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Publication Number:  FHWA-HRT-15-063     Date:  March 2017
Publication Number: FHWA-HRT-15-063
Date: March 2017


Enhanced Analysis of Falling Weight Deflectometer Data for Use With Mechanistic-Empirical Flexible Pavement Design and Analysis and Recommendations for Improvements to Falling Weight Deflectometers



LTPP Data Analysis

A detailed sensitivity analysis on a relatively large sample of FWD test results from the LTPP database was conducted to determine the following: (1) prevalence of dynamics, (2) how prevalence of nonlinear behavior, and (3) measurement issues based on apparently erroneous deflection sensor time histories. The data covered all climatic zones, seasons, and temperature ranges. It was observed that dynamics were present in about 65 percent of the cases, while nonlinearity could be prevalent in a range from as low as 24 percent of the cases to as high as 65 percent of the cases, depending on severity level and sensor location. Nonlinearity was more prevalent for the sensors that were far from the center of the load. Because of the prevalence of dynamic behavior (in the form of free vibrations of deflection sensor time histories) observed in the large sample of LTPP FWD test data, it was hypothesized that in the great majority of the cases, the stiff layer condition might not correspond to the presence of shallow bedrock. Such bedrock would be highly unlikely given that it typically lies at much greater depths. Instead, the stiff layer condition could manifest anytime the soils below the subgrade layer are stiffer than the subgrade layer itself. This could be caused by increased confinement with depth, overconsolidation, or existence of shallow groundwater table for example; these situations are very common in any soil profile. This would explain the high percentage of sections from the LTPP database that showed dynamic behavior.

Viscoelastic Approach

As part of this effort, two multilayered viscoelastic algorithms were developed. The first algorithm (called LAVA/LAVAP) assumes the AC layer as a linear viscoelastic material and unbound layers as linear elastic. The second algorithm (called LAVAN) also assumes the AC layer as a linear viscoelastic material; however, it can consider the nonlinear (stress-dependent) elastic moduli of the unbound layers. These two models were used to develop two GA-based backcalculation algorithms (called BACKLAVA/BACKLAVAP and BACKLAVAN) for determining the E(t) or |E*| master curve of AC layers and unbound material properties of in‑service pavements.

The research team drew the following conclusions:

Dynamic Viscoelastic Approach

A new solution and its associated computer program were developed for dynamic viscoelastic time-domain backcalculation of multilayered flexible pavement parameters under FWD tests in the time domain. The method uses a time-domain viscoelastic solution as a forward routine (ViscoWave-II) and a hybrid routine (DYNABACK-VE: GA and modified LM method) for backcalculation analysis. For the GA-based backcalculation procedure, the research team recommends using DYNABACK-VE with a population size of 300 and a number of generations of 15. The advantage of the new solution is that it can analyze the response of pavement systems in the time domain and can therefore accommodate time-dependent layer properties and incorporate wave propagation. Also, because the backcalculation is performed in the time domain, the algorithm is not sensitive to truncation in the deflection time histories. The new algorithm is capable of backcalculating layer moduli, including the master curve of the AC layer at every reduced time and the depth to the stiff layer and its modulus value, if it exists. The results using simulated deflection time histories and field FWD data show excellent stability and accuracy.

The sensitivity of dynamic backcalculation solutions to signal noise and synchronization problems is high. The remedy to noise is to preprocess the raw data by filtering out the high-frequency content of the signal (anything above 100 Hz) in deflection and load pulse data. Also, in the analysis presented in chapter 5, the percent error between the computed and measured displacement was used as the minimizing error. If percent error were used as the minimizing objective, it could lead to overemphasis of lower magnitudes of deflections at the later portion of the time history, which typically includes noise and integration errors. Hence another fit function was proposed in which the percent error was calculated with respect to the peak of deflection at each sensor. This de-emphasized the tail data by normalizing them with respect to the peak.

If synchronization problems occur, the dynamic backcalculation algorithm may not work as well, although one could shift the signals similar to what was done in the quasi-static viscoelastic solution (chapter 4). Because the quasi-static solution presented in chapter 4 is already coded to remove the time delay between sensors, the research team recommends the use of BACKLAVA instead of DYNABACK-VE when such a synchronization problem exists.

The results from dynamic analyses clearly showed the superiority of a fully dynamic solution with a viscoelastic AC layer modulus in predicting deflection responses that are in line with the physical reality, as evidenced by the close match in the details of the deflection time histories between theory and observation. The theoretical predictions from ViscoWave-II showed very good agreement with the measured deflection time histories. The fact that theory and measurement showed the same behavior with time was proof that these observations were physically real. This is important in that it reinforces the following: (1) a comprehensive model that takes into account viscoelasticity of the AC layer, damping in the unbound layers and dynamics in terms of inertial and wave propagation effects can explain the measured data with all their complexities; and (2 )the FWD sensor measurements, if properly calibrated, can show the physical behavior for most of the time range, with the exception of the drift problems at the tail of the records.

