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Nondestructive Evaluation of Riprap Rocks


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NONDESTRUCTIVE EVALUATION OF RIPRAP ROCKS By CHRISTIAN BASSOLI DE CARVALHO A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLOR IDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2004

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Copyright 2004 by Christian Bassoli de Carvalho

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I dedicate this document to my mother w hose endless support and faith through all the years never ended while I work ed to achieve this goal.

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ACKNOWLEDGMENTS I would like to express my sincere gratitude and appreciation to many people who made this masters thesis possible. Special thanks go to Dr. Christopher Niezrecki for his guidance and support throughout my research. I would like to thank Drs. John Schueller and Bjorn Birgisson for serving on my committee. Many thanks are due to my mother for her support throughout all the years I have studied. I would also like to thank my lab mates for their guidance. Many more other persons participated to ensure my research succeeded and to all those persons I am very thankful. iv

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TABLE OF CONTENTS page ACKNOWLEDGMENTS .................................................................................................iv LIST OF TABLES............................................................................................................vii LIST OF FIGURES .........................................................................................................viii ABSTRACT .....................................................................................................................xiv CHAPTER 1 NON-DESTRUCTIVE EVALUATION METHODS......................................................1 1.1 Modal Analysis.......................................................................................................1 1.1.1 Modal Analysis on Rocks.............................................................................2 1.1.2 Modal Analysis on Fruits.............................................................................5 1.2 Nonlinear Elastic Wave Spectroscopy....................................................................8 1.2.1 Nonlinear Wave Modulation Spectroscopy..................................................8 1.2.2 Single-Mode Nonlinear Resonance Acoustic Spectroscopy......................10 1.2.3 Nonlinear Resonant Ultrasound Spectroscopy...........................................15 1.2.4 Simple Mode Nonlinear Resonant Ultrasound Spectroscopy....................16 1.3 Impedance-Based Analysis...................................................................................16 1.4 Impact-Echo Analysis...........................................................................................21 1.5 Other Non-destructive Evaluation Methods.........................................................24 2 STANDARD TEST METHOD FOR SOUNDNESS OF AGGREGATE BY USE OF SODIUM SULFATE..................................................................................................25 2.1 Sodium Sulfate Solution.......................................................................................25 2.2 Samples.................................................................................................................26 2.3 Test Sample Preparation.......................................................................................28 2.4 Testing Procedure.................................................................................................28 2.5 Quantitative Sample Examination........................................................................29 3 EXPERIMENTAL SETUP.............................................................................................30 3.1 Modal Analysis Experimental Setup....................................................................30 3.1.1 Modal Analysis Instrumentations...............................................................30 3.1.2 Modal Analysis Equipment and System Analyzer Setup...........................31 v

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3.1.3 Testing Procedure.......................................................................................33 3.2 Acoustic Experimental Setup...............................................................................34 3.2.1 Instrumentation...........................................................................................34 3.2.2 Acoustic Equipment and System Analyzer Setup......................................35 3.2.3 Testing Procedure.......................................................................................37 3.3 Calibration............................................................................................................37 4 RESULTS.......................................................................................................................39 4.1 Modal Analysis.....................................................................................................39 4.1.1 Comparison of Averaged Data...................................................................44 4.2 Acoustic Experiment............................................................................................47 4.2.1 Impact Hammer..........................................................................................47 4.2.2 Sound Pressure Level Results....................................................................47 4.2.3 Data Averaging Approach..........................................................................49 4.2.4 Comparison of Averaged Sound Pressure Level........................................50 5 SUMMARY AND CONCLUSIONS.............................................................................52 5.1 Summary of Results..............................................................................................52 5.2 Conclusions...........................................................................................................53 5.3 Future Work..........................................................................................................53 APPENDIX A MODAL ANALYSIS TRANSFER FUNCTIONS & COHERENCES........................55 B SOUND PRESSURE LEVEL PLOTS..........................................................................78 LIST OF REFERENCES...................................................................................................86 BIOGRAPHICAL SKETCH.............................................................................................89 vi

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LIST OF TABLES Table page 1.1 Modal frequencies as defects were introduced..............................................................4 2.1 Sieve sizes used for fine aggregate samples................................................................27 2.2 Sieve sizes and required masses for coarse aggregate samples..................................27 4.1 Rock samples mass and first resonant frequency.......................................................43 vii

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LIST OF FIGURES Figure page 1.1 Rock used to conduct modal analysis experiment.........................................................2 1.2 Grid showing hammer impact points.............................................................................3 1.3 Instrumentation and setup..............................................................................................3 1.4 Elastic cords used to suspend the melon........................................................................6 1.5 FRF curve and coherence obtained from the melon......................................................7 1.6 Schematic overview of the dynamic response for a one-dimensional wave propagation.................................................................................................................8 1.7 Experiment schematic....................................................................................................9 1.8. Wave modulation spectra of uncracked and cracked Plexiglas....................................9 1.9 Sandstone wave modulation spectra............................................................................10 1.10 Experimental setup for SIMONRAS experiments.....................................................11 1.11 SIMONRAS results. Intact (left) and micro damaged (right) slate beam. Fundamental accelerations are shown for ten drive voltage levels..........................12 1.12 Cyclic fatigue loading experiment: a) relative resonance frequency shift as a function of the measured peak acceleration amplitude at different stages of the fatigue process; b) amplitude dependence of the third harmonic; c) second harmonic...................................................................................................................14 1.13 Damage detection illustration using NRUS method..................................................15 1.14 Various objects that have been tested for nonlinearity using NRUS method............16 1.15 Model of the impedance-based method.....................................................................18 1.16 -Scale Steel Bridge Setup........................................................................................19 1.17 Damage Metric Chart for the PZTs...........................................................................20 viii

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1.18 The AndeScope..........................................................................................................21 1.19 Schematic of the structure and test set-up..................................................................22 1.20 Frequency spectrum showing an example of VP.......................................................22 1.21 Frequency spectrum showing an example of PB.......................................................23 1.22 Frequency spectrum showing an example of FB.......................................................23 1.23 Frequency spectrum showing an example of VGB...................................................23 2.1 Large sieve shaker........................................................................................................26 2.2 Small sieve shake.........................................................................................................26 3.1 Experimental hardware for modal hammer tests.........................................................31 3.3 Riprap sample suspended by bungee cords.................................................................32 3.4 Modal Analysis Signal Analyzer Windows.................................................................33 3.5 Experimental hardware for acoustic experiment equipments......................................35 3.6 Acoustic experimental setup block diagram................................................................35 3.7 Acoustic signal analyzer windows...............................................................................36 4.1 Transfer function magnitude of a good sample, rock L11...........................................43 4.2 Superimposed magnitude and coherence for the good rock L11.................................44 4.3 Transfer function magnitude of a damaged sample, rock X3......................................45 4.4 Superimposed magnitude and coherence for the damaged rock X3............................46 4.5 First resonant frequency as a function of rock mass....................................................48 4.6 First resonant frequencies of all rock sample..............................................................49 4.7 Frequency as a function of rock length in the impact direction...................................50 4.8 Transfer function magnitude comparison between damaged and undamaged rock samples.....................................................................................................................51 4.9 Transfer function phase comparison between damaged and undamaged rock samples52 4.10 Husky hammers transfer function magnitude...........................................................53 ix

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4.11 SPL from representative good rock sample, rock L12, using a modified Husky hammer.....................................................................................................................54 4.12 SPL from representative damaged rock sample, rock X5, using a modified Husky hammer.....................................................................................................................55 4.13 Averaged SPL of good rocks and damaged rocks.....................................................57 A.1 Transfer function magnitude for rock X1...................................................................55 A.2 Transfer function phase for rock X1...........................................................................55 A.3 Transfer function coherence for rock X1....................................................................56 A.4 Transfer function magnitude for rock X2...................................................................56 A.5 Transfer function phase for rock X2...........................................................................56 A.6 Transfer function coherence for rock X2....................................................................57 A.7 Transfer function magnitude for rock X3...................................................................57 A.8 Transfer function phase for rock X3...........................................................................57 A.9 Transfer function coherence for rock X3....................................................................58 A.10 Transfer function magnitude for rock X4.................................................................58 A.11 Transfer function phase for rock X4.........................................................................58 A.12 Transfer function coherence for rock X4..................................................................59 A.13 Transfer function magnitude for rock X5.................................................................59 A.14 Transfer function phase for rock X5.........................................................................59 A.15 Transfer function coherence for rock X5..................................................................60 A.16 Transfer function magnitude for rock X6.................................................................60 A.17 Transfer function phase for rock X6.........................................................................60 A.18 Transfer function coherence for rock X6..................................................................61 A.19 Transfer function magnitude for rock X7.................................................................61 A.20 Transfer function phase for rock X7.........................................................................61 A.21 Transfer function coherence for rock X7..................................................................62 x

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A.22 Transfer function magnitude for rock X8.................................................................62 A.23 Transfer function phase for rock X8.........................................................................62 A.24 Transfer function coherence for rock X8..................................................................63 A.25 Transfer function magnitude for rock X9.................................................................63 A.26 Transfer function phase for rock X9.........................................................................63 A.27 Transfer function coherence for rock X9..................................................................64 A.28 Transfer function magnitude for rock X10...............................................................64 A.29 Transfer function phase for rock X10.......................................................................64 A.30 Transfer function coherence for rock X10................................................................65 A.31 Transfer function magnitude for rock X11...............................................................65 A.32 Transfer function phase for rock X11.......................................................................65 A.33 Transfer function coherence for rock X11................................................................66 A.34 Transfer function magnitude for rock L2..................................................................66 A.35 Transfer function phase for rock L2.........................................................................66 A.36 Transfer function coherence for rock L2..................................................................67 A.37 Transfer function magnitude for rock L3..................................................................67 A.38 Transfer function phase for rock L3.........................................................................67 A.39 Transfer function coherence for rock L3..................................................................68 A.40 Transfer function magnitude for rock L4..................................................................68 A.41 Transfer function phase for rock L4.........................................................................68 A.42 Transfer function coherence for rock L4..................................................................69 A.43 Transfer function magnitude for rock L5..................................................................69 A.44 Transfer function phase for rock L5.........................................................................69 A.45 Transfer function coherence for rock L5..................................................................70 A.46 Transfer function magnitude for rock L6..................................................................70 xi

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A.47 Transfer function phase for rock L6.........................................................................70 A.48 Transfer function coherence for rock L6..................................................................71 A.49 Transfer function magnitude for rock L7..................................................................71 A.50 Transfer function phase for rock L7.........................................................................71 A.51 Transfer function coherence for rock L7..................................................................72 A.52 Transfer function magnitude for rock L8..................................................................72 A.53 Transfer function phase for rock L8.........................................................................72 A.54 Transfer function coherence for rock L8..................................................................73 A.55 Transfer function magnitude for rock L9..................................................................73 A.56 Transfer function phase for rock L9.........................................................................73 A.57 Transfer function coherence for rock L9..................................................................74 A.58 Transfer function magnitude for rock L10................................................................74 A.59 Transfer function phase for rock L10.......................................................................74 A.60 Transfer function coherence for rock L10................................................................75 A.61 Transfer function magnitude for rock L11................................................................75 A.62 Transfer function phase for rock L11.......................................................................75 A.63 Transfer function coherence for rock L11................................................................76 A.64 Transfer function magnitude for rock L12................................................................76 A.65 Transfer function phase for rock L12.......................................................................76 A.66 Transfer function coherence for rock L12................................................................77 B.1 Sound pressure level for rock X1................................................................................78 B.2 Sound pressure level for rock X2................................................................................78 B.3 Sound pressure level for rock X3................................................................................79 B.4 Sound pressure level for rock X4................................................................................79 B.5 Sound pressure level for rock X5................................................................................79 xii

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B.6 Sound pressure level for rock X6................................................................................80 B.7 Sound pressure level for rock X7................................................................................80 B.8 Sound pressure level for rock X8................................................................................80 B.9 Sound pressure level for rock X9................................................................................81 B.10 Sound pressure level for rock X10............................................................................81 B.11 Sound pressure level for rock X11............................................................................81 B.12 Sound pressure level for rock L2..............................................................................82 B.13 Sound pressure level for rock L3..............................................................................82 B.14 Sound pressure level for rock L4..............................................................................82 B.15 Sound pressure level for rock L5..............................................................................83 B.16 Sound pressure level for rock L6..............................................................................83 B.17 Sound pressure level for rock L7..............................................................................83 B.18 Sound pressure level for rock L8..............................................................................84 B.19 Sound pressure level for rock L9..............................................................................84 B.20 Sound pressure level for rock L10............................................................................84 B.21 Sound pressure level for rock L11............................................................................85 B.22 Sound pressure level for rock L12............................................................................85 xiii

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Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science NONDESTRUCTIVE EVALUATION OF RIPRAP ROCKS By Christian Bassoli de Carvalho August 2004 Chair: Christopher Niezrecki Major Department: Mechanical and Aerospace Engineering Within this study, two nondestructive evaluation techniques are developed to evaluate riprap rocks. Modal hammer testing and acoustic measurements are made on riprap rocks to determine possible defects within the rock structure. Two sets of rock samples (11 damaged and 11 undamaged) were visually categorized and provided by the Florida Department of Transportation for this research. Modal hammer testing is used to determine each rocks transfer function. The acceleration with respect to force magnitude and phase responses is measured and plotted for each rock. The average responses are plotted and compared for the damaged and undamaged rock samples. It is determined that the average first resonant frequency is 1,900 Hz and 3,900 Hz for the damaged and undamaged rock samples, respectively. The damaged samples average first resonant frequency shifted downward. This is characteristic of structures with damage due to the reduction in stiffness caused by the presence of cracks. The acoustic experiment is conducted to complement the modal hammer test results. The sound pressure level (SPL) of each rock is determined by impacting a modified Husky hammer xiv

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with a rock and measuring the response using a microphone. The average sound pressure levels of damaged and undamaged rock samples are plotted and compared, respectively. There were no variations in the average SPL between the damaged and undamaged rock samples. However, the average first resonant frequency of the damaged samples was 70 Hz lower compared with the undamaged samples. The preliminary results indicate that the nondestructive evaluation methods proposed to diagnose the quality of riprap rocks looks promising. However, due to the method used by the FDOT to separate the rock samples, it is possible that there is mixing between the piles of damaged and undamaged rock samples. For this reason, further work is needed to verify the preliminary findings in this study. xv

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CHAPTER 1 NON-DESTRUCTIVE EVALUATION METHODS There are several ways to conduct nondestructive evaluation (NDE) of structures. They include modal analysis, four different methods of nonlinear elastic wave spectroscopy (NEWS), impedance based analysis, impact-echo analysis, and several other methods. A summary of these NDE methods is presented in this chapter to provide a foundation and background of these methods and its possible use on the analysis of riprap rock. 1.1 Modal Analysis Modal analysis is a method of nondestructive testing that has the potential to distinguish between damaged and undamaged rock samples. Kam and Lee (1992) illustrated this method to detect cracks and their size on a cantilever beam. The detection of cracks was based on a reduced stiffness model. The estimation of the crack size was based on the strain energy equilibrium equation. Kam and Lee used a theoretical model to compare their results with the experiment conducted by Rizos (et al., 1990) and Qian (et. al., 1990). Kam showed that vibration frequencies and mode shapes of the cantilever beam were within ~5% error when compared to Rizos and Qians experiments. Kam concluded that, with slight modifications of the equations, the theoretical model used in this analysis can be applied to different structures with multiple cracks. Los Alamos National Laboratory (Doebling et al., 1996) presented a comprehensive literature review on damage identification methods from changes in system vibration characteristics. Their overall conclusion on 135 references is that 1

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2 measured vibration data provides enough evidence to claim whether or not damage is present in a structure. The modal analysis experiments summarized in this chapter are most relevant to the research of interest. 1.1.1 Modal Analysis on Rocks Sun and Hardy (1992) conducted a modal analysis experiment on a large rock along the side of Interstate Highway I-81 in Luzerne county, Pennsylvania. Figure 1.1 shows a photograph of the rock. Figure 1.1 Rock used to conduct modal analysis experiment (Sun and Hardy, 1992) The modal analysis was conducted with a hammer used excite the modes of vibration of the rock. A grid, shown in Figure 1.2, was used to locate the impact points. Five rows of five impact points were chosen. Because of the rocks surface irregularities, a steel plate was mounted at each reference point for optimum signal transmission to the accelerometer. Figure 1.3 shows a schematic of their experimental setup.

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3 Figure 1.2 Grid showing hammer impact points (Sun and Hardy, 1992) Figure 1.3 Instrumentation and setup (Sun and Hardy, 1992) The initial experiments started by conducting modal tests on rock block A. Artificial defects were introduced to simulate damage to the rock. This way, modal analysis could be used to predict failure on the remaining portions of the rock. Modal analysis was conducted and recorded after different sets of modifications were made.

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4 Artificial defects were introduced to the rock blocks by four different methods: (1) Drilling holes with a rotary hammer; (2) Combination of drilling and wedging; (3) Driving a steel wedge into a fracture point; (4) Driving a steel wedge until part of the block was completely slid off. Two weeks was allowed between the second and third modifications to account for weathering phenomena. After experiments were conducted, Sun observed that the modal frequencies decreased for each mode of vibration with the introduction of defects. Table 1.1 presents these results. Table 1.1 Modal frequencies as defects were introduced (Sun and Hardy, 1992) The modal frequencies decreased for the block modifications with the exception of modification from MDXXB2 to MDXXB3, which were modified due to weathering. Weathering phenomena covered the defects that were made, and thus strengthened the rock. The second mode of vibration was the only mode that was not consistent. However, the other modes of vibrations showed a tendency to decrease with the introduction of defects. Sun and Hardy (1990) also found that the transfer functions of experiments conducted in different temperature and humidity environments affected

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5 modal parameters but were insignificant. Weather effects on modal parameters were only briefly studied by Sun and their overall effects were not quantified. Sun and Hardy (1992) concluded that modal analysis was effective in assessing damage to rocks. Mode shape and modal frequency were reasonably sensitive to defect development in the rock. For most of the mode shapes, the frequency shifted downward with an increase in structure defect. Sun also concluded that modal analysis has great potentials in the geotechnical area as a nondestructive technique to assess structural damage. 1.1.2 Modal Analysis on Fruits Experimental modal analysis (EMA) has been used in engineering to study the dynamic properties of structures for decades. Researchers at Purdue University have extended this application to study the properties of fruits. EMA is conducted on fruits to study the fruits ripeness, bruises, and/or defects. These fruit properties are important in assessing the fruits overall condition (Cherng 1999). The method that is known to measure a fruits firmness was developed many decades ago by Magness and Taylor (Magness 1925). This method measured the force required to penetrate a fruit with a standardized cone. There were serious issues with this approach (Bajema et al., 1998; Baritelle 1999; Cherng 1999). Since there were no other methods to measure a fruits firmness, this method was used over the years. To scientifically measure the firmness of fruit, properties of the fruit must be related to the modulus of elasticity which is related to the resonant frequency. This became the foundation for using EMA to study the properties of fruits. Sumali, at the Agricultural and Biological Engineering Department at Purdue University, conducted a modal analysis experiment on a melon (Sumali 2002). The

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6 purpose of this experiment was to initiate modal analysis work on biological materials to characterize their physical properties. To retrieve accurate data from modal analysis tests on the melon, the melon had to be suspended from a rigid structure with elastic cords. The elastic cords have a low resonant frequency of vibration. Therefore, measurements taken from the melon will not be affected by the apparatus (elastic cords) that holds the melon. Figure 1.4 shows a photograph of the apparatus. Figure 1.4 Elastic cords used to suspend the melon (Sumali 2002) One of the problems encountered by Dr. Sumali and his students was that the surface of the melon was too porous to attach the accelerometer. They solved this problem by applying wax to the surface of the accelerometer and attaching it to the melon at the desired position. Another problem they encountered was that the surface of the melon was too soft to excite the melons mode of vibrations greater than 200 Hz. To overcome this, a metal disk was used as an impact point.

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7 A modal hammer was used to excite the melon. The result of a single test was averaged over 10 impacts. Figure 1.5 shows some of the results. Figure 1.5 FRF curve and coherence obtained from the melon (Sumali 2002) The coherence shows that accurate data can be obtained for frequencies less than 500 Hz. The fourth and fifth modes of vibration become less apparent compared to the first three. This is because of the modal damping factors at higher frequencies. It was concluded from this experiment that modal analysis can be used effectively to study the dynamic response of fruits. While this research topic is relatively new, it provided a foundation for future research of modal analysis on fruits and other biological materials.

