Purdue University Purdue e-Pubs JTRP Technical Reports Joint Transportation Research Program 2009 Validation of NCAT Structural Test Track Experiment Using INDOT APT Facility Eyal Levenberg Purdue University Rebecca S. McDaniel Purdue University Jan Olek Purdue University Recommended Citation Levenberg, E., R. S. McDaniel, and J. Olek. Validation of NCAT Structural Test Track Experiment Using INDOT APT Facility. Publication FHWA/IN/JTRP-2008/26.
FHWA/IN/JTRP-2008/26 Final Report VALIDATION OF NCAT STRUCTURAL TEST TRACK EXPERIMENT USING INDOT APT FACILITY Eyal Levenberg Rebecca S.
Final Report FHWA/IN/JTRP-2008/26 VALIDATION OF NCAT STRUCTURAL TEST TRACK EQUIPMENT USING INDOT APT FACILITY By Eyal Levenberg Postdoctoral Researcher Rebecca S. McDaniel Technical Director and Jan Olek Professor of Civil Engineering and Director North Central Superpave Center School of Civil Engineering Purdue University Joint Transportation Research Program Project No. C-36-31R File No.
TECHNICAL REPORT STANDARD TITLE PAGE 1. Report No. 2. Government Accession No. 3. Recipient's Catalog No. FHWA/IN/JTRP-2008/26 4. Title and Subtitle 5. Validation of NCAT Structural Test Track Experiment Using INDOT APT Facility Report Date September 2009 6. Performing Organization Code 8. Performing Organization Report No. 7. Author(s) Eyal Levenberg, Rebecca S. McDaniel, and Jan Olek FHWA/IN/JTRP-2008/26 9. Performing Organization Name and Address 10. Work Unit No.
ACKNOWLEDGMENTS The principal author is thankful to various individuals for their assistance and involvement during the completion of the report.
TABLE OF CONTENTS ACKNOWLEDGMENTS........................................................................................ ii LIST OF TABLES .................................................................................................. vi LIST OF FIGURES ............................................................................................... viii CHAPTER 1 - INTRODUCTION ........................................................................ 1-1 1.1 BACKGROUND AND MOTIVATION......................
CHAPTER 4 - BASIC MECHANISTIC ANALYSIS ......................................... 4-1 4.1 SCOPE AND APPROACH.................................................................................................... 4-1 4.2 LAYERED ELASTIC ISOTROPIC MODEL ....................................................................... 4-2 4.2.1 Theory and Computational Implementation........................................................... 4-2 4.2.2 Calibration to APT Conditions ...........................................
LIST OF TABLES Table 2.1.1: Breakdown of axle properties for an ‘average’ NCAT truck (Priest and Timm, 2006) ................................................................................................................. 2-3 Table 2.2.1: HMA design parameters for mixes 1 to 4 (Timm and Priest, 2006) ........................ 2-8 Table 2.3.1: Resilient modulus of subgrade soil with average compaction level of 96%. Raw test results from laboratory reports .....................................................
Table 5.1.1: Backcalculated anisotropic layer moduli for pass #5,000 ...................................... 5-10 Table 5.1.2: Adjusted anisotropic HMA moduli for FWD response prediction ........................ 5-13 Table 5.2.1: Backcalculated material properties for the layered viscoelastic model during APT pass #5,000 ............................................................................................. 5-27 Table 5.2.
LIST OF FIGURES Figure 2.1.1: Schematic layout of the 46 test sections at NCAT (Phase II) experiment .............. 2-2 Figure 2.1.2: Photograph of a typical NCAT truck (Priest and Timm, 2006) .............................. 2-3 Figure 2.2.1: Structural layers for sections N1 to N8 (Priest and Timm, 2006)........................... 2-4 Figure 2.2.2: Final gradation of upper subgrade soil at N1 and N2 sections (Timm and Priest, 2006) ............................................................................
Figure 3.3.5: Mix 4 dynamic modulus and phase angle master curves @ 15.5ºC ..................... 3-15 Figure 3.3.6: Superimposed dynamic modulus master curves @ 15.5ºC for mixes 1 to 4 .................................................................................................................................. 3-15 Figure 3.3.7: Superimposed phase angle master curves @ 15.5ºC for mixes 1 to 4 .................. 3-16 Figure 3.3.8: Peak FWD deflections measured in the center of sections n1 and n2 ........
Figure 4.3.4: Layout of N1 gauge array (refer to Figure 2.4.3) and travel path positioning of the center point of the rightmost truck tire (connecting arrows) ........................................................................................................................ 4-21 Figure 4.3.5: Travel paths of center of rightmost truck wheels over the N1 gauge array at NCAT for the different axles in Table 2.1.1 ........................................................... 4-22 Figure 4.3.
Figure 5.2.6: Comparison of isotropic LVT projections with measured N1 responses right side of drive axle (1D and 2D). Isotropic case reproduced from Figure 4.3.7 ............................................................................................................................ 5-34 Figure 5.2.7: Comparison of isotropic LVT projections with measured N1 responses right side of first trailer axle (1T). Isotropic case reproduced from Figure 4.3.8 .......................................................
CHAPTER 1 - INTRODUCTION 1.1 BACKGROUND AND MOTIVATION Despite years of systematic research the design and analysis of asphalt pavements still includes dominant empirical components.
experimental sections paved with Hot Mix Asphalt (HMA). The 2003 - 2005 testing phase at NCAT, also known as Phase II, included the construction, loading and continuous monitoring of eight different instrumented pavement structures, referred to as sections N1 to N8. The primary objective of this so-called ‘structural study’ was to provide high quality data for validating the Mechanistic-Empirical Pavement Design Guide (MEPDG) (ARA Inc., 2004).
only. Therefore, the problem is how to interpret APT experimental results such that they could be applied to different environmental and loading conditions. The main objective of this study is to devise and validate an analysis scheme by which experimental data collected in the APT experiment can be used to successfully forecast the corresponding pavement behavior at the NCAT test track.
includes only the tasks required to achieve the aforementioned study objectives. The scope and purpose of each task are described hereafter. Task 1 consists of careful study, systematic documentation and presentation of pertinent test data from both the APT and NCAT experiments. The aim here is to familiarize the reader with relevant details of the work done. It is mostly descriptive in nature with limited pre-processing of the data. The raw test results are contained in Appendix A.
test sections and recorded field and laboratory behavior. Chapter 3 summarizes the APT work; it includes a description of the loading history and environment prevailing during the experiment, some preliminary analyses of available the test data and identification of dataset most suitable for structural investigation. This chapter also presents the recorded structural behavior for the selected dataset.
CHAPTER 2 - THE NCAT EXPERIMENT This chapter summarizes the ‘structural study’ experiment conducted by NCAT between the years 2003 and 2005 (phase II). The focus is on sections N1 and N2 which were later replicated in the APT experiment. Reference to the original reports is provided so the reader can trace the source and obtain additional data. 2.1 FACILITY DESCRIPTION The NCAT test track is a 1.7 miles (2.8 km) oval shaped closed-loop asphalt road located near Opelika, Alabama.
vertical compressive stresses on top of the base and subgrade, moisture in the unbound materials and temperature within the HMA. Additionally, these sections were investigated by periodic deflection testing and monitored for structural distresses by employing routine surface condition surveys. Reportedly this was done to allow for later validation of the MEPDG. The focus herein is on sections N1 and N2, which were the only sections from the ‘structural study’ replicated in the INDOT APT. Figure 2.1.
1.7% to 4.9% (average of 3.1%). Standard tires were used (Priest et al., 2005) identified as 275/80R22.5 and inflated to 100 psi. Figure 2.1.2: Photograph of a typical NCAT truck (Priest and Timm, 2006). Table 2.1.1: Breakdown of axle properties for an ‘average’ NCAT truck (Priest and Timm, 2006). Axle-name AxleNumber Steer Axle-type SingleAxle No.
N5 to N8 were designed with 7 in. (178 mm) of HMA each. It is important to note that these are design values and that the actual as-constructed thicknesses varied slightly. Figure 2.2.1: Structural layers for sections N1 to N8 (Priest and Timm, 2006). 2.2.2 Subgrade The upper subgrade for all eight test sections (N1 to N8) was processed to a depth of 30 in. (762 mm) from the pavement surface (Timm and Priest, 2006). The material was then compacted in layers using vibratory pad-foot rollers (e.g.
moisture contents for sections N1 and N2 were 10% and 11% respectively. The average in-place wet unit weight was 132.0 pcf (2116 kg/m³) for both sections, and the corresponding dry unit weights were 120.0 and 118.9 pcf (1924 and 1906 kg/m³). From this information it may be concluded that the relative in-place degree of compaction, based on dry densities, was 100.3% and 99.4% for sections N1 and N2 respectively. Figure 2.2.
dry density values were 138.0 (2213 kg/m³) for both sections. With respect to dry densities, the relative compaction degree for the base layer in both sections was 100.1%. The as-built moisture content varied slightly: 6.4% in section N1 and 6.6% in section N2. Figure 2.2.3: Gradation of base material at N1 and N2 sections (Timm and Priest, 2006). 2.2.4 Hot Mix Asphalt Figure 2.2.4 presents the sub-layering of the HMA in the different test sections in the ‘structural study’ (Timm and Priest, 2006).
Figure 2.2.4: Sub-layering of HMA in test sections N1 to N8 (Timm and Priest, 2006). Table 2.2.1 presents the individual mixture design parameters for mixes 1 to 4 which were paved in the N1 and N2 sections. It may be seen that the surface mixes 1 and 3 differ by the type of binder and corresponding preparation temperatures. SBS modified PG 76-22 was used for Mix 1, and unmodified PG 67-22 was used for Mix 3. Both mixes (see Figure 2.2.
