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Modeling the locked-wheel skid tester to determine the effect of pavement roughness on the international friction index

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Title:
Modeling the locked-wheel skid tester to determine the effect of pavement roughness on the international friction index
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Cummings, Patrick
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University of South Florida
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Subjects / Keywords:
Speed constant
Dynamic load coefficient
Measured skid number
Friction prediction
Megatexure
Dissertations, Academic -- Civil & Environmental Engineering -- Masters -- USF   ( lcsh )
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non-fiction   ( marcgt )

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Abstract:
ABSTRACT: Pavement roughness has been found to have an effect on the coefficient of friction measured with the Locked-Wheel Skid Tester (LWT) with measured friction decreasing as the long wave roughness of the pavement increases. However, the current pavement friction standardization model adopted by the American Society for Testing and Materials (ASTM), to compute the International Friction Index (IFI), does not account for this effect. In other words, it had been previously assumed that the IFI's speed constant (SP), which defines the gradient of the pavement friction versus speed relationship, is an invariant for any pavement with a given mean profile depth (MPD), regardless of its roughness. This study was conducted to quantify the effect of pavement roughness on the IFI's speed constant. The first phase of this study consisted of theoretical modeling of the LWT using a two-degree of freedom vibration system. The model parameters were calibrated to match the measured natural frequencies of the LWT. The calibrated model was able to predict the normal load variation during actual LWT tests to a reasonable accuracy. Furthermore, by assuming a previously developed skid number (SN) versus normal load relationship, even the friction profile of the LWT during an actual test was predicted reasonably accurately. Because the skid number (SN) versus normal load relationship had been developed previously using rigorous protocol, a new method that is more practical and convenient was prescribed in this work. This study concluded that higher pavement long-wave roughness decreases the value of the SP compared to a pavement with identical MPD but lower roughness. Finally, the magnitude of the loss of friction was found to be governed by the non-linear skid number versus normal load characteristics of a pavement.
Thesis:
Thesis (MSCE)--University of South Florida, 2010.
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Includes bibliographical references.
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by Patrick Cummings.
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ABSTRACT: Pavement roughness has been found to have an effect on the coefficient of friction measured with the Locked-Wheel Skid Tester (LWT) with measured friction decreasing as the long wave roughness of the pavement increases. However, the current pavement friction standardization model adopted by the American Society for Testing and Materials (ASTM), to compute the International Friction Index (IFI), does not account for this effect. In other words, it had been previously assumed that the IFI's speed constant (SP), which defines the gradient of the pavement friction versus speed relationship, is an invariant for any pavement with a given mean profile depth (MPD), regardless of its roughness. This study was conducted to quantify the effect of pavement roughness on the IFI's speed constant. The first phase of this study consisted of theoretical modeling of the LWT using a two-degree of freedom vibration system. The model parameters were calibrated to match the measured natural frequencies of the LWT. The calibrated model was able to predict the normal load variation during actual LWT tests to a reasonable accuracy. Furthermore, by assuming a previously developed skid number (SN) versus normal load relationship, even the friction profile of the LWT during an actual test was predicted reasonably accurately. Because the skid number (SN) versus normal load relationship had been developed previously using rigorous protocol, a new method that is more practical and convenient was prescribed in this work. This study concluded that higher pavement long-wave roughness decreases the value of the SP compared to a pavement with identical MPD but lower roughness. Finally, the magnitude of the loss of friction was found to be governed by the non-linear skid number versus normal load characteristics of a pavement.
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PAGE 1

Modeling the Locked-Wheel Skid Tester to Determine the E ffect of Pavement Roughness on the International Friction Index by Patrick Cummings A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Civil Engineering Department of Civil and Environmental Engineering College of Engineering University of South Florida Major Professor: Manjriker Gunaratne, Ph.D. Abdul Pinjari, Ph.D. Qing Lu, Ph.D. Date of Approval: June 11, 2010 Keywords: speed constant, dynamic load coefficient, measured skid number, friction prediction, megatexure Copyright 2010 Pa trick Cummings

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DEDICATION I dedicate this manuscript to my wife Heather, without whom I would not have had the courage to finish, and to my parents Russell and Marcie, who instilled in me the thirst for knowledge.

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ACKNOWLEDGMENTS I would like to thank Dr. Manjriker Guna ratne for giving me the opportunity to participate in the Masters Degree program. He inspired and provoked the thoughts related to this manuscript. I would also like to thank Dr. Abdul Pinjari and Dr. Qing Lu for agreeing to serve on my committee. Special th anks to the members of my research group who helped me to complete my research and testing.

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i TABLE OF CONTENTS LIST OF TABLES iii LIST OF FIGURES iv ABSTRACT vi CHAPTER 1 INTRODUCTION 1 1.1 Background 1 1.2 Principles of Pavement Friction 2 1.3 Locked-Wheel Skid Tester 4 1.4 Limitations of the Inte rnational Friction Index 5 1.5 Objectives of Study 6 CHAPTER 2 EXPERIMENTAL ANALYSIS AND RESULTS 7 2.1 Proposed Vibration Modeling System 7 2.2 Verification of the Program 9 2.2.1 Modeling of a Two Degree of Freedom System Without Damping 9 2.2.2 Modeling of an Uncoupled Two De gree of Freedom System With Damping 10 2.2.3 Modeling of a One Degree of Freedom System With Damping 12 2.3 Determination of LWT Parameters Using Modeling Techniques 15 2.4 Verification of LWT Parameters Using Fi eld Measurements 16 2.5 Determination of the Relationship Between the Friction and Normal Loads 19 2.6 Verification of Friction Load Modeling 25 2.7 Modeling the Effects of Pavement Roughness on the IFI 27 2.8 Field Verification of the Effects of Pa vement Roughness on the IFI 32 2.9 Modeling the Effects of the Normal Load versus Friction Load Relationship 34 2.10 Alternative Method for Determining Relationship Between SN and Normal Load 37 CHAPTER 3 CONCLUSIONS AND RECOMMENDATIONS 40 3.1 Current Research Proponents 40 3.2 Contribution 1 – Theoretical Prediction of LWT Friction Values 40

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ii 3.3 Contribution 2 Effects of Pavement Roughness on the IFI 41 3.4 Contribution 3 Effects of Fric tional Dependency on Normal Load on the IFI 41 LIST OF REFERENCES 42