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8 1.2 Nonlinear Elastic Wave Spectroscopy Nonlinear Elastic Wave Spectroscopy (NEWS) is a method of nondestructive testing that uses the dynamic response of a system to analyze structural integrity of solids. There are four types of NEWS: nonlinear wave modulation spectroscopy (NWMS), single-mode nonlinear resonance acoustic spectroscopy (SIMONRAS), nonlinear resonant ultrasound spectroscopy (NRUS), and simple mode nonlinear resonant ultrasound spectroscopy (SIMONRUS). This method utilizes the harmonics and sum and difference of the frequency to distinguish between undamaged and damaged samples. Van Den Abeele, Johnson, and Sutin (Van Den Abeele, et. al, 2000) applied this technique to Plexiglas, an engine component, and sandstone. 1.2.1 Nonlinear Wave Modulation Spectroscopy A solid possesses a nonlinear dynamic response if it contains any damage (cracks, flaws, etc.) within the structure. Therefore, NWMS was used to distinguish between damaged and undamaged structures, since it analyzes the dynamic response of a system. Figure 1.6 shows the responses for a dynamic one-dimensional wave propagation of a finite-amplitude monofrequency signal. Figure 1.6 Schematic overview of the dynamic response for a one-dimensional wave propagation (Van Den Abeele et al. 2000)

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9 Figure 1.7 shows the experiment schematic conducted by Van Den Abeele, Johnson, and Sutin Figure 1.7 Experiment schematic (Van Den Abeele et al. 2000) A piezoelectric transducer was used to apply two continuous waves, one at low frequency of 5-20 kHz and another at high frequency of 70-120 kHz. A calibrated accelerometer captured the response of the system. The nonlinearity of the response was illustrated by holding one frequency at constant amplitude while varying the other from 0-10 volts. They showed that the undamaged samples had nearly no nonlinearities. The damaged samples showed nonlinearity by the presence of harmonics and side bands. Figure 1.8 illustrates these results for Plexiglas. Figure 1.8. Wave modulation spectra of uncracked and cracked Plexiglas (Van Den Abeele et al. 2000)

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10 The same results were obtained for sandstone. Figure 1.9 shows these results. The presence of sidebands in the cracked sample spectra illustrates the nonlinearity associated with the presence of cracks within that sample. Figure 1.9 Sandstone wave modulation spectra (Van Den Abeele et al. 2000) Van Den Abeele, Johnson, and Sutin showed that NEWS is an effective nondestructive method used to distinguish between damaged and undamaged solids. Sandstone, by its very structural nature, already has some nonlinearities. However, the presence of cracks and flaws within the structure further nonlinearizes the dynamics response of the system. This method has also shown to be far more sensitive to nonlinearities than any linear acoustical methods. 1.2.2 Single-Mode Nonlinear Resonance Acoustic Spectroscopy One of the NEWS methods introduced in the previous section, single-mode nonlinear resonance acoustic spectroscopy (SIMONRAS), concentrates on the acoustic nonlinear response of the material when subjected with small wave amplitudes. Van Den Abeele and his co-workers (Van Den Abeele et al. 2000) illustrated this method on

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11 artificial slate tiles, used in roofing construction, to detect damage on the structure. Figure 1.10 shows a schematic of their experimental apparatus. Figure 1.10 Experimental setup for SIMONRAS experiments (Van Den Abeele et al. 2000) The sample was held by nylon wires at the two nodal positions of the structure. The speaker was used to induce a low frequency wave. An accelerometer was attached to one end of the beam to measure the output response. LabVIEW was used to post process the data. The resonance frequency and the attenuation do not depend on amplitude for the undamaged samples. There is also no presence of harmonics. For the damaged sample, however, there was an amplitude-dependent resonance frequency shift. The drive voltage

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12 of the speaker was increased in order to increase the amplitude of the response and plot the frequency shift. Figure 1.11 shows the results. Figure 1.11 SIMONRAS results. Intact (left) and micro damaged (right) slate beam. Fundamental accelerations are shown for ten drive voltage levels. (Van Den Abeele et al. 2000)

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13 By observing the top two figures of Figure 1.11, one can clearly see that there is a significant frequency shift in the acceleration amplitude of the damaged sample. The frequency shift is not as clear for the intact sample. Therefore, the relative resonance frequency shift was plotted. One can see that the intact sample also possess a frequency shift. However, the frequency shift for the damaged sample can be observed to be much greater, as amplitude increases, than that for the undamaged sample. Also observed by Van Den Abeele is the dramatic change of the harmonic spectrum. The third harmonic became dominant with the presence of flaws in the structure. The second harmonic did not have a significant impact because hysteresis has little effect on the even harmonics. A phenomenological model was introduced and is explained in Van Den Abeele 2000. Analysis of the lowest amplitude resonance after each impact showed that the nonlinearity parameter had a relative change of 1000%, far exceeding the percent change in any other parameter. Van Den Abeele also found that linear damping is a better measurement of nonlinearity then resonance frequency shift in cyclic fatigue loading. Figure 1.12 illustrates this result. Van Den Abeele concluded that NEWS is a more effective method to detect damage in structures by looking at its nonlinearity responses compared to linear acoustical method. The methods presented in section 1.2 can also be applied to any geometry, and thus broadening the range of applications of this method.

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14 Figure 1.12 Cyclic fatigue loading experiment: a) relative resonance frequency shift as a function of the measured peak acceleration amplitude at different stages of the fatigue process; b) amplitude dependence of the third harmonic; c) second harmonic (Van Den Abeele et al. 2000)

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15 1.2.3 Nonlinear Resonant Ultrasound Spectroscopy Another method of NEWS is nonlinear resonant ultrasound spectroscopy (NRUS). NRUS, along with all the other NEWS methods, focuses on the nonlinearity response of the structure due to damage and its amplitude dependence. The nonlinearity due to damage in this method is detected by observing a change in the wave frequency response with a change in the wave amplitude input. Johnson, (Johnson 1999), describes this method by impacting a bell with a hammer and getting the response with a listening speaker. Figure 1.13 illustrates the NRUS method on a bell. When a hammer is struck on the bell, the hammer excites the resonance modes of the bell. However, if the bell has a crack, possibly small enough not to be visible with the naked eye, striking it harder will cause frequency shifts. As the bell is struck harder, the presence of cracks causes nonlinearities in the response. This concept can be extended to numerous applications. Figure 1.14 shows various objects that have been tested for nonlinearity by NRUS method. The general idea can be explained by the change in the material nonlinear elastic wave behavior caused by the presence of cracks. This nonlinear behavior is shown by amplitude dependence frequency shifts of the resonant modes. Figure 1.13 Damage detection illustration using NRUS method (Johnson, 1999)

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16 Figure 1.14 Various objects that have been tested for nonlinearity using NRUS method (Johnson, 1999) While NEWS has been shown to be the most effective nondestructive method to detect damage in a structure, further studies are being done to detect the location of the damage using current NEWS methods. 1.2.4 Simple Mode Nonlinear Resonant Ultrasound Spectroscopy The single-mode version of NRUS is referred to as simple mode nonlinear resonant ultrasound spectroscopy (SIMONRUS). In SIMONRUS experiments, only one specific mode of the structure is excited (Windels, 2004). Papers on this method of nondestructive evaluation of structures have not been published by any researchers to date. However, a paper by Van Den Abeele titled Acoustic characterization of nonlinear and hysteretic geomaterials: single mode nonlinear resonant ultrasound spectroscopy (SIMONRUS) has been submitted for publication. 1.3 Impedance-Based Analysis Impedance-based analysis is another NDT method used to assess the presence of damage in structures. This method uses a piezoelectric (PZT) transducer at a high

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17 frequency (>30 kHz) to relate electrical impedance of the transducer to the mechanical impedance of the structure. Park and his colleagues (Park, et. al, 2000) present the effects of this method on masonry walls, -scale bridge element, and a pipe joint to verify the capabilities of this NDT method. The -scale bridge is discussed in this paper. The impedance based analysis was chosen in this experiment because of its autonomous capability and the applicability to various types of structures Piezoelectric transducers provide a relationship between mechanical strains and electric fields. If the transducer is mechanically stressed, it generates an electric field and vice versa. The PZT is driven by a fixed, high frequency, alternating current resulting in a mechanical response in the PZT and on the structure where it is attached. Because of this high frequency, only the area in the vicinity of the transducer on the structure experiences the mechanical response. This mechanical response is then transferred back to the PZT as an electric field. Figure 1.15 shows the PZT model. When the structure is damaged, the resulting frequency response of the structure will have a phase shift or magnitude change in its dynamic response. The impedance-based structural health-monitoring method evaluates the damage on a structure by the use of a scalar damage metric. A scalar damage metric is defined (Park, et. al, 2000) as the sum of the squared differences of the real impedance changes at each frequency step. The damage metric is used as a simplification of the impedance response curves. This can be used with a device that helps inspectors assess damages on a structure with a red/green light based on the threshold of the damage. Further details of the impedance based method of NDT is presented in (Sun et al. 1995; Park et. al. 2000).

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18 Figure 1.15 Model of the impedance-based method (Park et al. 2000) The impedance based approach advantages compared to other NDT methods are: (1) Approach is not model dependent and it can be applied to any structure; (2) Actuators used are small; (3) Under normal operating conditions the PZT possesses the following: wide range of linearity, fast response, lightweight, stability, high conversion efficiency; (4) Sensitive to small damages due to the high frequency used; (5) Easy to post-process data; (6) On-line monitoring; (7) Continuous analysis provides long term longevity of the structure (Rogers 1996). The -scale analysis of the bridge was performed to show the effectiveness of the impedance-based NDT method to assess structural damage with the presence of changing ambient boundary conditions. This is a compensation technique, built into the damage metric, to minimize the effects of external noise such as vibrations and thermal variations of the surroundings (Park et al. 1999). Figure 1.16 presents the schematic of the experimental setup for the -scale bridge analysis. This bridge is made up of steel angles, plates, and joints and held together by over 200 bolts. The PZT sensors were mounted on places of the structure where damage was most likely to occur.

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19 Figure 1.16 -Scale Steel Bridge Setup (Park et al. 2000) Preliminary tests conducted on this structure by (Ayres 1996) presents a clear variation in impedance measurements caused by damage. The ambient boundary conditions imposed on this experiment was (1) Repeatability monitoring variations of the signal over a given time; (2) Vibrations vibration being simulated by hammering the structure while measurements are taken; and (3) Loading a 15 kg load was added to the structure. First, readings were made with just the boundary conditions in order to identify its effects on the overall results. Then, damage was done to the structure by loosening some of the bolts by 1/8 of a turn. The compensation technique was applied by comparing the two responses, induced by boundary conditions only and by structural damage, and accounting for the change via the damage metric. Figure 1.17 presents the results.

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20 Figure 1.17 Damage Metric Chart for the PZTs (Park et al. 2000) The first 14 damages were caused by the three boundary condition effects mentioned previously. The other damages, shown in darker shade, shows the damages picked up by the PZTs due to damage in the structure caused by 1/8-turn of a single bolt in 3 different locations. These results shows the high sensitivity of the PZTs due to a minor (1/8-turn of 1 bolt) structural damage. This is critical for early detection of damage. The impedance-based NDT method to detect damage in a structure has shown to be very effective. When compared to other NDT methods, the impedance based method is the only approach that compensates for external noises such as unwanted vibrations. Due to the simplicity of its concept, the impedance based method can be applied to a wide variety of structure with multiple boundary conditions autonomously.

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21 1.4 Impact-Echo Analysis The impact-echo technique is a non-destructive method used to determine the location and characterization of internal discontinuities within concrete structures. Sadri (Sadri, 2003) applied this technique to assess the bonding condition between the facing stones, mortar, and inner rubble core in stone masonry structures. Figure 1.18 show the equipment used to perform the nondestructive, impact-echo tests. Figure 1.18 The AndeScope (Sadri, 2003) The stone masonry structures analyzed includes the inner wall, outer wall, and the buttresses. The outer walls of this structure were of primary concern because it had been exposed to extreme weather conditions. A summary of the impact-echo technique is as follows: A mechanical impact source and an electromechanical receiving transducer are placed on the same surface of the structure in interest. The impactor generates a P-wave which propagates into the object and experiences multiple reflections within the opposite end of the solid. Pressure waves, or P-waves as it is commonly known, are longitudinal waves in which the oscillation occurs in the same or opposite direction of wave propagation. The reflected

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22 wave is then detected by the transducer. The time-voltage responses are averaged over 10 impacts with FFT frequency analysis algorithms by a dynamic signal analyzer. The reflections or echoes are indicated by frequency peaks in the plots of displacements versus frequency. Figure 1.19 shows the schematic of the test set-up. Testing was conducted on both sides of the structure. Figure 1.19 Schematic of the structure and test set-up (Sadri, 2003) The results obtained in this paper categorized the structures in terms of four different bonding strength, very good bonding (VGB), fair bonding (FB), poor bonding (PB), and very poor bonding (VPB). Figures 1.20 1.23 shows the results. Figure 1.20 Frequency spectrum showing an example of VPB (Sadri, 2003)

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23 Figure 1.21 Frequency spectrum showing an example of PB (Sadri, 2003) Figure 1.22 Frequency spectrum showing an example of FB (Sadri, 2003) Figure 1.23 Frequency spectrum showing an example of VGB (Sadri, 2003)

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24 The second set of peaks (>5000 Hz) gives an idea of the number of defects present in the structure. As the bonding quality strengthens, the second set of peaks decreases, showing that there is minimal defect within the structure. In conclusion, the impact-echo technique successfully supplied enough information to categorize the bonding strength of the structure. 1.5 Other Non-destructive Evaluation Methods While many NDT methods have been discussed, there are many more out there. Fourney (Fourney and Dick, 1994) used explosive loading as an evaluation tool in geological materials. Khan (Khan, et. al., 2001) used ultrasonic to map formation damage on Berea rock samples. Grabco (Grabco, et. al., 2003) tested the brittleness of rocks by a microindentation method with the registration of acoustic emission signals. Many other methods and procedures for conduction of NDT on structures can further be found in the references mentioned in this paper.

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CHAPTER 2 STANDARD TEST METHOD FOR SOUNDNESS OF AGGREGATE BY USE OF SODIUM SULFATE Florida Department of Transportation (FDOT) is currently using the method discussed in this chapter to study the soundness of aggregates subject to weathering. To determine its resistance to disintegration, the aggregates are saturated in solutions of sodium sulfate for a specified period. Then the aggregates are dried in an oven. This procedure of soaking and drying the aggregates occurs approximately five times during a seven days period before the aggregates structure is analyzed. The re-immersion of the aggregates causes an internal expansive force due to the re-hydration of the salt. A more detailed explanation of this procedure is presented in AASHTO T 104-99 (2003). 2.1 Sodium Sulfate Solution The sodium sulfate (Na 2 SO 4 ) solution used for testing the aggregates is prepared by dissolving 225 grams of the salt per liter of distilled water. This is accomplished at a minimum temperature of 25C (77F). The volume of the solution should be at least five times the volume of the samples being tested. The solution should be stirred frequently as the salt is being added. After completion, the solution is covered and allowed to cool to 20.3 to 21.9C (68.5 to 71.5F). Before adding aggregates, the solution should be stirred for at least 48 hours. The specific gravity of the solution should also lie between 1.154 and 1.171 before testing can begin. 25

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26 2.2 Samples Samples used in the experiments are divided into two categories, fine and coarse aggregates. Figures 2.1 and 2.2 shows the mechanical shakers, each with sieves of different sizes, used to separate the samples into coarse and fine aggregates. These shakers provide vertical and lateral motion allowing fine aggregates to pass through to a smaller size sieve below. Figure 2.1 Large sieve shaker (AASHTO T 27) Figure 2.2 Small sieve shaker (AASHTO T 27)

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27 Fine aggregates are categorized by samples that have passed through a 9.5-mm (3/8-in) sieve. There are five different sample sizes that are categorized under fine aggregates. These sample sizes are presented in Table 2.1. Table 2.1 Sieve sizes used for fine aggregate samples (AASHTO T 104-99). There must be at least 100 grams of each of the five fine aggregate samples for testing. Coarse aggregate is defined as all the samples that does not include any 4.75-mm or smaller samples. The different categories and masses required for testing are presented in Table 2.2. Table 2.2 Sieve sizes and required masses for coarse aggregate samples (AASHTO T 104-99)

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28 Masses that are less than five percent of any of the sizes specified are not tested. There are several ways to break a large rock into large (> 19.0-mm) coarse aggregate. These may be obtained by crushing, splitting, or sawing. When sawing is used to break a larger rock, the pieces should be greater than 37.5-mm in any dimension. 2.3 Test Sample Preparation For fine aggregate samples, use a 300-m sieve to thoroughly wash the samples. The samples are then dried at 110 5C (230 9F). The five different sieves are then used to separate the samples into different size categories. The coarse aggregate samples are washed and dried at the same temperature as the fine aggregate samples. The coarse aggregate samples are then separated into different sizes in accordance with the coarse aggregate table (Table 2.2). 2.4 Testing Procedure Aggregate samples should be immersed in the sodium sulfate solution between 16 and 18 hours at a depth of at least 12.5-mm. For samples that float to the surface, weighted wire grids may be used to hold samples at the appropriate depth. The solution temperature should be maintained at a temperature between 20.3 to 21.9C (68.5 to 71.5F) during the immersion process. After the immersion phase, the aggregates should be allowed to drain for 15 5 minutes. Then, the aggregates are set to dry in an oven at a temperature of 110C 5C (230C 9C). Samples are dried until constant mass is achieved. Details of establishing constant mass are provided in (AASHTO T 104-99). Aggregate samples should then be cooled to 20 to 25C (68 to 77F). Once cooled, the samples are ready to be re-immersed in the sodium sulfate solution. Re-immersion should be made right after

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29 the samples come out of the oven. In the event that this procedure has to be interrupted, the samples should remain in the oven at the drying temperature provided above. After five cycles have been completed, the samples should be washed so that there is no more sodium sulfate present. This is accomplished by running water at 43 6C (110 10F) at the bottom of the containers and allow the water to overflow at the top. Washing of the samples is completed when there are no significant traces of sodium sulfate in the overflow water. This is verified by introducing 0.2 molar barium chloride into the overflow solution. If cloudiness is seen, the wash down process is not completed. Upon completion of the aggregate wash down, the samples are then dried in the oven similarly to the drying procedure of the testing phase. The samples are then categorized by using sieves similar to prior the testing phase. The entire testing procedure takes approximately seven days, given that there is no time set backs due to human error or machine failures. 2.5 Quantitative Sample Examination Damaged samples disintegrate during the testing phase because of the salt re-hydration when the samples are re-immersed. Therefore, to determine the amount of mass lost, the samples are tumbled with the same size sieves used prior to testing. For coarse aggregates, sieving is completed by hand with sufficient agitation so that only loose particles pass through the sieves. Then, the samples are categorized into their individual sizes, weighted, and compared to their initial weight prior to testing. The difference in weight is then reported as percent of the initial mass. A sample that has lost more than 12% (by mass) of its initial mass is considered a damaged sample. This percentage is the mass lost during the testing phase.