Table 2.2.1: HMA design parameters for mixes 1 to 4 (Timm and Priest, 2006). Property Units Mix 1 Mix 2 Mix 3 Mix 4 Binder Grade 76-22 67-22 Compactive Effort, gyrations 80 Mixing Temperature ºF (ºC) 345 (174) 325 (163) Effective Binder Content percent 6.13 4.27 6.13 4.27 Dust to Binder Ratio 0.88 1.10 0.88 1.10 pcf 147.8 153.6 147.8 153.6 Bulk Unit Weight of Compacted Pills (kg/m³) (2370) (2463) (2370) (2463) Air Void Content percent 4.3 Voids in Mineral Aggregate percent 17.9 14.5 17.9 14.5 Figure 2.2.
thickness in Section N1 was not constant at 5.0 in. (127 mm), but varied between 6.7 to 4.5 in. (170 to 114 mm). The as-built air void contents were also surveyed during construction. On average, all three lifts in Section N1 were compacted to an air void content of 7.0%. However, in Section N2 only the top lift was compacted to 7.0% voids while the two bottom lifts were compacted to an air void content of 6.0%. The asphalt content also varied slightly relative to the design values.
Table 2.3.1: Resilient modulus of subgrade soil with average compaction level of 96%. Raw test results from laboratory reports. Confining Pressure, psi (kPa) Peak Cyclic Stress psi (kPa) Resilient Modulus, psi (MPa) ω=7.2% 6.0 (41.4) 4.0 (27.6) 2.0 (13.8) 2.1 (14.5) 4.0 (27.6) 5.8 (40.0) 7.7 (53.1) 9.6 (66.2) 2.1 (14.5) 3.9 (26.9) 5.7 (39.3) 7.6 (52.4) 9.5 (65.5) 1.9 (13.1) 3.8 (26.2) 5.6 (38.6) 7.5 (51.7) 9.5 (65.5) 10,876 (75.0) 11,738 (80.9) 11,730 (80.9) 12,260 (84.5) 12,837 (88.5) 10,311 (71.
about 93% (recall that 100% compaction was achieved in the field). The test conditions included two levels of moisture content ( ω ): 5.3% and 9.8%; three levels of applied confining pressure: 2, 4 and 6 psi (13.8, 27.6 and 41.4 kPa); and five levels of applied cyclic axial stress between 2 and 10 psi (13.8 to 68.9 kPa). The raw test results are given in Table 2.3.2. Table 2.3.2: Resilient modulus of aggregate base with average compaction level of 93%. Raw test results from laboratory reports.
2.3.2 HMA Complex Modulus Complex modulus testing of the NCAT asphalt mixtures was conducted under the direction of Dr. Terhi Pellinen at Purdue University. A detailed description of the work is presented in a report by Barde and Cardone (2004) which can be found in Appendix C. The materials were sampled in loose state from the delivery trucks during construction and then shipped to Purdue University. Specimens were prepared and tested in accordance with the NCHRP 1-37A protocol (NCHRP, 2002).
ends. Specimens were instrumented with three linear variable displacement transformers (LVDTs), each spanning 100 mm, for measurement of axial (vertical) deformations; the LVDTs were mounted to the periphery of the specimen 120° apart. It should be noted that lateral strains were not monitored. The complex modulus test results are shown in Tables 2.3.3 to 2.3.6. Each table presents the dynamic moduli values and the corresponding phase angles.
Table 2.3.3: Average complex modulus test results for Mix 1 (Barde and Cardone, 2004). Test Temperature Test Frequency Dynamic Modulus Phase Angle ºC (ºF) -10.0 (+14) +4.4 (+40) +21.1 (+70) +37.8 (+100) +54.4 (+130) [Hz] MPa (ksi) [degrees] 25 10 5 1 0.5 0.1 25 10 5 1 0.5 0.1 25 10 5 1 0.5 0.1 25 10 5 1 0.5 0.1 25 10 5 1 0.5 0.
Table 2.3.4: Average complex modulus test results for Mix 2 (Barde and Cardone, 2004). Test Temperature Test Frequency Dynamic Modulus Phase Angle ºC (ºF) -10.0 (+14) +4.4 (+40) +21.1 (+70) +37.8 (+100) +54.4 (+130) [Hz] MPa (ksi) [degrees] 25 10 5 1 0.5 0.1 25 10 5 1 0.5 0.1 25 10 5 1 0.5 0.1 25 10 5 1 0.5 0.1 25 10 5 1 0.5 0.
Table 2.3.5: Average complex modulus test results for Mix 3 (Barde and Cardone, 2004). Test Temperature Test Frequency Dynamic Modulus Phase Angle ºC (ºF) -10.0 (+14) +4.4 (+40) +21.1 (+70) +37.8 (+100) +54.4 (+130) [Hz] MPa (ksi) [degrees] 25 10 5 1 0.5 0.1 25 10 5 1 0.5 0.1 25 10 5 1 0.5 0.1 25 10 5 1 0.5 0.1 25 10 5 1 0.5 0.
Table 2.3.6: Average complex modulus test results for Mix 4 (Barde and Cardone, 2004). Test Temperature Test Frequency Dynamic Modulus Phase Angle ºC (ºF) -10.0 (+14) +4.4 (+40) +21.1 (+70) +37.8 (+100) +54.4 (+130) [Hz] MPa (ksi) [degrees] 25 10 5 1 0.5 0.1 25 10 5 1 0.5 0.1 25 10 5 1 0.5 0.1 25 10 5 1 0.5 0.1 25 10 5 1 0.5 0.
2.3.3 Falling Weight Deflections Falling weight deflectometer (FWD) testing was conducted more or less on a monthly basis at NCAT. These tests were conducted at identical locations within each test section. The locations themselves were randomly selected at the beginning of the entire two year experiment. The FWD was a Dynatest 8000 model equipped with seven sensors spaced at 12 in. (304.8 mm) intervals starting from the center of the load plate. The load plate had a radius of 300 mm (5.91 in.
Table 2.3.7: FWD deflections at N1 section (location according to NCAT database: station 2 inside the wheel path). Date D0 [μm] D1 [μm] D2 [μm] D3 [μm] D4 [μm] D5 [μm] D6 [μm] Temp. ºC (ºF) Nov. 3, 2003 565.7 353.0 153.4 76.9 40.9 32.1 20.7 32.9 (91.2) Dec. 15, 2003 451.2 332.5 178.4 93.9 47.6 31.2 24.2 16.7 (62.1) Jan. 26, 2004 338.1 263.2 160.4 99.2 60.9 38.0 29.5 10.1 (50.2) Feb. 23, 2004 354.0 268.1 160.3 92.1 52.7 30.9 22.5 12.6 (54.7) Mar. 22, 2004 620.
2.4 EMBEDDED INSTRUMENTATION 2.4.1 Environmental Monitoring Instrumentation devoted to monitoring environmental changes included moisture probes and temperature gauges. Campbell Scientific moisture probes (model CS615) were installed at NCAT during the phase I experiment (Freeman et al., 2001). This type of gauge was also selected to be installed in the ‘structural study’ (Timm et al., 2004). These probes indicate changes in volumetric moisture content (i.e.
probes is ±0.3°C (±0.54°F). Unlike the moisture probes, the temperature probes do not need to be calibrated for the particular environment in which they are to be used. In Freeman et al. (2001) they were tested and found repeatable and accurate. 2.4.2 Mechanical Responses Mechanical responses at the ‘structural study’ were measured with strain gauges and pressure cells.
gap filled with de-aired hydraulic fluid. When external pressure is applied to the plates, the two plates are squeezed together causing a corresponding increase of fluid pressure inside the cell. High pressure stainless steel tubing connects the pressure cell to a semiconductor pressure transducer which converts the increased pressure of the compressed fluid into an electrical signal. This signal is transmitted through a signal cable to the readout location. D=230 mm t=6 mm Figure 2.4.
the base course and under the HMA course (z=5 in. or z=127 mm). It was designated to capture vertical stresses (i.e., stress in Z) at this interface. This gauge had a 36.3 psi (0.25 MPa) range. The ASC gauge was designated to measure the vertical stresses at the interface between the subgrade and the granular base (z=11 in. or z=280 mm). This gauge had a 14.5 psi (0.1 MPa) range given that it is placed at a greater depth.
2.5 STRUCTURAL BEHAVIOR AT NCAT 2.5.1 Resilient Response The resilient responses presented hereafter were obtained from Section N1 while in its pristine state. The data was collected soon after construction, on November 7, 2003, during which a single NCAT truck was doing multiple laps. The corresponding raw data file provided by NCAT for the purpose of this study contained three such laps (see Appendix A). Herein, the responses due to the first of the three passes is presented and discussed.
and ‘2D’ refer to the drive axle and ‘1T’ to ‘5T’ refer to the trailer axles. When reviewing the charts it should be borne in mind that the location of each axle relative to the gauges was not measured. In fact, the tractor unit and trailers did not follow a straight line and did not move along or parallel to the Y-axis in Figure 2.4.3.
18.0 BBC Stress in Z (z=5", x=0") [psi] 16.0 1D 14.0 2D 1T 2T 12.0 3T 10.0 4T 8.0 6.0 1S 5T 4.0 2.0 Time [s] 0.0 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 18.0 ASC Stress in Z (z=11", x=0") [psi] 16.0 14.0 12.0 2D 10.0 1T 2T 1D 4T 3T 8.0 5T 6.0 1S 4.0 2.0 Time [s] 0.0 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 Figure 2.5.1: Vertical stresses (i.e.
200 BLC 150 Strain in Y (z=5", x=0") [μstrain] 100 50 0 -50 -100 -150 5T 1S -200 4T 2D -250 1D 3T 1T -300 2T -350 Time [s] -400 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 200 ALC 150 Strain in Y (z=5", x=0") [μstrain] 100 50 0 -50 -100 1S -150 5T -200 3T 4T -250 2D -300 1T 1D 2T -350 Time [s] -400 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 Figure 2.5.2: Horizontal strains in the loading direction (i.e.