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iii LIST OF TABLES Table 2-1: Model Parameters for a Tw o Degree of Freedom System Without Damping 10 Table 2-2: Model Parameters for a Two Degree of Freedom System With Damping 11 Table 2-3: Model Parameters for a One De gree of Freedom Syst em Restricting the Motion of M2 13 Table 2-4: Model Parameters for a One De gree of Freedom System Restricting the Motion of M1 14 Table 2-5: Parameters of a Two Degree of Freedom System Representing the LWT 16 Table 2-6: Parameters for the SN vs. W Relationship for Pavements C and D (Fuentes et al., 2010) 20 Table 2-7: Parameters for Projection of SN vs. Normal Load Relationship Across a Range of Speeds for Pavement C (Fuentes et al., 2010) 24 Table 2-8: Parameters for Projection of SN vs. Normal Load Relationship Across a Range of Speeds for Pavement D (Fuentes et al., 2010) 24 Table 2-9: Inputs for Frequency Variation An alysis (A = 0.25 m) 28 Table 2-10: Results of Frequenc y Variation Analysis on Pavements C and D 29 Table 2-11: Inputs for Freque ncy Variation Analysis ( = 0.05 Hz) 30 Table 2-12: Results of Amplitude Variation Analysis on Pavements C and D 31 Table 2-13: Results from Pavement Roughness An alysis on Pavement B 33 Table 2-14: Results from Pavement Roughness An alysis on Pavement I 34 Table 2-15: Results from SN Variation Analysis on Pavements C, E, F, and G 37

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iv LIST OF FIGURES Figure 2-1: Two Degree of Freedom System with Displacement Input 7 Figure 2-2: Frequency Spectrum of a Tw o Degree of Freedom System Without Damping 11 Figure 2-3: Frequency Spectrum of a Tw o Degree of Freedom System With Damping 12 Figure 2-4: Frequency Spectrum of the One Degree of Freedom System Restricting the Motion of M2 14 Figure 2-5: Frequency Spectrum of the One Degree of Freedom System Restricting the Motion of M1 15 Figure 2-6: Frequency Spectrum of a Two Degree of Freedom System Representing the LWT 16 Figure 2-7: Longitudinal Pr ofile of Pavement H 17 Figure 2-8: Comparison of Experimental and Modele d Response of LWT at 20 mph 18 Figure 2-9: Comparison of Experimental and Modele d Response of LWT at 40 mph 18 Figure 2-10: Comparison of Experimental and Modeled Response of LWT at 60 mph 19 Figure 2-11: SN vs. W Relationship at 30 mph (Fuentes et al., 2010) 21 Figure 2-12: SN vs. W Relationship at 55 mph (Fuentes et al., 2010) 21 Figure 2-13: Derived Relationship of Frictional Force to Normal Load at 30 mph 22 Figure 2-14: Derived Relationship of Frictional Force to Normal Load at 55 mph 22 Figure 2-15: Relationship between SNi and Speed 23

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v Figure 2-16: Relationship between SNr and Speed 23 Figure 2-17: Relationship of SN vs. Normal Load for Pavement H at 55 mph 26 Figure 2-18: Relationship of Friction Load vs. Normal Load for Pavement H at 55 mph 26 Figure 2-19: Comparison of Model Prediction to th e Results of Friction Tests 27 Figure 2-20: Frequency Vari ation Effects on the Fricti on-Speed Relationship of Pavement C 28 Figure 2-21: Frequency Vari ation Effects on the Fricti on-Speed Relationship of Pavement D 29 Figure 2-22: Amplitude Variation Effect s on the Friction-Speed Relationship of Pavement C 30 Figure 2-23: Amplitude Variation Effect s on the Friction-Speed Relationship of Pavement D 31 Figure 2-24: Effect of Pavement Roughness on IFI Parameters for Pavement B 33 Figure 2-25: Effect of Pavement Roughness on IFI Parameters for Pavement I 33 Figure 2-26: Skid Relationship of SN vs. Normal Load for Pavements C, E, F, and G at 55 mph 35 Figure 2-27: Variation in SN versus Speed for Pavements C, E, F, and G 36 Figure 2-28: Effects of Variation in SN for Pavements C, E, F, and G with Speed 36 Figure 2-29: Relationship of SN vs. Normal Load for Pavement A at 25, 40, and 55 mph Using Schallamach’s Equation 38 Figure 2-30: Relationship of SN vs. Normal Load for Pavement I at 20, 30, and 40 mph Using Schallamach’s Equation 39

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vi Modeling the Locked-Wheel Skid Tester to Determine the Effect of Pavement Roughness on the International Friction Index Patrick Cummings ABSTRACT Pavement roughness has been found to have an effect on the coefficient of friction measured with the Locked-Wheel Skid Test er (LWT) with measur ed friction decreasing as the long wave roughness of the pavement increases. However, the current pavement friction standardization m odel adopted by the American Society for Testing and Materials (ASTM), to compute the Internati onal Friction Index (IFI), does not account for this effect. In other words, it had been prev iously assumed that th e IFI’s speed constant ( SP), which defines the gradient of the paveme nt friction versus speed relationship, is an invariant for any pavement with a given m ean profile depth (MPD), regardless of its roughness. This study was conducted to quantify the effect of pavement roughness on the IFI’s speed constant. The first phase of this study consisted of theo retical modeling of the LWT using a two-degree of freedom vibra tion system. The model parameters were calibrated to match the measured natural frequencies of the LWT. The calibrated model was able to predict the normal load variation during actual LWT tests to a reasonable accuracy. Furthermore, by assuming a previously developed skid number ( SN ) versus normal load relationship, even the friction pr ofile of the LWT during an actual test was predicted reasonably accurately. Because the skid number ( SN ) versus normal load

PAGE 10

vii relationship had been developed previously us ing rigorous protocol, a new method that is more practical and convenient was prescribed in this work. This study concluded that higher pavement long-wave roughne ss decreases the value of the SP compared to a pavement with identical MPD but lower roughne ss. Finally, the magnitude of the loss of friction was found to be governed by the non-linear skid number versus normal load characteristics of a pavement.

PAGE 11

1 CHAPTER 1 INTRODUCTION 1.1 Background Evaluation and maintenance of friction in all pavement sections of a highway network is a crucial task of transportation safety programs. The frictional interaction between vehicle tires and pavement has b een studied at many levels, and significant efforts have been made to determine the f actors that govern its mechanism. In early stages of highway pavement maintenan ce, pavement friction was measured and quantified using static testing devices combined with theoretical physi cal models. At that time, the principal attributes of friction were assumed to be centered solely on pavement texture. As technology improved, full-scal e dynamic friction testing devices that resembled the vehicles in motion in term s of the magnitude of pavement friction experienced, were developed. It has been found recently that pavement friction is, in fact, governed by several factors including pavement lubrication, pa vement roughness, and ve hicle behavior in addition to pavement texture. Innovative fric tion measuring devices are constantly being developed with the measuring mechanisms of each being different from the others. However, most of the current devices in use have been found to produce significantly different results when used on the same pa vement [2]. This observation has led to

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2 research regarding harmonization of devi ces and standardization of the friction evaluations. 1.2 Principles of P avement Friction The coefficient of pavement friction, is defined as follows: =F W (1a) where F is the friction force exerted by the pavement on a wheel and W is the normal load of the device acting on that pavement. However, full-scale friction testing devices quantify and report pavement friction as the Skid Number, SN defined as; SN=100* (1b) It has been shown that the slip speed, S at which friction is m easured, has a significant effect on the value of the measured SN S= *%Slip (1c) where VV is the vehicle speed and the Percen t Slip is determined by Equation 1d. %Slip (1d) VT is the speed of rotation of the tire during the test. The Penn State Model [1] expresses the speed dependency of SN as follows; SNS=SN0ePNG 100 S (2) where SNS is the skid number meas ured at a slip speed of S SN0 is the skid number at zero speed, and PNG is the percent normalized gradient expressing the rate of decrease of friction with speed. SN0 is a factor that has been hi ghly correlated to the pavement microtexture, and PNG is presumed to be dependent only on the pavement macrotexture.

