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Keywords:

  • Hazardous materials;
  • modal safety;
  • rail transport;
  • risk assessment;
  • truck transport

Abstract

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. LITERATURE REVIEW
  5. 3. EC FRAMEWORK
  6. 4. COMPUTATIONAL EXPERIMENTS
  7. 5. CONCLUSION
  8. ACKNOWLEDGMENTS
  9. Appendix
  10. REFERENCES

A significant majority of hazardous materials (hazmat) shipments are moved via the highway and railroad networks, wherein the latter mode is generally preferred for long distances. Although the characteristics of highway transportation make trucks the most dominant surface transportation mode, should it be preferred for hazmat whose accidental release can cause catastrophic consequences? We answer this question by first developing a novel and comprehensive assessment methodology—which incorporates the sequence of events leading to hazmat release from the derailed railcars and the resulting consequence—to measure rail transport risk, and second making use of the proposed assessment methodology to analyze hazmat transport risk resulting from meeting the demand for chlorine and ammonia in six distinct corridors in North America. We demonstrate that rail transport will reduce risk, irrespective of the risk measure and the transport corridor, and that every attempt must be made to use railroads to transport these shipments.

1. INTRODUCTION

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. LITERATURE REVIEW
  5. 3. EC FRAMEWORK
  6. 4. COMPUTATIONAL EXPERIMENTS
  7. 5. CONCLUSION
  8. ACKNOWLEDGMENTS
  9. Appendix
  10. REFERENCES

Hazardous materials (hazmat) are harmful to humans and the environment because of their toxic ingredients, but their transportation is  essential to sustain our industrial lifestyle. A significant majority of hazmat shipments are moved via the highway and railroad networks. In Canada, for example, 94% of hazmat shipments are moved by trucks and trains, and the amounts shipped via the two modes are 83 million tons and 29 million tons, respectively.[1] On the other hand, in the United States, around 130 million tons of hazmat were moved by railroads in 2007, whereas trucks accounted for around 1.2 billion tons over the same period.[2] It may appear that railroads are not the predominant mode for surface transportation of hazmat (i.e., 5% of rail freight in the United States), but they are almost always preferred to move shipments over long distances. In fact, railroads account for around 29% of hazmat movement in ton-miles compared to 32.2% for trucks, which in turn translated into a 27.9% increase from 2002.

The characteristics associated with highway transportation—such as flexibility, accessibility, reliability, etc.—render it preferable to railroads, especially when shipments do not have to be moved over long distances. Although an analysis of the historical incident record in the United States[2] reveals that trucks account for a major proportion of the hazmat incidents (Fig. 1), a definitive statement regarding modal safety requires much more than a simple extrapolation from such statistics. This is because modal choice decision, especially for hazmat shipments, necessitates appropriate consideration of the associated catastrophic consequences. The question of modal safety has been investigated over the past two decades, where the early studies provided recommendations with conditions, and the most recent studies have concluded in favor of railroads. Although we will critically review all the relevant studies in the next section, we note that all these studies made use of either a single origin-destination (OD) pair or a single hazmat for modal comparison—and hence the resulting insights could not be generalized. Moreover, none of the studies considered either the accident characteristics of both transportation modes in the determination of hazmat risk, or explicitly incorporated the impact of hazmat volume when commenting on their relative safety. It should be evident that for an accurate estimation of hazmat transport risk, it is important to account for the nature of accidents for the respective mode. For example, a freight train can carry a number of hazmat railcars, one or more of which could derail and release following a train accident. On the other hand, a hazmat truck constitutes a single source of release.

image

Figure 1. Percentage of total incidents.

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Fortunately risk assessment methodology for highway shipments is well developed, but railroads—until recently—had not received commensurate attention from academic researchers. All the works, including the ones used for modal comparisons that we review in the next section, have been rather straightforward extensions of road risk models, and hence have ignored the differentiating features of railroads. In an effort to close this gap, we first develop a comprehensive risk assessment model that captures the characteristics of railroads in moving hazmat shipments. More precisely, the expected consequence (EC) methodology takes into consideration the probability of train derailment, the conditional derailment and release probability for every position in the train, and the resulting undesirable consequence. Second, to develop generalizable results, the proposed methodology is applied to study hazmat risk, from transporting chlorine and ammonia, in six different transportation corridors in North America. Finally, in identifying the safer mode of transport for the two given hazmat, we also report results using the two other popular measures of transport risk: incident probability and population exposure. Recently, realistic models based on these measures were developed for railroads.