200 BLR Strain in Y (z=5", x=+24") [μstrain] 150 100 50 0 1S -50 1T 2D -100 1D 2T -150 -200 3T 4T -250 -300 5T -350 Time [s] -400 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 200 ALR Strain in Y (z=5", x=+24") [μstrain] 150 100 50 1S 0 -50 1D -100 2D 1T 2T -150 3T -200 4T -250 -300 5T -350 Time [s] -400 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.20 Figure 2.5.3: Horizontal strains in the loading direction (i.e.
microstrains in magnitude were induced in the transverse direction by all axles except for the last one (axle 5T). As mentioned earlier, the reason for this change in sign is related to the location of the load relative to the gauge. 150 BTC 100 5T Strain in X (z=5", x=0") [μstrain] 50 0 -50 1S -100 4T -150 -200 -250 3T -300 1D 2D 1T 2T -350 -400 Time [s] -450 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 1.60 1.80 2.00 2.
2.5.2 Cracking and Rutting Performance Sections N1 and N2 experienced cracking in a very similar manner (Priest and Timm, 2006; Timm et al., 2006). Both failed in fatigue within two months of each other (see Figure 2.5.5. Section N1 (modified HMA) failed prior to section N2 (unmodified HMA) after six months of traffic. First, small transverse cracks appeared in the wheel path. Then the cracks progressed to the edge of the wheel path and often curled in the direction of traffic.
Table 2.5.2: Tabulated progression of N1 and N2 rutting levels vs. number of applied ESALs. # Cumulative ESALs Measurement Date Rutting in N1 mm, (in.) Rutting in N2, mm (in.
9.0 N1 N2 8.0 Average Rutting [mm] 7.0 6.0 5.0 4.0 3.0 2.0 1.0 ESALs 0.0 - 1,000,000 2,000,000 3,000,000 4,000,000 5,000,000 Figure 2.5.6: Graphical progression of N1 and N2 rutting levels vs. number of applied ESALs at the Track.
CHAPTER 3 - THE APT EXPERIMENT This chapter summarizes the APT work conducted jointly by INDOT and Purdue University through the North Central Superpave Center between the years 2004 and 2006. It describes the loading history and environment prevailing during the APT experiment and some preliminary analyses of pertinent test data. Here, a subset of the available data is identified as suitable and sufficient for carrying out the main study objective.
air-conditioning unit. In its maximum capacity, the air temperature inside the test area can be reduced relative to warmer outdoor conditions to 60ºF (15.5ºC). In this study the temperature in the testing area was set to 60ºF (15.5ºC). A humidity detector is positioned close to the test pit; in principle, it is possible to increase the humidity in the test area by intentionally ponding water. Figure 3.1.1: Schematic floor plan of INDOT APT facility.
interconnected pneumatic cylinders. A precision air pressure gauge is used to adjust and control the magnitude of the force throughout the test. The downward force is applied to the pavement surface through a wheel assembly. Two tire assembly types are available: dual/conventional and single wide-base. The tire inflation pressures in each case are adjustable, up to a maximum of 120 psi (0.84 MPa). Either assembly is mounted on a carriage capable of traversing the test pit by traveling on the steel beams.
Depending on the desired mode of application, the wheel assembly can be raised from the ground by reversing the action of the four pneumatic cylinders and returned to the startup position for another loading cycle; this will result in a unidirectional mode of loading. Alternatively, the pavement can also be loaded while the carriage travels back to the startup position; this will result in a bidirectional mode of loading.
should be noted that whenever wander was applied, the lateral carriage position was not recorded. Hence, the exact location of the load relative to the embedded gauge array is known only for the initial part of the experiment in which passes were applied without wander. 3.2 COMPOSITION OF TEST SECTIONS The pavement structures (and subgrade) of sections n1 and n2 in lanes 1 and 2 respectively (see Figure 3.1.1) are shown in Figure 3.2.1.
The subgrade in the APT was compacted in lifts, each up to 6 in. (152 mm) thick, using vibratory plate equipment. The average compaction densities for each layer are given in Llenin and Pellinen (2004). Referring to the top 19 in. (483 mm) of the subgrade, the average as-built wet density was 126.9 and 128.0 pcf (2035 and 2052 kg/m³) for sections n1 and n2 respectively. The corresponding average moisture contents were 14.7% and 14.3%. Hence, the following average dry densities were obtained: 110.6 and 112.
Section n2 was: 7.3%, 9.7% and 9.4%. Recall from Chapter 2 (Subsection 2.2.4) that at NCAT the corresponding average void contents were about 6 to 7% for all lifts. 3.3 MECHANICAL TESTING AND PRELIMINARY ANALYSIS 3.3.1 Resilient Modulus of Unbound Materials The accepted mathematical expression for representing resilient modulus test results, unlike equation 2.3.1, is (Uzan, 1985; 1992; Witczak and Uzan, 1988): ⎛θ M R = (k1 ⋅ Pa ) ⋅ ⎜⎜ ⎝ Pa k2 k3 ⎞ ⎞ ⎛ τ oct ⎟⎟ ⋅ ⎜⎜ + 1⎟⎟ ................................
in which the additional (positive) parameter k 6 , having units of stress, represents suction effects. If we further assume that all moisture sensitivity is lumped into k 6 , i.e., k 6 = k 6 (ω ) , then the remaining three parameters in equation 3.3.2 (namely: k1 , k 2 and k 3 ) are independent of moisture content (all four parameters remain density dependent).
compaction to 7.2 psi at 97.5% compaction; at a moisture level of 9.8% k 6 was found negligible (in the low density case). The as-constructed subgrade moisture content at NCAT was about 10.5% (see Chapter 2, Subsection 2.2.2) and about 14.5% in the APT (see Section 3.3). Based on the above results the suction component in the subgrade should be negligible. The asconstructed base moisture content was 6.5% at NCAT (see Chapter 2, Subsection 2.2.3) and about 3.5% in the APT (see Section 3.3).
100,000 Subgrade 96% Resilient Modulus - Model [psi] Base 93% Base 97.5% 10,000 Resilient Modulus - Test Data [psi] 1,000 1,000 10,000 100,000 Figure 3.3.1: Resilient modulus of unbound materials - a cross plot of calibrated equation 3.3.2 values and test data. 3.3.2 HMA Complex Modulus In this subsection the complex modulus test results presented in Chapter 2 (Tables 2.3.3 to 2.3.6) are analyzed.
the stress amplitude (constant) and ω as the angular frequency (units of radians per second), the resulting steady state strain response is also sinusoidal. The quotient of stress and strain in the frequency domain is may be represented by a complex number: E* = E * ⋅ (cos φ + i ⋅ sin φ ) = E1 + i ⋅ E 2 .......................................................... (3.3.
polymers (Plazek, 1996), and for a limited range of temperatures, aT tend to follow the Williams-Landel-Ferry equation (Williams et al., 1955): log(aT ) = − c1 ⋅ (T − T0 ) ................................................................................. (3.3.6) c 2 + (T − T0 ) where c1 and c2 are both positive constants ( c1 is unitless and c2 has units of temperature). This equation was found applicable to HMA mixtures (e.g., Di Benedetto et al., 2007).
Table 3.3.2: Complex modulus analysis results for a reference temperature of 15.5ºC based on the approach in Levenberg and Shah (2008). Relaxation Modulus Parameters (equation 3.3.7) Mix Equilibrium Modulus Time-Temperature Shifting Parameters (equation 3.3.6) a1 , MPa (ksi) a 2 ⋅10 3 a3 ⋅10 5 , s E∞ , MPa (ksi) c1 c2 , ºC (ºF) 1 1,983 (287.6) 9.84 3.91 172 (24.9) 26.8 215.7 (420.3) 2 2,421 (351.1) 10.63 8.81 159 (23.1) 35.6 338.2 (640.8) 3 1,822 (264.3) 12.10 17.79 91 (13.
100,000 45 15.5 ºC Dynamic Modulus (data) Phase Angle (data) Viscoelastic Model 40 Dynamic Modulus [MPa] 30 25 1,000 20 15 100 Phase Angle [degrees] 35 10,000 10 5 Reduced Frequency [Hz] 10 1E-08 1E-06 1E-04 1E-02 1E+00 1E+02 1E+04 1E+06 0 1E+08 Figure 3.3.3: Mix 2 dynamic modulus and phase angle master curves @ 15.5ºC. 100,000 45 15.
100,000 45 15.5 ºC Dynamic Modulus (data) Phase Angle (data) Viscoelastic Model 40 Dynamic Modulus [MPa] 30 25 1,000 20 15 100 Phase Angle [degrees] 35 10,000 10 5 Reduced Frequency [Hz] 10 1E-08 1E-06 1E-04 1E-02 1E+00 1E+02 1E+04 1E+06 0 1E+08 Figure 3.3.5: Mix 4 dynamic modulus and phase angle master curves @ 15.5ºC. Dynamic Modulus [MPa] 100000 Mix 1 Mix 2 Mix 3 Mix 4 10000 1000 Reduced Frequency [Hz] 100 1.00E-07 1.00E-05 1.00E-03 1.00E-01 1.00E+01 1.00E+03 1.00E+05 1.
30 Mix 1 Mix 2 Mix 3 Mix 4 Phase Angle [degrees] 25 20 15 10 5 Reduced Frequency [Hz] 0 1.00E-07 1.00E-05 1.00E-03 1.00E-01 1.00E+01 1.00E+03 1.00E+05 1.00E+07 Figure 3.3.7: Superimposed phase angle master curves @ 15.5ºC for mixes 1 to 4. 3.3.3 Falling Weight Deflections FWD testing was conducted in the APT on June 14, 2004, before passes were applied (embedded instrumentation was not activated during the test). The FWD loading plate was 11.81 in. (300 mm) in diameter.