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CHAPTER 3 EXPERIMENTAL SETUP The objective of this experiment is to perform nondestructive evaluation on riprap rocks. This is accomplished by exciting the rocks resonant frequencies through modal analyses and acoustic experiments. It is proposed that rocks categorized as defective will have lower resonant frequencies than the structurally stable rocks. This chapter discusses the instrumentations and procedures for conducting modal analyses and acoustic experiments on riprap rocks. 3.1 Modal Analysis Experimental Setup Modal analysis is used as a nondestructive method of health monitoring objects by exciting the object physically and measure the response. For this specific experiment, the object in question is the riprap rocks. The rocks are excited with a modal hammer and are measured using an accelerometer. This allows the transfer function, force divided by acceleration, to be plotted. The resonant frequencies are clearly seen by sharp peaks in the transfer functions response. 3.1.1 Modal Analysis Instrumentations There are five components used to conduct the modal analysis experiments. They consist of an accelerometer, modal hammer, signal conditioner, dynamical signal and system analyzer (SigLab), and computer. The accelerometer used is the PCB model 353B15, serial no. 62013. This shear accelerometer has a voltage sensitivity of 9.85 mV/g and a frequency range of 1-18 kHz. There is a 5% and 10% response error on frequencies ranging between 1-12 kHz and 12-18 kHz, respectively. Calibration for the 30

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31 accelerometer is discussed in section 3.1.3. The modal hammer is manufactured by PCB Piezotronics, serial no. 13167. The modal hammer was used with a copper tip to excite a large frequency range. The signal conditioner is the PCB model 482A16, serial no. 2074. The SigLab model 50-21, serial no. 2000-1379, signal analyzer is used to receive the output voltage from the signal conditioner. The computer used to gather all data is a 450 MHz, Pentium III processor running Windows 2000 operating system with 128 MB of RAM. BNC cables are used to connect all the equipment together. 3.1.2 Modal Analysis Equipment and System Analyzer Setup The initial setup is accomplished with all the equipment turned off. Figures 3.1 and 3.2 presents the experimental setup for the modal analysis experiments. Figure 3.1 Experimental hardware for modal hammer tests Figure 3.2 Modal analysis experimental setup block diagram

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32 Before testing begins, the rock is brushed off of any loose debris on its surface. The rock is then suspended with bungee cords from the ceiling, Figure 3.3. Figure 3.3 Riprap sample suspended by bungee cords Bungee cords are used because they have very low stiffness and will not affect the measurements when the resonant frequencies of the rock are excited. The accelerometer is attached to the rock with a thin coat of wax. This allows the accelerometer to be securely attached given that there is no loose debris on the rocks surface. Once everything is connected, the equipment is turned on with SigLab being turned on before the computer. The dynamic signal analyzer (vna) is then started by typing vna in the command prompt of MATLAB. Figure 3.4 shows a sample vna window used for the modal analysis experiments. The peak voltage for channels 1 & 2 is chosen so that there are no overloads during the experiments. This number varied slightly depending on the

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33 rock being tested. The maximum frequency is set to 20 kHz, which is slightly higher than the maximum accelerometer frequency of 18 kHz. The record length is chosen to record data over the maximum time period allowed by the signal analyzer. The trigger is set to manual arm so that data starts to record when the modal hammer impacts the rock and the force input exceeds 9% of the full scale range of the input. Each set of data recorded is averaged over 8 times. This allows for any irregular response to be disregarded, through averaging, on the final set of data. After setting up all the necessary parameters, testing commences. Figure 3.4 Modal Analysis Signal Analyzer Windows 3.1.3 Testing Procedure Testing is initiated by clicking on the average and arm buttons, respectively. The modal hammer is used to impact the rock at a location on the opposite side of the rock compared to the location of the accelerometer. After each impact, the channels are checked for overload. If an overload is present, the data is discarded and the process is

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34 repeated. The force response is another parameter that was carefully observed after each impact. A double impact will create two peaks in the force response, and thus, is discarded because the acceleration response will differ from a single impact force. Depending on the impact, the force response will have different peak sharpness. A long impact will cause the force response peak to concentrate energy in the lower frequency range while a sharper peak distributes more energy into higher frequencies. Therefore, a desirable impact consists of no overloads, triggering of the signal analyzer, and sharp peaks of the force response. After impacting the rock eight times, the raw averaged data is saved to the hard drive. 3.2 Acoustic Experimental Setup The acoustic experiment is used to measure the sound pressure level when a hammer strikes the riprap rocks. A microphone is used to measure the response of a hammer impacting a rock. The sound pressure level data is used to compare responses between defective and structurally stable rocks. 3.2.1 Instrumentation There are six components used in the acoustic experiment. They include a hammer, microphone, microphone preamplifier, conditioning amplifier, dynamical signal and system analyzer (SigLab), and computer. A hammer was chosen so that it generates the minimum sound when it impacts the rocks. The microphone is a B&K Type 4190, serial no. 2175107. It has a sensitivity of 53.7 mV/Pa. A foam sphere is used to protect the microphone from wind fluctuations. Calibration for the microphone is presented in section 3.2.3. The microphone preamplifier is a B&K Type 2669, serial no. 2188131. Used to transmit the voltage signal to SigLab is a B&K Nexus conditioning amplifier, serial no. 2218569. The SigLab model 50-21, serial no. 2000-1379, signal

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35 analyzer is used to receive the output voltage from the signal conditioner. The computer used to gather all data is a 450 MHz, Pentium III processor running Windows 2000 operating system with 128 MB of RAM. 3.2.2 Acoustic Equipment and System Analyzer Setup First, the rock is suspended as shown in Figure 3.3. A picture of the equipment and block diagram of the setup is shown in Figures 3.5 and 3.6. The microphone is attached to the preamplifier. The preamplifier is held with a microphone stand. The preamplifier is connected to channel 1 of the Nexus amplifier. A BNC cable is used to connect the preamplifier to SigLab. The microphone is positioned 1 meter away and at the same height as the rock. Figure 3.5 Experimental hardware for acoustic experiment equipments Figure 3.6 Acoustic experimental setup block diagram

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36 Figure 3.7 shows a sample vna window for the acoustic experiment. The peak voltage for channel 1, the only channel used, is chosen so that there are no overloads during the experiments. This number varied slightly depending on the rock being tested. The maximum frequency is set to 20 kHz, which is much higher than the resonant frequencies of the rocks. The record length is chosen to record data over the maximum time period allowed by the signal analyzer. The trigger is set to manual arm so that data starts to record when the hammer impacts the rock. Each set of data recorded is averaged over 8 times. The Nexus amplifier is programmed to output a 100 mV/Pa signal from the microphone. The microphones sensitivity, 53.7 mV/Pa is also inputted into the amplifier. The output signal from the amplifier is converted to 10 Pa/V and inputted into the signal analyzer. Finally, the reference pressure, 20e-06 Pa, is also set on the signal analyzer. After setting up all the necessary parameters, testing commences. Figure 3.7 Acoustic signal analyzer windows

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37 3.2.3 Testing Procedure To begin testing, the average and arm buttons are pressed, respectively. The signal analyzer is automatically triggered once the hammer impacts the rock. Striking the rock with the hammer required some initial experience, similar to the modal analysis tests. If excessive force is used to strike the rock, the channel overloads. If the rock is stroked with little force, the signal analyzer does not trigger and thus the data is not recorded. Careful attention was paid to the microphones response after each impact. If any overload was seen, the data was discarded and the process was repeated. After impacting the rock eight times, the raw averaged data is saved to the hard drive. 3.3 Calibration The accelerometer used in this experiment is the PCB model no. 353B15, serial no. 62013. A B&K Type 4294 calibration exciter is used to calibrate this accelerometer. The exciter generates a frequency of 159.2 Hz at an acceleration of 10 m/s 2 A PCB signal conditioner model no. 482A16 is used to send the accelerometers voltage to SigLabs data analyzer. The multiplier in SigLab is adjusted to match the manufacturers acceleration at the specified frequency. There were no adjustments made since the accelerometer produced a 10 m/s 2 response at a frequency of 159 Hz. The microphone used in this experiment is the B&K Type 4190, serial no. 2175107. It is calibrated using a pistonphone calibrator Type 4229, serial no. 2368878, with a Type 8103 attachment. The attachment allows for the calibration of microphones. The calibrator was verified on October 17, 2002. The calibrator produces sound pressure level of 165.8 dB referenced to 1Pa. A B&K Nexus amplifier, serial no. 2218569, is used to send the voltage from the microphone to the SigLab. The Nexus amplifier is programmed to output a 100mV/Pa signal from the microphone using 200V

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38 as the supply voltage. The amplification is converted to 10 Pa/V and is inputted into SigLab. Depending on the microphones response, the multiplier is adjusted to match the manufacturers calibrated sound pressure level. Since the microphone produced a 165.8 dB sound pressure, the multiplier was kept at 10 Pa/V. It must be noted that the calibration is done with no significant external noise sources, since this affects the microphones response.

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CHAPTER 4 RESULTS This chapter presents the results obtained from modal analyses and acoustic experiments. Experiments were conducted on 22 different rocks. Half of the rocks are structurally good samples, and the rest are internally damaged samples. The good samples are labeled L2 through L12. The damaged samples are labeled X1 through X11. There are no specific reasons why this labeling system was chose other than to simply distinguish between good and damaged samples. First, modal hammer impact testing was used to acquire the transfer functions of good and damaged rock samples. Then, the data was post-processed using MATLAB. The rocks transfer functions magnitude and phase were averaged for the good rocks and damaged rocks, respectively. The data was then compared between the two sets of rocks. The acoustic tests were conducted to further verify the results obtained from modal analysis tests. In the acoustic experiments, careful consideration was paid to the choice of impacting hammers. Once the hammer was chosen, the experiment was conducted on good and damaged rock samples. The sound pressure level (SPL) was found for each rock. The SPL was then averaged for the good and damaged samples, respectively. The averaged SPL was then compared between the two sets of rocks. 4.1 Modal Analysis The modal analysis results allow for the comparison of each rocks dynamic characteristics. Figure 4.1 shows the transfer function of a good sample, rock L11. It is clearly seen that the first resonant frequency of rock L11 occurs around 3,900 Hz, the 39

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40 first observed peak in the rocks transfer function. Figure 4.2 presents the superimposed transfer function magnitude and coherence plots for rock L11. While data is shown for frequencies up to 20 kHz, only data where the coherence was above 90% show meaningful results. Furthermore, only the first resonant frequency of the rocks were analyzed and compared, since this is the dominant resonant frequency. Modal analysis results obtained from the other rocks are presented in Appendix A. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 10-4 10-3 10-2 10-1 100 101 Acceleration wrt. Force Magnitude [g/N]Frequency [Hz] Figure 4.1 Transfer function magnitude of a good sample, rock L11 A typical response of a damaged sample is presented in Figure 4.3. The first resonant frequency is approximately 1,900 Hz, the first peak of the transfer functions magnitude. To appreciate the value of this response, the magnitude and coherence plots are superimposed and presented in Figure 4.4. The representative damaged sample, rock X3 has a lower resonant frequency than the representative good sample, rock L11.

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41 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 10-4 10-3 10-2 10-1 100 101 Frequency [Hz] Magnitude [g/N]Coherence Figure 4.2 Superimposed magnitude and coherence for the good rock L11 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 10-4 10-3 10-2 10-1 100 101 Acceleration wrt. Force Magnitude [g/N]Frequency [Hz] Figure 4.3 Transfer function magnitude of a damaged sample, rock X3

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42 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 10-4 10-3 10-2 10-1 100 101 Frequency [Hz] Acceleration wrt. Force Magnitude [g/N]]Coherence Figure 4.4 Superimposed magnitude and coherence for the damaged rock X3 Table 4.1 presents each rocks mass and first resonant frequency. Figure 4.5 shows a plot of first resonant frequency as a function of mass. While the first resonant frequencies of damaged rock samples were lower compared the undamaged rock samples for most cases, some damaged samples had a higher resonant frequency. Figure 4.6 presents the first resonant frequency for all rock samples. For this reason, the data was averaged for good and damaged samples, respectively.

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43 Table 4.1 Rock samples mass and first resonant frequency ROCK Mass (kg) fr (Hz) X1 17.25 5562 X2 7.26 4237 X3 13.36 1918 X4 6.45 3312 X5 6.55 5719 X6 8.63 3662 X7 8.02 4775 X8 8.41 5000 X9 6.78 7245 X10 11.71 5693 X11 9.38 4387 L2 8.33 5444 L3 9.14 6405 L4 10.09 7818 L5 8.73 5444 L6 9.22 5812 L7 5.56 3145 L8 6.82 4682 L9 13.17 6275 L10 13.38 3957 L11 6.21 3856 L12 16.18 4538 0 2 4 6 8 10 12 14 16 18 0 1000 2000 3000 4000 5000 6000 7000 8000 Mass [kg]Frequency [Hz] Undamaged as told by FDOTDamaged as told by FDOT Figure 4.5 First resonant frequencies as a function of rock mass

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44 1000 2000 3000 4000 5000 6000 7000 8000 1000 2000 3000 4000 5000 6000 7000 8000 Frequency HzFrequency Hz UndamagedDamaged Figure 4.6 First resonant frequencies of all rock samples Further data quantification was completed to verify the accuracy of the results used to predict which rocks are damaged. Figure 4.7 shows a plot of frequency as a function of rock length in the impact direction. Theoretically, impacts made in the direction of shorter lengths should produce higher resonant frequencies. This was not true for most of cases in these experiments. 4.1.1 Comparison of Averaged Data The data for the good and damaged samples were averaged to further quantify the results. The transfer function was averaged over 10 good and 10 damaged samples respectively. The data for rock X4 was discarded because of erroneous magnitude and coherence results. This reduced the number of bad samples from 11 to 10.

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45 1000 2000 3000 4000 5000 6000 7000 8000 10-0.9 10-0.8 10-0.7 Frequency [Hz]Rock Length in Impact Direction [m] UndamagedDamaged Figure 4.7 Frequency as a function of rock length in the impact direction To get an even comparison between good and damaged samples, one rocks data from the good pile of rocks was discarded. The rock chose was L7, which had the lowest coherence of all good rocks. Figures 4.8 and 4.9 present the average transfer function magnitude and phase, respectively, of the good versus damaged samples. It is clearly seen that, on average, the damaged samples have a lower resonant frequency compared with the undamaged samples. The average resonant frequency of the damaged and undamaged samples is approximately 1,900 and 3,900 Hz, respectively. Based on these results, the damaged and undamaged rock samples can be distinguished from each other by comparing the averaged first resonant frequency.

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46 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 10-3 10-2 10-1 100 101 Acceleration wrt. Force Magnitude [g/N]Frequency [Hz] DamagedUndamaged Figure 4.8 Transfer function magnitude comparison between damaged and undamaged rock samples 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 -200 -150 -100 -50 0 50 100 150 200 Frequency [Hz]Phase [deg] DamagedUndamaged Figure 4.9 Transfer function phase comparison between damaged and undamaged rock samples

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47 4.2 Acoustic Experiment The acoustic experiment was conducted to further verify the results obtained by the modal analysis tests and to provide as alternate approach to distinguish between good and damaged rock samples. The sound pressure level (SPL) for each rock was determined. To quantify the results, the average SPL for the good and damaged samples was calculated and used to compare the response between good and damaged samples. 4.2.1 Impact Hammer A modal analysis test was conducted on the Husky hammer to determine its resonant frequencies. An accelerometer was placed on one end and a modal hammer was used to impact the opposite end of the Husky hammers head. Figure 4.10 show the modal analysis result. The first four resonant frequencies are approximately 1, 3.1, 5.7, and 8.2 kHz, respectively. This will determine if the peak SPL is caused by the hammer or the rock when the two are impacted together. Peak SPL at the hammers resonant frequencies are caused by the hammer and hence does not describe the rocks acoustic characteristics. 4.2.2 Sound Pressure Level Results A representative good and damaged rock sample SPL is presented in Figures 4.11 and 4.12. The first observed peak occurs around 1,000 Hz. This is the first resonant frequency of the hammer used to impact the rock. However, the SPL represents the sound generated from both the hammer and the rock when the two are impacted together. To quantify the results, the average SPL was calculated and compared between the good and damaged samples and is presented in section 4.2.3. Sound pressure level results for individual rocks are presented in Appendix B.

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48 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 10-10 10-9 10-8 10-7 Acceleration wrt. Force Magnitude [g/N]Frequency [Hz] Figure 4.10 Husky hammers transfer function magnitude 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 20 30 40 50 60 70 80 90 SPL dB rms(Pa)Frequency [Hz] Figure 4.11 SPL from representative good rock sample, rock L12, using a modified Husky hammer

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49 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 20 30 40 50 60 70 80 90 SPL dB rms(Pa)Frequency [Hz] Figure 4.12 SPL from representative damaged rock sample, rock X5, using a modified Husky hammer 4.2.3 Data Averaging Approach The root-mean-square (rms) pressure and SPL was found from the rms voltage output of the signal analyzer. Equation 4-1 show how to compute the SPL from the output rms voltage of the signal analyzer. 210265010logRMSREFVSPLP Eq. 4-1 Where the sensitivity and multiplier is equal to 650 Pa/Volt and P REF is 20e-06 Pa. The numerator inside the parentheses is equal to the rms pressure. The total rms pressure is found by adding the rms pressure of all damaged and undamaged rocks, respectively. The average rms pressure is found by dividing the total rms pressure by the number of rock samples, 10, of each of the two categories. Finally, the average SPL is found using

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50 the average rms pressure for the damaged and undamaged rocks in Equation 4-2, respectively. ,20logrmsavgavgrefPSPLP Eq. 4-2 4.2.4 Comparison of Averaged Sound Pressure Level The SPL was averaged for two main reasons. First, by performing the modal analysis experiments, an average result closely represents a group of rocks and thus automatically puts less weight on any irregularities that may arise from individual rocks. Second, the SPL produced by a hammer impacting with different rocks will vary because the sound is radiated from both objects. Therefore one can compare between the average and the individual SPL of the rocks and determine any differences. The observed differences are due to the rock and not the hammer. Figure 4.13 presents the average SPL for good and damaged rock samples. It is clearly seen that the first peak occurs at approximately 1,000 Hz. This is the resonant frequency of the hammer used to impact the rocks. There is a 70 Hz difference between the damaged and undamaged rocks first resonant frequency. Based on the frequencies of the structural resonances of the hammer and the resonant frequencies in Figure 4.13, it appears that the sound radiation is dominated by the hammer.

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51 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 101.8 101.9 Frequency [Hz]SPL average UndamagedDamaged Figure 4.13 Averaged SPL of good rocks and damaged rocks

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CHAPTER 5 SUMMARY AND CONCLUSIONS Several rock samples were provided by FDOT already separated into damaged and undamaged categories. The results presented provide two nondestructive evaluation methods to distinguish between damaged and undamaged rock samples. Modal analysis was used to retrieve the dynamic properties of the rocks and the average transfer function magnitude and phase were plotted. Results were also presented using acoustic experiments to compliment the modal analysis experiments and to provide an alternate approach to health monitor the structure of riprap rocks. The average SPL was plotted and compared between damaged and undamaged rock samples. 5.1 Summary of Results Each rocks resonant frequencies were found by using modal analysis experiments. The damaged and undamaged rock samples first resonant frequency was plotted. The average transfer function magnitude and phase for damaged and undamaged rock samples were plotted. The damaged and undamaged samples had an average natural frequency of 1,900 and 3,900 Hz, respectively. The acoustic experiments were conducted and the average SPL was plotted for the damaged and undamaged rock samples. The average SPL was the same at all frequencies for the two categories of rocks. However, the average first resonant frequency of the damaged samples shifted downwards by 70 Hz compared to the undamaged samples. There were no other conclusive result from the acoustic experiments that distinguishes between the damaged and undamaged rock samples. 52

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53 5.2 Conclusions Within this work, two nondestructive evaluation techniques were developed to evaluate riprap rocks. The use of modal analysis and acoustic tests to distinguish between damaged and undamaged rocks was investigated. The modal analysis experiments showed that, on average, there was a first resonant frequency shift between the damaged and undamaged rock samples. The damaged rock samples had a lower natural frequency. However, there was not a consistent pattern among all rocks. Some damaged and undamaged rock samples had high and low resonant frequencies, respectively. It can be concluded that there may have been some mixing between the damaged and undamaged rock samples when they were initially categorized. The acoustic experiments did not provide enough convincing evidence to be used as a method to distinguish between the damaged and undamaged rock samples. However, there was an increase in SPL at the average first resonant frequency of the undamaged samples. The nondestructive evaluation methods developed in this work shows promising results for future evaluation of riprap rocks. There is enough evidence in both the modal analysis and acoustic experiment results to conclude that they can provide an effective means in which to health monitor riprap rocks. However, further work is needed in order to better quantify the results. 5.3 Future Work The averaging of the data in the results obtained from both nondestructive evaluation methods used in this work provides evidence of future success in using these methods to distinguish between damaged and undamaged riprap rocks. However, there are a couple of suggestions to consider prior to future testing. A better categorization of damaged and undamaged rocks is needed to avoid mixing of rock samples and to better

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54 quantify the results. In addition, in order to get a better comparison between different rocks responses, the rock samples should be more consistent in shape and size. This may be achieved by cutting each of the rock samples into cylindrical shapes. The specific gravity of the rocks material should also be obtained if the rock samples are taken from different locations. If the rock samples come from different locations, their specific gravity should be the same if they will be compared with each other. Once the new results are obtained, a sensitivity analysis of the proposed methods needs to be completed in order to match that of the FDOT. The modal analysis and acoustic test methods were only two nondestructive evaluation methods proposed to health monitor riprap rocks. There are several other methods that may be applied to rocks. An impedance-based analysis can also serve as a nondestructive evaluation method. Damaged rocks should produce an impedance variation compared with the undamaged rocks. Currently, NEWS methods are being explored by researchers at Los Alamos National Laboratories as an alternate method to health monitor structures. These methods may provide a more effective way in which to determine damaged from undamaged rock samples and should be considered as an alternate method in future work.

