DYNAMIC MONITORING OF RAIL AND BRIDGE DISPLACEMENTS USING DIGITAL IMAGE CORRELATION

Transcription

1 DYNAMIC MONITORING OF RAIL AND BRIDGE DISPLACEMENTS USING DIGITAL IMAGE CORRELATION by Christopher Murray A thesis submitted to the Department of Civil Engineering In conformity with the requirements for the degree of Master of Applied Science Queen s University Kingston, Ontario, Canada (September, 2013) Copyright Christopher Murray, 2013

2 Abstract Rail and bridge infrastructure assets are critical elements of Canada s transportation network and their continued efficient and safe operation is necessary to ensure the nation s economic livelihood. Monitoring technologies that can detect changes in performance as well as precursors to failure are an important element of ensuring this efficient and safe operation. Digital Image Correlation (DIC) is a monitoring technology that has the potential to provide critical data for infrastructure assessment and to replace various conventional sensors with one integrated monitoring solution. In this research, the accuracy of DIC is evaluated using numerical, laboratory and fieldbased experiments. The sources of error of particular relevance to dynamic measurement using DIC are identified as (i) bias error in the sub-pixel interpolation scheme, (ii) the ratio of sample rate to the frequency of the signal being monitoring and (iii) the signal to noise ratio. It is also shown that the chosen sub-pixel interpolation scheme can greatly affect the accuracy of dynamic measurements. The use of DIC was investigated for field monitoring of both horizontal and vertical railway displacements at sites with good and poor subgrade conditions under dynamic train loading. It is shown that there is a significant benefit to using an absolute displacement measurement system rather than a relative displacement measurement system as the former can capture irrecoverable rail displacements in both the vertical and horizontal directions. Finally, DIC was also used for field monitoring of a very stiff reinforced concrete bridge during static and dynamic load tests. It is shown that when using DIC for deflection monitoring, corrections may have to be made to compensate for errors such as camera jitter and drift to acquire the most accurate results. Two potential correction methods were the use of a fixed reference point and generating composite images using average pixel intensity values from multiple images. It was found that using a fixed reference point was the optimal choice in this ii

3 bridge test. It is concluded that DIC can be used as an effective displacement measurement tool for bridge assessment because it shows excellent correlation with linear potentiometer results and it can allow measurements to be taken without having to close the bridge. iii

4 Acknowledgements This research was performed under the supervision of Dr. Neil Hoult and Dr. Andy Take. Without their guidance and enthusiasm, this project would not have been possible. Thank you. This research was financially supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) under the Discovery Grant, Strategic Grant and Research Tools and Instruments Grant programs. I was also supported by a NSERC Canada Graduate Scholarship as well as an Ontario Graduate Scholarship during my two years at Queen s University. I would like to thank the Canadian National Railway Company, specifically, Mario Ruel, Maxime Paradis and Simon Bédard-Goulet for their assistance and interest in this research. Without their help much of my field monitoring would not have been possible. Thank you to my co-researchers Ryan Regier and Michael Dutton for your great assistance in this research. Thank you to Keelin Scully, Sarah Bryant, Emily Jacobs, Josh Potvin, Nik Wootton, Stefano Arcovio, Ryley Beddoe, Michael Bentley and Alex Burnett for always volunteering to help with the laboratory and/or field work. The assistance provided by Adam Hoag in image processing and Yan Yu in the coding of the infinite beam on elastic foundation model is also gratefully acknowledged. Thank you to the Queen s University Civil Engineering Department technical staff including: Paul Thrasher, Neil Porter, and Jaime Escobar for your various contributions to this project. Your assistance was vital to the success of this research. I would also like to thank my family for their endless support and understanding throughout my education. Finally, I would like to thank all my friends at Queen s University for making my Master s experience the best one possible. iv

5 Table of Contents Abstract... ii Acknowledgements... iv List of Figures... vii List of Tables... ix Chapter 1 Introduction Research Need Objectives Organization of Thesis... 2 Chapter 2 The Accuracy of Dynamic Displacement, Velocity and Acceleration Measurements using Digital Image Correlation Introduction Background Digital Image Correlation Sources of Error Dynamic Measurement Procedure Impact of Sub-pixel Interpolation Scheme on Measurement Accuracy Impact of Monitoring Frequency and Signal to Noise Ratio Verification Experiment Conclusions References Chapter 3 Measurement of Horizontal and Vertical Rail Displacements using Digital Image Correlation Introduction Background Digital Image Correlation Infinite Beam on Elastic Foundation Model Materials and Methods Railway Monitoring Track displacement on high quality subgrade Track displacement on poor quality subgrade Application of beam on elastic foundation model Conclusions v

6 3.7 References Chapter 4 Field Monitoring of a Reinforced Concrete Bridge using Digital Image Correlation Introduction The Black River bridge Instrumentation Bridge Loading Static Load Tests Dynamic Load Tests Image Processing Static Load Test Results Dynamic Load Test Results Conclusions References Chapter 5 Summary and Conclusions Summary of Research Future Work Appendix A The Solution of the Infinite Beam on Elastic Foundation Model Appendix B The Calculation of Wheel Loads for Observed Locomotives B.1 GE Transportation Systems P42DC Passenger Locomotive B.2 GM Electro-Motive Division SD70M-2 Freight Locomotive vi

7 List of Figures Figure 2.1: The three main sources of error using DIC in vibration monitoring Figure 2.2: Digitally generated reference image used for all tests Figure 2.3: Comparison of DIC displacement measurements Figure 2.4: Comparison of the velocity measurements from DIC Figure 2.5: Comparison of the acceleration measurements from Figure 2.6: Maximum displacement error versus sample / signal frequency ratio Figure 2.7: Normalized maximum velocity versus sample / signal frequency Figure 2.8: Normalized maximum acceleration error versus sample / signal frequency ratio Figure 2.9: The experimental setup used for the verification experiment Figure 2.10: Instrumentation setup for the beam experiment Figure 2.11: Comparison of DIC and LP displacement measurements Figure 2.12: An illustration of the beam vibration damping caused by the LP Figure 2.13: Comparison between DIC and MEMS accelerometer measurements Figure 2.14: Ruler test results compared to the normalized acceleration error Figure 2.15: The setup of and images from the camera angle experiment Figure 2.16: The experimental setup for the varying camera angle test Figure 2.17: Acceleration versus time for different camera angles Figure 3.1: The camera setup used for railway monitoring at the high quality subgrade site Figure 3.2: Patches used on the rail, sleeper and foreground for Camera Figure 3.3: The uncorrected and corrected displacement time history of a freight train Figure 3.4: Displacement time history of arrival of 2 locomotives and first freight car Figure 3.5: Vertical displacement with time for a freight train from all four cameras Figure 3.6: Displacement caused by a freight locomotive a passenger locomotive Figure 3.7: The horizontal displacement with time due to the passage of a freight train Figure 3.8: The horizontal displacement of the rail caused by 5 consecutive trains Figure 3.9: Vertical displacement with time due to the passage of a train Figure 3.10: Horizontal movement of the rail caused by a freight train Figure 3.11: RMS error plot of model versus real passenger train plot for Camera Figure 3.12: RMS vertical displacement error plot of model versus freight train data Figure 3.13: Model and measured passenger train vertical displacement versus time Figure 3.14: Model and measured freight train vertical displacement versus time Figure 4.1: Elevation view of the Black River bridge from the south vii

8 Figure 4.2: Cross section of the Black River bridge Figure 4.3: Instrumentation layout for Beam Figure 4.4: A cross section of the stud walls used to mount the cameras Figure 4.5: Field of view of DSLR camera at the midspan of the bridge Figure 4.6: Western Star load truck dimensions Figure 4.7: Cross section of the bridge showing the position of the load truck Figure 4.8: Load steps from Southern elevation view Figure 4.9: Western Star load truck during the 36 block static load test Figure 4.10: Deflection measurements corrected using a fixed reference point Figure 4.11: Deflection measurements corrected using averaged images Figure 4.12: Deflection comparison for the static 12 Block load stage Figure 4.13: Deflection comparison for the static 24 Block load stage Figure 4.14: a) The DIC deflections for each load stage at all load steps Figure 4.15: DIC versus LP deflection measurements for a dynamic test at 80 km/h Figure 4.16: A comparison of midspan deflections for both static and dynamic tests Figure B.1: GE Transportation Systems P42DC passenger locomotive Figure B.2: GM Electro-Motive Division SD70M-2 freight locomotive viii

9 List of Tables Table 3.1: A record of all the trains on the HQ subgrade rail over the monitoring period Table 3.2: A record of all the trains on the peat subgrade rail over the monitoring period Table 3.3: Variability of the foundation parameters based on location Table 4.1: Axle loading of the Western Star load truck for each load stage ix

10 Chapter 1 Introduction 1.1 Research Need Rail and bridge infrastructure are critical elements of Canada s transportation network and their continued efficient and safe operation is necessary to ensure the nation s economic livelihood. Monitoring technologies that can detect changes in performance as well as precursors to failure are an important element of ensuring this efficient and safe operation. Currently the main measurement of interest in the monitoring of railways is the vertical displacement of the rail and ties under dynamic train loading. However, the horizontal rail displacement is also discussed within this thesis as, though it has not previously been monitored, significant horizontal displacements can also occur and need to be evaluated. In the case of reinforced concrete bridges, an understanding of the distribution of vertical deflection and strains resulting from loading are required for any comprehensive bridge assessment. Digital Image Correlation (DIC) has the potential to be used for infrastructure monitoring as a viable solution to all of these monitoring requirements. DIC is a method of calculating displacements from sequences of digital images in which the location of areas of interest, known as subsets, in a reference image are compared to the locations of these subsets in subsequent images during loading allowing for the displacements of the subsets to be accurately measured. The ultimate goal of using DIC in monitoring is to allow cameras to replace conventional sensors such as, but not limited to, strain gauges, linear potentiometers and accelerometers. By replacing these sensors with one method such as DIC, it could cut down on monitoring costs and instrumentation installation times, and eliminate the need for contact with the object being monitored. 1

11 1.2 Objectives The objectives of this research are to: 1. Investigate the most significant sources of error associated with DIC, define their relationships to one another, and examine the effect on the accuracy of 2D displacement, velocity and acceleration measurements. 2. Develop experimental methods to enable the measurement of both horizontal and vertical rail displacements in good and poor subgrade conditions using DIC and compare the observed vertical displacements in good subgrade conditions to a simple beam on elastic foundation model to investigate whether it can be used to calculate system parameters. 3. Explore what is needed to get accurate measurements, and then to demonstrate the achievable accuracy of DIC in the field for both static and dynamic measurements of a stiff reinforced concrete bridge. 1.3 Organization of Thesis This thesis is presented in manuscript format as outlined by the School of Graduate Studies at Queen s University. Chapter 1 is a general introduction followed by Chapters 2 through 4 consisting of manuscripts. General conclusions are presented in Chapter 5. In Chapter 2, the accuracy of DIC is investigated for use in dynamic displacement and acceleration monitoring through the use of both computer generated images and laboratory experiments. The challenges that must be overcome before this technique can be used in real monitoring applications are examined. Based on these findings, recommendations are made along with issues to consider before undertaking this type of monitoring in order to ensure that optimal results are obtained. Chapter 3 explores the use of DIC for the dynamic measurement of both horizontal and vertical rail displacements in good and poor subgrade conditions. A method is introduced that can be used to reduce the errors associated with using DIC and high speed cameras in certain cases. An infinite beam on 2

12 elastic foundation model is then used to demonstrate how DIC data can be used to estimate important foundation parameters under good subgrade conditions. In Chapter 4, DIC is evaluated as a non-contact static and dynamic bridge monitoring technique. This is done by monitoring displacements during full scale static and dynamic load tests on a very stiff reinforced concrete bridge. A comparison between DIC and more traditional sensors is performed to evaluate the potential accuracy of using DIC for monitoring of bridges in the field. Finally, Chapter 5 gives a summary of the research carried out and the conclusions that can be drawn from the work. 3

13 Chapter 2 The Accuracy of Dynamic Displacement, Velocity and Acceleration Measurements using Digital Image Correlation 2.1 Introduction In the near future, a large group of bridges built in the 1960 s and 1970 s will reach the end of their design service life in North America and many other areas. It is not feasible to replace all of these bridges at once and therefore tools are required to help determine which bridges have adequate capacity to remain in service and which ones require retrofit or replacement. One method of classifying the condition of a bridge, and many other types of structures, is by measuring the change in natural frequencies over time (Salawu 1997), which can be done by taking dynamic vibration measurements. Dynamic measurements can be a valuable tool in the monitoring of various civil infrastructure assets including rail bridges (e.g. Karoumi 2005), road bridges (e.g. Brownjohn et al. 2003), railways over various soil types (e.g. Priest et al. 2010) and many others. When combined with numerical models, dynamic measurements are a powerful tool that can accurately access the current condition of a structure to ensure that it is still fit for purpose. One method of taking dynamic vibration measurements is to use digital image correlation (DIC), which is a method of calculating displacements from digital image sequences. The ultimate goal of using DIC is to allow cameras to replace conventional sensors including, but not limited to, strain gauges, linear potentiometers and accelerometers in monitoring applications. Using high speed cameras for this purpose is an ideal solution as the cameras can be set up at a safe distance from the structure with no requirement for contact with the structure enabling efficiencies to be achieved in terms of surface preparation, sensor installation and site access. DIC has been used extensively for static measurements such as displacement (e.g. Chu et al. 1985; Sun et al. 1997; White et al. 2003; Zhang et al. 2006; Tiwari et al. 2007) and strain (e.g. Tong et al. 2005; Hoult et al. 2013) in various fields of research but is still relatively untested for 4