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3 SN0 and PNG can be determined from linear regressi on of friction data at various speeds using Equation 2. In order to address the n eed for standardization of measurement of different devices, the Permanent Interna tional Association of Road Co ngresses (PIARC) [2] met in France in 1995 to coordinate and conduct an experiment to standardize full-scale pavement friction testing. This experiment, known as the International PIARC Experiment to Compare and Harmonize Te xture and Skid Resistance Measurements encompassed sixty-seven parameters from fi fty-four pavement sites measured by fortyseven different devices from sixteen countries [2]. Based on the analysis of the results, the International Friction Inde x (IFI) concept was developed. Subsequently, the American Society for Testing and Materials (ASTM) adopted the IFI and formulated the Standard Practice for Calculating Inte rnational Friction Index of a Pavement Surface (E1960-072009) [3] The IFI standard is a calibration method in which full-scale friction testers are calibrated against a static fr iction tester, the Dynamic Friction Tester (DFT). The DFT measured friction value at 20 km/h, DFT20 is used as a baseline for calibration. In order to express the speed dependency of fric tion, the following PIARC model has been developed by revising the Penn State Model [2]; FRS=FR0eS S P (3) where FRS is friction measure at a slip speed S FR0 is the friction at zero speed, and SP is the speed gradient which expresses the rate at which friction reduces with speed. Just as in the case of the original Penn State Model [2] in Equation 2, FR0 has been highly correlated to pavement microtexture, while SP has been shown to be correlated to a

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4 pavement’s mean profile depth (MPD). The CT Meter is the standard laser device that is recommended for evaluation of the macrotextu re of a pavement in terms of MPD. FR0 and SP can be found using linear regression of fr iction data acquired at varying speeds, using Equation 3. In order to calibrate full-scale frictio n measuring devices using Equation 3, the FR60 values of a given pavement measured with a full-scale device are compared to the F60 values gathered by the DFT on the same pavement [2]. The FR60 values are found by converting friction values found at various sp eeds back to the friction value at 60 km/h using the SP value of the pavement measured wi th the CT meter using the rearranged form of Equation 4; FR60=FRSeS-60 S P (4) Then, using linear regression of the corresponding values of FR60 and F60 for several test sections, the following calibration equation can be developed and subsequently applied to standardize pavement friction measurements at any speed; F60=A+B*FR60 (5) where A and B device specific consta nts. Finally, using F60 from Equation 5 and the SP readings obtained from the CT Meter, the Inte rnational Friction Index (IFI) of a pavement is reported as [ F60, SP] [2]. 1.3 Locked-Wheel Skid Tester Among the many different types of full-scale friction measuring devices, the Locked-Wheel Skid Tester (LWT) has been known to collect the repeatable and consistent data. It is for this reason that State Departments of Transportation (DOT) and

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5 the Federal Highway Administration (FHWA) have adopted the LWT as the standard friction measuring device. The LWT is a full slip device, since the measurements are carried out at a slip of 100 percent with th e measuring wheel completely locked during testing. ASTM regulates the manufacturing and measuring standard of the LWT in Standard Test Method for Skid Resistance of Paved Surfaces Using a Full-Scale Tire (E274-06-2009) [4]. 1.4 Limitations of the Int ernational Friction Index The above IFI concept has inherent li mitations because the dynamic effects experienced by full-scale testing devices such as the LWT are not fully expressed when calibrated against a static testing device such as the DFT. It has been documented that pavement long-wave roughness has a significant effect on the measured skid values [5]. Pavement long-wave roughness, also known as the megatexture, causes the normal load of the measuring device to fluctuate. This normal load fluctuation can be quantified by the Dynamic Load Coefficient, DLC expressed as; DLC=WWSTATIC (6a) where W is the standard deviation of the normal load and WSTATIC is the static weight of the device. An increased DLC over a pavement section has b een shown to lower the skid values measured by the LWT [5]. This effect is seen to affect the ca librated IFI values of pavements that produce significantly high DLC values. The factor contributing to the variation of the measured skid resistance with the DLC is the dependency of the measured skid values on the normal load. Fuentes et al. [5]

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6 showed that the following approximate equati on can be used to express the relationship between normal load and SN ; SN=SN+SNi-SNr1+e(W-w i ) b (6b) where SNi is the SN at relatively low normal loads, SNr is the SN at relatively high normal loads, W is the instantaneous normal load, and wi and b are parameters specific to the LWT. Fuentes’ pavement friction depe ndency on normal load deviations can be compared to the empirical equation devel oped by Schallamach [6] to express the dependence of rubber friction on the normal load; =cW 1 3 (7) where is the observed friction, W is the normal load, and c is dependent on the velocity. 1.5 Objectives of Study Due to the above discussed limitations of the IFI and the observed effect of DLC on measured skid values, an i nvestigation was proposed to fu rther quantify the effects of DLC on the IFI. By theoretically modeling th e dynamics of the LWT and comparing the model’s predicted behavior with the corres ponding field measurements, the effect of pavement roughness on the IFI calibrati on standard would be quantified.

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7 CHAPTER 2 EXPERIMENTAL ANALYSIS AND RESULTS 2.1 Proposed Vibration Modeling System In previous research completed at the Un iversity of South Florida (USF) [5], it was shown that the dominant natural frequenc y of the LWT is approximately 1.9 Hz. An additional natural frequency around 11 Hz was al so revealed, but with a nearly damped out corresponding deflection. Therefore, a damp ed two-degree of free dom system with a dominant natural frequency cl ose to 1.9 Hz is proposed to model the LWT appropriately. Figure 2.1 illustrates the proposed mode l and the associated parameters; Figure 2-1: Two Degree of Freedom System with Displacement Input M1 is the mass of the first degree of freedom of the model, and its displacement is given by the function q1(t) K1 and C1 are the respective spring constant and damping value for the first degree of fr eedom of the model. M2 is the mass of the s econd degree of freedom

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8 of the model, and its displacement is given by the function q2(t) K2 and C2 are the respective spring constant and damping valu e for the second degree of freedom of the model. The input for the proposed model is a displacement corresponding to the pavement profile, y=f(x) that is transformed into a tim e dependent vertical displacement input, y=f(t) using the following equation; t=x S (8) where x is the longitudinal distance along the pavement profile, and S is the speed of the LWT. The proposed modeling program wa s built around the following equation of motion in space state form; z =Az +B y+C y (9) where z is the array of state of variables in Equation 10, A B and C are array variables in Equations 11, 12, and 13, y is the first derivative of the pavement profile with respect to time, and is the first derivative of the variable z z = [ q2 q2 q1 q1 ] (10) A= 0 1 0 0 -K2M2 0K2M1 -C2M2 K2M2 C2M2 001C2M1 -( K2+ K1) M1 -( C2+ C1) M1 (11) B = 0 0 0 K1M1 T (12) C = 0 0 0 C1M1 T (13) Using the above variables, the following numerical forms of the first and second derivatives of the displacement functions, q1(t) and q2(t), were used to solve for the system’s response explicitly;