Table 3.3.3: Peak FWD deflections measured in the center of sections n1 and n2. Lane n1 n2 0 Load Level MPa, (psi) D0 [μm] D1 [μm] D2 [μm] D3 [μm] D4 D5 D6 [μm] [μm] [μm] 0.448 (65) 501.9 360.0 268.0 106.8 47.7 28.1 18.8 0.586 (85) 661.3 482.6 362.7 149.2 67.6 39.0 26.4 0.724 (105) 826.3 610.5 459.4 194.9 88.4 51.4 34.6 0.448 (65) 576.4 413.7 298.7 117.3 50.6 29.2 19.5 0.586 (85) 750.1 547.1 395.1 158.2 70.3 39.6 26.3 0.724 (105) 941.4 697.2 501.3 202.4 91.5 51.5 34.
Loading of Section n1 began on July 19, 2004. About 90,000 passes were applied by August 11, 2004, all without wander. The last 2,500 cycles where applied overnight, during which a bond failure occurred between the surface and intermediate HMA lifts. At the onset of failure, the surface lift in the wheel path area was sheared-off in the direction of loading, exposing the intermediate HMA lift. Subsequently the loading of lane 1 was stopped, and the APT loading frame was switched to lane 2.
wander was employed for the reminder of the test. Trafficking of section n2 was discontinued because another bond failure was seen to take place, this time at the interface between the intermediate and bottom lifts. This sequence of events is shown in Table 3.4.2. Table 3.4.2: APT pass application log for Section n2 (rehabilitated structure).
instrumentation, so that another research project could be installed in the APT. This sequence of events is shown in Table 3.4.3. Table 3.4.3: APT pass application log for Section n1 (rehabilitated structure).
3.4.2 Identification of Dataset for Structural Investigation In general terms, this research aims at devising a method for applying APT results to field conditions. As put forward in Chapter 1: (i) the scope is limited to the case of duplicate pavement systems; (ii) the work plan consists of calibrating a mechanistic model to APT conditions and extending it using laboratory data; and (iii) the extended model is to be validated using NCAT results.
be shown in the following section, large differences were recorded between gauges installed in Section n1 that were expected to measure identical responses. These differences are assumed to originate from structural heterogeneity and slight dissimilarity in gauge installation conditions. Consequently, any inherent dissimilarity in the response to load of the two sections is masked by these differences.
Early synthetic work by Taylor (1945) and Monfore (1950) have shown that measurement errors can be reduced by minimizing the thickness to diameter ratio of the cell and making it as incompressible as possible. Based on experimental work, Peattie and Sparrow (1954) have shown that if these criteria are fulfilled then the measurement error relative to the ‘true’ stress level (in percent) equals 0.6 times the thickness to diameter ratio.
loading direction was from left to right along the Y-axis as indicated by the arrow. The entire gauge array is seen to be located in an eight foot (2.44 m) long strip, 2 ft (0.61 m) wide, in the central part of the test section. The first and last 6 ft (1.83 m) of the test section were not instrumented because the loading speed in these zones is not constant, with the carriage either accelerating or decelerating.
the centerline of the loading path. Strain gauges G-5, G-6, G-7 and G-8 were located along a parallel line positioned two feet (0.61 m) from the loading path. Gauges G-2, G4, G-5 and G-7 were measuring horizontal strains in the loading direction (i.e., strain in Y) while gauges G-1, G-3, G-6 and G-8 were measuring horizontal strains in the transverse direction (i.e., strain in X). Table 3.5.1: Location of APT instrumentation in Section n1 (relate to Figure 3.5.1). Location in X, in.
Figure 3.5.2 presents the vertical stresses measured on top of the subgrade and on top of the base course by the four pressure gauges. As can be seen, the resulting curves are bell-shaped and nearly symmetric. For loading pass #5,000, peak vertical stresses on top of the base course were 30 and 35 psi (0.21 and 0.24 MPa). On top of the subgrade, the measured peak stresses were 16 and 20 psi (0.11 and 0.14 MPa). In theory the readings of each gauge pair should be identical.
bottom of the HMA goes into compression. Then, the strain direction is reversed and the gauges go into tension. The point of maximum tension occurs when the APT carriage has passed the gauge positions along the Y-axis by about 1 to 3 in. (25 to 76 mm). Finally, when the load is receding (APT carriage moves further along), the tensile strains are reversed and compression is induced once more at the bottom of the HMA. This pattern is more pronounced for the gauges aligned along the centerline (G-2 and G4).
431 and 314 microstrains in tension (respectively). For gauges G-5 and G-7 (both offcenter gauges) the peak compressive stains were 2 and 15 microstrains while the peak tensile strains were 50 and 100 microstrains (respectively). In theory, the readings from each gauge pair should be identical. When comparing the response between pass #5,000 and pass #80,000 the most noticeable difference is seen in the peak tensile strain magnitudes for gauges G-2 and G-4 (the centerline gauges).
the G-8 gauge. At this point we do not have a good explanation for these obscure behaviors. 200 Bottom of HMA Strain (in X) [microstrains] Loading Direction 150 G-8, 2ft Off-Center 100 G-6, 2ft Off-Center 50 0 -50 G-1, Centerline G-3, Centerline -100 Pass #5,000 Pass #80,000 -150 APT Carriage Location [in.] -200 0 40 80 120 160 200 240 Figure 3.5.
the overhanging APT beams that span the test pit thus providing a fixed reference for the measurements throughout the experiment. In an effort to assess the accuracy of the profiler, a nominally flat concrete surface was measured repeatedly along the same line. The standard deviation of readings was found to be 0.015 in. (0.38 mm). Referring to a single point on the pavement, the maximum difference between two individual profile readings taken at different times was found to be 0.069 in. (1.75 mm).
0.45 0.40 100 Passes 1000 Passes 10000 Passes 50000 Passes 70000 Passes 0.35 0.30 0.25 Surface Rutting [in.] 0.20 500 Passes 5000 Passes 20000 Passes 60000 Passes 90000 Passes 0.15 0.10 0.05 0.00 -0.05 -0.10 -0.15 -0.20 -0.25 -0.30 -0.35 -0.40 -0.45 Offset in X from Loading Center Line [in.] -0.50 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 Figure 3.5.5: Rutting development in Section n1 at the central cross section during the first 90,000 load passes (applied without wheel wander).
-0.65--0.50 -0.50--0.35 -0.35--0.20 -0.20--0.05 -0.05-0.10 0.10-0.25 0.25-0.40 0.40-0.55 -30 -25 -20 -10 -5 0 5 10 15 Lateral Offset in X -15 20 Pass #100 24 30 36 42 48 54 60 66 72 78 84 90 25 30 96 102 108 114 120 126 132 138 144 150 156 162 168 174 180 186 192 198 204 210 216 Location in Y [in.] Figure 3.5.6: Contour plot of Section n1 rutting after 100 passes. -0.65--0.50 -0.50--0.35 -0.35--0.20 -0.20--0.05 -0.05-0.10 0.10-0.25 0.25-0.40 0.40-0.
-0.65--0.50 -0.50--0.35 -0.35--0.20 -0.20--0.05 -0.05-0.10 0.10-0.25 0.25-0.40 0.40-0.55 -30 -25 -20 -10 -5 0 5 10 15 Lateral Offset in X -15 20 Pass #1,000 24 30 36 42 48 54 60 66 72 78 84 90 25 30 96 102 108 114 120 126 132 138 144 150 156 162 168 174 180 186 192 198 204 210 216 Location in Y [in.] Figure 3.5.8: Contour plot of Section n1 rutting after 1,000 passes. -0.65--0.50 -0.50--0.35 -0.35--0.20 -0.20--0.05 -0.05-0.10 0.10-0.25 0.25-0.40 0.40-0.
-0.65--0.50 -0.50--0.35 -0.35--0.20 -0.20--0.05 -0.05-0.10 0.10-0.25 0.25-0.40 0.40-0.55 -30 -25 -20 -10 -5 0 5 10 15 Lateral Offset in X -15 20 Pass #10,000 24 30 36 42 48 54 60 66 72 78 84 90 25 30 96 102 108 114 120 126 132 138 144 150 156 162 168 174 180 186 192 198 204 210 216 Location in Y [in.] Figure 3.5.10: Contour plot of Section n1 rutting after 10,000 passes. -0.65--0.50 -0.50--0.35 -0.35--0.20 -0.20--0.05 -0.05-0.10 0.10-0.25 0.25-0.40 0.40-0.
-0.65--0.50 -0.50--0.35 -0.35--0.20 -0.20--0.05 -0.05-0.10 0.10-0.25 0.25-0.40 0.40-0.55 -30 -25 -20 -10 -5 0 5 10 15 Lateral Offset in X -15 20 Pass #30,000 24 30 36 42 48 54 60 66 72 78 84 90 25 30 96 102 108 114 120 126 132 138 144 150 156 162 168 174 180 186 192 198 204 210 216 Location in Y [in.] Figure 3.5.12: Contour plot of Section n1 rutting after 30,000 passes. -0.65--0.50 -0.50--0.35 -0.35--0.20 -0.20--0.05 -0.05-0.10 0.10-0.25 0.25-0.40 0.40-0.
-0.65--0.50 -0.50--0.35 -0.35--0.20 -0.20--0.05 -0.05-0.10 0.10-0.25 0.25-0.40 0.40-0.55 -30 -25 -20 -10 -5 0 5 10 15 Lateral Offset in X -15 20 Pass #50,000 24 30 36 42 48 54 60 66 72 78 84 90 25 30 96 102 108 114 120 126 132 138 144 150 156 162 168 174 180 186 192 198 204 210 216 Location in Y [in.] Figure 3.5.14: Contour plot of Section n1 rutting after 50,000 passes. -0.65--0.50 -0.50--0.35 -0.35--0.20 -0.20--0.05 -0.05-0.10 0.10-0.25 0.25-0.40 0.40-0.
-0.65--0.50 -0.50--0.35 -0.35--0.20 -0.20--0.05 -0.05-0.10 0.10-0.25 0.25-0.40 0.40-0.55 -30 -25 -20 -10 -5 0 5 10 15 Lateral Offset in X -15 20 Pass #70,000 24 30 36 42 48 54 60 66 72 78 84 90 25 30 96 102 108 114 120 126 132 138 144 150 156 162 168 174 180 186 192 198 204 210 216 Location in Y [in.] Figure 3.5.16: Contour plot of Section n1 rutting after 70,000 passes. -0.65--0.50 -0.50--0.35 -0.35--0.20 -0.20--0.05 -0.05-0.10 0.10-0.25 0.25-0.40 0.40-0.
