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I-1 APPENDIX I. ANALYSIS METHODOLOGIES OF LARGE-SCALE TANK TEST DATA The laboratory testing program for flexible and rigid pavements included a series of instrumentation that included accelerometers, LVDTs, earth pressure cells, and strain gauges. The instrumentation program was designed to assess several aspects of the influence of the base reinforcement on pavement responses under a variety of realistic pavement loading conditions. A database of pertinent pavement responses with and without reinforcement collected under dynamic and static pavement loading conditions was assembled. The pavement response database was used to assess the validity and applicability of the finite element numerical modeling of reinforced pavement structures. In particular, the instrumentation plan focused on the mechanisms associated with the interaction between the geosynthetic and the unbound materials, including (a) assessment of the deflection profile of the geosynthetic; (b) investigation of the slippage at the interface between the unbound material and the geosynthetic; (c) review of the stress transfer across the geosynthetic; and (d) examination of the load-induced strains in the geosynthetic. While the last two aspects could be addressed based on direct measurements from pressure cells (vertical and horizontal) and strain gauges, the first two aspects needed to be evaluated based on the deflections at many interior locations within the pavement. The slippage investigation at the interface required measurements for the deflections in the geosynthetic and in the adjacent unbound material to examine the relative movements between the two of them. The role of the geosynthetic affecting the load transfer across the geosynthetic itself is generally referred to as shell/membrane action. Understanding the deformed shape of the geogrid or geotextile located within the unbound pavement layers during the application of the pulse loading is important to evaluate the shell/membrane action of the reinforced layer. The dynamic (instantaneous) deformation of the geosynthetic can be related to the change in vertical stress that can occur across the reinforced crushed aggregate base layer. Accordingly, high-gain accelerometers were used, with the recording measurements being twice integrated to get the displacement under dynamic loading. It was important to find the best methodology for the double integration of accelerometer readings to get the displacement. Subsequently, these displacements obtained from the integration could be used to assess the shell/membrane action of the embedded geogrid or geotextile. Establishment of the Double-Integration Process Many attempts to perform double integration of measured acceleration have been proposed by researchers, and they generally consist of (a) use of various types of filters, and (b) adoption of various baseline correction schemes. Though substantial research has been done to validate the applicability of integration procedures by seismologists and others, almost all of those efforts have focused on earthquake-induced acceleration histories. The earthquake acceleration histories have the bulk of the energy in the 0.02 to 30 Hz range. Unlike the acceleration histories recorded under seismic loading, the histories resulting from impact-type loading used in the LST program have a much wider frequency spectrum that is rich, especially in the higher frequency range (50 to 70 Hz). Without any correction, double integration clearly shows a noticeable drift with significantly large displacements that steadily increase even after the cessation of the load pulse. Many options are available with the integration procedures. For