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9 q i t =qi t+ t -qi tt 2 t (14) q i t =qi t+ t +qi tt -2qi(t) t2 (15) A Microsoft Excel program, LWT Prediction Model was developed to solve Equations 815 and hence model the response of two degree of freedom systems. 2.2 Verification of the Program Due to the fact that the developed pr ogram has the capacity to model any given two degree of freedom system that experi ences a time dependent displacement input, several verifications were conducted to en sure the accuracy of the program. These verifications are outlined in the following sections. 2.2.1 Modeling of a Two Degree of Freedom System Without Damping Since the vibration response of damped systems is relatively complex, the verifications started with an undamped two degree of freedom system. Das [7] shows that the natural frequencies of an undamped two degree of freedom system can be found using the following closed form solutions: 1 n=1 2 K1+K2M1 + K2M2 + K1+K2M1 -K2M2 2+4K2 2M1M2 1 2 1 2 (16) 2 n=1 2 K1+K2M1 + K2M2 K1+K2M1 -K2M2 2+4K2 2M1M2 1 2 1 2 (17)

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10 where the parameters are described by th e proposed model in Figure 2-1. Table 2-1 shows the parameters for one sample model in which undamped natural frequencies were obtained using the above closed form solutions. Table 2-1: Model Parameters for a Two De gree of Freedom System Without Damping M2 100 Kg M1 100 Kg C2 0 N*s/m C1 0 N*s/m K2 10000 N/m K1 10000 N/m The frequency spectrum was generated for the above system using th e computer program LWT Prediction Model This is shown in Figure 2-2, wh ich displays the system’s two natural frequencies at 16.2 Hz and 6.2 Hz. Fr om the closed-form solutions in Equations 16 and 17, the natural frequencies were f ound to be 16.180 Hz and 6.180 Hz respectively. Figure 2-2 also shows that the frequency re sponse of the program agrees well with the corresponding closed-form solutions. 2.2.2 Modeling of an Uncoupled Two Degree of Freedom System With Damping The natural frequencies of some damped two degree of freedom systems can be found by uncoupling the damping parameters fr om the stiffness parameters and solving the eigenvalue problem. To verify that th e response of the developed program was accurate with damping, a solved example from Inman [8] was modeled for verification of the program. Table 2-2 shows the system para meters of the damped vibration system used in this case.

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11 Figure 2-2: Frequency Spectru m of a Two Degree of Freedom System Without Damping Table 2-2: Model Parameters for a Two Degree of Freedom System With Damping M2 1 Kg M1 1 Kg C2 1 N*s/m C1 2 N*s/m K2 4 N/m K1 5 N/m According to Inman’s solution, the natural freq uencies of the first and second degrees of freedom of the system described by Table 2-2 are 3.33 Hz and 1.343 Hz respectively. The above system was then used as an input in the computer program LWT Prediction Model and the frequency spectrum was generated to determine the two natural frequencies. Figure 2-3 shows that the program results ag ree well with the two natural frequencies derived by Inman [8]. 0 5 10 15 20 25 30 0510152025Amplitude, A (m)Frequency, (s-1) q1(t) q2(t)

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12 Figure 2-3: Frequency Spectrum of a Two Degree of Freedom System With Damping 2.2.3 Modeling of a One Degree of Freedom System With Damping Damped one degree of freedom systems can be solved relatively easily for their natural frequencies. Due to this fact, a tw o degree of freedom system was selected to emulate the response of two one degree of fr eedom systems by each time restraining one of the degrees of freedom. In the first of these two cases, the degree of freedom of M2 was restricted using the parameters presente d in Table 2-3, and the natural frequency of the first degree was determined using the following basic equations [8]; n= KiMi (18a) i=Ci2 KiMi (18b) d= n 1i (18c) 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 051015202530Amplitude, A (m)Frequency, (s-1) q1(t) q2(t)

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13 where Mi, Ki, and Ci correspond to the parameters of the model in Figure 2-1, ni is the undamped natural frequency of the ith degree of freedom, i is the damping ratio of the ith degree of freedom, and di is the damped natura l frequency of the ith degree of freedom. Table 2-3: Model Parameters for a One De gree of Freedom System Restricting the Motion of M2 M2 10 Kg M1 1000 Kg C2 0 N*s/m C1 5000 N*s/m K2 20000 N/m K1 20000 N/m According to Equations 18a-18c, the natural frequency of the firs t degree of the above system is 3.708 Hz. Then, the above parame ters were input to the program and a frequency spectrum was generated to determin e the system’s natural frequency. Figure 24 shows that the corresponding natural freque ncy is 3.7 Hz. Also, one can see that the first and second degrees of freedom coincided, thus verifying the simp lified one degree of freedom motion anticipated in this case. In the second case, M1 was made to always follow the input displacement function of the pavement profile. This would allow the second degree of freedom to act freely and describe a single degree of freed om motion. This condition was achieved using the parameters outlined in Table 2-4. The corresponding damped natu ral frequency of the second degree of freedom was found to be 3.708 Hz using Equations 18a-18c. The above system was then modeled using the program LWT Prediction Model and a frequency spectrum was generated to determine the damp ed natural frequency. Figure 2-5 shows the

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14 frequency response producing a natural frequency of 3.7 Hz thus verifying the accuracy of the computer program. Figure 2-4: Frequency Spectrum of the One Degree of Freedom System Restricting the Motion of M2 Table 2-4: Model Parameters for a One De gree of Freedom System Restricting the Motion of M1 M2 1000 Kg M1 Kg C2 5000 N*s/m C1 N*s/m K2 20000 N/m K1 N/m 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 024681012Amplitude, A (m)Frequency, (s-1) q1(t) q2(t)

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15 Figure 2-5: Frequency Spectrum of the One Degree of Freedom System Restricting the Motion of M1 2.3 Determination of LWT Parameters Using Modeling Techniques After verifying the accuracy of the computer program LWT Prediction Model it was necessary to determine the parameters of a damped two degree of freedom system that closely matched the vertical response of the LWT to any pavement profile. In order to do this, trial combinations of model parame ters were iteratively input to the program and the corresponding frequency was determin ed until the experimentally dominant natural frequency was obtained by the mode l [5]. As mentioned in Section 2.1, the measured dominant natural frequency of the LWT from previous research [5] was shown to be around 1.9 Hz. Table 2-5 demonstrates the parameters of a system that closely matches the response of the LWT, in term s of the predominant natural frequency. The frequency response of the modele d two degree of freedom system is represented in Figure 2-6. It is seen that the modeled na tural frequency is around 1.9 Hz, which closely matches the experimentally measured dominant natural frequency of 1.9 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 024681012Amplitude, A (m)Frequency, (s-1) q1(t) q2(t)