The remainder of the article is organized as follows: Section 'LITERATURE REVIEW' provides a detailed literature review of the pertinent works, and the EC model is developed in Section 'EC FRAMEWORK' Section 'COMPUTATIONAL EXPERIMENTS' outlines the various problem instances used in computational experiments, followed by the solution, analysis, and discussion on limitations. Finally, conclusions and directions of future research are outlined in Section 'CONCLUSION'.

2. LITERATURE REVIEW

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. LITERATURE REVIEW
  5. 3. EC FRAMEWORK
  6. 4. COMPUTATIONAL EXPERIMENTS
  7. 5. CONCLUSION
  8. ACKNOWLEDGMENTS
  9. Appendix
  10. REFERENCES

For expositional reasons and also to position this work in the context of the existing literature, this section is divided into two parts: the first part will introduce the three most popular measures of hazmat transport risk, and then briefly review the works done in the highway and the railroad domains; and the second will critically evaluate the works comparing the two transportation modes for hazmat shipments.

2.1. Three Measures of Risk

Risk is most commonly defined as the product of the probability and the consequence of an undesirable event.[3] This EC approach has been used in a number of works to mostly evaluate risk from highway transport of hazmat and that from fixed facilities.[4-6] Although this approach is simple to use and to justify, absence of detailed data on probability and/or consequence necessitated the development of alternate risk measures. To that end, the first group of researchers focused only on the probability of a hazmat incident, and proposed incident probability as the measure of hazmat transport risk. Since this measure does not include consequence, it is appropriate for hazmat with relatively small danger zones.[7, 8] Concurrently, the second stream of researchers was focusing on just consequence, and more specifically on the total number of people exposed to the possibility of an undesirable consequence due to a hazmat shipment (i.e., population exposure). These researchers contended that population exposure constituted a worst-case approach to transport risk, and hence would be particularly suitable for assessing risk as perceived by the public, as well as for estimating required emergency response capability.[9, 10] Since trucks move the majority of hazmat shipments in North America, it is not surprising that the majority of research has been carried out in the highway domain, including the development of the three risk measures outlined above.[11] On the other hand, most of the research initiatives in the railroad domain, until recently, were driven by the industry, and mainly dealt with analyzing past accident data in an effort to increase safety by improving rail tracks or railcar tank designs.[12] Fortunately, the past few years have witnessed a tremendous increase in the number of academic initiatives associated with rail hazmat shipments. Although we review the works involving both the application and the development of the three risk measures for rail hazmat shipments next, we refer the reader to Ref. 13 for all other relevant works.

One of the earliest applications of incident probability within the railroad domain focused on reducing the probability of a hazmat railcar getting involved in a train derailment,[14] and suggested that the front of the train was more prone to derailment under loaded conditions, and hence hazmat railcars should be placed in the rear of the train. A later study commissioned by the Federal Railroad Administration (FRA) and the Department of Transportation (DOT) concluded that derailment probabilities are highest in the first and lowest in the fourth quarter of the train.[15] Most recently, Bagheri et al.[16] made use of the incident probability approach to motivate additional marshalling operations at yards as a way to reduce hazmat transport risk along predefined corridors, and used a binary indicator variable to model undesirable consequence. The proposed approach was subsequently augmented to outline a placement strategy for hazmat railcars.[17] Finally, Verma and Verter[18] developed a population-exposure-based risk assessment methodology for hazmat rail shipments, where the Gaussian dispersion plume model was used to capture the impact of volume in the determination of transport risk.

