. Different parameters related to the prestressed concrete model
have been investigated to provide a valid technique to identify the PF. Experimental
results have shown that the ultrasonic technology is applicable for PF monitoring in
new and existing prestressed concrete box-girder bridges with good accuracy. It is
evident that the novel method developed in this research can effectively identify the
PF in box-girder using the ultrasonic technology.
iv
Table of Contents
Keywords .................................................................................................................................. i
Abstract .................................................................................................................................... ii
Table of Contents .................................................................................................................... iv
List of Tables ......................................................................................................................... viii
List of Figures ......................................................................................................................... ix
List of Abbreviations ............................................................................................................. xiii
Statement of Original Authorship .......................................................................................... xv
Publications ........................................................................................................................... xvi
Acknowledgements .............................................................................................................. xvii
Chapter 1: Introduction ...................................................................................... 1
1.1 Background .................................................................................................................... 1
1.2 Research problem ........................................................................................................... 3
1.3 Research aim and objectives .......................................................................................... 4
1.4 Significance of the developed method and scope of research ........................................ 4
1.5 Thesis outline ................................................................................................................. 7
Chapter 2: Literature Review ............................................................................. 9
2.1 Introduction .................................................................................................................... 9
2.2 Destructive methods ..................................................................................................... 10
2.3 Semidestructive methods ............................................................................................. 12
2.4 Nondestructive methods ............................................................................................... 13
2.4.1 Vibration-based techniques in prestress evaluation ................................. 13
2.4.2 Non-vibration techniques in prestress evaluation .................................... 15
2.5 Summary and conclusion remark ................................................................................. 24
Chapter 3: Ultrasonic Guided Wave and Linear and Nonlinear Acoustic
Theory .......................................................................................................... 26
3.1 Introduction .................................................................................................................. 26
3.2 Ultrasonic testing and linear acoustoelastic theory ...................................................... 29
3.2.1 Linear acoustoelastic theory .................................................................... 30
3.2.2 Wave propagation in isotropic elastic media ........................................... 35
3.2.3 Phase velocity and group velocity ........................................................... 43
3.3 Ulatrsonic testing and Nonlinaer acoustic parameter ................................................... 45
3.3.1 Contact acoustic nonlinearity ................................................................... 46
3.3.2 Nonlinear Acoustic theory ....................................................................... 48
3.3.3 Ultrasonic wave interaction with discontinuous surface.......................... 52
3.4 Summary ...................................................................................................................... 53
v
Chapter 4: Research Design .............................................................................. 54
4.1 Requirement of study ....................................................................................................54
4.2 Methodology .................................................................................................................54
4.2.1 Achieving objective 1 .............................................................................. 55
4.2.2 Achieving objective 2 .............................................................................. 56
4.2.3 Achieving objective 3 .............................................................................. 56
4.3 Summary .......................................................................................................................56
Chapter 5: Effect of Prestress Force on Ultrasonic Wave Characteristics .. 57
5.1 Introduction ..................................................................................................................57
5.2 Numerical model and the effect of the bonded and unbonded tendon..........................58
5.3 Effect of the PF on the box-girder ................................................................................64
5.4 ABAQUS /explicit and numerical integration ..............................................................66
5.5 Theoretical analysis of wave propagation ....................................................................68
5.6 Mesh and load ...............................................................................................................69
5.7 Results and discussion ..................................................................................................75
5.7.1 Hanning window signal results ............................................................... 75
5.7.2 Sinusoidal signal results .......................................................................... 78
5.8 Summary .......................................................................................................................82
Chapter 6: Experimental Study and Box-Girder Model Preparation .......... 83
6.1 Experimental model ......................................................................................................83
6.2 Prestressing tendons details ..........................................................................................85
6.3 Construction of lab model ............................................................................................86
6.3.1 Stage 1 ..................................................................................................... 88
6.3.2 Stage 2 ..................................................................................................... 88
6.3.3 Stage 3 ..................................................................................................... 89
6.4 Apply the prestressed force on the unbonded tendons .................................................91
6.5 Ultrasonic measurement system ...................................................................................92
6.6 Material properties of the constructed box-girder model .............................................95
6.7 Parameters that can affect ultrasonic testing .................................................................96
6.8 Experimental strategy ...................................................................................................98
6.9 Summary .....................................................................................................................101
Chapter 7: Monitoring Prestressed Concrete Using Linear Acoustic
Parameters of the Ultrasonic Wave ...................................................................... 103
7.1 Experimental study .....................................................................................................103
7.2 Test prototyping ..........................................................................................................104
7.3 Stress state analysis of the box-girder.........................................................................107
7.4 Cross-correlation for time delay estimation................................................................110
vi
7.5 The effect of the receivers’ position ........................................................................... 112
7.5.1 Results of the receivers attached at the web slab ................................... 113
7.5.2 Data analysis and PF identification from the web data .......................... 120
7.5.3 Results from receivers attached under the bottom slab of the girder ..... 123
7.5.4 Data analysis and PF identification using data from the bottom slab .... 127
7.6 Effect of distance between transducer and receiver ................................................... 130
7.7 Wave amplitude energy ............................................................................................. 133
7.8 Recommendations for identifying the PF using linear acoustic parameter for practical
application ............................................................................................................................ 137
7.9 Approach to identify the PF from the Linear acoustic parameter of the Ultrasonic wave
.................................................................................................................................... 137
7.10 Conclusion ................................................................................................................. 139
Chapter 8: Effect of PF on the Nonlinear Acoustic Parameter ( 𝜷 ) of the
Ultrasonic Wave ..................................................................................................... 140
8.1 Experimental set-up ................................................................................................... 140
8.2 Experimental results ................................................................................................... 143
8.3 Calculating the PF using Beta data ............................................................................ 150
8.4 Results analysis .......................................................................................................... 154
8.5 Recommendations for identifying the PF using nonlinear acoustic parameter for
practical application ............................................................................................................. 155
8.6 Approach to identify PF from the nonLinear acoustic parameter for practical
applications ........................................................................................................................... 156
8.7 Conclusion ................................................................................................................. 157
Chapter 9: Conclusions and Future Work .................................................... 159
9.1 Requirements of the study .......................................................................................... 159
9.2 Study approach ........................................................................................................... 159
9.3 Key findings of this research...................................................................................... 160
9.3.1 Numerical study results ......................................................................... 160
9.3.2 Identifying the PF using linear acoustic parameters .............................. 161
9.3.3 Identifying the PF using nonlinear acoustic parameters ........................ 162
9.4 Comparison study between using linear and nonlinear acoustic parameters of ultrasonic
testing in pf identification..................................................................................................... 163
9.5 Contributions of the developed methods .................................................................... 164
9.6 Future recommendations ............................................................................................ 164
Bibliography ........................................................................................................... 166
Appendix A ............................................................................................................. 173
Appendix B.............................................................................................................. 175
Appendix C ............................................................................................................. 178
vii
viii
List of Tables
Table 5-1. Material Properties Used during the Simulation for the Prestressed
Concrete Beam............................................................................................... 59
Table 5-2. Material Properties Used during the Simulation for the Box-girder ................... 66
Table 6-1. Material Properties of Each Section of the Box-Girder ...................................... 95
Table 6-2 Prestress Force Levels .......................................................................................... 99
Table 7-1. Stress Values of the Receivers Located in Web Slab of the Model .................. 109
Table 7-2. Stress Values of the Receivers Located Under the Bottom Slab of the
Model ........................................................................................................... 110
Table 7-3. Relative Change in the Wave Velocity (Web Part of the Model) Due to
PF ................................................................................................................. 119
Table 7-4. PF Calculated from the Ultrasonic Data at the Receivers Attached at the
Web Slab of the Girder with the Error Percentage ...................................... 122
Table 7-5. Positions of the Receivers under the Model ...................................................... 125
Table 7-6. PF Calculated from the Ultrasonic Data at the Receivers Attached Under
the Bottom Slab of the Girder with the Error Percentage ............................ 130
Table 8-1. PF Calculated from Nonlinear Acoustic Data with the Error Percentage ......... 154
Table 9-1. Comparison between the linear and nonlinear acoustic parameters used in
the PF identifications ................................................................................... 163
ix
List of Figures
Figure 1-1. Components of concrete prestressing system (AMSYSCO, 2010). .................... 2
Figure 1-2. Collapse of pedestrian bridge outside Lowe’s Motor Speedway, North
Carolina (Penamakuru, 2008). ......................................................................... 3
Figure 1-3. The collapse of Melle Bridge in Belgium (Schutter, 2012). ............................... 6
Figure 2-1. Destructive methods used to determine the PF ................................................. 11
Figure 2-2. The experimental setup including the prestressing strand, and EMAT run
by Penamakuru (2008) .................................................................................. 16
Figure 2-3. Schematic diagram of instrumentation set-up for MsS used to inspect
rebar (Bartels et al., 1999) ............................................................................. 18
Figure 2-4. Illustrated layout of the test run by Joh et al. (2013). ........................................ 19
Figure 3-1. Transverse and longitudinal waves (Han, 2007). .............................................. 28
Figure 3-2. Direction of wave propagation. ......................................................................... 31
Figure 3-3. Mode shapes of symmetric and assymetric fundamental Lamb wave
modes across the plate thickness Lee and Oh (2016) .................................... 41
Figure 3-4. Theoretical phase velocity dispersion curves for a concrete slab
(determined by WAVESCOPE software). .................................................... 44
Figure 3-5. Shows theoretical group velocity dispersion curves for a concrete slab
(WAVESCOPE softwa) ................................................................................ 45
Figure 3-6. An example of an imperfect contact interface at the box-girder surface........... 47
Figure 3-7. Schematic model of contacting interface adopted in this research. ................... 49
Figure 3-8. The signal propagation in surface with micro crack. ........................................ 52
Figure 4-1. Aim and objectives ............................................................................................ 55
Figure 5-1. FEM model adopted in this section with bonded and unbonded tendons ......... 59
Figure 5-2. Stress distribution of the beam due to prestressing ........................................... 60
Figure 5-3. The ultrasonic wave propagation between the transmitter and the receiver
on the prestressed concrete surface (A) at the beginning (B) at the end
of the simulation ............................................................................................ 62
Figure 5-4. Acceleration response of the node in the receiver point for the bonded
tendons at different PF levels ........................................................................ 63
Figure 5-5. Acceleration response of the node in the receiver point for the unbonded
tendons at different PF levels ........................................................................ 63
Figure 5-6. Relative change in the wave velocity due to apply PF for bonded and
unbonded tendons .......................................................................................... 64
Figure 5-7. Cross-section of the box-girder used in the FE (dimensions in m). .................. 65
Figure 5-8. The model after applying the symmetric boundary condition at the
middle of the girder ....................................................................................... 65
Figure 5-9. Fine mesh along the direction of wave propagation. ......................................... 70
Figure 5-10. Stress distribution in the box-girder (A) before applying the PF and ............. 71
x
Figure 5-11. Transducer and receiver locations at the top part of the FEM model. ............. 72
Figure 5-12. Transducer and receiver locations at the side part of the FEM model ............. 73
Figure 5-13. Excitation signals used in the simulations. ...................................................... 74
Figure 5-14. Acceleration at the receiver RFEM1 components for different PF ................. 75
Figure 5-15. Acceleration at the receiver RFEM2 components for different PF ................. 76
Figure 5-16. Acceleration at the receiver RFEM3 components for different PF
(Hanning window). ........................................................................................ 76
Figure 5-17. The relationship between the relative change in the wave velocity vs.
% of the PF increasing (Hanning window results). ....................................... 77
Figure 5-18. Acceleration at the receiver RFEM1 components for different PF
(sinusoidal signal). ......................................................................................... 79
Figure 5-19. Acceleration at the receiver RFEM2 components for different PF
(sinusoidal signal). ......................................................................................... 79
Figure 5-20. Acceleration at the receiver RFEM3 components for different PF
(sinusoidal signal). ......................................................................................... 80
Figure 5-21. The relative change in wave velocity due to application of different PF
(sinusoidal signal). ......................................................................................... 81
Figure 6-1. Cross-section of the lab model. ......................................................................... 84
Figure 6-2. Reinforcement details of the lab model. ............................................................ 84
Figure 6-3. Tendon profile. .................................................................................................. 85
Figure 6-4. End anchorage of strand. ................................................................................... 86
Figure 6-5. Construction steps for the box-girder. ............................................................... 87
Figure 6-6. Proposed formwork arrangement. ..................................................................... 87
Figure 6-7. Construction of the model, Stage 1 (bottom slab). ............................................ 88
Figure 6-8. Construction of model, Stage 2 (webs). ............................................................. 89
Figure 6-9. Construction of model, Stage 3 (top slab). ........................................................ 90
Figure 6-10. (A) Dead end and (B) live end anchorage and load cells. ............................... 91
Figure 6-11. (A) Prestressing equipment and process. (B) Load cell reading during
tensioning. ...................................................................................................... 92
Figure 6-12. (A) Agilent 33500B waveform generator and (B) RIGOL DS 1204B. ........... 93
Figure 6-13. Piezoelectric transducers used in the experimental test. .................................. 94
Figure 6-14. Modulus of elasticity test. ................................................................................ 96
Figure 6-15. Surfaces that need to be avoided with ultrasonic technology. ......................... 97
Figure 6-16. Strategy of experimental tests. ....................................................................... 100
Figure 7-1. Box-girder while applying the load on the tendon. ......................................... 105
Figure 7-2. Ultrasonic test set-up. ...................................................................................... 106
Figure 7-3. Stress distribution in prestressed box-girder beam under working load
moment. Adapted from the Australian Standard AS 3600-2009. ................ 108
Figure 7-4. Calculated Δt between two signals using cross-correlation method. ............... 111
xi
Figure 7-5. Ultrasonic wave phase velocity of the box-girder determined using
WAVESCOPE software. ............................................................................. 113
Figure 7-6. Position of the transmitters and the receivers on the web of the model
(Not: the dimensions are not to scale). ........................................................ 114
Figure 7-7. Test set-up at the web part of the box-girder. .................................................. 114
Figure.7-8. Signals received at Receiver 1 (RW1) due to applying different PF, with
a close-up of the first part of the signal. ...................................................... 115
Figure 7-9. Signals received at Receiver 2 (RW2) due to applying different PF, with
a close-up of the first part of the signal. ...................................................... 116
Figure 7-10. (A) and (B) Results of time lag estimation using a cross-correlation
method. ........................................................................................................ 118
Figure 7-11. Relative changes in the wave velocity as a function of applied stress in
the web part of the model. ........................................................................... 119
Figure 7-12. PF calculated from the ultrasonic wave data (web part results). ................... 121
Figure 7-13. Positions of the transmitters (TB) and the receivers(RB) under the
bottom slab of the girder. (Note: the sketch is not to scale.) ...................... 124
Figure 7-14. Experimental prototype with transducers placed under the bottom slab
of the box-girder. ......................................................................................... 125
Figure 7-15. Relative change in the wave velocity as a function of applied stress of
the receivers attached under the bottom slab of the model.......................... 127
Figure 7-16. Camber created under the box-girder due to applying PF. ............................ 129
Figure 7-17. Calculated PF from the ultrasonic wave data under the bottom slab of
the girder ..................................................................................................... 129
Figure 7-18. Relative change in the wave velocity as a function of applied stress
when the distance between the transmitter and the receiver is equal to
50 cm, (A) web slab (B) under the bottom slab of the box-girder. ............. 132
Figure 7-19. An example of signal received during application of different PF. .............. 134
Figure 7-20. Received signal and the created envelope to calculate the area under the
signal. .......................................................................................................... 134
Figure.7-21. Measurement of the transmitted energy (face-to-face contact). .................... 135
Figure 7-22. Waveform energy vs. stresses developed due to applying PF. ...................... 136
Figure 8-1. Schematic of the experimental set-up. ............................................................ 141
Figure 8-2. Lamb wave phase velocity dispersion curves for prestressed concrete .......... 142
Figure 8-3. FFT calculation process. ................................................................................. 143
Figure 8-4. FFT spectra of signals detected by the ultrasonic transducers at receiver
RB1.............................................................................................................. 145
Figure 8-5. FFT spectra of signals detected by the ultrasonic transducers at receiver
RB2.............................................................................................................. 146
Figure 8-6. FFT spectra of signals detected by the ultrasonic transducers at receiver
RB3.............................................................................................................. 147
Figure 8-7. FFT spectra of signals detected by the ultrasonic transducers at receiver
RB4.............................................................................................................. 148
xii
Figure 8-8. FFT spectra of signals detected by the ultrasonic transducers at receiver
RB5. ............................................................................................................. 149
Figure 8-9. Nonlinear parameter for second harmonic vs. developed stresses at the
receivers’ locations due to applying PF to the tendons................................ 150
Figure.8-10. Nonlinear parameter for second harmonic as a function of load applied
to the free strand (Bartolie et al. 2009) ........................................................ 151
Figure 8-11. shows the non-linear parameter from 2nd harmonic as a function of load
applied to the embedded strand (Bartolie et al. 2009) ................................. 152
Figure 8-12. Calculating the PF from β data. ..................................................................... 153
xiii
List of Abbreviations
𝑓𝑐𝐵 compressive stress
𝑓𝑐𝑇 tensile stress
AE acoustic emission
ALID absorbing layer increase damping
CCO cross-correlation coefficient
Cg group velocity
CL longitudinal wave
Cp phase velocity
CT transverse wave
e eccentricity from the natural axis
EMAT electromagnetic ultrasonic technology
GUW guided ultrasonic wave
K acoustoelastic constants
𝛽 beta
MsS magnetostrictive sensor.
NA natural axis
NDT nondestructive technology
NDE nondestructive evaluation
PF prestressed force
PSC prestressed concrete
PSCBs prestressed concrete bridges
SHM structure health monitoring
SI system identification
THD total harmonic disorder
xiv
UTS ultimate tensile strength
PZT piezoelectric
FFT fast Fourier transform
xv
Statement of Original Authorship
The work contained in this thesis has not been previously submitted to meet
requirements for an award at this or any other higher education institution. To the best
of my knowledge and belief, the thesis contains no material previously published or
written by another person except where due reference is made.
Signature:
Date: 12/4/2018
QUT Verified Signature
xvi
Publications
Hussin, M. Chan, T. H.T., Fawzia, S, & Ghasemi, N. (2015). Finite element
modelling of Lamb wave propagation in prestress concrete and effect of the prestress
force on the wave’s characteristic. In 10th RMS Annual Bridge Conference: Bridges –
Safe and Effective Road Network, 2–3 December 2015, Ultimo, NSW.
xvii
Acknowledgements
My special gratitude presented to Prof. Tommy Chan for being an excellent
adviser and supportive during my research journey.
I would also like to take this opportunity to extend my appreciation to my
associate supervisors Dr Negareh Ghasemi and Dr Sabrina Fawzia for their valuable
advice and the useful discussion. Assistance and experience of Dr Andy Nguyen the
manager of my project were extremely helpful for the successful completion. My
special thank goes to him for his support.
My particular thanks go to the technical staff members in the Banyo Pilot Lab
for their excellent practical support and guidance. It was a great experience to work
together with my team members in the lab.
I gratefully acknowledge the financial support provided by Queensland
University of Technology during my research journey. I would like to express my
gratitude to members of structure health monitoring research team. My special thanks
to my project team members Thisara Pathirage and Ziru Xiang for sharing their
knowledge and experience, and being with me and helping me at my hard work.
My sincere thanks to my husband Atef Jabar and lovely family for their support,
understanding and encouragement during these great years.
Last but not least, my special thanks to Professional editor, Robyn Kent,
provided copyediting services according to the guidelines laid out in the university-
endorsed national ‘Guidelines for editing research theses’.
1
Chapter 1: Introduction
Introducing the research, this chapter outlines the background (section 1.1) and
research problem (section 1.2). Section 1.3 describes the research aim and objectives.
Section 1.4 presents the significance and scope of this research. Section 1.5 includes
an outline of the remaining chapters of the thesis.
1.1 BACKGROUND
Since the development of prestressed concrete by Freyssinet in the early 1930s,
the materials have found extensive application in the construction of medium and long-
span bridges, gradually replacing steel that needs costly maintenance due to the
inherent disadvantage of corrosion under environmental conditions (Bhivgade, 2014).
The purpose of using prestressing is to control cracking, reduce tensile strain and
reduce deflection of the beam. This is done by introducing compressive stress to the
reinforced concrete by tensioning the steel tendons to balance the expected tensile
stress developed under service loading. This results in improved serviceability, and
allows for stronger, lighter sections and a reduced dead load to live load ratio.
Tensioning of the tendons can be undertaken before (pretensioning) or after
(posttensioning) the concrete itself is cast. The tendons are located either within the
concrete volume (internal prestressing) or outside of it (external prestressing).
Whereas pretension concrete by definition uses tendons directly bonded to the
concrete, posttensioned concrete uses either bonded or unbonded tendons.
The large forces required to tension the tendons result in a significant permanent
compression being applied to the concrete once the tendon is “locked-off” at the
anchorage (Bartoli, Nucera, Srivastava, Salamone, Phillips, Scalea, et al., 2009; Lin &
Burns, 1981). However, over prestressing can cause cracking or possibly failure before
even any external loading is applied, therefore prestressed concrete is requiring a
higher level of technology and expert people in its construction. Figure 1.1 shows the
components of a typical modern prestressed system.
2
Figure 1-1. Components of concrete prestressing system (AMSYSCO, 2010).
In this type of bridge system, because of the nature of the long-term material
behaviour of concrete and steel, tensile forces induced by prestressing tendons
decrease over time. This phenomenon is called long-term prestress force loss. The
long-term behaviour that causes prestress loss in the PSCB can be categorised into
three interdependent components, which are creep, drying shrinkage of concrete and
steel relaxation of the tendons (Jang, Hwang, Lee, & Kim, 2013).
Monitoring the PF in PSCBs without affecting serviceability has been one of the
most suitable approaches to achieve a timely decision-making process concerning the
health status of civil infrastructure, including emergency cases such as possible
structural failures. Therefore, it is important to manage and estimate the actual PF level
when the PSCBs are in service appropriately. Failures in PF management result in an
increase of the deflection or crack and lead to high degradation of performance or, in
the worst cases, a collapse of the structure. Figure 1.2 shows the collapse of a
pedestrian bridge in May 2000 outside Lowe’s Motor Speedway in Concord, North
Carolina, due to a lack of effective inspection (Penamakuru, 2008).
3
Figure 1-2. Collapse of pedestrian bridge outside Lowe’s Motor Speedway, North Carolina
(Penamakuru, 2008).
1.2 RESEARCH PROBLEM
As mentioned earlier, PF in the tendon is the most important factor that determines the
load-carrying capacity of prestressed structures. However, inspecting these tendons
using any nondestructive evaluation (NDE) method has been a challenging task as they
are embedded in concrete. Visual inspection of the PSCB in most cases has failed to
identify the PF in the tendon that is hidden under the concrete cover without any signs
of specific degradation.
In the last few years, therefore, significant researches have been conducted to
identify the PF of different types of PSCBs, as will be presented in Chapter 2. A
number of destructive methods have been proposed, for example, the cracking moment
tests, to identify and evaluate the PF of the PSCBs. However, these specification
methods have been destructive to either concrete or tendon surfaces, which reduces
their applicability for use with in-service bridges.
With recent advances in sensor technology in SHM, the trend has now turned
towards using nondestructive technology (NDT) to determine the effective PF of
PSCBs. As a result, a number of approaches have been developed. However, almost
all previous efforts with regard to this problem were either focused on prestressed
beams or used for accessible tendons (where the ends of the tendons are accessible or
4
not hidden under the concrete). No record of a successful method was found to evaluate
the effective prestress level of box-girder bridges with embedded tendons, which are
another important form of prestressed bridge structures.
1.3 RESEARCH AIM AND OBJECTIVES
Having identified the gap in knowledge about PF identification, this study was
aimed to develop a simple yet comprehensive NDE method to identify the PF in new
and existing prestressed post-tension box-girder bridges. To meet this aim, ultrasonic
technology has been employed for this purpose. This technology has been proven to
be a highly efficient method for the NDE and SHM of structures with finite dimensions
such as PSCBs.
In order to achieve the above aim, the following objectives were accomplished.
1. Carry out comprehensive literature review to explore current knowledge on
effect of the prestressing force on the behaviour of the ultrasonic wave linear
and nonlinear acoustic parameters.
2. Develop FEM to study the effect of the PF on the ultrasonic wave
characterises. Then, study the feasibility of using these parameters in the
inverse calculation to identify the PF of the PSCB.
3. Develop scaled-down version of prestressed concrete box-girder bridge with
unbonded tendons and perform the ultrasonic tests in the laboratory.
4. Validate the PF identification method (developed in objective 3) against the
experimental results.
1.4 SIGNIFICANCE OF THE DEVELOPED METHOD AND SCOPE OF
RESEARCH
There are more than 130,000 bridges in the United State constructed using
prestressing strands, of which more than 37,000 bridges are at least 30 years old
(Washer, 2001). In Australia, more than 60% of current in-service bridges are PSCBs,
according to the Bureau of Transport and Communities Economics (1997). Some of
the current in service bridges are more than 50 years old and designed to carry lower
traffic load.
5
PSCBs deteriorate during their service life due to factors such as ageing of
materials, excessive use, losses of PF, overloading, environmental conditions and
deficient maintenance. The PF of these bridges is one of the most important parameters
that are responsible for the load carrying capacity of the structure. As a result,
monitoring the PF of these structures is one of the considerable importance in view of
the immense loss of life and property that may result from structural failure.
The unique features of large size and complexity of the PSCBs render visual
inspection very time consuming, expensive and sometimes unreliable. The need for
quick assessment of the PF necessitated research for the development of an automated,
real-time and in site health monitoring technique. This kind of technique allows
monitoring the bridge while the structure is in service.
Further, monitoring can be performed throughout the service life of the structure;
such technique is useful not only to improve reliability but also reduce maintenance
and inspection costs of the bridge and to prevent them from the collapse through
monitoring the PF in the steel tendons of these bridges.
The collapse of several bridges, all over the world, due to defective prestressing
systems, has alarmed authorities to pay attention to the safety of these important
structures. For example, the sudden collapse of Melle Bridge in Belgium due to
corroded tendons (Schutter, 2012) as shown in Figure 1.3. Subsequent investigation
found that the collapse of the bridge was due to corroded tendons (Schutter, 2012).
6
Figure 1-3. The collapse of Melle Bridge in Belgium (Schutter, 2012).
As discussed earlier, effective PF is the main factor in the load-carrying capacity
of the PSCB. However, currently there is no acceptable method that can effectively
identify such important parameters unless the tendons are not hidden under the
concrete surface, that is where the tendon ends were exposed, or the tendons were
completely exposed (external). While in reality, most of the PSCBs are designing and
constructed with embedded tendons.
Therefore, the findings of this research will enable the PF to be identified without
causing any damage to the surface or affecting the serviceability of the structure.
Further, the technology can be either used for the PSCBs with new construction and
exciting brides with either accessible or embedded tendons.
The scope of this research is limited to a simply supported box-girder of a uniform
cross-section with internal unbonded prestressing tendons’. However, this technology
can be an important base for future development for other PSCBs.
7
1.5 THESIS OUTLINE
This thesis consists of nine chapters.
Chapter 1: Begins with a general introduction to the research and a brief discussion
on the background. It further illustrates research and the current problem of identify
the PF of the PSCBs, followed by illustration of the aim, objectives, significance and
scope of this study.
Chapter 2: Reviews the existing destructive, semi destructive and nondestructive
methods for identifying PF and the relative area, followed by a summary of the
researchers’ important findings.
Chapter 3: Begins with a general introduction to the ultrasonic technology adopted to
achieve the objectives of this research. Section 3.1 presents the linear acoustic
parameters of the ultrasonic wave and the related acoustoelastic theory. Section 3.2
presents the nonlinear acoustic parameters of the ultrasonic wave and the related
nonlinear acoustic theory.
Chapter 4: Discusses the methodology adopted to achieve the aim and objectives of
this research
Chapter 5: Mainly concentrates on finite element modelling that was carried out to
study the effect of the PF on the ultrasonic wave characteristic.
Chapter 6: Details the laboratory test model, its construction process and
experimental set-ups.
Chapter 7: Details the experimental set-ups and results calculated using the linear
acoustic parameters of the ultrasonic waves.
Chapter 8: Details the experimental set-up and results calculated using the nonlinear
acoustic parameters of the ultrasonic wave.
