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 specific Jointed Plain Concrete Pavement (JPCP) structure (LTPP section 31-3024) located on Interstate 80 in Hamilton County, Nebraska, 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.

highway insights

This rigid section, which opened to traffic in 1984, and became part of the Long-Term Pavement Performance (LTPP) experiment in 1987, is in the slow westbound lane of a four-lane divided highway with concrete shoulders at an elevation of 1,810-ft (550 m). It sits in a wet freeze climatic zone with an annual precipitation of 29.4-inch (75 cm), a freezing index of 755°F-days (420°C-days), and an annual temperature of 51°F (10.5°C). This highway is a rural principal arterial, handling an AADT of 8,520 and AADTT of 1,480.

The LTPP section consists of a 500-ft (152.4 m) lane, 12-ft (3.5 m) wide, featuring undoweled and skewed transverse joints spaced randomly at 13, 14, 17, and 18 ft (4.0, 4.3, 5.2, and 5.5 m). Tie bars measuring 30-inch (75 cm) are placed along the transverse joints, spaced at 35-inch (90 cm) intervals. The pavement structure includes a 14.4-inch (37 cm) Portland Cement Concrete (PCC) layer and a 3.5-inch (9 cm) base layer made up of a soil-aggregate mixture (mostly fine-grained) over an untreated lean clayey subgrade.

FWD testing

FWD testing was performed on the rigid test section over five testing periods between 1989 and 2010 on a nominal five year interval, before the section received an asphalt concrete overlay in 2012. The FWD testing dates are:

1. August 16, 1989
2. August 17, 1994
3. November 9, 1999
4. April 27, 2004
5. May 19, 2010

The testing plan encompassed a comprehensive FWD assessment, which systematically covered the centers, edges, and corners of designated slabs within the section. The drop sequence protocol involved three seating drops from drop height 3, followed by four repeated measurements at each of drop heights 2, 3, and 4. The complete load-deflection time histories were recorded for the final drop at each designated drop height.

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 during the initial two testing periods. Subsequently, two additional sensors were introduced at 48-inch (120 cm) and -12-inch (-30 cm) for the remaining three testing periods.

For the determination of layer properties, FWD data obtained from the center of slab testing is analyzed. This investigation centered on data from station 4+74 (0+144.5), toward the end of the section, and the normalized deflections at 16 kips (70 kN) corresponding to the highest drop are graphically presented for selected sensors. The deflections are progressively escalating over time, suggesting deterioration in the pavement structure.

nonlinear dynamic backcalculation

Nonlinear dynamic backcalculation was performed using nbak for the rigid pavement, treating it as a two-layer system consisting of the PCC surface layer and the subgrade layer. For backcalculation purposes, the base layer was included within the subgrade layer due to its composition closely resembling subgrade material and its minimal layer thickness.

In the model, the PCC layer was characterized as linear elastic, while the subgrade layer was represented using a variant of the Uzan 1985 model, accounting for bulk stress and octahedral shear stress. Rayleigh damping coefficients were applied to simulate damping effects, and Poisson’s ratios and densities were obtained from the LTPP database or assumed as necessary.

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

The moduli of the PCC layer demonstrated a steady yet noteworthy decline, decreasing from 6,100 ksi (42 GPa) in 1989 to 4,300 ksi (30 GPa) in 2010. Conversely, the moduli of the subgrade layer within the influence zone remained comparatively stable, fluctuating between 6.3 ksi (43 MPa) in 2010 to 6.9 ksi (48 MPa) in 1999.

The subgrade layer was modeled as nonlinear; consequently, the moduli are anticipated to vary among the different subgrade finite elements based on (1) their positions within the subgrade layer, (2) the FWD load amplitude, and (3) the FWD load level or drop height. Average moduli of the subgrade layer under peak load conditions are provided herein for the upper portion of the subgrade layer, covering a 6-ft (1.8 m) wide by 6-ft (1.8 m) deep area referred to as the influence zone.

pavement performance

Manual distress surveys were conducted in 1999, 2002, 2004, 2007, 2009, and 2011, during which joint deficiencies were identified in the initial survey. The occurrence of map cracking, a material-related distress, was documented for the first time in the 2007 survey, extending across the entire section. The LTPP distress identification manual defines map cracking as a series of cracks that extend only into the upper surface of the slab.