14 vibration monitoring. As such, there are still challenges that must be overcome before this technique can be used in vibration monitoring applications including minimizing the effects of sources of error including (i) bias error in the sub-pixel interpolation scheme, (ii) the ratio of sample rate to the frequency of the signal being monitoring and (iii) the signal to noise ratio. The goals of this paper are to (1) introduce each of these sources of error, (2) define their relationships to one another, and (3) examine their effect on the sources of error on the accuracy of 2D displacement, velocity and acceleration measurements. The paper starts with an introduction to DIC and the sources of error, the experimental procedures to isolate the effects of these sources of error are then outlined, the results are presented and finally recommendations of how to optimize the accuracy of DIC for dynamic monitoring are made. 2.2 Background Digital Image Correlation Digital Image Correlation (DIC) is a widely used method of calculating displacements using digital images. It is carried out by defining regions within an image, referred to as patches or subsets, containing unique texture (i.e. sharp changes in color) in an initial reference image. By locating these patches in subsequent images, the displacement can be calculated using the difference between the patch locations in the two images. When the displacement needs to be resolved to less than a single pixel, a subpixel interpolation scheme must be implemented to estimate the location of the patch. This sub-pixel interpolation scheme is a curve fit of the peaks of the cross correlation results; common functions used for sub-pixel interpolation in digital image correlation include polynomials and B-splines. The choice of subpixel interpolation scheme has a significant impact on the accuracy of the DIC method as will be investigated further in this research. Many implementations of DIC programs exist but follow the same fundamental principles and thus the findings presented in this chapter are not specific to any one DIC program. 5

15 The program that was used for this research is called GeoPIV and was first introduced by White et al. (2003) for use in geotechnical testing. PIV is an acronym for particle image velocimetry which was introduced by Adrian (1991) and is used extensively in experimental fluid mechanics. Since being introduced many improvements have been made to GeoPIV and now it is capable of not only monitoring large displacements in soils but also small displacements in structures and even strains (e.g. Lee et al. 2012; Hoult et al. 2013). The original paper investigating the application of DIC techniques to experimental mechanics was written by Chu et al. in Sources of Error There are numerous sources of error that can lead to a loss of accuracy when using the DIC technique such as image quality, noise, the correlation algorithm chosen, bias error in the sub pixel interpolation scheme, and under matching of the subset shape function (e.g. Schreier et al & 2002). Of particular relevance to dynamic measurement, as illustrated in Figure 2.1, are the bias error in the subpixel interpolation scheme, the ratio of sample rate to the frequency of the signal being monitoring and the signal to noise ratio. 6

16 Figure 2.1: The three main sources of error to consider when using DIC in vibration monitoring include: a) Bias error, b) Sample rate, c) Signal to noise ratio. Schreier et al. (2000) showed that there is an inherent bias error based on the sub pixel position of the patch. This bias error follows a distinct trend, as shown in Figure 2.1a, where the magnitude of error depends on the sub-pixel position of the patch. It is a maximum when the position of the patch is at approximately 0.25 and 0.75 pixels and is zero when the sub-pixel position is at 0.5 and 1 pixel. Shown in Figure 2.1a are examples of the errors due to using a cubic polynomial versus an 8 coefficient B-Spline sub-pixel interpolation scheme. The magnitude of the maximum cubic polynomial bias error is on the order 0.01 pixels while the magnitude of the maximum 8 coefficient B-spline bias error is on the order of pixels (Schreier et al. 2000; Cheng et al. 2002; Lee et al. 2012). 7

17 Figure 2.1b shows one of the possible effects of under-sampling dynamic data (using any measurement technique). It is well established that to accurately monitor a dynamic event the sample rate must be at least twice the Nyquist frequency to avoid aliasing. In other words, when trying to monitor something vibrating, the sample rate used should be at least 2 times the frequency of the signal of interest. If this constraint is not met, the higher frequency signal can be aliased into a lower frequency signal as shown in Figure 2.1b (i.e. the data can be fitted to multiple possible sinusoids). The Nyquist frequency is a minimum but for practical purposes more data points are required to accurately capture the signal, especially if more than one frequency exists within the signal. Figure 2.1c shows the effect that a low signal to noise ratio can have on the monitoring of dynamic signals. In the case shown, even though the overall trend of the monitored data follows the real signal, the sampled data represents a poor fit to the real signal and it would be impossible to take this displacement data and accurately calculate velocity and acceleration from it. However, this noise would have a reduced impact on the displacement measurement accuracy as well as the velocity and acceleration calculations if the amplitude of the real signal, and thus the measured signal, were larger as the noise would have less relative influence on estimating the slope of the line. The noise examined in this chapter is caused solely by bias error but in practice noise can be added to the signal in numerous ways including through camera errors (Luo et al. 2001), thermal effects (Handel 2000), lens distortion (Zhang 1996) and camera vibration. It is important to understand the camera equipment that is being used for monitoring and calculate the field of view such that the signal to noise ratio is minimized as much as possible. In practice, this error can be reduced by moving the cameras closer to the target which makes the field of view smaller but at the same time increases the movement of the object relative to the potential noise. 2.3 Dynamic Measurement Procedure In order to quantify the error within the DIC algorithms, all other sources of error (i.e. the camera) were removed entirely from the experimental setup. This was done by using digitally generated images produced using MATLAB. The reference image for all tests was created by adding 5000 white 8

18 dots of 10 pixel size to randomly seeded locations on a pixel black background. The intensity values of the pixels (0 is black, 255 is white, and values in between represent shades of grey) composing each white dot were fitted to a Gaussian curve to ensure their distribution realistically represented images that could be acquired by a camera (Lee et al. 2012). This reference image can be seen in Figure 2.2. Figure 2.2: The digitally generated reference image used for all tests with the patches used for the DIC analysis overlaid. After creating the reference image, the dots were translated in subsequent images in the y- direction only. The vertical movement followed a sine wave being viewed only at set increments of time. In other words, the time between points was chosen to simulate different sample rates of a camera viewing the y translation of the dots moving on a perfect undamped sine curve. The sine wave was chosen for this dynamic accuracy test as it is a good representation of vibration in real situations since every point on the curve simultaneously has a constantly changing displacement, velocity and acceleration. Using such a continuous function also meant that the true displacement, velocity and acceleration values are 9

19 known at all times and that the error is simply the difference between the true value and the measured value found using DIC. 2.4 Impact of Sub-pixel Interpolation Scheme on Measurement Accuracy Figure 2.3 shows a 6 Hz 2 pixel amplitude sine function as a solid line that was used as the basis for the digitally generated image movement sequence and was also measured using the DIC technique. Figure 2.3a shows the DIC displacement measurements using a cubic polynomial sub-pixel interpolation scheme while Figure 2.3b shows the measurements using an 8 coefficient B-spline sub pixel interpolation scheme. The displacement measurements were taken at an equivalent monitoring rate of 750 Hz in this instance (since digitally generated images were used the data is not actually time based in the traditional sense) and were calculated by taking the mean of all twenty five pixel patches. The patch size was recommended by White et al. (2003) for the balance it achieves between accuracy and computational time. 10

20 Figure 2.3: Comparison of DIC displacement measurements (open circles) to the true values (solid line): a) cubic polynomial and b) 8 Coefficient B-spline. The velocity was then calculated by using the averaged displacement data from the 25 patches and the gradient function in MATLAB. This function calculates the central difference between data points by utilizing the points before and after the point of interest to give the best approximation of the slope of the curve at that point, which in this case is the velocity. Figure 2.4 shows the calculated velocity values for the 6 Hz, 2 pixel amplitude displacement curve (Figure 2.3) resulting from both the cubic polynomial (Figure 2.4a) and 8 coefficient B-spline sub-pixel interpolation schemes (Figure 2.4b). 11

21 Figure 2.4: Comparison of the velocity measurements from DIC (open circles) to the true values (solid line): a) cubic polynomial and b) 8 Coefficient B-spline As seen in Figure 2.4, the DIC velocity measurements using the cubic polynomial begin to lose accuracy, especially near the peaks where the gradient changes rapidly, while the 8 coefficient B-spline measurements are still very accurate. Similar to the velocity, the acceleration can also be calculated by using the gradient function of the measured velocity data (Figure 2.4). Figure 2.5 shows the calculated accelerations from the second derivative of the 6 Hz, 2 pixel amplitude sine curve for both the cubic polynomial (Figure 2.5a) and 8 coefficient B-spline sub-pixel interpolation schemes (Figure 2.5b). 12

22 Figure 2.5: Comparison of the acceleration measurements from DIC (open circles) to the true values (solid line): a) cubic polynomial and b) 8 Coefficient B-spline As seen in Figure 2.5, the accelerations calculated from the cubic polynomial sub-pixel interpolation scheme are erroneous, especially in the peak regions where the gradient changes quickly. This is a result of the accuracy that was lost, first due to the bias error associated with the cubic polynomial when measuring displacement and then compounded when the data was differentiated to get velocity that was further compounded when the data was differentiated again to get acceleration. The 8 coefficient B-spline, on the other hand, allows for the relatively accurate calculation of acceleration although it is evident that it is beginning to lose accuracy in the peak regions. Based on this example it can be seen that the 8 coefficient B-spline sub-pixel interpolation scheme offers greater accuracy than the cubic polynomial sub-pixel interpolation scheme due to the lower bias errors associated with the 8 coefficient B-spline. The accuracy of this scheme becomes increasingly 13

23 important if one intends to differentiate the data to measure velocity and acceleration as differentiation compounds the effects of these errors. The remainder of this chapter will deal exclusively with the 8- coefficient B-Spline sub-pixel interpolation scheme. 2.5 Impact of Monitoring Frequency and Signal to Noise Ratio In the previous section the impact of bias error on a displacement curve with a constant amplitude to noise ratio was explored where the noise was due exclusively to bias error. However, as noted earlier, the impact of noise on measurement accuracy is dependent on the ratio of the signal amplitude to the noise. In this section the effects of varying this ratio, as well as the monitoring frequency will be explored. A series of numerical experiments were conducted by varying the amplitude and monitoring frequency of a sinusoidal displacement curve, the only constant was that the frequency of digitally generated image movement was always 6 Hz. The original digitally generated image sequences were created to simulate a sampling rate of 1500 Hz (i.e. for every full period of the sine curve 250 images were created). To explore the effect of sampling rate on error, images were skipped when carrying out the DIC analysis to simulate other sampling rates. For example, by only using every second frame of an image sequence the sampling rate would fall from 1500 Hz to 750 Hz. This was done in increments down to a minimum sampling rate 15 Hz. To explore the effect of signal to noise ratio, the amplitude of the curve, in pixels, was changed since the bias error magnitude remains the same. The amplitude of the sine curves was changed in increments between 0.25 and 64 pixels to change the signal to noise ratio. The results of these numerical experiments are illustrated in Figures 2.6, 2.7 and 2.8. Figure 2.6 shows the maximum displacement error in pixels for sinusoidal displacement curves with varying amplitudes plotted against the sampling frequency normalized by the signal frequency (6 Hz). In other words, a value of 250 on the x-axis indicates that the data was sampled at 250 times the frequency of the digitally generated image movement. 14

24 0.005 Maximum Displacement Error (Pixels) Signal Amplitude (Pixels) Sample Frequency/Signal Frequency Figure 2.6: Maximum displacement error versus sample / signal frequency ratio As seen in Figure 2.6, the maximum displacement error is constant and is the bias error of the 8 coefficient B-spline sub-pixel interpolation scheme as suggested earlier and is not affected by signal amplitude or sampling frequency. This means that using this interpolation scheme the best error that can be achieved is the bias (approximately pixels). The slight differences in error at the lower sampling ratios are most likely caused by the fact that the data using the low sampling rate is missing the points where bias error is maximized which are at translations of 0.25 and 0.75 pixels as discussed in the introduction and so the error is smaller. Figure 2.7 shows the maximum velocity error normalized against the amplitude of the velocity curve (to give a unitless ratio of the error) plotted against the sampling frequency normalized by the signal frequency. The numerical error curve plotted in Figure 2.7 was created by first calculating the true 15

25 displacement values at every sample location for a given sample rate using the sine function. Those true values were then used in the gradient function in MATLAB to calculate the velocity. For all curves the calculated velocity was then subtracted from the true velocity to give the error. The maximum error was divided by the amplitude of the true velocity curve at that location to give the normalized error for a specific sampling rate. The numerical error curve is solely the result of the numerical differentiation scheme used. In other words, it is the error associated with estimating the velocity using the gradient function in MATLAB and true sine curve displacement values which provides a baseline for the minimum expected error to compare with the DIC results Maximum Velocity Error/Amplitude of Velocity Curve Signal Amplitude (Pixels) Numerical Error Sample Frequency/Signal Frequency Figure 2.7: Normalized maximum velocity versus sample / signal frequency As seen in Figure 2.7, the velocity error from the DIC measurements and the numerical error give similar values and are minimized when sampling at about 25 times the signal frequency. The agreement 16

26 of these curves is not surprising given that the maximum displacement error of the interpolation scheme used is so small and so the majority of the error is associated with the numerical differentiation scheme rather than differentiation of the DIC measurements. Interestingly, although most of the errors are uniform from a sample ratio of 25 onward, the measurement errors of the 0.25 pixel amplitude sine curve get larger as the sampling frequency is increased. This is most likely caused by the high signal to noise ratio for the 0.25 pixel amplitude sine wave. Although the bias error is on the order of and the amplitude of the sine curve is 250 times that, the ratio is small enough that once the data is differentiated it has an impact. This result suggests that it is possible to oversample using the DIC technique, which is an unusual outcome in dynamic monitoring applications where more data is usually beneficial. Figure 2.8 shows the maximum acceleration error normalized against the amplitude of the acceleration curve (to again give a unitless ratio of the error for various amplitudes of the sine curve) plotted against the sampling frequency normalized by the signal frequency. The numerical error curve was generated following a similar procedure to the numerical error curve for velocity except that the velocity values calculated from the true displacement values at various sample rates were used in conjunction with the gradient function in MATLAB. This was done to create a baseline minimum numerical error due to numerical differentiation to compare the DIC measurements errors against. 17

27 1.40 Maximum Acceleration Error/Curve Acceleration Amplitude Numerical Error Sample Frequency/Signal Frequency Signal Amplitude (Pixels) Figure 2.8: Normalized maximum acceleration error versus sample / signal frequency ratio As seen in Figure 2.8, the acceleration error is equal to the numerical error until a dimensionless sampling frequency to signal frequency ratio of about 50. At that point the DIC measurement errors are greater than the numerical error and the magnitude of the measurement error depends on the amplitude of the sine curve. Since the bias error is the same for all amplitudes, the curves with higher amplitudes have higher signal to noise ratios. Thus it can be seen that signal to noise ratio has a much more significant impact on acceleration measurements than it did on the velocity measurements. Also much more pronounced in this figure is the effect of oversampling where above a certain sample to signal frequency ratio the accuracy of the acceleration measurements begins to decrease significantly for all the potential signal to noise ratios. Based on the results in Figure 2.8, it is recommended to use a sample to signal frequency ratio of between 25 to 50 as this minimizes the expected acceleration error measurement. 18

