Injury-Based Surrogate Resilience Measure: Assessing the Post-Crash Traffic Resilience of the Urban Roadway Tunnels

Abstract

Crash injuries not only result in huge property damages, physical distress, and loss of lives, but arouse a reduction in roadway capacity and delay the recovery progress of traffic to normality. To assess the resilience of post-crash tunnel traffic, two novel concepts, i.e., surrogate resilience measure (SRM) and injury-based resilience (IR), were proposed in this study. As a special kind of semi-closed infrastructure, urban tunnels are more vulnerable to traffic crashes and injuries than regular roadways. To assess the IR of the post-crash roadway tunnel traffic system, an over-one-year accident dataset comprising 8621 crashes in urban roadway tunnels in Shanghai, China was utilized. A total of 34 variables from 11 factors were selected to establish the IR assessment indicator system. Methodologically, to tackle the skewness issue in the dataset, a binary skewed logit (Scobit) model was found to be superior to a conventional logistic model and subsequently adopted for further analysis. The estimated results showed that 15 variables were identified to be significant in assessing the IR of the roadway tunnels in Shanghai. Finally, the formula for calculating the IR levels of post-crash traffic systems in tunnels was given and would be a helpful tool to mitigate potential trends in crash-related resilience deterioration. The findings of this study have implications for bridging the gap between conventional traffic safety research and system resilience modeling.

1. Introduction

Traffic crash injuries are one of the main causes of death in modern society. According to the WHO, 1.35 million people die from roadway traffic crashes each year worldwide [1]. Studies on crash injury severities have long been one of the most urgent public issues in the field of traffic safety. It should be noted that accidents that have happened in special urban infrastructures such as overpasses, elevated bridges, and tunnels [2] may occupy a lower proportion of the whole roadways but could induce a chain reaction of consequences and more severe casualties.

According to existing traffic risk studies, the major factors affecting crash injury severities include the driver’s behavioral characteristics, the vehicle’s technical features, roadway conditions, and environmental factors at the time and place when the crash occurs [3]. Investigating the significant factors affecting the occurrence and the injury severities of traffic crashes has long been a vital issue in the field of traffic safety study. There are two mainstream methodologies commonly used in traffic safety study, i.e., the statistical analytic method based on previous crash data, and the simulation method based on numerical or software-based modeling. Apart from ordinary urban roadways or freeways, scholars have depicted the important contributors such as drivers, roads, vehicles, and environment to crash injuries on/in some other road transportation infrastructures, such as bridges [4] and tunnels [5]. Jiang et al. [5] investigated single-vehicle crash injury severities in urban river-crossing road tunnels in Shanghai. Xing et al. [6] investigated the factors that influence the safety of roadway long tunnels using the Vissim simulation platform. Traffic offense behaviors, including drunk driving, jaywalking, and hit-and-runs [7,8], are highly correlated with crash injury severities. Moreover, given that collecting crash data is usually time-consuming and costly, a surrogate safety measure (SSM) such as time to collision (TTC) has been an efficient alternative to evaluate the crash risks using vehicle trajectory data [9].

The concept of resilience originates from the Latin Resilio and has been widely used in other fields since it was first introduced to the ecosystem by Holling [10] in 1973. Resilience generally refers to the ability of a system to resist a perturbation and absorb the effects to maintain a stable state or to recover to pre-disaster conditions or better [11]. In recent years, resilience has gradually become a research hotspot of the transportation network, energy and power, and other critical infrastructure systems or fields. The resilience of a system under a perturbation mainly consists of two processes, i.e., the ability to resist the effects of perturbation, and the ability to recover from perturbation [12], which is similar to the effects of a traffic collision/crash on the roadway capacity. Higher crash risk events do not necessarily result in crashes because the traffic has the ability, its safety resilience, to prevent crashes [13].

Several studies have recently focused on the resilience assessment of urban critical infrastructures such as tunnels. Yang et al. [14] conducted a systematic overview of the indicator-based resilience assessment for critical infrastructures. More specifically, Du et al. [15] reviewed the methodological development, applicability, and future research needs from an earthquake engineering perspective. Huang et al. [16] proposed a framework combining fragility and restoration functions for assessing the robustness of tunnels exposed to different seismic scenarios, and the recovery rapidity considering different damage levels. Khetwal et al. [17] identified tunnel resilience’s sensitivity for parameters using a Monte-Carlo Simulation (MCS) model that estimates overall tunnel resilience for a given period. Liu et al. [18] bridged the linkages between urban underground space (UUS) and urban resilience, revealed the various disaster prevention services that underground facilities can provide, and set up a monetary valuation framework for the benefits of these services. Rinaudo et al. [19] proposed a novel methodology for the optimal placement of sensors in a tunnel to obtain the temperature evolution at any point along its lining during a fire. Caliendo et al. [20] developed a traffic simulation model to quantitatively assess the resilience of a twin-tube motorway tunnel in the event of a traffic accident or fire occurring within a tube using the macro-simulation software PTV Visum version 17. Under the scenarios of hypothetical node failures and disruptions, Bai et al. [21] utilized simulation and network disintegration techniques to assess the resilience of the global liner shipping network using automatic identification system (AIS) data, network connectivity, and the scale of congested ports as measures of resilience assessment. The aforementioned studies, together with their comparison with this current study, are presented in Table 1.