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APPENDIX A MODAL ANALYSIS TRANSFER FUNCTIONS & COHERENCES This appendix contains each rocks transfer function and coherence obtained from the modal analysis experiments. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 10-5 10-4 10-3 10-2 10-1 100 Acceleration wrt. Force Magnitude [g/N]]Frequency [Hz] Figure A.1 Transfer function magnitude for rock X1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 -200 -150 -100 -50 0 50 100 150 200 Acceleration wrt. Force Phase [deg]Frequency [Hz] Figure A.2 Transfer function phase for rock X1 55

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56 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Acceleration wrt. Force CoherenceFrequency [Hz] Figure A.3 Transfer function coherence for rock X1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 10-3 10-2 10-1 100 101 Acceleration wrt. Force Magnitude [g/N]]Frequency [Hz] Figure A.4 Transfer function magnitude for rock X2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 -200 -150 -100 -50 0 50 100 150 200 Acceleration wrt. Force Phase [deg]Frequency [Hz] Figure A.5 Transfer function phase for rock X2

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57 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Acceleration wrt. Force CoherenceFrequency [Hz] Figure A.6 Transfer function coherence for rock X2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 10-4 10-3 10-2 10-1 100 101 Acceleration wrt. Force Magnitude [g/N]]Frequency [Hz] Figure A.7 Transfer function magnitude for rock X3 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 -200 -150 -100 -50 0 50 100 150 200 Acceleration wrt. Force Phase [deg]Frequency [Hz] Figure A.8 Transfer function phase for rock X3

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58 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Acceleration wrt. Force CoherenceFrequency [Hz] Figure A.9 Transfer function coherence for rock X3 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 10-3 10-2 10-1 100 101 102 103 104 Acceleration wrt. Force Magnitude [g/N]]Frequency [Hz] Figure A.10 Transfer function magnitude for rock X4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 -200 -150 -100 -50 0 50 100 150 200 Acceleration wrt. Force Phase [deg]Frequency [Hz] Figure A.11 Transfer function phase for rock X4

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59 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 -1 0 1 2 3 4 5x 104 Acceleration wrt. Force CoherenceFrequency [Hz] Figure A.12 Transfer function coherence for rock X4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 10-3 10-2 10-1 100 101 Acceleration wrt. Force Magnitude [g/N]]Frequency [Hz] Figure A.13 Transfer function magnitude for rock X5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 -200 -150 -100 -50 0 50 100 150 200 Acceleration wrt. Force Phase [deg]Frequency [Hz] Figure A.14 Transfer function phase for rock X5

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60 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Acceleration wrt. Force CoherenceFrequency [Hz] Figure A.15 Transfer function coherence for rock X5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 10-5 10-4 10-3 10-2 10-1 100 101 Acceleration wrt. Force Magnitude [g/N]]Frequency [Hz] Figure A.16 Transfer function magnitude for rock X6 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 -200 -150 -100 -50 0 50 100 150 200 Acceleration wrt. Force Phase [deg]Frequency [Hz] Figure A.17 Transfer function phase for rock X6

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61 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Acceleration wrt. Force CoherenceFrequency [Hz] Figure A.18 Transfer function coherence for rock X6 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 10-3 10-2 10-1 100 101 Acceleration wrt. Force Magnitude [g/N]]Frequency [Hz] Figure A.19 Transfer function magnitude for rock X7 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 -200 -150 -100 -50 0 50 100 150 200 Acceleration wrt. Force Phase [deg]Frequency [Hz] Figure A.20 Transfer function phase for rock X7

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62 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Acceleration wrt. Force CoherenceFrequency [Hz] Figure A.21 Transfer function coherence for rock X7 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 10-3 10-2 10-1 100 101 Acceleration wrt. Force Magnitude [g/N]]Frequency [Hz] Figure A.22 Transfer function magnitude for rock X8 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 -200 -150 -100 -50 0 50 100 150 200 Acceleration wrt. Force Phase [deg]Frequency [Hz] Figure A.23 Transfer function phase for rock X8

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63 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Acceleration wrt. Force CoherenceFrequency [Hz] Figure A.24 Transfer function coherence for rock X8 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 10-3 10-2 10-1 100 101 Acceleration wrt. Force Magnitude [g/N]]Frequency [Hz] Figure A.25 Transfer function magnitude for rock X9 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 -200 -150 -100 -50 0 50 100 150 200 Acceleration wrt. Force Phase [deg]Frequency [Hz] Figure A.26 Transfer function phase for rock X9

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64 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 -100 -50 0 50 100 150 Acceleration wrt. Force CoherenceFrequency [Hz] Figure A.27 Transfer function coherence for rock X9 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 10-3 10-2 10-1 100 101 Acceleration wrt. Force Magnitude [g/N]]Frequency [Hz] Figure A.28 Transfer function magnitude for rock X10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 -200 -150 -100 -50 0 50 100 150 200 Acceleration wrt. Force Phase [deg]Frequency [Hz] Figure A.29 Transfer function phase for rock X10

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65 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Acceleration wrt. Force CoherenceFrequency [Hz] Figure A.30 Transfer function coherence for rock X10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 10-4 10-3 10-2 10-1 100 101 Acceleration wrt. Force Magnitude [g/N]]Frequency [Hz] Figure A.31 Transfer function magnitude for rock X11 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 -200 -150 -100 -50 0 50 100 150 200 Acceleration wrt. Force Phase [deg]Frequency [Hz] Figure A.32 Transfer function phase for rock X11

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66 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Acceleration wrt. Force CoherenceFrequency [Hz] Figure A.33 Transfer function coherence for rock X11 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 10-3 10-2 10-1 100 Acceleration wrt. Force Magnitude [g/N]]Frequency [Hz] Figure A.34 Transfer function magnitude for rock L2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 -200 -150 -100 -50 0 50 100 150 200 Acceleration wrt. Force Phase [deg]Frequency [Hz] Figure A.35 Transfer function phase for rock L2

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67 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Acceleration wrt. Force CoherenceFrequency [Hz] Figure A.36 Transfer function coherence for rock L2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 10-2 10-1 100 Acceleration wrt. Force Magnitude [g/N]]Frequency [Hz] Figure A.37 Transfer function magnitude for rock L3 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 -200 -150 -100 -50 0 50 100 150 200 Acceleration wrt. Force Phase [deg]Frequency [Hz] Figure A.38 Transfer function phase for rock L3

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68 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Acceleration wrt. Force CoherenceFrequency [Hz] Figure A.39 Transfer function coherence for rock L3 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 10-3 10-2 10-1 100 101 Acceleration wrt. Force Magnitude [g/N]]Frequency [Hz] Figure A.40 Transfer function magnitude for rock L4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 -200 -150 -100 -50 0 50 100 150 200 Acceleration wrt. Force Phase [deg]Frequency [Hz] Figure A.41 Transfer function phase for rock L4

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69 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Acceleration wrt. Force CoherenceFrequency [Hz] Figure A.42 Transfer function coherence for rock L4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 10-3 10-2 10-1 100 101 Acceleration wrt. Force Magnitude [g/N]]Frequency [Hz] Figure A.43 Transfer function magnitude for rock L5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 -200 -150 -100 -50 0 50 100 150 200 Acceleration wrt. Force Phase [deg]Frequency [Hz] Figure A.44 Transfer function phase for rock L5

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70 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Acceleration wrt. Force CoherenceFrequency [Hz] Figure A.45 Transfer function coherence for rock L5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 10-3 10-2 10-1 100 101 L6 A1/F1 Transfer FunctionAcceleration wrt. Force Magnitude [g/N]]Frequency [Hz] Figure A.46 Transfer function magnitude for rock L6 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 -200 -150 -100 -50 0 50 100 150 200 Acceleration wrt. Force Phase [deg]Frequency [Hz] Figure A.47 Transfer function phase for rock L6

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71 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Acceleration wrt. Force CoherenceFrequency [Hz] Figure A.48 Transfer function coherence for rock L6 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 10-3 10-2 10-1 100 101 Acceleration wrt. Force Magnitude [g/N]]Frequency [Hz] Figure A.49 Transfer function magnitude for rock L7 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 -200 -150 -100 -50 0 50 100 150 200 Acceleration wrt. Force Phase [deg]Frequency [Hz] Figure A.50 Transfer function phase for rock L7

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72 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Acceleration wrt. Force CoherenceFrequency [Hz] Figure A.51 Transfer function coherence for rock L7 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 10-4 10-3 10-2 10-1 100 101 Acceleration wrt. Force Magnitude [g/N]]Frequency [Hz] Figure A.52 Transfer function magnitude for rock L8 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 -200 -150 -100 -50 0 50 100 150 200 Acceleration wrt. Force Phase [deg]Frequency [Hz] Figure A.53 Transfer function phase for rock L8

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73 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Acceleration wrt. Force CoherenceFrequency [Hz] Figure A.54 Transfer function coherence for rock L8 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 10-4 10-3 10-2 10-1 100 101 Acceleration wrt. Force Magnitude [g/N]]Frequency [Hz] Figure A.55 Transfer function magnitude for rock L9 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 -200 -150 -100 -50 0 50 100 150 200 Acceleration wrt. Force Phase [deg]Frequency [Hz] Figure A.56 Transfer function phase for rock L9

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74 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Acceleration wrt. Force CoherenceFrequency [Hz] Figure A.57 Transfer function coherence for rock L9 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 10-3 10-2 10-1 100 101 Acceleration wrt. Force Magnitude [g/N]]Frequency [Hz] Figure A.58 Transfer function magnitude for rock L10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 -200 -150 -100 -50 0 50 100 150 200 Acceleration wrt. Force Phase [deg]Frequency [Hz] Figure A.59 Transfer function phase for rock L10

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75 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Acceleration wrt. Force CoherenceFrequency [Hz] Figure A.60 Transfer function coherence for rock L10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 10-4 10-3 10-2 10-1 100 101 L11 A1/F1 Transfer FunctionAcceleration wrt. Force Magnitude [g/N]]Frequency [Hz] Figure A.61 Transfer function magnitude for rock L11 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 -200 -150 -100 -50 0 50 100 150 200 Acceleration wrt. Force Phase [deg]Frequency [Hz] Figure A.62 Transfer function phase for rock L11

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76 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Acceleration wrt. Force CoherenceFrequency [Hz] Figure A.63 Transfer function coherence for rock L11 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 10-4 10-3 10-2 10-1 100 101 Acceleration wrt. Force Magnitude [g/N]]Frequency [Hz] Figure A.64 Transfer function magnitude for rock L12 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 -200 -150 -100 -50 0 50 100 150 200 Acceleration wrt. Force Phase [deg]Frequency [Hz] Figure A.65 Transfer function phase for rock L12

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77 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Acceleration wrt. Force CoherenceFrequency [Hz] Figure A.66 Transfer function coherence for rock L12

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APPENDIX B SOUND PRESSURE LEVEL PLOTS This appendix contains the sound pressure level measurements from the impact of the Husky hammer with each rock. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 20 30 40 50 60 70 80 90 SPL dB rms(Pa)Frequency [Hz] Figure B.1 Sound pressure level for rock X1 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 20 30 40 50 60 70 80 90 SPL dB rms(Pa)Frequency [Hz] Figure B.2 Sound pressure level for rock X2 78

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79 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 20 30 40 50 60 70 80 90 SPL dB rms(Pa)Frequency [Hz] Figure B.3 Sound pressure level for rock X3 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 20 30 40 50 60 70 80 90 SPL dB rms(Pa)Frequency [Hz] Figure B.4 Sound pressure level for rock X4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 20 30 40 50 60 70 80 90 SPL dB rms(Pa)Frequency [Hz] Figure B.5 Sound pressure level for rock X5

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80 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 20 30 40 50 60 70 80 90 SPL dB rms(Pa)Frequency [Hz] Figure B.6 Sound pressure level for rock X6 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 30 40 50 60 70 80 90 100 SPL dB rms(Pa)Frequency [Hz] Figure B.7 Sound pressure level for rock X7 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 20 30 40 50 60 70 80 90 SPL dB rms(Pa)Frequency [Hz] Figure B.8 Sound pressure level for rock X8

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81 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 20 30 40 50 60 70 80 90 SPL dB rms(Pa)Frequency [Hz] Figure B.9 Sound pressure level for rock X9 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 20 30 40 50 60 70 80 90 SPL dB rms(Pa)Frequency [Hz] Figure B.10 Sound pressure level for rock X10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 20 30 40 50 60 70 80 90 SPL dB rms(Pa)Frequency [Hz] Figure B.11 Sound pressure level for rock X11

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82 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 20 30 40 50 60 70 80 90 SPL dB rms(Pa)Frequency [Hz] Figure B.12 Sound pressure level for rock L2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 20 30 40 50 60 70 80 90 SPL dB rms(Pa)Frequency [Hz] Figure B.13 Sound pressure level for rock L3 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 20 30 40 50 60 70 80 90 100 SPL dB rms(Pa)Frequency [Hz] Figure B.14 Sound pressure level for rock L4

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83 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 20 30 40 50 60 70 80 90 SPL dB rms(Pa)Frequency [Hz] Figure B.15 Sound pressure level for rock L5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 20 30 40 50 60 70 80 90 SPL dB rms(Pa)Frequency [Hz] Figure B.16 Sound pressure level for rock L6 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 20 30 40 50 60 70 80 90 SPL dB rms(Pa)Frequency [Hz] Figure B.17 Sound pressure level for rock L7

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84 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 10 20 30 40 50 60 70 80 90 SPL dB rms(Pa)Frequency [Hz] Figure B.18 Sound pressure level for rock L8 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 20 30 40 50 60 70 80 90 SPL dB rms(Pa)Frequency [Hz] Figure B.19 Sound pressure level for rock L9 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 20 30 40 50 60 70 80 90 SPL dB rms(Pa)Frequency [Hz] Figure B.20 Sound pressure level for rock L10

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85 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 20 30 40 50 60 70 80 90 100 SPL dB rms(Pa)Frequency [Hz] Figure B.21 Sound pressure level for rock L11 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 104 20 30 40 50 60 70 80 90 SPL dB rms(Pa)Frequency [Hz] Figure B.22 Sound pressure level for rock L12

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LIST OF REFERENCES Ayres, J., Lalande, F., Chaudhry, Z., and Rogers, C. A. (1996). "Qualitative health monitoring of a steel bridge structure via piezoelectric actuator/sensor patches." Proc., SPIE Nondestructive Evaluation Techniques for Aging Infrastruct. and Manufacturing 2946: 211-218. Bajema, R. W., Hyde, G. M. (1998). "Instrumented pendulum for impact characterization of whole fruit and vegetable specimens." Transactions of the ASAE 41(5): 1399-1405. Baritelle, A., Hyde, G. M. (1999). "Strain rate and size effects on pear tissue failure." ASAE Paper No. 99 6003. Cherng, A. P. (1999). "Vibration modes of melons of ellipsoidal shape." ASAE Paper No. 99 6005. Doebling, S. W., Farrar, C. R., Prime, M. B., Shevitz, D. W. (1996). "Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: a literature review." Los Alamos National Laboratory(LA-13070-MS). Fourney, W. L., Dick, R. D. (1994). "The utilization of explosive loading as nondestructive evaluation tool in geologic materials." International Journal of Solids and Structures 32(17-18): 2511-2522. Grabco, D., Palistrant, N., Shikimaka, O., Zhitaru, R., Rahvalov, V., and Zugravescu, D. (2003). "Hardness and brittleness of rocks studied by microindentation method in combination with the registration of acoustic emission signals." NDT.net 8(4). Guyer, R. A., Johnson, P. A. (April 1999). "Nonlinear mesoscopic elasticity: Evidence for a new class of materials." American Institute of Physics: 30-36. Johnson, P. A. (September 1999). The new wave in acoustic testing. Materials World: 544-546. Kam, T. Y., Lee, T. Y. (1992). "Detection of cracks in structures using modal test data." Engineering Fracture Mechanics 42(2): 381-387. Khan, M. A., Jilani, S. Z., Menouar, H., and Al-Majed, A. A. (2001). "A non-destructive method for mapping formation damage." Ultrasonics 39: 321-328. 86

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87 Magness, J. R., Taylor, G. F. (1925). "An improved type of pressure tester for the determination on fruit maturity." USDA Circular 350. Ostrovsky, L. A., Johnson, P. A. (2001). Dynamic nonlinear elasticity in geomaterials. Rivista Del Nuovo Cimento. 24: 1-47. Park, G., Kabeya, K., Cudney, H., and Inman, D. J. (1999). "Impedance-based health monitoring for temperature varying applications." JSME Int. J. 42: 249-258. Park, G., Cudney, H. H., Inman, D. J. (2000). "Impedance-based health monitoring of civil structural components." Journal of Infrastructure Systems 6(4): 153-160. Qian, G. L., Gu, S. N., Jiang, J. S. (1990). "The dynamic behaviour and crack detection of a beam with a crack." Journal of Sound Vibrations 138(2): 233-243. Rizos, P. F., Aspragathos, N., Dimarogonas, A. D. (1990). "Identification of crack location and magnitude in a cantilever beam from the vibration modes." Journal of Sound Vibrations 138(3): 381-388. Rogers, C. A., and Lalande, F. (1996). "Solid-state active sensing for in-situ health monitoring." Proc., MFPT 50th Meeting, Tech. Showcase: 301-308. Sadri, A. (2003). "Application of impact-echo technique in diagnoses and repair of stone mansory structures." NDT&E International 36: 195-202. Sumali, H. (2002). Exploring dynamic properties of fruit, Purdue University. Sun, F., Chaudhry, Z., Liang, C., and Rogers, C. A. (1995). "Truss structure integrity identification using PZT sensor-actuator." J. Intelligent Mat. Sys. and Structure 6: 134-139. Sun, X., Hardy, H. R. Jr. (1990). A feasibility study of modal analysis in geotechnical engineering, laboratory phase. Proceedings of the 31st U.S. Rock Mechanics Symposium, Rotterdam ; Brookfield, A. A. Balkema. Sun, X., Hardy, H. R. Jr. (1992). A feasibility study of modal analysis in geotechnical engineering field phase.: Proceedings of the 33rd U.S. symposium, Sweeney Convention Center, Santa Fe, New Mexico, A. A. Balkema. Van Den Abeele, K. E. A., Carmeliet, J., Ten Cate, J. A., Johnson, P. A. (2000). "Nonlinear elastic wave spectroscopy (NEWS) techniques to discern material damage, part II: single-mode nonlinear resonance acoustic spectroscopy." Res. Nondestr. Eval. 12: 31-42. Van Den Abeele, K. E. A., Johnson, P. A., Sutin, A. (2000). "Nonlinear elastic wave spectroscopy (NEWS) techniques to discern material damage, part I: nonlinear wave modulation spectroscopy (NWMS)." Res. Nondestr. Eval. 12: 17-30.

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88 Windels, F. and K. Van Den Abeele (2004). "The influence of localized damage in a sample on its resonance spectrum." Ultrasonics 42(1-9): 1025-1029.

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BIOGRAPHICAL SKETCH The author was born in So Paulo, Brazil. He graduated with a Bachelor of Science in Mechanical Engineering with honors in August 2002 from the University of Florida, Gainesville, FL. Then, he completed his Master of Science degree in mechanical engineering from University of Florida in August 2004. 89


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Permanent Link: http://ufdc.ufl.edu/UFE0005403/00001

Material Information

Title: Nondestructive Evaluation of Riprap Rocks
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0005403:00001

Permanent Link: http://ufdc.ufl.edu/UFE0005403/00001

Material Information

Title: Nondestructive Evaluation of Riprap Rocks
Physical Description: Mixed Material
Copyright Date: 2008

Record Information

Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
System ID: UFE0005403:00001


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Full Text












NONDESTRUCTIVE EVALUATION OF RIPRAP ROCKS


By

CHRISTIAN BASSOLI DE CARVALHO


















A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA


2004

































Copyright 2004

by

Christian Bassoli de Carvalho
































I dedicate this document to my mother whose endless support and faith through all the
years never ended while I worked to achieve this goal.















ACKNOWLEDGMENTS

I would like to express my sincere gratitude and appreciation to many people who

made this master's thesis possible. Special thanks go to Dr. Christopher Niezrecki for his

guidance and support throughout my research. I would like to thank Drs. John Schueller

and Bjorn Birgisson for serving on my committee. Many thanks are due to my mother

for her support throughout all the years I have studied. I would also like to thank my lab

mates for their guidance. Many more other persons participated to ensure my research

succeeded and to all those persons I am very thankful.
















TABLE OF CONTENTS

page

A C K N O W L E D G M E N T S ......... .................................................................................... iv

LIST OF TABLES ............... ................. ........ ................ .................. vii

LIST OF FIGURES ........... ............... .......... ........... .. ............... .. viii

ABSTRACT ........ .............. ............. ...... ...................... xiv

CHAPTER

1 NON-DESTRUCTIVE EVALUATION METHODS................................................... 1

1.1 M o d al A n aly sis .................................................... ................. .
1.1.1 M odal A analysis on R ocks....................................... .......................... 2
1.1.2 M odal A analysis on Fruits ........................................ ......... ............... 5
1.2 Nonlinear Elastic W ave Spectroscopy ............... ............................................ 8
1.2.1 Nonlinear W ave M odulation Spectroscopy...............................................8
1.2.2 Single-Mode Nonlinear Resonance Acoustic Spectroscopy ....................10
1.2.3 Nonlinear Resonant Ultrasound Spectroscopy................ .... ........... 15
1.2.4 Simple Mode Nonlinear Resonant Ultrasound Spectroscopy ..................16
1.3 Im pedance-B ased A nalysis........................................................ ............... 16
1.4 Im pact-E cho A nalysis................................................. .............................. 21
1.5 Other Non-destructive Evaluation M ethods ............................... ................24

2 STANDARD TEST METHOD FOR SOUNDNESS OF AGGREGATE BY USE OF
SOD IUM SU LFA TE .......................................................... ...... .........25

2 .1 Sodium Sulfate Solution .......................................................................... ...... 25
2 .2 S am p le s ....................................................... ................ 2 6
2 .3 T est Sam ple P reparation .......................................................................... ...... 28
2.4 Testing Procedure .................. ...................................... .... .. ...... .... 28
2.5 Quantitative Sam ple Exam nation .............................................. .................. 29

3 EXPERIM ENTAL SETUP.......................................................................... 30

3.1 M odal A analysis Experim mental Setup ........................................ .....................30
3.1.1 M odal Analysis Instrumentations.................................... ...... ...............30
3.1.2 Modal Analysis Equipment and System Analyzer Setup.........................31









3.1.3 Testing Procedure ....................................................................... 33
3.2 A acoustic Experim ental Setup ........................................ .......... ............... 34
3.2.1 Instrum entation ................. .... .. ............................. ........... 34
3.2.2 Acoustic Equipment and System Analyzer Setup....................................35
3.2.3 Testing Procedure ....................................................................... 37
3 .3 C alib ratio n .................................................................3 7

4 R E S U L T S ..............................................................................3 9

4.1 M odal Analysis ................................ .......... .......... .. ...... .... 39
4.1.1 Comparison of Averaged Data .................................... ...............44
4.2 A acoustic Experim ent .................................................. .............................. 47
4.2.1 Im pact H am m er ................................................ ......... .... .. .. .. .......... 47
4.2.2 Sound Pressure Level Results ....................................... ............... 47
4.2.3 Data Averaging Approach.. ...................... .. ................................... 49
4.2.4 Comparison of Averaged Sound Pressure Level................... ..............50

5 SUM M ARY AND CONCLUSIONS ........................................ ........................ 52

5.1 Sum m ary of R esults.......... ............................................................ .. .... .. .... .. 52
5 .2 C o n c lu sio n s ..................................................................................................... 5 3
5 .3 F u tu re W o rk .................................................................................................... 5 3