To the best of our knowledge, Ref. 12 is the only published work that deals with the development of an EC approach specifically for hazmat rail shipments. An EC approach that incorporated hazmat release from multiple sources, and made use of the FRA database to determine conditional derailment probabilities for the 10 deciles (i.e., 10 equal parts) along the train length, was proposed. For example, for a 100-railcar train, the conditional derailment and release probability for the 81st and 89th railcars were identical, since both belonged to the 9th train-decile. Note that since the proposed approach was driven by the FRA data set, not much attention was paid to position-specific derailment probabilities for every railcar slot in the train, nor to the initial point of derailment. It is important that Bagheri et al.[16] is not included in this category since the proposed approach made use of a simple binary indicator variable to ascertain whether the derailed slot contained a hazmat railcar, and did not contain any explicit term to capture consequence. Furthermore, all the works using F–N curves—which we review in the context of mode comparison—adapted the existing EC approach to study transport risk from trucks and railcars. This is crucial since ignoring the impact of hazmat volume implies that one is assuming identical consequence from a truck tanker and a rail tanker, when in fact the latter carries roughly three times more in volume. Hence, in an effort to fill this gap and also to carry out a more accurate study of transport risk for rail hazmat shipments, we develop an assessment methodology that takes into consideration the derailment probability of every position in the train, the initial point of derailment, the number of railcars derailed, and the resulting consequence from multiple sources.

2.2. Mode Comparison

The question involving the relative safety of road hazmat shipments vis-à-vis rail has been investigated over the past 20 years, primarily in Europe—though without consensus. Saccomanno et al.[19] was the first study in this direction, but it could only provide conclusion with qualification. The authors pointed out that differing volumes complicated comparison, and showed that the safer mode varied with the hazmat being shipped. In a more detailed work, Purdy[20] studied chlorine transportation between two locations (100 km apart) in England, by road and rail. The author made use of the 80 spill cases for rail and 25 for road to estimate the spill frequency, and a dense gas dispersion model to simulate consequences. Although the article recommended road for hazmat with large impact areas and rail for other types of hazmat, the author admitted that the result was largely specific to Great Britain and that one could expect different results for other settings. The indicated recommendations were analogous to those arrived by Glickman,[21] who concluded that accident rate for significant spills (when release quantities exceed five gallons) was higher for for-hire truck tankers compared to rail tank cars, where the latter were more prone to small spills. Unfortunately, the discussion surrounding modal safety got further clouded with the findings of Leeming and Saccomanno.[22] They too looked at the road and rail transportation options for chlorine shipments to a major industrial handling facility in England, and concluded that risk from using the two modes was not significantly different, although rail shipments posed more risk to the residents around the facility. Around the same time, Kornhauser et al.[23] studied a case involving anhydrous ammonia shipments to DuPont's facility in Mississippi (United States). The authors made use of a linear adjustment factor to handle the difference in shipment volume for the two modes, and concluded that railroad was a safer option than road.

Finally, a number of studies focused on hazmat shipments in and around Sicily (Italy) have been undertaken over the past few years. The first study[24] presented a quantitative risk analysis approach for hazmat transportation, wherein risk mainly depended on the hazardous characteristics of the product. On the basis of data for Italy, the author made the case for moving some transport activity from road to rail, since the latter had lower accident rates, and contended that the impact areas would be larger for rail to account for volume. Subsequently, a set of three related projects was completed by the same team of researchers in Italy. In the first study, Bubbico et al.[25] selected a few average values of the pertinent parameters, from a product database containing the impact areas for a number of predefined accident scenarios, to propose a simplified approach for risk analysis for road and rail transportation of hazmat. The authors divided the pertinent factors into route-independent and route-dependent categories, and considered only two release scenarios, that is, medium and severe. Finally, although the authors were able to get hold of reasonably good data for different road types in Italy, absence of equivalent data for railroads forced them to assume a single value for the whole network. The outlined technique was applied to study risk stemming from transporting ethylene oxide from Priolo to Messina (Italy), and to conclude that the total risk from using road transport was much higher than that from rail transport. The second study[26] looked at the transportation of ammonia from an installation located near Priolo to another located near Gela (Italy). In an effort to take into account both the on- and off-route population density, buffers were created on both sides of the road and rail network at 150 m and 1,500 m, and the conclusion was in favor of railroads. The most recent work, Bubbico et al.,[27] made use of three classes of hazmat to show that risk mitigation was possible by not just changing the route but also by using a different transportation mode. The authors made use of the product database indicated earlier and the geographic information system application developed in an earlier work to determine the F–N curves (i.e., societal risk) for a total of 51 road and 4 rail cases. Given the absence of a real alternative to road for some OD pairs, the resulting analysis suggested that it was worthwhile to move some hazmat from road to rail or intermodal modalities to reduce risk.

