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Increasing the axle load causes track deterioration and permanent settlement of the ballast layer. In the ballasted railway tracks, due to the inevitability of unequal settlements in the ballast layer, part of the rail due to high flexural rigidity will become suspended, which causes the formation of the track with unsupported and partially supported sleepers. This situation increases rail vertical displacement and reactions on adjacent sleepers. Several models have been presented to study the effect of unsupported sleepers on dynamic responses of train-track interaction. In this paper, by applying mathematical model, unsupported and partially supported sleepers have been modeled and equations of motions for train-track interaction were written by assuming nonlinear behavior of rail and wheel contact. Following by solving the equations via numerical integration in the time domain, the effect of axle load and pad stiffness on rail vertical displacement were investigated. Results of the analysis suggested that through increasing the axle load rail displacement increased by 13 % in the unsupported sleeper and from 5 to 10 % in the partially supported sleeper. Also, by increasing the pad stiffness rail displacement decreased from 2 to 13 % in the unsupported sleeper and from 1 to 6 % in the partially supported sleeper.

This research empirically evaluates the access gap between transit and automobile to examine the extent of auto-access-orientation within and between the 50 American Metropolitan Areas. The Modal Access Gap (MAG) index is calculated over space and travel time to test three hypotheses: (1) MAG is a function of space and travel time, (2) MAG is CBD-centric, and (3) MAG is associated with transit use. Results indicate that (1) MAG merely possesses negative values ranging between −0.98 and −0.79, regardless of the travel-time thresholds or metropolitan areas, and the travel time lag between transit and automobile ranges from 35 minutes in New York to 51 minutes in Riverside for a 60-minute commute, (2) MAG decreases as one moves away from the central area, and (3) a 1% increase in MAG increases transit use by 1.37% on average.

This study examines the correlates of the Modal Access Gap (MAG) between transit and automobile to employment opportunities in the 45 most populated American metropolitan areas by testing spatial lag regression models and employing the bivariate local indicator of spatial autocorrelation (BiLISA) at the census block group geographical level. Four findings are discerned. First, MAG is positive regardless of the metropolitan area and travel-time threshold and ranges from 0.22 to 0.98. This indicates transit trails automobile in offering access to employment opportunities. Second, millennials and carless households tend to reside in areas with a narrower MAG, while people with disabilities reside in areas with a wider MAG. Third, areas with a high share of carless households and relatively low transit access to employment opportunities are primarily clustered in the suburbs and exurbs of American metropolitan areas. Fourth, the MAG disproportionately affects socially vulnerable populations, including the elderly, people with disabilities, low-income households, Hispanics, and African Americans. Compared with the national average, modal access inequity is prevalent for the elderly in 27, for people with disabilities in 22, for low-income households in 17, for Hispanics in 14, and for African Americans in 12 metropolitan areas. This research is a necessary step forward for instilling social equity into transport planning strategies in parallel with governmental efforts.

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