APPENDIX

A MODAL ANALYSIS TRANSFER FUNCTIONS & COHERENCES........................55

B SOUND PRESSURE LEVEL PLOTS ............................................... .....................78

L IST O F R E FE R E N C E S ......... .. ............. ................................................................86

B IO G R A PH IC A L SK E TCH ..................................................................... ..................89
















LIST OF TABLES

Table page

1.1 Modal frequencies as defects were introduced............................ ...............4

2.1 Sieve sizes used for fine aggregate sam ples ..................................... .................27

2.2 Sieve sizes and required masses for coarse aggregate samples ................................27

4.1 Rock sample's mass and first resonant frequency ....................................... .......... 43
















LIST OF FIGURES


Figure p

1.1 Rock used to conduct modal analysis experiment ....................................................2

1.2 G rid show ing ham m er im pact points.................................................................... .. 3

1.3 Instrum entation and setup ......... ............................... ..................................... 3

1.4 Elastic cords used to suspend the m elon................................... ......................... 6

1.5 FRF curve and coherence obtained from the melon................................. ...............7..

1.6 Schematic overview of the dynamic response for a one-dimensional wave
p ro p ag atio n ...................... .. .. ......... .. .. ......... ..................................... 8

1.7 E xperim ent scheme atic ...................... .. .. ......... .. ..................... .............................. 9

1.8. Wave modulation spectra of uncracked and cracked Plexiglas.............................9

1.9 Sandstone wave modulation spectra........................... ............ .............. 10

1.10 Experimental setup for SIMONRAS experiments................................ ..................11

1.11 SIMONRAS results. Intact (left) and micro damaged (right) slate beam.
Fundamental accelerations are shown for ten drive voltage levels..........................12

1.12 Cyclic fatigue loading experiment: a) relative resonance frequency shift as a
function of the measured peak acceleration amplitude at different stages of the
fatigue process; b) amplitude dependence of the third harmonic; c) second
h a rm o n ic ...................................................................... 14

1.13 Damage detection illustration using NRUS method ..............................................15

1.14 Various objects that have been tested for nonlinearity using NRUS method............ 16

1.15 M odel of the im pedance-based m ethod ......................................................... ......... 18

1.16 /4-Scale Steel B ridge Setup............................................... ............................. 19

1.17 Damage M etric Chart for the PZTs .............. ................................ .......... ..... 20









1.18 The AndeScope ............... ..................................... ...... ....... 21

1.19 Schem atic of the structure and test set-up....................................... ............... 22

1.20 Frequency spectrum showing an example of VP...................................................22

1.21 Frequency spectrum showing an example of PB.....................................................23

1.22 Frequency spectrum showing an example of FB.....................................................23

1.23 Frequency spectrum showing an example of VGB .......... .................................23

2 .1 L arg e siev e sh ak er........... ................................................ ................ ........ .. ..... ... 2 6

2.2 Sm all sieve shake ............... ................. ........... ............. ........... 26

3.1 Experimental hardware for modal hammer tests ......................................................31

3.3 Riprap sample suspended by bungee cords ...................................... ............... 32

3.4 Modal Analysis Signal Analyzer Windows .......................................... ...........33

3.5 Experimental hardware for acoustic experiment equipments................................35

3.6 Acoustic experimental setup block diagram ........................................ ..........35

3.7 Acoustic signal analyzer window s ..................................................... ............. 36

4.1 Transfer function magnitude of a good sample, rock L11 ............... .................43

4.2 Superimposed magnitude and coherence for the good rock L 11...............................44

4.3 Transfer function magnitude of a damaged sample, rock X3 ....................................45

4.4 Superimposed magnitude and coherence for the damaged rock X3..........................46

4.5 First resonant frequency as a function of rock mass ................................................48

4.6 First resonant frequencies of all rock sample ................................... .................49

4.7 Frequency as a function of rock length in the impact direction..............................50

4.8 Transfer function magnitude comparison between damaged and undamaged rock
sam ples ..................................... ................................... ........... 51

4.9 Transfer function phase comparison between damaged and undamaged rock samples52

4.10 Husky hammer's transfer function magnitude ................. .................................53









4.11 SPL from representative good rock sample, rock L12, using a modified Husky
h am m er ...................................... .................................................. 5 4

4.12 SPL from representative damaged rock sample, rock X5, using a modified Husky
ham m er ..................................... .................. ................ ......... 55

4.13 Averaged SPL of good rocks and damaged rocks ...............................................57

A. 1 Transfer function magnitude for rock X ....................................... ............... 55

A .2 Transfer function phase for rock X ........................................ ........ ............... 55

A.3 Transfer function coherence for rock X ....................................... ............... 56

A.4 Transfer function magnitude for rock X2 ....................................... ............... 56

A.5 Transfer function phase for rock X2 ................................................ .. ... .......... 56

A.6 Transfer function coherence for rock X2 ..................................... ...............57

A.7 Transfer function magnitude for rock X3 ....................................... ............... 57

A .8 Transfer function phase for rock X 3 ........................................ ........ ............... 57

A.9 Transfer function coherence for rock X3 ....................................... ............... 58

A. 10 Transfer function magnitude for rock X4 .............. ............................................58

A 11 Transfer function phase for rock X 4 ......................................................... .........58

A. 12 Transfer function coherence for rock X4 .............. ...........................................59

A. 13 Transfer function magnitude for rock X5 .............. ...........................................59

A 14 Transfer function phase for rock X 5 ........................................................................59

A. 15 Transfer function coherence for rock X5 ............ .............................................60

A. 16 Transfer function magnitude for rock X6 ............... ......................................60

A 17 Transfer function phase for rock X 6 ........................................................................60

A. 18 Transfer function coherence for rock X6 .............. ...........................................61

A. 19 Transfer function magnitude for rock X7 .............. ............................................61

A .20 Transfer function phase for rock X 7 ......................................................... ..........61

A.21 Transfer function coherence for rock X7 .............. ...........................................62









A.22 Transfer function magnitude for rock X8 ...................................... ............... 62

A .23 Transfer function phase for rock X 8 .............................................. ............... 62

A.24 Transfer function coherence for rock X8 .............. .............................................63

A.25 Transfer function magnitude for rock X9 ...................................... ............... 63

A .26 Transfer function phase for rock X9 ............................................ ... .............. 63

A.27 Transfer function coherence for rock X9.......................................64

A.28 Transfer function magnitude for rock X10 ........................................ ..... ......64

A.29 Transfer function phase for rock X10. .. .. .......................... ........................... 64

A.30 Transfer function coherence for rock X10.............. .......................65

A.31 Transfer function magnitude for rock X 11 .................................... ............... 65

A.32 Transfer function phase for rock X 1 ............................... .. ....................... 65

A.33 Transfer function coherence for rock X 1 ..................................... .................66

A.34 Transfer function magnitude for rock L2...................................... ............... 66

A .35 Transfer function phase for rock L2 ........................................ ...... ............... 66

A.36 Transfer function coherence for rock L2 ...................................... ............... 67

A.37 Transfer function magnitude for rock L3............... ......................67

A .38 Transfer function phase for rock L3 ............................... ................................ 67

A.39 Transfer function coherence for rock L3 ...................................... ............... 68

A.40 Transfer function magnitude for rock L4...................................... ............... 68

A .41 Transfer function phase for rock L4 ........................................ ...... ............... 68

A.42 Transfer function coherence for rock L4 ...................................... ............... 69

A.43 Transfer function magnitude for rock L5............................................ 69

A .44 Transfer function phase for rock L5 .............................................. ............... 69

A.45 Transfer function coherence for rock L5 ...................................... ............... 70

A.46 Transfer function magnitude for rock L6...................................... ............... 70









A .47 Transfer function phase for rock L6 ........................................ ...... ............... 70

A.48 Transfer function coherence for rock L6 ...................................... ............... 71

A.49 Transfer function magnitude for rock L7...................................... ............... 71

A .50 Transfer function phase for rock L7 .............................................. .....................71

A.51 Transfer function coherence for rock L7 ...................................... ............... 72

A. 52 Transfer function magnitude for rock L8...................................... ............... 72

A .53 Transfer function phase for rock L8 .............................................. ............... 72

A.54 Transfer function coherence for rock L8 ...................................... ............... 73

A.55 Transfer function magnitude for rock L9...................................... ............... 73

A .56 Transfer function phase for rock L9 ........................................ ...... ............... 73

A.57 Transfer function coherence for rock L9 ...................................... ............... 74

A.58 Transfer function magnitude for rock L10.................................... ............... 74

A .59 Transfer function phase for rock L10 ............................................ ............... 74

A.60 Transfer function coherence for rock L10 ............... ....... ................... 75

A.61 Transfer function magnitude for rock L11 ............... ....... ................... 75

A.62 Transfer function phase for rock L 11 .............................. ........................... 75

A.63 Transfer function coherence for rock L11 .......................... ................. 76

A .64 Transfer function m agnitude for rock L12..................................... .....................76

A.65 Transfer function phase for rock L12 ............................... .. ....................... 76

A.66 Transfer function coherence for rock L12 ..................................... .................77

B 1 Sound pressure level for rock X ........................................ .......................... 78

B .2 Sound pressure level for rock X 2.................................................................... ...... 78

B .3 Sound pressure level for rock X 3 ........................................ .......................... 79

B.4 Sound pressure level for rock X4.............. ...................................... ........... .... 79

B.5 Sound pressure level for rock X5 ..................... ......... ..................................... 79









B .6 Sound pressure level for rock X 6...................... .... ......................... .... ............ 80

B .7 Sound pressure level for rock X 7...................... .... ......................... ... ............. 80

B.8 Sound pressure level for rock X8 .......................... ..................... ............... 80

B .9 Sound pressure level for rock X 9...................... .... ......................... .... ............ 81

B .10 Sound pressure level for rock X 10..................................... ......................... 81

B 11 Sound pressure level for rock X 1 ........................................ ........................ 81

B .12 Sound pressure level for rock L2 ........................................ ......................... 82

B 13 Sound pressure level for rock L3 ............................... .. ................................. 82

B .14 Sound pressure level for rock L4 ........................................ ......................... 82

B .15 Sound pressure level for rock L5 ........................................ ......................... 83

B 16 Sound pressure level for rock L6 ........................................ ......................... 83

B 17 Sound pressure level for rock L7 ........................................ ......................... 83

B .18 Sound pressure level for rock L8 ........................................ ......................... 84

B 19 Sound pressure level for rock L9 ........................................ ......................... 84

B .20 Sound pressure level for rock L 10 ........................................ ........................ 84

B .21 Sound pressure level for rock L 11 ........................................ ........................ 85

B .22 Sound pressure level for rock L 12 ........................................ ........................ 85




















xiii















Abstract of Thesis Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Master of Science

NONDESTRUCTIVE EVALUATION OF RIPRAP ROCKS

By

Christian Bassoli de Carvalho

August 2004

Chair: Christopher Niezrecki
Major Department: Mechanical and Aerospace Engineering

Within this study, two nondestructive evaluation techniques are developed to

evaluate riprap rocks. Modal hammer testing and acoustic measurements are made on

riprap rocks to determine possible defects within the rock structure. Two sets of rock

samples (11 damaged and 11 undamaged) were visually categorized and provided by the

Florida Department of Transportation for this research. Modal hammer testing is used to

determine each rock's transfer function. The acceleration with respect to force

magnitude and phase responses is measured and plotted for each rock. The average

responses are plotted and compared for the damaged and undamaged rock samples. It is

determined that the average first resonant frequency is 1,900 Hz and 3,900 Hz for the

damaged and undamaged rock samples, respectively. The damaged samples' average

first resonant frequency shifted downward. This is characteristic of structures with

damage due to the reduction in stiffness caused by the presence of cracks. The acoustic

experiment is conducted to complement the modal hammer test results. The sound

pressure level (SPL) of each rock is determined by impacting a modified Husky hammer









with a rock and measuring the response using a microphone. The average sound pressure

levels of damaged and undamaged rock samples are plotted and compared, respectively.

There were no variations in the average SPL between the damaged and undamaged rock

samples. However, the average first resonant frequency of the damaged samples was 70

Hz lower compared with the undamaged samples.

The preliminary results indicate that the nondestructive evaluation methods

proposed to diagnose the quality of riprap rocks looks promising. However, due to the

method used by the FDOT to separate the rock samples, it is possible that there is mixing

between the piles of damaged and undamaged rock samples. For this reason, further

work is needed to verify the preliminary findings in this study.














CHAPTER 1
NON-DESTRUCTIVE EVALUATION METHODS

There are several ways to conduct nondestructive evaluation (NDE) of structures.

They include modal analysis, four different methods of nonlinear elastic wave

spectroscopy (NEWS), impedance based analysis, impact-echo analysis, and several

other methods. A summary of these NDE methods is presented in this chapter to provide

a foundation and background of these methods and its possible use on the analysis of

riprap rock.

1.1 Modal Analysis

Modal analysis is a method of nondestructive testing that has the potential to

distinguish between damaged and undamaged rock samples. Kam and Lee (1992)

illustrated this method to detect cracks and their size on a cantilever beam. The detection

of cracks was based on a reduced stiffness model. The estimation of the crack size was

based on the strain energy equilibrium equation. Kam and Lee used a theoretical model

to compare their results with the experiment conducted by Rizos (et al., 1990) and Qian

(et. al., 1990). Kam showed that vibration frequencies and mode shapes of the cantilever

beam were within -5% error when compared to Rizos and Qian's experiments. Kam

concluded that, with slight modifications of the equations, the theoretical model used in

this analysis can be applied to different structures with multiple cracks.

Los Alamos National Laboratory (Doebling et al., 1996) presented a

comprehensive literature review on damage identification methods from changes in

system vibration characteristics. Their overall conclusion on 135 references is that










measured vibration data provides enough evidence to claim whether or not damage is

present in a structure. The modal analysis experiments summarized in this chapter are

most relevant to the research of interest.

1.1.1 Modal Analysis on Rocks

Sun and Hardy (1992) conducted a modal analysis experiment on a large rock

along the side of Interstate Highway 1-81 in Luzerne county, Pennsylvania. Figure 1.1

shows a photograph of the rock.


t"
~2: ir =I~:' .LLt
-L~
'r. t *-
jjri: rc_

~t'~

4 ~ ,,. ~
d~,
~~L~4~ ~n
~r'r~y

rJ
~s. ,,_r'


Figure 1.1 Rock used to conduct modal analysis experiment (Sun and Hardy, 1992)

The modal analysis was conducted with a hammer used excite the modes of

vibration of the rock. A grid, shown in Figure 1.2, was used to locate the impact points.

Five rows of five impact points were chosen. Because of the rock's surface irregularities,

a steel plate was mounted at each reference point for optimum signal transmission to the

accelerometer. Figure 1.3 shows a schematic of their experimental setup.





























Figure 1.2 Grid showing hammer impact points (Sun and Hardy, 1992)


Figure 1.3 Instrumentation and setup (Sun and Hardy, 1992)

The initial experiments started by conducting modal tests on rock block A.

Artificial defects were introduced to simulate damage to the rock. This way, modal

analysis could be used to predict failure on the remaining portions of the rock. Modal

analysis was conducted and recorded after different sets of modifications were made.









Artificial defects were introduced to the rock blocks by four different methods: (1)

Drilling holes with a rotary hammer; (2) Combination of drilling and wedging; (3)

Driving a steel wedge into a fracture point; (4) Driving a steel wedge until part of the

block was completely slid off. Two weeks was allowed between the second and third

modifications to account for weathering phenomena.

After experiments were conducted, Sun observed that the modal frequencies

decreased for each mode of vibration with the introduction of defects. Table 1.1 presents

these results.

Table 1.1 Modal frequencies as defects were introduced (Sun and Hardy, 1992)


Mode 1st 2nd 3rd 4th 5th


MDXX 75 121 146 195 430
NOffXB 69 97 138 180 430
MDXXi267 107 135 180 387
IMDXXB3 70 104 137 190 415
MfDXXB4 82 132 392


The modal frequencies decreased for the block modifications with the exception of

modification from MDXXB2 to MDXXB3, which were modified due to weathering.

Weathering phenomena covered the defects that were made, and thus strengthened the

rock. The second mode of vibration was the only mode that was not consistent.

However, the other modes of vibrations showed a tendency to decrease with the

introduction of defects. Sun and Hardy (1990) also found that the transfer functions of

experiments conducted in different temperature and humidity environments affected









modal parameters but were insignificant. Weather effects on modal parameters were

only briefly studied by Sun and their overall effects were not quantified.

Sun and Hardy (1992) concluded that modal analysis was effective in assessing

damage to rocks. Mode shape and modal frequency were reasonably sensitive to defect

development in the rock. For most of the mode shapes, the frequency shifted downward

with an increase in structure defect. Sun also concluded that modal analysis has great

potentials in the geotechnical area as a nondestructive technique to assess structural

damage.

1.1.2 Modal Analysis on Fruits

Experimental modal analysis (EMA) has been used in engineering to study the

dynamic properties of structures for decades. Researchers at Purdue University have

extended this application to study the properties of fruits. EMA is conducted on fruits to

study the fruit's ripeness, bruises, and/or defects. These fruit properties are important in

assessing the fruit's overall condition (Cherng 1999).

The method that is known to measure a fruit's firmness was developed many

decades ago by Magness and Taylor (Magness 1925). This method measured the force

required to penetrate a fruit with a standardized cone. There were serious issues with this

approach (Bajema et al., 1998; Baritelle 1999; Cherng 1999). Since there were no other

methods to measure a fruit's firmness, this method was used over the years. To

scientifically measure the firmness of fruit, properties of the fruit must be related to the

modulus of elasticity which is related to the resonant frequency. This became the

foundation for using EMA to study the properties of fruits.

Sumali, at the Agricultural and Biological Engineering Department at Purdue

University, conducted a modal analysis experiment on a melon (Sumali 2002). The









purpose of this experiment was to initiate modal analysis work on biological materials to

characterize their physical properties.

To retrieve accurate data from modal analysis tests on the melon, the melon had to

be suspended from a rigid structure with elastic cords. The elastic cords have a low

resonant frequency of vibration. Therefore, measurements taken from the melon will not

be affected by the apparatus (elastic cords) that holds the melon. Figure 1.4 shows a

photograph of the apparatus.




















Figure 1.4 Elastic cords used to suspend the melon (Sumali 2002)

One of the problems encountered by Dr. Sumali and his students was that the

surface of the melon was too porous to attach the accelerometer. They solved this

problem by applying wax to the surface of the accelerometer and attaching it to the melon

at the desired position. Another problem they encountered was that the surface of the

melon was too soft to excite the melon's mode of vibrations greater than 200 Hz. To

overcome this, a metal disk was used as an impact point.










A modal hammer was used to excite the melon. The result of a single test was

averaged over 10 impacts. Figure 1.5 shows some of the results.

n: pot :chcusrccac~sgamtsl-m5pon 2-n


- ... i J .i ..' ... n .... .. .. .. ... I

Figure 1.5 FRF curve and coherence obtained from the melon (Sumali 2002)

The coherence shows that accurate data can be obtained for frequencies less than

500 Hz. The fourth and fifth modes of vibration become less apparent compared to the

first three. This is because of the modal damping factors at higher frequencies.

It was concluded from this experiment that modal analysis can be used effectively

to study the dynamic response of fruits. While this research topic is relatively new, it

provided a foundation for future research of modal analysis on fruits and other biological

materials.









1.2 Nonlinear Elastic Wave Spectroscopy

Nonlinear Elastic Wave Spectroscopy (NEWS) is a method of nondestructive

testing that uses the dynamic response of a system to analyze structural integrity of

solids. There are four types of NEWS: nonlinear wave modulation spectroscopy

(NWMS), single-mode nonlinear resonance acoustic spectroscopy (SIMONRAS),

nonlinear resonant ultrasound spectroscopy (NRUS), and simple mode nonlinear resonant

ultrasound spectroscopy (SIMONRUS). This method utilizes the harmonics and sum and

difference of the frequency to distinguish between undamaged and damaged samples.

Van Den Abeele, Johnson, and Sutin (Van Den Abeele, et. al, 2000) applied this

technique to Plexiglas, an engine component, and sandstone.

1.2.1 Nonlinear Wave Modulation Spectroscopy

A solid possesses a nonlinear dynamic response if it contains any damage (cracks,

flaws, etc.) within the structure. Therefore, NWMS was used to distinguish between

damaged and undamaged structures, since it analyzes the dynamic response of a system.

Figure 1.6 shows the responses for a dynamic one-dimensional wave propagation of a

finite-amplitude monofrequency signal.





i-.
'"'NI

I

"I i .

II



Figure 1.6 Schematic overview of the dynamic response for a one-dimensional wave
propagation (Van Den Abeele et al. 2000)










Figure 1.7 shows the experiment schematic conducted by Van Den Abeele,

Johnson, and Sutin


Figure 1.7 Experiment schematic (Van Den Abeele et al. 2000)

A piezoelectric transducer was used to apply two continuous waves, one at low

frequency of 5-20 kHz and another at high frequency of 70-120 kHz. A calibrated

accelerometer captured the response of the system. The nonlinearity of the response was

illustrated by holding one frequency at constant amplitude while varying the other from

0-10 volts. They showed that the undamaged samples had nearly no nonlinearities. The

damaged samples showed nonlinearity by the presence of harmonics and side bands.

Figure 1.8 illustrates these results for Plexiglas.