Table 1. Review of related studies regarding the resilience assessment of urban tunnels.

No.	Studies	Disruption Types	Scenarios	Evaluation Tools or Utilized Technique	Data Set	Performance Metrics
1	Huang et al. [16]	Earthquake	Circular tunnels in alluvial deposits	Numerical simulation in fragility, restoration	FEMA	Soil conditions, tunnel burial depths, construction quality, and aging of the tunnel lining
2	Khetwal et al. [17]	Random and planned events	Twenty-two tunnels in the US	Stochastic Monte-Carlo Simulation (MCS)	US National Tunnel Inventory (NTI)	Traffic volume, fire suppression systems, changes in maintenance, and operation parameters
3	Liu et al. [18]	Earthquake and war	Urban metro lines and tunnels	Mathematical modeling	Shanghai Metro, Xiong’an tunnels	Reducing car accidents service
4	Rinaudo et al. [19]	Fire	Fire in tunnels	Numerical simulation	Virgolo Tunnel in Italy	Location of the sensors, the cost of the monitoring system, and the accuracy of the estimated temperatures
5	Caliendo et al. [20]	Traffic Accident or Fire	Traffic accidents or fires occurring within a tube	Traffic simulation	Macro-simulation software PTV Visum 17	Resilience loss, recovery speed, and resilience index
6	Bai et al. [21]	Global liner shipping network	Hypothetical node failure and disruption	Simulation and network disintegration techniques	Automatic Identification System (AIS)	Network connectivity and the scale of congested ports
7	This study	Traffic crash	Traffic crash in Shanghai tunnels	Econometric models	Urban roadway tunnels in Shanghai	Crash injury severity levels

Table 1. Review of related studies regarding the resilience assessment of urban tunnels.

No.	Studies	Disruption Types	Scenarios	Evaluation Tools or Utilized Technique	Data Set	Performance Metrics
1	Huang et al. [16]	Earthquake	Circular tunnels in alluvial deposits	Numerical simulation in fragility, restoration	FEMA	Soil conditions, tunnel burial depths, construction quality, and aging of the tunnel lining
2	Khetwal et al. [17]	Random and planned events	Twenty-two tunnels in the US	Stochastic Monte-Carlo Simulation (MCS)	US National Tunnel Inventory (NTI)	Traffic volume, fire suppression systems, changes in maintenance, and operation parameters
3	Liu et al. [18]	Earthquake and war	Urban metro lines and tunnels	Mathematical modeling	Shanghai Metro, Xiong’an tunnels	Reducing car accidents service
4	Rinaudo et al. [19]	Fire	Fire in tunnels	Numerical simulation	Virgolo Tunnel in Italy	Location of the sensors, the cost of the monitoring system, and the accuracy of the estimated temperatures
5	Caliendo et al. [20]	Traffic Accident or Fire	Traffic accidents or fires occurring within a tube	Traffic simulation	Macro-simulation software PTV Visum 17	Resilience loss, recovery speed, and resilience index
6	Bai et al. [21]	Global liner shipping network	Hypothetical node failure and disruption	Simulation and network disintegration techniques	Automatic Identification System (AIS)	Network connectivity and the scale of congested ports
7	This study	Traffic crash	Traffic crash in Shanghai tunnels	Econometric models	Urban roadway tunnels in Shanghai	Crash injury severity levels

Introducing the concept of resilience to the field of traffic safety has been a novel viewpoint in the past decade, of which the two most representative conceptions are traffic safety resilience and injury resilience. Murray-Tuite [22] considered safety as one of the 10 main dimensions considered in traffic resilience. In addition, Calvert and Snelder [23] considered traffic resilience as “the ability of a road section to resist and to recover from disturbances in traffic flow”. Wang et al. [13] defined their traffic safety resilience as the ability of a road section to resist safety disturbances, or safety-critical events, such as vehicle violations, driver maneuver or judgment errors, or any other disturbances in traffic which could result in a crash. The low-traffic condition has the highest resilience resulting in the lowest crash risk, while the high-traffic condition has the lowest resilience resulting in the highest crash risk [13]. More specifically, injury resilience, which is mentioned infrequently in studies, usually refers to the ability of a sufferer to recover from the injuries resulting from a physical traffic collision. For example, females are relatively less resilient to severe injury than males, which probably reflects the lower injury resilience of female drivers [24], and younger individuals can often recover from some critical injuries that would be fatal to older persons [25].

As we can see from the existing literature on traffic safety resilience and injury resilience, the former focuses on the ability of traffic to naturally avoid a crash by its safety resilience, while the latter refers to a sufferer’s physical recovery from a traffic crash. Thus, there is an obvious gap between the two concepts in the scenario where, after a crash has occurred, the disruptive traffic order could recover to normal by the proper disposal of the involved parties themselves, or by the traffic policemen. Therefore, how to correlate the crash injury data with assessing the nonobjective resilience of a given roadway traffic system remains to be further investigated; this is the question that this study is trying to figure out. Based on these viewpoints, on one hand, taking the example of SSM in traffic safety, this study proposed a new conception, termed a surrogate resilience measure (SRM), and uses the crash injury as an SRM. On the other hand, this study also refines the concept of crash injury-based resilience (IR) as the ability of the traffic system to regain a normal state after a crash being evaluated by the crash injury/fatality.