-0.65--0.50 -0.50--0.35 -0.35--0.20 -0.20--0.05 -0.05-0.10 0.10-0.25 0.25-0.40 0.40-0.55 -30 -25 -20 -10 -5 0 5 10 15 Lateral Offset in X -15 20 Pass #90,000 24 30 36 42 48 54 60 66 72 78 84 90 25 30 96 102 108 114 120 126 132 138 144 150 156 162 168 174 180 186 192 198 204 210 216 Location in Y [in.] Figure 3.5.18: Contour plot of Section n1 rutting after 90,000 passes. 3.
responses were shown in Figures 3.5.2 to 3.5.4. In contrast to the NCAT case, each APT pass resulted in one stress (or strain) pulse; also, the pavement was allowed to rest for 8 seconds between passes. It should be noted that the APT was operated on weekends also. Graphically, the response traces from the two experiments are very much different and any attempt to directly compare them is futile given that they embody many dissimilarities: (i) Loading Speed: 45 mph at NCAT vs. 5 mph in the APT.
CHAPTER 4 - BASIC MECHANISTIC ANALYSIS This chapter addresses the primary study objective by establishing a relation between the NCAT and APT experiments. The scope and approach are discussed in Section 4.1. Section 4.2 contains the development of a basic mechanistic model for the pavement systems considered; it is based on layered elastic theory (LET) with the necessary material properties obtained via inverse analysis of APT results. Section 4.
although stress-state sensitive, are assumed unaffected by the changes in the HMA stiffness. This may be justified, at least as a first order approximation, considering that there are preexisting effective confining stresses in these materials (of unknown magnitudes) originating from the construction process; these include vertical stresses due to self weight, locked-in horizontal stresses from the compaction process, and confining stresses due to negative pore pressures (see Subsection 3.3.1).
εθ = 1 ν ⋅ σ θ + ⋅ (σ r + σ z ) ............................................................................ (4.2.1b) E E εz = ν 1 ⋅ σ z + ⋅ (σ θ + σ r ) ............................................................................ (4.2.1c) E E ⎛ 1 +ν ⎞ ⎟ ⋅ τ rz ........................................................................................... (4.2.1d) ⎝ E ⎠ ε rz = ⎜ ε zθ = ε rθ = 0 ................................................................................................. (4.2.
coordinate system is placed at the surface of the first layer with the z -axis drawn into the medium and the r -axis parallel to the layers. The depth to the individual interfaces, measured from the surface, is denoted by z i ( i = 1, 2, .. n − 1 ). Hence, z1 is the thickness of layer 1, z 2 is the combined thickness of layers 1 and 2, and so on. The combined thickness of the n − 1 layers is denoted by H (i.e., H = z n −1 ).
in which the asterisk is used to indicate that the response is due to vertical surface loading m ⋅ J 0 (m ⋅ ρ ) as can also be seen in equations 4.2.4a-b. Equations 4.2.4c-f express the continuity of stresses and displacements inside the structure at the layer interfaces; full bonding is suggested by equation 4.2.4f. Equation 4.2.4g means that all response types (denoted using R ) must vanish for the n th layer and at infinite depth (i.e., lim z →∞ R = 0 ).
The program’s user interface is shown in Figure 4.2.1. As can be seen (from top to bottom), the input of material properties and layer thicknesses is done in the topmost table. For each layer three attributes are required: Young’s modulus, Poisson’s ratio, and thickness. In the example shown in Figure 4.2.1 only four layers are considered because identical material properties are assigned to layers 3 and 4 (recall that all layers are fully bonded).
there is no requirement to press a ‘run’ button to execute the code; in fact, any change of value in one of the input tables will be automatically reflected in real time in the results table. This feature is what makes this program extremely easy to use and appealing for further analyses compared to any other available LET code. Note also that no units are specified as the computations are done in dimensionless form (see Equation 4.2.3); the user must be consistent with his choice.
For performing the backcalculation, the n1 pavement system was represented using four layers. The three HMA lifts were combined into one (top) layer, 5 in. (127 mm) thick with an assumed Poisson’s ratio of ν 1 = 0.30 . The second layer from the top represented the crushed aggregate base course, with a thickness of 6 in. (152.4 mm) and ν 2 = 0.35 (assumed). Because no instrumentation was embedded in the subgrade (only on top), there was no available data to support its sub-layering.
and the subgrade modulus ( E3 ). In order to derive their numerical values, an objective (scalar) function describing the agreement between the model and test data was formulated. First, for each gauge separately, out of the total twelve gauges available, an error term was defined as follows: ERRg = 1 ⋅ N ∑ [R N n =1 APT n − Rnmodel ] 2 .................................................................... (4.2.6) in which N is the number of data points used for the comparison for the g th gauge (i.
min( ERRg ) obtained for pass #5,000 were also used for the backcalculation of pass #80,000. 4.2.3 Interim Results and Discussion Table 4.2.1 presents the backcalculated layer moduli for pass #5,000 and pass #80,000. The global error term (equation 4.2.7) was 4.89% for pass #5,000 and 6.27% for pass #80,000. In both cases it can be seen that the stiffness of the pavement structure is decreasing from top to bottom. During pass #5,000 the HMA is 14.6 times stiffer than the underlying aggregate base.
and in Y (right) for gauges located along the loading centerline. The charts in the middle of the figure show horizontal strains in X (left) and in Y (right) for gauges positioned outside the loading path. The bottom charts show vertical stresses as measured by pressure cells located on top of the base (left) and on top of the subgrade (right). In each chart the measured gauge data is represented by solid markers.
stress measurements compared to the strain readings. During pass #5,000 the maximum relative difference in the peak stress readings with respect to the average reading at the peak is 10.6% (for pressure gauges 1178 and 1185). Similarly, the maximum relative difference in the peak strain readings with respect to their average at the peak is 35.0% (for strain gauges G5 and G7). During pass #80,000 the corresponding differences are 10.8% (again, pressure gauges 1178 and 1185) and 44.
X and Y directions for the off-center gauges (G5 to G8). For the centerline gauges (G1 to G4), the horizontal strains are captured relatively well only in the direction of loading (G2 and G4). The fit is not very good for the strains in the transverse direction (G1 and G3). The vertical stress peaks on top of the base (1178 and 1185) and on top of the subgrade (1179 and 1184) are underpredicted by the model. The above findings, however, should not be expected to hold in general.
3 E2com ⎡h ⋅3 E + h ⋅3 E ⎤ 1 2 ,1 2 2, 2 ⎥ ...................................................................... (4.3.2) =⎢ h1 + h2 ⎥ ⎢ ⎦ ⎣ * Ecom = (E ) + (E ) com 2 1 com 2 2 .............................................................................. (4.3.3) ⎛ E2com ⎞ ⎟ ....................................................................................... (4.3.4) com ⎟ ⎝ E1 ⎠ φcom = arctan⎜⎜ in which h1 = 1.0 in. (25.4 mm) is the lift thickness of Mix 1, h2 = 4.0 in.
NCAT the trucks are traveling at 45 mph (20.1 m/s); this speed is 9.0 ( = 45 / 5 ) times higher than in the APT. Now, if the temperature was 15.5ºC (60ºF) then aT = 1.0 and the reduced frequency would become 0.2088 Hz ( = 0.0232 ⋅ 9.0 ⋅ 1.0 ); the corresponding modulus (using Figure 4.3.1) is therefore 4,028 MPa (584,100 psi). If, on the other hand, the HMA temperature at NCAT was 30.0ºC (86ºF) instead of 15.5ºC (60ºF), then aT = 0.0308 and the reduced frequency would become 0.0064 Hz ( = 0.
Table 4.3.1: Combined complex modulus properties for APT n1 / NCAT N1 (based on equations 4.3.1 to 4.3.4). Test Temperature Test Frequency Dynamic Modulus Phase Angle ºC (ºF) -10.0 (+14) +4.4 (+40) +21.1 (+70) +37.8 (+100) +54.4 (+130) [Hz] MPa (ksi) [degrees] 25 10 5 1 0.5 0.1 25 10 5 1 0.5 0.1 25 10 5 1 0.5 0.1 25 10 5 1 0.5 0.1 25 10 5 1 0.5 0.
1E+05 Time-Temperature Shift Factor [-] -10.0ºC 1E+03 +4.4ºC 1E+01 aT=1.0 +21.1ºC 1E-01 +37.8ºC 1E-03 +54.4ºC 15.5ºC 0 Temperature [ C] 1E-05 -20.0 -10.0 0.0 10.0 20.0 30.0 40.0 50.0 60.0 Figure 4.3.2: Combined HMA time-temperature shifting for a reference temperature of 15.5ºC (based on Table 4.3.1). 4.3.2 Falling Weight Deflections In this subsection an attempt is made to use the layered model, calibrated against APT data (Subsection 4.2.
fr Dec. 03 fr Jan. 04 = 0.0232 ⋅ 3.35 ⋅ 0.704 = 0.055 Hz .................................................... (4.3.5b) = 0.0232 ⋅ 3.35 ⋅ 3.987 = 0.310 Hz .................................................... (4.3.5c) in which 0.0232 is the reduced frequency derived from inverse analysis of APT conditions (see Subsection 4.3.1). Using Figure 4.3.1 the corresponding HMA moduli are: EHMA Nov. 03 = 1,000 MPa (145,000 psi), EHMA Dec. 03 = 2,900 MPa (420,500 psi) and EHMA Jan. 04 = 4,600 MPa (667,000 psi).