Chapter 9: Concludes the research with some recommendations for future research.
9
Chapter 2: Literature Review
This chapter reviews the literature on the PF identifications of the prestressed
concrete structures. Sections 2.2–2.4 review different methods of evaluating residual
stresses and effective PF of existing structures. Section 2.5 summarises the key
findings in the literature and highlights the identified gap in knowledge.
2.1 INTRODUCTION
Prestressed concrete bridges (PSCBs) are large, spatially distributed engineered
systems that will gradually deteriorate with time if they cannot be managed and
maintained properly. Considering their invaluable societal functionality, the long-term
health management of these bridges is just as important as their design and
construction.
To assess the structural reliability of bridges, a precise and cost-effective
measurement technology is necessary to ensure their safe and reliable operation.
Visual inspection is the simplest and oldest inspection technique that can provide
information on the state of prestressed concrete structures. This is often the only
method available to bridge engineers (Claudio, 2010; Williams & Hulse, 1995). This
type of inspection usually performed by trained inspectors to assess the condition of
the structure. However, PF identification using the visual inspection is known to have
limitations and shortcomings, and has failed to identify the PF in tendons, especially
those hidden under the concrete cover without any signs of degradation or those placed
in locations that are difficult for the inspectors to reach.
Strain gauges could be used for load monitoring and fatigue inspection for a
structural member (Mandracchia, 1995), However, strain gauges can be time-
consuming to install because paint removal is most likely to be necessary as part of the
surface preparation. When dealing with lead-based paints, which are considered
hazardous waste and many time-consuming (Eligehausen, Fuchs, & Sippel, 1998).
Further, measuring the PF using a strain gauge cannot be accomplished by
conventional procedures for experimental stress analysis, since the strain sensor is
10
totally insensitive to the history of the part, and measures only the changes in strain
after the sensor has been installed (Vishay, 2005).
As a result, researchers have attempted to use different methods and technologies
to identify the PF of the PSCBs. Some of these studies ended without success
(Abraham, Park, & Stubbs, 1995), while some other studies developed different
approaches to quantify the PF. These methods can be broadly categorised as
destructive, semi destructive and nondestructive. The next sections will review some
of these methods found in the literature.
2.2 DESTRUCTIVE METHODS
Destructive methods of assessment often employed a gradually increasing load
until the concrete member cracked or ultimately failed. Their application is mostly
limited to laboratory tests.
Halsey and Miller (1996) used different destructive methods to evaluate the
stress level of prestressing tendons of a forty-year-old PSCB beam. The methods
measured the PF in different ways, such as:
1. The cracking moment tests. In this method, the force in the prestressing
strands was calculated from the observed cracking moment.
2. Decompression load. The beam is cracked and unloaded. On reloading, the
beam is checked to determine the load at which the crack opens.
3. Cutting the strand tests. The strand was cut with bolt cutters and strain
gauged. In this method, a strand is exposed, and then a strain gauge is
installed and used to measure strains that develop when the strand is cut.
The corresponding PF in the strand can then be determined.
Figure 2.1 shows cracking moment, decompression load and cutting the strand
tests used to determine the PF.
11
Figure 2-1. Destructive methods used to determine the PF
(Bagge, Nilimaa, & Elfgren, 2017).
A cracking moment test was been used to determine the effective PF of seven
PSCB girders after forty-two years in service (Osborn, Barr, Petty, Halling, & Brackus,
2010). The authors used a cracking moment test in which a slowly increasing point
load was applied at the mid span of the simply supported bridge girder until a clearly
visible vertical crack propagated across the bottom flange.
The beam was unloaded again so that the induced crack closed due to the PF. A
strain gauge was then attached across the so formed crack and the beam was reloaded
until the crack reopened. The stress of the bottom most fibres at which the crack
reopened was used to estimate the effective PF. Testing this way is accurately quantify
the effective PF. However, it cannot be applied to in-service bridges, as it requires
damaging the bridge girder.
Chen and Gu (2005) proposed a simplified way to calculate the ultimate capacity
of an externally prestressed beam when the effective prestress is known. The effective
PF can be calculated using this method if the ultimate failure load is known. However,
this method cannot be used with bridges currently in service.
12
2.3 SEMIDESTRUCTIVE METHODS
The most widely used technique for measuring residual stress is the Standard
Test Method E837-13 Hole-Drilling Strain Gauge method of stress relaxation (ASTM,
1992). This method is used for determining residual stress profiles near the surface of
an isotropic linearly elastic material. The measurement procedure involves these basic
steps:
1. Drilling a small-diameter hole in the flange of the girder, and initiating a
small crack at the perimeter of the hole parallel to the longitudinal axis of
the beam.
2. A special three- (or six-) element strain gauge rosette is installed on the test
part at the point where the residual stress is to be determined.
3. Readings are made of the relaxed strains, corresponding to the initial
residual stress.
4. Using special data-reduction relationships, the principle residual stresses
and their angular orientation are calculated from the measured strains.
The introduction of a small hole into the test surface is one of the most critical
operations in this method. It is imperative that the hole is drilled without introducing
significant additional residual stress. To the degree that any of the foregoing
requirements fail to be met, accuracy will be sacrificed accordingly. Further, it is
important that the hole depth at each drilling increment is measured as accurately as
possible, since a small absolute error in the depth can produce a large relative error in
the calculated stress. McGinnis, Pessiki, and Turker (2005) demonstrated that the
applicability of the Hole-Drilling Strain Gauge Method to concrete structures is
uncertain because the heterogeneous nature of the concrete complicated strain
measurement over small gauge length.
Each of the presented destructive and semi destructive methods require
permanent damage to concrete or steel, or both in some methods, which reduces their
applicability to real structures. Further, each method needs people with the expertise
to run such testing. Therefore, there is an urgent demand to find a nondestructive
technology that can identify the PF of the PSCBs without causing any damage or
affecting future serviceability. These difficulties and limitations are the motivation for
13
exploring other approaches and nondestructive technologies (NDT) to evaluate the
health monitoring of PSCBs.
If high-precision facilities were evaluated by NDT, it would be possible to
continue operating and maintaining an existing structure for a long time. Further, by
using NDT, the operation of the PSCB can be maintained more efficiently and thus
contribute to the creation of a safer and more secure environment. A review of various
techniques and methods currently used for inspecting PSCBs are presented here. The
overall attempt is to study the literature and identify recently developed techniques and
refinements of NDE methods.
2.4 NONDESTRUCTIVE METHODS
Nondestructive methods (NDMs) are defined as a process of evaluating the
condition of the structure without affecting its future use and application. A material
under test is loaded with some form of energy and, based on the response to that
loading; the quality of the components is inferred. This process can be used to
determine material characteristics and properties and to evaluate the PF of the PSCBs.
The recently available inspection technologies for identifying PF are described as
follows.
2.4.1 Vibration-based techniques in prestress evaluation
Several existing SHM systems have used the vibration-based method to monitor
PSCB by observing changes in their dynamic characteristics, for example, shifts in
natural frequencies and changes in vibration mode shapes in relation to change in the
PF (Abraham et al., 1995; Ho, Kim, Stubbs, & Park, 2012; Miyamoto, Tei, Nakamura,
& Bull, 2000; Saiidi, Douglas, & Feng, 1994).
Researchers such as Abraham et al. (1995) tried to predict the loss of PF based
on the damage index derived from derivatives of the mode shape. Abraham reported
that the natural frequencies increased as the prestress in the structure decreased.
However, the mode shapes remained almost identical with different PF in the beam.
Because of the latter results, Abraham et al. failed to identify the PF.
Saiidi et al. (1994) reported a study of the change of modal frequency due to PF,
with laboratory tests results. The authors showed that the sensitivity of the modal
14
frequency to prestress decreased with higher vibration modes, and the PF affected the
first few lower modes more significantly than the higher ones.
Miyamoto et al. (2000) investigated the dynamic behaviour of a prestressed
composite girder with an impact hammer load. It was found that the natural frequency
tended to decrease as the amount of PF increased (Miyamoto et al., 2000). The authors
also derived a flexural vibration equation of a composite girder subjected to a
prestressing force implemented by external tendons. They considered the change in
tendon force along with the compressive force effect by an incremental formulation of
the equations of motion of the beam. However, the authors ignored the change in the
tendon’s eccentricity.
Ho et al. (2012) identified the PF in a PSC girder using modal parameters and
system identification method. In this method, the authors first used the measured
change in model parameters to estimate the prestress loss and then used a system
identification approach to identify the baseline model that represents the target
structure. This method identified the PF with an error as low as 1.24%. However, it
required vibration response at two prestress levels, which may not be possible for
existing structures.
Li, Lv, and Liu (2013) evaluated a prestressed girder in a bridge using structure
dynamic response under a moving vehicle. The authors carried out a numerical
simulation to identify the magnitude of the PF in a highway bridge, by making use of
the dynamic responses from moving vehicular loads. A single-span prestressed-T
beam and two-span prestressed box-girder bridge employed for that purpose. Li et al.
identified the PF with a maximum error of 4.11% in just 15 iterations with 10% noise
level. However, this method was limited to numerical simulations. Further, the authors
considered the PF as the only parameter to update the model and assumed that all the
other parameters of the model were perfectly matched with the real structure. This
assumption is far from reality where the initial model is often associated with a number
of complexities and different degrees of parameter uncertainties for real structures
(Kodikara, Chan, Nguyen, & Thambiratnam, 2016).
Research that is being conducted by Pathirage, Chan, Thambiratnam, Nguyen,
and Moragaspitiya (2016) presents a new approach to evaluate the effective PF of
plate-like structures with simply supported boundary conditions using their vibration
responses. According to the authors, the proposed method quantifies the prestress
15
effect with reasonable accuracy, even with noisy measurements using both periodic
and impulsive excitations.
Law, Wu, and Shi (2008) used a wavelet-based method for moving load and
prestress identification with a good accuracy. Furthermore, it has the advantage of
making use of any type of measured dynamic response with no assumption on the
initial condition of the system.
Generally, the main difficulty with this system identification technique is that
reducing the PF does not necessarily reflect changes in the global dynamic properties
of the entire structure until the problem is too severe. Further, this method still has
limitations in estimating the PF locally and directly (Claudio, 2010; Joh, Lee, &
Kwahk, 2013).
2.4.2 Non-vibration techniques in prestress evaluation
2.4.2.1 Electromagnetic acoustic transducers
The transducer that converts electromagnetic energy to acoustic energy and vice
versa in conductive materials such as steel prestressing tendons is called an
electromagnetic acoustic transducer (EMAT). EMATs are the devices that operate on
the process of electromagnetic transduction of ultrasonic waves.
This is the process of including ultrasonic waves in solid materials with the help
of an electrically driven coil in the presence of a magnetic field. The propagation
characteristics of these waves can be used to study the tensile stress, deterioration and
damage (Penamakuru, 2008).
Two types of EMAT have been found in the literature: EMATs based upon the
magnetostrictive principle and EMATs based upon Lorentz force and a Villari effect
mechanism. Each type of these transducers has advantages and disadvantages and
these will be presented in the next sections.
A. Elastomagnetic permeability sensors
These sensors are based on the inverse of the magnetostrictive (or
magnetostriction phenomena) effect. Magnetostrictive is a changing of materials’
physical dimensions in response to changing its magnetisation (Penamakuru, 2008).
The changes in the dimensions are the results of reorientation of magnetic domains
within the material. Some ferromagnetic materials such as high-strength steel obey
16
magnetostrictive phenomena. That is, the material exhibits a mechanical deformation
under an applied magnetic field (Sumitro, Kurokawa, Shimano, & Wang, 2005).
Conversely, the magnetic permeability (the degree of magnetisation) of such
material changes as a function of the applied mechanical stress. A measure of the
permeability thus allows the applied stress in tendons and cables to be estimated
(Bouchilloux, Lhermet, & Claeyssen, 1999; Claudio, 2010; Sumitro et al., 2005).
The magnetic sensors can be embedded in concrete structures, and they can be
considered waterproof and resistant to highly corrosive environments. Such
characteristics, in addition to the capacity to withstand large mechanical stress for
periods comparable to the life of the host structure, make these sensors suitable for
estimating the stress level in the prestressed tendons (Claudio, 2010).
Penamakuru (2008) optimised the design parameters of a magnetostrictive
EMAT. Figure 2.2 shows the experimental test set-up to identify the PF of a
prestressing strand using EMAT.
Figure 2-2. The experimental setup including the prestressing strand, and EMAT run by
Penamakuru (2008)
17
A significant limitation of these transducers is the low-level signals of the EMAT
and significant attenuation that is characteristic of acoustic waves propagating in these
embedded steel elements. Therefore, these transducers are not suitable to evaluate the
PF on the concrete surface of the bridge since it depends on the magnetic phenomena.
Further, since these transducers should be attached to the embedded tendons during
the construction stage, they cannot be used with existing in-service bridges.
B. Magnetostructive sensors
The magnetostrictive sensor (MsS) is a type of transducer that can generate and
detect time-varying stresses or strains in ferromagnetic materials such as prestressing
tendons (Kwun & Bartels, 1998). These sensors are working depending on the Lorentz
force mechanism. Considering the physics behind Lorentz force, a coil of wires is
driven by an altering current at the desired ultrasonic frequency. The sensors then
placed near the surface of an electrically conducting object to produce a time-varying
magnetic field, which in turn induces an eddy current in the material under test
(Bartels, Dynes, Lu, & Kwun, 1999). The generated waves are propagated in both
directions along the length of the strand and the inverse magnetostrictive or Villari
effect is used in wave detection.
The changes in magnetic induction and elastic voltage are signalled in the
receiving coil via the Faraday Effect. The detected signals are amplified, filtered and
digitised. Figure 2.3 shows the instrumentation set-up for MsS used for an inspection
of rebar or strand.
18
Figure 2-3. Schematic diagram of instrumentation set-up for MsS used to inspect rebar
(Bartels et al., 1999)
Researchers such as Rizzo and Discalea (2004), Washer (2002) employed these
sensors in cables and strands for identifying PF. Kwun, Bartels, and Hanley (1998)
investigated the effect of the tension load on wave propagation in a seven-wire
prestressing strand. It was observed that under tensile loading a certain portion of the
frequency components of the wave became highly attenuated and, thus, absent in the
frequency spectrum of the wave. The centre frequency of this missing portion, called
notch frequency, was found to increase linearly with log N, where N is the applied
tensile load (Kwun et al., 1998).
The major limitation of these sensors is that they are typically affected by the
low efficiency of transactions. Their efficiency rapidly decreases when the strands are
embedded in concrete. It was found that the attenuation increased dramatically when
the distance between the material surface and the sensors is more than 2.5 cm and that
limits inspection distance (Bartels et al., 1999). Joh et al. (2013) overcame these
limitations by deriving a method measuring the prestressed load on bonded
prestressing tendons in a PSCB using the Villari effect and an induced magnetic field
generated by an electromagnet. The feasibility of the method was verified
experimentally through scaled models as shown in Figure 2.4.
19
Figure 2-4. Illustrated layout of the test run by Joh et al. (2013).
The test results showed that, within the stress range (from 14% of the ultimate
tensile strength [UTS] to 81% of UTS) of the prestressing tendons used in the field,
there is a linear relationship between the stress of the tendons and induced magnetic
induction. Further, the magnetic flux density produced in the tendons depended on the
intensity of the electromagnet and the separation distance (between the transducer and
the tendons) and was not affected by the concrete cover. However, additional studies
need to be conducted on the practical applications of the method. In addition, this
method enables to consider the effect of the various details in actual PSCBs, such as
the effect of longitudinal and transverse reinforcements.
2.4.2.2 Impact-echo test
A practical experimental formula to estimate the existing PF level non-
destructively by only measuring the longitudinal stress wave velocity has been
presented by Kim, Lee, and Cho (2012).
Kim et al. (2012) presented a nondestructive way to evaluate the tensile force
levels applied on grouted bonded seven-wire tendons embedded in a posttensioned
concrete structure. For this purpose, an experimental programme has been carried out
for PSC specimens subjected to longitudinal vibration of an impact. Based on detailed
20
analyses and evaluations for experimental responses of acceleration time histories and
power spectra, it has been found that:
• The longitudinal natural frequency, elastic wave velocity and elastic modulus
are independent of the applied tension, which is not consistent with
acoustoelastic theory and the findings of other researchers.
• The longitudinal elastic wave velocity of the strands increased nonlinearly with
respect to the applied tensile stress level increment.
• Furthermore, it was observed that the method could estimate the exciting
tensile stress of bonded PSC tendons by measuring the stress wave velocity
only if the applied stress level is lower than 40% of the UTS.
• Finally, the method is a scanning technique that requires point-by-point
inspection rather than continuous monitoring (Claudio, 2010).
2.4.2.3 Ultrasonic testing
Ultrasonic testing is one of the most widely used methods for NDE and SHM of
various waveguide structures. The potential use of an ultrasonic system for monitoring
the stress level in the prestressed components (strands, bars anchorage bolts, etc.) has
been known for decades (Chaki & Bourse, 2009; Fuchs et al., 1998). This last
application exploits the acoustoelastic theory relating to nonlinear elasticity and elastic
waves.
Ultrasonic testing used in identifying the PF of PSCBs is divided into two types,
depending on the ultrasonic wave parameters used during the testing. A number of
researchers working in the area of PF identification using ultrasonic testing have
depended on the linear parameters of the ultrasonic wave and acoustoelastic theory,
such as the relative change in the wave velocity. Others have used the nonlinear
acoustic theory and nonlinear parameter of the ultrasonic wave, which depends on the
amplitudes of the second or third harmonic of the fast Fourier transform (FFT). Each
of these methods has advantages and limitations, as will be explained in the next two
sections.
21
A. Ultrasonic testing using linear acoustoelastic theory
This technique is based on the acoustoelastic theory for which the change in
propagation velocity of the ultrasonic wave presents the existence and the level of the
stress on prestressing tendons (Joh et al., 2013).
Chen, Yidong, and GangaRao (1998) explored measuring of PF in steel rods in
research. The authors used threaded bar approximately 9000 mm long and 15 mm
diameter. Piezoelectric transducers were employed to generate (transmitter) and
receive (receiver) the ultrasonic waves. A measurement of PF obtained by measuring
changes in arrival times of the longitudinal waves and a simplified calculation
procedure for predicting these time shifts were described.
Such a measurement tool was used in the work of Laguerre, Aime, and Brissaud
(2002) where the guided wave propagation was used as an indicator for detecting the
PF of seven-wire strands. In multiwire steel strands, Rizzo and Di Scalea (2004)
generated the ultrasonic wave using transducers based on magnetostrictive effect. The
experimental results showed that the amplitudes of the ultrasonic waves linearly
decreased as the tensile load increased. The authors recommended that the centre wire
of the strand should be monitored rather than the other wires because of the errors
incurred from the relative sliding of the wires, which changes the acoustic energy of
the detected waves.
A guided ultrasonic wave method using acoustoelastic measurement to measure
the stress in a seven-wire steel strand using acoustoelastic theory was also proposed
by Chaki and Bourse (2008). The experimental results showed the potential and the
suitability of the proposed guided wave method for evaluating the service stress levels
in the prestressed seven-wire steel strands.
Kim et al. (2012) estimated the stress in prestressing tendons from the change in
the velocity of the longitudinal stress wave along the tendons, which is proportional to
the prestressed force. This method enables measurement of the stress wave at any
position, even in bonded prestressing longer than 40 m.
The last few studies discussed above are the most recent in PF identification
using linear parameters of the ultrasonic wave, such as relative change in wave
velocity. However, all of these studies were focused on prestressed concrete beams
22
and mostly limited to exposed tendons, that is where the tendon ends were exposed, or
the tendons were completely exposed (external).
B. Ultrasonic testing depending on nonlinear acoustic theory
Recently, the nonlinear ultrasonic wave has been used for health monitoring of
prestressing tendons in posttensioned concrete bridges. However, this is a new area so
the research in this area is still limited.
Salamone et al. (2010) presented a health monitoring system for prestressing
tendons embedded in posttensioned structures. The system used ultrasonic guided
waves and embedded piezoelectric sensors to provide, simultaneously and in real time,
(a) measurements of the applied prestress load level and (b) defect detection at early
growing stages. The proposed system measurement technique exploited the sensitivity
of ultrasonic waves to the internal wire contact developing in a multi wire strand as a
function of the prestressing level.
In particular, the nonlinear ultrasonic behaviour of the tendon under changing
levels of prestressing is monitored by tracking higher-order harmonics at (nω) arising
under a fundamental guided-wave excitation at (ω). Salamone et al. (2010)
demonstrated that this technology shows promise for the simultaneous detection of
defects and monitoring of the prestressing level in the prestressing tendon by using the
same ultrasonic sensing system. Therefore, the ultrasonic technology is a promising
technique to be used for long-term inspection and SHM of prestressed concrete
bridges. Further, the authors improved that the technology is applicable for monitoring
both new structures and existing structures.
Claudio (2010) developed a methodology to assess the PF level applied to the
strands of the prestressed concrete beam using ultrasonic nonlinearity. The author
generated the ultrasonic wave using the piezoelectric transducers. It has been found
that the higher harmonic generation of ultrasonic guided waves propagating in
individual wires of the strand varies monotonically with the prestressing force applied
on free and embedded stands. Further, the author presented numerical studies
(nonlinear finite element analysis) to identify the PF on free strands.
Researchers at the University of California, San Diego (UCSD), in collaboration
with the California Department of Transport (Caltrans), monitor the stress level and
damage in posttensioned concrete structures using the nonlinear behaviour of the
23
ultrasonic wave generated using the piezoelectric transducers. In collaboration with
this research, Bartoli, Nucera, Srivastava, Salamone, Phillips, di Scalea, et al. (2009)
used this technique to monitor the prestress level in seven-wire prestressed tendons.
The technique relies on the fact that an axial stress on the tendons generates a
proportional radial stress between the adjacent wires. In turn, the internal wire stress
modulates the nonlinear effect in the ultrasonic propagation through both the presence
of finite strain and the interwire contact.
The studies discussed above are the most recent in PF identification using the
ultrasonic technology that show good identification accuracy compared to another
exiting nondestructive method. Therefore, the ultrasonic technology will be used to
identify the PF in the research program due to many advantages of this method
including:
• Long-range inspection: ultrasonic waves propagate for long distances, which
gives the opportunity to inspect a large-scale structure such as a PSCB from a
single point using a single transducer. Hence, it avoids the time-consuming
point-by-point scanning required by conventional inspection methods such as
Impact-echo test.
• The technique shows promises for the simultaneous detection of defects and
monitoring of prestressing levels in the tendons based on Guided Ultrasonic
Waves (GUWs) (Salamone et al., 2010). Therefore, the ultrasonic transducers
can be permanently attached to the strand or concrete surface of the PSCBs for
long-term SHM as well as PF identification.
• The potential for providing simultaneous defect detection and stress
monitoring capabilities for the strands with the same ultrasonic sensing system
(Salamone et al., 2010).
• The ultrasonic transducers can be attached on the concrete surface as well as
the steel tendons; therefore, the technology can be either used with the PSCBs
with embedded or accessible tendons. In other transducers such as EMAT, the
efficiency rapidly decreases when the strands are embedded in concrete.
• The ultrasonic system benefits from lower cost and simple structure and
controls compared with the other commercial systems such as RITEC-Ram
that is usually used with the EMAT transducers.
24
Despite these advantages of the ultrasonic technology, the studies presented
previously were focused on identifying the PF directly from attaching the ultrasonic
transducers on the prestressing tendons. Based on extensive literature survey, no
research has been found on identifying the PF from the inverse calculation of the
compressive stress developed on the concrete surface due to applying the PF. Further,
as this method showed promising and accurate results, more research needs to be
conducted in this area to be ready for practical implementation.
2.5 SUMMARY AND CONCLUSION REMARK
The issue of monitoring prestressed concrete structures has been addressed using
several methods to evaluate the effective PF. Some of these methods are destructive,
in which case the applications usually are limited to laboratory testing. Others methods
are semi destructive and can be applied to some real structures. However, these
methods also make some small permanent damage to the structure.
With the development of sensor technology and advantages in SHM techniques,
researchers were then interested in nondestructive methods of PF evaluation, such as
ultrasonic testing, impact-echo or magnetostrictive methods and applied them to lab
models and real-life structures. This chapter summarised some of these important
methods and discussed their advantages and disadvantages. Ultrasonic technique using
the piezoelectric transducers generally is one of the most practical and attractive
approaches that has been used in the area of PF identification, as a large area of a
structure can be evaluated using a single transducer. Hence, it avoids the time-
consuming point-by-point scanning required by conventional inspection methods.
However, the studies presented before on PF identification using the ultrasonic
technology have been focused only on beam-like members or prestressed concrete
with external tendons, where the transducers and the receivers attached at the ends of
the steel tendons and PF can directly be calculated. No method has been developed to
assess the PF of prestressed concrete box girder bridges with embedded tendons that
are another important type of prestressed concrete bridges. This has been identified as
a significant gap in knowledge in the literature review. Therefore, this research is
aiming to fill this gap by extending current knowledge in prestress force evaluation
using the ultrasonic technology to other types of prestressed structures, such as box-
girder bridges with embedded tendons.
25
Since the piezoelectric transducers can be either working effectively on the
concrete surface or with the steel tendons. Therefore, this research is aiming to fill this
gap by attaching the ultrasonic transducers and the receivers on the concrete surface.
The stress developing at the concrete surface due to the applied PF is using then for
the inverse calculating of the PF applied on the steel tendons.
26
Chapter 3: Ultrasonic Guided Wave and
Linear and Nonlinear Acoustic
Theory
Section 3.1 reviews a general introduction on the ultrasonic wave and its
application in SHM and NDT. Section 3.2 reviews the linear ultrasonic testing and the
acoustoelastic theory. Section 3.3 reviews the nonlinear ultrasonic testing and the
nonlinear acoustic theory. Section 3.4 summarises the key findings in the literature.
3.1 INTRODUCTION
Ultrasonic waves (or elastic waves) are high-frequency sound waves greater than
20 kHz, occurs because of the restoring forces between particles when the material is
elastically displaced (Han, Palazotto, & Leakeas, 2009). When the elastic waves are
excited in the media, they transmit changes in stress and velocity inside the material.
This change in stress and velocity influences the quantitative wave characteristics such
as the frequency, period, phase, wavelength, wave speed, wave number and amplitude
(Han et al., 2009).
The most important property of ultrasonic waves is that they remain confined
inside the wall of a thin-walled structure and hence can travel over a considerable
distance (Giurgiutiu, 2008). Therefore, it has been widely used for SHM and NDT of
different structures such as pipes, railroad, rail plates and PSCBs. Ultrasonic waves for
SHM and NDT applications are usually generated by ultrasonic piezoelectric
transducers or piezo-ceramic patches mounted to the specimen. Piezoelectric
transducers and patches are used as a transmitter to generate, and as receivers to receive
the ultrasonic wave (Kundu, 2014).
The ultrasonic waves are classified as either guided waves such as Lamb waves,
or bulk waves, that is pressure and shear waves (Han et al., 2009; Mutlib, Baharom,
El-Shafie, & Nuawi, 2016). The fundamental differences between the bulk wave and
27
the guided wave are; bulk wave travel in a bulk of material, hence away from the
boundaries. However, often there is interaction with boundaries by way of reflection
and refraction, and mode conversion occurs between longitudinal and shear waves.
While the guided waves are dispersive waves; therefore, they travel on the surface of
a material or through the thickness of thin materials and exhibit infinite numbers of
wave modes (Han, 2007). However, the energy of the guided waves is concentrated
near a boundary or between parallel boundaries and the direction of propagation is
parallel to these boundaries (Naresh, 2008).
Although bulk and guided waves are fundamentally different, they are governed
by the same set of partial differential wave equations (Rose, 2004). Mathematically,
the principal difference is that: for bulk wave, there are no boundary conditions that
need to satisfy by the proposed solution. In contrast, the solution of guided wave
problem must satisfy the governing equations as well as some physical boundary
conditions (Rose, 2004).
Lamb (1917) first studied the propagation of guided waves in a free plate.
Thereafter, guided waves in a plate were called Lamb waves. Although Lamb proposed
the dispersion equation for acoustic wave propagation in a plate in 1917, it was not
used until 1961 when Worlton (1961) gave an experimental confirmation of Lamb
waves at megacycle frequencies and confirmed that Lamb waves could be utilised for
NDT purposes. Worlton (1961) noted that Lamb waves could adequately reveal the
subsurface laminar flaws and overcome some of the problems encountered in
traditional ultrasonic testing, such as near-surface defects.