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16 Hz. The second experimental natural frequenc y of the LWT was seen to be around 11 Hz, but its amplitude was almost completely damped out. Therefore, the second natural frequency of the above modele d system is insignificant. Table 2-5: Parameters of a Two Degree of Freedom System Representing the LWT M2 440 Kg M1 60 Kg C2 1000 N*s/m C1 250 N*s/m K2 5000 N/m K2 2000 N/m Figure 2-6: Frequency Spectru m of a Two Degree of Freedom System Representing the LWT 2.4 Verification of LWT Parame ters Using Field Measurements In order to model the friction response of the LWT correctly, a comparison was made between the experimental response of th e LWT for a given profile to that of the program LWT Prediction Model for the same profile. The Profile H tested for this 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 05101520Amplitude, A (m)Frequency, (s-1) q1(t) q2(t)

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17 purpose is shown in Figure 2-7. A series of fi eld tests was conducted at different speeds over the above profile to determine the real time (actual) response of the LWT. This spatial profile was first converted to a time dependent profile for modeling purposes. Finally the profile was input to the co mputer-based LWT model and normal load response of the modeled LWT was predicted. Figures 2-8, 2-9, and 2-10 show the actual normal load response of the LWT at 20, 40, a nd 60 mph plotted against the response of the modeled system. Figure 2-7: Longitudinal Profile of Pavement H Review of Figures 2-8, 2-9, and 2-10 reveals that the modeled response is more accurate at higher speeds than at lower speeds. This c ould be attributed to th e back torque created by the frictional force which at lower sp eeds causes the trailer to bounce more vigorously. However, the back torque eff ects cannot be modeled using the author’s simplified system. -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 0.10 0.15 0.20 0.25 01020304050607080Vertical Displacement, y (m)Longitudinal Distance, x (m)

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18 Figure 2-8: Comparison of Experimental and Modeled Response of LWT at 20 mph Figure 2-9: Comparison of Experimental and Modeled Response of LWT at 40 mph 600 700 800 900 1000 1100 1200 020406080Normal Load, W (lbs.)Distance, x (m) LWT @ 20 mph LWT @ 20 mph LWT @ 20 mph Model @ 20 mph 600 700 800 900 1000 1100 1200 1300 1400 020406080Normal Load, W (lbs.)Distance, x (m) LWT @ 40 mph LWT @ 40 mph LWT @ 40 mph Model @ 40 mph

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19 Figure 2-10: Comparison of Experimental and Modeled Response of LWT at 60 mph Although the overall response of the LWT at 20 mph is not predicted accurately, the predicted average is close to those of the actual response t hus showing that the model is somewhat valid even at lower speeds such as 20 mph. On the other hand, at speeds of 40 mph and 60 mph, the deviations in normal lo ad are much more accurate, and prove that the proposed two degree of freedom system represents the response of the LWT more accurately over a given profile at higher speeds. 2.5 Determination of the Relationship Be tween the Friction and Normal Loads One objective of this research is to accurately predict the pavement friction measured by an LWT using a two degree of freedom system. After verifying that the normal load deviations are accurately modeled, the next step was to verify the friction predictions of the LWT. In order to predict the frictiona l force experienced by the LWT on any given pavement, the relationship of fric tion load to normal load on that pavement 0 200 400 600 800 1000 1200 1400 1600 1800 020406080100Normal Load, W (lbs.)Distance, x (m) LWT @ 60 mph LWT @ 60 mph LWT @ 60 mph Model @ 60 mph

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20 must be determined. In order to perform this task, the relationship between the skid number, SN and the normal load proposed by Fuentes et al. [5] in equation (6b) will be used. The experimental procedure followed by Fuentes et al. [5] to determine this relationship for a given pavement is rigorous and painstaking. Thus, in order to avoid recreating this experiment, the friction data obtained by Fuentes et al. [5] in the above experiment was used in the author’s anal ysis. Table 2-6 contains the friction data presented by Fuentes et al. [5] for two Pavements C and D. Figures 2-11 and 2-12 illustrate the relationship determined from Equation 6b for speeds of 30 and 55 mph respectively. The frictional force vs. normal load relationship is deduced by simply multiplying the SN by the corresponding normal load at any se lected point on the curves in Figures 211 and 2-12. Figures 2-13 and 2-14 illustrat e the corresponding re lationships between frictional force and normal load derived from Figures 2-11 and 2-12 respectively. Table 2-6: Parameters for the SN vs. W Relationship for Pavements C and D (Fuentes et al., 2010) Pavement Speed SNi ln(SNi) SNr ln(SNr) C 30 47.5 3.861 41.5 3.726 C 55 42.5 3.750 36.4 3.595 D 30 51.7 3.945 34.5 3.541 D 55 35 3.555 21 3.045

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21 Figure 2-11: SN vs. W Relationship at 30 mph (F uentes et al., 2010) Figure 2-12: SN vs. W Relationship at 55 mph (F uentes et al., 2010) 0 10 20 30 40 50 60 050010001500200025003000Skid Number, SNNormal Load, W (lbs.) Pavement C Pavement D 0 5 10 15 20 25 30 35 40 45 050010001500200025003000Skid Number, SNNormal Load, W (lbs.) Pavement C Pavement D

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22 Figure 2-13: Derived Relationship of Fric tional Force to Normal Load at 30 mph Figure 2-14: Derived Relationship of Fric tional Force to Normal Load at 55 mph In order to model the SN vs. normal load at speeds other than 30 and 55 mph, a logarithmic re-arrangem ent of the fundamental frictionspeed relationship in Equation 3 can be used as shown in Equation 19. ln(SN)=-S SP +ln(SN0) (19) 0 200 400 600 800 1000 1200 050010001500200025003000Friction Load, F (lbs.)Normal Load, W (lbs.) Pavement C Pavement D 0 100 200 300 400 500 600 700 800 900 1000 050010001500200025003000Friction Load, F (lbs.)Normal Load, W (lbs.) Pavement C Pavement D

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23 Figures 2-15 and 2-16 depict how the relationships of SNi and SNr versus speed were determined respectively using Equation 19 fo r Pavement C and D for a range of speeds used in the current analysis. Figure 2-15: Relationship between SNi and Speed Figure 2-16: Relationship between SNr and Speed Pavement C y = -0.0044x + 3.9942 Pavement D y = -0.0156x + 4.4136 3.00 3.10 3.20 3.30 3.40 3.50 3.60 3.70 3.80 3.90 4.00 0204060ln (SNi)Speed, S (mph) Pavement C Pavement D Pavement C y = -0.0052x + 3.883 Pavement D y = -0.0199x + 4.1367 3.00 3.10 3.20 3.30 3.40 3.50 3.60 3.70 3.80 0204060ln (SNr )Speed, S (mph) Pavement C Pavement D

