Normalised Aggregate Force and Fourth-Power Forces
Figure 1 is a comparative plot of the fleet normalised aggregate forces generated by the four simulation methods.
Figure 1: Comparison of fleet normalised aggregate force histories for each of the four simulated vehicle fleets
The ‘reference’ and ‘target’ time histories agree very well, while the time histories from the phase shifted and randomised QCM fleets appear to follow a similar pattern. This comes down to the inherent dynamics of each model; the ‘reference’ and ‘target’ histories were generated by pitch-plane models, the randomised QCMs and phase-shifted models used QCMs that lack pitch interaction and wheelbase filtering.
SRI Curves
Figure 2 and Figure 3 are comparative plots of the SRI curves generated by each of the four simulated fleets and a re-plotting of the region 0.8<SRI<1, respectively. From Figure 2 and Figure 3 it can be seen that the ‘target’ and the phase-shifted SRI curves agree well, as expected.
Due to the fact that vehicles with similar suspension characteristics correlate well with each other, all curves show a sharp peak close to the maximum value of one and a secondary peak in the region of SRI=0.85, corresponding respectively to those vehicles that are entirely air sprung and those that have leaf-sprung trailers.
Figure 2: Comparison plot of SRI curves for each of the four simulation methods
Figure 3: Comparison plot of SRI curves re-plotted for the range 0.8<SRI<1
Computation Time and Summary of Results
Table 1 provides a summary of computation time and accuracy metrics for each simulation method.
Table 1: Summary of simulation time, goodness-of-fit, and correlation of normalised aggregate forces for all four simulated fleets
Although the phase-shifted method includes the overhead time of generating the ‘target’ SRI curve first (i.e., from measured data or more realistic simulations), this is a ‘one-time’ cost and the phase-shifted models still represent a significant decrease in computation time. For example, if one was simulating 20 years worth of traffic in weekly intervals, 1040 separate traffic calculations would be required. Using the randomised pitch-plane models of the ‘target fleet’ would take approximately one month of CPU time. Conversely, the phase-shifted method would require only 1.5 days of CPU time, accounting for the overhead of generating the ‘target’ SRI distribution; a 99.5% reduction in computing time.
Given the substantial computational benefit of the phase-shifting method, and the excellent agreement of the SRI statistics, it is believed that the phase-shifted QCMs are still the best available method for simulating dynamic tyre forces for whole-life pavement performance calculations in which the effects of millions of axle loads need to be simulated over the lifetime of the road surface.
Figure 1 is a comparative plot of the fleet normalised aggregate forces generated by the four simulation methods.
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Figure 1: Comparison of fleet normalised aggregate force histories for each of the four simulated vehicle fleets
The ‘reference’ and ‘target’ time histories agree very well, while the time histories from the phase shifted and randomised QCM fleets appear to follow a similar pattern. This comes down to the inherent dynamics of each model; the ‘reference’ and ‘target’ histories were generated by pitch-plane models, the randomised QCMs and phase-shifted models used QCMs that lack pitch interaction and wheelbase filtering.
SRI Curves
Figure 2 and Figure 3 are comparative plots of the SRI curves generated by each of the four simulated fleets and a re-plotting of the region 0.8<SRI<1, respectively. From Figure 2 and Figure 3 it can be seen that the ‘target’ and the phase-shifted SRI curves agree well, as expected.
Due to the fact that vehicles with similar suspension characteristics correlate well with each other, all curves show a sharp peak close to the maximum value of one and a secondary peak in the region of SRI=0.85, corresponding respectively to those vehicles that are entirely air sprung and those that have leaf-sprung trailers.
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Figure 2: Comparison plot of SRI curves for each of the four simulation methods
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Figure 3: Comparison plot of SRI curves re-plotted for the range 0.8<SRI<1
Computation Time and Summary of Results
Table 1 provides a summary of computation time and accuracy metrics for each simulation method.
| Method | Simulation Time (One Run) [sec] | Simulation Time (20 years, @ 1 per week) [days] | R2 of SRI Curves Relative to ‘Reference’ | R2 of SRI Curves Relative to ‘Target’ | Correlation of ATFs to ‘Reference’ Fleet | Correlation of ATFs to ‘Target’ Fleet |
| Reference | 147600 | 1777 | 1 | - | 1 | - |
| Target | 26000 | 313 | 0.91 | 1 | 0.99 | 1 |
| Random QCM | 24000 | 290 | 0.76 | 0.76 | 0.75 | 0.74 |
| Phase Shifted QCM | 90 | 1.5 | 0.53 | 0.89 | 0.52 | 0.48 |
Table 1: Summary of simulation time, goodness-of-fit, and correlation of normalised aggregate forces for all four simulated fleets
Although the phase-shifted method includes the overhead time of generating the ‘target’ SRI curve first (i.e., from measured data or more realistic simulations), this is a ‘one-time’ cost and the phase-shifted models still represent a significant decrease in computation time. For example, if one was simulating 20 years worth of traffic in weekly intervals, 1040 separate traffic calculations would be required. Using the randomised pitch-plane models of the ‘target fleet’ would take approximately one month of CPU time. Conversely, the phase-shifted method would require only 1.5 days of CPU time, accounting for the overhead of generating the ‘target’ SRI distribution; a 99.5% reduction in computing time.
Given the substantial computational benefit of the phase-shifting method, and the excellent agreement of the SRI statistics, it is believed that the phase-shifted QCMs are still the best available method for simulating dynamic tyre forces for whole-life pavement performance calculations in which the effects of millions of axle loads need to be simulated over the lifetime of the road surface.