Mathematically, Lamb and Raleigh waves use the same equations, and several
methods exist for defining the characteristics of propagating guided waves in an elastic
plate. The two most popular methods are: the method of potential and the partial wave
techniques (Brekhovskikh, 2012; Rose, 1999, 2004). In this research, the dispersion
relation of guided waves have been obtained using the method of potential (Rose,
1999).
When a free plate is excited, the excitation will generate guided Lamb waves in
the plates. The Lamb waves are composed of the coupling between the x and the
directed elastic displacements of particles. The x-direction displacement of particles is
called the longitudinal waves and the y-direction displacement of particles is called the
transverse waves or vertical shear waves. If z-direction is considered in Lamb wave
28
propagation, the resulting waves in this direction will be referred to as horizontal shear
waves. Similar to vertical shear waves, horizontal shear waves propagate
perpendicular to the longitudinal waves (Han et al., 2009).
Figure 3.1 shows the particle motion in transverse and longitudinal directions. The
black lines present the direction of particle motion, and the red arrows indicate the
direction of wave propagation (Han, 2007).
Figure 3-1. Transverse and longitudinal waves (Han, 2007).
Due to the advantages of guided waves (which are also known as Lamb waves)
they have been used in this research to provide an approach to identify the PF of PSC
nondestructively. The velocity and amplitude energy of these waves are sensitive to
the effects of texture, anisotropy, temperature, and stress in the isotropic material.
These phenomena all cause changes in the various higher order elastic constants that
determine wave velocity and amplitude of the second harmonic of FFT curve, and
these relationships are known as the acoustoelastic and nonlinear acoustic effects.
More information about these two theories and the related applications will be
presented in sections 3.2 and 3.3 respectively.
29
3.2 ULTRASONIC TESTING AND LINEAR ACOUSTOELASTIC
THEORY
Ultrasonic stress evaluation techniques are based on the acoustoelastic effect,
which refers to the relationship of stress and relative variation in wave velocity of the
elastic wave propagation in a structure undergoing static elastic deformation (Payan,
Garnier, Moysan, & Johnson, 2009; Pei & Demachi, 2010).
Acoustoelastic-derived nonlinear properties of isotropic homogeneous materials
have been studied for at least half a century. Such measurements provide insight into
the nano-to-mesoscale features that determines the elastic nonlinear response and can
be used to get important physical characteristics, such as material modulus, and to
predict the material strength (Payan et al., 2009).
The principles of acoustoelastic effect and ultrasonic wave velocity
measurements have been used in laboratory and field tests in many engineering
applications. The residual stresses in welded steel plates and railroad rails have been
measured by (Leon. & Bray, 1996) and (Tanala, Bourse, Fremiot, & De Belleval,
1995). Hirao, Ogi, and Fukuoka (1994) and Manchem, Srinivasan, and Zhou (2014)
measured the stress level in bars and multiwire strands.
In addition, Clark, Fuchs, and Schaps (1995) have developed a practical
instrument, which operates based on acoustoelastic effect, for measuring live load
stresses in highway bridges. The researchers focused on the use of the Rayleigh waves
generated on the surface of an I-beam to measure live stress in a bridge. This research
demonstrated that the acoustoelastic effect could be used effectively to measure the
applied stress in a four-point bending test in the lab. In a subsequent publication, Clark,
Fuchs, Lozev, Gallagher, and Hehman (1998) demonstrated that an instrument could
be constructed to perform these measurements successfully under field conditions.
Chen and Wissawapaisal (2002) were interested in acoustoelastic measurement
applied to seven-wire strands exploiting conventional piezoelectric transducers
positioned at the end of the centre wire. In this study, the authors utilised the Wigner-
Vill time-frequency analysis to measure the time of flight of the frequency components
constituting the propagation signals according to the applied stress.
Washer (2001) exploited the magnetostrictive transduction for acoustoelastic
measurement in prestressed strands excited by a burst signal at a frequency of 320 kHz.
30
This measurement configuration enables the elongation effect on the time-of-flight
evolution to be avoided. However, in this case the acoustoelastic measurements
become very difficult because the acoustoelastic effect is inherently low. The
acoustoelastic measurements were carried out on both a separated central wire and an
assembled seven-wire strand. In another case, it was found that the acoustoelastic
effect had a nonlinear behaviour, especially in the case of an assembled strand. It was
also observed that for the assembled strand the velocity under stress increased until a
load of 50% UTS (ultimate tensile strength) and after that, it decreased.
3.2.1 Linear acoustoelastic theory
Linear acoustoelastic theory is based on a series of assumptions concerning the
performance of a material undergoing deformation. The theory assumes that
deformations in the material are infinitesimal and reversible, and that there exists a
linear stress–strain relationship (Washer, 2001).
This accurately describes most metallic and isotropic materials sufficiently for
engineering. However, other approaches differ from the linear elastic theory in two
ways. First, the relationship between the stress and the strain may not be linear.
Second, deformations may be so large that the conventional linear elasticity theory is
not accurate (Hughes & Kelly, 1953).
For the latter case, a theory is required, in which the original coordinates of a
point in the material are not interchangeable with the coordinates of the same point
following deformation. Therefore, the theory of finite deformation developed to
address this situation.
Considering the box-girder in Figure 3.2 subjected to a uniaxial stress in the x-
direction, the expression for the wave velocities in different directions derived by
Hughes and Kelly (1953) can be used for a uniaxial stress state and presented a
theoretical description of the acoustoelastic effect.
31
Figure 3-2. Direction of wave propagation.
The velocity of a plane wave propagation in the x direction and having particle
displacement in the x, y and z directions in an initially isotropic body under a triaxial
strain fields:
𝜌0𝑉112 = 𝜆 + 2𝜇 + (2𝑙 + 𝜆)𝜃 + (4𝑚 + 4𝜆 + 10𝜇)𝛼1 3.2.1
𝜌0𝑉122 = 𝜇 + (𝜆 + 𝑚)𝜃 + 4𝜇𝛼1 + 2𝜇𝛼2 −
1
2𝑛𝛼3 3.2.2
𝜌0𝑉132 = 𝜇 + (𝜆 + 𝑚)𝜃 + 4𝜇𝛼1 + 2𝜇𝛼3 −
1
2𝑛𝛼2 3.2.3
1 is the x-direction
2 is the y-direction
3 is the z-direction
Where:
𝜌0 Initial density
Vxx
Vyy
Vyz
𝑃𝐹
𝑃𝐹
X
Y
Z
Vyx
Vxz
32
𝑉11, 𝑉12, 𝑉13 Wave velocities in x-direction with displacement in the x, y or
z directions respectively
𝜆, µ Second-order elastic constants for isotropic materials
(Lamé constant)
𝑙, 𝑚, 𝑛 Third-order elastic constant
𝛼1, 𝛼2, 𝛼3 Components of the homogenous triaxial principle strains in the
x, y and z directions respectively
𝜃 = 𝛼1 + 𝛼2 + 𝛼3 3.2.4
In case of plate under uniaxial tension
𝛼1 = 휀, 𝛼2 = 𝛼3 = −𝑣𝛼1 3.2.5
Where:
𝑣 Poisson’s ratio
Equation 3.2.1 reduce to equation 3.2.6:
𝜌0𝑉112 = 𝜆 + 2𝜇 + [4(2𝜇 + 𝜆) − 2(𝜇 + 2𝑚) + 𝑣𝜇 (1 +
2𝑙
𝜆)]휀 3.2.6
Equations 3.2.2 and 3.2.3 reduce to equation 3.2.7:
𝜌0𝑉122 = 𝜌0𝑉13
2 = 𝜇 + [4𝜇 + 𝑣 (𝑛
2) + 𝑚(1 − 2𝑣)]휀 3.2.7
Note that these equations are now in the form for isotropic solids when the
strain=zero, that is:
For the longitudinal wave:
𝑉11 = 𝐶𝐿 = √𝑀
𝜌0 3.2.8
33
Where:
𝑀 =𝐸(1−𝑣)
(1−𝑣−2𝑣2) 3.2.9
CL Longitudinal wave velocity
𝐸 Modulus of Elasticity
For the shear wave:
𝑉12 = 𝐶𝑇 = √𝐺
𝜌0 3.2.10
Where:
CT Shear wave velocity
𝐺 =𝐸
2(1+𝑣) 3.2.11
Lamb waves are naturally dispersive. However, at this point, the longitudinal
and transverse waves are nondispersive since their wave velocity is only a function of
material properties, not frequency.
Using equations 3.2.6 and 3.2.7 and includes both the second and third elastic
constants. The equations can be reduced, assuming the relative changes are small, to
calculate the corresponding wave velocity changes due to axial strains (Washer, 2001).
𝑑𝑉11
𝑉110 = [2 +
𝜇+2𝑚+𝑣𝜇(1+2𝑙
𝜆)
𝜆+2𝜇] 𝑑휀 3.2.12
𝑑𝑉12
𝑉120 = [2 +
𝑚
4𝜇+
𝑚
2(𝜆+𝜇)] 𝑑휀 3.2.13
Where:
𝑉110 & 𝑉12
0 Ultrasonic wave velocity at zero strain and they are equal to the
phase velocity Cp. More information about calculating the phase
velocity will be presented in section 3.2.3.
34
For the particular case of measuring the stress level in prestressing concrete, the
second- and third-order elastic constants are not required and may be grouped into a
single factor. To place these equations in term of stress, the strain is evaluated
according to linear theory. Therefore, equations (3.2.12) and (3.2.13) will be rewritten
as:
𝑑𝑉11
𝑉110 = 𝐾11𝑑𝜎 3.2.14
𝑑𝑉11
𝑉110 = 𝐾12𝑑𝜎 3.2.15
Where:
𝑑𝜎 Change in applied stress from initial condition
𝐾11 & 𝐾12 Acoustoelastic constant for the longitudinal and shear waves
respectively.
It represents the response of the stressed material to the wave investigation and
can be generally expressed as (Chaki & Bourse, 2008):
𝐾 =1
2(𝜆+2𝜇)(3𝜆+2𝜇)[λ+μ
𝜇(4𝜆 + 10𝜇 + 4𝑚 ) + 𝜆 + 2𝑙] 3.2.16
The acoustoelastic constant is not preliminary known for test materials because
of the lack of a third-order elastic constant. Moreover, the evaluation of these constants
is very difficult and their cumulated uncertainties will significantly affect the accuracy
of the stress measurement. Therefore, the acoustoelastic constant can be obtained from
the acoustoelastic calibration test in the laboratory.
Further, it should be noted that the value of K depends on material properties,
waveguide diameter and the probing frequency. A large value of |K| indicates that the
wave is more sensitive to stress (Song, Xu, Pan, & Song, 2016), while a negative value
of K indicates that the structure is under uniaxial tensile stress, which means the wave
velocity decreases as the stress increases. In this research, the constant K is obtained
35
from the calibration tests run in different locations on the surfaces of the prestressed
concrete box-girder.
For a unit stress, the acoustoelastic constant is simply the percentage of the
change in velocity of the ultrasonic wave. Assuming the velocity at zero stress (zero
strain) is known, the acoustoelastic constant can be used to solve for a given stress in
terms of the measured ultrasonic velocity in the following equations (Mandracchia,
1995):
𝑉11 = 𝑉110 + 𝐾11𝜎𝑉11
0 3.2.17
𝑉12 = 𝑉120 + 𝐾12𝜎𝑉12
0 3.2.18
3.2.2 Wave propagation in isotropic elastic media
As mentioned previously, Lamb wave is a type of guided ultrasonic wave
propagating in the isotropic elastic material such as prestressed concrete. When the
ultrasonic wave propagates in the plate made with isotropic elastic material there will
be a gradual smooth change of the surface wave where the Rayleigh wave becomes
Lamb wave. While the ultrasonic wave will be acted like A0 and S0 Lamb modes at a
half of the plate thickness.
The propagation of an elastic wave in an infinite isotropic, homogenous solid is
well understood and derivations of the wave equations can be found in numerous text
books such as Achenbach (2012). The equations that are reproduced here are found
for all acoustic wave theories and will be used as a starting point for several following
calculations.
To understand Lamb wave behaviour, the governing equations need to be
considered. Using basic elastic equation using Cartesian tensor notation (Rose, 2004).
𝜎𝑖𝑗,𝑗 + 𝜌𝑓𝑖 = 𝜌𝑢𝑖̈ 3.2.19
Yield three equations of motion 𝑖 = 1,2,3
The independent strain displacement equations:
휀𝑖𝑗 =1
2(𝑢𝑖,𝑗 + 𝑢𝑗,𝑖) 3.2.20
Yield six independent strain displacement equations
The independent constitutive equations (for the isotropic materials):
36
𝜎𝑖𝑗 = 𝜆휀𝑘𝑘𝛿𝑖𝑗 + 2𝜇휀𝑖𝑗 3.2.21
Yield six independent constitutive equations for isotropic materials
Equations 3.2.19 and 3.2.20 are valid for any continuous media while equation
3.2.21 is only valid for the isotropic materials. Eliminating the stress-strain terms from
the previous equations, the following equations of motions can be derived:
𝜇𝑢𝑖,𝑗𝑗 + (𝜆 + 𝜇)𝑢𝑗,𝑗𝑖 + 𝜌𝑓𝑖 = 𝜌𝑢𝑖 ̈ 3.2.22
Where :
𝜆 𝑎𝑛𝑑 𝜇 Lamé constant
𝑢 Displacement
𝑓 Applied load
𝑖 𝑎𝑛𝑑 𝑗 𝑎𝑟𝑒 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜 𝑥, 𝑦 𝑜𝑟 𝑧
The last equation describes the governing partial differential equations for
displacement. When the ultrasonic excitation occurs at one point in the plate, ultrasonic
energy from the excitation region encounters the upper and lower bounding surfaces
of the plate, resulting in mode conversion (longitudinal wave to transverse wave, and
vice versa). After some travel in the plate, superposition causes the formation of wave
packets, namely, guided wave modes in the plate (Han, 2007).
Based on the entry angle of the wave and the frequency used, the number of the
different modes (created in the sample) can be predicted. In order to apply it to a plate,
the solution of the free plate problem could be obtained as follows.
In the absence of body force, equation 3.2.22 becomes:
𝜇𝑢𝑖,𝑗𝑗 + (𝜆 + 𝜇)𝑢𝑗,𝑗𝑖 = 𝜌𝑢𝑖 ̈ 3.2.23
Using the vector notation, equation 3.2.22 becomes:
𝜇∇2𝑢 + (𝜆 + 𝜇)∇∇𝑢 = 𝜌�̈� 3.2.24
Considering the decomposition of the displacement vector of the forms:
37
𝑢 = ∇∅ + ∇𝜓Ë 3.2.25
Where:
𝑢 Displacement vector
∅ Scalar potential
𝜓 Vector potential.
Equation 3.2.25 is expressed using Helmholtz decomposition of a vector. For
this plane strain problem, the following condition holds:
𝑢𝑧 = w ≡ 0,𝜕
𝜕𝑧() ≡ 0 3.2.26
Equation 3.2.25 then reduces to
𝑢𝑥 = u =𝜕∅
𝜕𝑥+
𝜕𝜓
𝜕𝑦 3.2.27
𝑢𝑦 = v =𝜕∅
𝜕𝑦−
𝜕𝜓
𝜕𝑥 3.2.28
For the simplicity of notation, the subscript z has been omitted from 𝜓 in
equations 3.2.27 and 3.2.28.
The relevant components of the stress tensor follow from Hook’s law as:
𝜎𝑦𝑥 = 𝜇 [𝜕𝑢𝑦
𝜕𝑥+
𝜕𝑢𝑥
𝜕𝑦] = 𝜇[2
𝜕2∅
𝜕𝑥𝜕𝑦−
𝜕2𝜓
𝜕𝑥2 +𝜕2𝜓
𝜕𝑦2] 3.2.29
𝜎𝑦𝑦 = 𝜆 [𝜕𝑢𝑥
𝜕𝑥+
𝜕𝑢𝑦
𝜕𝑦] + 2𝜇
𝜕𝑢𝑦
𝜕𝑦= 𝜆 [
𝜕2∅
𝜕𝑥2 +𝜕2𝜙
𝜕𝑦2] + 2𝜇 [𝜕2∅
𝜕𝑦2 +𝜕2𝜓
𝜕𝑥𝜕𝑦] 3.2.30
Substitution of equation 3.2.24 into equation 3.2.25 yields:
𝜇∇2[∇∅ + ∇Λ𝜓] + (𝜆 + 𝜇)∇∇[∇∅ + ∇Λ𝜓] = 𝜌𝜕2
𝜕𝑡2 [∇∅ + ∇Λ𝜓] 3.2.31
38
Since ∇ ∇∅ = ∇2∅ and ∇∇Λ𝜓 = 0
Rearranged equation 3.2.31:
∇[(λ + 2µ)∇2ϕ − 𝜌𝜙 +̈ ∇Ë𝜇∇2𝜓 − ρ�̈�] = 0 3.2.32
Clearly, equation 3.2.25 satisfies the equation of motion if:
∇2∅ =1
𝐶𝐿2 ∅̈ 3.2.33
∇2ψ =1
𝐶𝑇2 �̈� 3.2.34
∇2=𝜕2
𝜕𝑥2 +𝜕2
𝜕𝑦2 +𝜕2
𝜕𝑧2 3.2.35
Rewritten equations 3.2.33 and 3.2.34 for plain strain:
𝜕2∅
𝜕𝑥2+
𝜕2∅
𝜕𝑦2+
1
𝐶𝐿 2
𝜕2∅
𝜕𝑡2 Governing longitudinal waves 3.2.36
𝜕2𝜓
𝜕𝑥2+
𝜕2𝜓
𝜕𝑦2+
1
𝐶𝑇 2
𝜕2𝜓
𝜕𝑡2 Governing shear waves 3.2.37
Since the time depends on assumed harmonic in the form𝑒−𝑖𝑤𝑡 , the general
solutions to equations 3.2.36 and 3.2.37 .i.e, 𝜙 𝑎𝑛𝑑 𝜓 are found to take the form:
𝜙 = Φ(𝑦) exp(𝑖𝑘𝑥 − 𝜔𝑡) 3.2.38
Ψ = Ψ(𝑦)exp (𝑖𝑘𝑥 − 𝜔𝑡) 3.2.39
Where
𝜔 Circular frequency of the external pulse applied to the surface
39
𝑘 Parameter to be determined called the wave number
numerically equal to 𝜔/𝐶𝑃
𝐶𝑃 Phase velocity will be discussed subsequently.
Substitution of these solutions into equation 3.2.36 and 3.2.37 yields equations
governing the unknown functions Φ 𝑎𝑛𝑑 Ψ. The solutions to these equations are:
𝜙(𝑦) = A1𝑠𝑖𝑛(𝑝𝑦) + A2𝑐𝑜𝑠(𝑝𝑦) 3.2.40
Ψ(y) = B1𝑠𝑖𝑛(𝑞𝑦) + B2𝑐𝑜𝑠(𝑞𝑦) 3.2.41
Where:
𝐴1,𝐴2, 𝐵1, 𝐵2 are constants which can be found from the boundary conditions,
the unknown amplitude constant 𝐴 and 𝐵 denote longitudinal and shear waves, and
subscript 1 and 2 indicate propagation in the outward and inward directions with
respect to the plate, respectively.
The parameters p and q can be expressed in terms of the angular frequency (𝜔),
the circular wavenumber (k) and the longitudinal and transverse wave speeds CL and
CT.
𝑝2 = (𝜔
𝐶𝐿)
2
− 𝑘2 3.2.42
𝑞2 = (𝜔
𝐶𝑇)
2
− 𝑘2 3.2.43
With these results, the displacements and stresses obtained directly from
equation 3.2.27 and 3.2.30. Omitting the term exp [i (kx-wt)] in all expressions, the
results are follows:
𝑢𝑥 = [𝑖𝑘Φ +𝑑Ψ
𝑑𝑦] 3.2.44
𝑢𝑦 = [𝑑Φ
𝑑𝑦− 𝑖𝑘Ψ] 3.2.45
40
Produces the stress components in the unabridged form:
𝜎𝑦𝑦 = [𝜆 (−𝑘2Φ +𝑑2Φ
𝑑𝑦2 ) + 2𝜇 (𝑑2Φ
𝑑𝑦2 − 𝑖𝑘𝑑Ψ
𝑑𝑦)] 3.2.46
𝜎𝑦𝑥 = 𝜇 (2𝑖𝑘𝑑Φ
𝑑𝑦+ 𝑘2Ψ +
𝑑2Ψ
𝑑𝑦2) 3.2.47
Since the field variables involve sines and cosines with the variable y which are
odd (or even for cosines) functions about y=zero, the solution is split into two sets of
modes (i.e. symmetric (S) and asymmetric (A) modes).
Specifically, for displacement in the x-direction, the motion will be symmetric
with respect to the mid-plane of the plate, if 𝑢𝑥contains cosines, but will be asymmetric
if 𝑢𝑥contains sines. The opposite is true for displacements in the y-direction. Thus, the
modes of wave propagation in the plate are split into two systems (Rose, 1999, 2004):
Symmetric modes
Φ = 𝐴2 cos(𝑝𝑦)
Ψ = 𝐵1 sin(𝑞𝑦)
𝑢 = 𝑢𝑥 = 𝑖𝑘𝐴2 cos(𝑝𝑦) + 𝑞𝐵1cos (𝑞𝑦)
𝜈 = 𝑢𝑦 = −𝑝𝐴2 sin(𝑝𝑦) − 𝑖𝑘𝐵1 sin(𝑞𝑦)
𝜎𝑦𝑥 = 𝜇[−2𝑖𝑘𝑝𝐴2 sin(𝑝𝑦) + (𝑘2 − 𝑞2)𝐵1 sin(𝑞𝑦)]
𝜎𝑦𝑦 = −𝜆[(𝑘2 − 𝑝2)𝐴2 cos(𝑝𝑦) − 2𝜇[𝑝2𝐴2 cos(𝑝𝑦) + 𝑖𝑘𝑞𝐵1cos (𝑞𝑦)] 3.2.48
Asymmetric modes
Φ = 𝐴1 sin(𝑝𝑦)
Ψ = 𝐵2 cos(𝑞𝑦)
𝑢 = 𝑢𝑥 = 𝑖𝑘𝐴1 sin(𝑝𝑦) − 𝑞𝐵2sin (𝑞𝑦)
𝜈 = 𝑢𝑦 = 𝑝𝐴1 cos(𝑝𝑦) − 𝑖𝑘𝐵2 cos(𝑞𝑦)
𝜎𝑦𝑥 = 𝜇[2𝑖𝑘𝑝𝐴1 cos(𝑝𝑦) + (𝑘2 − 𝑞2)𝐵2 cos(𝑞𝑦)]
41
𝜎𝑦𝑦 = −𝜆[(𝑘2 + 𝑝2)𝐴1 sin(𝑝𝑦) − 2𝜇[𝑝2𝐴1 sin(𝑝𝑦) − 𝑖𝑘𝑞𝐵2sin(𝑞𝑦)] 3.2.49
For the symmetric modes, the wave structure across the thickness of the plate is
symmetric for u and asymmetric for v. On the other hand, for asymmetric modes, the
wave structure across the thickness is symmetric for v and asymmetric for u. Figure
3.3 shows the symmetric and asymmetric particle motion across the plate thickness.
Figure 3-3. Mode shapes of symmetric and assymetric fundamental Lamb wave modes
across the plate thickness Lee and Oh (2016)
The constants A1, A2, B1 and B2 are still unknown. They can be determined by
applying the traction-free boundary condition for a free plate in the case of plain strain
(Rose, 2004):
𝜎𝑦𝑥 = 𝜎𝑦𝑦 ≡ 0 𝑎𝑡 𝑦 = ∓𝑑
2= ±ℎ 3.2.50
The resulting displacement, stress, and strain fields depend upon the type of
mode. However, applying the boundary conditions will give a homogeneous system
of two equations for the appropriate two constants A2, B1 for the symmetric case and
A1, B2 for the asymmetric case.
For homogeneous equations, the determinant of the coefficient matrix vanishes
in order to ensure solutions other than the trivial one. From equation 3.2.50 the
42
following relations are found from computing the determination of the coefficient
matrix for both symmetric and asymmetric modes (Rose, 2004):
For the symmetric modes
(𝑘2−𝑞2)sin (𝑞ℎ)
2𝑖𝑘𝑝(sin(𝑝ℎ))=
−2𝜇𝑖𝑘𝑞(cos(𝑞ℎ))
(𝜆𝑘2+𝜆𝑝2+2𝜇𝑝2)cos (𝑝ℎ) 3.2.51
For the asymmetric modes
(𝑘2−𝑞2)sin (𝑝ℎ)
2𝑖𝑘𝑝(sin(𝑞ℎ))=
−2𝜇𝑖𝑘𝑞(cos(𝑝ℎ))
(𝜆𝑘2+𝜆𝑝2+2𝜇𝑝2)cos (𝑞ℎ) 3.2.52
After some rearrangement, equation 3.2.51 rewritten as:
tan (𝑞ℎ)
tan(𝑝ℎ)=
4𝑘2𝑞𝑝𝜇
(𝜆𝑘2+𝜆𝑝2+2𝜇𝑝2)(𝑘2−𝑞2) For the symmetric modes 3.2.53
The denominator on the right-hand side (RHS) of equation 3.2.53 can be
simplified by using the wave velocities and the definitions of p and q from equations
3.2.42 and 3.2.43. Using equation 3.2.7 to simplify:
𝜆 = 𝐶𝐿2𝜌 − 2𝜇 3.2.54
Then RHS of equation 3.2.53 will be as follows:
𝜆𝑘2 + 𝜆𝑝2 + 2𝜇𝑝2 = 𝜆(𝑘2 + 𝑝2) + 2𝜇𝑝2
= (𝐶𝐿2𝜌 − 2𝜇)(𝑘2 + 𝑝2) + 2𝜇𝑝2 = 𝜌𝐶𝐿
2(𝑘2 + 𝑝2) − 2𝜇𝑘2 3.2.55
Rewriting equation 3.2.55 by using equations 3.2.42, 3.2.43 and 3.2.9:
43
𝜆𝑘2 + 𝜆𝑝2 + 2𝜇𝑝2 = 𝜌𝜔2 − 2𝜌𝐶𝑇2𝑘2 3.2.56
= 𝜌𝐶𝑇2 [(
𝜔
𝐶𝑇)
2
− 2𝑘2] = 𝜌𝐶𝑇2(𝑞2 − 𝑘2) = 𝜇(𝑞2 − 𝑘2) 3.2.57
Substitution of equation 3.2.57 into an initial form of the dispersion equation
3.2.51, the dispersion equation for symmetric modes will be:
tan (𝑞ℎ)
tan (𝑝ℎ)= −
4𝑘2𝑝𝑞
(𝑞2−𝐾2)2
3.2.58
By similar procedures, the direction equation for asymmetric modes can be
written:
tan (𝑞ℎ)
tan (𝑝ℎ)= −
(𝑞2−𝐾2)2
4𝑘2𝑝𝑞
3.2.59
For a 𝜔 and derived k, the displacement can be determined from equation 3.2.48.
These equations can be used to determine the velocity at which a wave of a particular
frequency will prograde within the plate.
3.2.3 Phase velocity and group velocity
Phase velocity is defined as the velocity at which a wave of a single frequency
propagates. Due to dispersion, Lamb waves become distorted as they propagate
(Olson, 2005). These individual waves interact, and resulting waves propagate at a
group velocity, which may be different from the individual phase velocities (Han et
al., 2009; Olson, 2005).
Numerical methods for calculating phase and group velocities’ dispersion curves
are outlined by Rose (2004) to solve equations 3.2.58 and 3.2.59. However, to avoid
the hard mathematical calculations, the University of South Carolina College Of
Engineering and Computing in connection with LAMSS (Laboratory for Active
Materials and Smart Structures) developed WAVESCOPE software. The program can
display the following graphs: phase velocity vs. frequency; group velocity vs.
frequency, wavelength vs. frequency, directly rather than using the mathematical
equations. Figure 3.4 presents the phase velocity dispersion curve determined by
44
WAVESCOPE of a concrete slab with 150 mm thickness. The modulus of elasticity
32 × 109 N/m2, density 2400 kg/m3 and assumed Poisson’s ratio 0.2.
