Identifying Outliers in TSDDs

flexible pavement in Denmark

case study summary 

Traffic Speed Deflection Device (TSDD) and Falling Weight Deflectometer (FWD) testing were conducted on a flexible pavement in Denmark. The purpose of this case study is to conduct an in-depth investigation comparing the responses measured by both devices. The FWD deflections are shown to be uniform for the evaluated segment, while the TSDD deflection slopes and deflections are shown to be noisy when reported at 1 m intervals, but sensitive to temperature and spatial variations. Nonlinear dynamic backcalculation is performed and the resulting layer properties are used in a three-dimensional (3D) finite element (FE) model to simulate the TSDD’s moving dual wheel load. Acceptable, though not ideal, matching is achieved between the calculated and TSDD-measured deflection slopes, with multiple outliers identified.

case study insights

TSDD testing was conducted on June 13, 2023, over a 33-mile loop near Copenhagen, Denmark. The TSDD testing was performed in three replicates. In addition, FWD testing was performed on three sections along this loop, each ranging in length from 0.25 to 0.30-mile (400 to 500 m), using a SWECO PRIMAX 1500 device. A 250 m flexible pavement segment is selected in this study to conduct an in-depth investigation comparing the responses measured by the TSDD and FWD.


The asphalt concrete layer thickness is determined through coring, while the aggregate base layer thickness is determined through the review of the construction records.

normalized deflections

The TSDD deflections for the three runs are reported at 1 m intervals, whereas the FWD testing is performed at 10 m intervals. A linear trendline is fitted through the TSDD data by considering the three runs to highlight the underlying trend in the deflection response.


Four general observations are made:

  1. The TSDD deflections exhibit considerable noise when reported at 1 m intervals. Aggregating the data to standard network- or project-level reporting intervals would significantly reduce or eliminate this noise. In contrast, the FWD deflections are relatively uniform.
  2. Both devices show a similar increasing trend in deflections from the beginning to the end of the segment.
  3. Differences exist in the magnitudes of the measured deflections; however, direct comparison is not appropriate due to differences in loading mechanisms and measurement principles between the two devices.
  4. The FWD captures a localized area of relatively high deflection in the middle of the segment, which is not identified by the TSDD.

nonlinear dynamic backcalculation

Nonlinear dynamic backcalculation is performed using nbak to determine the layer properties from four FWD test points that represent the average conditions over the 250 m segment. The backcalculation is performed by fitting the entire deflection time histories for the all drops simultaneously. The asphalt concrete is modeled as linear viscoelastic, while the unbound base and subgrade layers are modeled as nonlinear elastic. In addition, Rayleigh damping is considered for the two sublayers. The asphalt concrete layer modulus is reported at the tested temperature of 81.2°F and a frequency of 17 Hz, whereas average moduli are reported for the unbound layers since they are modeled as nonlinear. In addition, static backcalculation is performed using a well-known application, and the results are presented.


Differences are shown to exist between the layer moduli, mainly for the base and subgrade layers. The Danish Road Directorate (DRD) was contacted to determine which set of layer moduli is more reliable. It was confirmed that an operator drilled through the base layer and found it to be unbound (i.e., not stabilized). Additionally, drilling through the subgrade layer was not possible, possibly indicating stabilization. In summary, DRD’s observations during field exploration support the reliability of the layer moduli obtained from nonlinear dynamic backcalculation, in contrast to those derived from static backcalculation.


layer h nbak static backcalculation
asphalt concrete 8.25-inch 585 ksi 650 ksi
aggregate base 11.8-inch 37.0 ksi 110 ksi
subgrade --- 37.8 | 50.8 ksi 25 ksi

moving load modeling

Moving-load modeling is conducted using 3moD, a pulsuus application that employs 3D FE analysis to model the TSDD moving dual-wheel load and compute pavement responses. Alternatively, the analysis can be performed using bakML, which is more efficient than 3moD.


The deflection slopes are calculated using the layer properties generated by nbak as input (blue solid line). The slopes measured by the TSDD are shown in orange, along with the 5th and 95th percentiles to illustrate measurement variability. Acceptable agreement is obtained between the measured and calculated slopes using the properties from nbak, despite the presence of two outliers at −0.66 ft (−200 mm) and 2.95 ft (900 mm).


In addition, the modeling is repeated using the layer moduli obtained from static backcalculation, and the corresponding slopes are reported (gray dotted line). None of the measured slopes are shown to fall on the gray dotted line, which confirms the earlier findings regarding discrepancies in the backcalculated layer moduli.

moving load backcalculation

Despite the inadequacy of the measured TSDD slopes for backcalculation purposes, moving-load backcalculation is still performed using bakML by assigning zero weights to the sensors at −0.66 ft (−200 mm) and 2.95 ft (900 mm). This exercise is conducted to demonstrate the robustness of bakML.


The backcalculation is performed for two scenarios:

  1. the measured slopes as reported, and
  2. the measured slopes reduced by 10 microns.


The decision to reduce the slopes in the second scenario is based on observations from the previous section, where four out of the five measured slopes between offsets of 0 and +2 ft are shown to be higher than the blue line obtained from modeling using the properties from nbak. This scenario accounts for potential inaccuracies in the zero-slope assumption at the reference Doppler laser location.


The results, as shown in the bar chart, are comparable to those obtained using nbak, although they are not identical due to inherent variability and noise in the data.

acknowledgments and disclaimer

pulsuus acknowledges the Danish Road Directorate (DRD) for providing access to the FWD and TSDD data used in this case study. Furthermore, DRD assumes no responsibility for any recommendations or conclusions derived from this publicly available information.