28 2.6 Verification Experiment To verify the results of the numerical experiments, a physical experiment was conducted using a 1 metre long simply supported aluminum alloy beam with a cross section of mm. A view of the experimental setup can be seen in Figure 2.9 while the Styrofoam target as seen from the Phantom V9.0 high speed camera used to take the images for the DIC analysis is shown in Figure The Phantom V9.0 camera was used with a 50 mm lens and is capable of recording 1000 frames per second (fps) with a resolution of pixels and at higher frame rates if the resolution of the image is reduced. The experimental setup consisted of a mm Styrofoam block that was textured with black spray paint to enhance the accuracy of the DIC technique (as discussed by Dutton 2012). The block was epoxied to the top of the simply supported aluminum beam. A wireless microelectromechanical systems (MEMS) accelerometer was placed on top of the foam block and a 100 mm linear potentiometer (LP) was placed under the beam at midspan to measure acceleration and displacement, respectively. Figure 2.9: The experimental setup used for the verification experiment. 19

29 Figure 2.10: Instrumentation setup for the beam experiment The Phantom high speed camera was set to record pixel images at 1500 frames per second (fps), the 100 mm LP was attached to a data acquisition system set to record at 200 Hz and the MEMS accelerometer was attached to a separate data acquisition system set to record at 128 Hz. To start the vibrations the aluminum beam was pushed down approximately 50 mm, released and then allowed to recover and enter free vibration while the camera, LP and accelerometer were recording. A displacement comparison from one of these tests can be seen in Figure

30 30 PIV 20 LP 10 Displacement (mm) Time (s) Figure 2.11: Comparison of DIC and LP displacement measurements As seen in Figure 2.11, the DIC and LP displacement measurements are in excellent agreement with one another. Initially displacement measurements from a DIC analysis are expressed in pixels. To convert these measurements from pixel space to real space, scale factors, which are commonly in units of pixels per millimetre, are employed. To determine the scale factor an object in the plane of interest with known dimensions is required. For this test, the DIC scale factor was determined to be 2.26 pixels/mm. The average difference between LP and DIC displacement measurements was mm meaning that the average error in pixels for this test was a maximum of pixels (assuming that the LP results are completely accurate, which is not the case). This value is higher than the bias error for the 8 coefficient B- Spline interpolation scheme seen in earlier sections and is most likely a result of the error introduced by 21

31 using a real camera as opposed to digitally generated images as well as any errors in the LP measurements. To compare the acceleration of the beam measured using the MEMS accelerometer to that calculated using the DIC displacement data, the LP was removed from the experimental setup as the spring within the LP caused the beam vibration to be damped out too quickly as illustrated in Figure The accelerations from the MEMS accelerometer and those calculated from DIC displacements are compared in Figure LP No LP 10 Displacement (mm) Time (s) Figure 2.12: An illustration of the beam vibration damping caused by the LP 22

32 Acceleration (g) Free Vibration Initial Impulse MEMS PIV Time (s) Figure 2.13: Comparison between DIC and MEMS accelerometer measurements As shown in Figure 2.13 the MEMS accelerometer and the accelerations calculated using the DIC data agree are in reasonably good agreement with a 10% difference in local peaks. There is much better agreement between the PIV and MEMS data once the vibrations are below 2g. A possible reason for this is that the accelerometers used were 2g MEMs accelerometers and therefore are optimized and calibrated for readings of less than 2g. With this in mind, the agreement between the DIC measurements and the MEMS accelerometer is a 5% difference in local peaks under 2g and a 2.5% difference in local peaks when the accelerations are below 1g. This lab test data was also used to validate the numerical experiment results. This was possible since the phantom V9.0 high speed camera was recording at 1500 fps and so was oversampling the natural frequency of the aluminum beam, which was just over 7 Hz. As such the effect of different 23

33 sampling rates on the measurement error could be explored. Similar to the digitally generated image tests, the sampling rate was altered by skipping images in the sequence. By varying the number of images skipped and then taking the maximum error as the difference between the acceleration calculated using the DIC measurements and that recorded by the MEMS accelerometer, errors at various sampling frequencies were plotted on Figure 2.14, which shows the normalized maximum acceleration error versus sample ratio plot. There are several potential sources of error such as the assumption that the MEMS accelerometer is perfectly accurate, which is not the case. Also the maximum error usually occurred while the beam acceleration was over 2g, which is just outside the operating limits of the accelerometer used. Maximum Acceleration Error/Curve Acceleration Amplitude Signal Amplitude (Pixels) 64 Ruler Test Numerical Error Sample Frequency/Signal Frequency Figure 2.14: Ruler test results compared to the normalized maximum acceleration error versus sample to signal frequency ratio 24

34 With these sources of potential error in mind, the real data corresponds reasonably well to the digitally generated image tests. In the experiment, the maximum displacement amplitude of the aluminum beam was 105 pixels and so the results correspond most closely to the 64 pixel amplitude digitally generated image test. This makes sense as it does not appear that the errors are increasing due to oversampling even at the highest sample ratio reached. Though the error does not get worse at the highest sampling rate it does increase rapidly as expected below a sample to signal frequency ratio of 25. Interestingly, below a sample to signal ratio of about 35, the errors from the DIC method are actually smaller than the errors that would be expected due to the numerical differentiation technique alone. The results confirm that a sampling rate of at least 25 times the frequency of interest is best to minimize error when using the DIC technique to measure accelerations. To this point the physical experiments have been conducted with cameras that were set up so that the lens was parallel to the plane of movement, which is not always possible in real applications. For this reason a test was devised to explore the effect of camera angle relative to the plane of movement using five synchronized Allied Vision Technology (AVT) GX bit monochrome high speed cameras recording at 100 frames per second (fps) and streamed to a RAID server with ten 1 TB hard disk drives (2 per camera). The cameras record pixel images using a Truesense KAI Type 1/2 (5.632 mm mm) charge-coupled device (CCD) sensor. The lenses used for this test had 24 mm focal lengths. A diagram of the experimental setup can be seen in Figure

35 Figure 2.15: Setup and images from camera angle experiment. As shown in Figure 2.15 cameras at almost the same distance from the beam but at different angles can still see the target (at different scale factors) but can still potentially track displacements, velocities and accelerations. The only differences are that the scale factor must be taken in the plane of interest and all movement must occur in that plane (i.e. no out of plane movement) (Sutton et al. 2008). As seen in the figure, there is a considerable difference between the scale factors for Cameras 1 and 2, even though the cameras are as close as possible (restricted by the tripods used) to the same distance from the target. The main difference is camera angle where Camera 1 is looking directly at the foam block and sitting perfectly level while Camera 2 is at an angle of about

36 Using this setup, an experiment was conducted to examine the difference between the readings taken by cameras positioned at different angles monitoring the same vibrating aluminum beam. In total four cameras were used: Cameras 1 and 2 were positioned so the lens and the movement plane were parallel at the same distance from the beam but on opposite sides; Camera 3 was positioned just behind Camera 1 and was aimed at a downward angle of approximately 21.5 ; Camera 4 was positioned behind Cameras 1 and 3 aimed at a downward angle of This camera setup can be seen as Figure Figure 2.16: The experimental setup for the varying camera angle test The beam was pushed down initially by about 50 mm and then allowed to enter into free vibration. The resulting accelerations of the beam from this test as calculated using the data from each 27

37 camera are shown in Figure Accelerations were chosen as a means of comparison for this test as they have the largest potential error. 3.0 Camera Camera 2 Camera 3 Camera Acceleration (g) Time (s) Figure 2.17: Acceleration versus time for different camera angles. As seen in Figure 2.17, the calculated accelerations are visually very close to one another with only minor differences in peak values at some points. The root mean squared errors calculated for acceleration below 2g and using camera 1 as a control were 0.04 g, 0.05 g and 0.09 g for cameras 2, 3 and 4, respectively. The minor differences between the results are possibly caused by the difference in the distance of the cameras to the target rather than the angles at which the cameras are positioned. This is because the further the camera is from the plane of interest, the smaller the scale factor. As per the earlier discussion, a smaller scale factor results in a lower signal to noise ratio and the potential for higher acceleration errors. However, this experiment has shown that almost exactly the same acceleration can be 28

38 calculated from a camera at any angle less than 30. This is significant as it may not always be possible to have a perfectly level view of a region of interest (i.e. rail, bridge, etc.) in field monitoring applications and these results suggest that it is not necessary to achieve accurate results. It should be noted that using a camera not perfectly planar to the object of interest will result in different scale factors in the horizontal and vertical directions which must be taken into account in the data analysis. 2.7 Conclusions The goal of this chapter was first investigate the sources of error associated with using DIC for dynamic measurements, define their relationships to one another, and examine their effect on the accuracy of 2D displacement, velocity and acceleration measurements. This was accomplished using both digitally generated image sequences and physical experiments. The sources of error of particular importance to dynamic measurement accuracy were first identified as (i) bias error in the sub-pixel interpolation scheme, (ii) the ratio of sampling rate to the frequency of the signal being monitoring and (iii) the signal to noise ratio. Using the data from the experiments it was established that the choice of sub-pixel interpolation scheme is important for dynamic monitoring as any error is amplified when going from displacement to velocity and acceleration. It was also found that a sampling to signal frequency ratio of 25 is the minimum required to ensure that the accuracy of the measurements is not reduced when going from displacement to acceleration due to the numerical differentiation procedure. A maximum sampling to signal frequency ratio of 50 is also recommended as oversampling can also reduce the accuracy of the calculated accelerations. This upper limit is dependent on multiple factors and could be increased depending on the signal to noise ratio. Also, angles between the camera and the movement plane of less than 30 do not influence the accuracy of acceleration measurements as long as the scale factor is taken in the plane of interest and all movement occurs in that plane. 2.8 References Adrian, R. J Particle-imaging techniques for experimental fluid mechanics. Annual review of fluid mechanics, 23(1):

39 Brownjohn, J. M. W., Moyo, P., Omenzetter, P., & Lu, Y Assessment of highway bridge upgrading by dynamic testing and finite-element model updating. Journal of Bridge Engineering, 8(3): Cheng, P., Sutton, M. A., Student, H. W. S. P. D., & McNeill, S. R Full-field speckle pattern image correlation with B-spline deformation function. Experimental mechanics, 42(3): Chu, T. C., Ranson, W. F., & Sutton, M. A Applications of digital-image-correlation techniques to experimental mechanics. Experimental mechanics, 25(3): Dutton, M Digital Image Correlation for Evaluating Structural Engineering Materials. MASc Thesis, Queen s University, Kingston, On. Handel, H Analyzing the influences of camera warm-up effects on image acquisition, In Computer Vision ACCV 2007 (pp ), Springer Berlin Heidelberg. Hoult, N. A., Andy Take, W., Lee, C., & Dutton, M Experimental accuracy of two dimensional strain measurements using Digital Image Correlation. Engineering Structures, 46: Karoumi, R., Wiberg, J., & Liljencrantz, A Monitoring traffic loads and dynamic effects using an instrumented railway bridge. Engineering structures, 27(12): Lee, C., Take, W. A., & Hoult, N. A Optimum Accuracy of Two-Dimensional Strain Measurements Using Digital Image Correlation. Journal of Computing in Civil Engineering, 26(6): Luo, G., Chutatape, O., & Fang, H Experimental study on nonuniformity of line jitter in CCD images. Applied Optics, 40(26): Priest, J. A., Powrie, W., Yang, L., Grabe, P. J., & Clayton, C. R. I Measurements of transient ground movements below a ballasted railway line. Geotechnique, 60(9): Salawu, O. S Detection of structural damage through changes in frequency: a review. Engineering structures, 19(9): Schreier, H. W., Braasch, J. R., & Sutton, M. A Systematic errors in digital image correlation caused by intensity interpolation. Optical Engineering, 39(11): Schreier, H. W., & Sutton, M. A Systematic errors in digital image correlation due to undermatched subset shape functions. Experimental Mechanics, 42(3): Sun, Z., Lyons, J. S., & McNeill, S. R Measuring microscopic deformations with digital image correlation. Optics and Lasers in Engineering, 27(4): Sutton, M. A., Yan, J. H., Tiwari, V., Schreier, H. W., & Orteu, J. J The effect of out-of-plane motion on 2D and 3D digital image correlation measurements. Optics and Lasers in Engineering, 46(10): Tiwari, V., Sutton, M. A., & McNeill, S. R Assessment of high speed imaging systems for 2D and 3D deformation measurements: methodology development and validation. Experimental mechanics, 47(4): Tong, W., Tao, H., Zhang, N., & Hector Jr, L. G Time-resolved strain mapping measurements of individual Portevin Le Chatelier deformation bands. Scripta materialia, 53(1):

40 White, D. J., Take, W. A., & Bolton, M. D Soil deformation measurement using particle image velocimetry (PIV) and photogrammetry. Geotechnique, 53(7): Zhang, G., Liang, D., & Zhang, J. M Image analysis measurement of soil particle movement during a soil structure interface test. Computers and Geotechnics, 33(4): Zhang, Z On the epipolar geometry between two images with lens distortion. In Pattern Recognition, Proceedings of the 13th International Conference on (Vol. 1, pp ). IEEE. 31

41 Chapter 3 Measurement of Horizontal and Vertical Rail Displacements using Digital Image Correlation 3.1 Introduction Excessive rail displacements can result in slow orders and are thought to be a possible cause of train derailments which can have tremendous economic, environmental and public safety impacts. The measurement of vertical and horizontal rail displacement can give insights into the current foundation conditions, verify that track rehabilitations have been implemented successfully, indicate where stress concentrations are present in the rails and allow for damage detection through long-term monitoring. There are numerous components to a railway foundation system but those that have the largest influence on the displacements experienced by the train are the underlying soil foundation system, the ties (or sleepers) and the rails themselves. When choosing a monitoring strategy, it is important to keep in mind that each of these components can experience different displacements when exposed to train loading. For example, there can be a gap between the rail and the tie that has to be closed before the rail can engage the tie and the underlying soil. Another important issue in the rail industry is the so-called running rail phenomena, where the passage of a train pushes the rails horizontally potentially causing a build-up in longitudinal stresses in the rail at locations where this displacement is constrained. Thus, it is often important to take the absolute displacement behaviour into account so that the critical behaviour can be isolated. Several methods have been proposed for the measurement of vertical rail displacement, which is a vital component in determining the track system stiffness. Some of the available methods include point measurements with geophones (Priest et al. 2010) or linear extensometers (Hendry 2012), laser Doppler sensors on a moving rail vehicle (Rasmussen et al. 2002), accelerometers on a moving rail vehicle (Sussmann 2007), line-lasers mounted on a moving rail vehicle to measure the relative deflection between 32