It is important to note that all these works were useful effort in the modal safety realm, although their insights could not be generalized for a variety of reasons. First, almost all the studies looked at either a single OD pair or a single hazmat, and hence were not sufficient to make general deductions. Second, the train accident rate data were not detailed enough to have an impact on the analysis. Third, the accident rate determination for each mode should capture the relevant accident characteristics. For example, a train can carry multiple hazmat railcars, and the conditional derailment and the release probability of each railcar is different because of varying kinetic forces. Finally, but as importantly, none of the reviewed works take into account the impact of hazmat volume in consequence analysis. This is significant since the consequence resulting from a single hazmat railcar is not the same as that from a truck tanker, and this becomes even more crucial when considering a train with multiple hazmat railcars, and when a single network accident rate is used in the analysis.

Hence, to close the indicated gap and also to build general observations, we first develop the comprehensive risk assessment methodology, and then apply it to study transport risk from shipping chlorine and ammonia in six distinct transportation corridors in North America. These two chemicals (both class 2 hazmat) are toxic by inhalation and jointly account for around 70% of the total transportation-related risks associated with this group of chemicals in North America.

3. EC FRAMEWORK

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. LITERATURE REVIEW
  5. 3. EC FRAMEWORK
  6. 4. COMPUTATIONAL EXPERIMENTS
  7. 5. CONCLUSION
  8. ACKNOWLEDGMENTS
  9. Appendix
  10. REFERENCES

In this section, we first develop a novel EC methodology for assessing transport risk from rail hazmat shipments, and then outline the parameter estimation technique.

3.1. Risk Assessment Methodology

As indicated earlier, the proposed EC framework takes into consideration both the sequence of events leading to hazmat release from derailed railcars, and also the associated consequence from multiple sources of release. To make this explicit, consider a rail segment l and a hazmat railcar that is in the ith position along the train length. Transport risk stemming from the ith hazmat railcar on rail segment l can be defined as the product of the derailment probability for position i, inline image, and consequence, inline image:

  • display math(1)

where the probability of derailment for position i can be calculated as the product of the probability of train derailment on segment l, that is, inline image, and the conditional probability that position i is the point where derailment starts (POD) given that the train has derailed, that is, inline image. Note that the proposed framework focuses on railcars after the point of derailment in the computation of risk,

  • display math(2)

and the consequence of derailment can be calculated as the product of the conditional probabilities that m railcars derail as a result of derailment beginning at position i on the given rail segment, that is, inline image and j hazmat railcars among the m derailed will release, that is, inline image together with the population exposure associated with j railcars, inline image:

  • display math(3)

where n is the number of railcars after the point of derailment. Substituting Equations (2) and (3) in Equation (1), and summing over all the rail segments of a route R, the complete expression for determining transport risk is:

  • display math(4)

3.2. Parameter Estimation

In this section, we will discuss the techniques to calculate and/or estimate various components in Equation (4).

3.2.1. Train Derailment

Probability of train derailment is calculated using the model proposed in Anderson and Barkan,[28] which was developed using the FRA accident data. It was concluded that derailment probability on segment l, which is a function of travel distance, train length, and track quality, can be calculated as:

  • display math(5)

where inline image is the length of segment l, inline image is the length of the train on segment l, inline image is the derailment rate per billion freight carmiles, and inline image is the derailment rate per million freight trainmiles. On the basis of aggregate data from 1992 to 2001, the derailment rate for different types of tracks was estimated (Table I).[28]

Table I. Derailment Rates
 FRA Track Class
Derailments per12345 and 6
Million freight train miles48.56.12.00.50.3
Billion freight car miles720.192.731.57.84.9
3.2.2. Point of Derailment