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24 Tables 2-7 and 2-8 contain data on the variations of SNi and SNr with speed generated using Figures 2-15 and 2-16 for Pavements C and D. Table 2-7: Parameters for Projection of SN vs. Normal Load Relationship Across a Range of Speeds for Pavement C (Fuentes et al., 2010) Pavement Speed SNi ln(SNi) SNr ln(SNr) C 20 49.710 3.906 43.772 3.779 C 25 48.628 3.884 42.649 3.753 C 30 47.570 3.862 41.554 3.727 C 35 46.535 3.840 40.488 3.701 C 40 45.522 3.818 39.449 3.675 C 45 44.532 3.796 38.436 3.649 C 50 43.563 3.774 37.450 3.623 C 55 42.615 3.752 36.489 3.597 C 60 41.687 3.730 35.552 3.571 Table 2-8: Parameters for Projection of SN vs. Normal Load Relationship Across a Range of Speeds for Pavement D (Fuentes et al., 2010) Pavement Speed SNi ln(SNi) SNr ln(SNr) D 20 60.437 4.102 42.043 3.739 D 25 55.902 4.024 38.061 3.639 D 30 51.707 3.946 34.457 3.540 D 35 47.827 3.868 31.193 3.440 D 40 44.239 3.790 28.239 3.341 D 45 40.919 3.712 25.564 3.241 D 50 37.849 3.634 23.143 3.142 D 55 35.009 3.556 20.951 3.042 D 60 32.382 3.478 18.967 2.943 Then, the data shown in Tables 2-7 and 2-8 can be used to model the SN vs. normal load relationship for Pavements C and D at any speed using Equations 6b and 19.

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25 2.6 Verification of Friction Load Modeling After determining the relationship of fricti on load to normal load, an experimental verification was extended to ensure that the program models correctly the friction load experienced by the LWT as well. Using Equati on 6b and the data from Tables 2-7 and 28 combined with the normal load deviation prediction capability of the modeling program LWT Prediction Model an attempt was made to pr edict the pavement friction on Pavement H. Since the experimental procedure to dete rmine the relationships of skid number and friction to normal load were not recreated for Pavement H, it was assumed that the curve corresponding to Pavement H was geometrical ly similarly to that of Pavement D in Fuentes’ experimentation. Therefore, SN versus normal load (Figure 2-12) and friction load versus normal load (Figure 2-14) curves were replotted in Figur es 2-17 and 2-18. In the experiment conducted by Fuentes et al. [5], the SN0 in Equation 6b was found to be the same as the SN value of the pavement under normal loads used in standard LWT testing conditions. Thus, assuming that the SN measured at the standard LWT normal load for Pavement H as SN0 corresponding to that pavement, curves for Pavement H in Figures 2-17 and 2-18 were generated for SN and friction load. Then, friction tests were conducted on Pavement H using the LWT, and those results were compared to the responses pr edicted by the modeling program. Figure 2-19 shows the comparison of the model predictions to the actual test results conducted in three trials.

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26 Figure 2-17: Relationship of SN vs. Normal Load for Pavement H at 55 mph Figure 2-18: Relationship of Friction Load vs Normal Load for Pavement H at 55 mph 0 5 10 15 20 25 30 35 40 45 050010001500200025003000Skid Number, SNNormal Load, W (lbs.) Pavement C Pavement D Pavement H 0 100 200 300 400 500 600 700 800 900 1000 050010001500200025003000Friction Load, F (lbs.)Normal Load, W (lbs.) Pavement C Pavement D Pavement H

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27 Figure 2-19: Comparison of Model Predic tion to the Results of Friction Tests As one can see from Figure 2-19, the fricti on load of the pavement is reasonably accurately modeled by the program LWT Prediction Model The average SN of the skid tests was 29.6, while the program predicted an average of 30.3. 2.7 Modeling the Effects of Pavement Roughness on the IFI After verifying that the modeling program correctly modeled the normal load and the frictional load deviation of the LWT, friction data from the Fuentes experiment [5] were used to determine the effects of pave ment roughness on the IFI parameters. In order to achieve this, an analysis was performe d to investigate the individual effects of frequency and amplitude variations on the SN predicted by the program LWT Prediction Model First, a range of pavement profiles with varying fr equencies with identical amplitudes were modeled by the program LWT Prediction Model to determine the effects 0 100 200 300 400 500 600 020406080100Normal Load, W (lbs.)Distance, x (m) LWT @ 55 mph LWT @ 55 mph LWT @ 55 mph Model @ 55 mph

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28 of the frequency variations on the friction-sp eed relationship. Tabl e 2-9 shows the input values of the modeling program. Table 2-9: Inputs for Frequency Va riation Analysis (A = 0.25 m) PavementFrequency, (Hz) C 0.00 0.05 0.50 5.00 D 0.00 0.05 0.50 5.00 Figures 2-20 and 2-21 display the results corresponding to the a bove input values. Figure 2-20: Frequency Vari ation Effects on the Fricti on-Speed Relationship of Pavement C The SN0 evaluated from these plots is the fric tion value at zero speed. The magnitudes of SN0 and the changes of the slope of the fricti on-speed relationship (speed gradient) for Pavements C and D are shown in Table 2-10. As seen in Table 2.10, for a given pavement, as the frequency increases the gr adient of the friction versus speed curve 3.60 3.65 3.70 3.75 3.80 3.85 3.90 3.95 020406080ln (SN)Speed S (mph) = 0.00 Hz = 0.05 Hz = 0.50 Hz = 5.00 Hz

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29 increases while the SN0 remains more or less constant. T hough the gradient increases, the SP decreases as defined in Equation 19. Figure 2-21: Frequency Vari ation Effects on the Fricti on-Speed Relationship of Pavement D Table 2-10: Results of Frequency Vari ation Analysis on Pavements C and D Pavement CharacteristicsFrequency, (Hz) Speed Gradient, SP SN0 Pavement C 0.00 227.27 54.21 Pavement C 0.05 227.27 54.22 Pavement C 0.50 217.39 54.39 Pavement C 5.00 200.00 52.28 Pavement D 0.00 64.10 82.29 Pavement D 0.05 63.69 82.36 Pavement D 0.50 61.35 83.20 Pavement D 5.00 56.18 75.71 Similar to the previously performed frequency variation analysis, an amplitude variation analysis was conduc ted on Pavements C and D. Table 2-11 demonstrates the input values used in the program LWT Prediction Model Figures 2-22 and 2-23 display the results of the inputs from Table 2-11. 3.00 3.20 3.40 3.60 3.80 4.00 4.20 020406080ln (SN)Speed S (mph) = 0.00 Hz = 0.05 Hz = 0.50 Hz = 5.00 Hz