42 the bogie and the rail (Norman 2004) and digital image based methods such as Particle Image Velocimetry (PIV) (Priest et al. 2010) also known as digital image correlation (DIC). Each of these methods has advantages and disadvantages that are discussed in the references given for each method. Some of the methods measure absolute tie displacements (geophone and linear extensometers) while others measure relative rail displacements (laser Doppler sensors, accelerometers and mounted linelasers) but only DIC can give absolute and relative rail and sleeper displacements. This is important for railway monitoring where poor subgrade conditions are present as the vertical rail displacement can have both a recoverable and an irrecoverable component. Measuring relative rail displacements in these scenarios therefore effectively ignores the plastic component. Only DIC can measure the horizontal rail displacement due to train loading although in the literature to date it has only been used for the measurement of vertical rail deflections (Priest et al. 2010). Since DIC has been validated in Chapter 2 and found to perform well in dynamic monitoring applications it should provide accurate measurements of both absolute vertical and horizontal displacement for railway monitoring applications. The objectives of this chapter are to (i) apply the methodology of Chapter 2 to use a system of synchronized high speed cameras and DIC to measure absolute horizontal and vertical rail displacements, (ii) observe what factors influence the relative magnitudes of horizontal and vertical displacements under both short passenger and long freight train loading on both high quality and peat subgrades, and (iii) compare the observed vertical displacements on high quality subgrade conditions to a simple beam on elastic foundation model to investigate whether DIC measurements can be used to calculate the stiffness and damping parameters for the rail foundation system. 3.2 Background Digital Image Correlation DIC is a technique that uses digital images to accurately measure displacements. GeoPIV is a DIC program developed by White et al. (2003) for use in geotechnical testing. To carry out the displacement measurements, an image is taken of the undeformed object and then subsequent images are 33

43 taken as loading / deformation is applied to the object. Regions of interest within the images, called patches or subsets, can be tracked between the undeformed, or reference image, and the subsequent images. Using these displacements, a complete history of the deformation of the object over time can be developed. Since its introduction, DIC has been used extensively in geotechnical applications as it is able to accurately track displacements of objects with good texture to an accuracy of 0.1 pixels. The idea of using DIC to monitor railway displacements was first explored by Bowness et al. (2007) and further researched by Priest et al. (2010) as a means of gathering dynamic railway deflection data caused by the passage of a train. This initial work was conducted using a webcam with a capture rate of 30 frames per second (fps), a target mounted near the end of the track ties and a telescope to allow the monitoring system to be an adequate distance from the track to avoid the effects of ground vibrations. The study by Bowness et al. (2007) showed that DIC could be used to measure vertical rail displacements for rail frequencies less than 2 Hz. This study also showed the high variability in vertical tie displacements that can exist even when different ties are subjected to the same loading within a relatively short length of rail. Advances in the DIC technique for use in railway monitoring applications introduced in the current work include the use of synchronized high speed cameras, an 8-coefficient B-spline sub-pixel interpolation scheme that has greatly increase the accuracy of PIV (Lee et al. 2012) and making use of naturally occurring texture on the rail itself in addition to using targets mounted on the ties. Using texture on the rails makes monitoring easier as it allows for monitoring teams to remain at a safe distance from the track and eliminates the need to have a flagman on site when the targets are installed on the ties, which can be very costly. It also allows for vibration in the rail itself to be measured, and detecting excessive vibrations that could play an integral role in avoiding derailments in areas of soft clay soil Infinite Beam on Elastic Foundation Model Vertical track displacement is a function of foundation system stiffness, and so if the displacement is known then the system parameters can be estimated by using an appropriate foundation 34

44 model. The Winkler foundation model (Winkler 1867) is a representation of a continuous elastic foundation where the foundation is replaced by a series of spring elements. Using the Winkler model, the deformation of the foundation within the loaded area is related to the pressure on this specific area, and outside of the loaded area the deformation is zero. To overcome the shortcomings (e.g., the independent springs and discontinuity of the adjacent displacements) of the Winkler model, the Pasternak foundation model (Pasternak 1954) was proposed where the shear interactions between the spring elements are considered. This represented an improvement in predicting the deformation of the foundation by accounting for the shear interaction and resulted in deformations occurring outside the loaded area as they would in reality. To model the damping provided by the foundation, linear viscous elements (dashpots) are added in parallel to the spring elements of the Pasternak foundation model, which forms the viscoelastic Pasternak foundation model (Kerr 1964). The rail tracks can be modeled as Euler-Bernoulli beams or Timoshenko beams. The difference between these two models is that the Timoshenko beam model considers the transverse shear deformation and rotational inertia effects while the Euler-Bernoulli beam model does not (Timoshenko 1953). However, when considering foundations found in railway engineering applications, which have a modulus generally less than 10 8 N/m 2, the critical velocities produced using the Euler-Bernoulli beam are almost the same as those from the Timoshenko beam. Therefore it is adequate to use Euler-Bernoulli beam theory for modeling the railway tracks (Chen and Huang 2000). For a single concentrated load acting on an infinite Euler-Bernoulli beam and moving at a constant velocity, analytical solutions have been developed to analyze the beam response on the Winkler foundation (Kenney 1954), viscoelastic Winkler foundation (Thompson 1963), and viscoelastic Pasternak foundation (Mallik et al. 2006). The solutions for the Winkler foundation and viscoelastic Winkler foundation are special cases of the solutions for the viscoelastic Pasternak foundation. The response of the beam subjected to multiple concentrated loads moving at a constant velocity can be calculated by using superposition assuming the response remains elastic. 35

45 For an Euler-Bernoulli beam acting on the viscoelastic Pasternak foundation under a single concentrated load moving at a constant velocity, the partial differential equation can be written as (Mallik et al. 2006): [2-1] where E is the Young s modulus of the beam material (N/m 2 ); I is the second moment of area of the beam cross section about its neutral axis (m 4 ); w is the transverse deflection of the beam (m); x is the space coordinate along the length of the beam (m); k is the spring constant of the soil per unit beam length (N/m 2 ); k 1 is the shear parameter of the soil taken as 20% of k (N); ρ is the mass per unit length of the beam (kg/m); t is the time (s); c is the viscous damping coefficient per unit length of the beam (Ns/m 2 ); P is the applied concentrated load (N); δ is the Dirac s delta function (δ = 0 when x-vt 0 and δ = when x-vt = 0; x is measured from the location of the load at t = 0); and v is the velocity of the moving load (m/s). Equation [2-1] is based on the following assumptions (Mallik et al. 2006): (i) an initially straight beam, (ii) the beam and foundation materials are linearly elastic, (iii) there is no separation between the beam and foundation, (iv) small beam deformation, (v) negligible shear deformation and rotational inertia, (vi) negligible inertial forces of the vehicles when compared to their dead weight, and (vii) plane strain. By considering only a single location (i.e. the monitoring location), the rule of superposition can be used in conjunction with the characteristic equation of Equation [2-1] (see Appendix A) to determine the total deflection at that location resulting from all concentrated wheel loads of a train provided the wheel spacing, train speed and wheel loads are known. 3.3 Materials and Methods Five synchronized Allied Vision Technology (AVT) GX bit monochrome high speed cameras recording at 100 frames per second (fps) and streamed to a RAID server with ten 1 TB hard disk 36

46 drives (2 per camera) were used for this research. The cameras record pixel images using a Truesense KAI Type 1/2 (5.632 mm mm) charge-coupled device (CCD) sensor. The lenses used in this research have 85 mm focal lengths and were chosen as they provided a good field of view for the standoff distance required in this monitoring application. By using synchronized cameras multiple locations along the same track can be monitored under the same train loading, which can lead to an improved understanding of the foundation conditions over a section of track. Additionally, if the spacing between cameras is known, the speed of the train can be measured. A monitoring site was selected on a track near Kingston, Ontario, Canada that services both passenger and freight trains (44 13'40.80"N, 76 39'22.24"W). This site was chosen because it has high quality subgrade, it is a relatively straight section of track, it could be accessed from an adjacent access road, the tracks are slightly elevated allowing for the cameras to be positioned level with the rail and there was no vegetation to obstruct the field of view (FOV) during the passage of a train. The cameras were setup as seen in Figure 3.1 to capture both the sleepers and rails within the same field of view. As discussed, 85 mm camera lenses were used to compensate for the distance to the rail by ensuring that the scale factor was appropriate for the magnitude of displacements being measured. Since the ends of the sleepers were covered with ballast material and were therefore not visible to the cameras, L aluminum angles were mounted to the top of the sleepers of interest at the end closest to the camera. Texture was added to the angles by applying a speckling of black spray paint. At this site there was adequate texture on the rails to be tracked with DIC but some white spray paint was added to enhance the texture. The cameras were set up such that the distance between Camera 1 and 2 and Camera 3 and 4 was 920 mm, and the distance between Camera 2 and 3 was 460 mm so that they were monitoring adjacent ties. Camera 1 was placed with a FOV of a sleeper and part of the rail and was as close to the surrounding vegetation as possible without the field of view being blocked. Camera 2 was placed with a FOV containing a single sleeper that was two sleepers over from the one seen by Camera 1. Camera 3 was placed with a FOV of the sleeper adjacent to the one seen by Camera 2. Finally Camera 4 was placed with 37

47 a FOV containing a sleeper that was 2 sleepers away from Camera 3 as seen in Figure 3.1. This setup was chosen to investigate whether there was any difference between monitoring adjacent sleepers (and the corresponding rail segment) versus monitoring sleepers spaced further apart and also to monitor multiple locations to observe the variation in displacement. Figure 3.1: The camera setup used for railway monitoring at the high quality subgrade site The cameras were positioned metres from the rail, which is outside of the zone where access is restricted and eliminates the need for a flagman to be on site and the associated cost. Thus, by using DIC for railway monitoring there is the potential to substantially reduce monitoring costs. Using this camera and lens combination on this site resulted in each camera having a field of view as seen in Figure 3.2. As shown in this figure, the rail, aluminum angle and ballast material can all be seen in the field of view. This allowed for pixel patches to be defined on the rail, pixel patches to be defined on the aluminum angle mounted to the sleeper, and pixel 38

48 patches to be defined on the ballast material in the foreground. These tracking regions enabled redundancy of measurements of rail, tie and ballast movement. Figure 3.2: Patches used on the rail, sleeper and foreground for Camera 1 using an 85 mm lens (a similar layout was used for all cameras) Since there is the potential for vertical gaps to form in between the rail and ties due to nonuniform settlement of the ties both were monitored to observe if any differences in displacement occurred during the passage of a train. The ballast material was also of interest as any movement observed in it could either a) be used to measure subgrade deformation or b) be used as a check on camera stability depending on the properties of the subgrade. Camera image stability issues fall into two major categories: jitter and drift. Jitter is very small, non-uniform translations of the whole image occurring at a much higher frequency than camera drift and depends on the frame rate of the camera, camera shake, the quality of the camera and the fact that a camera will not take exactly the same picture twice (Luo 2001). Drift, on 39

49 the other hand, occurs over a longer period of time and can be a result of the heating of the chargecoupled device (CCD) during recording (Handel 2007). Drift of images when recording with the AVT GX1050 cameras is known to occur as it has been observed in the lab when monitoring perfectly stationary targets. To determine the effect of camera image stability issues during monitoring at the high quality subgrade site, the rail, sleeper and foreground displacement data were compared. The median displacement of each group of patches (rail, tie, foreground) was plotted in Figure 3.3a versus time for the passage of a freight train. The median displacement was used to account for the fact that if the DIC program cannot find a match to the reference image for a patch it generally sets the displacement as the maximum allowed, which results in a spike in the displacement data. Although these spikes can have a significant impact on the mean displacement of a patch group, they do not affect the median displacement of the group. It can be seen in Figure 3.3a that although the rail, sleeper and foreground displacements all have different magnitudes, there is a net change of 1 mm in the rail and sleeper displacement over the 200 second period that it takes the train to pass. This same net displacement change can be seen in the foreground ballast material, which does not actually move vertically downward. Since this is a high quality subgrade site it is reasonable to assume that the observed net rail displacement is function of camera drift rather than permanent displacement of the rail. This drift is most likely a result of the heating of the CCD during recording and it seems that image jitter does not have a significant effect on the measurements. Camera drift has a significant impact in this instance due to the distance of the cameras from the rail which results in a relatively small scale factor combined with the relatively small displacement being measured. Thus the signal to noise ratio is low and camera drift has a significant impact. However, by using the foreground ballast as a fixed reference point (assuming the ballast does not actually move vertically), the effect of camera drift can be mitigated by subtracting the movement of the ballast from the overall movement. Since the patches on the rail, sleeper and the foreground are all at different distances from the camera, different scale factors had to be used for each to convert the patch displacements from pixels to millimetres prior to correcting the rail and sleeper displacements. Figure 40

50 3.3b shows the resulting corrected displacement caused by the passage of the freight train for the rail and sleeper. 41

51 a) Rail Sleeper Foreground Time (seconds) b) Rail Sleeper Time (seconds) Figure 3.3: The displacement time history of a freight train passing over the high quality subgrade site: a) uncorrected rail, sleeper and foreground displacement, b) corrected rail and sleeper displacement Y Deflection (mm) Y Deflection (mm) Figure 3.3: The displacement time history of a freight train passing the high quality subgrade site: a) uncorrected rail, sleeper and foreground displacement, b) corrected rail and sleeper displacement 42