I-2 example, features such as the use of low/high pass filters, baseline correction, and zero-th order correction significantly affect the results of the integration. The suitability of various options of the integration procedure for use with impact-type loading should be verified. Hence, it was important that a comparison between measured and double-integrated accelerograms be undertaken as part of this study to verify the applicability of any integration scheme being proposed. Accordingly, the deflections (LVDT measurements) and corresponding acceleration histories at three points on the pavement surface were measured during the laboratory testing program and were used for this purpose. The calibration of the integration scheme was based on the comparison between the measured LVDT surface deflection responses and those computed from the double integration. A recently proposed FWD calibration method (use of only the acceleration history after the initiation of the pulse) gives an appropriate result for the maximum displacement, but the displacement history has a drift with time after the cessation of the pulse. The FWD approach can be seen as reasonable because the FWD requires only the maximum FWD displacement at the sensor locations rather than the complete displacement histories. The initial phase of the laboratory testing program involved a pilot study in which many analyses with various integration schemes that involved many combinations of different correction procedures were examined. An overview of the attempts is presented here. High-gain accelerometers with maximum possible sampling rates (16 kHz) along with LVDTs were used to calibrate the suitability of various integration options. Figure I-1 shows the location of the sensors (LVDTs and accelerometers), and Figure I-2 shows the vertical acceleration measurements for the 49th to 55th loading cycles from all three accelerometers identified in Figure I-1. Figure I-3 shows the measured vertical displacements for the same loading cycles. The tests were conducted with the large-scale tank containing only the subgrade layer because the focus was on the double integration of acceleration records measured in the unbound layers. The accelerometers were located at 6 inches below the surface so that they were completely surrounded by the subgrade material, with the recordings representing the subgrade motions. Sample plots of measured acceleration (ACC 1) and displacement (DIS 1) histories are shown in Figure I-4 and Figure I-5, respectively. The presence of higher frequencies in the acceleration histories as a result of the impact-type loading mixed with high-frequency noise can significantly affect the integration results. Without any correction, the double integration shows significant drifts that are large, as shown in Figure I-6. The Fourier transform of the measured acceleration data for ACC1 is shown in Figure I-7. The Fourier amplitudes up to about 60 Hz are stronger, possibly indicating the dominant frequency range attributable to the applied load pulse. After 60 Hz, the amplitudes are not as strong, and the signals above 60 Hz may be due to noise. It is apparent that many options that are available with integration of earthquake-induced acceleration histories may not work for the impulsive-type of loading under consideration.
I-3 Figure I-1. Schematic of the pilot experimental study to calibrate the integration scheme Figure I-2. Vertical acceleration measurements from pilot experimental study (loading cycles 49 to 55) -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 49 50 51 52 53 54 55 Ac ce ler at io n (g ) Time (seconds) ACC 1 ACC 2 ACC 3 Large-Scale Tank Subgrade Loading Plate Hydraulic Ram
I-4 Figure I-3. Vertical LVDT measurements from pilot experimental study (loading cycles 49 to 55) Figure I-4. Measured acceleration history from pilot experimental study (ACC 1) -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 49 50 51 52 53 54 55 Di sp lac em en t ( in ch ) Time (seconds) DIS 1 DIS 2 DIS 3 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 0 0.2 0.4 0.6 0.8 1 Ac ce ler at io n (g ) Time (seconds)
I-5 Figure I-5. Measured displacement history from pilot experimental study (DIS 1) Figure I-6. Calculated displacement from the double integration of ACC 1 history without any corrections -0.02 0 0.02 0.04 0.06 0.08 0.1 0 0.2 0.4 0.6 0.8 1 Di sp lac em en t ( in ch ) Time (seconds) -0.05 0 0.05 0.1 0.15 0.2 0.25 0.3 0 0.2 0.4 0.6 0.8 1 Di sp lac em en t ( in ch ) Time (seconds)