Figure 3-4. Theoretical phase velocity dispersion curves for a concrete slab
(determined by WAVESCOPE software).
When the phase velocity or wave speed is independent of frequency, the phase
velocity is equivalent to the group velocity. However, in dispersive media, the phase
velocity is dependent on frequency. When the wave speed decreases with frequency,
the group velocity is less than the phase velocity. In a dispersive media, a wave packet
generally propagates at group velocity slower than the phase speed of the original
excitation signal (Han et al., 2009).
The group velocity depends on the frequency, and it provides the information of
the speed at which the mode carries the energy. The group velocity can be calculated
using equation 3.2.60
𝐶𝑔 =𝜕𝜔
𝜕𝑘 3.2.60
45
It is obtained by numerically differentiating the wavenumber dispersion curves
of each propagating mode. For the concrete slab analysed before, the group velocity
of the first six propagation modes are showing in Figure 3.5 determined by
WAVESCOPE software.
Figure 3-5. Shows theoretical group velocity dispersion curves for a concrete slab
(WAVESCOPE softwa)
3.3 ULATRSONIC TESTING AND NONLINAER ACOUSTIC
PARAMETER
Propagation of nonlinear ultrasonic waves in solid waveguides is a part of wave
mechanics that has received ever-increasing interest in the last few decades. The
physical mechanism of this method is as follow: as a sinusoidal ultrasonic wave
propagates through a solid material, the interaction of this wave with microstructure
features generates a second harmonic wave. This effect is quantified with the measured
acoustic nonlinearity parameter Beta (β) (Matlack, Kim, Jacobs, & Qu, 2014).
Nonlinear ultrasonic methods have a powerful ability to characterise
microstructural features in materials as they conveniently combine high sensitivity to
unusual structural conditions such as defects, cracks, quasistatic loads and instability
conditions (Nucera, Lanza di Scalea, & Francesco, 2012), therefore it has been widely
46
used in the SHM area and PF identification. Belyaeva, Ostrovsky, and Timanin (1992);
Nazarov and Kolpakov (2000); Ostrovsky (1991); Zaitsev, Sutin, Belyaeva, and
Nazarov (1995) indicated a close relationship between the nonlinear acoustic
parameter of the media and the inner structure properties, strength properties and value
of the internal stresses.
Further, it is well-documented (Dace, Thompson, Brasche, Rehbein, & Buck,
1991), that nonlinear parameters of the ultrasonic wave are, in general, much more
sensitive to structural conditions than their linear parameters such as the wave’s
velocity because it is directly related to the physical change in the structure. Therefore,
this method has been used to ensure safe operation of critical structures, for example,
in the energy, transportation, aviation industries and prestressed concrete bridges
(Matlack, Kim, Jacobs, & Qu, 2014).
3.3.1 Contact acoustic nonlinearity
The nonlinearity in any structure arises from an imperfect contact on the surface
and is called “contact acoustic nonlinearity”. This imperfect contact or unbonded
interface by definition cannot support tension and thus it is opening and closing. This
phenomenon is the origin of nonlinearity in any structure since the elastic media are
assumed to be otherwise linear (Richardson, 1979).
In case of the prestressed concrete surface, the imperfect contact generated from
a different source such as: Flexural micro cracking is generally found in continuous
girders, at the bottom of the girder in the positive moment area and at the top of the
girder in the negative moment area. Further, it can happen in or near the segment joints
(Podolny, 1985). Some of these micro cracks occur within a few hours (first six hours)
after the placement and compaction of concrete.
This type of micro crack happens before the PF is applied. The crack width at
the bottom part of the girder can be between 0.1 and 0.2 mm (Podolny, 1985). This
will create an imperfect contact interface in the bottom slab of the box-girder.
However, most of these micro cracks will be closed after the PF is applied, while others
remain open even after the PF has been applied (Podolny, 1985). When the acoustic
wave interacts with these micro cracks, it will lead to nonlinear acoustic effects
(Zaitsev, Sutin, Belyaeva, & Nazarov, 1995).
47
Surface voids can be another reason for the occurrence of an imperfect contact
interface that causes nonlinearity behaviour of the acoustic wave. These voids are little
holes that appear on the surface of concrete castings and can be about 1 to 3.2 mm.
After an inspection of the box-girder used during the experimental program, numerous
longitudinal cracks as well as voids were found on the surface, as shown in Figure 3.6.
Figure 3-6. An example of an imperfect contact interface at the box-girder surface.
For an imperfect interface, the increase in compression stress (caused by
applying the prestress load on the tendon) caused some of these cracks and voids to
close or reduce in size. Hence, this reducing in size caused the amplitude of the
fundamental reflected wave to decrease significantly due to increasing the
transmission through the contact interface.
The first theoretical predictions on the high harmonic proposed by Richardson
(1979) and modified by Biwa, Nakajima, and Ohno (2004) showed the mechanism by
which disparities between two contact interfaces lead to higher harmonics for the case
of the plane-wave incident. Biwa et al. (2004) presented an analysis based on a
nonlinear interface stiffness model where the stiffness property of the contact interface
is described as a function of the nominal contact pressure.
Cracks at the Box-girder surface
Voids at the Box-girder surface
48
3.3.2 Nonlinear Acoustic theory
A scheme of the nonlinear acoustic diagnostics that enable to determine the PF
from the inverse calculation of the stresses developed on the concrete surface is
considered below. This scheme is similar to that of nonlinear tomography applied for
the reconstruction of a smooth spatial distribution of nonlinear acoustic parameters
(Biwa et al., 2004; Zaitsev et al., 1995).
According to the suggested scheme, the acoustic sounding performed using
high-frequency harmonic wave and high-power pulse wave generator. The main idea
of this method can be formulated as follows: The longitudinal wave propagation into
the positive x-direction and through the contact interface as shown in Figure3.7. A
change in the compressive stress at the concrete surface of the prestressed concrete
model due to apply the PF alert cracks closing or reducing in the width. Change the
condition of reflection and transition of the ultrasonic wave will be accrued due to
crack nonlinearity
Biwa et al. (2004) showed the mechanism by which asperities between two
contacts surfaces lead to high harmonics for the case of plane wave incident.
According to the Biwa: for longitudinal wave propagation into the positive x-direction
and through the contact interface as shown in Figure 3.7, the equation of motion, as
well as the stress-displacement relation, are presented in equations 3.3.1 and 3.3.2.
49
Figure 3-7. Schematic model of contacting interface adopted in this research.
𝜌𝜕2𝑢
𝜕𝑡2=
𝜕𝜎
𝜕𝑥 3.3.1
𝜎 + 𝑝0 = 𝐸 𝜕𝑢
𝜕𝑥 3.3.2
Where:
𝜌 Density
𝑢 Displacement
𝜎 Stress component
𝐸 Modulus of elasticity
𝑝0 Contact pressure in the interface due to the PF
The general solution to equations 3.3.1 and 3.3.2 is the combination of the
reflected and transmitted plane waves. The boundary condition at the interface is:
Incident wave Transmitted wave
Reflected wave
Gap distance h
Close up photo from the concrete surface
50
𝜎(𝑋−, 𝑡) = 𝜎(𝑋+, 𝑡) = −𝑝(ℎ(𝑡)) 3.3.3
𝑝(ℎ0) = 𝑝0 3.3.4
Where:
𝑥 = 𝑋−
𝑥 = 𝑋+ The locations of the mated surface
𝑝 Contact pressure which depends upon the nominal gap between
the interface (ℎ)
The governing equations and the resulting wave can be written as a function of
the gap distance; the gap distance is expressed as a sum of the initial nominal gap (ℎ0)
and the time-dependent change of the gap distance (Y):
ℎ(𝑡) = ℎ0 + 𝑌(𝑡) 3.3.5
Expanding the contact pressure in Taylor series gives up to second-order term as
shown in equation 3.3.6:
𝑝(ℎ) = 𝑝(ℎ0 + 𝑌) = 𝑝0 − 𝐾1𝑌 + 𝐾2𝑌2 3.3.6
Where:
𝐾1 = −𝑑𝑝
𝑑ℎ]
ℎ=ℎ0
3.3.7
𝐾2 =1
2
𝑑2𝑝
𝑑ℎ2]
ℎ=ℎ0
3.3.8
𝐾1 Linear stiffness
𝐾2 Second-order stiffness of the contact interface
51
Both K1 and K2 are dependent on the initial gap (created from the voids or crack)
or equivalently the applied pressed force 𝑝0. Equation 3.3.8 accounts for the nonlinear
nature of the contact stiffness. When the pure harmonic wave with frequency 𝜔 is sent
through the gap, a simple perturbation analysis gives the transmitted and reflected
waves containing the static fundamental and second harmonic components. Denoting
the density and the wave velocity of the contacting solid, the amplitude transmission
and reflection coefficient of the fundamental components are given by (Biwa et al.,
2004):
𝑇 =2𝐾1̂
√1+4�̂�12 3.3.9
𝑅 =1
√1+4�̂�12 3.3.10
�̂�1 =𝐾1
𝜌𝑐𝜔 3.3.11
When the absolute displacement amplitudes of the fundamental and the second
harmonic components in the transmitted wave are denoted by A1 and A2 respectively,
their ratio is given by:
𝐴2
𝐴1=
𝐾2𝐴
2𝐾1√1+4�̂�12 √1+�̂�1
2
3.3.12
Where A is an amplitude of the incident wave. In this study , the nonlinearity
parameter is defined by the second harmonic amplitude divided by the square of the
fundamental amplitude, which is given by (Biwa et al., 2004):
𝛽 = 𝑎𝑚𝑝𝑙𝑖𝑡𝑢𝑑𝑒 𝑜𝑓 𝑡ℎ𝑒 2𝑛𝑑 ℎ𝑎𝑟𝑚𝑜𝑖𝑛𝑐 𝑎𝑡 2𝑓
(𝑎𝑚𝑝𝑙𝑡𝑖𝑢𝑑𝑒 𝑜𝑓 𝑝𝑟𝑖𝑚𝑎𝑟𝑦 𝑒𝑥𝑐𝑖𝑎𝑡𝑡𝑖𝑜𝑛 𝑎𝑡 𝑓 )2=
𝐴2
𝐴12 =
𝜌𝑐𝜔𝐾2
4𝐾12√1+�̂�1
2 3.3.13
52
Where β is the nonlinear acoustic constant and these pervious expressions show
that the second harmonic amplitude is directly depending on the applied prestress
force.
3.3.3 Ultrasonic wave interaction with discontinuous surface
Let consider the possibilities of this method by means of a simple model with a
discontinuity surface, such as the prestressed concrete. Assumed the concrete surface
has a micro crack normal to its x-axis.
The consequence is when the sine wave with a frequency equal to 𝜔 input to a
concrete surface with any defects, micro cracks and voids, it will not produce a sine
wave output. This change in procedure is due to an appearance of high order harmonic
in the response such as sin(2𝜔𝑡), 𝑠𝑖𝑛𝑒 (3𝜔𝑡) etc. as shown in Figure 3.8.
Figure 3-8. The signal propagation in surface with micro crack.
Assumed 𝑥(𝑡) = sin (𝜔𝑡) the input to the system.
The output will be generally represented as a fast Fourier transform (FFT)
compose of harmonicas and written as:
𝑦(𝑡) = 𝐴1 sin(𝜔𝑡 − ∅1) + 𝐴2 sin(2𝜔𝑡 − ∅2) + 𝐴3 sin(3𝜔𝑡 − ∅3) 3.3.14
As the ultrasonic transducers and the receivers will be attached to the concrete
surface of the box-girder in this research, the sinusoidal signal with frequency ω will
A 1 Sin 𝜔t
A 2 Sin 2𝜔t
A n Sin 𝑛𝜔t
Y
X
Sin 𝜔t
53
be distorted as it propagates inside the non-homogeneous material. The second and
higher harmonic will be generated and β can be calculated using equation 3.3.13. Due
to limited information about the value of this constant, a number of calibration tests
need to conduct in different locations of the box-girder to build a relationship between
β and the stress developed on the concrete surface due to apply PF and hence provide
a valid technique to identify the PF as will show in chapter 8.
3.4 SUMMARY
This chapter divided in to two parts: the first part presented the basics of guided
ultrasonic wave propagation in plates with theoretical consideration of Lamb wave
characteristics. It has been shown both theoretically and experimentally that the state
of stress in isotropic materials will induced anisotropy in their elastic properties. As a
result, the propagation velocities of the ultrasonic waves in an elastic media subjected
to deformation are stress dependent. The change in the propagation velocities of
ultrasonic waves due to change in the stress state are referred to as acoustoelastic
effects. Acoustoelastic theory, which is directly related to the linear parameters of the
ultrasonic wave, has been presented as a part of this chapter, and reviewed monitoring
stresses in numerous studies show potential for enabling practical ultrasonic waves to
identify the PF of PSCBs.
The second part of this chapter presented the basics of nonlinear acoustic
parameters of the ultrasonic waves and its application in identifying the PF of
prestressed concrete structures and another SHM application. Nonlinear Acoustic
theory of the ultrasonic wave has been presented as a part of this chapter, and reviewed
monitoring stresses in a number of studies show potential for enabling practical
ultrasonic wave to identify the PF of prestressed concrete box-girder bridges using
nonlinear acoustic behaviour.
54
Chapter 4: Research Design
This chapter describes the method adopted by this research to achieve the aim
and objectives stated in section 1.3. Section 4.1 describes the requirement of the study.
Section 4.2 discusses the methodology used to achieve the objectives of this study.
4.1 REQUIREMENT OF STUDY
As discussed in Chapter 1, a large number of old bridges that were designed to
unpreceded design standards are still in use in Australian road network. These bridges
are not only old but also experiencing much higher traffic load than their original
intended load. Further, the traffic load is increasing at a rate of 10% per decade
(Heywood & Ellis, 1998). The PF has been identified as an important factor that
governs the performance of prestressed structures. A number of bridges have failed in
the last few years due to defective prestressing systems. Moreover, these types of
failures usually collapse with no warning. This has emerged a requirement of the
condition and capacity assessment of in-service bridges for their safe operation.
However, lack of knowledge in estimating the effective PF in an existing PSCB has
become a drawback for capacity assessment.
In order to overcome this, a number of studies have been conducted in this area.
However, those methods were limited for prestressed beams with accessible tendons.
No method has been developed to assess the PF of prestressed concrete box girder
bridges with embedded tendons that are another important type of prestressed bridges.
This gap in knowledge highlights the requirement of studying towards developing a
PF identification methodology for box girder bridges.
4.2 METHODOLOGY
Ultrasonic technology has been identified as the best method to be used in PF
identification due to its nondestructive manner and proven accuracy for different types
of prestressed concrete beams and bridges as mentioned in the literature review. This
technology requires ultrasonic transducers that are sensitive to the change in the stress
developed on the concrete surface due to apply PF. The developed stresses can be used
55
in an inverse calculation to calculate the unknown PF applied to the steel tendons. In
order to address the requirement of study, the aim and objectives of this research are
outlined in Figure 4.1.
Figure 4-1. Aim and objectives
4.2.1 Achieving Objective 1
To develop a novel method for PF identification using an ultrasonic technology,
finite element studies have been carried out using ‘ABAQUS’ software. Prestressed
concrete beam models have been developed; two prestressing systems have been used
to investigate the effect of bond and unbounded tendons on the ultrasonic wave
characteristic. The FEM models were tested at four PF levels, the relative change in
the wave velocity and the amplitude energy due to applied PF were collected at each
PF level. Further, the effects of different parameters such as the location of the
transmitters and the receivers, the distance between the transducers, the ultrasonic
signal type on the ultrasonic wave characteristic were also studied.
Objective 1
Identify the effect of PF
on the Ultrasonic wave
Behaviour
Develop a new method to identify the PF
in prestressed concrete box-girder bridge
using the Ultrasonic technology
AIM
Objective 2
Verification–Lab testing
Linear Acoustic
Parameter of Ultrasonic
wave
Objective 3
Verification–Lab testing
Nonlinear Acoustic
Parameter of Ultrasonic
wave
56
4.2.2 Achieving Objective 2
Prestress force determination process for box girder bridges was developed in
objective one by using finite element simulation results. In order to validate this
method, a scale-downed version of a box girder bridge was tested under laboratory
conditions. Lab model was tested at four PF levels. The effective PF in tendons were
measured using installed load cells. Relative change in the wave velocity due to
applied PF were collected at each prestress level. The data collected were used to
calculate the acoustoelastic constant (K), then used in the inverse calculation to verify
the proposed method.
4.2.3 Achieving Objective 3
Same lab model, PF levels, ultrasonic system were used to identify the effect of
PF on the amplitude of the second harmonic of the FFT signal. The data collected used
to build a relationship between the nonlinear acoustic constant (β) and the stress
developed on the concrete surface due to apply the PF. The data collected at each PF
level were used in the inverse calculation to verify the proposed method.
4.3 SUMMARY
After a comprehensive literature review, it was found that no successful method
has been developed to assess the effective PF in prestressed concrete box girder
bridges in a non-destructive manner. In order to address this identified gap in
knowledge, this research was aimed to develop a new method to identify the PF in
prestressed concrete box girder bridges. To achieve this target, three main objectives
were set as showed in Figure 4.1.
57
Chapter 5: Effect of Prestress Force on
Ultrasonic Wave Characteristics
Previous studies presented in Chapter 2 have shown the possibility of identifying
PF using ultrasonic technology. In order to verify the effect of the PF on the ultrasonic
wave characteristics, a finite element analysis and a parametric study were carried out
as a preliminary study of this research. This chapter shows the details and results of
this study.
5.1 INTRODUCTION
To model ultrasonic wave propagation phenomena in any structure, the
governing differential equations of motion need to be solved numerically with
appropriate boundary conditions. This approach is used for simple geometries;
however, these equations become difficult for geometries that are more complicated
such as bridges, or when some features are included, such as damage or prestressing
effects. Therefore, most of the PF measurement in the prestressed concrete structures
with ultrasonic wave found in the literature was mainly studied with experimental
methods.
Significant advantages of analytical modelling over experimental testing include
the ability to investigate different wave propagation cases quickly and applicability to
examine the wave behaviour through the entire thickness of the material rather than
only based on surface measurements. In such cases, different computational techniques
can be used to analyse wave propagation along the structure. These include the time
domain finite element model. Both implicit and explicit schemes can be used for this
purpose (Naresh, 2008).
In implicit schemes, the dynamic equilibrium is satisfied at the end of each time
step, and the displacement can be obtained by solving the wave’s equations. The main
disadvantage of using this procedure is that the matrix inversion of the order number
of degree of freedom is needed, and large time steps are allowed (Naresh, 2008).
58
Explicit finite element methods, which step through the solution in time, are one
of the most popular techniques since various finite element codes exist and there is no
need to develop specific code. The acceleration at the beginning of the time step is
calculated directly by using the net mass and force acting on each element. Therefore,
this scheme does not require any large matrix inversion (Naresh, 2008). The
acceleration is then integrated twice to obtain the displacement after a time step ∆t.
Since the method integrated constant acceleration, the time increments must be quite
small for the method to produce accurate results. Therefore, particular and temporal
discretisation of the finite element model must be assigned carefully to obtain the
correct solution.
5.2 NUMERICAL MODEL AND THE EFFECT OF THE BONDED AND
UNBONDED TENDON
The effect of bonded and unbonded nature of tendons on the acoustoelastic effect
was investigated using finite element methods (FEM). A finite element model of the
beam was developed using the commercially available finite element (FE) software
ABAQUS. ABAQUS has been used for modelling and analysing prestressed concrete
structure by many researchers, including Oliva and Okumus (2011).
To study the effect of bonded and unbonded tendons, two FE models were
developed with identical properties of materials and dimensions except for the
interface between tendon and concrete. The bonded tendons were modelled using
embedded 3D truss elements (T3D2). The ABAQUS has the option to apply the PF as
an initial tension stress. The tension in the bonded tendon is then transferred as a
compression to the concrete through the interface between the concrete and the
embedded truss element (Systèmes, 2012). While the PF due to unbonded tendon was
simulated as an external pressure force option that is available in ABAQUS applied on
the concrete ends and results in a uniform compression stress in between. The concrete
beam was modelled using 3D solid elements, each with 8 nodes (C3D8R). The
material properties of the beam model, based on typical prestressed concrete, are
shown in Table 5.1.
59
Table 5-1.
Material Properties Used during the Simulation for the Prestressed Concrete Beam
Materials
Young
modules
(N/m2)
Poisson’s
ratio
Density
(kg/m3) Damping effect
Steel 200E9 0.3 7800 Negligible
Concrete 30E9 0.2 2400 Negligible
Analyses in this section were carried out to study the effect of tendon type of one
metre simply supported prestressed concrete beam on ultrasonic wave characterises
due to applied PF. The distance between the transducers was kept constant at 30 cm,
assuming any change in travel time was due to PF changing only, and not a change in
the spacing of transducers. The analyses were carried out at different prestress levels
and PFs were selected to the resultant concrete stresses of 0 MPa, 2.5 MPa, 5 MPa and
10 MPa. Figure 5.1 shows the prestressed concrete beam cross-section with bonded
and unbonded tendons adopted during the FE. Stress distribution of the beam due to
prestressing is shown in Figure 5.2 (A) for bonded tendon and (B) for unbonded tendon
respectively. In Figure 5.2 the stresses distribution in the transmitter and the receiver
points (under the NA) due to the application of 10 MPa is quite similar quantitatively
in both cases for different tendons types. However, the stresses are qualitatively
different in both cases as expected due to using different tendon type.
Figure 5-1. FEM model adopted in this section with bonded and unbonded tendons
60
(A)
(B)
Figure 5-2. Stress distribution of the beam due to prestressing
bonded tendon (A) unbonded tendon (B)
61
The wave propagation behaviour was studied with 5 cycles of Hanning window
and frequency of 300 kHz excitation signal to generate Lamb wave. Two ultrasonic
wave transducers were arranged in particular constant location (compression zone
under the NA) at the vertical face of a 3D prestressed concrete model. One transducer
acted as a transmitter and the other acted as a receiver to receive the ultrasonic signal.
Four PF of 0 MPa, 2.5 MPa, 5 MPa and 10 MPa have been applied to the model
respectively.
Two-step loading has been considered: a stationary loading to generate a stressed
body and explicit solver based on the central different scheme used in simulating high-
speed events (such as Lamb wave). Excitation of the model at the second step of the
simulation was completed using point force at transmitter’s location and the signal
received at receiver’s location. Figure 5.3 shows the ultrasonic wave propagation
between the transmitter and the receiver on the prestressed concrete surface.
A
62
(B)
Figure 5-3. The ultrasonic wave propagation between the transmitter and the receiver on the
prestressed concrete surface (A) at the beginning (B) at the end of the simulation
The simulation results of the acceleration responses were showed that the
ultrasonic wave characteristics were affected by changing the magnitudes of the PF
for both the bonded and unbonded tendons as shown in Figures 5.4 and 5.5
respectively. The velocities responses show a significant change in the TOF, as the
arrivals time were reducing with increasing PF. While, the amplitudes energy were
increasing with the increase of the PF level applied to the model. These changes in the
ultrasonic wave characteristics were similar for the FEM model with bonded and
unbonded tendons.
Although, the velocity response show a significant change in the TOF, the
relative change in the wave velocity could not be calculated directly. Therefore, cross-
correlation method has been used for this purpose (more information about this method
will be presented in section 7.4). Effects of the bonded and unbonded tendons on the
relative change in the wave velocity due to apply the PF are shown in Figure 5.6.
63
Figure 5-4. Acceleration response of the node in the receiver point for the bonded tendons at
different PF levels
Figure 5-5. Acceleration response of the node in the receiver point for the unbonded tendons
at different PF levels
-1
-0.5
0
0.5
1
0 0.0001 0.0002 0.0003 0.0004
Am
pli
tud
e V
olt
Time Sec
Acceleration at the receiver point for different
PF (Bonded tendon)
0 MPa 2.5 MPa 5 MPa 10 MPa
-1
-0.5
0
0.5
1
0 0.0001 0.0002 0.0003 0.0004
Am
pli
tud
e V
olt
Time Sec
0 MPa 2.5 MPa 5 MPa 10 MPa
Acceleration at the receiver point for different
PF (Unbonded tendon)
64
Figure 5-6. Relative change in the wave velocity due to apply PF for bonded and unbonded
tendons
Figure 5.6 shows the relative change in the wave velocity is increasing with
increasing the PF levels for bonded and unbonded tendon, because increasing the PF
level is increasing the homogeneity of the prestressed concrete surface. While from
Figure 5.2 (A and B) it can be observed that stress distribution in the models with
bonded and unbonded tendons was quite similar quantitatively in both cases and the
tendons’ type did not show any significant effect on the results as the ultrasonic wave
propagates in the concrete surface. For further studying the effect of the PF on the
ultrasonic wave characteristics, different physical parameters related to the model and
different ultrasonic signal will be further studied, to find out the best parameters use
in PF identification.
5.3 EFFECT OF THE PF ON THE BOX-GIRDER
As the current study focused on simply supported box-girder bridges, a FE
analysis was carried out on six-metre-long simply supported box-girder with initial
homogenous uniaxial stress and two embedded prestressed tendons in two webs.
Figure 5.7 shows the prestressed concrete box-girder cross-section adopted
during the FE. Symmetric boundary condition at horizontal-direction has been used at
R² = 0.9683
R² = 0.9578
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0 2 4 6 8 10 12Rel
ati
ve
chn
ag
e in
th
e w
av
e v
elo
icty
Stress MPa
Relative change in the wave velocity due to
apply PF
Bonded tendon Unbonded tendon
65
the middle part of the model in order to reduce the model size, as shown in Figure 5.8.
The material properties of the model, based on typical prestressed concrete, are shown
in Table 5.2.
Figure 5-7. Cross-section of the box-girder used in the FE (dimensions in m).
Figure 5-8. The model after applying the symmetric boundary condition at the middle of the
girder
Symmetric Boundary Condition
66
Table 5-2
Material Properties Used during the Simulation for the Box-girder
Materials
Young
modules
(N/m2)
Poisson’s
ratio
Density
(kg/m3)
CL*
(m/s)
CT*
(m/s)
Damping
effect
Steel 200E9 0.3 7800 5875.1 3140.4 Negligible
Concrete 30E9 0.2 2400 3726 2357 Negligible
Note.
*CL Longitudinal wave velocity
*CT Transvers wave velocity
*Reinforcement in the prestressed concrete box-girder model not modelled.
Four levels of PF were applied during the simulation. Analyses were carried out
to study the effect of the PF on the ultrasonic wave characteristics. Different
parameters related to the model have been further studied, for example, the
transducers’ locations and the distance between the transducers and the receiver. The
same parameters have been studied during the experimental program as will be
presented in Chapter 6.
5.4 ABAQUS /EXPLICIT AND NUMERICAL INTEGRATION
The equation of equilibrium for our system is expressed using Newton’s second
law in term of the mass, damping and stiffness matrix and external load vector, as
shown in equation 5.1.
[𝑀]�̈� + [𝐶]�̇� + [𝐾]𝑢 = 𝑓 5.1
Where
[𝑀] Mass matrix
67
[𝐶] Damping matrix
[𝐾] Stiffness matrix
f Applied load
ABAQUS/Explicit uses a diagonal mass matrix instead of the consistent mass
matrix, giving a simpler system to be calculated at each time step (Olsson, 2012). The
explicit solver solves systematically, utilising the central difference integration scheme
together with mass, stiffness and damping matrix to advance the equation of motion.
To arrive at the equation used, one starts with the Taylor expansion of the defamation
around the time (Olsson, 2012):
𝑡𝑖+0.5 at 𝑡𝑖, 𝑡𝑖+1 denoting 𝑢 (𝑡𝑖) = 𝑢𝑖 .