52 As seen in Figure 3.3b, the corrected results show no net displacement of the rail or the sleeper after the passage of the train, which would be expected for an elastic system. It is worth noting that there are several instances when using this technique to adjust the displacement data would be inappropriate or not required. If the system is not elastic and the foreground displacement is likely to be affected by the passage of a train, this technique should not be employed. Also, if the displacement errors due to camera stability issues are a small percentage of the total displacement being measured, the effect of the errors can most likely be ignored. Another approach that could be taken to correct for camera stability issues would be to apply a high pass filter to the data. This technique would eliminate any measurement errors that occur over a relatively long period (i.e. low frequency) compared to the sampling period. This technique was used to remove the effects of camera vibration from PIV data by Priest et al. (2010) who then compared their data to numerically integrated geophone data with reasonably good results. This technique was used in an attempt to correct for the effect of camera drift and the results are shown in Figure 3.4. The resulting rail and sleeper displacements still showed some permanent displacements, although greatly reduced, after the passage of the train. For this reason it was decided that the foreground subtraction method would be used for all data collected from this site as it was both numerically efficient and appeared to provide appropriately corrected results (i.e. no permanent displacements were measured). Another potential issue with data collected from railway sites is the high frequency content within the displacement data, which is caused by vibrations within the rail system, camera vibration if the camera system is poorly supported or too close to the tracks, bias error associated with the use of DIC (as discussed in Chapter 2) and images where patches cannot be located properly during the analysis (due to a shadow or debris moving through the patches). In this study the objective was to monitor the displacement caused by train loading and therefore the high frequency content is not required for any subsequent analysis. One technique for mitigating the effects of lost patches is to take the median displacement of a patch group (i.e. rail, tie or foreground) which will work as long as only a few patches 43

53 are affected as discussed previously. A second method for mitigating the effects of lost patches, as well as other high frequency content such as rail and camera vibrations, is to use a low pass filter on the data. The filter will remove the spikes in the displacement data caused by lost patches as well as the higher frequency vibration data. However, an important consideration when employing a low pass filter is the selection of the appropriate cut-off frequency. The effect of filtering and the choice of cut-off frequency is shown in Figure 3.4 where a) shows the displacement time history before a filter is applied, b) the data with a 9 th order Butterworth 10 Hz low pass filter applied and c) the data with a 9 th order Butterworth 6 Hz filter applied. 44

54 1 0 a) Rail Sleeper b) Rail Sleeper c) Rail Sleeper Time (seconds) Figure 3.4: Displacement time history of 2 locomotives and a freight car: a) unfiltered displacement, b) displacement data filtered with a low pass filter at 10Hz and c) displacement data filtered with a low pass filter at 6Hz Y Deflection (mm) Figure 3.4: Displacement time history of arrival of 2 locomotives and first freight car 45

55 As seen in Figure 3.4a, there is some high frequency content within both the rail and sleeper displacement data but it has a much lower magnitude than the displacements that are required for the purposes of modeling the foundation. Figure 3.4b still shows the large displacements caused by the passage of the locomotives as well as the foundation response to the individual wheels in both the sleeper and the rail however the high frequency content has been greatly reduced. Figure 3.5c still captures the maximum displacements caused by the passage of the bogies but the individual wheels cannot be seen and therefore this cutoff frequency has removed important data from the time-displacement plot. Thus it was decided that a 9 th order Butterworth low pass filter at 10 Hz would be applied to all of the data to remove the high frequency noise content from the data while preserving the true foundation response to the train loading. Another important thing to notice from Figure 3.4 is the difference between sleeper displacement and rail displacement. While the end of the sleeper only experiences maximum displacements of about 0.5 mm, the rail directly on top of the sleepers experiences maximum displacements of about 2 mm, which is four times that of the end of the sleeper. One reason for this could be that the sleeper behaves as a beam and experiences more displacement directly beneath the rail than it does at the end of the sleeper where it is monitored. Another possible reason for this could be the presence of a gap between the top of the sleeper and the bottom of the rail that can form if the spikes connecting the rails to the sleepers loosen over time. Since the displacements that the train experiences are generally the most useful component in the monitoring of railways, the system stiffness was explored in this research by using the rail displacement data. 46

56 3.4 Railway Monitoring Track displacement on high quality subgrade Table 3.1 outlines all the trains passing the monitoring location on the rail of interest over a two day monitoring period including the train type, direction, velocity, peak vertical displacement and permanent horizontal displacement due to the passage of each train. Horizontal displacement has not previously been measured or discussed in the literature. Table 3.1: Trains on the rail of interest over the monitoring period Date/Time Type Direction Velocity Length Length Peak Δy Final Δy Final Δx (m/s) (m) (s) (mm)* (mm)* (mm)* Jun 18 2:00 PM Passenger East Jun 18 2:20 PM Passenger East Jun 18 2:50 PM Passenger West Jun 19 9:30 AM Passenger West Jun 19 10:30 AM Freight West , Jun 19 11:40 AM Passenger East Jun 19 11:50 AM Freight East , Jun 19 12:30 PM Freight West , Jun 19 1:20 PM Passenger West Jun 19 2:20 PM Passenger East Jun 19 2:50 PM Passenger West * the peak Δy and final Δy and Δx measurements are taken from Camera 1. As shown in Table 3.1, there were 11 trains on the rail of interest over the 2 day monitoring period; eight of these trains were passenger trains which travelled past the monitoring site at approximately 120 km/h. The remaining three trains were freight trains and were much heavier, longer and slower than the passenger trains seen on this line. The freight trains had an observed top speed of 70 47

57 km/h. It can also be seen in this table that even though the freight trains are much heavier than the passenger trains the peak vertical displacements are very similar to one another. Based just on this table there does not appear to be any trend in the horizontal movement of the rail as very similar trains traveling in the same direction can cause very different horizontal displacements. Figure 3.5 shows the vertical displacement with time for the freight train passing on June 19 th at 12:30 PM measured using each of the four cameras. Shown in the figure is the vertical displacement of the rail in response to two locomotives as well as the first three cars. Figure 3.5: Vertical displacement with time for a freight train from all four cameras The first thing to note from Figure 3.5 is that the displacement data for each camera has a slight temporal offset from the other cameras. This is due to the fact that the cameras are all recording on the same synchronized time scale but are at different locations. Since the train was traveling towards the West, it reached Camera 4 first followed by Cameras 3, 2 and 1. Another important feature to note is that 48

58 the rail displacement caused by the same load is different at each of the camera locations. Camera 4 measures the highest vertical displacement of about 3 mm while Camera 1 measures the lowest vertical displacement of about 2 mm. The four cameras are all within a 2 metre section of track and yet they measure a difference in rail deflection of approximately 1 mm, which speaks to the highly variable nature of rail foundation systems also observed by Priest et al. (2010). This difference can have a significant impact when trying to model the foundation and calculate the stiffness of the foundation system as discussed in later sections. Even though there are differences in terms of vertical displacement measured by each camera, when considering the measurements from a single camera there is not a very large difference between vertical displacements measured during the passage of passenger and freight locomotives. This is illustrated by Figure 3.6, which shows the vertical displacement with locomotive position for both a freight and a passenger locomotive as they pass the same camera location. The x-axis is plotted as train position rather than time to allow for comparison as passenger trains travel at a much higher speed than freight trains. These very similar deflections are perhaps counterintuitive considering the difference in locomotive weights (185,100 kg for the freight locomotive versus 121,900 kg for the passenger locomotive). However, the vertical displacements are similar because the load per wheel for both of these locomotives is about the same at roughly 150 kn per wheel (see Appendix B), but the freight locomotives have 3 axles per bogie while the passenger locomotives only have 2 axles per bogie. 49

59 1 0.5 Y Displacement (mm) Passenger Freight Train Position (m) Figure 3.6: A comparison of displacement caused by a freight train locomotive versus that caused by a passenger train locomotive As noted earlier, very little research has been carried out to measure horizontal rail movements caused by train loading. Since the cameras measure rail displacements relative to a fixed position, it is possible to use DIC to investigate the horizontal rail movement. Figure 3.7 shows the horizontal rail movement with time as measured by each of the four cameras. 50

60 Camera 1 Camera 2 Camera 3 Camera 4 X Displacement (mm) Time (Seconds) Figure 3.7: The horizontal displacement with time due to the passage of a freight train As seen in Figure 3.7, unlike for the vertical displacement measurements, the horizontal displacement of the rail is essentially the same at each camera location. Since there is no difference between the horizontal displacement measurements from individual cameras, the remainder of the discussion on horizontal rail movement will focus on data from Camera 1. Figure 3.8 shows the horizontal movement with time of five consecutive trains on the rail of interest between 10:30 AM and 1:20 PM on June 19 th. In this figure displacement to the West is taken as positive and train displacements are plotted over a 120 second period. Also indicated in the figure is the direction each train was travelling in (west or east) with an arrow. 51

61 5 0 a) West b) East X Displacement (mm) c) d) East 5 West e) West Time (seconds) Figure 3.8: The horizontal displacement of the rail caused by 5 consecutive trains on June 19 th, a) 10:30 AM freight train; b) 11:40 AM passenger train; c) 11:50 AM freight train; d) 12:30 PM freight train; e) 1:20 PM passenger train 52

62 As seen in Figure 3.8, each of these trains caused horizontal rail movement of varying magnitudes, which is a function of the direction of travel of the previous train. The first train observed in the sequence, shown as Figure 3.8a, was a freight train traveling towards the West. Even though this train is almost 3 km long, it only moves the rail in the direction of travel by a total of 0.8 mm. This is substantially less than the movement caused by both of the other freight trains as illustrated in Figure 3.8c and 3.8d. It can also be seen in Figure 3.8a that the rail initially moves in the opposite direction to the direction of train travel as though it is encountering resistance from built up stresses within the rail and there is very little slack in the rail that can be pushed forward. The previous train to pass the site on this rail was also a freight train that was traveling to the West. The second train in the sequence (Figure 3.8b), was a passenger train traveling to the East. Due to the high speed and relatively short length of passenger trains compared to freight trains it only takes about 15 seconds for passenger trains to pass this monitoring location and therefore the plot of displacement is much shorter when plotted on the same time scale as freight trains. Even though this train is substantially lighter than the freight train that passed just before it, this train caused 2.9 mm of horizontal movement in the direction of travel. This much larger horizontal displacement is due to the fact that the passage of this train is pushing the rail back in the other direction, rather than continuing to push the rail to the west. The third train, (Figure 3.8c), was a freight train also traveling towards the East. As a result of the weight, length and direction of travel of this train, it further moved the rail from the West towards the East. The total horizontal movement caused by the passage of this freight train was 6.2 mm, meaning that the net movement due to the passage of the previous two eastbound trains was 9.1 mm towards the East. The horizontal displacement caused by the next train in the sequence, shown in Figure 3.8d, was a Freight train headed to the West. As shown in the figure, this train caused a total movement of 9.5 mm to the West. The passage of this train effectively shifted the rails at this site from the East to the West again. 53

63 The horizontal displacement from the final train in the sequence, shown in Figure 3.8e, was a passenger train headed towards the West. Unlike the previous passenger train in the sequence, this passenger train was traveling in the same direction as the freight train that passed immediately before it. As a result, this passenger train did not cause any horizontal movement in the rail. This is a due to the fact that passenger trains are much lighter and shorter than freight trains as well as the fact that the train was traveling in the same direction as the previous train. This sequence highlights the importance of train type and direction of travel on horizontal rail movement. In general, freight trains were observed to cause much more horizontal movement in the rails during passage. The direction of travel of the train is important as more horizontal movement is seen when trains are traveling in the opposite direction to the previous one. The magnitude of vertical displacement could also play a role since when a train travelling along a track, it is always causing a vertical deflection, and thus more likely to generate a horizontal force to push track forwards Track displacement on poor quality subgrade So far, the monitoring results discussed in this chapter have focused on track displacements on high quality subgrade; this section will examine the effect of poor quality subgrade on displacement monitoring results. Monitoring was carried out at a site on a rail spur through a peat bog near Levis, Quebec (46 47'15.19"N, 71 1'40.57"W). This site has been observed to have large vertical displacements by Konrad et al. (2007) using linear potentiometers anchored to the bedrock. The DIC monitoring was carried out over a two day period from December 3 rd to 4 th, Although it was late in the year the temperature was still moderate and the ground was not frozen. Over the two day monitoring period, the rail displacements caused by three trains were measured. It is common on this rail spur for empty freight cars to travel to the West and for full freight cars to travel to the East. The camera setup at this site was similar to that used at the high quality subgrade site except that the cameras could be placed closer to the rails since there was a flagman on site during this monitoring. This led to a more favourable scale factor (more pixels were used to measure each millimetre of 54

64 displacement), which increased the signal to noise ratio and meant that the data collected did not require correcting for camera errors such as drift. This was important since due to the soil conditions at this site, the ballast in the foreground actually displaced with the passage of the train, which would have made the use of the ballast subtraction correction technique presented earlier impossible. Since this monitoring site was in a bog, accelerometers were placed on top of the cameras to see if they experienced any vibration from the passage of the trains but no movement beyond the noise floor of the accelerometer was observed in the acceleration data. This result suggested that camera vibration was minimal, which was an important result since the foreground subtraction correction technique could not be employed to correct the results if this was not the case. Table 3.2 shows the train type, direction, velocity, length, peak vertical displacement, permanent vertical displacement and permanent horizontal displacement due to the passage of each train for the three trains observed over the 2 day monitoring period. Table 3.2: Trains on the rail of interest over the monitoring period Date/Time Type Direction Velocity Length Length Peak Δy Final Δy Final Δx (m/s) (m) (s) (mm)* (mm)* (mm)* Dec 03 Freight 8:50 PM (full cars) East Dec 04 Freight 6:40 PM (full cars) East 4.2 1, Dec 04 Freight 7:30 PM (empty cars) West * the peak Δy, final Δy and final Δx measurements are taken from Camera 1 As seen in Table 3.2, the 3 trains have very low velocities as the speed is limited to 10 mph (16.1 km/h) on the line due to safety concerns with regard to derailment. The final vertical displacement, Δy, column shows that there is a significant residual displacement that is caused by the passage of some trains. It should be noted that final Δx and Δy displacements are taken immediately after the passage of the train when the recording was stopped and the process of time-dependent recovery is still ongoing. 55

65 The vertical displacement with time caused by the passage of a full freight train on December 4 th is shown in Figure Displacement (mm) Time (s) Figure 3.9: Vertical displacement with time due to the passage of a train As shown in Figure 3.9, the vertical displacement of the rail is much higher than seen in the high quality subgrade monitoring data (approximately 28 mm versus 3 mm). There was also an apparent irrecoverable deformation of 10.5 mm. This is an interesting result since in order to capture this phenomenon and effectively quantify the foundation deformation due to loading an absolute measurement system such as DIC or a linear potentiometer anchored to bedrock (Hendry 2012) is required. Relative measurement systems that monitor deformation relative to a moving railcar and estimate foundation system parameters based on these results (e.g. Norman 2004) would treat foundations such as this like an elastic foundation as they are not able to capture the irrecoverable portion of the deformation. This makes DIC an ideal tool for monitoring rail foundation systems over soils with a non-linear time varying response such as peat or clay. 56

