The objective of this case study is to highlight the benefits of employing nonlinear dynamic backcalculation over the conventional linear elastic static backcalculation, currently prevalent in the industry, for the evaluation of pavement properties. The focus is on a traditional flexible pavement structure (LTPP section 46-0804) located on State Route 1804 in Walworth County, South Dakota, USA. The case study aims to demonstrate how nonlinear dynamic backcalculation, when applied to Falling Weight Deflectometer (FWD) data, provides a more insightful assessment of pavement properties and performance.

roadway insights

This section was part of the Long-Term Pavement Performance (LTPP) experiment, designed to evaluate the environmental effects without heavy loads. It opened to traffic in 1993, measuring 500-ft (152.4 m) in length and 12-ft (3.5 m) in width. Positioned in the southbound lane of a two-lane undivided roadway at an elevation of 1,680-ft (510 m), it falls in a dry freeze climatic zone with an annual precipitation of 17.6-inch (45 cm), a freezing index of 1,730°F-days (960°C-days), and an annual temperature of 45°F (7°C). The roadway is classified as a rural major collector, with an AADT of 100 and an AADTT of 7.

The pavement structure comprises a 7.1-inch (18 cm) asphalt concrete layer and a 12-inch (30 cm) unbound granular base layer over an untreated silty clayey subgrade.

FWD testing

The section underwent extensive FWD testing from 1993 to 2014, totaling 53 days. In some instances, testing was repeated multiple times within a day for selected locations. The testing was conducted at 25-ft (7.5 m) intervals, both in the middle of the lane and the outer wheelpath. 

For this case study, data from the testing in the middle of the lane at station 4+00 (0+121.9) over two dates was analyzed. These two dates correspond to the asphalt concrete layer being at its warmest and coldest states, while the unbound base and subgrade layers are unfrozen and have similar moisture contents. The selection was made to solely focus on the temperature effects on the flexible pavement behavior. 

In 1994, FWD testing was performed over eight days: June 8, July 14, July 15, August 12, September 27, October 25, November 22, and December 20. Notably, on July 15, 1994, testing was repeated four times during the day for selected stations at 8 AM, 10 AM, 12 PM, and 2 PM. The 2 PM testing coincided with the period of the highest asphalt concrete temperature among all the tests conducted in 1994. Additionally, the testing on October 25 at 11 AM coincided with the period of the lowest asphalt concrete temperature before the freezing initiation that started in November. Therefore, the data from July 15 and the morning of October 25 are analyzed in this case study.

The FWD was configured with seven deflection sensors placed at 0, 8, 12, 18, 24, 36, and 60-inch (0, 20, 30, 45, 60, 90, and 150 cm) offsets from the center of the load. The drop sequence protocol involved three seating drops from drop height 3, followed by four repeated measurements at each of drop heights 1, 2, 3, and 4. The complete load-deflection time histories were recorded for the final drop at each designated drop height.

The normalized deflections at 16 kips (70 kN) corresponding to the highest drop are graphically presented for selected sensors for the July 15 and the morning of October 25, 1994 testing, along with the asphalt concrete temperatures. Notably, the center deflections exhibit substantial variation in response to changes in temperature as anticipated.

nonlinear dynamic backcalculation for July 15, 1994

Nonlinear dynamic backcalculation was performed using nbak for the flexible pavement, treating it as a three-layer system. The asphalt concrete layer was modeled as linear viscoelastic, while the unbound base and subgrade layers were treated as nonlinear using the Uzan 1985 model. This model accounts for moduli variations utilizing bulk stress and octahedral shear stress. Poisson’s ratios and densities were obtained from the LTPP database or assumed as necessary. Rayleigh damping coefficients were applied to simulate damping effects for the unbound layers.

Load-deflection time histories were employed in the backcalculation process for the 6, 9, 12, and 16 kips (25, 40, 55, and 70 kN) load levels. Multiple load levels are simultaneously employed to capture the nonlinearity of unbound materials.

The backcalculation was executed for the July 15 date across the four testing times to determine the pavement layer properties and asphalt concrete temperature sensitivity. The quadratic polynomial time-temperature superposition model was employed to address the variation in asphalt concrete temperatures. The four FWD test points, corresponding to various testing times, were employed in the backcalculation utilizing common variables. The use of common variables ensures that each property for every layer remains identical between the test points.