𝑢𝑖+1 = 𝑢𝑖+0.5 +𝛥𝑡
2�̇�𝑖+0.5 +
(∆𝑡)2
2�̈�𝑖+0.5 + 0(∆𝑡)3 5.2
𝑢𝑖 = 𝑢𝑖+0.5 −𝛥𝑡
2�̇�𝑖+0.5 +
(∆𝑡)2
2�̈�𝑖+0.5 − 0(∆𝑡)3 5.3
Subtracting equation 5.3 from equation 5.2 yields:
�̇�𝑖+0.5 =𝑢𝑖+1−𝑢𝑖
∆𝑡 5.4
In the same manner, a Taylor expansion is made around 𝑡𝑖 at time 𝑡𝑖+1 and 𝑡𝑖−1
𝑢𝑖+1 = 𝑢𝑖 + 𝛥𝑡 �̇�𝑖 +(𝛥𝑡)2
2�̈�𝑖+0.5 + 0(∆𝑡)3 5.5
𝑢𝑖−1 = 𝑢𝑖 − 𝛥𝑡 �̇�𝑖 +(𝛥𝑡)2
2�̈�𝑖 − 0(∆𝑡)3 5.6
68
Adding equations 5.5 and 5.6 yields:
𝑢𝑖+1 + 𝑢𝑖−1 = 2𝑢𝑖 + ∆𝑡2�̈�𝑖 5.7
Substituting equation 5.5 in equation 5.7 yields:
�̇�𝑖+0.5 =𝑢𝑖−𝑢𝑖−1
∆𝑡+ ∆𝑡𝑢𝑖 =̈ �̇�𝑖−0.5 + ∆𝑡𝑢𝑖̈ 5.8
Taking the time step to evaluate at the point of integration gives the following
equations that are used by the explicit dynamic solver in ABAQUS:
�̇�𝑖+0.5 = 𝑢𝑖−0.5̇ +∆𝑡𝑖+1+∆𝑡𝑖
2𝑢𝑖̈ 5.9
𝑢𝑖+1 = 𝑢𝑖 + ∆𝑡𝑖+1�̇�𝑖+0.5 5.10
The central difference integration scheme has an error term of 0(∆𝑡)3 and is thus
correct up to second order (Olsson, 2012).
5.5 THEORETICAL ANALYSIS OF WAVE PROPAGATION
The package used in this study, ABAQUS/ Explicit, used an explicit integration based
on a central difference method. The stability of the numerical solution is dependent on
the temporal and spatial resolution of the analysis. To avoid numerical instability
ABAQUS/ Explicit recommended a stability limit for the integration time step (∆t)
equal to:
∆𝑡 =𝐿𝑚𝑖𝑛
𝐶𝐿 5.11
69
Where:
𝐿𝑚𝑖𝑛 Smallest dimension of the smallest finite element of the model
𝐶𝐿 Longitudinal wave velocity through the material.
The size of the finite element Lmin is typically derived from the smallest
wavelength ( 𝜆𝑚𝑖𝑛) to be analysed. For a good spatial resolution, 10 nodes per
wavelength are normally required (Chen, Dong, Meng, & Liang, 2012).
𝐿𝑚𝑖𝑛 =𝜆𝑚𝑖𝑛
20 5.12
Per equation 5.11, the simulation ran from zero to 400 𝜇𝑠, and the integration
time step was set to ∆t =5e–7 sec throughout the analysis.
5.6 MESH AND LOAD
After defining the geometric properties, attention was focused on mesh
definition. The mesh definition was a critical phase where it was necessary to find a
balance between accuracy and computational cost. For the convergence of the
simulation, the mesh of the structure should be fine enough for at least 10 elements to
exist per wavelength, especially along the direction of wave propagation, as shown in
Figure 5.9.
70
Figure 5-9. Fine mesh along the direction of wave propagation.
The concrete beam was discretised by a 3D-stress, 8-node linear-brick element
with three degrees of freedom per node (C3D8R). Two parabolic steel embedded
tendons were discretised by a two-node linear 3D truss element (T3D2). The analysis
of the PF applied to the model involved two different steps. The loads applied inside
the first step concerned the preload phase and consisted of a uniform pressure (to
model a tension) applied to the ends of the tendon. Stress distribution in the box-girder
due to prestressing shows a pattern similar to that expected, with tension in the top slab
and compression in the bottom slab, as shown in Figure 5.10.
71
(A)
(B)
Figure 5-10. Stress distribution in the box-girder (A) before applying the PF and
(B) after applying the PF.
72
Three different locations were been chosen during the FE analysis: two at the
top part of the model above the NA (tensile stress zone) and one at the web part of the
model under the NA close to the tendon location (compressive strength zone), as
shown in Figures 5.11 and 5.12 respectively.
Two ultrasonic wave transducers were arranged in particular constant locations
of a 3D prestressed concrete box-girder beam. One transducer acted as a transmitter
and the other as a receiver for PF measurements. At the top part of the model, the
distance between the transducers was kept constant at 22.5 and 30 cm respectively, to
find out the effect of the distance between the transducer and the receivers on the
accuracy of the results. The distance between the transducers was kept constant at
30 cm at the web part of the box-girder model. Assuming that any change in travel
time is due to PF changing, and not a change in the spacing of transducers. Four levels
of PF – 0 %, 25 %, 50 % and 75 % of the ultimate tensile strength (UTS), which is
about 200 kN – have been applied on the model respectively.
Excitation of the model at the second step was completed using point force at T
(transmitter’s location) and the signal received at R (receiver’s location). The steps
were completed to focus on the relative change in the ultrasonic wave velocity and its
relationship to the force applied to the tendons.
Figure 5-11. Transducer and receiver locations at the top part of the FEM model.
Not in scale
73
Figure 5-12. Transducer and receiver locations at the side part of the FEM model
The ultrasonic wave was introduced as a transient excitation pulse inserted at the
top part and at the side part of the 3D model. Two excitation signals, namely Hanning
window and sinusoidal signals were used in the simulation, as shown in Figure 5.13.
MATLAB software was used to generate five cycles of Hanning window
excitation signal at 300 kHz frequency. This signal has been used by different
researchers such as Chen et al. (2012) and Han et al. (2009) due to a number of
advantages such as:
• Reduces the energy at frequencies other than the excitation or “centre”
frequency.
• Since the signal is based on a limited cycle sinusoidal tone burst, the
undesired reflections between the packets are reduced, allowing the time
of flight (TOF) to be calculated (Han et al., 2009).
The wave propagation behaviour was further studied with one damped cycle of
a 45 kHz sinusoidal signal for reasons of comparison. LabVIEW software was used to
generate the signal. The last excitation signal was equal to the pulse generated by the
available ultrasonic piezoelectric transducers in the QUT labs.
Not in scale
74
(A) Hanning window excitation signal
(B) Sinusoidal signal excitation signal
Figure 5-13. Excitation signals used in the simulations.
75
The simulation excitation signals were applied directly into the FEM as forcing
functions on the top and side parts of the model with uniform x-displacement and y-
displacement distribution.
5.7 RESULTS AND DISCUSSION
Analytical simulations implemented using the 3D plane strain model excited at
two different excitation frequencies, 300 kHz and 45 kHz respectively five-cycle
Hanning window and sinusoidal wave signals were utilised for this purpose.
The model ran for various input (PF): 0 %, 25%, 50% and 75% of the UTS. The
acceleration response was determined at the receivers RFEM1, RFEM2 and RFEM3.
5.7.1 Hanning window signal results
Figures 5.14, 5.15 and 5.16 show the corresponding normalised sensor signals
vs. TOF for the Hanning window signal of the received signal at RFEM1, RFEM2 and
RFEM3, respectively, due to the application of different (PF).
Figure 5-14. Acceleration at the receiver RFEM1 components for different PF
(Hanning window).
-1
-0.5
0
0.5
1
0 0.0001 0.0002 0.0003 0.0004
Am
plt
uid
e V
olt
Time Sec
Acceleration at the receiver RFEM1 for
different PF (Hanning Window)
0% U.T.S 25 % U.T.S 50 % U.T.S 75 % U.T.S
S
0
A
0 S0
A0
UTS UTS UTS UTS
76
Figure 5-15. Acceleration at the receiver RFEM2 components for different PF
(Hanning window).
Figure 5-16. Acceleration at the receiver RFEM3 components for different PF
(Hanning window).
-1
-0.5
0
0.5
1
0 0.0001 0.0002 0.0003 0.0004 0.0005
Am
plt
uid
e V
olt
Time sec
0% U.T.S 25% U.T.S 50% U.T.S 75% U.T.S
-1
-0.5
0
0.5
1
0 0.0001 0.0002 0.0003 0.0004
Am
plt
uid
e V
olt
Time sec
Acceleration at the receiver RFEM3
for different PF (Hanning Window)
0 % U.T.S 25% U.T.S 50 % U.T.S 75 % U.T.S
S0
A0
UTS UTS UTS 75%UTS
S
0
A
0 S0
A0
UTS UTS UTS UTS
77
As shown in Figures 5.14 to 5.16, the analytical results detected the arrival of
the fundamental symmetric mode (S0) and asymmetric mode (A0) wave at various
locations very well. However, the lowest asymmetric mode (A0) was dominant and
the lowest symmetric mode (S0) was hardly visible for the Hanning window signal.
Further, it can be observed from the Figures 5.14 to 5.16, there were more than
one pulse arrived roughly at the S0 arrival time, that can be attributed to the non-
homogeneity of the concrete surface where the ultrasonic waves were propagated. This
non-homogeneity has caused some distortion to the pulse echo. Therefore; some of
these waves were reflected while they propagated through the concrete surface, while
the others were transmitted quite easily.
Further, from the Figures 5.14 to 5.16, it can be observed that the time delay
induced by PF is visible and tiny at the same time. Therefore, to calculate the relative
change in wave velocity indirectly, a method based on the cross-correlation method
needed to be implemented. The delay time ∆t can be precisely decided when the
correlation coefficient reaches the maximum (more information about this method will
be presented in section 7.4). The results of the relative change in the wave velocity vs.
the percentage of the applied PF is plotted in Figure 5.17.
Figure 5-17. The relationship between the relative change in the wave velocity vs. % of the
PF increasing (Hanning window results).
R² = 0.7559
R² = 0.7075
R² = 0.9703
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0% 20% 40% 60% 80%
Rel
ata
ive
cha
ng
e in
th
e w
ave
vel
oci
ty
% of the PF increasing
Relative change of the wave velocity in different
locations on the model (Hanning Window)
R1 R2 R3RFEM1 RFEM2 RFEM3
78
From Figure 5.17, it can be seen that two different behaviours were observed
from the simulation results. The first behaviour was for the RFEM1 and RFEM2
receivers, where they attached at the top part of the model. It can be observed that
relative change in the wave velocity reduced with increasing the PF level in RFEM1
and RFEM2. The reduction of relative change in the wave velocity can be attributed
to the micro cracks that start to propagate in the concrete surface of the box girder due
to developing the tensile stress at the top part and created a nonhomogeneous concrete
surface. Thus the micro crack width increase further with increasing PF and some of
the wavelengths cannot pass them. Therefore; it can be expected that the presence of
tensile stresses developed at the top part of the concrete would reduce the ultrasonic
wave velocity. However, the effect was not clear enough till reach 50% of the UTS,
and that can be explained why the blue and grey colour lines seems not aligning with
the blue and grey colour markers, for 25% PF increasing. While, the distance between
the transmitter and the receiver did not make a notable difference in the results but the
R2-value decreased slightly.
The receiver RFEM3, attached at the side part, behaved differently due to its
location where the compressive stress developed due to the effect of the PF. The wave
velocity increased with increasing PF applied on the tendons, which caused the
structure to compress and try to be more homogenous, which is the main reason for
using prestressed concrete. As a result, this location was used during the experimental
program where the effect of the PF on the ultrasonic wave characteristics could easily
be investigated.
5.7.2 Sinusoidal signal results
The same simulation was repeated in the same locations and the sinusoidal signal
was used to excite the transmitter. This signal was used as it can easily be generated
using the available signal generator in the QUT lab. Figures 5.18, 5.19 and 5.20 show
the corresponding normalised sensors signal vs. TOF for the sinusoidal signal of the
received signal at RFEM1, RFEM2 and RFEM3, respectively, due to the application
of different prestress forces (PF).
79
Figure 5-18. Acceleration at the receiver RFEM1 components for different PF
(sinusoidal signal).
Figure 5-19. Acceleration at the receiver RFEM2 components for different PF
(sinusoidal signal).
-1
-0.5
0
0.5
1
0 0.0001 0.0002 0.0003 0.0004 0.0005
Am
plt
uid
e V
olt
Time Sec
Acceleration at the receiver RFEM1 for
different PF (Sinusoidal signal )
0 % U.T.S 25 % U.T.S 50 % U.T.S 75 % U.T.S
-1
-0.5
0
0.5
1
0 0.0001 0.0002 0.0003 0.0004 0.0005
Am
plt
uid
e V
olt
Time Sec
Acceleration at the receiver RFEM2 for different
PF (Sinusoidal signal )
0 % U.T.S 25 % U.T.S 50 % U.T.S 75 % U.T.SUTS U
T
UTSUTS
UTS UTS UTS UTS
80
Figure 5-20. Acceleration at the receiver RFEM3 components for different PF
(sinusoidal signal).
From the Figures 5.18-5.20, it can be observed that the time delay induced by
PF is visible for the sinusoidal signal. Therefore, to calculate the relative change in
wave velocity indirectly, the same method used in the previous section based on the
cross-correlation method was implemented. The delay time ∆t was decided when the
correlation coefficient reaches the maximum. The results of the relative change in the
wave velocity vs. the percentage of the applied prestressed force for the sinusoidal
signal are plotted in Figure 5.21.
-1
-0.5
0
0.5
1
0 0.0001 0.0002 0.0003 0.0004
Am
plt
uid
e V
olt
Time Sec
Acceleration at the receiver RFEM3 for
different PF (Sinusoidal signal )
0 % U.T.S 25% U.T.S 50% U.T.S 75 % U.T.SUTS UTS UTS UTS
81
Figure 5-21. The relative change in wave velocity due to application of different PF
(sinusoidal signal).
From Figure 5.21, it can be observed that relative change in the wave velocity
reduced with increasing the PF level in RFEM1 and RFEM2. The reduction of relative
change in the wave velocity can be attributed to the micro cracks that start to propagate
in the concrete at a stress level about 25% of the UTS. The micro crack started to
increase further with increasing PF due to increasing the tensile stress at the top part;
thus, some of the wavelengths cannot pass them. Then it can be expected that the
presence of tensile stresses developed at the top part of the concrete would reduce the
ultrasonic wave velocity. The same behaviour was observed when the Hanning
window signal was applied.
An increase in the relative change in the wave velocity with increasing PF was
observed in RFEM3. This receiver was attached at the compression zone, where the
structure started to become more homogenous and most of the micro cracks had closed
due to the application of the PF. A similar trend was observed while using Hanning
window excitation signal to excite the transformation. This demonstrated the
possibility to relate the change in wave velocity to the applied PF.
RFEM1 RFEM2 RFEM3
82
5.8 SUMMARY
A number of studies have been carried out on prestress members and researchers
have observed that ultrasonic waves can be utilised for stress monitoring of a
prestressed concrete beam and box-girder models. For further investigation of this
effect, a FE analysis was carried out to study the effect of the PF and other system
parameters on the ultrasonic wave characteristics.
Paramedic studies were carried out to identify the effect of system parameters
(such as the tendon type, location of the receivers and the distance between the
transmitter and the receiver) on the relative change of the wave velocity with the
changing of the PF level. Results confirmed the different effects of the receiver’s
location on the relative change of the wave velocity of the ultrasonic wave due to the
application of PF. However, the effect of increasing the homogeneity (through
increasing the wave velocity) of the model due to the application of PF clearly appears
in the compression zone. Therefore, all the transducers and the receivers were attached
at this zone during the experimental program. Tendon type and distance between the
transducer and the receiver showed a minor effect on the results.
The simulation results showed that there is a direct relationship between the
relative change in the wave velocity and the PF applied on the tendons for both
Hanning and sinusoidal signals. Therefore, further work in these areas needs to be
conducted to investigate these relationships experimentally and to use them for inverse
calculation of the PF, as will be discussed in Chapter 7.
Both Hanning window and sinusoidal signals indicated satisfactory results
during the simulations. However, due to a lack of equipment, a sinusoidal signal was
used to excite the piezoelectric ultrasonic transducers during the experimental
program.
83
Chapter 6: Experimental Study and Box-
Girder Model Preparation
6.1 EXPERIMENTAL MODEL
After a comprehensive study using finite element models, it was found that there
is a linear relationship between the relative change in the ultrasonic wave velocity and
the PF. This relationship can be used to identify the PF according to acoustoelastic
theory. For further studies and validation of the technology, a promising technique
based on ultrasonic guided waves to monitor the PF is presented in this chapter. The
experimental tests developed during the research involved a box-girder prestressed
concrete beam to analyse the outputs of the signals and their relationship with the PF
of the tendons. The outcome of this research will be used to validate the PF monitoring
method based on ultrasonic testing. Therefore, this chapter briefly presents the design,
construction and test prototype of the laboratory model.
In this study, the relative change in the ultrasonic wave parameter was used to
determine the PF in the prestressed concrete model according to acoustoelastic theory.
Other ultrasonic wave parameters such as the amplitude energy and the amplitude of
the second harmonic of the FFT curve have been tested to determine the feasibility of
using these parameters to evaluate and identify the PF of the PSCBs.
A scaled-down physical model of a six-metre-long continuous concrete bridge
was designed and constructed to represent a typical full-scale bridge. The cross-section
of the lab model was selected as similar to the one used by Madhavi, Sekar, and
Paramasvam (2006) in their experimental study. However, due to limited resources,
some minor variations were made. Figure 6.1 shows the cross-section dimensions of
the lab model; all of the dimensions are in millimetres.
Sufficient longitudinal and shear reinforcement was provided to the box-girder,
as shown in Figure 6.2, to ensure monolithic behaviour of the beam and to avoid
84
cracking during handling. More drawings detailed of the reinforcement are presented
in Appendix A.
Reinforcements required to resist busting at the prestressing tendon anchorage
were checked and provided according to ACI guidelines (ACI committee 318, 2008).
Figure 6-1. Cross-section of the lab model.
Figure 6-2. Reinforcement details of the lab model.
85
6.2 PRESTRESSING TENDONS DETAILS
The model was single-span, prestressed, posttensioned with a box-girder cross-
section, equipped with various sensors to continue monitoring strain, deflection,
displacement, acceleration and support reaction forces.
The model was symmetrical about the centre point, which divided the whole
model length into two equal spans of three metres each, 440 mm in height and
1000 mm in width. The beam was posttensioned concentrically with two parabolic
tendons, symmetrical about the centre line as shown in Figure 6.3.
Figure 6-3. Tendon profile.
Each tendon consisted of seven wires with nominal diameters of 15.2 mm
embedded in a 20 mm diameter duct was used in each web. Two steel plates of size
85 mm × 150 mm × 20 mm, together with wedge barrels, were used at both ends to
anchor the tendons, as shown in Figure 6.4.
86
Figure 6-4. End anchorage of strand.
The tendons were unbonded and encapsulated within a protective sleeve and
placed adjacent to the concrete. At each end of each tendon was an anchorage assembly
firmly fixed to the surrounding concrete.
Once the concrete had been casted and set, the tendons were tensioned
(“stressed”) by pulling the tendon ends through the anchorages while pressing against
the concrete. The main and general advantages of using unbonded tendons in PSCBs
are:
1. Reduced concrete cover as the smaller size of the unbonded tendons allows
some reduction in the thickness of concrete elements.
2. Increased corrosion protection compared to ducted tendons may allow them
to be placed closer to the concrete surface.
3. Simpler replacement and/or adjustment. Being permanently isolated from
the concrete, unbonded tendons are able to be readily de-stressed, re-
stressed and/or replaced should they become damaged or need their force
levels to be modified in service.
6.3 CONSTRUCTION OF LAB MODEL
The long hollow section (6 m long), with a small cross-section, means pre-
planning of the construction method is imperative, especially for removing the inner
framework. Therefore, the model was casted in three sequences, as shown in Figure
6.5; the minimum duration between two sequences was 10 days. For each sequence,
the model was moist-cured for seven days by covering it with saturated burlap and
plastic sheeting. Beyond eight days, the model was kept in laboratory air.
87
Figure 6-5. Construction steps for the box-girder.
As the formwork was supposed to be used once only, and for easy handling, it
was decided to use plywood formwork with timber supports, as shown in Figure 6.6.
The concrete grade was selected as 32 MPa and the nominal aggregate size as 10 mm
to compact well in narrow vertical sections.
Figure 6-6. Proposed formwork arrangement.
88
6.3.1 Stage 1
The bottom slab was the first part of the box-girder model that was constructed.
It was an 80 mm thick reinforced concrete slab connected to the web along its longer
edge. Sufficient reinforcements were provided across the joint to avoid cracks and to
allow the model to behave as a single unit. Figure 6.7 shows Stage 1 of the model
construction before and after concreting.
(A) Stage 1 before concreting (B) Stage 1 after concreting
Figure 6-7. Construction of the model, Stage 1 (bottom slab).
6.3.2 Stage 2
To improve the bond between the surface of the bottom slab and the web of the
box-girder, the surface of the hardened concrete was chipped. The duct of the
prestressing stand and the longitudinal rebar were tied to the vertical reinforcement as
shown in Figure 6.8.
89
(A)Locating the ducts. (B) Formwork for webs.
(C) Concreting the webs. (D) After removing formwork.
Figure 6-8. Construction of model, Stage 2 (webs).
6.3.3 Stage 3
To build the top slab of the box-girder model, the same procedures used during
Stage 2 were repeated. To improve the bonding between the two surfaces (the webs
and the top slab), the surfaces of the construction joints were made rough. Further,
formwork for the slab inside the hole was created carefully so that it could be removed
easily from the two ends. Figure 6.9 shows Stage 3 of the construction model.
Duct for prestressing strands
90
(A)Reinforcing and formwork for the top slab. (B) Top slab after concreting.
(C) Completed model.
Figure 6-9. Construction of model, Stage 3 (top slab).
In reality, a box-girder is usually built up with end diaphragm to resist torsional
distortions and reduce the deflection resulting from concentrated loading due to
support condition. Therefore, a steel cross frame was located at the support locations
to act as a diaphragm, as shown in Figure 6.9 C. it has been made with 5 mm thick,
50 mm × 50 mm steel box sections, which were tightly fitted to the box-girder model
and welded in position.
End Diaphragm
91
6.4 APPLY THE PRESTRESSED FORCE ON THE UNBONDED
TENDONS
After locating the required tendons in the desired or predetermined profile, the
tendons were enclosed in a watertight cover. The box-girder was located on two half-
cylindrical steel supports, leaving a simply supported beam with a 5.8 m long span.
Prestressing of tendons was carried out at one end using a hydraulic mono jack,
while the other end of the strand was anchored to the concrete using a wedge barrel
and steel plate. Tension forces in the strands were measured through a cellular load
cell that was installed between the live end anchor and the concrete beam. Figure 6.10
shows the dead and live ends anchorage and load cells.
(A) (B)
Figure 6-10. (A) Dead end and (B) live end anchorage and load cells.
When the required concrete strength was achieved, the stressing or post-
tensioning process was started to produce the required tension in the strands.
Tensioning of the strands was carried out in three steps by the AUSPT (Australian
Post-Tensioning) Company to get different prestress levels. The PF in the strands was
measured during tensioning and while testing. Figure 6.11 shows the prestressing
equipment, process and load cell reading during tensioning.
Load cell
Anchor Plate
Wedge Barrel
92
(A)
(B)
Figure 6-11. (A) Prestressing equipment and process.
(B) Load cell reading during tensioning.
6.5 ULTRASONIC MEASUREMENT SYSTEM
In this section, a brief description of the electronic devices and instrumentation
involved in all experiments is presented. An Agilent 33500B waveform generator with
40–50 kHz frequency was used to excite the transmitter and generate a sinusoidal
93
signal. It is a 30 MHz synthesised waveform generator with built-in arbitrary
waveform and pulse capabilities.
A high-performance 4-channel RIGOL digital oscilloscope with sample rate, up
to 200 MHz bandwidth, RIGOL DS 1204B was used to measure and capture the output
of the receiver. Figure 6.12 shows the utilised Agilent waveform generator and RIGOL
oscilloscope. Additional information about the experimental tests and the equipment
is provided in the next section. Compared to the available systems for measuring
ultrasonic wave response, the system benefits from lower cost and simple structure and
controls.
The developed system measures the PF from the captured signal data. The
relative change in the wave velocity during the unstressed state and due to the
application of the PF will be employed for that purpose. Additional ultrasonic wave
parameters were measured during the experimental program. These include; the
amplitude energy and the amplitude of the second harmonic in the FFT curves. The
effect of the PF on these parameters will be investigated to find the ability to use them
in identifying the PF.
(A) (B)
Figure 6-12. (A) Agilent 33500B waveform generator and (B) RIGOL DS 1204B.
The piezoelectric transducers are the main part of the ultrasonic system,
converting electrical energy to mechanical energy and vice versa (Ghasemi, 2012;
Ghasemi et al., 2012). The Piezoelectric material exhibits the sensing ability results
94
from piezoelectric effect, that is, a surface charge is generated in response to an applied
mechanical stress (direct effect) and conversely, a mechanical strain is produced in
response to an applied electric field (converse effect) (Kevin & Liangsheng, 2004).
The piezoelectric materials of possess advantages of high sensitivity, high
renounce frequency and high stability. These advantages of the make the piezoelectric
traducers are very sensitive in detecting any change in the stress, temperature and
cracks of the concrete structure (Baoguo, Yu, & Ou, 2015). Therefore, these sensors
have been widely used in SHM and stress monitoring in the concrete structure for
example; Kevin and Liangsheng, (2004); Wen, Chen, Li, Jiang, and Guo (2006); Yi
and Weijian (2011).
Due to the advantages of these transducers and their high sensitivity to detect
any change in the stress state of the materials. They will be used in the research as a
part of the ultrasonic system.
Since an underside electric excitation signal can affect the performance of a
piezoelectric transducer, it is important to derive piezoelectric transducers by a signal
with low total harmonic disorder (THD). Two piezoelectric transducers, as shown in
Figure 6.13, were used to generate and receive the ultrasonic waves. Each piezoelectric
transducer can be in charge of the transmitter, the receiver, or both, in the system. As
a transmitter, once the transducer has been excited by electrical energy, piezoelectric
materials start to vibrate and generate mechanical energy in the form of ultrasonic
waves. These waves can transmit through a medium (prestressed concrete surface) and
will be converted to electric energy by the receiver.
Figure 6-13. Piezoelectric transducers used in the experimental test.
95
Coupling between the transducers and the surface is necessary; otherwise, the
acoustic impedance mismatch between air and solids will be large. Thus, nearly all the
energy would be reflected, and a small portion of it would be transmitted through the
test material (Claudio, 2010). Therefore, a thin layer of ultrasonic gel was used
between the transducers and the tested surface.
The captured data is studied in time domain for the linear acoustic parameters
(relative change in wave velocity and amplitude energy) and in frequency domain for
the nonlinear acoustic parameters (second harmonic amplitude) of the ultrasonic wave
using MATLAB software. The experimental results are discussed in Chapters 7 and 8.
6.6 MATERIAL PROPERTIES OF THE CONSTRUCTED BOX-GIRDER
MODEL
After leaving the model to gain sufficient strength, a number of tests were
performed on the model, such as compressive strength, density and modulus of
elasticity. Table 6.1 shows the material properties of each part of the model. Figure
6.14 shows the modulus of elasticity testing.
Table 6-1.
Material Properties of Each Section of the Box-Girder
Property Section
Top slab Web slab Bottom slab
Compressive strength
(MPa)
47.43 49.89 53.12
Modulus of elasticity
(GPa)
30.6 31.38 32.38
Density (kg/m3) 2319.58 2319.58 2319.58
96
Figure 6-14. Modulus of elasticity test.
6.7 PARAMETERS THAT CAN AFFECT ULTRASONIC TESTING
The procedure for conducting an ultrasonic test is influenced by a number of
factors that are related to the model characteristics, such as the surface type and the
geometry of the testing surface. To get the desired and accurate results from the
ultrasonic technology, it is very important to avoid rough surfaces, locations close to
the strain gauges or any electric devices, and surfaces with voids or micro cracks, as
shown in Figure 6.15.
Concrete sample
Extensometer
97
Figure 6-15. Surfaces that need to be avoided with ultrasonic technology.
Secure holding to the transducers while attaching to the model during testing can
be another parameter effected the testing results. Therefore, special holders were used
with the transducers to keep them secured and fixed during the experimental program.
Further, it is very important to avoid the places above the NA of the box-girder,
as it will be expected to have a higher amount of micro crack due to developing tensile
stress in these parts because of prestressing process. In addition, to maximise the
Voids
Rough surface
Strain gauge
98
convenience of measurement, it is recommending selecting a suitable position that
allows easy installation and removal of the transducer and the receiver.