66 Figure 3.10 shows the horizontal rail displacement for the two trains seen on the evening of December 4 th. These trains followed one after the other and the only difference was that the eastbound train was full while the westbound train was empty. Displacement (mm) Displacement (mm) a) b) Time (s) Time (s) Figure 3.10: Horizontal movement of the rail caused by a) a fully loaded freight train versus b) an unloaded freight train (positive displacement indicates movement to the East) As seen in Figure 3.10a, the full eastbound freight train caused horizontal rail displacements as high as 12.5 mm and caused a permanent horizontal rail displacement of 10.5 mm as the rail experienced some rebound after the train had passed. Figure 3.10b shows the total horizontal movement caused by the empty freight train was only 9.2 mm meaning during this monitoring period there was potentially a net horizontal displacement of 1.3 mm to the East (since the horizontal displacement was not measured between trains it is not possible to determine if part of this displacement was recovered during this time). If this rail continues to experience net horizontal movement to the East, it could be detrimental to the rails. If there is not a long transition zone over which large horizontal movements can be dissipated before a more restrained section of track, then stresses in the rails along with the risk of buckling will 57

67 increase and cause an increase in required maintenance and cost. In the future, monitoring will be undertaken at this site to explore rail displacements within the transition zone. 3.5 Application of beam on elastic foundation model Modeling of the foundation at the high quality subgrade site was undertaken using the infinite beam on elastic foundation model to determine if DIC could be used to quantify the system foundation parameters. Modeling was only conducted on the high quality subgrade site data and not on the peat subgrade data as the rail deformations in the latter case were not elastic and thus did not meet the requirements of the chosen model. As the locomotive dimensions and weight information were publically available and relatively consistent, only these values were used in calibrating the model and any passenger/freight cars included were then estimated based on response (see Appendix B for the locomotives observed and wheel load calculation). The speed of the locomotive was found using the images from the cameras as the position of the wheel with time could be tracked through the images. With this information defined, it could be input to the model to determine both the system stiffness and damping. The results of the model were then fitted to the measured vertical displacement using a trial and error approach to minimize the root mean squared (RMS) displacement error between the model and the experimental data. A range of possible combinations of Winkler spring constant and viscous damping coefficient within a realistic range of values was tried and at every stage the RMS error of the modeled vertical deflection to the observed vertical deflection was calculated. The combination of Winkler spring constant and viscous damping coefficient that led to the minimum error could then be selected. Figure 3.11 shows the RMS error plot when modeling the Camera 3 data against the model for the passenger train displacement data captured on June 18 th at 2:00 PM (see Table 3.1). 58

68 2000 RMS Error Viscous damping coefficient, c (N s/m 2 ) Winkler spring constant, k (kn/m 2 ) x Figure 3.11: RMS error plot of model versus real passenger train plot for Camera 3 From Figure 3.11, the RMS error for this particular passenger train is minimized with a Winkler spring constant of approximately kn/m 2 and a viscous damping coefficient between 1500 and 2000 N s/m 2. The same method can be used to estimate these parameters for freight trains. Figure 3.12 shows the RMS error of the model when compared to the Camera 3 vertical displacement data for the freight train that passed at 10:30 AM on June 19 th. 59

69 1600 RMS Error 0.5 Viscous damping coefficient, c (N s/m 2 ) Winkler spring constant, k (kn/m 2 ) x Figure 3.12: RMS vertical displacement error plot of model versus freight train data for Camera 3 As seen in Figure 3.12, the RMS error for the freight train data is minimized with a Winkler spring constant of approximately kn/m 2, corresponding well to that observed for the passenger train. It should be noted that due to the length of the freight trains observed and the uncertainty of the loads in each of the freight cars, only the locomotives (which have very well-defined parameters) and one or two freight cars were modeled. The viscous damping coefficient lies between 100 and 800 N s/m 2, which differs considerably from the damping coefficient calculated from the passenger train data (1500 and 2000 N s/m 2 ). This can be explained by the fact that damping is a function of speed and the passenger train is travelling at almost twice the speed of the freight train. 60

70 Figure 3.13 shows the measured and calculated vertical displacement of the passenger train with time plot for the train that passed on June 18 th at 2:00 PM. The parameters used for the model in this case were a Winkler spring constant of kn/m 2 and a viscous damping coefficient of 1700 N s/m Measured Calculated 0 Rail Deflection (mm) Time (s) Figure 3.13: Model and measured passenger train vertical displacement versus time Figure 3.13 illustrates that there is visually a very good match between the vertical displacement predicted by the model and the real displacement data as measured using DIC from Camera 3 data. The primary difference between the real data and the model occurs during the uplift between axles under both locomotive and passenger car loading. One potential reason for this disparity is that the rail is not firmly clamped to the tie, which is a basic assumption of the model used. Figure 3.14 shows the measured and calculated vertical displacement versus time of the freight train that passed on June 19 th at 10:30 AM. The parameters used in this case were a Winkler spring constant of kn/m 2 and a viscous damping coefficient of 100 N s/m 2. 61

71 1 0.5 Measured Calculated 0 Rail Deflection (mm) Time (s) Figure 3.14: Model and measured freight train vertical displacement versus time As seen in Figure 3.14, there is relatively good agreement between the calculated displacements and the displacements measured using DIC. Both Figures 3.13 and 3.14 suggest that the modeling parameters have been chosen correctly. The RMS analysis was used for every train in Table 3.1 for each of the four cameras and the results of these analyses can be seen in Table 3.3. A cell with n/a indicates that there were technical problems with the camera and displacement data was not available for that particular test. 62

72 Table 3.3: Foundation parameters at each camera location (k is in kn/m and c is in N s/m 2 ) Date Time Jun 18 2:00 PM Jun 18 2:20 PM Jun 18 2:50 PM Jun 19 9:30 AM Jun 19 10:30AM Jun 19 11:40AM Jun 19 12:30PM Jun 19 1:20 PM Jun 19 2:20 PM Jun 19 2:50 PM Type Direction Velocity (m/s) Location 1 Location 2 Location 3 Location 4 k c k c k c k c Passenger East , , , ,100 Passenger East , , , ,100 Passenger West , , , ,000 Passenger West ,250 n/a n/a 3.1 1,500 n/a n/a Freight West Passenger East , , ,700 n/a n/a Freight West Passenger West , , , ,100 Passenger East 33.2 n/a n/a n/a n/a 3.2 1, ,150 Passenger West , , , ,100 Mean 3.1 1,229* 2.9 1,192* 3.1 1,644* 2.0 1,092* Standard Deviation * * * * *Ignoring freight train results As seen in Table 3.3, the Winkler spring constants were relatively consistent for each of the locations when considering both passenger and freight trains, which indicates that DIC data can be used in conjunction with this spring model and an RMS error minimization approach to determine the local system stiffness. The viscous damping is more variable and seems to be more dependent on the speed of the train as passenger trains have much higher viscous damping values than freight trains. Overall, the consistency of the parameters found at each location can be seen by the mean and standard deviation values given for each monitoring location. The lower and upper bounds of the Winkler spring constant 63

73 over this section of track are kn/m 2 and kn/m 2, respectively. Esveld (1989) gives a range of Winkler spring constants for railway foundations with kn/m 2 being a poor foundation and kn/m 2 being a very good foundation. In this case the average Winkler spring constant for this section of track is somewhere between 2 and kn/m 2 which fits well within this range. 3.6 Conclusions The objectives of this chapter were to develop the experimental methodology to measure both horizontal and vertical displacements of rail systems founded on both good and poor subgrades using DIC, to investigate the factors that influence the magnitude of horizontal rail displacements, and to investigate whether a beam on elastic foundation model could be used to infer rail foundation system parameters. It was found that using DIC in conjunction with high speed cameras is a viable method to measure both horizontal and vertical displacements. In the case of the high quality subgrade site, the displacement had to be corrected for errors due to camera drift, which was a result of the small displacements measured and the small scale factor used due to the large distance between the camera and the rail. This correction did not have to be used at the peat subgrade site since the cameras were installed much closer to the rail creating a more favourable scale factor and the displacements being measured were larger. The peat subgrade data also highlighted the benefits of using an absolute displacement measurement system rather than a relative displacement measurement system as it was able to capture irrecoverable rail displacements in both the vertical and horizontal directions. The horizontal movement measured during the field monitoring was in many cases larger than the vertical displacements observed. The magnitude of horizontal displacement was dependent on the direction of travel, length and weight of the train as well as the previous trains on the rail. The horizontal displacement data could potentially be used in the future to estimate stresses in the rail. Finally, an infinite beam on elastic foundation model was used to model the vertical displacements due to train loading at the site with the good subgrade to determine the spring stiffness and 64

74 damping coefficient using a RMS displacement error minimization approach. The parameters were determined for multiple trains using four different camera views and although variability was seen between the results from each camera, the parameters determined for each train type and camera were in good agreement. This result indicates that for railway foundations, the foundation parameters must be bounded rather than trying to determine a specific foundation parameter due to the variable nature of railway foundations over even a short length of rail. 3.7 References Bowness, D., Lock, A.C., Powrie, W., Priest, J.A., & Richards, D.J Monitoring the dynamic displacements of railway track, Proc. IMechE, Part F: Journal of Rail and Rapid Transit, 221(F1): Chen, Y.H. and Huang, Y.H Dynamic stiffness of infinite Timoshenko beam on viscoelastic foundation in moving co-ordinate. International Journal for Numerical Methods in Engineering, 48:1 18. Esveld, C Modern railway track. Handel, H Analyzing the influences of camera warm-up effects on image acquisition, In Computer Vision ACCV 2007 (pp ), Springer Berlin Heidelberg. Hendry, M The geomechanical behaviour of peat foundations below rail-track structures. PhD dissertation, University of Saskatchewan. Kenney, J.T., Steady-state vibrations of beam on elastic foundation for moving load. Journal of Applied Mechanics, 21: Kerr, A.D Elastic and viscoelastic foundation models. Journal of Applied Mechanics, 31: Konrad, J.-M., Grenier, S., and Garnier, P Influence of Repeated Heavy Axle Loading on Peat Bearing Capacity. In 60th Canadian Geotechnical Conference. Ottawa, pp Lee, C., Take, W. A., & Hoult, N. A Optimum Accuracy of Two-Dimensional Strain Measurements Using Digital Image Correlation, Journal of Computing in Civil Engineering, 26(6): Luo, G., Chutatape, O., & Fang, H Experimental study on nonuniformity of line jitter in CCD images. Applied Optics, 40(26): Mallik, A.K., Chandra, S., and Singh, A.B Steady-state response of an elastically supported infinite beam to a moving load. Journal of Sound and Vibration, 291: Norman, C. D Measurement of track modulus from a moving railcar, Master s thesis, University of Nebraska. Pasternak, P.L On a new method of analysis of an elastic foundation by means of two foundation constants, Gosudarstvenrwe Izdatelslvo Literaturi po Stroitclstvu i Arkhitekture,Moscow, USSR, (in Russian). 65

75 Priest, J. A., Powrie, W., Yang, L., Grabe, P. J., & Clayton, C. R. I Measurements of transient ground movements below a ballasted railway line. Geotechnique, 60(9): Rasmussen, S., Krarup, J. A., & Hildebrand, G Non-contact deflection measurement at high speed. In 6th International Conference on the Bearing Capacity of Roads, Railways and Airfields. Sussmann, T. R Track Geometry and Deflection from Unsprung Mass Acceleration Data. In Proceedings from Railway Engineering Conference, London. Timoshenko, S.P., History of strength of materials, McGraw-Hill, New York. Thompson, W.E Analysis of dynamic behavior of roads subject to longitudinally moving loads. Highway Research Record, 39:1 24. Winkler, E., Die Lehre von der Elasticitaet und Festigkeit. Prag, Dominicus. White, D. J., Take, W. A., & Bolton, M. D Soil deformation measurement using particle image velocimetry (PIV) and photogrammetry. Geotechnique, 53(7):

76 Chapter 4 Field Monitoring of a Reinforced Concrete Bridge using Digital Image Correlation 4.1 Introduction A large proportion of bridges are coming to the end of their design service lives in North America and many other areas. It is neither practical, nor feasible, to replace all of these bridges at once and therefore tools are required to help determine which bridges have adequate capacity to remain in service and which ones require retrofit or replacement. Structural health monitoring is one such tool that can be used in the assessment of aging infrastructure to help determine when bridges need to be either repaired or replaced. Bridge inspections play a key role in the assessment process. However, bridge inspections are also subjective and rely on the skills and experience of the individual inspector as well as mainly qualitative measurements. A recent study of bridge inspection done by Phares et al. (2004) showed that there was significant variability depending on the inspector and demonstrated how unreliable bridge inspections can be. What is needed is a cost effective means of gathering quantitative bridge data to supplement bridge inspection data and support bridge assessment. The main measurements of interest when performing a bridge assessment are the bridge deflections and strains at critical locations, which can reveal if the bridge is in the linear elastic range of the load-displacement curve as well as any unexpected behaviour. By measuring the bridge deflections at critical locations, an understanding of the as-built support conditions of the bridge as well as the response to loading can be developed. Currently there are a number of sensors available for monitoring bridge performance, including linear potentiometers (LPs), strain gauges, and fiber optics. LPs are very common in both laboratory and field monitoring applications for measuring displacements. However, one of the problems with using LPs in the field is that they must be placed in contact with the structure and mounted on a fixed reference 67

77 point. This can be difficult with bridges built over water or treacherous terrain. LPs also have to be wired into a data acquisition system, which requires extensive and expensive cabling to be run. Finally, LPs only provide a single measurement location and as such have a high cost per reading (including both the cost of the sensor, ~$250, and the cost of the data logger, ~$15,000) that precludes their use on many bridges where there is a limited budget for monitoring. Strain gauges, either electrical resistance or vibrating wire, are the most commonly used strain sensors for field monitoring. However, they too have several disadvantages including the need for cabling, the cost and time associated with installation, the need to be bonded to the substrate material, the influence of cracks on the readings and the lack of correlation with reinforcement strains. An alternative to using discrete strain gauges for bridge monitoring is to use a fibre optic system to monitor strains. Unlike strain gauges these systems give continuous strain data along the length of the fibre which must be installed on the bridge in the areas of interest (Regier 2013). Because these systems measure strain data along the full length of a beam, curvatures, and thus deflections, can also be calculated from the strain data if the fibres are placed at two different heights on a section (Regier 2013). However, like LPs and strain gauges, these are contact sensors and the installation of these fibres can be an intensive and expensive process. Digital image correlation, which uses digital images to measure displacement and strain fields, is an alternative method that can be used for bridge monitoring in the field that overcomes many of the disadvantages of conventional sensors because it is potentially much cheaper to operate, is non-contact and has the potential to offer much more data such as vertical and horizontal displacements, strain (Pan et al. 2009; Dutton et al. 2013) and crack width (Corr et al. 2007; Dutton 2012) which could all be measured with a single camera depending on the field of view. One of the challenges of using technologies such as DIC is that their accuracy can be affected by apparent camera movements. These movements can be placed into two distinct groups: jitter and drift. Jitter is very small, non-uniform translations of the whole image occurring at a much higher frequency than camera drift and depends on 68