The objectives or motivations of this study are threefold: (1) based on the concept of IR proposed, this study aims to construct the assessment indicator system for evaluating the resilience of an urban roadway tunnel traffic system using a historical crash injury dataset; (2) utilizing two econometric estimation techniques, this study aims to then identify those statistically significant crash-related indicators/variables contributing the most to assessing the resilience of the urban roadway tunnel traffic system; (3) considering the estimation outputs of the Scobit model, this study aims finally to propose a quantitative IR assessment model that could be useful in assessing the resilience-related influences of crash events on the tunnel traffic’s returning to normality.

This study contributes to the literature from the following three facets:

• As far as the authors know, this study is the first work to propose the novel concept of surrogate resilience measure (SRM) in the field of transportation resilience assessment.
• The injury-based resilience (IR) proposed by this study for the first time bridges the research gap between the existing concept of safety resilience of depicting the pre-crash risk and the injury resilience in sufferers’ physical recovery from a crash, and enriches the connotation of IR in the field of traffic safety.
• As a special, semi-closed urban transportation infrastructure, urban tunnels are novelly chosen to conduct a case study to testify to the proposed assessing framework of crash injury-based resilience, resulting in a quantitative assessment model with high classification accuracy.

The remainder of this paper is organized as follows: Section 2 describes the data and the variables used to develop the models. Section 3 discusses the methodology used to conduct the resilience assessment framework of the urban roadway tunnels in Shanghai. Section 4 presents the empirical results and discussion. Section 5 concludes this study, as well as future directions.

2. Data Preparation

To examine the key factors affecting injury-based resilience (IR) at urban roadway tunnels, a dataset derived from the Shanghai Public Security Bureau from January 2011 to July 2012 was employed in this study. After eliminating repetitive, missing, and false alarm records, a total of 8621 motor vehicle crashes that occurred in the tunnels in Shanghai were available for this study.

To make the results more explicit and easier to comprehend, relative to normal traffic without any crashes, the IR was divided into two categories, i.e., the dependent variable of non-injury resilience (coded as 0), and injury-incurred resilience (coded as 1). A total of 2612 of 8621 observations were recognized as injury crashes. Therefore, the number of the two levels of IRs in this study, i.e., non-injury resilience coded as 0, and injury-incurred resilience coded as 1, account for 69.7% and 30.3% of all the observations, respectively.

Recall that this study reasonably assumes the relationship between a crash and the resilience of a post-crash traffic system, which means that (1) the non-injury crash correlates with a lower level of resilience (IR = 0) than the normal scenario without any crash that the capacity of the roadway decreases by the effects of the crash; and (2) an injury crash correlates with the lowest resilience (IR = 1) because it would be more complex and time-consuming to treat the injured and divide the responsibility than a non-injury crash. Thus, the dependent variable IR levels in this study are set to be a dichotomous variable. To assess the IR of the post-crash traffic system, a vital task is to set up an assessment indicator system. As the concept of injury-based resilience proposed in this study is highly correlated to injury severity levels, it is intuitive to refer to the existing studies in crash injuries. As listed in

Table 2. Descriptions of indicators in the resilience assessment system.

Factors	Indicators	Description of Indicators	No. of Crashes	Percentage
Season of year	Spring	1 if from March to May, 0 otherwise	3029	35.1%
	Summer	1 if from June to August, 0 otherwise	1914	22.2%
	Autumn	1 if from September to November, 0 otherwise	1478	17.1%
	Winter	1 if from December to February, 0 otherwise	2200	25.5%
Day of week	Weekends	1 if on weekends = 1, 0 otherwise	1453	16.9%
Time of day	A.M. peak hours	1 if 7 a.m.–10 a.m., 0 otherwise	2262	26.2%
	Day time	1 if 10 a.m.–5 p.m., 0 otherwise	3602	41.8%
	P.M. peak hours	1 if 5 p.m.–8 p.m., 0 otherwise	1669	19.4%
	Nighttime	1 if 8 p.m.–7 a.m., 0 otherwise	1088	12.6%
Weather conditions	Rainy	1 if involved a rainy day, 0 otherwise	3434	39.8%
	Snowy	1 if involved a snowy day, 0 otherwise	62	0.7%
	Sunny	1 if involved a sunny day, 0 otherwise	5144	59.7%
Locations in the tunnel	Entrance	1 if involved the entrance, 0 otherwise	4033	46.8%
	Interior	1 if involved the interior, 0 otherwise	2801	32.5%
	Exit	1 if involved the exit, 0 otherwise	1787	20.7%
The tunnel speed limit posted	Sl40	1 if involved 40 km/h, 0 otherwise	1052	12.2%
	Sl60	1 if involved 60 km/h, 0 otherwise	236	2.7%
	Sl80	1 if involved 80 km/h, 0 otherwise	7333	85.1%
No. of unidirectional lanes	Lane 2	1 if involved a 2-lane tunnel, 0 otherwise	4313	50.0%
	Lane 3 or 4	1 if involved a 3- or 4-lane tunnel, 0 otherwise	1842	21.4%
Crash types	Rear-end	1 if involved rear-end, 0 otherwise	516	6.0%
	Rollover	1 if involved rollover, 0 otherwise	35	0.4%
	Lateral impact	1 if involved lateral impact, 0 otherwise	8077	93.7%
No. of vehicles involved	One	1 if involved just one vehicle, 0 otherwise	431	5.0%
	Two	1 if involved two vehicles, 0 otherwise	7591	88.1%
	Three or more	1 if involved three vehicles or more, 0 otherwise	599	6.9%
Vehicle types involved	Two-wheeled vehicles	1 if involved a two-wheeled vehicle, 0 otherwise	66	0.8%
	Light vehicles	1 if involved a light vehicle, 0 otherwise	6686	77.6%
	Bus	1 if involves a bus, 0 otherwise	309	3.6%
	HGV	1 if involved a heavy goods vehicle, 0 otherwise	3656	42.4%
	Unknown	1 if the vehicle involved is unknown, 0 otherwise	44	0.5%
Violation	Alcohol	1 if involved alcohol, 0 otherwise	4	0.05%
	Hit-and-run	1 if involved hit-and-run, 0 otherwise	376	4.4%
	None	1 if no violation, 0 otherwise	8244	95.63%
Injury-based resilience	IRs	1 if a crash with injury, 0 if a crash without injury	2612	30.3%