44.1%. If the isotropic LET model was directly calibrated using the NCAT deflections, allowing only for the HMA modulus to differ in each case, the errors would have been 12.8 microns and 22.2% respectively. Therefore, although the trend in the computations follows the trend in the data, the forecasting errors are 2.5 to 2.0 times higher compared to the calibrated case. 4.3.
In the forward computations, the radius of contact area for each of the tires was always taken as 4.0 in. (101.6 mm). The corresponding stress intensity was calculated using the axle weights in Table 2.1.1. For the dual axles, center to center tire spacing was taken as 13.5 in. (343 mm); for the dual tandem axles, axle spacing was taken as 50 in. (1.27 m). The moving NCAT truck was simulated by applying the array of tire loads at different locations relative to the gauges.
Y-axis [ft] X1 ASC 6 S=45 mph =792 in./s 4 ALR ALC 2 ATC X-axis [ft] -2 -4 BTC 2 4 BTL -2 BLC BLR -4 X0 BBC -6 Figure 4.3.4: Layout of N1 gauge array (refer to Figure 2.4.3) and travel path positioning of the center point of the rightmost truck tire (connecting arrows). The resulting numerical values of X 0 and X 1 are shown in Figure 4.3.5 for the different axles. Note that in this figure (and unlike Figure 4.3.
the axles following the drive axle to drift to the right side relative to the Y-axis. This is realistic considering the fact that the NCAT trucks traversed the N1 Section after completing a left turn on the East curve (see Figure 2.1.1). 8 ASC Y-axis [ft] 6 4 ALC ALR 2 ATC X-axis [ft] 0 -2.0 -1.6 BTL -1.2 -0.8 -0.4 0.0 BTC -2 BLC 0.4 0.8 1.2 1.6 2.0 S BLR D 1T 2T -4 BBC 5T 3T 4T -6 Figure 4.3.
to the APT case (refer to Subsection 4.2.3), better matching is usually achieved for the strains in the travel (longitudinal) direction (i.e., strains in Y) compared to the strains in the transverse direction (i.e., strains in X). The forecastability of the vertical stresses cannot be assessed because these were used to allocate the loads. Quantitatively, the matching errors in Figures 4.3.6 to 4.3.10, between the isotropic LET predictions and NCAT measured responses, are summarized in Table 4.3.2.
100 8 Stress in Z (z=5", x=0") [psi] Strain in Y (z=5", x=0") [μstrain] BBC_S Data Model 7 6 5 4 3 2 1 0 50 0 -50 -100 -150 Time [s] -1 0.000 0.050 0.100 0.150 0.200 0.250 0.300 0.350 -200 0.000 0.400 20 0 -20 -40 BLR_S Data Model -60 -80 0.000 0.050 0.100 Time [s] 0.150 0.200 0.250 0.300 0.350 0.150 0.200 0.250 0.300 0.350 0.200 0.250 0.300 0.350 0.400 0.250 0.300 0.350 0.400 0.450 0.250 0.300 0.350 0.400 0.450 0.
18 200 Stress in Z (z=5", x=0") [psi] 14 Strain in Y (z=5", x=0") [μstrain] BBC_D Data Model 16 12 10 8 6 4 2 0 -2 0.350 0.400 0.450 0.500 0.550 0.600 0.650 -200 -300 BLR_D Data Model 100 50 0 -50 -100 -150 0.400 0.450 0.500 0.550 0.600 0.650 0.700 40 20 0 -20 Strain in X (z=5", x=0") [μstrain] BTL_D Data Model 60 0.550 0.600 0.650 0.700 0.550 0.600 0.650 0.700 0.750 0.550 0.600 0.650 0.700 0.750 0.550 0.600 0.650 0.700 0.750 0.
18 200 Stress in Z (z=5", x=0") [psi] 14 Strain in Y (z=5", x=0") [μstrain] BBC_1T Data Model 16 12 10 8 100 0 -100 6 4 -200 2 0 -300 -2 Time [s] -4 0.700 0.725 0.750 0.775 0.800 0.825 0.850 0.875 0.900 -400 0.750 Strain in X (z=5", x=0") [μstrain] Strain in Y (z=5", x=+24") [μstrain] 50 0 -50 -100 -200 0.750 BLR_1T Data Model 0.775 0.800 0.825 0.850 0.875 0.900 0.925 0.
18 150 Stress in Z (z=5", x=0") [psi] 14 Strain in Y (z=5", x=0") [μstrain] BBC_3T Data Model 16 12 10 8 100 50 0 -50 -100 6 -150 4 -200 2 -250 0 -2 Time [s] -4 1.150 1.175 1.200 1.225 1.250 1.275 1.300 1.325 1.350 -300 -350 1.200 100 50 0 -50 -100 -150 -200 -250 -300 BLR_3T Data Model -350 1.200 1.225 1.250 1.275 1.300 1.325 1.350 1.375 1.400 1.275 1.300 1.325 1.350 1.375 1.325 1.350 1.375 1.400 1.
8 100 Stress in Z (z=5", x=0") [psi] 6 Strain in Y (z=5", x=0") [μstrain] BBC_5T Data Model 7 5 4 3 2 0 -50 -150 Time [s] -2 1.600 1.650 1.700 1.750 1.800 1.850 1.900 1.950 2.000 -200 1.600 100 0 -100 -200 -300 -400 -500 1.600 BLC_5T Data Model 1.650 1.700 Time [s] 1.750 1.800 1.850 1.900 BLR_5T Data Model 1.650 1.750 1.800 1.850 60 40 20 0 -20 1.900 1.950 Time [s] -40 1.650 2.000 1.700 1.750 1.800 1.850 1.900 1.
4.
deflections and stresses and strains induced by a moving truck. Considering all simplifying assumptions made in the aforementioned scheme and the relatively few free parameters used to represent the pavement system, the extended model performed relatively well in projecting resilient responses at NCAT.
CHAPTER 5 - ADVANCED MECHANISTIC METHODS In this chapter two more advanced models compared with the preceding chapter are developed with the aim of establishing a superior link between the APT and NCAT experiments. The first involves LET with anisotropic material properties and the second involves layered viscoelastic theory (LVT) with isotropic material properties. The underlying theories and computational implementations are discussed in subsections 5.1.1 and 5.2.1. In subsections 5.1.2 and 5.2.
In terms of a cylindrical coordinate system ( r , θ , z ), with z as the axis of material symmetry, and assuming an axially symmetric deformation field (i.e., ε zθ = ε rθ = 0 ), the constitutive law becomes: ε r = a11 ⋅ σ r + a12 ⋅ σ θ + a13 ⋅ σ z ................................................................... (5.1.2a) ε θ = a12 ⋅ σ r + a11 ⋅ σ θ + a13 ⋅ σ z ................................................................... (5.1.2b) ε z = a13 ⋅ σ r + a13 ⋅ σ θ + a33 ⋅ σ z .............................
u = (a12 − a11 ) ⋅ (1 − b) ⋅ ∂ 2φ ......................................................................... (5.1.3e) ∂r∂z w = (2 ⋅ a13 ⋅ a − a33 ⋅ d ) ⋅ ⎛ ∂φ 2 1 ∂φ ⎞ ∂ 2φ a − 44 ⎜ ⎜ ∂r 2 + r ⋅ ∂r ⎟⎟ ........................................ (5.1.3f) ∂z 2 ⎠ ⎝ in which the parameters a , b , c and d are functions of the elastic constants: a= a13 ⋅ (a11 − a12 ) ....................................................................................... (5.1.
(ν zx ) i , (ν xy ) i and (G xz ) i . Layers are numbered serially, the layer at the top being layer 1 and the half-space, layer n . Similar to the isotropic case (see Subsection 4.2.1), the origin of the cylindrical coordinate system is placed at the surface of the first layer with the z -axis pointing into the medium and the r -axis parallel to the layers. As before, the depth to the individual interfaces (measured from the surface) is denoted by z i ( i = 1, 2, .. n − 1 ).
( ) ⎛ K iα ⋅ Ai ⋅ e − m⋅α i ⋅( λi −λ ) − Bi ⋅ e − m⋅α i ⋅( λ −λi−1 ) (σ z* )i = m ⋅ J 0 (m ⋅ ρ ) ⋅ ⎜ ⎜ + K β ⋅ C ⋅ e −m⋅βi ⋅( λi −λ ) − D ⋅ e − m⋅βi ⋅( λ −λi−1 ) i i i ⎝ ( ( ) ⎛ Lαi ⋅ Ai ⋅ e − m⋅α i ⋅( λi −λ ) + Bi ⋅ e − m⋅α i ⋅( λ −λi−1 ) (τ rz* ) i = m ⋅ J1 (m ⋅ ρ ) ⋅ ⎜ β ⎜ + L ⋅ C ⋅ e − m⋅β i ⋅( λi −λ ) + D ⋅ e −m⋅βi ⋅( λ −λi−1 ) i i ⎝ i ( ( ⎞ ⎟ ................... (5.1.7c) ⎟ ⎠ ) ⎞ ⎟ ..................... (5.1.
the stresses and displacements must vanish; this leads to An = C n = 0 . For a vertical load of the form m ⋅ J 0 (m ⋅ ρ ) applied to the surface of layer 1 (i.e., i = 1 , λ = 0 ), and in the absence of shearing forces, we obtain the two conditions: (σ z* )1 = m ⋅ J 0 (m ⋅ ρ ) and (τ rz* )1 = 0 . Using equations 5.1.7c and 5.1.7d these conditions can be written explicitly as follows: ( ) ( ) K1α ⋅ A1 ⋅ e− m⋅α1 ⋅λ1 − B1 + K1β ⋅ C1 ⋅ e− m⋅ β1 ⋅λ1 − D1 = 1 ........................................ (5.1.
R = (q ⋅ α ) ⋅ ∞ R* ∫ m ⋅ J1 (m ⋅ α ) ⋅ dm ................................................................. (5.1.10) m=0 in which α = a / H and R* is any stress or displacement of interest from equations 5.1.7a-f. Thereafter, the strains are calculated from equations 5.1.2a-d. The aforementioned derivation was programmed into an Excel worksheet (see program ELLEA2 in Appendix B).