In contrast, the layered viscoelastic solution cannot simulate the true deflection time histories because it cannot account for inertial and wave propagation effects. As such, it cannot predict the time delays in the response, the initial rebounds of the farther sensors and the free vibrations after the load is applied. Also, the layered viscoelastic solution significantly underestimates the deflections when a stiff layer is presented. This is because it cannot account for dynamic amplification caused by the wave energy trapped in the unbound layers when a stiff layer condition exists.

Practical Implications and Recommendations

The research team makes the following recommendations regarding FWD data collection, based on both viscoelastic and dynamic analyses conducted in this study:

FWD Equipment Analysis

A set of experimental procedures, conducted both in the laboratory and in the field, were performed using seismometers, geophones, and accelerometers. The experiments were designed to evaluate the performance of the sensors in term of accuracy and sensitivity, with the objective of including the effects of these parameters in the tools studied in earlier chapters of this report.

Based on the observations, the following issues were discussed:

In addition, a study was presented to illustrate the effects of numerical integrations and drifts, confirming their significant influence on the output results.

For all the tests presented, a high-precision laser system was used in the experimental setups as a reference system and also to evaluate limitations on potential recommendation of its use in FWD systems. Even though the laser system performed flawlessly under laboratory conditions and was successfully used as a reference for characterizing the other devices, it was much more difficult to use it in the field. Given the high accuracy of the laser, even small vibrations were picked up in the signal. Therefore, field measurements from the laser also had to be filtered and adjusted. The advantages of using a laser were mainly that it eliminated all the undesirable effects from numerical artifacts because it directly measured the deflection. This is similar to seismometers but with the added advantage that it was a noncontact method so there were no seating errors. The main disadvantage was that lasers still need a fixed reference in the system to extract the true pavement’s surface motion. This could be achieved by either disconnecting the rigid bar that holds the sensors from the FWD machine frame, thus isolating the frame from the vibration noise, or by placing an external reference mechanism away from the influence of the deflection basin induced by the load drop. The external reference could be position sensors that track the movement of the beam holding the sensors. This was previously done using accelerometers but would not solve the problem because it would require a double integration for the accelerometer data.

Geophones have the advantage of not requiring an added reference, but it was shown in studies reported in chapter 6 that data were relatively less reliable post-peak. Geophones are based on the inertia of a suspended mass, which means that they have performance issues at low frequencies. Furthermore, the requirement for a numerical integration induces several numerical artifacts such as errors in post-peak amplitude and drifts.

The issue with time synchronization between the load and the measurements output was an easy technological fix. The focus of existing FWD systems has been to determine the response peaks, which are not affected by the synchronization problem. This becomes important when the whole time response is of interest. This issue could be resolved by adding a position sensor that records the exact position of the dropping mass. The position sensor should be connected to the same data acquisition system as all the sensors so that it uses the same timer.


The tools developed in this project are standalone applications that could be used on most computers. The following four time-domain backcalculation software products were developed:

All these tools are engineering software applications that allow the user to backcalculate the master curve of the AC layer (four sigmoidal coefficients and two time-temperature shift factors) and the resilient moduli for the unbound base/subbase and subgrade materials. DYNABACK-VE could also backcalculate the modulus of the stiff layer and the depth to the stiff layer, if one is present.

With good seed values for the moduli (e.g., previous information about the moduli), one could also implement a simple gradient-based method along with LAVA, LAVAP, LAVAN, and ViscoWave-II as forward routines. If the measured deflections are reasonably free from errors, a simple RMS objective function can be selected; otherwise, it is better to first apply any remedies as discussed in chapter 2, (subsection Review of Status of FWD Data Collection, Analysis, and Interpretation) before running the program.

Owing to the searching method used, DYNABACK-VE could take more time to run compared with current backcalculation programs. Thus, continued study is needed on reducing the runtime of the program. For example, the current version of DYNABACK-VE takes approximately the following times on various computers:

These translate to backcalculation runs of approximately the following times and costs:

As shown in this study, the influence of the parameters in the GA (size of population, number of generations, mutation rate, etc.) on the backcalculation procedure is significant, which could be an interesting topic for future study. Recently, a variety of optimization techniques have been developed with several advantages and disadvantages. A comparative study of these techniques could help better understand the moduli optimization and improve the backcalculation method. In addition, while the approach in this effort has assumed the layer thickness is known, DYNABACK-VE could be extended in the future to reliably backcalculate layer thicknesses as well. Also, the current DYNABACK-VE program assumes linear elastic pavement layers. The nonlinearity of unbound layers should be considered in the backcalculation procedure, especially under high surface loads. The algorithm could also be improved to consider the thermal effect in future versions.




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