# Track Modulus Assessment of Engineered Interspersed Concrete Sleepers in Ballasted Track
## 4 Results and Discussion
### Wheel Load and Displacement Comparison Results  
The distribution of wheel loads measured at the field site for both passenger coaches and locomotives matched the expected loads based on the nominal static load ratings that were acquired previously (Figure 9).  
Figure 8: An example of track displacement and wheel load data.  
The data showed a minimal difference in track displacements between the two sleeper types (Figure 10) independent of load source (passenger coach or locomotive). The observed median displacement values under the passenger coaches were 2.26 mm (0.089 in.) and 2.21 mm (0.087 in.) for timber and EIC sleepers, respectively. The observed median displacement values under the locomotives were 2.70 mm (0.1062 in.) and 2.74 mm (0.1078 in.) for timber and EIC sleepers, respectively. The locomotive data were also useful because they provided a proxy for the expected behavior of these sleeper types under loaded HAL freight-train loads.  
The field results (Figure 11) showed that the sleepers' positional variability exceeded that of the observed variability between sleeper types. For example, the displacement results of the first ten sleepers ranged from 1.22 mm (0.048 in.) to 3.02 mm (0.119 in.). Within this range, both the minimum and maximum peak values were recorded for timber sleepers. The highest median values were measured in sleepers 21 to 24, ranging from 3.81 mm (0.150 in.) to 4.32 mm (0.170 in.), and included both sleeper types. When we compared sleeper-displacement results alone, it was difficult to distinguish variability between timber and EIC sleepers, a finding that was also documented in prior research [9].  
Using both the loading data and the corresponding track displacements, the track-modulus values for all axes were determined using the single-point load method (Figure 12). As discussed in Section 3, any potential contribution for slack in the system was mitigated by capturing many replicate sleepers (23 in total). The timber-sleeper and EIC-sleeper median track-modulus values were 12.95 N/mm/mm (1878 lbs./in./in.) and 12.79 N/mm/mm (1855 lbs./in./in.), respectively. The five-sleeper moving-average track  
Figure 10: Comparison of the track displacement between the timber and EIC sleepers.  
Figure 9: The distribution of the wheel loads measured at site.  
modulus result showed a minimal difference in track response to load when the rail was supported by either a timber sleeper or an EIC sleeper (Figure 13). The calculated results are not independent measurements; they are dependent on the specific site conditions and interspersed arrangement, so the modulus of the EIC sleepers was dependent on the adjacent sleepers, and vice versa. Nevertheless, the obtained results indicated that the EIC sleepers provided a similar stiffness response to the timber sleepers in this interspersed installation.  
Figure 11: The displacement results for each individual sleeper (passenger coaches only).  
Figure 12: Comparison of the track modulus between the timber and EIC sleepers, considering all measured locomotive and passenger coach field data.