Spatial repeatability 2

Spatial repeatability arises because trucks are similar in weights, dimensions, and dynamic characteristics and travel at similar speeds. As a result, each vehicle will apply its peak forces at approximately the same places along the pavement surface (Cole, Cebon 1992).
Cole et al. defined the spatial repeatability index (SRI) as the correlation coefficient between a dynamic tyre force histories,
                                                                                                         (1)
where x and y are dynamic tyre forces histories,
m_x and m_y are the mean forces of x and y, respectively,
and σ_x and σ_y are the standard deviations of x and y, respectively (Cole, Cebon 1992; Cole et al. 1996).
An alternate measure of spatial repeatability, suggested by Cole, is the fleet normalised aggregate tyre force,
                                                                                                                              (2)
where
F_i,jk is the tyre force at the i-th road point due to the k-th axle of the j-th vehicle,
m is the number of axles on each vehicle,
N_V is the total number of vehicles,
and is the mean of the double sum in the numerator (Cole et al. 1996).
The fleet normalised aggregate force gives a spatial (time-domain) picture of the cumulative pattern of traffic loading.

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