6.8 EXPERIMENTAL STRATEGY
In order to identify the PF of the prestressed concrete box-girder model, various
parameters were considered, such as the relative change in the wave velocity, wave
amplitude energy and amplitude energy of the second harmonic frequencies. Figure
6.16 shows the strategy of experimental tests.
This research is being developed to identify the PF from the inverse calculation
of stress developed on the concrete surface due to apply the PF on the steel tendons.
The piezoelectric ultrasonic transducers are bonded to the concrete surface, and excited
with high-frequency (40-50 kHz) acoustic signal. The wavelength of this signal is
small enough to be sensitive to any developing stress on the concrete surface due to
applying the PF in the steel tendons.
As the linaer and nonlinaer acoustic constants (K) and Beat (β) are very
important parameters in PF identification, calibration tests have been conducted in
three different locations on the concrete surface to calculate these constants.
Zero-stress state has been considered as the base data, in order to compare with
other results due to changing the stress state (applying the PF levels). Three
prestressing levels were applied on the box-girder. Table 6.2 shows the prestress forces
applied to each tendon during the experimental program. During these levels of
prestressing, both linear and nonlinear acoustic parameters were recording and used in
the inverse calculation of the PF. More elaboration about the experimental strategy and
the process of prestressing identification in a box-girder prestressed concrete bridge is
developed and discussed in Chapters 7 and 8.
99
Table 6-2
Prestress Force Levels
PF level Tendon 1 (kN) Tendon 2 (kN) Total PF (kN)
PF0 0 0 0
PF1 85 86 171
PF2 142.402 141.607 284.009
PF3 186.16 192.133 378.29
In this research, different sets of experimental investigation are performed on the
6 meter long box-girder prestressed concrete beam. Finding summarized from the
experimental results are analytically confirmed by a series of numerical investigations
and comparing with the other researchers finding.
100
Figure 6-16. Strategy of experimental tests.
Develop measuring procedures to identify PF for new and
exciting bridges
Calculate PF from the nonlinear parameters
(Amplitude energy of the 2nd harmonic of FFT)
Calculate PF from the linear parameters
(Relative change in the wave velocity)
PF0 Measures the linear and nonlinear acoustic parameters of the
ultrasonic waves (data base)
PF1, PF2, PF3 Measures the linear and non-linear acoustic parameters
of the ultrasonic waves
101
6.9 SUMMARY
This chapter summarises the design and construction procedure of the lab model
adopted during the experimental program. Due to the limited availability of resources,
the length of the box-girder was limited to 6 m. The prestressing system of the lab
model was constructed as an internal unbonded tendon with parabolic tendon profile.
Then it was stressed to different PF levels that were measured through an attached load
cell.
Ultrasonic tests were performed on the prestressed box-girder concrete beam
using two piezoelectric transducers. The ultrasonic system was used to generate and
receive the ultrasonic wave. Different parameters related to the ultrasonic waves were
investigated, such as the relative change in the wave velocity, wave amplitude energy
and the amplitude of second harmonic of the FFT, to find out the most appropriate
parameter that can be employed to identify the PF.
103
Chapter 7: Monitoring Prestressed
Concrete Using Linear Acoustic
Parameters of the Ultrasonic
Wave
This chapter describes the mechanics for loading of the model, materials, test
prototyping and other test configurations used as part of the study. The influencing
factors such as the location of the receivers, and the ultrasonic bath (distance between
transducer and receiver), are investigated experimentally.
7.1 EXPERIMENTAL STUDY
The prestressing force (PF) level in prestressed concrete bridges is an important
parameter in their design, construction and service stages. However, as explained in
the previous chapters, it is hard to measure via traditional approaches.
Among the current methods of NDT, ultrasonic technology has received the
most research attention. Guided ultrasonic waves, which propagate parallel to the
surfaces of the materials with a sufficient depth, have shown great potential as an
effective measurement approach (Li, He, Teng, & Wang, 2016).
The propagation of ultrasonic waves in a solid medium is affected by the internal
stress of the medium. A linear relationship was found between the velocity of the
ultrasonic waves and the material’s stress, which is calling “acoustoelastic”. Some of
the research work carried out in this area, and the theory behind this phenomenon,
were presented in Chapters 2 and 3.
The experimental results of this project revealed that there is another linear
relationship between the amplitude energy of the ultrasonic wave and the stress of the
104
prestressed concrete model, which was developed due to the application of PF as will
show in section 7.7. The attenuation level in transmitted ultrasonic waves can be
measured based on the difference between the amplitudes of the voltages across the
transmitter and receiver.
Several experimental tests were carried out using two piezoelectric transducers
(transmitter and receiver) fixed in different locations on the surface of the beam.
Various levels of tensile force starting from about 0 kN, 85 kN, 140 kN and 190 kN
were applied on each tendon.
7.2 TEST PROTOTYPING
The acoustoelastic calibration test consists of applying a known tensile force to
a given reference testing tendon using a hydraulic jack device provided by the AUSPT
company (Australian Post-Tensioning), as explained in Chapter 6. The transfer of
tensile force to the tendon was assured through a mechanical device according to the
industrial anchorage system (anchorage plates + conic wedges) provided by AUSPT.
Figure 7.1 shows the experimental set-up for applying different levels of tensile force.
The tendons used in this research were composed of seven steel wires with high
mechanical strength (six helical wires twisted around a straight wire). The nominal
diameter of the strand is 15.2 mm, while the effective cross-section area of the tendon
is 1.420 × 10–4 m2.
105
Figure 7-1. Box-girder while applying the load on the tendon.
Figure 7.2 shows the ultrasonic system utilised in the experimental tests. The
measurement system included: two piezoelectric transducers (one as a transmitter and
one as a receiver) placed on holders and attached to the model, a signal generator and
an oscilloscope, which were all located inside a safety box for health and security
purposes. The operating frequency was tuned to the resonant frequency of the
transducers. A sinusoidal tone burst signal with a frequency between 40 and 50 kHz
was generated to excite the transmitter, while the value of the excitation was limited
to 60 Vpp due to Health and Safety limitation at QUT lab.
The receiver signals were digitised and captured by the (RIGOL DS 1204B
digital), commercially available oscilloscope. MATLAB software was used for
analysing the captured data.
Anchorage plates
Prestressing tendons
Load cell Hydraulic Jack
106
Figure 7-2. Ultrasonic test set-up.
The unbonded tendon was loaded to a certain level of the tensile force, about
85 kN, and stopped, then kept at that level for about seven days to measure the velocity
and the amplitude energy of the ultrasonic waves in different locations on the surfaces
of the box-girder.
The load was released, and the beam loaded again to a higher level, about 140
kN. The loading stopped, and the parameters were measured at this load level. The
process continued in this cycle until about 190 kN. The applied tensile forces were
limited to about 30%, 50% and 80% of the ultimate tensile strength (UTS is about
261 kN) of the tested tendons. With the previous process, we obtained the same stress
distribution as in site conditions.
The relative change of the wave velocity was determined from the travel time of
the waves between the transmitter and the receiver attached on the surface of the
concrete. The propagation length between the transmitter and the receiver was set to
30 cm and 50 cm respectively.
Signal Generator
PZT Transmitter
Digital Oscilloscope
PZT Receiver
Holder
107
These propagation distances have been chosen after running a number of
ultrasonic tests. At these two distances (30 cm and 50 cm respectively), the received
voltage achieved was better resolution and highest amplitude based on the pulse-echo
signal using the ultrasonic transmitter.
Eight transducers and receivers were fixed on the concrete surface of the box-
girder model during the experimental program in different locations. Two test set-ups
were used for measuring the relative changes in the wave velocity achieved for
different prestressed loads. Both of these set-ups were in the compression zone of the
box-girder. Therefore, the effect of the PF would appear very clear through consulting
the model and resultant in a more homogenous zone.
Through the first experimental test (which is used also as a calibration tests to
calculate the acoustoelastic constant K), the velocities of the ultrasonic waves were
determined on the side of the model at three different locations. These three locations
were chosen close to the tendons’ location under the natural axis (NA).
Whilst, for the second experimental test, transducers were placed under the
bottom slab of the box-girder, where the transmitter and the receiver aligned along the
centre line of the model. The purpose of adopting different experimental set-ups was
to find out the most efficient locations and distances used to identify the PF. The
findings of this experimental program were used to validate the developed method and
will enable to provide guidelines on identifying the PF of a prestressed concrete box-
girder using the linear acoustic parameter of the ultrasonic wave.
7.3 STRESS STATE ANALYSIS OF THE BOX-GIRDER
As the transducers and the receivers were attached on the concrete surfaces, the
relative change that developed in the wave velocity was caused by changes in the stress
states at the concrete surface due to the application of different PF on the tendons
(assuming the stress due to the dead weight is constant).
Figure 7.3 illustrates a typical section of prestressed box-girder used in the
experiment with an eccentricity (eB) from the NA.
For the section shown in Figure 7.3, under working load moment (Mw), the
following equations 7.1 and 7.2 (to calculate the stress) can be written by virtue of the
principle of superposition.
108
Figure 7-3. Stress distribution in prestressed box-girder beam under working load moment.
Adapted from the Australian Standard AS3600-2009.
For the top-fibre stresses
𝑓𝑐𝑇 =𝑃𝐹
𝐴+
𝑃𝐹(−𝑒𝑻)(𝑌𝑇)
𝐼+
𝑀𝑤(𝑌𝑇)
𝐼 7.1
For the bottom-fibre stresses
𝑓𝑐𝐵 =𝑃𝐹
𝐴+
𝑃𝐹(−𝑒𝑩)(−𝑌𝐵)
𝐼+
𝑀𝑤(−𝑌𝐵)
𝐼 7.2
Where:
𝑓𝑐𝐵 Compressive stress
𝑓𝑐𝑇 Tensile stress
PF Prestressed force applied
A Cross-section area
I Moment of inertia
109
𝑒𝑻 𝒐𝒓 𝑩 Eccentricity of the tendons
Y Distance between the receivers’ location and the NA
Therefore, all the stresses at the transducers’ location are calculated in this
chapter and next chapter according to equation 7.2 depending on the receivers’
locations and the eccentricity of the tendons. Tables 7.1 and 7.2 show the stresses
calculated at the web part and under the bottom slab of the box-girder, respectively.
Table 7-1.
Stress Values of the Receivers Located in Web Slab of the Model
Receiver ID
Stress at the receiver’s position (MPa)
PF0 PF1 PF2 PF3
RW1 -7.79E+04 8.89E+05 1.63E+06 2.20E+06
RW2 -3.57E+05 9.86E+05 1.71E+06 2.43E+06
RW3 -4.11E+05 1.02E+06 1.97E+06 2.80E+06
110
Table 7-2.
Stress Values of the Receivers Located Under the Bottom Slab of the Model
Receiver ID Stress at the receiver’s position (MPa)
PF0 PF1 PF2 PF3
RB1 -2.9E+05 1.2E+06 2.0E+06 2.6E+06
RB2 -6.4E+05 1.6E+06 2.6E+06 3.5E+06
RB3 -8.3E+05 1.8E+06 3.0E+06 4.0E+06
RB4 -8.6E+05 1.9E+06 3.0E+06 4.0E+06
RB5 -6.5E+05 1.6E+06 2.6E+06 3.5E+06
As can be read from the Tables 7.1 and 7.2, the stresses at these locations
changed from tension to compression after applying the PF, which is the main aspect
of using prestressed concrete.
7.4 CROSS-CORRELATION FOR TIME DELAY ESTIMATION
A precise method based on the cross-correlation method for time delay
estimation was implemented to calculate the relative change in wave velocity (Pei &
Demachi, 2010; Stähler, Sens-Schönfelder, & Niederleithinger, 2011).
Assuming two measurement performances are compared with the same
acquisition geometry from one sample in an undistributed state and a stress state, the
precision can be increased by calculating the cross-correlation coefficient (CCO)
according to equation 7.3 (Pei & Demachi, 2010)
111
𝑟(𝑖 ∗ 𝑑𝑡) =∑ [(𝑥(𝑘)−𝑚𝑥).(𝑦(𝑘−𝑖)−𝑚𝑦)]𝑁
𝑘=1
√∑ (𝑦(𝑘−𝑖)−𝑚𝑦)2𝑁𝑘=1 √∑ (𝑥(𝑘)−𝑚𝑥)2 𝑁
𝑘=1
7.3
Where:
dt Interval between the time resolution
r Correlation coefficient at delay i*dt
x and y Two series of wave signal
mx and my The means of the two series
Between the time window of length N centred around K of the original
seismogram x (k) with the same time window of y (k-i) from the disturbed state. The
time lag for which 𝑟(𝑖 ∗ 𝑑𝑡) reaches the maximum is then a robust estimator of the
time lag (∆𝑡) of the wave train.
Figure 7.4 shows an example the results of time lag estimation using a CCO for
signals received at one location. The time delay ∆t can be precisely determined when
the correlation coefficient reaches the maximum. MATLAB code for calculating the
time delay between the signals is presented in Appendix B.
Figure 7-4. Calculated Δt between two signals using cross-correlation method.
Δt
112
The relative change of the wave velocity was calculated using equation 7.4 (Pei
& Demachi, 2010):
∆𝐶
𝐶0=
𝐶1−𝐶0
𝐶0= −
𝐶0∆𝑡
𝑠+𝐶0∆𝑡 7.4
Where:
C0 Wave velocity without applied load
C1 Wave velocity with applied load
S Distance between the two transducers
∆𝑐 Velocity change due to applied load
To decrease the error in the calculation of wave velocity, the C0 was set as
3726.66 m/sec for the theoretical value of wave velocity without any stress. This value
was calculated using WAVESCOPE software as shown in Appendix C.
7.5 THE EFFECT OF THE RECEIVERS’ POSITION
Since the prestressed concrete in a structure is usually under stress, it is important
to investigate whether these stresses influence the measuring wave velocity or
amplitude energy. If they do, and this influence is significant, then it should be taken
into account when interpreting data on ultrasonic wave velocity in prestressed concrete
for PF estimation or another purpose.
Since we could not find detailed, quantitative information in the literature
concerning this phenomenon in prestressed concrete box-girder, laboratory
experiments were undertaken to determine the effect of various applied PF on the
ultrasonic wave velocity
In these tests, the wave velocities were detected by measuring a delay that was
obvious in the captured signals compared to the stress-free state (reference signal)
results using the cross-correlation method. The reference velocity C0 (same as V0) in
the un-stress state was 3726.66 m/s. This value corresponds to the phase velocity of
113
zero symmetric modes at frequency f=44 kHz as shown in Figure 7.5. WAVESCOPE
software was used for this purpose; this software can easily determine the wave
velocity after introducing the material properties of the model.
Figure 7-5. Ultrasonic wave phase velocity of the box-girder determined using
WAVESCOPE software.
7.5.1 Results of the receivers attached at the web slab
In this subsection, the effects of the transducers’ locations on the web of the
model will be studied. The distance between the transducer and the receiver was fixed
to be 30 cm. This distance has been tested during the simulation as explained in chapter
five and satisfy results have been obtained. Three different locations under the NA
(compressive stresses part) were marked on the left-hand side of the girder (close to
the tendon’s position inside the prestressed box-girder model) as shown in Figure 7.6.
Figure 7.7 demonstrates the set-up used for this experimental program.
X=44
Y=3726.66
114
Figure 7-6. Position of the transmitters and the receivers on the web of the model
(Not: the dimensions are not to scale).
Figure 7-7. Test set-up at the web part of the box-girder.
115
To remove any unwanted noise, all measured response signals were normalised
and filtered using MATLAB software. Examples of the normalised signals received
by receivers RW1 and RW2, with a close-up for the first part of the signal under
different levels of PF, are shown in Figures 7.8 and 7.9 respectively.
Figure.7-8. Signals received at Receiver 1 (RW1) due to applying different PF, with a close-
up of the first part of the signal.
∆𝑡
116
‘
Figure 7-9. Signals received at Receiver 2 (RW2) due to applying
different PF, with a close-up of the first part of the signal.
∆𝑡
117
The wave velocity is usually determined by measuring the time-of-flight (TOF)
of the wave. The precision of such measurement is determined by the accuracy of the
oscilloscope in recording the pick and arrival time of the signal. Since the signal has a
finite width, this is inherently imprecise and strongly affected by noise. Therefore, the
arrival time of the signal in this research has been calculated based on the Peak value
of the Pulse. The time delay between two signals due to applying the PF levels has
then been used to calculate the relative change in the wave velocity. In Figures 7.8 and
7.9, it is obvious that the time delay induced by the stress is visible and very small, so
it is hard to directly assess the relative change in wave velocity. Therefore, the relative
change in wave velocity due to the application of different PF was evaluated using the
cross-correlation method, as explained in section 7.4.
Figure 7.10 A and B show examples of the results of time lag estimation using
the CCO for two signals received at RW1 and RW2. The time delay ∆t can be precisely
determined when the CCO reaches the maximum, as explained previously.
(A)
Δt
Cross-Correlation between two signals
118
(B)
Figure 7-10. (A) and (B) Results of time lag estimation using a cross-correlation method.
After processing and analysing all the signals received by the receivers attached
at the web of the model, Table 7.3 presented an example of the results of the relative
changes in the wave velocity due to the application of PF at the tendons as calculated
using equation 7.4.
Figure 7.11 shows the relationship between the relative change in the wave
velocity and the stresses at the web of model. These data correspond to three
acoustoelastic calibration tests in three different locations, which were performed on
the web of the box-girder and covered the same stress distribution as in site conditions
starting from PF1: the low prestressed level, PF2: medium prestressed level and PF3:
high prestressed level.
Δt
Cross-Correlation between two signals
119
Table 7-3.
Relative Change in the Wave Velocity (Web Part of the Model) Due to PF
Receiver ID PF0 PF1 PF2 PF3
RW1 0 0.23 0.67 0.72
RW2 0 0.23 0.6 0.75
RW3 0 0.23 0.6 0.70
Figure 7-11. Relative changes in the wave velocity as a function of applied stress in the web
part of the model.
120
7.5.2 Data analysis and PF identification from the web data
It can be observed from Figure 7.11 that there was a minor increase in the relative
change of the wave velocity up to PF1 (0.23%), which caused a small increase in the
velocity of the ultrasonic wave. That can be attribute to the presence of the voids and
flexural micro cracks on the concrete surface due to the self-weight of the model, as
well as the micro cracks created where two surfaces meet, such as the joint between
the web and the bottom slab, as explained in Chapter 3. However, after applying the
PF1, the PF was not enough to close all the voids and micro cracks. Thus, the effect of
the prestressing was not yet clear.
After applying the PF2 level, it can be observed from the same figure that there
was roughly a high increase in the relative change in the wave velocity: up to 50%. At
this level of PF, the effect of the PF appeared very clear and closed most of the voids
and micro cracks by compressing the model. Conversely, after applying PF3 there was
a slight increase in the relative change of the wave velocity, which can be attributed to
the fact that the box-girder had already reached the desired compression state at this
prestressed level.
From Figure 7.11, the measured trend exhibits a nearly perfect linear relationship
between the stresses developed in the concrete surface due to the application of PF (at
the web) and the relative change in the wave velocity and monotonic suggesting that
linear curves can be fitted using the least square regression to calculate the
acoustoelastic constant K.
This finding is consistent with others scholars’ research results such as Washer
(2001) , and acoustoelastic theory, which demonstrated that the proposed method is
suitable for the PF evaluation of the prestressed concrete members. The increase in
wave velocity was due to the increase in compressive stress and hence modulus of
elasticity and the density of the concrete surface of the box-girder, resulting from PF
applied to the tendons.
In order to calculate the stresses from the acoustoelastic equation 7.5, the
acoustoelastic constant (K) needed to be determined from the slopes of Figure 7.11.
After governing the data of the previous experimental setup, it was found that K is
equal to 2.6 × 10-7 (the average value for three calibration tests in three different
locations). This value has been used in all calculations presented in this chapter.
121
𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑡ℎ𝑒 𝑤𝑎𝑣𝑒 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 = 𝐾 ∗ 𝜎 7.5
Where:
K Acoustoelastic constant
𝜎 Stresses at the locations of the receivers in MPa
The stresses value calculated using equation 7.5 were employed for the inverse
calculation of the PF using equation 7.2, as described previously in section 7.3. Figure
7.12 shows the values of the real PF applied during the experiment and the PF
calculated from the ultrasonic data. Table 7.4 tabulates the values of the PF calculated
from the ultrasonic data with the values of error for each location.
Figure 7-12. PF calculated from the ultrasonic wave data (web part results).
0.00E+00
5.00E+04
1.00E+05
1.50E+05
2.00E+05
2.50E+05
3.00E+05
3.50E+05
4.00E+05
4.50E+05
PF1 PF2 PF3
PF
kN
PF Calculated at the Web From the Ultrasonic Wave Data
R1 R2 R3 PF applyRWRW1 RW2 RW3 PF APPLY
122
Table 7-4.
PF Calculated from the Ultrasonic Data at the Receivers Attached at the Web Slab of the
Girder with the Error Percentage
PF PF Apply (kN) PF calculated
at RW1 (kN)
PF calculated
at RW2 (kN)
PF calculated
at RW3 (kN)
PF1 1.71E+05 1.19E+05 1.44E+05 1.21E+05
PF1 % error 30.64% 15.68% 29.29%
PF2 2.84E+05 3.09E+05 2.64E+05 2.57E+05
PF2 % error -8.63% 7.16% 9.50%
PF3 3.78E+05 3.51E+05 4.04E+05 3.19E+05
PF3 % error 7.01% -6.97% 15%
After calculating the error value for each PF level, as shown in Table 7.4., it can
be observed that PF2 and PF3 were successfully identified in RW2 with a reasonable
percentage of error: less than 10%. This can be attributed to its location on the web
slab close to the tendon with reasonable distance from the natural axis. Meanwhile,
RW1 gave the second percentage of error. Conversely, the error in RW3 was roughly
high compared with the other’s data, which can be attributed to the location of RW3
near the joint between the web and the bottom slab. As mentioned previously, this
position usually has a high percentage of micro cracks; however, some of these micro
cracks remained open even after applying the PF, which directly affected the results,
as explained previously in section 3.3.1.
It was observed that the PF2 and PF3 identifications were better than PF1, which
can be attributed to the fact that changing the wave velocity highly depends on the
change of the material properties such as density and modulus of elasticity. At this
123
prestress level, the change was not high enough to be detected; therefore, no significant
results were observed. Further, the quality of the piezoelectric transducers as well as
the ultrasonic system used to generate and receive the signal can be another reason for
not detecting such a small change, as the ultrasonic system and the transducers used
during the experimental program were for general and commercial purposes.
7.5.3 Results from receivers attached under the bottom slab of the girder
The test was performing on the bottom slab under the box-girder. Five
transmitters and receivers were distributed along the centre line of the box-girder, as
shown in Figure 7.13. Table 7.5 shows the locations of the receivers under the model.
A picture of a developed experimental prototype is shown in Figure 7.14.
A thin layer of the coupling gel is needed and care should be taken to ensure no
air bubbles contaminate the coupling area. Two holders were used to keep the
transducer and the receiver fixed while the experiment was being set up. Further, it is
very important that the transducers be aligned accurately with each other to avoid any
undesired results
124
Figure 7-13. Positions of the transmitters (TB) and the receivers(RB) under the bottom slab
of the girder. (Note: the sketch is not to scale.)
RB1 TB1
TB2
TB3
TB4
TB5 RB5
RB2
RB3
RB4
Centre Line of the
Box-girder
125
Table 7-5.
Positions of the Receivers under the Model
Receiver ID Distance from the edge of the
box-girder (cm)
RB1 60
RB2 150
RB3 285
RB4 342
RB5 450
Figure 7-14. Experimental prototype with transducers placed under the bottom slab of the
box-girder.
126
The same ultrasonic system that was used to generate and receive the sinusoidal
signal in the web part was used in this experimental prototype. The same procedure
for applying the PF was repeated for this experiment. The relative change in the wave
velocity was calculated using the cross-correlation method, as described in section 7.4.
Figure 7.15 A, and B. show the relative change in the wave velocity as a function
of stresses developed in the receiver’s location under the bottom slab of the box-girder.
(A)
y = 2E-07x + 0.1101
R² = 0.9513
y = 3E-07x + 0.2302
R² = 0.9178
y = 3E-07x + 0.2824
R² = 0.8496
0
0.2
0.4
0.6
0.8
1
1.2
1.4
-1.0E+06 0.0E+00 1.0E+06 2.0E+06 3.0E+06 4.0E+06
Rel
ati
ve
chan
ge
in t
he
wave
vel
oci
ty %
Stress MPa
Relative changes in the wave velocity vs. stresses at
receivers under the bottom slab
R1 R2 R5RB1 RB2 RB5
127
(B)
Figure 7-15. Relative change in the wave velocity as a function of applied stress of the
receivers attached under the bottom slab of the model.
7.5.4 Data analysis and PF identification using data from the bottom slab
The experimental results conducted from the receivers attached at the bottom
slab of the box-girder indicated two acoustoelastic behaviours, as shown in Figure 7.15
A and B. The first expression observed for RB1 and RB2 and RB5 in Figure 7.15 (A)
was an increase in the relative change in the wave velocity with an increase in the
compressive stress due to the application of PF. This behaviour was similar to the
response of the ultrasonic transducers at the web part of the model.
The second behaviour indicated for RB3 and RB4 is shown in Figure 7.15 (B).
The behaviour started after applying PF2, where the relative change in the wave
velocity reduced significantly and continued reducing even after applying PF3. This
-2
-1
0
1
2
3
4
5
6
7
-2.0E+06 -1.0E+06 0.0E+00 1.0E+06 2.0E+06 3.0E+06 4.0E+06 5.0E+06
Rel
ati
ve
cha
ng
e in
th
e w
av
e v
elo
city
%
Stress MPa
Relative changes in the wave velocity vs. stresses
at receivers under the bottom slab
RB3 RB4
128
can be attributed to the off-centre location of the prestressing steel, which caused a
cambered shape to the box-girder before applying the live load. The cumulative results
at this part are directly related to the wave velocity at zero stress. However, at this
stress level (zero) the deflection was about 5 mm downward calculated according to
equation 7.6 (Hibbeler, 1995), which is prevented the transducers and the receivers
from aligning correctly. Hence, the receivers did not catch the signal appropriately at
the middle part of the box-girder. After applying the PF, the same position was under
camber, which was due to subscripting the displacement upwards from the
displacement downwards calculated according to equation 7.7 (Hibbeler, 1995), as
shown in Figure 7.16.
𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛 (𝑑𝑜𝑤𝑛 𝑤𝑖𝑟𝑑 ) =𝑊𝐿4
384𝐸𝐼 7.6
𝑑𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑜𝑛 (𝑢𝑝𝑤𝑎𝑟𝑑 ) =𝑀𝐿2
8𝐸𝐼 7.7
Where:
W Dead load
L Length of the box-girder
E Modulus of Elasticity
I Moment of inertia
M Moment due to PF
Therefore, the receivers RB3 and RB4 were attached in unstable places and
could not receive the signal appropriately. Therefore, the signals detected at these two
positions have been excluded from the final calculation. This drawback might be
overcome in real prestressed concrete bridges due to applying service and a live load.
129
Figure 7-16. Camber created under the box-girder due to applying PF.
The same producers were used to identify the PF at RB1, RB2 and RB5. Figure
7.17 shows the final identification of the PF from the ultrasonic data. Table 7.6
tabulates the values of the PF calculated from the ultrasonic data with the value of the
error.
Figure 7-17. Calculated PF from the ultrasonic wave data under the bottom slab of the
girder
0.00E+00
5.00E+04
1.00E+05
1.50E+05
2.00E+05
2.50E+05
3.00E+05
3.50E+05
4.00E+05
PF1 PF2 PF3
PF
kN
PF Calculated under the Bottom Slab of the Girder From
the Ultrasonic Wave Data
RB1 RB2 RB5 PF APPLY
RB4 RB3
TB4
TB3
130
Table 7-6.
