Developing safety performance functions incorporating reliability-based risk measures

Current geometric design guides provide deterministic standards where the safety margin of the design output is generally unknown and there is little knowledge of 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 implication of deviation from design standards. However, there is currently no link between measures of design reliability and the quantification of safety using collision frequency. The analysis presented in this paper attempts to bridge this gap by incorporating a reliability-based quantitative risk measure such as the probability of non-compliance (Pnc) in safety performance functions (SPFs). Establishing this link will allow admitting reliability-based design into traditional benefit–cost analysis and should lead to a wider application of the reliability technique in road design. The present application is concerned with the design of horizontal curves, where the limit state function is defined in terms of the available (supply) and stopping (demand) sight distances. A comprehensive collision and geometric design database of two-lane rural highways is used to investigate the effect of the probability of non-compliance on safety. The reliability analysis was carried out using the First Order Reliability Method (FORM). Two Negative Binomial (NB) SPFs were developed to compare models with and without the reliability-based risk measures. It was found that models incorporating the Pnc provided a better fit to the data set than the traditional (without risk) NB SPFs for total, injury and fatality (I + F) and property damage only (PDO) collisions.

► Many researchers have shown the advantages of using reliability analysis for the evaluation of the risk level associated with geometric design. The establishment of the linkage between reliability measures and safety (expected collisions) is, therefore, of considerable interest. The models developed in this paper should help establish this linkage which will hopefully lead to a wider application of reliability-based geometric design and to admit reliability based design into traditional benefit-cost analysis.
► Using a data set that comprises geometric design features, collision and traffic volume data for the Trans-Canada Highway in British Columbia, three safety performance functions relating the probability of non-compliance (reliability measure) to total, severe (I+F), and property damage only (PDO) collisions were developed.
► The results can be used to aid the decision maker in determining the safety implications of deviating from geometric design standards and quantifying the safety level built in design values that are deemed acceptable (or unacceptable).
► It is hoped that this paper will add another step into the direction of developing fully probabilistic (risk-based) geometric design standards.