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UBC Theses and Dissertations

Risk-based design of horizontal curves with restricted sight distance Ibrahim, Shewkar El-Bassiouni


Current geometric design guides provide deterministic standards where the safety margin of the design output is generally unknown and there is little knowledge on the safety implications of deviating from these standards. Several studies have advocated probabilistic geometric design where reliability analysis can be used to account for the uncertainty in the design parameters and to provide a risk measure of the degree of deviation from design standards. In reliability analysis, this risk is represented by the probability of non-compliance (Pnc) defined as the probability that the supply exceeds the demand. However, there is currently no link between measures of design reliability and the quantification of safety using collision frequency. The analysis presented in this thesis attempts to incorporate a reliability-based quantitative risk measure in the development of Safety Performance Functions (SPFs). The thesis considers the design of horizontal curves, where non-compliance occurs whenever the available sight distance (ASD; supply) falls short of the stopping sight distance (SSD; demand). The inputs of SSD are random variables and appropriate probability distributions were assumed for each. A comprehensive database for the Trans-Canada Highway was used to compute the probability of non-compliance (Pnc) for 100 segments of horizontal curves. Several Negative Binomial (NB) Safety Performance Functions (SPFs) were developed and the predicted collisions were found to increase with risk (Pnc) and that the rate of increase varies by severity level. The likelihood ratio test showed that the inclusion of a risk parameter (Pnc) has generated better predictive models that have significantly outperformed the traditional models. Further, a spatial analysis was carried out which showed that the spatial models were successful in overcoming potential model misspecification resulting from incorporating only exposure and Pnc in the SPFs as relevant covariates might have been omitted. The optimization of cross-section design to minimize the risk associated with restricted sight distance was also considered using a multiple objective function that involves new Collision Modification Factors (CMFs) incorporating Pnc. The results indicated that accounting for the random variations due to drivers’ behavior proactively at the design stage would decrease collisions in addition to achieving an overall risk reduction.

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