I-6 Figure I-7. Fourier transform of ACC 1 recording measurements An attempt at integration with baseline correction (cubic polynomial) only without any filtering is compared with the measured displacement in Figure I-8. Though the shape of the pulse is captured well, the computed displacements prior to and after the cessation of the impact show noticeable negative values (upward movement). The origin of this occurrence can be traced to noise that is present in the accelerometer readings prior to the start and after the end of the displacement pulse. Another source for this may be the consequence of the use of the baseline correction routine. Figure I-9 shows the comparison of the measured and computed maximum pulse displacement for 18 recordings with this approach. Figure I-8. Comparison between measured and computed (with baseline correction) displacement histories (DIS 1 and ACC 1) -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 0 0.2 0.4 0.6 0.8 1 Di sp lac em en t ( in ch ) Time (seconds) Measured Displacenent (DIS 1) Computed Displacement with Baseline Correction
I-7 Figure I-9. Comparison between measured and computed maximum displacements for 18 recording measurements with baseline correction Use of only the acceleration history after the initiation of the pulse as recommended by Irwin et al. (1) for integration of accelerations measured under FWD testing was another attempt to get reasonable displacement. In this approach, pulse initiation was correctly captured and the maximum pulse displacement was predicted well (within 5 percent). However, the displacement history still increased with time after the cessation of the pulse (see Figure I-10). This approach may be seen as reasonable for FWD testing because FWD requires only the maximum displacement at the sensor locations rather than the complete displacement histories. Figure I-11 shows the comparison of measured and computed maximum pulse displacements, and it is clear this procedure gives better results than the previous approach. It has been found that a very effective way to get a reasonable displacement time history as well as maximum displacement is the correction of the acceleration history before double integration by subtracting the mean value from the entire acceleration record. This is known as the zero-th order correction. Figure I-12 shows the displacement history obtained using this approach. Figure I-13 shows a good agreement between the directly measured and the computed maximum displacements from the double integration for 18 data records. As another attempt, only a portion of the data was considered by eliminating data at the start and at the end (for noise elimination), and then subtracting the mean acceleration value of the selected data range. This effort produced very good results. Figure I-14 shows the comparison of the measured displacement and computed displacement with this approach. As the figure shows, data between 0.3 second and 0.9 second (0.6 second time period) were considered. It is clear that this approach eliminates noise before strike (no displacement before pulse initiation) and provides good agreement with the measured displacement after the maximum displacement. This procedure seemed to match the entire measured displacement history well. However, it should be noted that the selection of the data range for integration was somewhat arbitrary. Therefore, it was recommended that a calibration of the integration scheme be y = 1.2036x R² = 0.9873 0 0.02 0.04 0.06 0.08 0.1 0 0.02 0.04 0.06 0.08 0.1 Me as ur ed M ax im um D isp lac em en t ( in ch ) Computed Maximum Displacement (inch)
I-8 undertaken between measured and integrated displacements to verify the appropriateness of the integration scheme. Figure I-10. Comparison between measured and computed displacement histories using FWD correction procedure (ignoring acceleration history before pulse initiation) Figure I-11. Comparison between measured and computed maximum displacements for 18 recording measurements with FWD correction procedure -0.02 0 0.02 0.04 0.06 0.08 0.1 0.12 0 0.2 0.4 0.6 0.8 1 Di sp lac em en t ( in ch ) Time (seconds) FWD Correction Procedure Measured Displacement Max. FWD Procedure Displacement = 0.0934 inch Max. Measured Displacement = 0.0884 inch y = 0.9794x R² = 0.9893 0 0.02 0.04 0.06 0.08 0.1 0 0.02 0.04 0.06 0.08 0.1 Me as ur ed M ax im um D isp lac em en t ( in ch ) Computed Maximum Displacement (inch)
I-9 Figure I-12. Measured and double-integrated displacement history with zero-th order correction Figure I-13. Comparison between measured and computed maximum displacements for 18 recording measurements with zero-th order correction -0.02 0 0.02 0.04 0.06 0.08 0.1 0 0.2 0.4 0.6 0.8 1 Di sp lac em en t ( in ch ) Time (seconds) Max. Computed Displacement = 0.0879 inch Max. Measured Displacement = 0.0884 inch Measured Displacement Computed Displacement y = 0.9886x R² = 0.98 0 0.02 0.04 0.06 0.08 0.1 0 0.02 0.04 0.06 0.08 0.1 Co m pu te d Ma xim um D isp lac em en t ( in ch ) Measured Maximum Displacment (inch)