PF Calculated from the Ultrasonic Data at the Receivers Attached Under the Bottom Slab of
the Girder with the Error Percentage
PF PF Apply (kN) PF calculated
at RB1 (kN)
PF calculated at
RB2 (kN)
PF calculated
at RB5 (kN)
PF1 1.71E+05 2.00E+05 1.90E+05 2.10E+05
PF1 % error -17% -11.26% -23%
PF2 2.84E+05 2.92E+05 2.70E+05 2.60E+05
PF2 % error -2.82% 4.93% 8.45%
PF3 3.78E+05 3.94E+05 4.00E+05 3.96E+05
PF3% error -4.23% -5.82% -4.76%
According to the experimental results of this section, it was found that there was
a direct relation between the receivers’ positions and stress monitoring of the
prestressed concrete box-girder. However, the ultrasonic technology failed to identify
PF1 in all the receivers attached under the bottom slab. The PF was successfully
identified in RB1, RB2 and RB5 for PF2 and PF3 with an acceptable percentage of
error: less than 10% similar to the results detected at the receivers attached at the web
slab of the box-girder.
7.6 EFFECT OF DISTANCE BETWEEN TRANSDUCER AND RECEIVER
In order to provide completed guideline about using the ultrasonic technology in
identifying PF, another parameter was tested: the distance between the transducer and
the receiver. The same box-girder prestressed concrete lab model was employed in this
section to investigate the effect of the change in the distance between the transducer
and the receiver on the accuracy of the proposed method. The scenarios of the
experimental tests were the same as previous tests except for the distance between the
transducer and the receiver, which was changed to 50 cm.
131
Figure 7.18 A and B show the relationship between the relative change in the
wave velocity and the stresses due to the application of PF, for the web part and under
the bottom slab of the box-girder respectively.
(A)
Relative changes in the wave velocity vs. stresses
(Web slab)
Rel
ati
ve
chan
ge
in t
he
wav
e v
elo
city
%
Stress MPa
132
(B)
Figure 7-18. Relative change in the wave velocity as a function of applied stress when the
distance between the transmitter and the receiver is equal to 50 cm, (A) web slab (B) under
the bottom slab of the box-girder.
From Figure 7.18, it can be observed that the relationship between the relative
changes in the wave velocity increased with an increase in the PF level for most of the
receivers attached at the web slab and under the bottom slab of the box-girder. The
same relationship has been observed when the ultrasonic path length reduces to 30 cm.
However, the rest of the receivers did not show a noticeable trend other than minor
random changes. Although the trend lines look similar for both tested results (30 cm
and 50 cm), the first one shows more promising results, as can be observed from the
regression analysis values shown in Figure 7.18.
According to the preliminary results achieved for both cases (with distances of
30 cm and 50 cm between transmitter and receiver), it can be concluded that it is
recommended to keep the distance between transmitter and receiver less than or equal
Relative changes in the wave velocity vs. stresses
(Bottom slab)
R
ela
tiv
e ch
an
ge
in t
he
wav
e v
elo
city
%
Stress MPa
133
to 30 cm to avoid any inconsistencies between the results. However, the quality of the
testing results can be improved by applying high power/voltage signal to excite the
piezoelectric ultrasonic transmitter, then a strong ultrasonic wave can be generated and
propagated smoothly on the concrete surface.
Further, from the testing results, it has been demonstrated that TOF between the
transmitter and the receiver is depending on the distance between the transducers,
therefore; the length of the model will not affect the final results. Hence, this method
can be adopted for practical and field application.
7.7 WAVE AMPLITUDE ENERGY
During the experimental program and depending on the previous sections, it was
observed that the amplitude of the ultrasonic signal was also affected when the PF
changed. To quantify such a variation, the signals detected at the web part of the model
have been used for this analysis. Figure 7.19 shows an example of the signal detected
at the web of the model, which was used for analysis.
The total energy of each waveform calculated as the area under the rectified
signal envelope, as shown in Figure 7.20, followed the method developed by Aggelis
and Shiotani (2008). The authors used this method to find the effect of the
inhomogeneity parameters on ultrasonic wave propagation in cementitious material.
This area under the envelope was then divided by the energy achieved as a response
of the face-to-face transducers demonstrated in Figure 7.21 to present the percentage
of the energy transmitted through the model. Figure 7.22 shows the waveform energy
as a function of stresses with different PF levels.
134
Figure 7-19. An example of signal received during application of different PF.
Figure 7-20. Received signal and the created envelope to calculate the area under the
signal.
135
Figure.7-21. Measurement of the transmitted energy (face-to-face contact).
136
Figure 7-22. Waveform energy vs. stresses developed due to applying PF.
In Figure 7.22, it is obvious that the waveform energy of the ultrasonic signal
increases with increases the PF level. This can be attributed to the fact that after
applying the PF, most of the micro cracks and inhomogeneity in the box-girder created
due to the dead load have been closed and resultants more homogenous section.
Therefore, the ultrasonic signal is propagating quite easier through the micro cracks
after applying the higher PF levels.
The conclusion of this section can be drawn, which is that any reduction in the
waveform energy of the ultrasonic received signal can give an indication about the
reduction in the PF level inside the prestressed concrete structure. However, this
phenomenon still needs to be addressed further as the literature about this topic is still
limited for cementitious materials. More research needs to be conducted for
prestressed concrete to develop final theory for this parameter.
0.5
0.7
0.9
1.1
1.3
1.5
1.7
1.9
0.000000 1.000000 2.000000 3.000000 4.000000 5.000000
Am
pli
tud
e E
ner
gy
%
Stress GPa
Wave form energy as a function of stresses with
diffent PF levels
R1 R2 R3
PF1
PF
RW1 RW2 RW3
137
7.8 RECOMMENDATIONS FOR IDENTIFYING THE PF USING LINEAR
ACOUSTIC PARAMETER FOR PRACTICAL APPLICATION
Depending on the previous results of sections 7.5.1 and 7.5.3, some
recommendations need to be considered while running the ultrasonic testing, to get the
desired results.
The acoustoelastic constant is an important parameter in the calculation process of the
PF; therefore, it is important to run the calibration test in three different locations on
the bridge’s surface to calculate this constant before starting the general testing.
The testing results and error analysis show the ability to identify the PF from the
transducers attached to the web and the bottom slab of the girder. However, there are
still some places that need to be avoided during the test, such as the middle span of the
box-girder.
Aligning the transducers and the receivers, choosing a prop contacting gel between the
transducers and the concrete surface and using a prop holder to keep the transducers
fixed and secure during the experiment are other important parameters that can affect
the results.
The distance between the transmitter and the receivers should be kept constant: equal
to or less than 30 cm. However, the distance between the transmitter and the receiver
can be increased by increasing the quality of the excitation signal as explained before
in section 7.6.
The wave velocity at Free State stress is the basis of the relative change of the wave
velocity. Therefore, this method can only be used for new bridges, and this technology
can be used to monitor the PF during the construction life service.
7.9 APPROACH TO IDENTIFY THE PF FROM THE LINEAR ACOUSTIC
PARAMETER OF THE ULTRASONIC WAVE
Prestressed force identification has been developed and successfully tested
through the FE analysis and laboratory testing. Application of this procedure has few
steps as described below.
1. Choose suitable piezoelectric ultrasonic transducers sensitive to the
change of the stress and are used with the concrete and steel surfaces.
138
2. Choose a proper ultrasonic system that is used to generate and receive
the ultrasonic signal.
3. Choose a proper ultrasonic signal such as sinusoidal signal or Hanning
window signal.
4. Design holders to keep the ultrasonic transducers fixed during the testing.
5. Depending on the experimental results, both the web and the bottom slab
can be used for the testing; however, some places need to be avoided as
mentioned before.
6. Align the transducer and the receiver correctly, as any small mistake is
causing large differences in the calculation data.
7. After finalising the numerical and the experimental results, it has been
found that 30 cm between the transducer and the receiver is the best
distance that can be used during the ultrasonic testing.
8. As this technology can be used for monitoring the new prestressed
concrete bridge, it is very important to calculate the wave velocity at
zero-state stress to be used as a data base during the service life of the
structure.
9. Before running the test, the acoustoelastic constant needs to be calculated
from at least three calibration tests in three different locations on the
concrete surface.
10. After preparing the data base depending on the previous steps, using the
relative change in the wave velocity data and the acoustoelastic constant
to calculate the stresses developed on the concrete surface. The stresses
data then will be used in the inverse calculation of the PF.
11. For practical application, any reduction in the relative change of the wave
velocity or wave amplitude energy can be an indication of the PF losses
in the bridge.
139
7.10 CONCLUSION
After reviewing the experimental results, the PF2 (1.58 MPa) and PF3 (2.1 MPa)
levels have been identified with very good accuracy (less than 10%) in most of the
receivers such as RW1, RW2, RB1, RB2 and RB5. This range of PF is the usual range
of prestressing for real structure that is 1 MPa to 3 MPa according to Khan and
Williams (1995). Therefore, the finding of this research demonstrates the effectiveness
of the proposed method to identify the PF of the PSCBs and to be successfully used in
the field applications.
However, scattering in the experimental results were observed in RW3, RB3,
RB4 due to their locations at the joints between the bottom and the web slabs, and at
the middle part of the bottom slab, therefore it is very important to avoid these two
places.
Scattering in the experimental results was also observed in the PF1 (about 0.95
MPa). This can be attributed to the fact that changing the wave velocity is directly
related to changing the material properties, such as the modulus of elasticity and
density. To enhance the received signal and enabled the PF identifying at any level,
high-quality ultrasonic transducers and analysis system need to be employed to avoid
scattering in the results. However, PF1 is not in the range of prestressing level for the
real structure as mentioned before. Thus, this technology is still very effective in
identifying the PF in the real PSCBs.
Further, it has been observed that there is a clear impact of the PF level on the
waveform energy of the ultrasonic wave during the experimental program. Results
showed that the amplitude of the ultrasonic received signal is increasing with
increasing the PF. Therefore, this parameter can also be used to monitor the PF level
during the life service of the bridge
140
Chapter 8: Effect of PF on the Nonlinear
Acoustic Parameter (𝜷) of the
Ultrasonic Wave
An introduction to the nonlinear acoustic parameters of ultrasonic waves and its
application in PF identification was presented in Chapters 2 and 3. In Chapter 3,
section 3.3, the attention focused on presenting the main characteristics of principal
causes of the onset of nonlinearity. This chapter will describe the experimental set-up
and results achieved from the tests performed using the prestressed concrete box-girder
laboratory model.
8.1 EXPERIMENTAL SET-UP
The piezoelectric transmitters and receivers were bonded to the bottom slab of
the box-girder using an ultrasonic gel between the transducers’ faces and the concrete
surface as explained before in section 7.5.3. The transducers were attached at five
different locations under the bottom slab of the model as shown previously in table 7.5
and figure 7.13. The tendons were post-tensioned at three force levels, PF1, PF2 and
PF3, as explained in the previous chapters. The ultrasonic data was recorded in an
unstressed state for the purpose of comparison.
Generation of the second harmonic of the nonlinearity acoustic parameter was
measured using a general process to generate the ultrasonic wave: an ultrasonic tone
burst at frequency ω is generated in the prestressed concrete surface, it propagates
some distance through the model, and the response is measured at some distance
(30 cm) from the transmitter. Figure 8.1 is a schematic of the experimental set-up.
Measurement of β was conducted with contact piezoelectric transducers. These
transducers can offer a robust solution since they can be used in the linear ultrasonic
measurement, and can be purchased at relatively low cost.
141
Figure 8-1. Schematic of the experimental set-up.
Oscilloscope Signal Generator
Under bottom slab of the box-girder
PZT transmitter PZT receiver
142
Once the experimental set-up was configured, the test started. A high-voltage
tone burst sinusoidal signal at a frequency of 45 kHz was generated by a high-powered
Agilent signal generator. The signal fed into narrow-band piezoelectric ultrasonic
transducers. At this driving frequency, the ultrasonic phase velocity was 3788.4 m/s,
calculated using WAVESCOPE software as shown in Figure 8.2.
Figure 8-2. Lamb wave phase velocity dispersion curves for prestressed concrete
3788.4 m/s
143
Figure 8-3. FFT calculation process.
8.2 EXPERIMENTAL RESULTS
In Figure 8.3, it can be observed the magnitude of the second harmonic seems to
be very small. Therefore; to ensure a robust extract of the second harmonic value
special signal processing techniques were implemented during the experiment
program such as:
1st Harmonic
2nd Harmonic
144
1. Use a high-performance 4-channel RIGOL DS 1204B, digital oscilloscope
with sample rate, up to 200 MHz bandwidth and 1μs sample time to capture
and save the captured data.
2. Import the data to MATLAB software for analysing in a time domain.
3. Analyse the captured data using MATLAB software in a frequency domain.
4. Extract the relative amplitudes of the first and second harmonic waves as a
function of frequency, Figure 8.3 shows the model developed using
MATLAB software, which was used to calculate FFT of the captured signal.
5. Compare the results while applying different PF levels and find the effect of
the PF on the amplitudes of the second harmonic of the FFT signal.
After processing all the signals, Figures 8.4 to 8.8 show the FFT of the signals
measured by the piezoelectric transducers and the nonlinear parameter β from the
second harmonic as a function of PF applied to the box-girder.
145
Figure 8-4. FFT spectra of signals detected by the ultrasonic transducers at receiver RB1.
146
Figure 8-5. FFT spectra of signals detected by the ultrasonic transducers at receiver RB2.
147
Figure 8-6. FFT spectra of signals detected by the ultrasonic transducers at receiver RB3.
148
Figure 8-7. FFT spectra of signals detected by the ultrasonic transducers at receiver RB4.
149
Figure 8-8. FFT spectra of signals detected by the ultrasonic transducers at receiver RB5.
After collecting and analysing the results obtained from the experimental
program, it can be observed that increasing the PF clearly appears to reduce the
amplitude of the harmonics. Hence, the nonlinear parameter β decreases with an
increase in the PF applied to the tendons. This characteristic can be attributed to the
increase in the contact interface and friction phenomena on the concrete surface of the
model due to applying the PF, as explained in Chapter 3.
150
8.3 CALCULATING THE PF USING BETA DATA
The stresses at the receiver’s location were calculated according to equation 7.2
in Chapter 7. While β calculated according to equation 3.3.13 in section 3.3.2. Figure
8.9 shows the nonlinear acoustic parameter of the second harmonic vs. developed
stresses at the receivers’ locations on the concrete surface due to applying PF to the
tendons.
Figure 8-9. Nonlinear parameter for second harmonic vs. developed stresses at the
receivers’ locations due to applying PF to the tendons.
y = -4E-09x + 0.0312
R² = 0.9237
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
-1000000 0 1000000 2000000 3000000 4000000
β
Stress MPa
Nonlinear acoustic paramter of the second harmoinc
vs. stresses
RB1 RB2 RB3 RB4 RB5
PF0
PF1
PF2PF3
151
After finding the best fitting curve between the received data, it can be observed
that the trend of β vs. stress is reasonably linear; similar results were obtained by
Bartoli, Nucera, Srivastava, Salamone, Phillips, Scalea, et al. (2009) as shown in
Figure 8.10 for free strand and in Figure 8.11 for embedded strand. Clearly, the slope
of β vs. load is different because of different wave propagation behaviour in the two
cases. However, the general result is consistent. Further, despite of applying three PF
levels during the experimental program (namely 30%, 50%, and 80% of UTS) the
trend line obtained from the data in Figure 8.9 was quite similar to the trend line in
Figure 8.10 in which Bartoli et al.’s (2009) used five stress levels (20%, 40%,60%,
80% and 100% of UTS). With the previous process, we covered all the stress
distribution as in site conditions
Figure.8-10. Nonlinear parameter for second harmonic as a function of
load applied to the free strand (Bartolie et al. 2009)
β vs. load
152
Figure 8-11. shows the non-linear parameter from 2nd harmonic as a function of load
applied to the embedded strand (Bartolie et al. 2009)
Overall results indicate the suitability for this parameter to provide a direct
indication of the stress and hence the PF in the strand once the slope of the β vs. stress
is known. Further, the lab testing results robust the ability to use the nonlinear acoustic
parameters for box-girder prestressed concrete with different types of tendons such as
free, embedded bonded and unbonded tendons. Therefore, this technology can be
extended to another type of box-girder bridges with different cross sections such as
multi-cell box girders, slab on I-girder and slab on I-beam and different tendon types.
However, the field application of this technique requires knowledge of the calibration
factor (β vs. stress) which will depend on the type of tendon and the shape of the box-
girder. Therefore, it is recommended to run a calibration test at least in three different
locations before starting the real testing
Figure 8.12 shows the calculation of the PF from the β data in each receiver.
Table 8.1 shows the PF calculated in each receiver with the error percentage.
β vs. load *10-3
153
Figure 8-12. Calculating the PF from β data.
0.00E+00
5.00E+04
1.00E+05
1.50E+05
2.00E+05
2.50E+05
3.00E+05
3.50E+05
4.00E+05
4.50E+05
PF1PF2
PF3
PF
kN
Calculation the PF from β data
PSF R1 R2 R3 R4 R5PF APPLY RB1 RB5 RB4 RB3 RB2
154
Table 8-1
PF Calculated from Nonlinear Acoustic Data with the Error Percentage
PF PF Apply
(kN)
PF
calculated
at RB1
(kN)
PF
calculated
at RB2
(kN)
PF
calculated
at RB3
(kN)
PF
calculated
at RB4
(kN)
PF
calculated
at RB5
(kN)
PF1 1.71E+05 1.84E+05 1.68E+05 7.87E+04 4.07E+04 1.46E+05
PF1 %
error -7.73% 1.71% 53.98% 76.18% 14.54%
PF2 2.84E+05 3.0E+05 2.76E+05 1.73E+05 1.23E+05 2.54E+05
PF2 %
error -5% 2.78% 39.25% 56.61% 10.50%
PF3 3.78E+05 4.09E+05 3.79E+05 2.26E+05 2.69E+05 3.62E+05
PF3 %
error -8.20% 0.35% 40.26% 28.85% 4.28%
8.4 RESULTS ANALYSIS
Experimental results in the previous sections indicate that the nonlinear
parameter (β) is a suitable feature for identifying the PF in the prestressed concrete
box-girder bridge. As shown in Figure 8.12 and Table 8.1, this parameter identifies the
PF with an acceptable ratio of error, even with low PF, for example, PF1. This can be
attributed to the sensitivity of this parameter to the physical change in the model
surface, such as the contact interface, and the friction features of the girder caused after
applying PF to the tendons.
The parameter identifies the PF successfully in three locations (RB1, RB2 and
RB5) with a reasonable percentage of error between them, as shown in Table 8.1.
However, the receivers attached at the middle of the girder (RB3 and RB4) showed
155
low values of PF and high values of error. This can be attributed to their locations at
the middle of the girder where the camber accurate because of the dead load and the
PF applied, as explained in the previous chapter. Further deflection downwards (due
to the dead load) and deflection upwards (due to the application of PF) in this circle
might create micro cracks at the middle part of the box-girder, which would not close
even when applying the PF.
8.5 RECOMMENDATIONS FOR IDENTIFYING THE PF USING
NONLINEAR ACOUSTIC PARAMETER FOR PRACTICAL
APPLICATION
After analysing the experimental data, it was found that the nonlinear parameter
can be used directly to identify the PF since access is provided to the strand’s anchored
end, as proved by Bartoli et al. (2009) experimental results, or from two points located
under the surface of the bottom slab of the prestressed concrete box-girder, as
presented previously. Therefore, this method can be applied in PSCBs with embedded
and accessible tendons. This method is also suitable to be used with different types of
tendons, such as free, embedded bonded and embedded unbonded tendons according
to the results of this research and experiments conducted by Bartoli et al. (2009).
However, some recommendations need to be considered while running the
nonlinear acoustic ultrasonic testing for practical application and laboratory testing, to
get the desired results.
1. The test results show the ability to identify the PF from the transducers attached
at the bottom slab of the girder. However, some places still need to be avoided
during the test, such as the middle span of the box-girder.
2. This method is not required a baseline data, as the wave amplitude energy of
the second harmonic at free state stress is not required in this type of testing.
Therefore, this method can be used for new bridges, as well as being used to
monitor the PF during the construction life service.
3. The test results can be used to monitor a PSCB with same material properties
and same box-girder shape. Hence, calculate the PF from the slope line
between the stress and the β data.
156
4. This is new testing technology; therefore, calibration testing is still very
important and needs to be conducted in at least three points on the bridge
surface.
8.6 APPROACH TO IDENTIFY PF FROM THE NONLINEAR ACOUSTIC
PARAMETER FOR PRACTICAL APPLICATIONS
General procedures to identify the PF for practical applications have been
developed as a part of this research. The procedure is described below:
1. Choose suitable piezoelectric ultrasonic transducers and ultrasonic system
that can be used with the concrete and steel surfaces.
2. Design holders to keep the ultrasonic transducers fixed during the testing.
3. Attach the transmitter and the receiver under the bottom slab of the box-
girder using suitable ultrasonic gel. However, some places need to be
avoided such as middle part of the box-girder as mentioned before.
4. Align the transducer and the receiver correctly, as any small mistake can
cause large differences in the calculated data.
5. Select a proper ultrasonic signal such as sinusoidal signal to excite the
piezoelectric ultrasonic transmitter.
6. Connect the piezoelectric receiver with the oscilloscope to receive and save
the ultrasonic signal in time domain. MATLAB software then can be used
to analysis the data in FFT.
7. Run the calibration test in at least three different locations on the bridge’s
surface for specific PF level to calculate β before starting the actual testing.
8. Establish the relationship between β and the stresses on the concrete surface.
Hence, PF can be calculated from slope line between the stress and the β
data.
9. After preparing the data base depending on the previous steps, any increase
in the amplitude of the second harmonic of the FFT and hence increase in
the value of β can be an indication of the PF losses in the bridge. Therefore,
this technology is applicable for SHM of the bridge during the life service.
157
10. The datasheet prepared between β and the stress can be used with any similar
box-girder having the same material properties and cross sections. Hence,
this data can be used for exciting box-girder bridges.
8.7 CONCLUSION
The experimental results have shown that the nonlinear ultrasonic parameter, β,
is a suitable factor for monitoring prestress levels in posttensioned concrete beams and
is sensitive to the stresses changes in the box-girder due to the application of PF. Such
a parameter has an ability to be used in the field, where the measurement of β would
require a number of ultrasonic transducers placed under the bottom slab of the bridge.
In this research, the ultrasonic transmitters and receivers were attached to the
prestressed concrete surface, assuming an increasing axial force in the tendons
generated a proportional increase in the contact pressure in the prestressed concrete
surface. Experimental studies illustrated that the nonlinearity decreased with
increasing PF, which was similar to the results presented in Bartoli et al. (2009) and
Salamone, Bartoli, Phillips, Nucera, and Scalea (2011). However, the methods adopted
by the Bartoli et al. (2009) and Salamone et al. (2011) were used directly on the PF
tendons, while in a real structure the tendons are not manageable in most cases.
Therefore, this experimental program aimed to fill this gap in the knowledge and
calculate the PF from the inverse calculation of the stresses developed on the concrete
surface due to applying PF.
The percentage errors obtained for the linear and nonlinear ultrasonic testing
were quite similar in both methods. However, the acoustic nonlinear test showed a
high ability to identify the PF levels in all ranging with very good accuracy with an
identification error of as low as 10.5% even at very low prestressed levels, such as PF1
(under 1 MPa). However, there are some locations still need to be avoided as explained
before.
Therefore, using the nonlinear acoustic parameter is further improving the
proposed method and prove the effectiveness of the ultrasonic test with real
measurement since the transducers and analysis system can offer a robust solution as
they can be used in the linear ultrasonic measurement as well.
158
159
Chapter 9: Conclusions and Future Work
9.1 REQUIREMENTS OF THE STUDY
Prestressed concrete box-girder bridges are gaining popularity in bridge
engineering systems because of their better stability, serviceability, economy, aesthetic
appearance and structural efficiency compared to other types of bridges. The main
factor that ensures the better performance of this structure is the PF level in the
tendons. It is imperative, therefore, to appropriately manage and estimate the actual
level of PF when the PSCBs are in service.
The effect of the PF on the ultrasonic wave has been subjected to extensive study
for many years. Different parameters of the wave have been tested to identify the PF
using ultrasonic technology. However, the comprehensive literature review of
literature in this area that was carried out during this research revealed that those
studies were mainly focused on beams with accessible tendons. Further, none of these
ultrasonic methods have been tested for box-girder bridges.
Therefore, this research aims to fill this gap in knowledge by developing a novel
method to identify the PF in new and existing prestressed concrete box-girder bridges
with embedded tendons using ultrasonic technology.
9.2 STUDY APPROACH
In order to achieve the main objective of this research, this study addressed the
following topics:
1. A number of previous studies and tests have been done on the effect of PF on
ultrasonic wave characteristics and have been reviewed during this research to
identify their strengths, weaknesses and limitations.
2. The current ultrasonic testing has focused on prestressed beams with accessible
tendons. Hence, this research focused on extending this technology for
prestressed concrete box-girder bridges with embedded tendons.
160
3. Having identified the strengths of the ultrasonic testing method in PF
identification, the effect of the PF on ultrasonic wave characteristics have been
studied using the FEM.
4. A new approach to identify the PF of prestressed concrete box-girders using the
linear and nonlinear acoustic parameters of the ultrasonic wave has been
introduced.
5. The developed approach has been further verified through comprehensive lab
tests that were done on a six-meter-long prestressed concrete beam with a box-
girder cross-section shape and embedded tendons.
9.3 KEY FINDINGS OF THIS RESEARCH
9.3.1 Numerical study results
An analytical models were developed and parametric studies were carried out
using ABAQUS software to identify the effect of the system parameters such as
bonded and unbonded tendons on the ultrasonic wave characteristics. Results
confirmed that there was a minor effect of bonded and unbonded tendons on the
relatives change of the ultrasonic wave velocity due to apply PF.
Other parametric studies were carried out on prestressed concrete with a six-
meter long box-girder cross-section (similar to the lab model). Four levels of
prestressing force (0%, 25%, 50% and 75% of UTS) were applied to the prestressing
tendons to perform a numerical investigation of the effect of the PF on the relative
change in the ultrasonic wave velocity. The simulation results are promising and
indicate that the relative change in wave velocity can be used as an indication to
identify the PF.
The prestressing concrete model with different PF levels was excited by different
excitation signals: a Hanning window signal and a sinusoidal signal. The simulation
results are promising, and show that it is possible to identify the PF of a prestressed
concrete structure using acoustoelastic theory. Therefore, sinusoidal signals were used
during the experimental program. Hanning window signals could be studied further in
the future.
161
9.3.2 Identifying the PF using linear acoustic parameters
A series of laboratory tests were performed to investigate the effect of PF on the
linear acoustic parameters of the ultrasonic wave. A six-meter-long prestressed
concrete beam with a box-girder cross-section shape was built and tested in the Banyo
pilot lab. Prestressing forces were applied to each tendon in three load steps: 85 kN,
140 kN and 190 kN.
Using the ultrasonic measurement system and the proposed methodology,
ultrasonic tests were performed on the box-girder, using varying transducer positions
and distances. Experimental results show:
1. The relative change in the ultrasonic wave velocity increases with increases in
the PF. Further, an almost perfect linear relationship is exhibited between the
relative change in the wave velocity and its corresponding stresses in the
prestressed member.
2. It was found that the wave amplitude energy increases with increases in the PF.
The relationship shown between the amplitude energy and the PF is also a
linear relationship.
3. The proposed measurement process is convenient and quick, and the results are
reliable and consistent with acoustoelastic theory.
4. The position of the receivers on the model affected the results when the
distances between the transducers were fixed. However, it was found that the
perfect, and recommended, positions for evaluating the PF level were close to
the location of the tendon, so the receivers can easily detect any change in the
PF, or under the bottom slab of the box-girder. The middle part of the bridge
is to be avoided due to camber effect.
5. The experimental results show that the distance between the transmitter and
the receiver should not be more than 30 cm in order to receive a clear signal.
However, for high power ultrasonic transducers used for the experimental test
in this research, if the high power/voltage signal applied to excite the
transmitters, a strong ultrasonic wave will be generated that can be penetrated
in the concrete bridges and will resulting high resolution. As a result, this
technology can also be applicable for the field-testing of the PSCBs when the
tendons embedded deep in the concrete.
162
6. The acoustoelastic constant was evaluated during the research. The
experimental results demonstrate that the constant can vary significantly for
materials that meet the same specifications. Therefore, it is recommended to
run a calibration test to calculate the constant before using the ultrasonic
technology.
7. It is recommended to use this method with newly constructed bridges, since
the value of the wave velocity at the free state stress (zero stress) is required.
8. The method identified the PF2 and PF3 levels successfully; however, it still
has some limitations in identifying low levels of PF, such as PF1.