Figure 5.1.1: User interface of the anisotropic LET program ELLEA2. Figure 5.1.2: ELLEA2 display of property and algorithm restriction for the example shown in Figure 5.1.1.
5.1.2 Calibration to APT Conditions The anisotropic LET properties were backcalculated using the APT study. This was performed for the initial stages of the experiment, during pass number 5,000. Similar to the isotropic analysis, a four layered structure was assumed with a semi-infinite (isotropic) concrete bottom. The properties of the HMA ( i = 1 ), aggregate base ( i = 2 ) and subgrade ( i = 3 ) were obtained by matching model generated responses with measured responses.
in which it can be seen that the two Poisson’s ratios ν xy and ν zx are dissimilar. Note that both equation 5.1.12b and equation 5.1.11 yield the isotropic shear modulus (as expected) when the isotropic case is introduced, with E z = E x = E and ν xy = ν zx = ν . Table 5.1.1 presents the calibrated (backcalculated) anisotropic elastic constants for APT pass number 5,000. The global error term (equation 4.2.7) was 4.73% which is only slightly lower compared to 4.
In the vertical ( z ) direction, the HMA is only 2.5 times stiffer than the underlying aggregate base; this ratio seems relatively low. The base itself is about 5.0 times stiffer than the subgrade; a ratio that is relatively high considering the thinness of the layer and structure. In the horizontal ( x − y ) direction, the HMA was found to be 33 times stiffer than the aggregate base; the value of E x seems too low for the base (only 1.2 stiffer than the subgrade), but reasonable for the HMA.
Computed Response Isotropic Case G1_measured G3_measured -60 -80 -100 -120 -140 -160 Offset [in.] 0 -80 -160 Computed Response Isotropic Case G2_measured G4_measured -240 -320 -400 -480 Offset [in.] -180 -70 -60 -50 -40 -30 -20 -10 -560 0 -70 -60 -50 -40 -30 -20 -10 0 180 150 120 90 60 30 0 40 Strain in X (z=5", x=24") [μstrains] Computed Response Isotropic Case G6_measured G8_measured Offset [in.
Referring first to peak FWD deflections, the first three basins obtained on Nov. 3, 2003, Dec. 15, 2003, and on Jan. 26, 2004 are considered (Table 2.3.9). In the isotropic analysis of these same deflections (see Subsection 4.3.2), the adjusted HMA moduli were: E HMA psi) and E HMA Nov . 03 Jan. 04 = 1,000 MPa (145,000 psi), E HMA Dec. 03 = 2,900 MPa (420,500 = 4,600 MPa (667,000 psi). These stiffness values reflected (respectively): 41.4%, 120.1% and 190.
Based on these findings it may be concluded that the anisotropic analysis FWD deflections offers little advantage over an isotropic analysis. 0.0 100.0 FWD Deflection [microns] th January 26 , 2004 200.0 Anisotropic LET Isotropic Case Nov. 2003 Data Dec. 2003 Data Jan. 2004 Data 300.0 400.0 th December 15 , 2003 500.0 rd 600.0 November 3 , 2003 Distance from Center of FWD Plate [mm] 700.0 0.0 200.0 400.0 600.0 800.0 1000.0 1200.0 1400.0 1600.0 1800.0 2000.0 Figure 5.1.
forward calculations in the anisotropic case. Recall that these were obtained by the requirement that the model matches the measured vertical stress responses (hence the stress responses should not used to assess the modeling and predictive scheme). Second, in order to position the axles longitudinally, the calculated and measured peaks were made (forced) to coincide with each other. With reference to Figure 2.1.2, Figure 5.1.5 is devoted to the responses caused by the steer axle (1S), and Figure 5.1.
8 100 BBC_S Data Model Isotropic Case 6 5 Strain in Y (z=5", x=0") [μstrain] Stress in Z (z=5", x=0") [psi] 7 4 3 2 1 0 50 0 -50 -100 -150 Time [s] -1 0.000 0.050 0.100 0.150 0.200 0.250 0.300 0.350 -200 0.000 0.400 0 -20 -40 -60 BLR_S Data Model Isotropic Case 0.050 0.100 0.150 Time [s] 0.200 0.250 0.300 0.350 0.400 0.150 Time [s] 0.200 0.250 0.300 0.350 0.250 0.300 0.350 0.400 0.300 0.350 0.400 0.450 0.300 0.350 0.400 0.450 0.
18 150 BBC_3T Data Model Isotropic Case 14 12 100 Strain in Y (z=5", x=0") [μstrain] Stress in Z (z=5", x=0") [psi] 16 10 8 6 4 2 0 -2 1.175 1.200 1.225 1.250 1.275 1.300 1.325 Strain in X (z=5", x=0") [μstrain] Strain in Y (z=5", x=+24") [μstrain] 50 0 -50 -100 -150 -300 -350 1.200 BLR_3T Data Model Isotropic Case 1.225 1.250 1.275 1.300 1.325 1.350 1.375 -250 BLC_3T Data Model Isotropic Case Time [s] 1.225 1.250 1.275 1.300 1.325 1.350 1.375 1.350 1.375 1.400 1.
5.2 LAYERED VISCOELASTIC ISOTROPIC MODEL 5.2.1 Theory and Computational Implementation The time-dependent response R ve (t ) of a linear viscoelastic (non-aging) system under isothermal conditions to a given time-dependent input I (t ) is fully characterized by a function RHve (t ) named indicial admittance (von Karman and Biot, 1940). This function represents the response of the system to a unit input applied as a step function in time, i.e.
R e (t ) = RHe (c1e , c 2e , ... ) ⋅ I (t ) ............................................................................ (5.2.2) in which I (t ) is the input and RHe is the indicial admittance of the associated elastic system. The function RHe is seen to depend on a set of elastic time-independent material constants denoted here as c1e , c2e , etc, corresponding to a set of viscoelastic (timedependent) material properties: c1ve , c2ve , etc.
length of the series increases the accuracy of the method, but at the cost of additional computation time. The second inversion method is known as the ‘direct method’. It is much easier and faster to apply, and although it offers little means of reducing error, several studies have found it adequate for practical (engineering) purposes (Schapery, 1965; Hufferd and Lai, 1978). The ‘direct’ method was selected for use herein, and is briefly described in what follows.
Without assuming the numerical value of β , equation 5.2.8b is first applied to equation 5.2.4, giving: ~ R Hve (t ) ≈ R Hve (β / t ) = R He (c~1ve ( β / t ), c~2ve ( β / t ), ...) ............................................ (5.2.9) After applying equation 5.2.8b again, this time to the right hand side of equation 5.2.9, the parameter β cancels out, resulting in: RHve (t ) ≈ RHe (c1ve (t ), c2ve (t ), ...) .......................................................................... (5.2.
(i.e., α = 1,2,...,63 ) to yield 63 unit response time functions RHveα (t ) at different offset distances. These offsets ranged from -76 in. (1.93 m) to +76 in. (1.93 m) relative to the evaluation point, with 31 points before (approaching) the evaluation point, 31 points after the evaluation point, and one additional point exactly in line with the evaluation point. Spacing of these points ranged between 4 in. (101.6 mm) to 1.0 in. (25.4 mm) with denser spacing closer to the evaluation point.
The upper part of Figure 5.2.1 shows the individual ‘input’ functions vs. time, illustrating the triangular load-unload shape applied to each point. Given that the loading points were not spaced uniformly apart, the time difference between adjacent load peaks (denoted as Δt ) was varied such that the load would appear to be moving at a constant speed of choice (denoted as V in the figure). Given a set of time-independent material properties, and a loading point α , R Hveα (t ) in equation 5.2.
evenly spaced on a logarithmic scale. Both extreme modulus values were obtained from * the combined dynamic modulus master curve in Figure 4.3.1 using E0 = lim f r → ∞ Ecom * and E ∞ = lim f r →0 E com . The constants τ D and nD were arbitrarily determined as: τ D = 35,000 seconds and nD = 0.240. 1.E+05 2.0 1.5 Offset=20.0 [in.] 0.5 Offset=10.0 [in.] 0.0 1.E+04 -0.5 -1.0 Offset=5.0 [in.] -1.5 1.E+03 -2.0 -2.5 -3.0 -3.5 1.E+02 Offset=0.0 [in.] -4.0 Strain Modulus -4.5 -5.0 -5.5 1.E-10 1.
shape of the viscoelastic response was adequately captured within the offset range of ±70 in. (±1.78 m). Physically, the calculation points were spaced 2 to 5 in. (50.8 to 127 mm) apart; a cubic spline interpolation scheme was used to generate intermediate responses. The parameter m ranged between 1 and 3,200 with values of τ m chosen such that each triangular load-unload ‘input’ (see Figure 5.2.1) was divided into 100 time intervals: 50 during loading and 50 during unloading.
the responses computed in the last simulated pass. However, due to computational power limitations, only one movement of the half-axle was simulated. Furthermore, it should be noted that unlike the previous analyses (refer to Figures 4.2.2 and 5.1.3), the matching of computed and measured responses was not limited to the approaching branches and was also performed for the receding branches. The pavement system was modeled as a four layered half-space.
resilient modulus range of test results), and a base modulus of 6,820 psi (47 MPa) appears too low for a material compacted to 97% (which is the compaction degree in the APT experiment). In comparison with the isotropic LET analysis (Table 4.2.1), the subgrade here is about 2.2 times stiffer; the base modulus here is merely 28% of that backcalculated in the time-independent isotropic case. Table 5.2.1: Backcalculated material properties for the layered viscoelastic model during APT pass #5,000.