I-10 Figure I-14. Measured and double-integrated displacement histories for a sampling frequency of 16,666 Hz with selected time history interval (0.3 to 0.9 second) and zero-th correction The pilot testing recorded only the surface responses, and therefore a much larger sampling rate was feasible (f = 16,666 Hz and Ît = 0.00006 sec) with the data acquisition system used in the laboratory testing program. However, in the subsequent experiments involving many more channels of recording, only a smaller sampling rate was possible. For finding the minimum sampling rate with a good agreement with the maximum measured displacement and entire displacement history, several analyses of double integration were completed by increasing the time interval of the measurements (i.e., skipping intermediate data). Table I-1 summarizes the results for the comparison of maximum displacements with various sampling frequencies. The original sampling frequency was 16,666 Hz, and the data show that the frequency of 2083 Hz can give very reasonable results (within 2 percent of the measured displacement at 16,666 Hz). Figure I-15 shows that the displacement history is also acceptable at this sampling frequency. Although the results for maximum displacement seemed to be good with 833 Hz, the displacement history was not appropriate (Figure I-16). 0 0.02 0.04 0.06 0.08 0.1 0 0.2 0.4 0.6 Di sp lac em en t ( in ch ) Time (seconds)
I-11 Table I-1. Comparison of Double-Integrated Displacement Results with Various Sampling Frequencies Time Spacing (sec) Frequency Max Measured Displacement (mi) Max Computed Displacement (mi) % Difference with Measured Displacement % Difference with Original Spacing 0.00006* 16,666* 88.40 89.81 1.58 0.00 0.00012 8,333 89.85 1.63 0.05 0.00018 5,555 89.93 1.73 0.14 0.00024 4,166 89.88 1.67 0.08 0.00030 3,333 90.15 1.97 0.38 0.00036 2,777 90.02 1.83 0.24 0.00042 2,380 90.06 1.87 0.28 0.00048 2,083 90.01 1.81 0.22 0.00054 1,851 90.83 2.74 1.14 0.00060 1,666 89.91 1.71 0.12 0.00120 833 89.82 1.60 0.02 0.00180 555 93.10 5.31 3.66 0.00240 416 86.96 1.63 3.17 0.00360 277 113.30 28.16 26.16 * Original spacing and frequency.
I-12 Figure I-15. Measured and double-integrated displacement histories for a sampling frequency of 2083 Hz with selected time history interval (0.3 to 0.9 second) and zero-th correction Figure I-16. Measured and double-integrated displacement histories for a sampling frequency of 833 Hz with selected time history interval (0.3 to 0.9 second) and zero-th correction Another issue is the presence of noise in the signal. It should be noted that while the signal-to-noise ratio is higher near the loaded area, the ratio is much lower at locations farther away on the surface and interior locations. Sources of noise are many, and they include background noise (e.g., heater/AC) and vibrations trapped within the large-scale tank from previous load pulses. As a first step, an effort to characterize the noise was attempted. This entailed scrutinizing the measured acceleration data before and after each pulse and also the 0 0.02 0.04 0.06 0.08 0.1 0 0.2 0.4 0.6 Di sp lac em en t ( in ch ) Time (seconds) Computed Displacement Measured Displacement 0 0.02 0.04 0.06 0.08 0.1 0 0.2 0.4 0.6 Di sp lac em en t ( in ) Time (seconds) Computed Disp. Computed Displacement Measured Displacement
I-13 measurements after the completion of the entire dynamic loading. However, this was not successful, mainly because it turned out that the noise was truly random. Noise is often associated with high-frequency signals, and therefore the elimination of such waves resulted in a better representation of the true signal. One of the correction schemes used in the past by researchers is band filters (band-pass or band-stop) in which certain frequencies of the excitation can be suppressed. Such suppressed frequencies are considered to be from noise. A proven method to get rid of noise is the use of low pass filters that eliminate the high-frequency signal. A range of low pass filters with cut-off (low pass filter) values of 55, 60, and 65 Hz were considered. Accordingly, the double integration consisted of first applying the filter followed by the zero-th order and baseline corrections. By