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30 Table 2-11: Inputs for Freque ncy Variation Analysis ( = 0.05 Hz) PavementAmplitude, A (m) C 0.00 0.05 0.50 5.00 D 0.00 0.05 0.50 5.00 The magnitudes of SN0 and the changes of the slope of the friction-speed relationship (speed gradient) for Pavements C and D are shown in Table 2-12. As seen in Table 2.12, for a given pavement, as the amplitude increases, the gradient of the friction versus speed curve increases while SN0 remains more or less constant. Though the gradient increases, the SP decreases as defined in Equation 19. Figure 2-22: Amplitude Variation Effect s on the Friction-Speed Relationship of Pavement C 3.60 3.65 3.70 3.75 3.80 3.85 3.90 3.95 020406080ln (SN)Speed S (mph) A = 0.00 m A = 0.05 m A = 0.50 m A = 5.00 m

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31 Figure 2-23: Amplitude Variation Effect s on the Friction-Speed Relationship of Pavement D Table 2-12: Results of Am plitude Variation Analysis on Pavements C and D Pavement Characteristics Amp litude, A (m) Speed Gradient, SP SN0 Pavement C 0.00 227.27 54.21 Pavement C 0.05 227.27 54.21 Pavement C 0.50 222.22 54.29 Pavement C 5.00 200.00 53.91 Pavement D 0.00 64.10 82.29 Pavement D 0.05 64.10 82.29 Pavement D 0.50 63.29 82.67 Pavement D 5.00 56.18 82.22 Due to the limited amount of data on the SN versus normal load relationship for different types of pavements, this analysis was designe d to illustrate typical results that would be seen on most pavements. 3.00 3.20 3.40 3.60 3.80 4.00 4.20 020406080ln (SN)Speed S (mph) A = 0.00 m A = 0.05 m A = 0.50 m A = 5.00 m

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32 2.8 Field Verification of the Effect s of Pavement Roughness on the IFI As shown in Section 2.7, pavement roughne ss can have a significant effect on the measured SN values and hence the computation of th e IFI. Another aspect of the Fuentes [5] experimentation consisted of analyz ing the effects of pavement roughness on measured skid values. Based on the anal ysis in Section 2.7, the variation in SP can be significantly different depending on the freque ncy and amplitude variations along a given pavement. This difference was verified in the field using data from Fuentes’ [5] original experiment, as well as friction tests conducted on an alternative Pa vement I located in Brandon, Florida. The friction testing on Pa vement I was conducted using the same protocol used by Fuentes to ensure that the results would not be skewed. In this regard, two sections were evaluated on Pavement I with one section found to be relatively rougher compared to the other, based on the significantly different profiles. After evaluating the macrotextu re using the CT Meter to ensure that macrotexture was identical on both of those sections, skid tests were performed on the two pavement sections with significantly diffe rent profiles. Reformulation of data from Fuentes’ [5] experiment on Pavement B is shown in Figure 2-24, with Table 2-13 displaying the values of SN0 and SP. The values of SN0 from these two secti ons are not significantly different, and it can be inferred from regression that the friction at zero speed is invariant for both pavement sections. On the other ha nd, Figure 2-25 shows the data from testing of Pavement I with Table 214 displaying the values of SN0 and SP.

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33 Figure 2-24: Effect of Pavement Rou ghness on IFI Parameters for Pavement B Table 2-13: Results from Pavement Roughness Analysis on Pavement B Section Speed Gradient, SP SN0 Smooth 100.00 49.74 Rough 74.63 44.46 Figure 2-25: Effect of Pavement Rou ghness on IFI Parameters for Pavement I 2.50 2.70 2.90 3.10 3.30 3.50 3.70 3.90 0102030405060ln(SN)Speed, S (mph) Rough Smooth 3.65 3.70 3.75 3.80 3.85 3.90 3.95 4.00 4.05 4.10 4.15 01020304050ln(SN)Speed, S (mph) Rough Smooth

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34 Table 2-14: Results from Pavement Roughness Analysis on Pavement I Section Speed Gradient, SP SN0 Smooth 92.59 73.05 Rough 93.46 61.52 The values of SN0 for both sections on Pavement B is more or less constant, while the SP decreases as the roughness increases. This fo llows the predictions made by the program LWT Prediction Model. However, the values of SN0 for both sections of Pavement I are significantly different, and it was concluded th at regression data is needed from higher speeds to make an appropriate conc lusion about their relationship. The SP variation for the Pavement I sections also does not conform to previous findings in this work, and it was concluded that tests at hi gher speeds are needed to dete rmine to true gradients of each section of pavement. Review of these two sets of data shows that the IFI parameters must be calculated from a larger range of speeds in order to be valid. 2.9 Modeling the Effects of the Normal Load versus Friction Load Relationship The friction load predictions for the LWT we re made in this work primarily based on the relationship between SN and normal load developed by Fuentes [5]. Therefore it is clear that the relationship of SN to normal load is critical to predicting the friction load response of the LWT from the program LWT Prediction Model Hence, an investigation was conducted to explore in detail the effects of the above relationship on skid resistance measurements. Equation 20 expresses SN which is maximum difference between SN observed during changes in the normal load of a given pavement and hence expressed by; SN=SNi-SNr (20)

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35 Using data from Pavement C in the Fuente s [5] experiments, three other hypothetical pavements (Pavement E, F, and G) were created with the same SNi but having different SN values to model the effects of the fric tion-speed relationship measured with the LWT. Figure 2-26 displays the representative SN versus normal load relationships of the pavements used in the above analysis, wh ile Figure 2-27 shows the variation of SN versus speed of the hypothetical paveme nts matching that of Pavement C. Figure 2-26: Relationship of SN vs. Normal Load for Pavements C, E, F, and G at 55 mph Using the data in Figures 2-26 and 2-27 an analysis was performed with the program LWT Prediction Model to determine the effect of SN of a given pavement on measured friction values. While the results are displaye d in Figure 2-28, and the magnitudes of the changes are displayed in Table 2-15. 0 5 10 15 20 25 30 35 40 45 050010001500200025003000Skid Number, SNNormal Load, W (lbs.) Pavement C Pavement E Pavement F Pavement G

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36 Figure 2-27: Variation in SN versus Speed for Pavements C, E, F, and G Figure 2-28: Effects of Variation in SN for Pavements C, E, F, and G with Speed 0 5 10 15 20 25 30 020406080Change in Skid Number, SNSpeed, S (mph) Pavement C Pavement E Pavement F Pavement G 3.65 3.70 3.75 3.80 3.85 3.90 3.95 020406080ln (SN)Speed, S (mph) Pavement C Pavement E Pavement F Pavement G