100,000 Relaxation Modulus [MPa] 15.5 ºC 10,000 From Complex Modulus Tests 1,000 From APT Inverse Analysis 100 Reduced Time [s] 10 1.E-10 1.E-08 1.E-06 1.E-04 1.E-02 1.E+00 1.E+02 1.E+04 1.E+06 1.E+08 1.E+10 Figure 5.2.3: Comparison of backcalculated relaxation modulus with that interconverted from complex modulus test results.
backcalculated viscoelastic properties are associated with strain levels that are about four times higher. Furthermore, the dissimilarity can originate from the differences in aggregate structure between an HMA prepared in the laboratory versus an HMA prepared using full-scale construction equipment. Figure 5.2.4 shows the measured and calibrated model responses for APT pass number 5,000. Six charts are included, each showing a different response vs. offset distance from the gauge.
150 20 100 Strain in Y (z=5"; x=0) [μstrain] Strain in X (z=5"; x=0) [μstrain] 40 0 -20 -40 -60 -80 -100 -120 Viscoelastic Model -140 G1_measured -160 G3_measured Offset [in.
As before, the elastic properties of the base and subgrade (and rigid bottom) were assumed to be identical in both experiments, unaffected by the different loading conditions. The appropriate HMA temperature at NCAT was determined in Subsection 4.3.3 to be 80.6ºF (27.0ºC); based on Figure 4.3.2 this temperature level is associated with a time temperature shift factor of 0.062 (i.e., aT = 0.062). Using a loading speed ( V in Figure 5.2.
Quantitatively, the matching errors in these figures were almost consistently lower than those in Figures 4.3.6 to 4.3.10. This is shown in Table 5.2.2, which lists the improvement in predictive power (in percent) of the viscoelastic model over the isotropic elastic case (as given in Table 4.3.2). As can be seen, the improvement ranged between 0.9% to 71.7% with an overall average of 27.8%; only a single negative (worsening) case was obtained (1S axle, ATC gauge). Table 5.2.
Figure 5.2.5: Comparison of isotropic LVT projections with measured N1 responses right side of steer axle (1S). Isotropic case reproduced from Figure 4.3.6.
Figure 5.2.6: Comparison of isotropic LVT projections with measured N1 responses right side of drive axle (1D and 2D). Isotropic case reproduced from Figure 4.3.7.
Figure 5.2.7: Comparison of isotropic LVT projections with measured N1 responses right side of first trailer axle (1T). Isotropic case reproduced from Figure 4.3.8.
Figure 5.2.8: Comparison of isotropic LVT projections with measured N1 responses right side of third trailer axle (3T). Isotropic case reproduced from Figure 4.3.9.
Figure 5.2.9: Comparison of isotropic LVT projections with measured N1 responses right side of fifth (last) trailer axle (5T). Isotropic case reproduced from Figure 4.3.10.
5.3 APPRAISAL OF ADVANCED METHODS As an extension to Chapter 4, two more advanced pavement models were employed here to address the primary study objective of linking the APT and NCAT experiments, namely: anisotropic layered elasticity, and isotropic layered viscoelasticity. The analyses were performed for the pavements in the very early stages of the experiment, focusing on resilient responses. First, the mathematical derivation of the models was presented in detail.
determined from complex modulus test results. The calibration to APT conditions was performed after assuming the numerical values of the Poisson’s ratios and manipulating the remaining material parameters. Hence, in effect, the viscoelastic analysis included only one additional free material parameter compared to the basic isotropic layered elastic analysis.
CHAPTER 6 - CONCLUSION This chapter offers a short summary of the entire report and highlights the main findings/results (Section 6.1). In Section 6.2, general recommendations are suggested including future research ideas, followed by specific advice on how INDOT should implement the study results. 6.
Chapter 2 included relevant information from the NCAT study. Chapter 3 summarized the APT work and laid the groundwork for commencing the mechanistic analyses. These two chapters revealed that: (i) Even though nominally identical pavement systems were constructed in the APT and at NCAT, the differences in loading and environmental conditions produced completely distinct responses and dissimilar cracking and rutting performances.
recorded). Mainly for this reason, subsequent analyses were focused on the initial stages of both experiments. Both Chapters 4 and 5 contained the development of mechanistic models for representing the pavement system. These were followed by calibration procedures and utilization of laboratory test results to enhance the applicability of these models to other loading and environmental conditions. Then, the models were used in forward calculation mode to forecast load induced resilient responses at NCAT.
Thereafter, the loading and environment at NCAT were simulated and the advanced models applied to forecast measured resilient responses. Referring first to the anisotropic model, it was found that only mild improvements over the isotropic elastic case were offered and hence concluded that the added complexity involved in the anisotropic analysis did not prove worthy.
similar constructions. Once such a methodology is available, huge financial benefits can be gained, for example by using the facility as a learning tool to improve pavement design methods or to promote the incorporation of new nontraditional materials. The present work offered a mechanistic approach to account for resilient (recoverable) responses. However, the proposed method was developed and validated using only one pavement type.
construction of APT test sections (e.g., organization, scheduling, gauge installations, etc) are covered in Llenín and Pellinen (2004). (i) Embedded Instrumentation. Before being installed, all gauge types should be checked for functionality, investigated for temperature sensitivity, and calibration factors validated. There is a need to devise ways to calibrate the gauges after installation in the pavement system given that their presence influences the free field behavior.
so that two new loading modes can be applied to the surface of the pavement: horizontal (shear) and turning (torsion); these will allow the study of intersection conditions. An investigation to study the effects of various tire pressures should also be targeted. In this connection, a way to measure the actual loading area and distribution of stresses under the APT tires should be explored. (iii) Structural Behavior.
sections are removed. Data sampling rates should be varied based on the current ‘action’; e.g., use 100 scans per second for APT passes (including when the wheels are lifted of the ground and returned to the startup location), use 5,000 scans per second for FWD tests, and record data every 5 to 10 minutes when monitoring environmental changes. The carriage position relative to the gauge array ought to be recorded at all time; this information is very important for performing inverse analysis.
REFERENCES Al-Qadi, I. L. (2007), “True Viscoelastic Analyses of Pavement Structures to Validate & Enhance Current Modulus Selection from Load Pulse Duration in NCHRP 1-37a Design Guide,” obtained through private communication from the FHWA, TFHRC. Andrei, D., Witczak, M. W., Schwartz, C. W., and Uzan, J. (2004), “Harmonized Resilient Modulus Test Method for Unbound Pavement Materials,” Transportation Research Record 1874, Journal of the Transportation Research Board, pp. 29-37. ARA Inc.
De Jong, D. L., Peatz, M. G. F., and Korswagen, A. R. (1973), “Computer Program Bisar Layered Systems Under Normal and Tangential Loads,” Konin Klijke ShellLaboratorium, Amsterdam, External Report AMSR.0006.73. Di Benedetto, H., Delaporte, B., and Sauzeat, C. (2007), “Three-Dimensional Linear Behavior of Bituminous Materials: Experiments and Modeling, ” International Journal of Geomechanics, Vol. 7(2), pp 149-157. Duncan, J. M., Williams, G. W., Sehn, A. L., and Seed, R. B.
Lakes, R. S. (1998), Viscoelastic Solids, CRC Press (Boca Raton, FL), p. 476. Lekhnitskii, S. G. (1963), “Theory of Elasticity of an Anisotropic Elastic Body, HoldenDay, San Francisco, p. 404. Levenberg, E. (2006), “Constitutive Modeling of Asphalt-Aggregate Mixes with Damage and Healing,” Ph.D. Dissertation, Technion - Israel Institute of Technology. Levenberg, E., and Shah, A. (2008), “Interpretation of Complex Modulus Test Results for Asphalt-Aggregate Mixes,” ASTM Journal of Testing and Evaluation, Vol.
Poulos, H. G., and Davis, E. H. (1974), “Elastic Solutions for Soil and Rock Mechanics, Center for Geotechnical Research,” John Wiley & Sons, Inc. (reprinted and corrected 1991). Powell, R. B., and Brown, E. R. (2004), “Construction of the 2003 NCAT Pavement Test Track,” National Center for Asphalt Technology, Draft Report. Priest, A. L., and Timm, D. H.
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von Karman, T., and Biot, M. A. (1940), Mathematical Methods in Engineering: An Introduction to the Mathematical Treatment of Engineering Problems, McGraw-Hill Inc., New York, p. 505. Weiler, W. A., and Kulhawy, F. H. (1982), “Factors Affecting Stress Cell Measurements in Soil,” ASCE Journal of the Geotechnical and Foundation Division, Vol. 108 (GT12), pp. 1529-1548. White, T. D., Albers, J. M., and Haddock, J. E.
APPENDICES (DVD UPON REQUEST) ‘Appendix_A’, ‘Appendix_B’ and ‘Appendix_C’ are available on a DVD from the JTRP Office upon request by e-mail jtrp@ecn.purdue.edu or call 765-494-9310. Each folder contains the associated appendix material. A short description of each is hereafter provided. APPENDIX A: RAW EXPERIMENTAL DATA The ‘Appendix_A’ folder on the DVD contains the raw experimental data collected during this entire study.
(iii) A33_FWD; (iv) A34_Reports&Presentations; (v) A35_HMA; (vi) A36_Resilient Modulus; (vii) A37_Response&Performance; (viii) A38_Spray Applications; and (ix) A39_Design&Spec. APPENDIX B: COMPUTER PROGRAMS The ‘Appendix_B’ folder on the DVD contains two structural analysis programs developed under this study: (i) ‘ELLEA1’ which is based on isotropic LET (see Chapter 4); and (ii) ‘ELLEA2’ which is based on anisotropic LET (see Chapter 5).
and Pellinen, November 2004); (viii) C8_Dynamic Modulus Testing of NCAT Mixes (Barde and Cardone, December 2004); (ix) C9_Interim Draft Final Report (Llenín and Pellinen, December 2004); (x) C10_APT Instrumentation and Loading Experiments (Pellinen and Webster, January 2005); (xi) C11_Preparation of Beams for SPR-2813 (Pellinen, Webster and Brower, February 2005); (xii) C12_Advanced Analysis of Beam Fatigue Test Results of NCAT mixes (Agrawal, August 2005); (xiii) C13_Laboratory Fatige Testing of HMA (Webst