, 34 variables from 11 factors were selected to establish the original IR assessment indicator system, in which the 11 factors include season of the year, day of the week, time of day, weather conditions, locations in the tunnel, tunnel speed limit posted (km/h), No. of unidirectional lanes, crash types, No. of vehicles involved, vehicle types involved, and violation. The descriptions and classifications of the 34 dichotomously dependent variable IRs and 11 independent factors are shown in Table 2.

3. Methodology

3.1. Theoretical Viewpoint

Figure 1 illustrates the viewpoint proposed in this study to assess the resilience of roadway tunnels using the crash injury level as a metric. Therefore, this study reasonably holds the view that an injury-incurred crash (i.e., the blue line in Figure 1) would be more complex and time-consuming in being handled to treat the injured and dividing the responsibility than a non-injury crash (i.e., the red line in Figure 1), which results in lower resilience and requires more resource to recover to the normality (i.e., no crash, the horizontal line in Figure 1).

The characteristics of the two IR levels and their relationships with injuries considered in this study are summarized in

Table 3. Relationship among IR levels, surrogate resilience measure (SRM), curves, codes, and frequency in the dataset.

Descriptions of IR Levels	Injury-Based SRM	Curves in Figure 1	Codes	Frequency (%)
Normal level	No crash	The horizontal line	-	-
Lower level (0)	Crashes without injury	The red curve	0	6009 (69.7%)
The lowest level (1)	Injury or fatality	The blue curve	1	2612 (30.3%)

.

3.2. The Standard Binary Logistic Model

In the field of traffic safety analysis, whether a crash results in injury or not can be affected by several factors, hence the injury severities can be modeled and predicted by using a statistical analysis technique based on a series of variables. For example, existing studies have found that a crash related to specific variables such as drivers’ speeding, drunk-driving, nighttime with poor illumination, etc., is more likely to induce injury or even fatality [26] because these factors will have significant negative effects on drivers’ normal physiological properties and reaction performances. Analogously, as stated earlier in this resilience-related study, a collision without injury could correspond with a lower non-injury resilience (IR level = 0), as a collision with injury or fatality corresponds with the lowest level of injury-incurred resilience (IR level = 1). The two levels of IRs are treated as a binary independent variable in this study and could also be assessed by an indicator system with weights. During the past two decades, the binary logistic regression model has been fully employed to model the similar effects of various factors on binary response variables. Specifically, the logit is the natural logarithm of the odds that the dependent variable is 1 (injury-incurred resilience level) as opposed to 0 (non-injury resilience). If the probability P_L of a crash which results in an injury-incurred resilience level (IR_L = 1) is expressed as the sigmoid function:

$$P_L\left(I{R}_L=1\left|x\right.\right)=1/\left[1+\exp \left(-x^{\prime }\mathsf{\beta }-\epsilon \right)\right]$$

(1)

Assume that $I{R_L}^{*}$ is a continuous variable to measure the effects of IR, and IR_L is the dependent indicator of IR in the binary logistic model; thus, we have

$$I{R_L}^{*}=Log\mathrm{it}(P)=\ln (\frac{P}{1-P})={\mathsf{\beta }}^{\mathbf{\prime }}x+\epsilon$$

(2)

where $\epsilon$ is the vector of the random term of the model that follows the logistic distribution in the standard logistic model, $\mathsf{\beta }$ is a vector of the coefficients to be estimated by maximum likelihood estimation (MLE), and $x$ is a vector of explanatory variables in the IRL assessment index system. For estimating $\mathsf{\beta }$ and $x$, the binary values of IRL could be predicted according to the calculated P_L using Formula (1). Thus, we have

$$I{R}_L=\left\{\begin{array}{ll}0& if{P}_L\in (0,0.5)\\ 1& if{P}_L\in [0.5,1)\end{array}\right.$$

(3)

When an independent variable xi increases by one unit as all other factors remain constant, the odds increase by the factor exp. (β), which is known as the odds ratio (OR), and it ranges from 0 to positive infinity.