The moduli of the asphalt concrete layer consistently decreased with rising temperatures, falling from 405 ksi (2,800 MPa) at 8 AM to 115 ksi (800 MPa) at 2 PM. These moduli are reported at a frequency of 17 Hz, identified as the FWD’s most dominant frequency. In contrast, the moduli of the base and subgrade layers remained relatively stable, fluctuating between 29.0 and 29.2 ksi (200 and 201 MPa) for the base layer and 12.8 and 13.0 ksi (88 and 90 MPa) for the subgrade layer.

Both the base and subgrade layers were modeled as nonlinear. Consequently, the moduli are expected to vary among different finite elements based on (1) their positions within each layer, (2) the FWD load amplitude, and (3) the FWD load level or drop height. Average layer moduli are presented herein under peak load conditions over a 6-ft (1.8 m) wide area for the base layer, and a 6-ft (1.8 m) wide and 6-ft (1.8 m) deep area, referred to as the influence zone, for the upper portion of the subgrade layer.

subgrade triaxial laboratory testing

In September 1992, subgrade materials were sampled at stations 2+50 (0+076.2) and 4+00 (0+121.9). Subsequent to the sampling, repeated load triaxial compression tests were conducted on both samples in 1997 and 1998 to determine the subgrade’s resilient moduli. Each specimen underwent testing with a combination of static confining pressures and dynamic cyclic stresses. The resilient (recoverable) axial deformation response was recorded for each combination, and the resilient moduli were then calculated.

The subgrade resilient moduli exhibited a range of 11.2 to 14.9 ksi (77 to 103 MPa) for both samples, with an average of 13.2 ksi (91 MPa). The backcalculated moduli for the subgrade layer during the two testing dates fell within the range of 12.8 to 13.4 ksi (88 to 92 MPa), as previously documented, perfectly aligning with the average subgrade moduli determined from laboratory testing.

The coherence of subgrade layer properties between laboratory testing and nonlinear dynamic backcalculation emphasizes the critical importance of employing advanced backcalculation and modeling techniques to assess the structural capacity of pavements.

comparison to static backcalculation

Static backcalculation, as implemented by LTPP, involved modeling the pavement layers as linear elastic, and the results are accessible through infopave.fhwa.dot.gov. The pavement structure was modeled as a four-layer system, with the subgrade layer divided into two sublayers: a 24-inch (60 cm) thick layer referred to as the upper subgrade layer and the semi-infinite subgrade layer beneath it. This approach is commonly employed in static backcalculation to enhance the fit and reduce the subgrade layer moduli.

The backcalculated moduli for the asphalt concrete layer exhibited consistent variations with temperature changes, decreasing from 365 ksi (2,500 MPa) at 8 AM to 115 ksi (800 MPa) at 2 PM on July 15 and then increasing to 1,800 ksi (12.4 GPa) on October 25. These moduli closely matched those determined through nonlinear dynamic backcalculation. In contrast, the moduli of the unbound layers displayed considerable variability and lacked clear distinctions between the layers, unlike the consistent outcomes observed in nonlinear dynamic backcalculation. The moduli of the upper subgrade layer were shown to be higher or almost equal to the base layer moduli in two instances, which is unrealistic. Additionally, the upper subgrade and subgrade layer moduli were higher than the laboratory-determined values by 70% and 20% on average, respectively. The upper subgrade and subgrade layers exhibited the most deviation from the laboratory-determined resilient moduli on October 25, with a 140% increase for the upper subgrade layer and a 40% increase for the subgrade layer.

The fit between the measured and calculated peak deflections in static backcalculation, assessed through RMSE calculations, ranged from 1.0% to 1.4%. While the obtained RMSE values are favorable, it is crucial to note that they alone should not be regarded as the sole indicator of the reliability of the backcalculated layer moduli, as suggested by the presented results.

It is noteworthy that alternative static backcalculation applications, capable of approximating the subgrade's nonlinearity, encounter comparable limitations in this particular instance.

In conclusion, the application of static backcalculation often yields unrealistic outcomes, compromising the reliability of performance predictions for both pavement design and pavement management system purposes.