78 the frame rate of the camera, camera shake, the quality of the camera and the fact that a camera will not take exactly the same picture twice (Luo 2001). Drift, on the other hand, occurs over a longer period of time and can be a result of the heating of the charge-coupled device (CCD) during recording (Handel 2007). DIC was first used in the early 1980s (Sutton et al. 1983) and there are many programs that employ this technique to track displacements. The principle of DIC is to measure the displacement of regions of interest, also known as patches or subsets, between an initial image of the undeformed object and subsequent images taken as loading / deformation is applied to the object. If an image of the initial state of an object, referred to as the reference image, is compared to all subsequent images of the object experiencing movement, a complete time history of the deformation can be developed. DIC has been used in the past for static displacement (e.g. Chu et al. 1985; White et al. 2003) and strain (e.g. Wattrisse et al. 2001; Hoult et al. 2013) in various fields of research and some work has already been done to monitor bridge deflections using DIC (e.g. Lee & Shinozuka 2006; Yoneyama et al. 2007). In this research a program called GeoPIV that was originally developed by White et al. (2003) for geotechnical testing was used to measure the response of a stiff reinforced concrete bridge during both static and dynamic load tests. Since the load test was done on a very stiff bridge, the program must be able to record very small displacements. GeoPIV initially measured displacement with an accuracy of 0.1 pixels (White et al. 2003) but with recent improvements in the sub-pixel interpolation scheme the accuracy has been increased to approximately pixels (Lee et al. 2011). When cameras and their associated errors are introduced into the equation, a more achievable accuracy that was achieved during the laboratory testing reported in Chapter 2 is approximately 0.01 pixels. The objectives of this research are to: (i) explore techniques to optimize the displacement measurement accuracy of the DIC technique when used for monitoring of a bridge during static and dynamic tests, (ii) to demonstrate the achievable accuracy of DIC measurements with LPs for both static and dynamic measurements, and (iii) to use these measurements to assess the performance of the bridge. 69

79 In the following sections the bridge test site will be introduced along with potential techniques for improving the measurement accuracy of the DIC technique. Then the DIC results from the static and dynamic load tests are compared to conventional sensors and the measurements are used to assess the performance of the bridge under both static and dynamic loading. Finally, conclusions are made based on the findings presented. 4.2 The Black River bridge The Black River bridge is located on the Trans-Canada Highway just North of Tweed, Ontario, Canada (44 32'22.34"N, 77 22'10.34"W). The bridge is a simply supported two span reinforced concrete structure that is approximately 32 metres long (16 m per span). The cast-in-place slab on beam reinforced concrete bridge was originally constructed in In 1978 new barrier walls were installed on both sides of the bridge. Figure 4.1 shows a photograph of the Black River bridge while Figure 4.2 shows a cross section schmatic. 70

80 Figure 4.1: Photograph of the Black River bridge from the south Figure 4.2: Cross section of the Black River bridge (Regier 2013) 71

81 4.3 Instrumentation Based on the layout of the Black River bridge and site access restrictions it was decided that only the western span of the bridge could be monitored. Since only half of this span was over dry land, and thus accessible for the installation of instrumentation, all monitoring was carried out on the western half of the western span of the bridge. As such the monitoring was focused on Beam 2 (see Figure 4.2). Figure 4.3 shows the layout of the instrumentation on Beam 2. Figure 4.3: Instrumentation layout for Beam 2 (modified from Regier 2013) As shown in Figure 4.3, four evenly spaced LPs were used to monitor the deflected shape of the beam for all load tests performed. A wooden stud wall (as seen in Figure 4.4) was constructed under Beam 2 to provide a fixed location to which the LPs could be attached. In addition to the four LPs used, cameras were used at two locations (quarter-span and mid-span) to monitor deflections. A second stud wall was constructed between Beam 1 and Beam 2 to mount the cameras on as well as to brace the two stud walls together to prevent movement of the frame. A cross section of these stud walls can be seen in Figure

82 Figure 4.4: A cross section of the stud walls used to mount the cameras and targets at quarter-span and mid-span (modified from Regier 2013) Foam blocks that were mm with a spray paint speckle pattern, referred to as targets, were epoxied to the bridge along the centerline of Beam 2 at the quarter-span and mid-span as well as on top of the stud wall supporting the LPs at the same points to give a fixed reference target to correct for camera errors as discussed later. Two different cameras were used at each location to provide redundancy of measurement for the static tests: an 18 megapixel (MP) Cannon t2i digital single-lens reflex (DSLR) camera with a 55 mm lens and an Allied Vision Technologies (AVT) GX bit monochrome 1MP high speed camera with an 85 mm lens. The cameras were mounted next to one another so that each one had both targets in the field of view (as seen in Figure 4.5 for the DSLR) and still remained level and planar to the targets. Since the main objective of this case study was to determine how accurately bridge deflections could be monitored in the field, the effect of camera angle was not explored in this study. 73

83 Figure 4.5: Field of view of DSLR camera at the mid-span of the bridge As shown in Figure 4.5, both the textured foam block targets can be seen in the field of view as well as a scale in millimetres so that the scale factor (which allows the measurements from GeoPIV in pixels to be converted into physical measurements in millimetres) could be determined. Due to space limitations on the underside of the beam, the targets and the LPs are not positioned at exactly the same location, which affected the measurements as will be discussed later in the results section. 74

84 4.4 Bridge Loading Static Load Tests The first four load tests performed on the bridge were static load tests that were done in stages (0 through 4) with each stage representing an increasing amount of load on the bridge. A Western Star load truck was used so that the load level could be increased by adding concrete blocks to the trailer. The axle spacing for the Western Star load truck can be found in Figure 4.6. Figure 4.6: Western Star load truck dimensions (Regier 2013) The axle loads for the western Star load truck based on the number of blocks loaded on the trailer are given in Table 4.1 (the axles are numbered in order from the front of the truck towards the rear). The blocks were loaded in 12 block groups to give a total of four load stages for the test. Table 4.1: Axle loading of the Western Star load truck for each load stage Stage Blocks Axle 1 (kn) Axle 2 (kn) Axle 3 (kn) Axle 4 (kn) Axle 5 (kn) Total Load (kn) The load truck followed a running lane where it was centred over Beam 2 as seen in Figure 4.7. The truck travelled from west to east across the bridge. 75

85 Figure 4.7: Cross section of the bridge showing the position of the load truck (Regier 2013) In order to permit static measurements to be taken, the load truck was stopped at predetermined locations along the bridge referred to as load steps that are illustrated in Figure 4.8. By taking measurements at each load step, the displacement behaviour leading up to the maximum displacement as well as the maximum displacement could be observed. Figure 4.8: Load steps from Southern elevation view (modified from Regier 2013) As shown in Figure 4.8, there were eight load steps with zero load readings being taken immediately before the truck drove onto the bridge and immediately after the truck drove off the bridge. The load steps were set based on the front wheel position of the truck with load step 1 occurring when its front wheels were at mid-span of Beam 2 and moving in 2 metre increments forward for each subsequent step. Figure 4.9 shows a picture of the load truck taken during the 36 block static load test and the tent with the data acquisition equipment can also be seen just beside the bridge and adjacent to the Black River. 76

86 Figure 4.9: Western Star load truck during the 36 block static load test Dynamic Load Tests In addition to the static load tests, three dynamic load tests were undertaken to compare the static and dynamic response of the bridge and the sensors. For the dynamic tests, the 24 block load configuration was used as that is equivalent to the legal load limit on most Ontario roads. Three load tests were performed with the truck traveling in the eastbound direction to compare to the static load tests. The first test was performed at a truck speed of 60 km/h while the next two were performed at speeds of 80 km/h. These speeds were chosen to explore the effects of different speeds on the bridge response as well as the repeatability of the measurements. 4.5 Image Processing To optimize the accuracy of the displacement measurements, two image processing measures were used to compensate for camera jitter and drift. The first strategy was to use fixed reference points 77

87 that did not move that could be seen in the field of view of all the cameras. The textured foam blocks that were mounted to the wood stud wall were used as these fixed reference points. Since both camera jitter and drift would affect the position of the patches on the foam blocks on the bridge and the stud wall by the same amount, the displacement of the bridge could be calculated as the differential movement between the two blocks. The uncorrected deflection data versus image number can be seen in Figure 4.10a while the corrected deflection data can be seen in Figure 4.10b Top Patches Bottom Patches 0.9 a) b) Deflection (mm) Deflection (mm) Image Number Image Number Figure 4.10: Mid-span deflection during the 24 block static load test: a) raw deflection measurements, b) corrected deflection measurements after subtracting the fixed reference point displacement As can be seen from Figure 4.10, after correcting the deflection using the fixed reference point method the data for each load step becomes much more precise as the effect of camera movement is significantly reduced. All eight load steps can be distinctly seen along with the two reference load steps at the beginning and end of the test when no live load was applied to the bridge. 78

88 An alternate strategy to correct for camera movement is to use averaged images to calculate the displacements, a strategy that was first introduced by Sutton et al. (1988). The averaging process involved using the 10 images taken during each load stage and averaging the pixel intensity values together to form a single image which could then be analyzed using DIC. This method is known to reduce camera jitter as it reduces the digitization errors associated with CCD cameras by redundancy of measurement (Vendroux & Knauss 1998) but is less effective at reducing errors due to camera drift, which could be an issue since each static load test took about 15 minutes to carry out. The averaging technique was employed and the uncorrected deflection data can be seen in Figure 4.11a while the averaged image deflection data can be seen in Figure 4.11b a) b) Deflection (mm) Deflection (mm) Image Number Load Stage Figure 4.11: Midspan deflection during the 24 block static load test: a) uncorrected data and b) averaged data As seen in Figure 4.11, the corrected data does little to counteract camera drift as evidenced by the fact that the averaged image deflection data does not return to zero following the test. 79

89 After testing both potential methods it was decided to subtract the fixed reference displacements from each image in the test and then average all of the images for each load step together to give one value. The fixed reference subtraction approach would account for any drift and most of the jitter while averaging the deflections from each image in the load step would further reduce the effects of jitter and other potential camera errors. The static displacement data will be adjusted using this procedure. The dynamic displacement data will only be adjusted using the fixed reference point approach, however since the duration of these tests was only a few seconds it is unlikely that camera drift would be a significant issue. 4.6 Static Load Test Results A comparison of the DIC and LP deflections measured at midspan for each step of the 12 block load stage can be seen in Figure 4.12 for the DSLR camera in a) and the high speed camera in b). 0.5 a) b) DIC LP 0.5 DIC LP Deflection (mm) Deflection (mm) Load Step Load Step Figure 4.12: Deflection comparison for the static 12 Block load stage: a) Cannon t2i DSLR versus LP and b) AVT GX1050 high speed camera versus LP 80

90 As seen in Figure 4.12, there is good agreement between the midspan LP and both midspan cameras. Both cameras measure almost exactly the same displacement after applying the image corrections. Even though there is a slight difference between the cameras and the LP meaurements, the RMS error of the Cannon t2i DSLR to the LP measurement is mm while the RMS error of the AVT GX1050 to the LP measurement is mm, which is close to the accuracy of most displacement transducers. A potential reason for the difference in DIC and LP measurements is the difference in camera target location versus the location of the LP, which can be seen in Figure 4.5. The LP was exactly at the midspan of the beam while the cameras and target had to be shifted to the west by 60 mm so that the camera could look directly at the target and not be partially blocked by the LP. A separate analysis of fibre optic data from this load test indicated that in fact the point of maximum displacement was to the west of the midspan of the bridge (Regier 2013). This would suggest that the DIC measurements should be higher than the LP measurements, as was seen to be the case. Figure 4.13 presents a comparison of the LP measurements with the a) DSLR and b) high speed camera displacement measurements for the 24 block load stage. 81

91 DIC LP 0.8 a) b) 0.7 DIC LP Deflection (mm) Deflection (mm) Load Step Load Step Figure 4.13: Deflection comparison for the static 24 Block load stage: a) the Cannon t2i DSLR versus LP and b) AVT GX1050 high speed camera versus LP As seen in Figure 4.13, there is once again good agreement between the midspan LP and both midspan cameras. For this load stage the RMS error of the Cannon t2i DSLR to the LP is mm while the error of the AVT GX1050 to the LP is only mm. This displacement data can be used to aid in assessing the bridge behaviour by determining whether the bridge response remains linear elastic over the full loading range. The deflection versus load step is plotted for each of the load stages in Figure 4.14a. Figure 4.14b shows the deflection versus load stage for a variety of different steps. 82

92 Blocks 12 Blocks 24 Blocks 36 Blocks 0.7 a) b) Step 2 Step 4 Step 6 Deflection (mm) Deflection (mm) Load Step Load Level (# of Blocks) Figure 4.14: a) The DIC deflections for each load stage at all load steps; b) The deflection versus load level behaviour As seen in Figure 4.14a, the deflection of the bridge increases in increments as the load increases. The load stage 1 deflection behaviour is noticeably different than the other three stages. This is due to the fact that the load distribution of the empty load truck is different than the other load stages (see Table 4.1). Figure 4.14b shows just the increase in deflection caused by the load blocks; the effect of the truck itself (the 0 block load stage) has been subtracted from the data because of the difference in axle load distribution. The resulting relationships are shown for load steps 2, 4 and 6. One can see that in each case the relationship is almost completely linear although there are subtle variations due to the change in load distribution on the truck axles as more blocks are added. This linear response to loading suggests that the bridge is still in good condition and can handle more than the 36 block load truck. 83