3.3. The Skewed Binary Logistic Model

Similarly, when the response variable is thought to be skewed, a skewed logit model is usually used to verify, in which the random term $\epsilon$ is assumed to follow a Burr-10 distribution [27], then we have the skewed logistic model or Scobit model [28], as follows:

$$P_S\left(I{R}_S=1\left|x\right.\right)=F\left(x^{\mathbf{\prime }}\mathsf{\beta };\alpha \right)=1/{\left[1+\exp \left(-x^{\mathbf{\prime }}\mathsf{\beta }-\epsilon \right)\right]}^{\alpha }$$

(4)

$$I{R_S}^{*}=Scob\mathrm{it}(P_S)=\ln (\frac{P_S^{{\alpha }^{-1}}}{1-P_S^{{\alpha }^{-1}}})={\mathsf{\beta }}^{\mathbf{\prime }}x+\epsilon$$

(5)

$$I{R}_S=\left\{\begin{array}{ll}0& ifI{R_S}^{*}\in (-\infty ,0)\\ 1& ifI{R_S}^{*}\in [0,+\infty )\end{array}\right.$$

(6)

in which the additional scale parameter $\alpha$ serves as a measure of skewness. If $\alpha =1$, then the Burr-10 distribution is equivalent to the logistic distribution, and the Scobit model is reduced to the standard logistic model [29]. Utilizing likelihood ratio tests for verifying the superiority of the Scobit model over the standard logistic model, the null hypotheses are investigated as follows:

Null Hypothesis (H₀).

The skewness parameter equals one ($\alpha =1$), i.e., the Scobit model is not significantly different from a standard logistic model in statistics.

When regression estimates are made, to evaluate the prediction efficiency of the IR assessment model, two commonly-used indexes, i.e., sensitivity and specificity, are used in this study. The sensitivity, which is also known as the true positive rate (TPR), indicates the percentage of all recognized true positive (TP) instances in all positive instances (i.e., TP and false negative [FN]) with Formula (7):

$$TPR=TP/\left(TP+FN\right)$$

(7)

Similarly, the specificity, which is known as the Ture Negative Rate (TNR), indicates the proportion of recognized true negative (TN) cases to all negative cases (i.e., TN and false positive [FP]) with calculation Formula (8):

$$TNR=TN/\left(FP+TN\right)$$

(8)

3.4. The Overhead (Time Complexity)

The models and corresponding post-estimations were conducted using the econometrics package Stata (v.17.0). Overhead (time complexity) is a critical issue in various computational science fields such as mobile fog computing [30] and lightweight authentication protocols [31]. The issue of overhead (time complexity) when conducting the logistic/Scobit models actually depends on the model complexity, sample size, and desired precision of the convergence gap. Given the dataset and the binary logistic/Scobit models adopted in this study, the Stata package took 10 to 20 seconds to achieve a convergent estimate using the MLE technique. Simple correlation tests between selected variables before carrying out a regression were conducted using a contingency table and Chi-square test, and no variables are omitted because of strong correlation.

4. Results of the IR Assessment Model and Discussions

4.1. The Assessment Model Results and Comparisons

The assessment model results of both the standard binary logistic model and the skewed logit model are presented in

Table 4. Model estimates of the final standard logistic and Scobit models.

The Number of Obs. = 8617	Zero Outcomes = 6009			Nonzero Outcomes = 2608
	Standard Logistic			Skewed Logistic
Log-likelihood (0)	−5283.076			−5283.076
Log-likelihood	−2432.6791			−2425.544
LR Chi2	Chi2(15) = 5700.79			--
LR test of alpha = 1	--			Chi2(1) = 14.27
Prob > Chi2	0.0000			0.0002
AIC	4897.358			4885.087
BIC	5010.342			5005.133
Variables	O.R.	S. E.	p-value	O.R.	S. E.	p-value	coefficients
Season of the year (relative to non-autumn)
Autumn	1.198	0.117	0.065	1.196	0.107	0.045	0.179 **
Day of the week (relative to Weekdays)
Weekends	1.503	0.145	0.000	1.452	0.129	0.000	0.373 ***
Time of day (relative to non-night time)
Night time	3.312	0.335	0.000	2.981	0.286	0.000	1.092 ***
Weather conditions (relative to Sunny)
Rainy	2.250	0.169	0.000	2.154	0.152	0.000	0.767 ***
Snowy	2.229	1.027	0.082	2.151	0.910	0.070	0.766 *
Locations of the tunnel (relative to exit)
Entrance	2.003	0.224	0.000	1.881	0.197	0.000	0.632 ***
Interior	47.941	6.144	0.000	33.713	4.840	0.000	3.518 ***
Posted speed limit (relative to 80 km/h)
Sl40	0.440	0.067	0.000	0.447	0.063	0.000	−0.805 ***
Sl60	0.436	0.134	0.007	0.424	0.121	0.003	−0.858 ***
No. of vehicles involved (relative to three or more)
One	0.018	0.005	0.000	0.030	0.007	0.000	−3.516 ***
Two	0.001	0.000	0.000	0.002	0.001	0.000	−6.460 ***
Vehicle types (relative to unknown)
Light vehicles	0.758	0.071	0.003	0.788	0.067	0.005	−0.238 ***
Bus	0.178	0.040	0.000	0.182	0.037	0.000	−1.706 ***
HGV	23.688	2.713	0.000	18.567	2.196	0.000	2.921 ***
Two-wheeled vehicles	33.533	12.119	0.000	20.604	7.218	0.000	3.025 ***
constant	7.569	2.085	0.000	2.546	0.883	0.007	0.935 ***
lnalpha				--	0.120	0.000	0.424
Alpha				--	0.183	-	1.528

Note: ***, **, * indicate that parameter estimates are significant at the 99%, 95%, and 90% confidence levels, respectively.