comparing maximum displacement values and their times of occurrence under all load levels, it was found that using the 60 Hz filter produced the most consistent and closely comparable surface displacement predictions with those directly measured by the LVDTs. Table I-2 summarizes the results for the computed displacements when using different filters. Table I-2. Typical Results When Using Low Pass Filter with Different Cut-Off Frequencies Item Values Time at Max. Disp. (sec) Cut-off Frequency = 55 Hz Max. Measured DisplacementâLVDT (mi) 24.06 86.906 Max. Displacement from Integration (mi) 23.43 86.910 Difference (mi) -0.63 0.004 Error (%) -2.6 Cut-off Frequency = 60 Hz Max. Measured DisplacementâLVDT (mi) 24.13 86.906 Max. Displacement from Integration (mi) 23.43 86.909 Difference (mi) -0.71 0.003 Error (%) -2.9% Cut-off Frequency = 65 Hz Max. Measured DisplacementâLVDT (mi) 24.21 86.906 Max. Displacement from Integration (mi) 23.43 86.909 Difference (mi) -0.79 0.003 Error (%) -3.3%
I-14 Based on the attempts to perform double integration of the accelerometer measurements described above, the following iterative procedure was adopted for integration in this study: ⢠Step 1: From the entire plot of measured vertical acceleration response at the loading plate (referred to as A1 subsequently), select as many as seven consecutive cycles that look similar beyond 50 cycles of loading. The 50th loading cycle limit was chosen to allow the materials in the large-scale tank enough time to fully stabilize under the repeated loading. ⢠Step 2: Obtain the Fourier transform of the measured vertical acceleration response (A1) for one of the loading cycles (say 50th cycle) and determine the relative strength of signals and select a cut-off frequency (low pass filter) above which the noise is assumed to be prevalent. ⢠Step 3: Select the start and end of the time history interval for analysis. Consider the start time as 0.1 second before the measured peak vertical displacement from the LVDT (referred to as L1 subsequently) and the end time as 0.4 second after the peak. ⢠Step 4: Perform zero-th order and baseline corrections (cubic polynomial) and obtain the corrected acceleration history for double integration. ⢠Step 5: Compare the double-integrated (computed) corrected acceleration history with the measured vertical displacement. ⢠Step 6: If the comparison in Step 5 is not acceptable for the entire displacement history, repeat Steps 2 to 5 with another selection of a loading cycle until an acceptable match between displacements is obtained. ⢠Step 7: Repeat Steps 1 to 6 for the surface accelerometers that are located away from the loaded plate. Illustration of Established Procedure For better clarification, the steps associated with the proposed iterative procedure are exemplified below using, as an example, data from the large-scale tank Experiment No. 2 (flexible pavement with crushed aggregate base thickness of 10 inches; dynamic load of 9 kip), which is seen as a representative case. Acceleration (A1 to A3) and LVDT (L1 to L3) measurements were made on top of the asphalt concrete layer at three locations, as shown in Figure I-17. The readings from these sensors provided the important basis for the selection of the integration method to be used.
I-15 Figure I-17. Instrumentation plan for large-scale tank Experiment No. 2 Figure I-18 shows the 50th to the 56th pulse cycles (seven cycles) for the recorded acceleration response of A1 (Step 1). The response of the 50th cycle (or pulse) was extracted from this plot and is shown in Figure I-19. The Fourier transform was then applied to the appropriate cut-off frequency (Step 2). After using the low pass filter, the start and end times of the acceleration response history were estimated to be 56.935 and 57.435 seconds, respectively, based on the LVDT time history of L1 (Step 3). Figure I-19 shows this selected window of the history. Step 4 involved zero-th order and baseline correction. In Step 5, the comparison between the measured and computed displacements was made (see Figure I-20). A close match between the measured and computed displacement histories was observed. However, if the match had been deemed not acceptable, Steps 2 to 5 would have been repeated with a different loading cycle. This iterative procedure revealed that the 53rd pulse produced the best overall match between the computed