V


Cmackd PN-mas


0 25 50 75 100
Fequervy [kHr[

Figure 1.8. Wave modulation spectra of uncracked and cracked Plexiglas (Van Den
Abeele et al. 2000)


r


Imacr pteaSlea
a
P
r
S










The same results were obtained for sandstone. Figure 1.9 shows these results. The

presence of sidebands in the cracked sample spectra illustrates the nonlinearity associated

with the presence of cracks within that sample.


Intact Sandstone






: Cracked Sandstone





65 82.5 100
Frequency [kHz]

Figure 1.9 Sandstone wave modulation spectra (Van Den Abeele et al. 2000)

Van Den Abeele, Johnson, and Sutin showed that NEWS is an effective

nondestructive method used to distinguish between damaged and undamaged solids.

Sandstone, by its very structural nature, already has some nonlinearities. However, the

presence of cracks and flaws within the structure further nonlinearizes the dynamics

response of the system. This method has also shown to be far more sensitive to

nonlinearities than any linear acoustical methods.

1.2.2 Single-Mode Nonlinear Resonance Acoustic Spectroscopy

One of the NEWS methods introduced in the previous section, single-mode

nonlinear resonance acoustic spectroscopy (SIMONRAS), concentrates on the acoustic

nonlinear response of the material when subjected with small wave amplitudes. Van Den

Abeele and his co-workers (Van Den Abeele et al. 2000) illustrated this method on






11

artificial slate tiles, used in roofing construction, to detect damage on the structure.

Figure 1.10 shows a schematic of their experimental apparatus.

Rigid Frame
Wires





Fru nSpc kcr elcrumpetcr
Power Amp l .
....... Ch.._..... .Charge
FrcqueTcv Snthlesizrl Amp


Function G(cr
' 4 ..


UPIB PCI-MIO-I6EX-10

Pentium 100
S LabVrEW Lock-In
FFT-TIHD


Figure 1.10 Experimental setup for SIMONRAS experiments (Van Den Abeele et al.
2000)

The sample was held by nylon wires at the two nodal positions of the structure.

The speaker was used to induce a low frequency wave. An accelerometer was attached to

one end of the beam to measure the output response. LabVIEW was used to post process

the data.

The resonance frequency and the attenuation do not depend on amplitude for the

undamaged samples. There is also no presence of harmonics. For the damaged sample,

however, there was an amplitude-dependent resonance frequency shift. The drive voltage








12



of the speaker was increased in order to increase the amplitude of the response and plot


the frequency shift. Figure 1.11 shows the results.


311 313
Frequency [HzJ


0 0 1 .- **. .

8 =

I ** **
00X)1 -- -.-.- ...
1 10 o)

Fundamental Acceleration Amplitude [m/s]


*i 40









| i;:i

27'9




,11




run
g -

0.0001l


Punda


Damaged Sample


2R3 2R7 291
Frequency [Hz!


.,Y'


I 10 1(i
mental Acceleration Amplitude rn/s']


a 2*f A.3f'
1 .01 5*f


O I . .

OO, X l .. ..


:-.A
AA A
AB IO.
11 No**


SI
010


S- K 011


. "


1 11 100

Fundamental Acceleration Amplitude [m/s1]


5

M .2

o
Sg I
e
V:
9 *c (10


m a b


S10 1K

Fundamental Acceleration Amplitude [Inh:]


& 2*f A 3*f A



A A "
LA 0.
l 8N%
e3


] 1 tr H[
Funldainend Acceleration Amplitude mtrn/|


i .





{ '(XMI


*.D U
U


SIFu1 11(A
Fundamental Acceleration Amplitude [mis]


Figure 1.11 SIMONRAS results. Intact (left) and micro damaged (right) slate beam.
Fundamental accelerations are shown for ten drive voltage levels. (Van Den

Abeele et al. 2000)


Intact Sample


D, 00.
402 '



o


''
~.~~ ".,~~
'' '
'' '
''- '-"
"' "'
' '"
''
"
:::"
"'
"'"""
11111!11111:









By observing the top two figures of Figure 1.11, one can clearly see that there is a

significant frequency shift in the acceleration amplitude of the damaged sample. The

frequency shift is not as clear for the intact sample. Therefore, the relative resonance

frequency shift was plotted. One can see that the intact sample also possess a frequency

shift. However, the frequency shift for the damaged sample can be observed to be much

greater, as amplitude increases, than that for the undamaged sample. Also observed by

Van Den Abeele is the dramatic change of the harmonic spectrum. The third harmonic

became dominant with the presence of flaws in the structure. The second harmonic did

not have a significant impact because hysteresis has little effect on the even harmonics.

A phenomenological model was introduced and is explained in Van Den Abeele 2000.

Analysis of the lowest amplitude resonance after each impact showed that the

nonlinearity parameter had a relative change of 1000%, far exceeding the percent change

in any other parameter. Van Den Abeele also found that linear damping is a better

measurement of nonlinearity then resonance frequency shift in cyclic fatigue loading.

Figure 1.12 illustrates this result.

Van Den Abeele concluded that NEWS is a more effective method to detect

damage in structures by looking at its nonlinearity responses compared to linear

acoustical method. The methods presented in section 1.2 can also be applied to any

geometry, and thus broadening the range of applications of this method.







14




ti I O.IWW-AL1^ I
S 7 0},0)t25*A"w''



I '001

Si i.9 X

1 a I 1i 0
Fundamental Acceleration Amplitude [mi/s]


10




I I


FE-
" < 0.0001


SI IntrlareinMg Iamaigp

0. X)21' Ac 0.0 1 *Ac t
tu *(3(XlX22*AuYI
S AO, .- ,,"

*A 01 I
OK I031*Acc" .(K){1(XI26Acc2-


Fundamental Acceleration Amplitude [m/s r


0] ......1
;(c)


0.01


O.(X1
*


-In----rasing Daage
e-f
+* Increasing Damage


F.IXmd1 ame- al Accelera- o--- Amplitude [

Fundamental Acceleration Amplitude [m/s:]


Figure 1.12 Cyclic fatigue loading experiment: a) relative resonance frequency shift as a
function of the measured peak acceleration amplitude at different stages of the
fatigue process; b) amplitude dependence of the third harmonic; c) second
harmonic (Van Den Abeele et al. 2000)


o -

14
o rA3
oE~4


. ..... ............-..---. .--- ..--.--- .. ......-..-...-- --- .


,


I










1.2.3 Nonlinear Resonant Ultrasound Spectroscopy

Another method of NEWS is nonlinear resonant ultrasound spectroscopy (NRUS).

NRUS, along with all the other NEWS methods, focuses on the nonlinearity response of

the structure due to damage and its amplitude dependence. The nonlinearity due to

damage in this method is detected by observing a change in the wave frequency response

with a change in the wave amplitude input. Johnson, (Johnson 1999), describes this

method by impacting a bell with a hammer and getting the response with a listening

speaker. Figure 1.13 illustrates the NRUS method on a bell. When a hammer is struck

on the bell, the hammer excites the resonance modes of the bell. However, if the bell has

a crack, possibly small enough not to be visible with the naked eye, striking it harder will

cause frequency shifts. As the bell is struck harder, the presence of cracks causes

nonlinearities in the response. This concept can be extended to numerous applications.

Figure 1.14 shows various objects that have been tested for nonlinearity by NRUS

method. The general idea can be explained by the change in the material nonlinear

elastic wave behavior caused by the presence of cracks. This nonlinear behavior is

shown by amplitude dependence frequency shifts of the resonant modes.


Fr iD m t dei 'ia'teu friqufle.NR eS pre(I1.M
hammer a


mrcxH 1 M nde ? inde 3
8 Ir nr i atr t roillcdic "-oldes F'uquincy
b. Oamgqrl i1 Stnkiry l alder, fr-quenciy siifts

ln ar 1& a T 7

I c MoX* 2 Mext 3
Rpli ing- a* it euionai ice modes. bul Jrpqui':_y
firseq-nr7'' rhargeis wil'h impact fer ce


Figure 1.13 Damage detection illustration using NRUS method (Johnson, 1999)




























Figure 1.14 Various objects that have been tested for nonlinearity using NRUS method
(Johnson, 1999)

While NEWS has been shown to be the most effective nondestructive method to detect

damage in a structure, further studies are being done to detect the location of the damage

using current NEWS methods.

1.2.4 Simple Mode Nonlinear Resonant Ultrasound Spectroscopy

The single-mode version of NRUS is referred to as simple mode nonlinear resonant

ultrasound spectroscopy (SIMONRUS). In SIMONRUS experiments, only one specific

mode of the structure is excited (Windels, 2004). Papers on this method of

nondestructive evaluation of structures have not been published by any researchers to

date. However, a paper by Van Den Abeele titled Acoustic characterization of nonlinear

and hysteretic geomaterials: single mode nonlinear resonant ultrasound spectroscopy

(SIMONRUS) has been submitted for publication.

1.3 Impedance-Based Analysis

Impedance-based analysis is another NDT method used to assess the presence of

damage in structures. This method uses a piezoelectric (PZT) transducer at a high









frequency (>30 kHz) to relate electrical impedance of the transducer to the mechanical

impedance of the structure. Park and his colleagues (Park, et. al, 2000) present the

effects of this method on masonry walls, /4-scale bridge element, and a pipe joint to

verify the capabilities of this NDT method. The 1'-scale bridge is discussed in this paper.

The impedance based analysis was chosen in this experiment because of its autonomous

capability and the applicability to various types of structures

Piezoelectric transducers provide a relationship between mechanical strains and

electric fields. If the transducer is mechanically stressed, it generates an electric field and

vice versa. The PZT is driven by a fixed, high frequency, alternating current resulting in

a mechanical response in the PZT and on the structure where it is attached. Because of

this high frequency, only the area in the vicinity of the transducer on the structure

experiences the mechanical response. This mechanical response is then transferred back

to the PZT as an electric field. Figure 1.15 shows the PZT model. When the structure is

damaged, the resulting frequency response of the structure will have a phase shift or

magnitude change in its dynamic response. The impedance-based structural health-

monitoring method evaluates the damage on a structure by the use of a scalar damage

metric. A scalar damage metric is defined (Park, et. al, 2000) "as the sum of the squared

differences of the real impedance changes at each frequency step." The damage metric is

used as a simplification of the impedance response curves. This can be used with a

device that helps inspectors assess damages on a structure with a red/green light based on

the threshold of the damage. Further details of the impedance based method of NDT is

presented in (Sun et al. 1995; Park et. al. 2000).









I = i sin(it-4) Coupled ctr0f"echiiica/l

I K i
i --- I

V vsin ((t) | M [




Figure 1.15 Model of the impedance-based method (Park et al. 2000)

The impedance based approach advantages compared to other NDT methods are:

(1) Approach is not model dependent and it can be applied to any structure; (2) Actuators

used are small; (3) Under normal operating conditions the PZT possesses the following:

wide range of linearity, fast response, lightweight, stability, high conversion efficiency;

(4) Sensitive to small damages due to the high frequency used; (5) Easy to post-process

data; (6) On-line monitoring; (7) Continuous analysis provides long term longevity of the

structure (Rogers 1996).

The /4-scale analysis of the bridge was performed to show the effectiveness of the

impedance-based NDT method to assess structural damage with the presence of changing

ambient boundary conditions. This is a compensation technique, built into the damage

metric, to minimize the effects of external noise such as vibrations and thermal variations

of the surroundings (Park et al. 1999).

Figure 1.16 presents the schematic of the experimental setup for the 1'/-scale bridge

analysis. This bridge is made up of steel angles, plates, and joints and held together by

over 200 bolts. The PZT sensors were mounted on places of the structure where damage

was most likely to occur.































m0.4
M -


Figure 1.16 /4-Scale Steel Bridge Setup (Park et al. 2000)

Preliminary tests conducted on this structure by (Ayres 1996) presents a clear

variation in impedance measurements caused by damage. The ambient boundary

conditions imposed on this experiment was (1) Repeatability monitoring variations of

the signal over a given time; (2) Vibrations vibration being simulated by hammering the

structure while measurements are taken; and (3) Loading a 15 kg load was added to the

structure. First, readings were made with just the boundary conditions in order to identify

its effects on the overall results. Then, damage was done to the structure by loosening

some of the bolts by 1/8 of a turn. The compensation technique was applied by

comparing the two responses, induced by boundary conditions only and by structural

damage, and accounting for the change via the damage metric. Figure 1.17 presents the

results.












1


80

70

60

50



S30
O

20

10

A


r =- T---


PZT 1 PZT 2

Figure 1.17 Damage Metric Chart for the PZTs (Park et al. 2000)

The first 14 damages were caused by the three boundary condition effects

mentioned previously. The other damages, shown in darker shade, shows the damages

picked up by the PZTs due to damage in the structure caused by 1/8-turn of a single bolt

in 3 different locations. These results shows the high sensitivity of the PZTs due to a

minor (1/8-turn of 1 bolt) structural damage. This is critical for early detection of

damage.

The impedance-based NDT method to detect damage in a structure has shown to be

very effective. When compared to other NDT methods, the impedance based method is

the only approach that compensates for external noises such as unwanted vibrations. Due

to the simplicity of its concept, the impedance based method can be applied to a wide

variety of structure with multiple boundary conditions autonomously.


l Variation ns
[ Damage 1
SODamaage 2
M Damage 3









1.4 Impact-Echo Analysis

The impact-echo technique is a non-destructive method used to determine the

location and characterization of internal discontinuities within concrete structures. Sadri

(Sadri, 2003) applied this technique to assess the bonding condition between the facing

stones, mortar, and inner rubble core in stone masonry structures. Figure 1.18 show the

equipment used to perform the nondestructive, impact-echo tests.


















Figure 1.18 The AndeScope (Sadri, 2003)

The stone masonry structures analyzed includes the inner wall, outer wall, and the

buttresses. The outer walls of this structure were of primary concern because it had been

exposed to extreme weather conditions.

A summary of the impact-echo technique is as follows: A mechanical impact

source and an electromechanical receiving transducer are placed on the same surface of

the structure in interest. The impactor generates a P-wave which propagates into the

object and experiences multiple reflections within the opposite end of the solid. Pressure

waves, or P-waves as it is commonly known, are longitudinal waves in which the

oscillation occurs in the same or opposite direction of wave propagation. The reflected











wave is then detected by the transducer. The time-voltage responses are averaged over


10 impacts with FFT frequency analysis algorithms by a dynamic signal analyzer. The


reflections or "echoes" are indicated by frequency peaks in the plots of displacements


versus frequency. Figure 1.19 shows the schematic of the test set-up. Testing was


conducted on both sides of the structure.


Core Impactor









Receiver



Stone Masonry

Groul


Figure 1.19 Schematic of the structure and test set-up (Sadri, 2003)

The results obtained in this paper categorized the structures in terms of four


different bonding strength, very good bonding (VGB), fair bonding (FB), poor bonding


(PB), and very poor bonding (VPB). Figures 1.20 1.23 shows the results.


6054
16
14
12
10
E8
6 1172
4
2

0 1000 2000 3000 4000 5000 6000 7000 BOOW 9000 10000


Figure 1.20 Frequency spectrum showing an example of VPB (Sadri, 2003)














7227
7- 6054

6

5 5176
V 878
=4-

3

2-

1-

0
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
Frequency (Hz)


Figure 1.21 Frequency spectrum showing an example ofPB (Sadri, 2003)


14

12- 5273

10 1269




E 6


4

2

0
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000


Figure 1.22 Frequency spectrum showing an example ofFB (Sadri, 2003)


20

18 1367

16

14

S12

10



6

4

2

0
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
Frequency (Hz)


Figure 1.23 Frequency spectrum showing an example of VGB (Sadri, 2003)









The second set of peaks (>5000 Hz) gives an idea of the number of defects present

in the structure. As the bonding quality strengthens, the second set of peaks decreases,

showing that there is minimal defect within the structure. In conclusion, the impact-echo

technique successfully supplied enough information to categorize the bonding strength of

the structure.

1.5 Other Non-destructive Evaluation Methods

While many NDT methods have been discussed, there are many more out there.

Fourney (Fourney and Dick, 1994) used explosive loading as an evaluation tool in

geological materials. Khan (Khan, et. al., 2001) used ultrasonic to map formation

damage on Berea rock samples. Grabco (Grabco, et. al., 2003) tested the brittleness of

rocks by a microindentation method with the registration of acoustic emission signals.

Many other methods and procedures for conduction of NDT on structures can further be

found in the references mentioned in this paper.














CHAPTER 2
STANDARD TEST METHOD FOR SOUNDNESS OF AGGREGATE BY USE OF
SODIUM SULFATE

Florida Department of Transportation (FDOT) is currently using the method

discussed in this chapter to study the soundness of aggregates subject to weathering. To

determine its resistance to disintegration, the aggregates are saturated in solutions of

sodium sulfate for a specified period. Then the aggregates are dried in an oven. This

procedure of soaking and drying the aggregates occurs approximately five times during a

seven days period before the aggregates' structure is analyzed. The re-immersion of the

aggregates causes an internal expansive force due to the re-hydration of the salt. A more

detailed explanation of this procedure is presented in AASHTO T 104-99 (2003).

2.1 Sodium Sulfate Solution

The sodium sulfate (Na2SO4) solution used for testing the aggregates is prepared by

dissolving 225 grams of the salt per liter of distilled water. This is accomplished at a

minimum temperature of 250C (77F). The volume of the solution should be at least five

times the volume of the samples being tested.

The solution should be stirred frequently as the salt is being added. After

completion, the solution is covered and allowed to cool to 20.3 to 21.90C (68.5 to

71.50F). Before adding aggregates, the solution should be stirred for at least 48 hours.

The specific gravity of the solution should also lie between 1.154 and 1.171 before

testing can begin.










2.2 Samples

Samples used in the experiments are divided into two categories, fine and coarse

aggregates. Figures 2.1 and 2.2 shows the mechanical shakers, each with sieves of

different sizes, used to separate the samples into coarse and fine aggregates. These

shakers provide vertical and lateral motion allowing fine aggregates to pass through to a

smaller size sieve below.


-C l,


Figure 2.1 Large sieve shaker (AASHTO T 27)


Figure 2.2 Small sieve shaker (AASHTO T 27)









Fine aggregates are categorized by samples that have passed through a 9.5-mm (3/8-in)

sieve. There are five different sample sizes that are categorized under fine aggregates.

These sample sizes are presented in Table 2.1.

Table 2.1 Sieve sizes used for fine aggregate samples (AASHTO T 104-99).

Passing Sieve Retained on Sieve
9.5 mm (1/I in.) 4.75 mm (No. 4)
4.75 mm (No. 4) 2.36 mm (No. 8)
2.36 mm (No. 8) I8 mm (No. 16)
1.18 mm (No. 16) 600 gm (No. 30)
600 pm (No. 30) 300 gm (No. 50)


There must be at least 100 grams of each of the five fine aggregate samples for testing.

Coarse aggregate is defined as all the samples that does not include any 4.75-mm or

smaller samples. The different categories and masses required for testing are presented in

Table 2.2.

Table 2.2 Sieve sizes and required masses for coarse aggregate samples
Sieve Size Mass, g
63-mm to 37.5-mnm (2'1 in. to 1 / in,) 5000 300
Consisting of:
50-mm to 37 5-mm (2-in. to I '1/in.) material 2000 20O
63-nmm to 50-mm (2':-in. to 2-in ) material 3000C' 300

37 5-mm to 19.0-mm (1 'I in. to '/in.) 1500 50
Consisting of:
25.0-mm to 19.0-mm (1-in. to 3'-in.) material 500 30
37.5-mm to 25.0-mm (l'/-in. to I-in.) material 1000 a 50

19.0-mm to 9.5-mm ('14 in. to'l in.) 1000 t 10
Consisting of:
12.5-mm to 95-mm ('/z-in. to 'Is-in.) material 330 5
19.0-mm to 12.5-mm ('/4-in. to '/-in.) material 670 10

95-mm to 4.75-mm (', in. to No. 4) 3003 5

(AASHTO T 104-99)









Masses that are less than five percent of any of the sizes specified are not tested. There

are several ways to break a large rock into large (> 19.0-mm) coarse aggregate. These

may be obtained by crushing, splitting, or sawing. When sawing is used to break a larger

rock, the pieces should be greater than 37.5-mm in any dimension.

2.3 Test Sample Preparation

For fine aggregate samples, use a 300-[tm sieve to thoroughly wash the samples.

The samples are then dried at 1100 50C (2300 90F). The five different sieves are then

used to separate the samples into different size categories.

The coarse aggregate samples are washed and dried at the same temperature as the

fine aggregate samples. The coarse aggregate samples are then separated into different

sizes in accordance with the coarse aggregate table (Table 2.2).

2.4 Testing Procedure

Aggregate samples should be immersed in the sodium sulfate solution between 16

and 18 hours at a depth of at least 12.5-mm. For samples that float to the surface,

weighted wire grids may be used to hold samples at the appropriate depth. The solution

temperature should be maintained at a temperature between 20.3 to 21.90C (68.5 to

71.5F) during the immersion process.

After the immersion phase, the aggregates should be allowed to drain for 15 5

minutes. Then, the aggregates are set to dry in an oven at a temperature of 1100C + 5C

(2300C 90C). Samples are dried until constant mass is achieved. Details of

establishing constant mass are provided in (AASHTO T 104-99). Aggregate samples

should then be cooled to 20 to 250C (68 to 770F). Once cooled, the samples are ready to

be re-immersed in the sodium sulfate solution. Re-immersion should be made right after









the samples come out of the oven. In the event that this procedure has to be interrupted,

the samples should remain in the oven at the drying temperature provided above.