. To determine whether the skewness of the dependent variable IR of the dataset is statistically significant or not, a likelihood ratio test to check whether H₀ holds or not was conducted. As shown from the final Scobit models in Table 4, the Chi-square value reported at the bottom of the output is 14.27, which is much larger than the critical value of 3.84 (degrees of freedom: 1) at the 95% confidence level. This suggests that the H₀ can be rejected, and the skewness of the dataset used is testified to be statistically significant. In addition, the values of AIC (4885.087) and BIC (5005.133) of the Scobit model were smaller than those (4897.358, 5010.342) of the standard binary logistic model, respectively, which also testifies to the superiority of the former model. Thus, the Scobit model is believed to fit the IR of the post-crash traffic system better than the standard binary logistic model and is preferable to conduct further assessment analysis. Except for the odds ratio (O.R.) of the two models, the coefficients of the preferable Scobit model are also reported in Table 4.

The receiver operator characteristic (ROC) curve of the IR assessment model of urban roadway tunnels is shown in Figure 2. The area under the curve to some extent reflects the assessment accuracy rate to correctly predict the resilience level of all cases in the dataset. Overall, the final Scobit IR assessment model fits the data quite well, with a high area under the ROC curve (0.9307) and a high percentage correctly classified (91.08%).

More specifically, the sensitivity and specificity curves of the IR assessment model of urban roadway tunnels are shown in Figure 3. The two curves indicate that the Scobit IR assessment model predicts the positive (IR = 1) and negative (IR = 0) data quite well with a large area under each curve.

4.2. The Discussion of Estimation Results

As stated in the previous Section 4.1, of the 34 variables from 11 factors in the assessment indicator system constructed in Table 2, the final standard/Scobit logistic models shown in Table 4 identified 15 statistically significant (p = 0.1) variables and their corresponding coefficients to evaluate or predict the worst IR (=1) of the post-crash traffic system in the Shanghai roadway tunnels. These 15 variables are autumn, weekends, nighttime, rainy, snowy, tunnel entrance, tunnel interior, speed limit 40 km/h, speed limit 60 km/h, single-vehicle crash, two-vehicle crash, light vehicles, bus, HGV, and two-wheeled vehicles. Note that, as we know, the econometric models, such as the standard binary logistic/Scobit models, are estimated and constructed using the MLE method; thus, those insignificant variables in the original indicator system will be excluded from the final model. These 15 contributors are attached to 8 out of 11 factors, and the 8 factors include season of the year, day of the week, time of day, weather conditions, location of the tunnel, speed limit posted, the number of vehicles involved, and vehicle types.

Day of the week. Whether or not weekdays contribute to crash injury severities in various crash scenarios has long been controversial. Some studies found it significantly contributive [32], while others found no significant differences [33]. However, in this study, relative to weekdays, a weekend crash is more closely associated with the lowest resilience level of injury or fatality (OR = 1.452). This result is reasonable because less traffic during weekends may lead to more speeding and drunk driving.

Time of day. Crash time of the day has been shown to be related to the crash and injury severities by previous studies [34]. The illumination fluctuations driving into and out of the tunnels would affect drivers’ visual ability to react in a timely manner to an emergency. The results show that, relative to non-nighttime, a crash that happened at nighttime (8 p.m.–7 a.m.) is more likely to induce injury or fatality, which hints at the lowest level of resilience (IR = 1, OR = 2.981).

Weather conditions. Relative to sunny days, a crash that happened on a rainy (OR = 2.154) or snowy day (OR = 2.151) is more likely to result in the worst scenario (IR = 1) with injury or fatality in the current assessment system. This result is expected because by reducing visibility and road surface friction [5], adverse weather conditions have been found to be highly related to crashes with more severe injuries or even deaths [35]. Therefore, it is also suggested that, compared with sunny days, crashes on rainy or snowy days would decrease the resilience of the traffic system by delaying accident handling and rescue.

Locations of the tunnel. Given the illumination variations from brightness out of the tunnels to relative darkness inside, the optesthesia of drivers would take time (several seconds or even longer) to adapt, which is known as dark adaptation in traffic safety science [36]. Crashes that happened at the forepart and middle part of the tunnel were found to greatly influence the single-vehicle crash severities in Shanghai roadway tunnels [5]. Analogously, this study found, that relative to the tunnel exit, crashes occurring at the entrance (OR = 1.881) or in the interior (OR = 33.713) of tunnels would significantly deteriorate the IR level of the traffic system, which is reasonable and in accordance with normal experience. Specifically, once collisions befall in the middle part of a semi-closed tunnel, the upstream traffic flow would not only be dramatically vibrated for the sake of capacity plummet, but the resilience of the tunnel traffic system would take a longer time to recover.

Posted speed limits. Existing evidence has shown that higher speed limits increase the probability of severe injury severity levels than lower ones [37]. Similarly, in this study, relative to the 80 km/h, a crash that happened in a tunnel with a lower posted speed limit of 40 mph (OR = 0.447) or 60 mph (OR = 0.424) would be helpful to avoid the IR from worsening with no injury being involved. Therefore, with the injury severity being the SRM, a higher posted speed limit may indicate the lowest IR level in the scenarios of Shanghai roadway tunnels.