While the visibility of map cracking emerged during the 2007 survey, it is evident that damage to the PCC layer had commenced much earlier, becoming apparent from the early stages of FWD testing. By the time the cracking was identified, the modulus of the PCC layer had already decreased by about 25-30% compared to the initial testing in 1989.

Map cracking, akin to any manifestation of pavement structural damage, can typically be discerned through periodic F/HWD testing and robust backcalculation techniques. Consequently, it is crucial to subject newly constructed pavement structures of any type to F/HWD testing within the first year to establish a baseline for subsequent comparative analyses during future testing periods. Obtaining insights into the pavement structural behavior before the onset of distress is vital for safeguarding the overall integrity of the pavement structure through the implementation of a proactive pavement management system. This approach empowers the owner to institute proper corrective actions in a timely manner, ensuring a smoother and safer user experience.

subgrade triaxial laboratory testing

Subgrade materials were sampled in August 1989 from two distinct locations—one at the beginning and another at the end of the section—both situated outside the limits of the 500-ft (152.4 m) test section. Repeated load triaxial compression tests were conducted on the two samples in 1995 and 1996 to determine the subgrade’s resilient moduli. Each specimen underwent a combination of static confining pressures and dynamic cyclic stresses during testing. The resilient (recoverable) axial deformation response was recorded for each combination, and the resilient moduli were subsequently calculated.

The subgrade resilient moduli exhibited a range of 11.6 to 16.7 ksi (80 to 115 MPa) for the sample collected at station -0+50 (-0+015.2) and 4.6 to 9.1 ksi (32 to 63 MPa) for the sample collected at station 5+61 (0+171). This disparity between the two samples underscores the substantial variability in pavement support conditions based on laboratory testing.

The backcalculated moduli for the subgrade layer during the five testing periods fell within the range of 6.3 to 6.9 ksi (43 to 48 MPa) for the assessed slab at station 4+74 (0+144.5), as previously documented. Notably, these values closely correspond with those obtained from the second subgrade laboratory sample, situated in close proximity to the evaluated slab.

The harmonization of subgrade layer properties between laboratory testing and nonlinear dynamic backcalculation underscores the critical importance of employing advanced backcalculation and modeling techniques for assessing the structural capacity of pavements.

comparison to static backcalculation

Static backcalculation, implemented by LTPP, involved modeling the layers as linear elastic, and the results can be accessed through infopave.fhwa.dot.gov. The pavement structure was represented as a three-layer system, with the base layer assumed to be 24-inch (60 cm) thick covering the thin base layer and upper portion of the subgrade layer. The backcalculated moduli for the PCC layer exhibited a relatively uniform distribution over the five testing periods, ranging from 4,500 to 5,700 ksi (31 to 39 GPa) for station 4+74 (0+144.5). While these moduli fall within the limits determined through nonlinear dynamic backcalculation, they fail to exhibit the expected gradual decrease in PCC layer moduli due to damage.

Conversely, the moduli of the base layer exhibited considerable variability, ranging from 5.6 to 102 ksi (39 to 700 MPa). These values are deemed unrealistic due to their departure from typical ranges and their pronounced variability. Furthermore, it is important to highlight that, in four out of the five testing periods, the moduli of the base layer were erroneously lower than their corresponding subgrade values.

Furthermore, the subgrade layer moduli also exhibited variability, ranging from 25 to 48 ksi (170 to 330 MPa). These values are not only unrealistic but also markedly deviate from the subgrade resilient moduli determined from laboratory testing. Moreover, they are 3.8 to 7.3 times higher than the layer moduli determined through nonlinear dynamic backcalculation, which fell within the range of 6.3 to 6.9 ksi (43 to 48 MPa).

The correspondence between the measured and calculated peak deflections in static backcalculation, as assessed through RMSE calculations, ranged from 1.2% to 2.8%. While the obtained RMSE values appear favorable, it is essential 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 and generate unreliable moduli in this particular instance.

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