9.3.3 Identifying the PF using nonlinear acoustic parameters
Using the same box-girder model, identification of the PF using nonlinear
acoustic parameters of the ultrasonic wave was tested. Five transducers and receivers
were attached under the bottom slab of the box-girder. Experimental results show:
1. The nonlinear parameter β reduces with increases in the PF. The relationship
between β and the stresses developed at the concrete surface due to apply PF
exhibit a perfect linear relationship.
2. The results derived from experiments conducted indicate the suitability of
using nonlinear acoustic parameters to provide a direct indication of the level
of PF in the tendons with high accuracy, even with a low value of PF.
3. Research results strengthen the idea that nonlinear acoustic parameters of the
ultrasonic wave are promising features for monitoring the PF of embedded and
accessible tendons in prestressed structures.
4. Such parameters can be used to monitor and identify the PF in existing and
new prestressed concrete bridges. However, the field application of this
technology will require knowledge of calibration factors, β that might differ
between free and embedded tendons.
Experimental results showed the ability to use this technology to identify the PF with
a good accuracy. While Salamone et al. (2010) improved the potential for providing
simultaneous defect detection and stress monitoring capabilities for the strands with
the same ultrasonic sensing system. For that reasons, this technology can be used for
long-term SHM of the in-service PSCBs.
163
9.4 COMPARISON STUDY BETWEEN USING LINEAR AND
NONLINEAR ACOUSTIC PARAMETERS OF ULTRASONIC
TESTING IN PF IDENTIFICATION
After reviewing all the experimental results conducted using linear and nonlinear
acoustic parameters of the ultrasonic waves, general comparisons between the two
developed methods are presented in Table 9.1.
Table 9-1
Comparison between the linear and nonlinear acoustic parameters used in the PF
identifications
Linear acoustic parameters Nonlinear acoustic parameters
Used for new bridges Used for new and existing bridges
Run the test on the web or the bottom slab
of the box-girder
Run the test on the bottom slab of the box-
girder
Need to know the wave velocity at free
stress state
No need to know the amplitude of the
second harmonic in the free stress state
High percentage of error during the
identification of PF1
Identify all the PF levels, even PF1, with an
acceptable percentage of error
This method depends on changes in the
material properties of the concrete surface
due to the application of PF, such as the
modulus of elasticity and the density
This method depends on the physical
change in the concrete surface such as
increasing the contact interface due to the
application of PF
164
9.5 CONTRIBUTIONS OF THE DEVELOPED METHODS
This research has made the following contributions to the current knowledge.
• A new approach to identify the PF of the box-girder bridges using the
ultrasonic technology was introduced.
Current methods in PF identification using the ultrasonic technology are limited
to attach the traducers and the receivers at the end of the steel tendons. Later this
method is extended to attach the traducers and the receivers at the concrete surfaces.
Hence, the PF level is identified from the inverse calculation of the stress developed
on the concrete due to apply PF. Therefore, the new approach method can be
considered as an improvement to current method which does not consider such
simplifications.
• The new approach method is applicable for new construction as well as
exciting prestressed concrete bridges.
Current methods in PF identification using the ultrasonic technology are either
concentrated on the linear or nonlinear parameters of the acoustic waves. Later this
research combined these parameters in one research since the ultrasonic system is used
for both of them. Therefore, this developed method can be used with any prestressed
concrete bridge (either new or exciting) depending on the available data.
Above introduced new approach were verified with finite element analysis and
comprehensive lab testing. Results of laboratory tests that were conducted on scaled
downed concrete box-girder model prove the accuracy of these methods and reliability
in real measurements
9.6 FUTURE RECOMMENDATIONS
• Future research efforts should focus on the measurement of PF, when
prestressed concrete box-girder members are subjected to more complex
loading conditions such as dynamic loading.
• The relationships between test results and other influencing factors, such as
temperature and type of transducers, are also recommended for future study.
• It should be noted that the developed method is highly depending on either
changing in the material properties or changing in the physical contact
165
developed on the concrete surface due to apply the PF. However, due to
limited time and resources meant that the scope of this research was limited
to a simply supported, straight, single-cell box-girder with unbonded
prestressing tendons. Whilst, the basis of the proposed method is valid for
any box-girder bridges after carrying out a detailed analysis to confirm the
validity.
• The parametric study of using the Hanning window excitation signal
exhibits satisfactory results in identifying the PF. Experimental tests need to
be conducted to identify the PF using different excitation signals and
frequency ranges.
• Ultrasonic waves have different linear and nonlinear parameters such as
attenuation behaviour and polarisation. Numerical and experimental tests
need to be conducted to investigate the ability of using the other parameters
in identifying PF.
• The mesh size (about 1mm) required to run the simulation prevented
numerical validation of the experimental results. Gradually increasing
damping layer such as ALID (absorbing layer with increased damping) used
by Drozdz, Skelton, Craster, and Lowe (2007) is recommended to reduce
the model size and avoid unwanted reflection from edges. Hence, it will be
easier to run the simulation flexibly and quickly.
By making these improvements, the quality of the testing data and the
measurement of existing PF should be increased significantly. Further, the proposed
technology will find immediate application in many areas of construction and industry.
166
Bibliography
1. Abraham, M. A., Park, S., & Stubbs, N. (1995). Loss of prestress prediction based
on nondestructive damage location algorithms. Paper presented at the Smart
Structures & Materials' 95.
2. Achenbach, J. (2012). Wave propagation in elastic solids (Vol. 16): Elsevier.
3. ACI committee 318, A. C. I. (2008). Building Code requiremnt for Strural
Concrete (ACI318-08) and Commentry. American Concrete Institute.
4. Aggelis, D. G., & Shiotani, T. (2008). Effect of inhomogeneity parameters on wave
propagation in cementitious material. ACI materials journal, 105(2), 187.
5. AMSYSCO. (2010). Diagram of post tensioning slab.
6. ASTM. (1992). E837-99: Standard Test Method for Determining Residual Stresses
by the Hole-Drilling Strain-Gage Method: American Society for Testing and
Materials, Philadelphia, PA.
7. Bagge, N., Nilimaa, J., & Elfgren, L. (2017). In-situ methods to determine residual
prestress forces in concrete bridges. Engineering Structures, 135, 41-52.
doi:http://dx.doi.org/10.1016/j.engstruct.2016.12.059
8. Baoguo, H., Yu, X., & Ou, J. (2015). Self-sensing concrete in smart structures.
9. Bartels, K. A., Dynes, C. P., Lu, Y., & Kwun, H. (1999). Evaluation of concrete
reinforcements using magnetostrictive sensors. Paper presented at the
Nondestructive Evaluation Techniques for Aging Infrastructures &
Manufacturing.
10. Bartoli, I., Nucera, C., Srivastava, A., Salamone, S., Phillips, R., di Scalea, F. L.,
.Sikorsky, C. S. (2009). Nonlinear ultrasonic guided waves for stress monitoring
in prestressing tendons for post-tensioned concrete structures. Paper presented at
the SPIE Smart Structures and Materials+ Nondestructive Evaluation and Health
Monitoring.
11. Bartoli, I., Nucera, C., Srivastava, A., Salamone, S., Phillips, R., Scalea, F. L.
Sikorsky, C. S. (2009). Nonlinear ultrasonic guided waves for stress monitoring
in prestressing tendons for post-tensioned concrete structures. Paper presented at
the SPIE Smart Structures and Materials + Nondestructive Evaluation and Health
Monitoring.
12. Belyaeva, I., Ostrovsky, L., & Timanin, E. (1992). Experiments on harmonic
generation in grainy media. Acoustics letters, 15(11), 221-224.
13. Bhivgade, M. P. (2014). Analysis and design of prestressed concrete box girder
bridge. Civil Engineering Portal, http://www. engineeringcivil. com/analysis-and-
designof-prestressed-concrete-box-girder-bridge. html.
167
14. Biwa, S., Nakajima, S., & Ohno, N. (2004). On the acoustic nonlinearity of solid-
solid contact with pressure-dependent interface stiffness. TRANSACTIONS-
AMERICAN SOCIETY OF MECHANICAL ENGINEERS JOURNAL OF
APPLIED MECHANICS, 71(4), 508-515.
15. Bouchilloux, P., Lhermet, N., & Claeyssen, F. (1999). Electromagnetic stress
sensor for bridge cables and prestressed concrete structures. Journal of intelligent
material systems and structures, 10(5), 397-401.
16. Brekhovskikh, L. (2012). Waves in Layered Media 2e (Vol. 16): Elsevier.
17. Cawley, P. (2007). Practical guided wave inspection and applications to structural
health monitoring. Paper presented at the 5th Australasian Congress on Applied
Mechanics (ACAM 2007).
18. Chaki, & Bourse, G. (2008). Stress Level Measurement in Prestressed Steel
Strands Using Acoustoelastic Effect. Experimental Mechanics, 49(5), 673-681.
doi:10.1007/s11340-008-9174-9
19. Chaki, & Bourse, G. (2009). Guided ultrasonic waves for non-destructive
monitoring of the stress levels in prestressed steel strands. Ultrasonics, 49(2), 162-
171. doi:http://dx.doi.org/10.1016/j.ultras.2008.07.009
20. Chen, Dong, Y., Meng, Q., & Liang, W. (2012). FEM simulation for Lamb wave
evaluate the defects of plates. Paper presented at the International Workshop on
Microwave and Millimeter Wave Circuits and System Technology, Chengdu,
China.
21. Chen, & Gu, P. (2005). Load carrying capacity of composite beams prestressed
with external tendons under positive moment. Journal of Constructional Steel
Research, 61(4), 515-530.
22. Chen, & Wissawapaisal. (2002). Application of Wigner-Ville Transform to
Evaluate Tensile Forces in Seven-Wire Prestressing Strands. Journal of
engineering mechanics, 128(11), 1206-1214. doi:doi:10.1061/(ASCE)0733-
9399(2002)128:11(1206)
23. Chen, Yidong, H., & GangaRao, H. (1998). Measurement of prestress force in the
rods of stressed timber bridges using stress waves. Materials evaluation, 56(8),
977-981.
24. Clark, Fuchs, P., & Schaps, S. R. (1995). Fatigue load monitoring in steel bridges
with Rayleigh Waves. Journal of nondestructive evaluation, 14(3), 83-98.
doi:10.1007/bf01183114
25. Clark, Fuchs, P. A., Lozev, M. G., Gallagher, D., & Hehman, C. S. (1998).
Ultrasonic Measurement of Stress in Bridges. In R. Green, Jr. (Ed.),
Nondestructive Characterization of Materials VIII (pp. 481-486): Springer US.
26. Claudio, N. (2010). Guided wave monitoring of prestressing tendons: UC San
Diego: b6940590. Retrieved from: https://escholarship.org/uc/item/0xd0t7q6.
27. Dace, G., Thompson, R. B., Brasche, L. J., Rehbein, D. K., & Buck, O. (1991).
Nonlinear acoustics, a technique to determine microstructural changes in materials
168
Review of progress in quantitative nondestructive evaluation (pp. 1685-1692):
Springer.
28. Drozdz, M., Skelton, E., Craster, R. V., & Lowe, M. J. S. (2007). Modeling Bulk
and Guided Waves in Unbounded Elastic Media Using Absorbing Layers in
Commercial Finite Element Packages. AIP Conference Proceedings, 894(1), 87-
94. doi:10.1063/1.2717958
29. Eligehausen, R., Fuchs, W., & Sippel, T. M. (1998). Anchorage to concrete.
Progress in Structural Engineering and Materials, 1(4), 392-403.
30. Fuchs, P., Clark, A., Lozev, M., Halabe, U., Klinkhachorn, P., Petro, S., &
GangaRao, H. (1998). Ultrasonic instrumentation for measuring applied stress on
bridges. Journal of nondestructive evaluation, 17(3), 141-152.
31. Ghasemi, N. (2012). Improving ultrasound excitation systems using a flexible
power supply with adjustable voltage and frequency to drive piezoelectric
transducers.
32. Ghasemi, N., Zare, F., Boora, A. A., Ghosh, A., Langton, C., & Blaabjerg, F.
(2012). Harmonic elimination technique for a single-phase multilevel converter
with unequal DC link voltage levels. IET Power Electronics, 5(8), 1418-1429.
33. Giurgiutiu, V. (2008). Structural Health Monitoring with Piezoelectric Wafer
Active Sensors Retrieved from
http://app.knovel.com/hotlink/toc/id:kpSHMPWAS3/structural-health-
monitoring-2/structural-health-monitoring-2
34. Halsey, J. T., & Miller, R. (1996). Destructive testing of two forty-year-old
prestressed concrete bridge beams. PCI journal, 41(5), 84-93.
35. Han, S. (2007). Finite element analysis of lamb waves acting within a thin
aluminum plate. DTIC Document.
36. Han, S., Palazotto, A. N., & Leakeas, C. L. (2009). Finite-element analysis of lamb
wave propagation in a thin aluminum plate. Journal of Aerospace Engineering,
22(2), 185.
37. Heywood, R., & Ellis, T. (1998). Australia's new bridge design load - improving
transport productivity. Paper presented at the 5th International Symposium On
Heavy Vehicle Weights And Dimensions, Melbourne, Victoria-Australia.
38. Hibbeler, R. C. (1995). Structural analysis: Simon & Schuster Books For Young
Readers.
39. Hirao, M., Ogi, H., & Fukuoka, H. (1994). Advanced Ultrasonic Method for
Measuring Rail Axial Stresses with Electromagnetic Acoustic Transducer.
Research in Nondestructive Evaluation, 5(3), 211-223.
doi:10.1080/09349849409409669
40. Ho, D.-D., Kim, J.-T., Stubbs, N., & Park, W.-S. (2012). Prestress-Force
Estimation in PSC Girder Using Modal Parameters and System Identification.
Advances in Structural Engineering, 15(6), 997-1012. doi:10.1260/1369-
4332.15.6.997
169
41. Hughes, D. S., & Kelly, J. L. (1953). Second-Order Elastic Deformation of Solids.
Physical Review, 92(5), 1145-1149.
42. Jang, J. B., Hwang, K. M., Lee, H. P., & Kim, B. H. (2013). An assessment of the
prestress force on the bonded tendon by SI and impact signal analysis techniques.
Nuclear Engineering and Design, 255, 9-15.
doi:http://dx.doi.org/10.1016/j.nucengdes.2012.10.004
43. Joh, C., Lee, J. W., & Kwahk, I. (2013). Feasibility study of stress measurement in
prestressing tendons using Villari effect and induced magnetic field. International
Journal of Distributed Sensor Networks, 2013.
44. Kevin, K. T., & Liangsheng, W. (2004). Smart piezoelectric transducers for in situ
health monitoring of concrete. Smart Materials and Structures, 13(5), 1017.
45. Khan, S., & Williams, M. (1995). Post-tensioned concrete floor. Great Britain
CRC press
46. Kim, Lee, I. K., & Cho, S. J. (2012). Estimation of existing prestress level on
bonded strand using impact-echo test. Paper presented at the 6th European
Workshop on Structural Health Monitoring, Dresden, Germany.
47. Kodikara, K. A. T. L., Chan, T. H. T., Nguyen, T., & Thambiratnam, D. P. (2016).
Model updating of real structures with ambient vibration data. Journal of Civil
Structural Health Monitoring, 6(3), 329-341. doi:10.1007/s13349-016-0178-3
48. Kundu, T. (2014). Ultrasonic and electromagnetic waves for nondestructive
evaluation and structural health monitoring. Procedia Engineering,
86(Supplement C), 395-405. doi:https://doi.org/10.1016/j.proeng.2014.11.053
49. Kwun, & Bartels, K. A. (1998). Magnetostrictive sensor technology and its
applications. Ultrasonics, 36(1–5), 171-178. doi:http://dx.doi.org/10.1016/S0041-
624X(97)00043-7
50. Kwun, Bartels, K. A., & Hanley, J. J. (1998). Effects of tensile loading on the
properties of elastic-wave propagation in a strand. The Journal of the Acoustical
Society of America, 103(6), 3370-3375. doi:Doi 10.1121/1.423051
51. Laguerre, L., Aime, J. C., & Brissaud, M. (2002). Magnetostrictive pulse-echo
device for non-destructive evaluation of cylindrical steel materials using
longitudinal guided waves. Ultrasonics, 39(7), 503-514.
doi:http://dx.doi.org/10.1016/S0041-624X(01)00088-9
52. Lamb, H. (1917). On waves in an elastic plate. Proceedings of the Royal Society
of London. Series A, Containing papers of a mathematical and physical character,
114-128.
53. Law, S. S., Wu, S. Q., & Shi, Z. Y. (2008). Moving Load and Prestress
Identification Using Wavelet-Based Method. Journal of Applied Mechanics, 75(2),
021014-021014-021017. doi:10.1115/1.2793134
54. Lee, Y. H., & Oh, T. (2016). The simple lamb wave analysis to characterize
concrete wide beams by the practical masw test. Materials, 9(6), 437.
170
55. Leon & Bray, D. F. (1996). Residual stress measurement in steel plates and welds
using critically refracted longitudinal (LCR) waves. Research in Nondestructive
Evaluation, 7(4), 169-184. doi:10.1007/bf01606385
56. Li, He, J., Teng, J., & Wang, Y. (2016). Internal Stress Monitoring of In-Service
Structural Steel Members with Ultrasonic Method. Materials, 9(4), 223.
57. Li, Lv, Z., & Liu, J. (2013). Assessment of prestress force in bridges using
structural dynamic responses under moving vehicles. Mathematical Problems in
Engineering, 151(4), 1-9. doi:10.1155/2013/435939
58. Lin, T. Y., & Burns, N. H. (1981). Design of prestressed concrete structures:
Wiley.
59. Madhavi, T. C., Sekar, M., & Paramasvam, V. (2006). Expermintal Invistagtions
on the Strutrual Behavior of Prestressed Concrete Box-girder using Inovative
Construction Technology. Journal of Structural Engineering, 33, 171-175.
60. Manchem, L. D., Srinivasan, M. N., & Zhou, J. (2014). Analytical Modeling of
Residual Stress in Railroad Rails Using Critically Refracted Longitudinal
Ultrasonic Waves With COMSOL Multiphysics Module. Paper presented at the
ASME 2014 International Mechanical Engineering Congress and Exposition.
61. Mandracchia, E. A. (1995). Ultrasonic measurement of applied stress in structural
members. Paper presented at the Nondestructive Evaluation of Aging
Infrastructure.
62. Matlack, K. H., Kim, J.-Y., Jacobs, L. J., & Qu, J. (2014). Review of Second
Harmonic Generation Measurement Techniques for Material State Determination
in Metals. Journal of nondestructive evaluation, 34(1), 273. doi:10.1007/s10921-
014-0273-5
63. McGinnis, M., Pessiki, S., & Turker, H. (2005). Application of three-dimensional
digital image correlation to the core-drilling method. Experimental Mechanics,
45(4), 359-367.
64. Miyamoto, A., Tei, K., Nakamura, H., & Bull, J. W. (2000). Behavior of
prestressed beam strengthened with external tendons. Journal of Structural
Engineering, 126(9), 1033-1044.
65. Naresh, J. (2008). Inspection of complex structures using guided waves (Doctor of
Philosophy ), University of London.
66. Nazarov, V. E., & Kolpakov, A. B. (2000). Experimental investigations of
nonlinear acoustic phenomena in polycrystalline zinc. The Journal of the
Acoustical Society of America, 107(4), 1915-1921.
67. Nucera, Lanza di Scalea, & Francesco. (2012). Modeling of nonlinear guided
waves and applications to structural health monitoring. The Journal of the
Acoustical Society of America, 132(3), 1933-1933.
68. Oliva, M. G., & Okumus, P. (2011). Finite element analysis of deep wide-flanged
pre-stressed girders to understand and control end cracking. Retrieved from
University of Wisconsin-Madison
171
69. Olson, S. E. (2005). Analytical modeling of Lamb waves for structural health
monitoring. Paper presented at the Third European Workshop on Structural Health
Monitoring.
70. Olsson, D. (2012). Numerical simulations of energy absorbing boundaries for
elastic wave propagation in thick concrete structures subjected to impact loading.
(Master of Science Programme in Engineering Physics), Umeå University, Faculty
of Science and Technology, Department of Physics, DiVA.
71. Osborn, G. P., Barr, P. J., Petty, D. A., Halling, M. W., & Brackus, T. R. (2010).
Residual prestress forces and shear capacity of salvaged prestressed concrete
bridge girders. Journal of Bridge Engineering, 17(2), 302-309.
72. Ostrovsky, L. (1991). Wave processes in media with strong acoustic nonlinearity.
The Journal of the Acoustical Society of America, 90(6), 3332-3337.
73. Pathirage, T. S., Chan, T. H. T., Thambiratnam, D. P., Nguyen, A., &
Moragaspitiya, H. N. P. (2016). Prestress evaluation in prestressed concrete plate-
like structures. International Journal of Lifecycle Performance Engineering.
74. Payan, C., Garnier, V., Moysan, J., & Johnson, P. (2009). Determination of third
order elastic constants in a complex solid applying coda wave interferometry.
Applied Physics Letters, 94(1), 011904.
75. Pei, & Demachi, K. (2010). Numerical simulation of residual stress measurement
with acoustic wave. EJ Adv Maint Jpn Soc Maintenol, 2, 160-167.
76. Penamakuru, S. K. C. (2008). Optimization of electromagnetic acoustic
transducers for nondestructive evaluation of concrete structures. University of
Missouri--Columbia.
77. Podolny, W. (1985). The cause of cracking in post-tensioned concrete box girder
bridges and retrofit procedures. Journal of the Prestressed Concrete Institute,
30(2), 82-139.
78. Richardson, J. M. (1979). Harmonic generation at an unbonded interface—I.
Planar interface between semi-infinite elastic media. International Journal of
Engineering Science, 17(1), 73-85.
79. Rizzo, P., & Di Scalea, F. L. (2004). Load measurement and health monitoring in
cable stays via guided wave magnetostrictive ultrasonics. Materials evaluation,
62(10), 1057-1065.
80. Rose. (1999). Ultrasonic waves in solid media. Cambridge;New York: Cambridge
University Press.
81. Rose. (2004). Ultrasonic waves in solid media: Cambridge university press.
82. Saiidi, M., Douglas, B., & Feng, S. (1994). Prestress force effect on vibration
frequency of concrete bridges. Journal of structural engineering New York, N.Y.,
120(7), 2233-2241.
83. Salamone, S., Bartoli, I., Phillips, R., Nucera, C., Di Scalea, F. L., Sikorsky, C., &
Tamutus, T. (2010). Health monitoring of prestressing tendons in post-tensioned
concrete structures. Paper presented at the Structural Materials Technology 2010.
172
84. Salamone, S., Bartoli, I., Phillips, R., Nucera, C., & Scalea, F. d. (2011). Health
Monitoring of Prestressing Tendons in Posttensioned Concrete Bridges.
Transportation Research Record: Journal of the Transportation Research Board,
2220, 21-27. doi:10.3141/2220-03
85. Schutter, G. (2012). Damage to concrete structures: Crc Press.
86. Song, W., Xu, C., Pan, Q., & Song, J. (2016). Nondestructive testing and
characterization of residual stress field using an ultrasonic method. Chinese
Journal of Mechanical Engineering, 29(2), 365-371.
87. Stähler, S. C., Sens-Schönfelder, C., & Niederleithinger, E. (2011). Monitoring
stress changes in a concrete bridge with coda wave interferometry. The Journal of
the Acoustical Society of America, 129(4), 1945-1952.
88. Standards Australia. (2009). Concrete structures (2nd ed. ed.). Australia: Standards
Australia.
89. Sumitro, S., Kurokawa, S., Shimano, K., & Wang, M. L. (2005). Monitoring based
maintenance utilizing actual stress sensory technology. Smart Materials and
Structures, 14(3), S68.
90. Systèmes, D. (2012). ABAQUS FEA User’s Manual Version 6.12: Providence, RI.
91. Tanala, E., Bourse, G., Fremiot, M., & De Belleval, J. F. (1995). Determination of
near surface residual stresses on welded joints using ultrasonic methods. NDT & E
International, 28(2), 83-88. doi:http://dx.doi.org/10.1016/0963-8695(94)00013-A
92. Vishay. (2005). Measurement of Residual Stresses by the Hole-Drilling Strain
Gage Method. Tech Note TN-5032007, 19-33.
93. Washer, G. A. (2001). The acoustoelastic effect in prestressing tendons. (PhD
ProQuest Dissertations And Theses), The Johns Hopkins University.
(AAI3006366)
94. Wen, Y., Chen, Y., Li, P., Jiang, D., & Guo, H. (2006). Smart Concrete with
Embedded Piezoelectric Devices: Implementation and Characterization. Journal
of intelligent material systems and structures, 18(3), 265-274.
doi:10.1177/1045389X06065885
95. Williams, H., & Hulse, M. (1995). From theory to experience with inspection of
post-tensioned bridges. Paper presented at the Proceedings of the sixth
international conference on structural faults and repair.
96. Worlton, D. (1961). Experimental confirmation of Lamb waves at megacycle
frequencies. Journal of Applied Physics, 32(6), 967-971.
97. Yi, M., & Weijian, Y. (2011). Application of a PVDF-based stress gauge in
determining dynamic stress–strain curves of concrete under impact testing. Smart
Materials and Structures, 20(6), 065004.
98. Zaitsev, V. Y., Sutin, A. M., Belyaeva, I. Y., & Nazarov, V. E. (1995). Nonlinear
Interaction of Acoustical Waves Due to Cracks and Its Possible Usage for Cracks
Detection. Modal Analysis, 1(3), 335-344. doi:10.1177/107754639500100305
173
Appendix A
174
175
Appendix B
1. MATLAB code to filter the received data
function [fitresult, gof] = createFit(time80, stress80)
%CREATEFIT(TIME80,STRESS80)
% Create a fit.
%
% Data for 'untitled fit 1' fit:
% X Input : time80
% Y Output: stress80
% Output:
%fitresult : a fit object representing the fit.
% gof : structure with goodness-of fit info.
%
% See also FIT, CFIT, SFIT.
% Auto-generated by MATLAB on 15-Nov-2016 14:51:23
%% Fit: 'untitled fit 1'.
[xData, yData] = prepareCurveData( time80, stress80 );
% Set up fittype and options.
ft = fittype( 'sin2' );
opts = fitoptions( 'Method', 'NonlinearLeastSquares' );
opts.Display = 'Off';
opts.Lower = [-Inf 0 -Inf -Inf 0 -Inf];
opts.StartPoint = [0.000367787735408326 272725.906488596
1.51753524588917 0.000312290632708217 262236.448546727
1.56988499080093];
% Fit model to data.
[fitresult, gof] = fit( xData, yData, ft, opts );
% Plot fit with data.
figure( 'Name', 'untitled fit 1' );
h = plot( fitresult, xData, yData );
legend( h, 'stress80 vs. time80', 'untitled fit 1', 'Location',
'NorthEast' );
% Label axes
xlabel time80
ylabel stress80
grid on
176
MATLAB code to identify the CCO
load Time0; load Time150; load Time200
load Force0; load Force150; load Force200
Fs=45e3;
%%
t1 = (0:length(Time0)-1)/Fs;
t2 = (0:length(Time150)-1)/Fs;
t3 = (0:length(Time200)-1)/Fs;
subplot(2,1,1)
plot(t1,Force0)
title('0 kn force ')
%%
subplot(2,1,1)
plot(t2,Force150)
title('150 kn force')
xlabel('Time (s)')
%%
subplot(2,1,1)
plot(t3,Force200)
title('200 kn force ')
%%
[acor1,lag1] = xcorr(Force150,Force0);
[~,I] = max(abs(acor1));
lagDiff1 = lag1(I)
timeDiff1 = lagDiff1/Fs
figure
plot(lag1,acor1)
%%
[acor2,lag2] = xcorr(Force0,Force200);
[~,I] = max(abs(acor2));
lagDiff2 = lag2(I)
timeDiff2 = lagDiff2/Fs
177
%% [acor3,lag3] = xcorr(Force150,Force200);
[~,I] = max(abs(acor3));
lagDiff3 = lag3(I)
timeDiff3 = lagDiff3/Fs
%% subplot(2,1,1);
plot(lag1,acor1);
legend('0-150Kn');
hold on
plot(lag2,acor2);
legend('0-200Kn');
hold off
178
Appendix C
An example of how to calculate the wave velocity at zero stress from the material
properties using WAVESCOPE software.
179