93 4.7 Dynamic Load Test Results Along with the static tests, three dynamic tests were performed to investigate whether there is any difference in the dynamic bridge displacement behaviour versus the static bridge displacement behaviour. By comparing the dynamic DIC measurements to the LP measurements, the accuracy of the DIC system could be evaluated. Additionally, by comparing the static and dynamic measurements the response of the Black River bridge, could be assessed. As noted earlier, all dynamic tests were performed using the 24 block Western Star load truck configuration as this represented the legal load limit allowed on Ontario highways. Figure 4.15 shows a comparison between the midspan deflection measured using DIC with an AVT GX1050 high speed camera at 100 fps to the midspan deflection measured using a LP that was being logged at 200 Hz. 0.8 Subtracted Patches LP 0.6 Deflection (mm) Time (sec) Figure 4.15: DIC versus LP deflection measurements with time for a dynamic test at 80 km/h. As seen in Figure 4.15, both the DIC and the LP displacement measurements are in good agreement. The DIC measurements are once again slightly higher than the LP measurements due to the 84

94 difference in sensor location. Both displacement sensors also measure a small upward deflection of the beam at midspan after the truck has moved on to the eastern span of the bridge. This is believed to be a result of rotational connectivity between the two spans of the bridge that causes this span to go up when the other one deflects down. This result suggests that the two spans of the bridge are not simply supported as assumed, which would impact the results of any numerical modeling done as part of a bridge assessment. A comparison of the deflection versus truck position for the three 24 block dynamic tests and the 24 block static test can be seen in Figure Dynamic1 Dynamic2 Dynamic3 Static Deflection (mm) Truck Location (m) Figure 4.16: A comparison of midspan deflections with truck location for both static and dynamic tests As seen in Figure 4.16, there is very good visual agreement between the static and dynamic load tests when plotted against truck location, which implies that for this bridge there is little to no difference between the static and dynamic response (i.e. the impact factor would be unity). In this case, simply performing a dynamic test would have yielded the same deflection results as the static test and reduced 85

95 the amount of time that the bridge had to be closed to traffic from about 15 minutes per static test to approximately 30 seconds per dynamic test. Another advantage of the dynamic tests over the static tests is that they give a continuous deflection with truck location response while the static tests only give the deflection response at discrete truck locations that have to be chosen carefully due to the time constraints involved with closing a bridge on a major highway. A closer examination of the dynamic deflection results shows subtle differences in the bridge response. For instance the first dynamic test (Dynamic 1) has a slightly different profile than the other two dynamic tests (Dynamic 2 and 3) which appear to be very similar. This can be explained by the difference in load truck speeds between these tests. The load truck in the first dynamic test was traveling at 60 km/h while the load truck was traveling at 80 km/h for the other two dynamic tests. The displacement data from the slower dynamic test shows better agreement with the static displacement data, which seems reasonable since the dynamic effects would be reduced with lower speed. It can also be seen from the data from dynamic load tests two and three that the results of the load tests were repeatable as both the deflection curves are nearly identical. 4.8 Conclusions A case study of a reinforced concrete bridge load test has been presented in which digital image correlation was used for monitoring deflections caused by both static and dynamic loads. To mitigate the effects of errors caused by camera jitter and drift, two potential methods were explored: (i) the use of a fixed reference point and (ii) generating composite images using average pixel intensity values from multiple images for each load step. After evaluating the results of both methods, it was found that using a fixed reference point can account for both camera jitter and drift, which made it the optimal choice in this case study. After the displacement results were corrected, it was shown that both the Cannon t2i DSLR and the AVT GX1050 high speed cameras could achieve accuracy equivalent to LPs during static testing. The 86

96 static displacement results were then used to determine the bridge response to increasing load and that response was found to be linear. It was also shown that the high speed cameras recording at 100 fps could provide accuracy equivalent to the LPs. For this particular bridge, the dynamic and static responses were found to be very similar. There were however subtle variations in the displacement response depending on the speed at which the loading truck was moving. Based on the findings presented in this chapter it can be concluded that DIC can be used as an effective tool for bridge assessment. This is of significant importance as in most cases cameras are much easier to set up than more traditional contact sensors such as LPs and can provide data that is of comparable accuracy. It may not be possible in all cases to set up the cameras so that they are in the same horizontal plane as the bridge beam. However, in this case study the effect of camera angle was not explored as the goal was to determine how accurately bridge deflections could be monitored in the field. It would be worthwhile to explore the effect of camera angle in the future as it would make it possible to use DIC in many more field monitoring applications. 4.9 References Chu, T. C., Ranson, W. F., & Sutton, M. A Applications of digital-image-correlation techniques to experimental mechanics. Experimental mechanics, 25(3): Corr, D., Accardi, M., Graham-Brady, L., & Shah, S Digital image correlation analysis of interfacial debonding properties and fracture behavior in concrete. Engineering Fracture Mechanics, 74(1): Dutton, M Digital image correlation for evaluating structural engineering materials. M.A.Sc. thesis, Queen s University. Dutton, M., Take, W. A., & Hoult, N. A Curvature Monitoring of Beams using Digital Image Correlation. Journal of Bridge Engineering, in press. Handel, H Analyzing the influences of camera warm-up effects on image acquisition, In Computer Vision ACCV 2007 (pp ), Springer Berlin Heidelberg. Hoult, N. A., Andy Take, W., Lee, C., & Dutton, M Experimental accuracy of two dimensional strain measurements using Digital Image Correlation. Engineering Structures, 46:

97 Lee, C., Take, W. A., & Hoult, N. A Optimum Accuracy of Two-Dimensional Strain Measurements Using Digital Image Correlation, Journal of Computing in Civil Engineering, 26(6): Lee, J. J., & Shinozuka, M Real-time displacement measurement of a flexible bridge using digital image processing techniques. Experimental mechanics, 46(1): Luo, G., Chutatape, O., & Fang, H Experimental study on nonuniformity of line jitter in CCD images. Applied Optics, 40(26): Pan, B., Qian, K., Xie, H., & Asundi, A Two-dimensional digital image correlation for in-plane displacement and strain measurement: a review. Measurement science and technology, 20(6): Phares, B. M., Washer, G. A., Rolander, D. D., Graybeal, B. A., & Moore, M Routine highway bridge inspection condition documentation accuracy and reliability. Journal of Bridge Engineering, 9(4): Regier, R Application of fibre optics on reinforced concrete structures to develop a structural health monitoring technique. M.A.Sc. thesis, Queen s University. Sutton, M. A., Wolters, W. J., Peters, W. H., Ranson, W. F., and McNeill, S. F Determination of displacements using an improved digital correlation method. Image and Vision Computing, 1(3): Sutton, M. A., McNeill, S. R., Jang, J., & Babai, M Effects of subpixel image restoration on digital correlation error estimates. Optical Engineering, 27(10): Vendroux, G., & Knauss, W. G Submicron deformation field measurements: Part 2. Improved digital image correlation. Experimental Mechanics, 38(2): Wattrisse, B., Chrysochoos, A., Muracciole, J. M., & Némoz-Gaillard, M Analysis of strain localization during tensile tests by digital image correlation. Experimental Mechanics, 41(1): White, D. J., Take, W. A., & Bolton, M. D Soil deformation measurement using particle image velocimetry (PIV) and photogrammetry. Geotechnique, 53(7): Yoneyama, S., Kitagawa, A., Iwata, S., Tani, K., & Kikuta, H Bridge deflection measurement using digital image correlation. Experimental Techniques, 31(1):

98 Chapter 5 Summary and Conclusions 5.1 Summary of Research In this thesis, the accuracy of digital image correlation (DIC) was first optimized by quantifying and mitigating the effects of several sources of error through the use of computer generated image sequences. The technique was then verified using laboratory experiments on a simply supported beam. DIC was then used in the field monitoring of railway tracks on both good and poor subgrades as a way of monitoring both vertical and horizontal rail displacements resulting from train loading. It was also used and compared to conventional monitoring techniques in both static and dynamic load tests of a very stiff reinforced concrete bridge. The key conclusions of this research project are: 1. Three sources of error of particular relevance to dynamic measurement using DIC were identified as (i) bias error in the sub-pixel interpolation scheme, (ii) the ratio of sample rate to the frequency of the signal being monitoring and (iii) the signal to noise ratio. 2. The DIC sub-pixel interpolation scheme used greatly affects the accuracy of dynamic measurements especially if differentiation of the displacement measurements is required (i.e. to get velocities and accelerations). 3. A sample rate of between 25 and 50 times the target frequency can minimize the errors associated with both under-sampling and over-sampling. 4. Angles of less than 30 do not influence the accuracy of dynamic displacement measurements as long as the scale factor is taken in the plane of interest and all movement occurs in that plane. 89

99 5. Using DIC in conjunction with high speed cameras is a viable method to measure both horizontal and vertical railway displacements at sites with good and poor subgrade conditions. 6. Site specific corrections must be made, in some cases, to correct the displacement measurements for the effects of camera errors, which can result from a low signal to noise ratio. 7. There is a significant benefit to using an absolute displacement measurement system rather than a relative displacement measurement system as it can capture irrecoverable rail displacements in both the vertical and horizontal directions. 8. The residual horizontal rail movement was potentially significant for one of the field monitoring sites suggesting that systems that do not monitor these displacements are missing critical behaviour. The magnitude of horizontal displacement was dependent on the direction of travel, length and weight of the train as well as the previous trains on the rail. 9. An infinite beam on elastic foundation model using a RMS displacement error minimization approach gave good agreement for vertical displacement with consistent stiffness and damping coefficients for the site with good subgrade. However, there were differences between the values obtained at different locations along the rail, which highlighted the need to bound foundation parameters rather than attempting to calculate a single value due to the variable nature of railway foundations over even a short length of rail. 10. When using DIC for monitoring, corrections for camera jitter and drift may have to be made in order to acquire the best results possible depending on the signal to noise ratio. 11. Two potential camera error correction methods that were explored were the use of a fixed reference point and generating composite images using average pixel intensity values from multiple images for each load step. After evaluating both methods it was found that using a 90

100 fixed reference point can account for both camera jitter and drift, which made it the optimal choice for bridge monitoring. 12. It was shown that both the Cannon t2i DSLR and the AVT GX1050 high speed cameras had accuracy equivalent to LPs during static testing. The AVT GX1050 high speed cameras recording at 100 fps could provide accuracy equivalent to the LPs during dynamic tests. 13. DIC can be used as an effective tool for bridge assessment providing information about the bridge response with increasing load as well as variable vehicle speed. This is important since in most cases cameras are easier to set up than conventional contact sensors and can provide data that is of comparable accuracy. 5.2 Future Work The work conducted in this thesis generated several opportunities for future work which were outside of the original scope of the project including: 1. The measurement of horizontal rail displacements using DIC for a series of trains could be used to estimate the residual horizontal stresses in the rail resulting from train loading. 2. The findings of this thesis indicate that for railway foundations, the foundation parameters must be bounded rather than trying to determine a specific foundation parameter due to the variable nature of railway foundations over even a short length of rail. This should be confirmed by carrying out monitoring at more sites with variable foundation conditions. 3. When monitoring trains over poor subgrade conditions it was seen that there was an apparent irrecoverable deformation immediately after train loading. Since the magnitude of this was not fully understood at the time of monitoring the cameras were stopped early and in the future should continue to be monitored to see how long it takes for the foundation to recover (if ever). 4. In the bridge monitoring case study, the effect of camera angle was not explored as the goal was to determine how accurately bridge deflections could be monitored in the field. It would 91

101 be worthwhile to explore the effect of camera angle in the field to verify the DIC technique can be used for bridges of varying height. This would make it possible to confidently use DIC in many more field monitoring applications. 92

102 Appendix A The Solution of the Infinite Beam on Elastic Foundation Model The infinite Euler-Bernoulli beam acting on the viscoelastic Pasternak foundation partial differential equation under a single concentrated load moving at a constant velocity is introduced in Chapter 3 and can be written as: [A.1] The characteristic equation for Equation [A.1] with a moving coordinate system where the coordinate of the beam moves with the load is: [A.2] where 2 [A.3a] [A.3b] 2 [A.3c] [A.3d] If 2 2, Equation [A.2] has four roots as below: [A.4a] [A.4b] [A.4c] 93

103 [A.4d] where p, q, and r are real positive numbers. The solutions for Equation [A.1] with 2 2 are provided as (for the under-damped case):, [A.5] where [A.6a] [A.6b] [A.6c] If 2 2, the four roots of Equation [A.2] are: [A.7a] [A.7b] [A.7c] [A.7d] where r and s are real positive numbers. The solutions for Equation [A.1] with 2 2 are provided as (for the over-damped case):, [A.8] where 94

104 2 [A.9a] [A.9b] 1 [A.9c] 1 [A.9d] By considering only a single location (i.e the monitoring location) the rule of superposition can be used to determine the total deflection at that location resulting from all concentrated wheel loads of a train provided the wheel spacing, train speed and train weight are known. For the rail modeling undertaken in this work the following parameters were used to define the foundation system in order to solve for k and c: / (modulus of elasticity of the rail) (second moment of area of the rail) 0.20 (soil shear parameter with units of N) If three dimensional results are desired the following parameters can be used although in this research plane strain was assumed and only one rail was monitored: 1,435 (separation of the rails from one another) 2,590 (centered below the rails) 95

105 Appendix B The Calculation of Wheel Loads for Observed Locomotives In order to perform foundation modeling in Chapter 3 using the infinite beam on elastic foundation model the wheel loads are required. The calculations for each of the observed locomotives are presented in this section. B.1 GE Transportation Systems P42DC Passenger Locomotive All passenger trains observed were powered by GE Transportation Systems P42DC dieselelectric locomotives similar to the one seen in Figure B.1. All specifications for this locomotive were taken directly from the VIA rail website. Figure B.1: GE Transportation Systems P42DC passenger locomotive ( The load per wheel can be calculated for this locomotive as follows assuming an even weight distribution and neglects variations caused by the weight of fuel onboard: 121, , , ,475 15, ,

106 B.2 GM Electro-Motive Division SD70M-2 Freight Locomotive All freight trains observed were powered by GM Electro-Motive Division SD70M-2 dieselelectric locomotives similar to the one seen in Figure B.2. All specifications for this locomotive were taken directly from Wikipedia. Figure B.2: GM Electro-Motive Division SD70M-2 freight locomotive ( The load per wheel can be calculated for this locomotive as follows assuming an even weight distribution and neglects variations caused by the weight of fuel onboard: 185, , , ,850 15,425 15,