After five cycles have been completed, the samples should be washed so that there

is no more sodium sulfate present. This is accomplished by running water at 430 6C

(1100 10F) at the bottom of the containers and allow the water to overflow at the top.

Washing of the samples is completed when there are no significant traces of sodium

sulfate in the overflow water. This is verified by introducing 0.2 molar barium chloride

into the overflow solution. If cloudiness is seen, the wash down process is not

completed. Upon completion of the aggregate wash down, the samples are then dried in

the oven similarly to the drying procedure of the testing phase. The samples are then

categorized by using sieves similar to prior the testing phase. The entire testing

procedure takes approximately seven days, given that there is no time set backs due to

human error or machine failures.

2.5 Quantitative Sample Examination

Damaged samples disintegrate during the testing phase because of the salt re-

hydration when the samples are re-immersed. Therefore, to determine the amount of

mass lost, the samples are tumbled with the same size sieves used prior to testing. For

coarse aggregates, sieving is completed by hand with sufficient agitation so that only

loose particles pass through the sieves. Then, the samples are categorized into their

individual sizes, weighted, and compared to their initial weight prior to testing. The

difference in weight is then reported as percent of the initial mass. A sample that has lost

more than 12% (by mass) of its initial mass is considered a damaged sample. This

percentage is the mass lost during the testing phase.














CHAPTER 3
EXPERIMENTAL SETUP

The objective of this experiment is to perform nondestructive evaluation on riprap

rocks. This is accomplished by exciting the rocks resonant frequencies through modal

analyses and acoustic experiments. It is proposed that rocks categorized as defective will

have lower resonant frequencies than the structurally stable rocks. This chapter discusses

the instrumentations and procedures for conducting modal analyses and acoustic

experiments on riprap rocks.

3.1 Modal Analysis Experimental Setup

Modal analysis is used as a nondestructive method of health monitoring objects by

exciting the object physically and measure the response. For this specific experiment, the

object in question is the riprap rocks. The rocks are excited with a modal hammer and

are measured using an accelerometer. This allows the transfer function, force divided by

acceleration, to be plotted. The resonant frequencies are clearly seen by sharp peaks in

the transfer function's response.

3.1.1 Modal Analysis Instrumentations

There are five components used to conduct the modal analysis experiments. They

consist of an accelerometer, modal hammer, signal conditioner, dynamical signal and

system analyzer (SigLab), and computer. The accelerometer used is the PCB model

353B15, serial no. 62013. This shear accelerometer has a voltage sensitivity of 9.85

mV/g and a frequency range of 1-18 kHz. There is a 5% and 10% response error on

frequencies ranging between 1-12 kHz and 12-18 kHz, respectively. Calibration for the









accelerometer is discussed in section 3.1.3. The modal hammer is manufactured by PCB

Piezotronics, serial no. 13167. The modal hammer was used with a copper tip to excite a

large frequency range. The signal conditioner is the PCB model 482A16, serial no. 2074.

The SigLab model 50-21, serial no. 2000-1379, signal analyzer is used to receive the

output voltage from the signal conditioner. The computer used to gather all data is a 450

MHz, Pentium III processor running Windows 2000 operating system with 128 MB of

RAM. BNC cables are used to connect all the equipment together.

3.1.2 Modal Analysis Equipment and System Analyzer Setup

The initial setup is accomplished with all the equipment turned off. Figures 3.1 and

3.2 presents the experimental setup for the modal analysis experiments.














tem Anal


Figure 3.1 Experimental hardware for modal hammer tests


Modal Hammer Ch.-1 Ch.1 Ch.1
Modal Hammer
In Out In
SIn Out Computer
-- Ch.2 Ch.2 Ch.2
Accelerometer In Out In

Signal Conditioner Dynamic Signal and
System Analyzer
Figure 3.2 Modal analysis experimental setup block diagram









Before testing begins, the rock is brushed off of any loose debris on its surface.

The rock is then suspended with bungee cords from the ceiling, Figure 3.3.


Figure 3.3 Riprap sample suspended by bungee cords

Bungee cords are used because they have very low stiffness and will not affect the

measurements when the resonant frequencies of the rock are excited. The accelerometer

is attached to the rock with a thin coat of wax. This allows the accelerometer to be

securely attached given that there is no loose debris on the rock's surface. Once

everything is connected, the equipment is turned on with SigLab being turned on before

the computer. The dynamic signal analyzer (vna) is then started by typing 'vna' in the

command prompt of MATLAB. Figure 3.4 shows a sample vna window used for the

modal analysis experiments. The peak voltage for channels 1 & 2 is chosen so that there

are no overloads during the experiments. This number varied slightly depending on the










rock being tested. The maximum frequency is set to 20 kHz, which is slightly higher

than the maximum accelerometer frequency of 18 kHz. The record length is chosen to

record data over the maximum time period allowed by the signal analyzer. The trigger is

set to manual arm so that data starts to record when the modal hammer impacts the rock

and the force input exceeds 9% of the full scale range of the input. Each set of data

recorded is averaged over 8 times. This allows for any irregular response to be

disregarded, through averaging, on the final set of data. After setting up all the necessary

parameters, testing commences.

-l -d- etup MC e5up CosChannel Dplay Peew FleStorage t Md

Hp




















Figure 3.4 Modal Analysis Signal Analyzer Windows

3.1.3 Testing Procedure

Testing is initiated by clicking on the average and arm buttons, respectively. The

modal hammer is used to impact the rock at a location on the opposite side of the rock

compared to the location of the accelerometer. After each impact, the channels are

checked for overload. If an overload is present, the data is discarded and the process is









repeated. The force response is another parameter that was carefully observed after each

impact. A double impact will create two peaks in the force response, and thus, is

discarded because the acceleration response will differ from a single impact force.

Depending on the impact, the force response will have different peak sharpness. A long

impact will cause the force response peak to concentrate energy in the lower frequency

range while a sharper peak distributes more energy into higher frequencies. Therefore, a

desirable impact consists of no overloads, triggering of the signal analyzer, and sharp

peaks of the force response. After impacting the rock eight times, the raw averaged data

is saved to the hard drive.

3.2 Acoustic Experimental Setup

The acoustic experiment is used to measure the sound pressure level when a

hammer strikes the riprap rocks. A microphone is used to measure the response of a

hammer impacting a rock. The sound pressure level data is used to compare responses

between defective and structurally stable rocks.

3.2.1 Instrumentation

There are six components used in the acoustic experiment. They include a

hammer, microphone, microphone preamplifier, conditioning amplifier, dynamical signal

and system analyzer (SigLab), and computer. A hammer was chosen so that it generates

the minimum sound when it impacts the rocks. The microphone is a 12" B&K Type

4190, serial no. 2175107. It has a sensitivity of 53.7 mV/Pa. A foam sphere is used to

protect the microphone from wind fluctuations. Calibration for the microphone is

presented in section 3.2.3. The microphone preamplifier is a 1/2" B&K Type 2669, serial

no. 2188131. Used to transmit the voltage signal to SigLab is a B&K Nexus conditioning

amplifier, serial no. 2218569. The SigLab model 50-21, serial no. 2000-1379, signal









analyzer is used to receive the output voltage from the signal conditioner. The computer

used to gather all data is a 450 MHz, Pentium III processor running Windows 2000

operating system with 128 MB of RAM.

3.2.2 Acoustic Equipment and System Analyzer Setup

First, the rock is suspended as shown in Figure 3.3. A picture of the equipment and

block diagram of the setup is shown in Figures 3.5 and 3.6. The microphone is attached

to the preamplifier. The preamplifier is held with a microphone stand. The preamplifier

is connected to channel 1 of the Nexus amplifier. A BNC cable is used to connect the

preamplifier to SigLab. The microphone is positioned 1 meter away and at the same

height as the rock.


Figure 3.5 Experimental hardware for acoustic experiment equipment


Conditioning
Amplifier
Dynamic Signal and
System Analyzer

Figure 3.6 Acoustic experimental setup block diagram










Figure 3.7 shows a sample vna window for the acoustic experiment. The peak

voltage for channel 1, the only channel used, is chosen so that there are no overloads

during the experiments. This number varied slightly depending on the rock being tested.

The maximum frequency is set to 20 kHz, which is much higher than the resonant

frequencies of the rocks. The record length is chosen to record data over the maximum

time period allowed by the signal analyzer. The trigger is set to manual arm so that data

starts to record when the hammer impacts the rock. Each set of data recorded is averaged

over 8 times. The Nexus amplifier is programmed to output a 100 mV/Pa signal from the

microphone. The microphone's sensitivity, 53.7 mV/Pa is also inputted into the

amplifier. The output signal from the amplifier is converted to 10 Pa/V and inputted into

the signal analyzer. Finally, the reference pressure, 20e-06 Pa, is also set on the signal

analyzer. After setting up all the necessary parameters, testing commences.

Tools Window Setup MCSetup Crosshannel Display Preview FleStorage Units Modal Help
i A 'l/
I


Figure 3.7 Acoustic signal analyzer windows









3.2.3 Testing Procedure

To begin testing, the average and arm buttons are pressed, respectively. The signal

analyzer is automatically triggered once the hammer impacts the rock. Striking the rock

with the hammer required some initial experience, similar to the modal analysis tests. If

excessive force is used to strike the rock, the channel overloads. If the rock is stroked

with little force, the signal analyzer does not trigger and thus the data is not recorded.

Careful attention was paid to the microphone's response after each impact. If any

overload was seen, the data was discarded and the process was repeated. After impacting

the rock eight times, the raw averaged data is saved to the hard drive.

3.3 Calibration

The accelerometer used in this experiment is the PCB model no. 353B15, serial no.

62013. A B&K Type 4294 calibration exciter is used to calibrate this accelerometer.

The exciter generates a frequency of 159.2 Hz at an acceleration of 10 m/s2. A PCB

signal conditioner model no. 482A16 is used to send the accelerometer's voltage to

SigLab's data analyzer. The multiplier in SigLab is adjusted to match the manufacturer's

acceleration at the specified frequency. There were no adjustments made since the

accelerometer produced a 10 m/s2 response at a frequency of 159 Hz.

The microphone used in this experiment is the 1/2" B&K Type 4190, serial no.

2175107. It is calibrated using a pistonphone calibrator Type 4229, serial no. 2368878,

with a Type 8103 attachment. The attachment allows for the calibration of 1/2"

microphones. The calibrator was verified on October 17, 2002. The calibrator produces

sound pressure level of 165.8 dB referenced to 1tpPa. A B&K Nexus amplifier, serial no.

2218569, is used to send the voltage from the microphone to the SigLab. The Nexus

amplifier is programmed to output a 100mV/Pa signal from the microphone using 200V






38


as the supply voltage. The amplification is converted to 10 Pa/V and is inputted into

SigLab. Depending on the microphone's response, the multiplier is adjusted to match the

manufacturer's calibrated sound pressure level. Since the microphone produced a 165.8

dB sound pressure, the multiplier was kept at 10 Pa/V. It must be noted that the

calibration is done with no significant external noise sources, since this affects the

microphone's response.














CHAPTER 4
RESULTS

This chapter presents the results obtained from modal analyses and acoustic

experiments. Experiments were conducted on 22 different rocks. Half of the rocks are

structurally good samples, and the rest are internally damaged samples. The good

samples are labeled L2 through L12. The damaged samples are labeled X1 through X11.

There are no specific reasons why this labeling system was chose other than to simply

distinguish between good and damaged samples. First, modal hammer impact testing

was used to acquire the transfer functions of good and damaged rock samples. Then, the

data was post-processed using MATLAB. The rocks transfer function's magnitude and

phase were averaged for the good rocks and damaged rocks, respectively. The data was

then compared between the two sets of rocks. The acoustic tests were conducted to

further verify the results obtained from modal analysis tests. In the acoustic experiments,

careful consideration was paid to the choice of impacting hammers. Once the hammer

was chosen, the experiment was conducted on good and damaged rock samples. The

sound pressure level (SPL) was found for each rock. The SPL was then averaged for the

good and damaged samples, respectively. The averaged SPL was then compared

between the two sets of rocks.

4.1 Modal Analysis

The modal analysis results allow for the comparison of each rock's dynamic

characteristics. Figure 4.1 shows the transfer function of a good sample, rock L11. It is

clearly seen that the first resonant frequency of rock L11 occurs around 3,900 Hz, the







40


first observed peak in the rock's transfer function. Figure 4.2 presents the superimposed

transfer function magnitude and coherence plots for rock L 1. While data is shown for

frequencies up to 20 kHz, only data where the coherence was above 90% show

meaningful results. Furthermore, only the first resonant frequency of the rocks were

analyzed and compared, since this is the dominant resonant frequency. Modal analysis

results obtained from the other rocks are presented in Appendix A.



101
10 ----------- -----i----- -----+---------- ----- -----------
I ----- I ----- I -- -------- I ----- I ------- ---- I -








IFrequency [Hz] x 10
o10 0 ------ ---- -----i




































superimposed and presented in Figure 4.4. The representative damaged sample, rock X3
S r r t f t t tt r
--10- A ----
(D ~ ~ ~~ ------ -l ^ -? W ---- ------ --------
y ----- ----i U- ^ l- j -1!^+-------^ ------+--- ---- --- -
0 --------- I ------
I -----


) -----
10 I r--3E-
S10 I -


0 ------0. 1 1. 14 1----- ------
I - I I I I
10-- ---- I --------

- - -~---I-- --I- -- -- - - ---- I - -
----------- i------i---- -i-----+---------- ------ ------------



Frequency [Hz] 4


Figure 4.1 Transfer function magnitude of a good sample, rock L 1

A typical response of a damaged sample is presented in Figure 4.3. The first resonant

frequency is approximately 1,900 Hz, the first peak of the transfer function's magnitude.

To appreciate the value of this response, the magnitude and coherence plots are


superimposed and presented in Figure 4.4. The representative damaged sample, rock X3

has a lower resonant frequency than the representative good sample, rock L 1.
















S Magnitude [g/N]
- Coherence


0.2 0.4 0.6 0.8 1 1.2
Frequency [Hz]


1.4 1.6 1.8 2

x 104


Figure 4.2 Superimposed magnitude and coherence for the good rock L11




101 __ _


z* 100
0)
0)
-o
nr


0)


C.2




0
L
o





0)
C-)

0


10-1







10-32


-I I__!_ l l
I -
ii
11


0 0.2 0.4 0.6 0.8 1 1.2
Frequency [Hz]


1.4 1.6 1.8 2

x 104


Figure 4.3 Transfer function magnitude of a damaged sample, rock X3


10-4
0












10
10 -- ------ 4-- -- --i-- --- ^----- -----i- --- --- -- -4 -- i------
----- -- Acceleration wrt. Force Magnitude [g/N]]
----- Coherence

100
-- --------- ---------t-----------





1010 --
---- -- \~ \ r-I-- ----I ----- T ^ -



lO---^ -1 -- --------- ------ ---


_10 ___ 1 ______ II_
SI---------J-------------
10







0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Frequency [Hz] x 10


Figure 4.4 Superimposed magnitude and coherence for the damaged rock X3

Table 4.1 presents each rock's mass and first resonant frequency. Figure 4.5

shows a plot of first resonant frequency as a function of mass. While the first resonant


frequencies of damaged rock samples were lower compared the undamaged rock samples

for most cases, some damaged samples had a higher resonant frequency. Figure 4.6


presents the first resonant frequency for all rock samples. For this reason, the data was
averaged for good and damaged samples, respectively.
SI----------- I-----
1-4-------------------------------------------------

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Frequency [Hz] X 104


Figure 4.4 Superimposed magnitude and coherence for the damaged rock X3

Table 4.1 presents each rock's mass and first resonant frequency. Figure 4.5

shows a plot of first resonant frequency as a function of mass. While the first resonant

frequencies of damaged rock samples were lower compared the undamaged rock samples

for most cases, some damaged samples had a higher resonant frequency. Figure 4.6

presents the first resonant frequency for all rock samples. For this reason, the data was

averaged for good and damaged samples, respectively.











Table 4.1 Rock sample's mass and first resonant frequency


X1 17.25 5562
X2 7.26 4237
X3 13.36 1918
X4 6.45 3312
X5 6.55 5719
X6 8.63 3662
X7 8.02 4775
X8 8.41 5000
X9 6.78 7245
X10 11.71 5693
X11 9.38 4387
L2 8.33 5444
L3 9.14 6405
L4 10.09 7818
L5 8.73 5444
L6 9.22 5812
L7 5.56 3145
L8 6.82 4682
L9 13.17 6275
L10 13.38 3957
L11 6.21 3856
L12 16.18 4538


8000

7000
0
6000 ------ -- -- ----- I--
6000

5000 0
S5000 ------- - ^ L

0)
4000 -

LL 3000


2000-

1000

x
0 2 4 6 8 10
Mass [kg]


Undamaged as told by FDOT
Damaged as told by FDOT
12 14 16 18


Figure 4.5 First resonant frequencies as a function of rock mass


ROCK


Mass (kg)


fr (Hz)











8000 -------


7000---

6000
6000 ------- -------------- ----------------------- -


I 5000
S0)



3000
(- 4000 -I----+------ ------ -


3000 ------- T------n-------- -------r7-------T ------- -------


2000 -- -
0 Undamaged
x0 Damaged
1000 -,-, ..--
1000 2000 3000 4000 5000 6000 7000 8000
Frequency Hz


Figure 4.6 First resonant frequencies of all rock samples

Further data quantification was completed to verify the accuracy of the results used

to predict which rocks are damaged. Figure 4.7 shows a plot of frequency as a function

of rock length in the impact direction. Theoretically, impacts made in the direction of

shorter lengths should produce higher resonant frequencies. This was not true for most of

cases in these experiments.

4.1.1 Comparison of Averaged Data

The data for the good and damaged samples were averaged to further quantify the

results. The transfer function was averaged over 10 good and 10 damaged samples

respectively. The data for rock X4 was discarded because of erroneous magnitude and

coherence results. This reduced the number of bad samples from 11 to 10.













0 Undamaged
-o 7 x Damaged
10



C X
o0

S1008
t5 10 .............. -------- -- ------^-------- -------


Q-



o 10
S10

X

1000 2000 3000 4000 5000 6000 7000 8000
Frequency [Hz]


Figure 4.7 Frequency as a function of rock length in the impact direction

To get an even comparison between good and damaged samples, one rock's data from the

good pile of rocks was discarded. The rock chose was L7, which had the lowest

coherence of all good rocks. Figures 4.8 and 4.9 present the average transfer function

magnitude and phase, respectively, of the good versus damaged samples. It is clearly

seen that, on average, the damaged samples have a lower resonant frequency compared

with the undamaged samples. The average resonant frequency of the damaged and

undamaged samples is approximately 1,900 and 3,900 Hz, respectively. Based on these

results, the damaged and undamaged rock samples can be distinguished from each other

by comparing the averaged first resonant frequency.














Damaged
- Undamaged


S100

o



2 10-
LL


0

-2
0

<


0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Frequency [Hz] x 104


Figure 4.8 Transfer function magnitude comparison between damaged and undamaged
rock samples


200
S-- Damaged
Undamaged
150 -----


100 -----


50




r-5



-100


-150 -----


-200
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Frequency [Hz] x 104


Figure 4.9 Transfer function phase comparison between damaged and undamaged rock
samples









4.2 Acoustic Experiment

The acoustic experiment was conducted to further verify the results obtained by the

modal analysis tests and to provide as alternate approach to distinguish between good and

damaged rock samples. The sound pressure level (SPL) for each rock was determined.

To quantify the results, the average SPL for the good and damaged samples was

calculated and used to compare the response between good and damaged samples.

4.2.1 Impact Hammer

A modal analysis test was conducted on the Husky hammer to determine its

resonant frequencies. An accelerometer was placed on one end and a modal hammer was

used to impact the opposite end of the Husky hammer's head. Figure 4.10 show the

modal analysis result. The first four resonant frequencies are approximately 1, 3.1, 5.7,

and 8.2 kHz, respectively. This will determine if the peak SPL is caused by the hammer

or the rock when the two are impacted together. Peak SPL at the hammer's resonant

frequencies are caused by the hammer and hence does not describe the rock's acoustic

characteristics.

4.2.2 Sound Pressure Level Results

A representative good and damaged rock sample SPL is presented in Figures 4.11

and 4.12. The first observed peak occurs around 1,000 Hz. This is the first resonant

frequency of the hammer used to impact the rock. However, the SPL represents the

sound generated from both the hammer and the rock when the two are impacted together.

To quantify the results, the average SPL was calculated and compared between the good

and damaged samples and is presented in section 4.2.3. Sound pressure level results for

individual rocks are presented in Appendix B.


















Z -7
| 10


r-
0)

010
0
LL



10-9
0
o
<


10-10 E EE I -I I
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
Frequency [Hz]



Figure 4.10 Husky hammer's transfer function magnitude


0 0.2 0.4 0.6 0.8 1 1.2
Frequency [Hz]


Figure 4.11 SPL from representative good rock sample,
Husky hammer


1.4 1.6 1.8 2
x 104


rock L12, using a modified











90


80 ---








50
70








40 -
30-------



20
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Frequency [Hz] x 104


Figure 4.12 SPL from representative damaged rock sample, rock X5, using a modified
Husky hammer

4.2.3 Data Averaging Approach

The root-mean-square (rms) pressure and SPL was found from the rms voltage

output of the signal analyzer. Equation 4-1 show how to compute the SPL from the

output rms voltage of the signal analyzer.