The number of vehicles involved and Vehicle types. Relative to multi-vehicle crashes, a single-vehicle crash (OR = 0.030) or a two-vehicle crash (OR = 0.002) are found to remarkably prevent the crashes from degenerating the resilience of the tunnel traffic system. This result is also expected because, once an accident has happened, a multi-vehicle crash, without doubt, is more likely to incur a larger-scale traffic congestion [38] and would require more resources and efforts for the traffic to regain unobstructed. Different vehicle types involved in the crashes are found to have discrepant effects on the resilience of the tunnel traffic state. Relative to crashes involving light vehicles (OR = 0.788) and buses (OR = 0.182), crashes involving HGV (OR = 18.567) or two-wheeled vehicles (OR = 20.604) are proven to be more relevant to a worse state of resilience. These outcomes are also reasonable because of the huge mass of HGV and the lack of physical protection of motorcyclists, and crashes involving the aforementioned two-vehicle types have been discovered to relate to more severe injury consequences. Thus, it is more burdensome for the resilience of the traffic system to resurgence.

Season of the year. The variable autumn of the factor season of the year is found to significantly contribute to the IR levels in this study. Relative to non-autumn seasons, a crash that happened on an autumn day is more likely to be an injury-incurred crash (OR = 1.196), resulting in the lowest resilience level (IR = 1). Nevertheless, this result should be interpreted with caution. Few existing roadway resilience-related literature have investigated the effects of seasons such as autumn on roadway resilience.

4.3. The Injury-Based Resilience Assessment Model

Finally, the injury-based resilience assessment model was obtained. Based on the model results shown in Table 4, we have the estimated value $\alpha$ in Formula (4), thus the probability of a crash resulting in an IR level being 1 can be given in Formula (9), in which the continuous variable $I{R_S}^{*}$ can be calculated using the model shown in Formula (10).

$$P\left(I{R}_S=1\left|x\right.\right)=F\left(x^{\mathbf{\prime }}\mathsf{\beta };\alpha \right)=1/{\left[1+\exp \left(-x^{\mathbf{\prime }}\mathsf{\beta }-\epsilon \right)\right]}^{1.528}$$

(9)

$$\begin{array}{ll}I{R}_S^{*}={\mathsf{\beta }}^{\mathbf{\prime }}x+\epsilon & =0.179x_{autumn}+0.373x_{weekend}+1.092x_{night}+0.767x_{rainy}+0.766x_{snowy}\\ & +0.632x_{entrance}+3.518x_{interior}-0.805x_{sl40}-0.858x_{sl60}-3.516x_{one}-6.460x_{two}\\ & -0.238x_{lightveh}-1.706x_{bus}+2.921x_{HGV}+3.025x_{two-wheel}+0.935\end{array}$$

(10)

Thus, the final assessment results of IR_s were confirmed using the piecewise function, as follows:

$$I{R}_S^{}=\left\{\begin{array}{ll}0& ifI{R_S}^{*}\in (-\infty ,0)\\ 1& ifI{R_S}^{*}\in [0,+\infty )\end{array}\right.$$

(11)

In terms of execution time under different scenarios, given that this study uses a static crash dataset, the IR assessment model proposed in this study is established beforehand. Once the assessment model, i.e., Formula (10) in this study, is achieved using an MLE method, for a given traffic crash, it would take millisecond-class execution time to output the IR assessment results under different scenarios.

4.4. Case Study on the Real-World Application

To demonstrate the application of the proposed IR assessment model, this section provides four different cases (i.e., cases #1–#4), as shown in

Table 5. Four cases used to demonstrate the real-world application of the proposed model.

Description of Indexes/Cases		Crash Case #1 (Min $\mathit{I}{{\mathit{R}}_{\mathit{S}}}^{*}$)	Crash Case #2 ( $\mathit{I}{{\mathit{R}}_{\mathit{S}}}^{*}$ < 0)	Crash Case #3 ( $\mathit{I}{{\mathit{R}}_{\mathit{S}}}^{*}$ > 0)	Crash Case #4 (Max $\mathit{I}{{\mathit{R}}_{\mathit{S}}}^{*}$)
No.	Indexes/Variables (Coefficients)	Description 1	Description 2	Description	Description 3
1	Autumn (+0.179)	0	0	0	1
2	Weekends (+0.373)	0	1	1	1
3	Night time (+1.092)	0	0	0	1
4	Rainy (+0.767)	0	0	0	1
5	Snowy (+0.766)	0	1	0	1 4
6	Entrance (+0.632)	0	1	0	0
7	Interior (+3.518)	0	0	1	1
8	Sl40 (−0.805)	0	0	0	0
9	Sl60 (−0.858)	1	0	0	0
10	One (−3.516)	0	0	0	0
11	Two (−6.460)	1	1	0	0
12	Light vehicles (−0.238)	1	1	0	0
13	Bus (−1.706)	1	0	0	0
14	HGV (2.921)	0	0	1	1
15	Two-wheeled vehicles (3.025)	0	0	0	1
constant		0.935
$\mathit{I}{{\mathit{R}}_{\mathit{S}}}^{*}$		−8.327	−3.992	7.7470	13.576
$\mathit{I}{{\mathit{R}}_{\mathit{S}}}^{*}$	$\mathit{I}{{\mathit{R}}_{\mathit{S}}}^{*}$ < 0, good $\mathit{I}{{\mathit{R}}_{\mathit{S}}}^{*}$ ≥ 0, bad	0	0	1	1
IR assessment results		good (best)	good	bad	bad (worst)
Managerial implications	This crash may result in_	no injury	no injury	injury	injury or even fatality
	The tunnel traffic_	could return to normal automatically and quickly	could return to normal automatically	can not return to normal automatically	would take a long time to return to normal
	Emergency contermeasures_	may be unnecessary	may be unnecessary	should be undertaken timely	must be undertaken timely

