# THE USE OF 3-D HIGHWAY DIFFERENTIAL GEOMETRY IN CRASH PREDICTION MODELING

2-14-2019

2019

## Degree Name

Doctor of Philosophy (PhD)

## Document Type

Doctoral Dissertation

Engineering

## Department/School/Program

Civil Engineering

## Abstract

The objective of this research is to evaluate and introduce a new methodology regarding rural highway safety. Current practices rely on crash prediction models that utilize specific explanatory variables, whereas the depository of knowledge for past research is the Highway Safety Manual (HSM). Most of the prediction models in the HSM identify the effect of individual geometric elements on crash occurrence and consider their combination in a multiplicative manner, where each effect is multiplied with others to determine their combined influence. The concepts of 3-dimesnional (3-D) representation of the roadway surface have also been explored in the past aiming to model the highway structure and optimize the roadway alignment. The use of differential geometry on utilizing the 3-D roadway surface in order to understand how new metrics can be used to identify and express roadway geometric elements has been recently utilized and indicated that this may be a new approach in representing the combined effects of all geometry features into single variables. This research will further explore this potential and examine the possibility to utilize 3-D differential geometry in representing the roadway surface and utilize its associated metrics to consider the combined effect of roadway features on crashes. It is anticipated that a series of single metrics could be used that would combine horizontal and vertical alignment features and eventually predict roadway crashes in a more robust manner.

It should be also noted that that the main purpose of this research is not to simply suggest predictive crash models, but to prove in a statistically concrete manner that 3-D metrics of differential geometry, e.g. Gaussian Curvature and Mean Curvature can assist in analyzing highway design and safety. Therefore, the value of this research is oriented towards the proof of concept of the link between 3-D geometry in highway design and safety. This thesis presents the steps and rationale of the procedure that is followed in order to complete the proposed research. Finally, the results of the suggested methodology are compared with the ones that would be derived from the, state-of-the-art, Interactive Highway Safety Design Model (IHSDM), which is essentially the software that is currently used and based on the findings of the HSM.

## Digital Object Identifier (DOI)

https://doi.org/10.13023/etd.2019.219

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