6502 V
SPL =10 log10 650 p Eq. 4-1
P2
K ^REF )

Where the sensitivity and multiplier is equal to 650 Pa/Volt and PREF is 20e-06 Pa. The

numerator inside the parentheses is equal to the rms pressure. The total rms pressure is

found by adding the rms pressure of all damaged and undamaged rocks, respectively.

The average rms pressure is found by dividing the total rms pressure by the number of

rock samples, 10, of each of the two categories. Finally, the average SPL is found using









the average rms pressure for the damaged and undamaged rocks in Equation 4-2,

respectively.


SPLg = 20 log Im avgEq. 4-2
I re )

4.2.4 Comparison of Averaged Sound Pressure Level

The SPL was averaged for two main reasons. First, by performing the modal

analysis experiments, an average result closely represents a group of rocks and thus

automatically puts less weight on any irregularities that may arise from individual rocks.

Second, the SPL produced by a hammer impacting with different rocks will vary because

the sound is radiated from both objects. Therefore one can compare between the average

and the individual SPL of the rocks and determine any differences. The observed

differences are due to the rock and not the hammer. Figure 4.13 presents the average

SPL for good and damaged rock samples. It is clearly seen that the first peak occurs at

approximately 1,000 Hz. This is the resonant frequency of the hammer used to impact

the rocks. There is a 70 Hz difference between the damaged and undamaged rock's first

resonant frequency. Based on the frequencies of the structural resonances of the hammer

and the resonant frequencies in Figure 4.13, it appears that the sound radiation is

dominated by the hammer.


































0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
Frequency [Hz]


Figure 4.13 Averaged SPL of good rocks and damaged rocks














CHAPTER 5
SUMMARY AND CONCLUSIONS

Several rock samples were provided by FDOT already separated into damaged and

undamaged categories. The results presented provide two nondestructive evaluation

methods to distinguish between damaged and undamaged rock samples. Modal analysis

was used to retrieve the dynamic properties of the rocks and the average transfer function

magnitude and phase were plotted. Results were also presented using acoustic

experiments to compliment the modal analysis experiments and to provide an alternate

approach to health monitor the structure of riprap rocks. The average SPL was plotted

and compared between damaged and undamaged rock samples.

5.1 Summary of Results

Each rock's resonant frequencies were found by using modal analysis experiments.

The damaged and undamaged rock samples' first resonant frequency was plotted. The

average transfer function magnitude and phase for damaged and undamaged rock

samples were plotted. The damaged and undamaged samples had an average natural

frequency of 1,900 and 3,900 Hz, respectively.

The acoustic experiments were conducted and the average SPL was plotted for the

damaged and undamaged rock samples. The average SPL was the same at all frequencies

for the two categories of rocks. However, the average first resonant frequency of the

damaged samples shifted downwards by 70 Hz compared to the undamaged samples.

There were no other conclusive result from the acoustic experiments that distinguishes

between the damaged and undamaged rock samples.









5.2 Conclusions

Within this work, two nondestructive evaluation techniques were developed to

evaluate riprap rocks. The use of modal analysis and acoustic tests to distinguish

between damaged and undamaged rocks was investigated. The modal analysis

experiments showed that, on average, there was a first resonant frequency shift between

the damaged and undamaged rock samples. The damaged rock samples had a lower

natural frequency. However, there was not a consistent pattern among all rocks. Some

damaged and undamaged rock samples had high and low resonant frequencies,

respectively. It can be concluded that there may have been some mixing between the

damaged and undamaged rock samples when they were initially categorized. The

acoustic experiments did not provide enough convincing evidence to be used as a method

to distinguish between the damaged and undamaged rock samples. However, there was

an increase in SPL at the average first resonant frequency of the undamaged samples.

The nondestructive evaluation methods developed in this work shows promising

results for future evaluation of riprap rocks. There is enough evidence in both the modal

analysis and acoustic experiment results to conclude that they can provide an effective

means in which to health monitor riprap rocks. However, further work is needed in order

to better quantify the results.

5.3 Future Work

The averaging of the data in the results obtained from both nondestructive

evaluation methods used in this work provides evidence of future success in using these

methods to distinguish between damaged and undamaged riprap rocks. However, there

are a couple of suggestions to consider prior to future testing. A better categorization of

damaged and undamaged rocks is needed to avoid mixing of rock samples and to better









quantify the results. In addition, in order to get a better comparison between different

rocks' responses, the rock samples should be more consistent in shape and size. This

may be achieved by cutting each of the rock samples into cylindrical shapes. The

specific gravity of the rock's material should also be obtained if the rock samples are

taken from different locations. If the rock samples come from different locations, their

specific gravity should be the same if they will be compared with each other. Once the

new results are obtained, a sensitivity analysis of the proposed methods needs to be

completed in order to match that of the FDOT.

The modal analysis and acoustic test methods were only two nondestructive

evaluation methods proposed to health monitor riprap rocks. There are several other

methods that may be applied to rocks. An impedance-based analysis can also serve as a

nondestructive evaluation method. Damaged rocks should produce an impedance

variation compared with the undamaged rocks. Currently, NEWS methods are being

explored by researchers at Los Alamos National Laboratories as an alternate method to

health monitor structures. These methods may provide a more effective way in which to

determine damaged from undamaged rock samples and should be considered as an

alternate method in future work.























APPENDIX A

MODAL ANALYSIS TRANSFER FUNCTIONS & COHERENCES


This appendix contains each rock's transfer function and coherence obtained from



the modal analysis experiments.



10


z 10

10 ========
4- --- -4--- --- --4 ^- -f A
-- 4 --- ---- L --- "J --J^





102




1 4
4I I I I I I
10 ==
Q ----t- ---- - -- ^ -





SI I -I- I -





0 02 04 06 08 1 12 14 16 18
Frequency [Hz] x 104

Figure A. 1 Transfer function magnitude for rock X1



200

150
150---- ----- ------ -- --







-50 I
,o 0 -




8 100 -


-150 ,

-200
0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] 104

Figure A.2 Transfer function phase for rock X1







































Frequency [Hz] 104

Figure A.3 Transfer function coherence for rock X1




10' I I L -d h I
10




S10 -= ====






10C -- _2_ __
210 1

10
I I- I- I- I I--4-
o i i i i I


02 04 06 08 1 12
Frequency [Hz]


14 16 18 2
x 104


Figure A.4 Transfer function magnitude for rock X2


-1 I------ --
2 100

50

0 6




I I I^-l -- ^ ^
50-


o 100---

150--- ---- -


-200 I
0 02 04 06 08 1 12
Frequency [Hz]


14 16 18 2


Figure A.5 Transfer function phase for rock X2





































Frequency [Hz] 104

Figure A.6 Transfer function coherence for rock X2


0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] x 104

Figure A.7 Transfer function magnitude for rock X3



200

150--- --- -- -




50 ii- -
o 0







150--- -1----- -
o -50 - - 1



-100 - --- -^[- -T F T -

-150 -I - ------ -I t -I I I -

200
0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] 104

Figure A.8 Transfer function phase for rock X3


I T= o



:T El I_
L_7
-1 I -
:T -

































0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] 104

Figure A.9 Transfer function coherence for rock X3


0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] 104

Figure A. 10 Transfer function magnitude for rock X4



200 1


0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] 104

Figure A. 11 Transfer function phase for rock X4


-I








59



x 104



4--------------- -----


S-
0




0 ---^----- - -- -- -

-1




0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] x 104

Figure A.12 Transfer function coherence for rock X4


10
10 1 - -- -- I- -- -











10 2 i
2 10











S1L00


1 5 0 - - -
210
0 02 04 06 08 1 1 2 14 16 18 2
Frequency [Hz] x 104

Figure A. 13 Transfer function coherencitude for rock X5
100 I






o 5100 -|


100



S200
I-4 4 ^ - --I- -


103 ---- I I I- I- I- -



























0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] 104

Figure A. 14 Transfer function phase for rock X5
200-------------------------

15 0 - I I F ^ I-r -








1 5 0 -- I - I I I I I




Frq ec ,H ]^^
FiueAo100nfrfncinpae o okX































0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] 104

Figure A. 15 Transfer function coherence for rock X5


10 # =


10


S10
10



10 4
< 10-


10 1
0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] x 104

Figure A. 16 Transfer function magnitude for rock X6


200

150 I ---- -

100 -
50- 0 1 i
50- -- -




S oo -
| 100 -- - I-- -------------

-150--- ----- ---- ----

200
0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] 104

Figure A. 17 Transfer function phase for rock X6


+i
,,E__?___





































0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] 104

Figure A. 18 Transfer function coherence for rock X6


Frequency [Hz] x 104

Figure A. 19 Transfer function magnitude for rock X7



200


100

50
00
o


U- 0


- J -


-tl


o 100 V

-150---
-1250 --- -- -- ,i

200
0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] x 104

Figure A.20 Transfer function phase for rock X7




































Frequency [Hz] 104

Figure A.21 Transfer function coherence for rock X7


0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] x 104

Figure A.22 Transfer function magnitude for rock X8



200

150 -- -- -T - -

j| 100 - - \ - -
150- -






I -50- -- --\- -- --- --
S100-- -- -
I 60I










-150 ----- -- -----

200
0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] 104

Figure A.23 Transfer function phase for rock X8





































Frequency [Hz] 104

Figure A.24 Transfer function coherence for rock X8



101


0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] x 104

Figure A.25 Transfer function magnitude for rock X9



200

150----- --- --

100 -




0 I


S-50 -




-150 --- --- --- -- --

200
0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] 104

Figure A.26 Transfer function phase for rock X9










64





150



100 T-



C 50 -
o


^ 0---4----- -^ - 4 - -
0


0

S -50---- -I I t --- I




100
0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] 104

Figure A.27 Transfer function coherence for rock X9



10





10
S10I
E I -
-1 - L - --1 F 1-- -- -











10





0 02 04 06 08 1 12 14 16 18 2













100 --- I -


50-
o 50 ------



o -50- - -


S- -- -0


-150 ---------- -- ---- ----


200
0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] x 104

Figure A.29 Transfer function phase for rock X10
------------------





















1 5 0 - - t t- - H


-200 --------------------------



Figure A.29 Transfer function phase for rock XI10




































0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] 104

Figure A.30 Transfer function coherence for rock X10


10-
0


Figure A.3


02 04 06 08 1 12 14 16 18 2
Frequency [Hz] x 104

1 Transfer function magnitude for rock X11


150 -

S100- -

I-50--- I tI
0

o 0 0







-150 -

200
0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] 104

Figure A.32 Transfer function phase for rock X11


_~___d-s
-i---Af~


1








































Frequency [Hz] 104

Figure A.33 Transfer function coherence for rock X 11



10

I--- -------I ---- -- ------









o 10- -- -----
S-- - I I I ~ ~ ~ ~
L --- -- L- --

4- +-- + -


02 04 06 08 1 12
Frequency [Hz]


14 16 18 2
x 104


Figure A.34 Transfer function magnitude for rock L2



200


150


100


S50

o o
U- 0


o -50


-100


150


0 02 04 06 08 1 12
Frequency [Hz]


14 16 18 2


Figure A.35 Transfer function phase for rock L2








67





09 4 --- -- -
08
oI




u-05--- ---- t- --t
04--- ---



Frequency [Hz] x104
L 06 4 I A I











Figure A.36 Transfer function coherence for rock L2
001




10
0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] X 104

Figure A.36 Transfer function coherence for rock L2


10 --4 --- ----- ---


S-- -I -- --- ------ -- ---- T I-

T --
c I T -
I 0 ^ I- -t- I -









-0 - -_

-150--- ---- ------ ------ ----


10











150 I I I I



r 50

0
u ---0






200
0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] 104

Figure A.38 Transfer function phase for rock L3
.g 1 0 4 - - I- -I- -4 4
I -- / - T I- --I- -
,
I I I I I --^ I
u_ I ^ - I I^^ r l i -
I -5 - - I I- -
I I I\




Fiur A. 3 8 TrnfrfnIo hs ookL






































0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] 104

Figure A.39 Transfer function coherence for rock L3


a 10 =l===== ==


I I I t -I I I t










10
O -ZZ ZZZiZZZ ZZZI

150---------------- ----- --
F -oT








0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] x 104

Figure A.40 Transfer function magnitude for rock L4



200

150
5 T I I

100 --- I- -I 4 -1 -



5 0 -i-
0I I




o 100 I I I I I I I I







-200
0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] x 104

Figure A.41 Transfer function phase for rock L4
S 2- 00 - - I I- I- I- I-






Frqu nc [Hz I II4
Fiur A.4 Trnse fucIo IhsookL









69








09 8-


S07

06





S03I



S02 04 06 08 1 12 14 16 18
02 -------- I -- t- ----- --


0TT1- ----------------------------
0 02 04 06 08 1 112 14 1 6 1 8 2
Frequency [Hz] 104

Figure A.42 Transfer function coherence for rock L4



10




"' 100
1 -- ----- ---

S 02 04 0-8 --4 -
tt



10











200
-1 0 -- I-- --- -- I- -- -- -- -
0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] x 104

Figure A.44 Transfer function magn e for rock L5



200---------------- ----I--



05








100 -- -




150---- -- -
02 04 06 08 1 12 14 16 18 2


Frequency [Hz] x 104

Figure A.44 Transfer function phase for rock L5










70







09



S07 I
08-- I-- -

i07 -I -- -I-- I





S036--- ---- --- -
06---
05
t
a 04 -

S03 -


01--- ---- ---I---
<02

01 I
T I T I I F T I T I-

0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] 104


Figure A.45 Transfer function coherence for rock L5


L6 A1/F1 Transfer Function
10

4 I - I - I






T0 ----- ------- -----















50--- ^----- -- --- --- S A rE


-50--- ---- --- ,- ^ ^ --7 ^ f^ ^
100 -










150--- --- ----9---- --- -
I I I





















200
F10r 0






Fii A 750u -fe ------okL


j| 100- --- -- - - T ~ ^











0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] x 104

Figure A.47 Transfer function phase for rock L6
2 I
I I20 60 21 61
orqec H]x0









71






09

0 08 -1 18























10
S07

o
I05--- -

i04 -- I -
10

<02--- ---- --

0 1 T- -- -- T- -- - - -


0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] 104

Figure A.48 Transfer function coherence for rock L6



101 :j -1 I-


S ---- ------- ----


































S 0 -
0 - -- - -
o 100
-5- iI-- --------- i --- 1 I|


10 I I 1 1 1
II






0 02 04 06 08 1 12 14 1 6 18



Frequency [Hz] x 104

Figure A.50 Transfer function phase for rock L7
100









0 --T--- I -- -- I----








150- - -- --
S0- --- --- E-E-- E --






o -I50 -I I

100 ---------- 2- -I -

150 II -I

-200 -
0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] x 104

Figure A. 50 Transfer function phase for rock L7



































Frequency [Hz] 104

Figure A. 51 Transfer function coherence for rock L7



10 .


02 04 06 08 1
Frequency [H:


12 14 16 18 2
z] x 104


Figure A.52 Transfer function magnitude for rock L8



200 1


150

" 100

50
00

U- 0

o -50

S-100
4


0 02 04 06 08 1 12
Frequency [Hz]


14 16 18 2
x 104


Figure A.53 Transfer function phase for rock L8


Pn


T -I





t

T


t -

- -- -




L L i
c----------
-








































Frequency [Hz] 104

Figure A.54 Transfer function coherence for rock L8




01 4 ---I ----I ---- ------

4I --- ------4 ----
10



z = == = = ==l== =| -- --I--
~~~ -- -- y- t l -!^--- -
10 -__ _____

10




1 0 3 I I I I -
8 10, -| -=
< == =l== = == ==================



104
0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] x 104

Figure A.55 Transfer function magnitude for rock L9


200

150- -


" 100 -



I
L 50 -------~--





8 -100-


-150


-200
-150 -


-200


0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] 104

Figure A.56 Transfer function phase for rock L9








74





09

08 - -


8, 0 6 - --- T-- - -
F 07- A T

06

0 I I
1 0 --- -----

S0 3 1 1 -

02- -- ---I -

0 1 -
10 T-- -- T-- F


0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] 104

Figure A.57 Transfer function coherence for rock L9


10



100
T 0 14 I -I _





0 02 04 06 08 1 12 14 16 18 2









Figure A.59 Transfer function pohaense for rock LO
102
I -- -
S-- -- I ===== L ======



0 02 04 06 08 1 12 14 16 18 2


Figure A. 5 8 Transfer function magnitude for rock L 10




-100---- --- -- -- -----l--







-150--- ---- -- --- -- -- -\ -- -
200





0 0
50 .







S 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] x 104

Figure A.59 Transfer function phase for rock L10
2 00 - - I- [ I I-

-150 - -- ^ I[- I ^ --
-200_ 50--------------------------






Fiur A. I I rnfrfnto hs o okL

















09

08 -



06










01
o 2 -r- -













0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] 104

Figure A.60 Transfer function coherence for rock L10


L11 A1/F1 Transfer Function
10
4 1 I I
I I I- --L I I- -


10, o - - - ^- -
I I I I I 1
























10
0" I-

10 --- -- I I I- I -- -
0 --- --- --- --- -- -- -- E- I-
0 ---- --------- -- -- ---- ------


0 02 04 06 08 1 12 14 16 18 2
Lll AI/F1 Transfer Function













































Frequency [Hz] x 104

Figure A.62 Transfer function phase for rock L11
10 -


-- - --- - - -






10 = = = == =


0 02 04 06 08 1 112 114 1 6 1 8 2
I -Ii










150 I t I I I

2100 .. L
-- I I I I-- ^ ^ + -












0 02 04 06 08 1 12 14 16 18 2

Figure A. 62 Transfer function mase for rock LI I





s -200 - I-- I-- I -






Figure A.62 Transfer function phase for rock LI11









76







09



08



057










S I I
C 06 - I 1

o
05 ---- -- -I



















10
8 10






104


































Frequency [Hz] x104

Figure A.64 Transfer function magnitude for rock L12
S03 -- -- -- -L

<02 -- --- -- --- -




























0 -- -
10

























S100--- -----
0 I I I 0

















o 100













0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] X 104








Figure A.65 Transfer function phase for rock L12
I ___ I -


1 E I I -
0 1 I L -




5103 W 1 =1 B 3 E 1= = 1
I - I -




I -I^ L'I I I I -
10 - 1 - - ---
I I :I I-I


104 4 I





-- I I+t ^ - - -
0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] X 104

Figure A. 64 Transfer function magnitude for rock L 12



200

150---------- T Ir


a 100 I I I I I


50 ----- -




o -50




150
-150 - - -t- ^ ^ -


-200 I III
0 02 04 06 08 1 1 2 14 16 18 2
Frequency [Hz] x 104

Figure A.65 Transfer function phase for rock L12































0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] 104

Figure A.66 Transfer function coherence for rock L12




















APPENDIX B
SOUND PRESSURE LEVEL PLOTS


This appendix contains the sound pressure level measurements from the impact of


the Husky hammer with each rock.



90

80 I

70

S60 I

50 I

40---

30----


Frequency [Hz] 104

Figure B.1 Sound pressure level for rock X1


90 1


0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] 104

Figure B.2 Sound pressure level for rock X2





































Frequency [Hz] 104

Figure B.3 Sound pressure level for rock X3



90


80


70


S60 I t -


50 4 -


40 -





0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] 104

Figure B.4 Sound pressure level for rock X4


0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] 104

Figure B.5 Sound pressure level for rock X5






























Frequency [Hz] 104

Figure B.6 Sound pressure level for rock X6


Frequency [Hz] 104

Figure B.7 Sound pressure level for rock X7


0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] 104

Figure B.8 Sound pressure level for rock X8






































Frequency [Hz] 104

Figure B.9 Sound pressure level for rock X9



90


80 -


70 -





60Figure B.10 Sound pressure level for rock X10


40


30


20
0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] X 104

Figure B10 Sound pressure level for rock X1O


0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] 104

Figure B. 11 Sound pressure level for rock X11







































Frequency [Hz] 104

Figure B. 12 Sound pressure level for rock L2



90


80 -


70


60


50 -


40 -


30 -


20
0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] 104

Figure B. 13 Sound pressure level for rock L3


0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] 104

Figure B. 14 Sound pressure level for rock L4






































Frequency [Hz] 104

Figure B.15 Sound pressure level for rock L5



90


80 -


70 -


60


50 -


40 -


30- -


20
0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] 104

Figure B. 16 Sound pressure level for rock L6


0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] 104

Figure B. 17 Sound pressure level for rock L7






































Frequency [Hz] 104

Figure B.18 Sound pressure level for rock L8



90


80 -


70





50 -


40 -


30 -


20
0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] 104

Figure B. 19 Sound pressure level for rock L9


0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] 104

Figure B.20 Sound pressure level for rock L10
















100










40
60


o 50 -- U I







20
0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] 104

Figure B.21 Sound pressure level for rock L 1



90


80


70






50 T T -
I I II
I I


0 02 04 06 08 1 12 14 16 18 2
Frequency [Hz] 104

Figure B.22 Sound pressure level for rock L12