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37 Table 2-15: Results from SN Variation Analysis on Pavements C, E, F, and G Pavement Speed Gradient, SP SN0 Pavement C 217.39 54.39 Pavement E 200.00 54.54 Pavement F 185.19 54.71 Pavement G 227.27 54.28 The results in Table 2-15 confirm that the SN of a given pavement can have a significant effect on the speed gradient, SP, and hence the measured friction values. This effect is also illustrated in Figures 2-24 a nd 2-25 where the pavements are seen to have significant differences in particular the SP values. In summary, it can be concluded that three factors will affect the computed IFI values of a rough pavement: 1. Frequency of roughness wave 2. Amplitude of roughness wave 3. SN dependence on the normal load ( SN ) 2.10 Alternative Method for Determining Re lationship Between SN and Normal Load In lieu of the rigorous method by which Fu entes [5] determined the relationship of SN versus normal load for a given pavement, this study proposes a more practical method for the convenience of implementation. Data from Pavement B in Fuentes’ [5] experiment was reformulated to reflect the relationship given by Schallamach in Equation 7. The average normal loads of each section we re normalized using a static LWT weight of 1085 lbs. and then plotte d against the corresponding SN of those tests. The basic form of Equation 7 used in this analysis is given in the following equation;

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38 SN=cWAVEWSTATIC a (21) where c is the speed-depe ndent parameter, a is a parameter specific to the pavement type, WAVE is the average normal load recorded dur ing a more or less uniformly rough section, and WSTATIC is the static weight of the LWT. Fi gure 2-29 shows the plots of Equation 21 at speeds of 25, 40 and 55 mph. Figure 2-29: Relationship of SN vs. Normal Load for Pavement A at 25, 40, and 55 mph Using Schallamach’s Equation Based on Figure 2-29, the mathematical form pr escribed in Equation 21 seems to provide a valid method for determining the relationship of SN versus normal load. The parameter a is nearly identical at 40 and 55 mph, showing that a can be assumed to be invariant for this pavement. The value of a at 25 mph is slightly differe nt from those at 40 and 55 mph, but friction testing at low speeds has b een found to be relatively unreliable and inconsistent due to the back-torque effect as outlined in Section 2.4. The values of c 25 mph y = 22.557x-6.931R = 0.9588 40 mph y = 16.199x-9.396R = 0.9601 55 mph y = 14.854x-9.222R = 0.9455 0 5 10 15 20 25 30 35 40 45 50 0.90.920.940.960.981Skid Number, SNWAVE/WSTATIC 25 mph 40 mph 55 mph

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39 decrease as speed increases, which follows the basic tenants of the friction-speed relationship. In order to develop these trends for other pavements, friction tests must be conducted at least on two relatively rough and sm ooth sections of a given pavement, and the resulting average normalized weights must be plotted against the average SN values as in the case of Figure 2-29. This procedur e was followed on Pavement I from Section 2.8, and the results are given in Figure 2-30. Figure 2-30: Relationship of SN vs. Normal Load for Pavement I at 20, 30, and 40 mph Using Schallamach’s Equation Review of Figure 2-30 shows th at the pavement parameter a varies slightly across the speeds tested. Also, the speed-d ependent parameter c is sk ewed at 40 mph. In addition, the relatively low R2 at 40 mph indicates possible erro r in the data at that speed. 20 mph y = 12.893x-17.82R = 0.9524 30 mph y = 9.9644x-18.69R = 0.9027 40 mph y = 16.103x-11.04R = 0.8335 0 10 20 30 40 50 60 70 0.90.9050.910.9150.920.9250.93Skid Number, SNWAVE/WSTATIC 20 mph 30 mph 40 mph

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40 CHAPTER 3 CONCLUSIONS AND RECOMMENDATIONS 3.1 Current Research Proponents Evaluation and maintenance of pavement friction in a highway network is a crucial aspect of transportation safety pr ograms. Researchers have made significant efforts to evaluate and standardize pavement friction measured with numerous full-scale friction testers. In this work, an attemp t has been made to understand the frictional response of the LWT for a given profile. A two degree of freedom vibration model was developed to simulate the LWT behavior a nd determine what effects pavement roughness has on the LWT measured friction and hence th e IFI value of a given pavement profile. 3.2 Contribution 1 Theoretical Pred iction of LWT Friction Values As outlined in Section 2.6, measured fric tion values can be predicted accurately using the program LWT Prediction Model developed in this study. The ability of the program LWT Prediction Model to predict friction on a given pavement is governed by the frictional dependency of that pavement on the normal load. This relationship was also shown to affect significantly th e reported values of the IFI due to its effect on the speed gradient, SP. Further modification of this method must be pursued by better evaluating the dependency of friction on the normal load.

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41 3.3 Contribution 2 Effects of Pavement Roughness on the IFI As outlined in Section 2.7, pavement r oughness can have significant effects on the computed IFI values of a pavement. As the roughness of a pavement increases, the friction-speed relationship is altere d, thus changing the values of SP and F60. Using linear regression of the data, it was shown that va rious friction-speed pl ots merge on a single value of SN0 ( SN at zero speed). The author’s LWT model predicts that generally the SP of a pavement decreases as pavement roughness increases. 3.4 Contribution 3 Effects of Frictional Dependency on Normal Load on the IFI In lieu of the relatively co mplicated process in which the SN vs. W relationship was developed by Fuentes [5], a new method wa s proposed to facilita te the prediction of SN values from the developed program. Using the form prescribed by Schallamach and the method outlined in Section 2.10, practitione rs can accurately develop an appropriate relationship between SN and normal load for a given pavement. Ideally, the parameters in Equation 21 can be standardized based on macr otexture values, and then input into the author’s model to accurately predict paveme nt friction over any given profile. Pavements with large SN values (maximum SN difference with respect to the normal load) were shown to be more sensitive to roughness a nd produce larger deviations in the IFI parameter. This effect can be minimized if pavements could be designed with materials that exhibit a minimal SN variation ( SN ). For instance, a pavement with SN of zero would exhibit no effects due to pavement roughness or elevated DLC

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42 LIST OF REFERENCES [1] Leu, M.C. and J.J. Henry. “Prediction of Skid Resistance as a function of Speed from Pavement Texture,” Transportation Resear ch Record 946, Transportation Research Board, National Council, Washington, D.C., 1983. [2] Wambold, J. C., C. E. Antle, J. J. Henry, and Z. Rado. “International PIARC Experiment to Compare and Harmonize Text ure and Skid Resistance Measurements”. Final Report submitted to the Permanent Inte rnational Association of Road Congresses (PIARC), State College, PA, 1995. [3] ASTM: “Standard Practice for Calculating International Friction Index of a Pavement Surface”, Standard No E1960-07, ASTM 2009 [4] ASTM: “Standard Test Method for Skid Resistance of Paved Surfaces Using a FullScale Tire”, Standard No E274-06, ASTM 2009 [5] Fuentes, L., M. Gunaratne, and D. Hess. “Evaluation of the Effect of Pavement Roughness on Skid-Resistance,” ASCE Journal of Transportation Engineering, Vol. 136 No. 7, Reston, Virginia, 2010. [6] Schallamach, A. “The Load Dependen ce of Rubber Friction”, Proc. Phys. Soc., Section B, Volume 65, Issue 9, pp. 657-661 (1952). [7] Das, B.M. “Fundamentals of Soil Dynamics ”. New York: Elsevier Science Publishing Co., Inc., 1983. Print. [8] Inman, D. J., “Vibration with Contro l”. New York: John Wiley and Sons, Ltd, 2006. Print.