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The existing crash modeling techniques for expressway tunnels must overcome the following difficulties: 1) The collected risk factors contributing to the tunnel crashes include narrow ranges, especially the pavement conditions and weather conditions of the tunnels are rarely taken into account. 2) Most researchers ignored the estimation deviation caused by the excess zero observations of tunnel crash datasets. 3) No existing tunnel crash model can combine the random-parameters approach and spatial-temporal approach to solve the estimation deviation caused by the inter-samples and spatial-temporal heterogeneity. To address these problems, this study presents an investigation of the safety effects of risk factors of tunnel design features, traffic conditions, pavement conditions and weather conditions utilizing a 12-quarter period (3 years) of data as well as five crash frequency models: 1) a fixed parameters negative binomial model (FPNB), 2) a random parameters negative binomial model (RPNB), 3) a random parameters negative binomial Lindley model (RPNBL), 4) a spatial and random parameters negative binomial Lindley model (SP-RPNBL), and 5) a spatial-temporal and random parameters negative binomial Lindley model (ST-RPNBL). The results showed that the ST-RPNBL model solves the deviation that arises from excess zero observations by introducing the Lindley distribution and considers the unobserved heterogeneity by introducing both the random parameters and spatial-temporal parameters that provided better goodness of fit and offered more insights into the factors that contribute to tunnel safety. Furthermore, the ST-RPNBL model detected 16 variables that were significantly correlated with tunnel crash frequency, of which 12 variables were associated with a higher crash frequency and four variables were associated with a lower crash frequency. The random variables of the curvature, the steep downgrade indicator, the proportion of class 5 vehicle and the skidding resistance index (SRI) were identified, and the influence of each significant variable on the crash frequency was analyzed.

Investigation of the Factors Influencing the Crash Frequency in Expressway Tunnels: Considering Excess Zero Observations and Unobserved Heterogeneity