¹ A two-vehicle crash involving a passenger car and a bus happened at the exit of a 60 km/h tunnel in the daytime on a sunny workday in spring; ² A two-vehicle crash involving two passenger cars happened at the entrance of an 80 km/h tunnel in the daytime on a snowy weekend in summer; ³ A multi-vehicle crash involving at least one HGV and a two-wheeled vehicle happened in the interior of an 80 km/h tunnel on a rainy and snowy weekend night in autumn; ⁴ Assume herein that rain and snow could occur simultaneously to achieve a maximum $\mathit{I}{{\mathit{R}}_{\mathit{S}}}^{*}$.

. Of the four cases, #1 and #4 are two extreme cases with the minimum (best with −8.327) and the maximum (worst with 13.576) $I{R_S}^{*}$ in the model presented in Formula (10), respectively, while #1 and #3 are two moderate cases derived from the 8621 real-world data-cases used in estimating this model.

Taking case #3 as an example, case #3 indicates a multi-vehicle crash that involved only several HGVs that happened at the interior of an 80 km/h tunnel on a sunny weekend morning peak in winter, for which the binary codes of the descriptive variables are also presented in the fourth column of the table. The scenario descriptions of the other three cases could be interpreted in the same manner. According to the proposed IR assessment model, when a case #3-like crash happens, the value $I{R_S}^{*}$ could be calculated by the Formula (10) to be 7.7470 with an IR assessment level as bad, which is larger than 0 and leads to the $I{R}_S$ being 1. These results indicate that (1) the occurrence of crash #3 may result in injury; (2) the tunnel traffic cannot return to normal automatically; and (3) emergency countermeasures should be undertaken in a timely manner by the authorities. As shown in Table 5, the applications to the other (three) crash cases could be similarly interpreted.

5. Conclusions

Though the conceptions of traffic/safety resilience and injury resilience have been proposed by previous studies, both of them focus on the properties of the traffic itself avoiding crashes, and the sufferers’ physical recovery from a crash. There is a research gap in evaluating the resilience of the ongoing, post-crash traffic system using crash injury as a surrogate resilience measure (SRM). It is legitimate to assume that it will take a longer time and more resources for traffic to recover from a more severe crash with injury or fatality.

Therefore, this study innovatively proposed the novel conceptions, termed as SRM and interpret crash injury-based resilience (IR), from a new vision. To assess the resilience of traffic using injury severity as an SRM, crash data obtained from urban roadway tunnels of Shanghai were used to conduct this study. A total of 34 variables were selected to establish the IR assessment indicator system. Accounting for the skewness of the data, a skewed binary logit (Scobit) model was utilized together with a traditional logistic model. The results showed that the Scobit model is superior to the traditional one with a better interpretation of the data and higher assessment accuracy (91.08%). Of all the 34 variables, 15 were found to be statistically significant in predicting the IR levels. Nine variables including autumn, weekends, night time, rainy, snowy, entrance, interior, HGV, and two-wheeled vehicles were found to have a contributive effect to the lowest IR level (=1), while crashes related to the remaining six variables including speed limit 40 mph, 60 mph, single vehicle crashes, two-vehicle crashes, light vehicles, and bus were found to more likely result in a lower resilience level of the tunnel traffic system. Finally, according to the estimation results in the Scobit model, a quantitative resilience assessment model was proposed to measure the resilience of roadway tunnels in Shanghai.

This study proposed a new vision for scholars to assess the abstract resilience of the traffic system using traffic injury severity as a novel, more specific SRM. It also provided a special perspective for the administrator to better evaluate, manage, and promote the resilience of urban transportation systems. In terms of the limitations, the crash dataset regarding the roadway tunnels of Shanghai was a bit outdated, and the response variable (i.e., the injury severity levels) was restricted to two levels (no injury versus injury/fatality), which might not be elaborate enough for the delicacy management for modern Shanghai. In the future, based on the viewpoints and model proposed in this study, efforts could be made in the following two facets to improve the performance of the IR assessment model. On one hand, given the rapid development of urban transportation infrastructure and information techniques, utilizing more recent, real-time traffic data is more and more important to establish a high-performance resilience assessment model. For example, with the aid of the 5G technique, transmitting real-time traffic (crash) data to the City Brain is being achieved. On the other hand, except for the crash injury severities, accounting for more resilience-related factors to assess the resilience of the transportation system is a promising research direction. For example, both the decreasing roadway capacities and the time duration from a disruption’s (e.g., a traffic collision) occurrence to returning to normality are promising alternatives for SRMs.