and measured displacements for all three surface locations (A1 and L1; A2 and L2; A3 and L3). The comparisons of the displacements for the 53rd load pulse are shown in Figure I-21 to Figure I-23. The steps were repeated for other load levels of 12 and 16 kip. The overall comparisons of the maximum displacements for all thee surface locations and load levels are presented in Figure I-24 to Figure I-26. When displacements are higher (i.e., A1/L1 location), the comparison is very good, with the computed displacement being underpredicted by less than 3.6 percent. At the further location (i.e., A3/L3 location) where the displacements are the lowest, there is an overprediction by the computed values overall by as much as 10 percent. These deviations are not considered to be large and are within the range of expected deviations. It was also noted that while the signal-to-noise ratio was higher near the loaded area, this ratio was much lower at locations farther away on the surface and interior locations. Once a good
I-16 match was found between the computed (i.e., double-integrated acceleration) and the LVDT measurements at a surface location, the integration procedure was used for the accelerometers located directly below that location. Experiments with either a geogrid or geotextile had the respective data processed in the same fashion. Figure I-18. Measured acceleration history for loading cycles 50 to 56 (Experiment No. 2, pulse load of 9 kip, A1) Figure I-19. Measured acceleration history for 50th loading cycle (Experiment No. 2, pulse load of 9 kip, A1)
I-17 Figure I-20. Comparison between measured (L1) and computed (A1) displacements for 50th loading cycle (Experiment No. 2, pulse load of 9 kip) Figure I-21. Comparison between measured (L1) and computed (A1) displacements for 53rd loading cycle (Experiment No. 2, pulse load of 9 kip) -0.005 0 0.005 0.01 0.015 0.02 0.025 0.03 86.7 86.8 86.9 87 87.1 87.2 87.3 Di sp lac em en t ( in ch ) Time (seconds) Dynamic-9kip-A1-L1-50th loading pulse Measured Disp. from Novotek Computed Disp. from Acc Max. Measured = 0.0246 inch Max. Computed = 0.024 inch -0.005 0 0.005 0.01 0.015 0.02 0.025 0.03 89.7 89.8 89.9 90 90.1 90.2 90.3 Di sp lac em en t ( in ch ) Time (second) Dynamic-9kip-A1-L1-53rd pulse Measured Disp. from Novotek Computed Disp. from ACC Max. Measured = 0.025 inch Max. Computed = 0.0246 inch
I-18 Figure I-22. Comparison between measured (L2) and computed (A2) displacements for 53rd loading cycle (Experiment No. 2, pulse load of 9 kip) Figure I-23. Comparison between measured (L3) and computed (A3) displacements for 53rd loading cycle (Experiment No. 2, pulse load of 9 kip) -0.005 0 0.005 0.01 0.015 0.02 0.025 0.03 89.7 89.8 89.9 90 90.1 90.2 90.3 Di sp lac em en t ( in ch ) Time (seconds) Dynamic-9kip-A2-L2-53rd pulse Measured Disp. from Novotek Computed Disp. from ACC Max. Measured = 0.00945 inch Max. Computed = 0.00878 inch -0.005 0 0.005 0.01 0.015 0.02 0.025 0.03 89.7 89.8 89.9 90 90.1 90.2 90.3 Di sp lac em en t ( in ch ) Time (seconds) Dynamic-9kip-A3-L3-53rd pulse Measured Disp. from Novotek Computed Disp. from ACC Line Max. Measured = 0.0057 inch Max. Computed = 0.0052 inch
I-19 Figure I-24. Comparison between measured (L1) and computed (A1) maximum displacements for 53rd loading cycle and all load levels (Experiment No. 2) Figure I-25. Comparison between measured (L2) and computed (A2) maximum displacements for 53rd loading cycle and all load levels (Experiment No. 2) y = 1.0364x R² = 0.9757 0 0.01 0.02 0.03 0.04 0.05 0 0.01 0.02 0.03 0.04 0.05 Ma x. Me as ur ed D isp lac em en t-L 1 ( in ch ) Max. Computed Displacement-A1 (inch) 9 kip 12 kip 16 kip y = 1.0942x R² = 0.9545 0 0.01 0.02 0.03 0.04 0.05 0 0.01 0.02 0.03 0.04 0.05 Ma x. Me as ur ed D isp lac em en t-L 2 ( in ch ) Max Computed Displacement-A2 (inch) 9 kip 12 kip kip
I-20 Figure I-26. Comparison between measured (L3) and computed (A3) maximum displacements for 53rd loading cycle and all load levels (Experiment No. 2) References 1. Irwin, L.H., Orr, D.P., and Atkins, D. (2009). FWD Calibration Center and Operational Improvements: Redevelopment of the Calibration Protocol and Equipment. Final Report FHWA-HRT-07-040, FHWA, Washington D.C., 268p. y = 0.9035x R² = 0.6133 0 0.01 0.02 0.03 0.04 0.05 0 0.01 0.02 0.03 0.04 0.05 Ma x. Me as ur ed D isp lac em en t-L 3 ( in ch ) Max Computed Displacement-A3 (inch)