A railcar can be involved in a derailment either by initiating a derailment or by being a part of the derailed block. Thus, in estimating the probability of derailment by position, two factors need to be considered: (1) point at which derailment begins (POD) and (2) number of cars derailing beyond the POD. Bagheri et al.[16] grouped derailment causes into three classes depending on the part of the train likely to derail first; more specifically, causes that affect the front of the train (CF), the rear of the train (CR), and the middle of the train (CM). In addition, trains were categorized into three types: short (up to 40 railcars); medium (between 41 railcars and 120 railcars), and long (more than 120 railcars). The authors then developed the best fit POD distributions for all nine length-cause combinations, and illustrated the use of fuzzy functions to account for uncertainty caused by overlap in train length at the boundaries (i.e., around 40 railcars and 120 railcars). Fig. 2, adapted from Bagheri et al.,[16] can be used to determine the two types of trains under consideration and the appropriate weights. For exposition purposes, we just provide a small illustrative instance, and refer the reader to Ref. 16 for complete details.

image

Figure 2. Weights for the train types.

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For example, for a 41-railcar train over a rail segment subject to cause CM, the respective weights are M1 = 0.68 for a short-train classification, and M2 = 0.32 for a medium-train classification. Now the probability of derailment for the 10th position with cause CM is obtained by (i) determining the weights for relevant train lengths (i.e., M1 and M2 estimated above); (ii) computing the normalized point of derailment, which for this example is 10/41 = 0.244; and (iii) obtaining the derailment probabilities for the position of interest by using the best-fit POD distributions table from Ref. 16, which for i = 10 are 0.033 and 0.07. Substituting the above numbers into the derailment equation for the given train segment will yield inline image

3.2.3. Number of Railcars Derailed

The number of railcars derailing is affected by the dissipation of kinetic energy following a train derailment, which implies that train speed and distance from the POD are important elements.[29] Note that the latter point is relevant because as the distance to the POD increases, forces of instability acting on the remaining railcars decrease. Given that risk is posed by a derailed hazmat railcar, all hazmat railcars placed before the POD or beyond the derailed block do not pose any risk on the given rail segment. Saccomanno and El-Hage[30] studied this problem and proposed the following truncated geometric expression to estimate the probability of m railcars derailing given that derailment started at position i:

  • display math(6)

where m = 1,2,…n, and n is the number of railcars in the train beyond the POD, while (1 − p) and p are the probabilities of derailment and no derailment, respectively, for a position beyond the point of derailment.

3.2.4. Number of Derailed Railcars Releasing

Although we estimate the parameters discussed so far using the available models from the existing literature, in an effort to take advantage of the empirical data set, we estimate the conditional probability of j railcars releasing from the FRA data set. To that end, and as evident from Equation (4), we assume that the conditional probability of release from a derailed hazmat railcar (q) is independent of each other, such that:

  • display math(7)

According to the FRA database (1997–2006), the conditional probability of release from a derailed hazmat railcar is 0.0903, obtained by dividing the total number of railcars releasing by the total number of hazmat railcars derailed.

3.2.5. Population Exposure

The last term in Equation (4) is the population exposure. In this article, we focus on chlorine and ammonia shipments, both of which can become airborne in the event of an accidental release. In such cases, the resulting plume can travel long distances due to wind and expose large areas to health and environmental risks. Spatial distribution of the toxic concentration level is estimated using three tools: the Gaussian dispersion air-plume model (GPM); ArcView geographic information system (GIS); and areal locations of hazardous atmosphere (ALOHA).

GPM is used to approximately capture the airborne characteristics of both chlorine and ammonia, and was chosen over other dispersion models because it can produce outputs very quickly,[31] and has been used to model consequence from hazmat rail shipments.[18] We used the methodology outlined in the literature[18] by first adopting GPM for a single source of release, and then extending the model to represent hazmat rail shipments—which would involve multiple sources of release. We use immediately dangerous to life and health (IDLH) concentration levels for both chlorine and ammonia in determining the threshold distances for exposure.[32] For example, the short-term exposure limit (i.e., threshold value) for ammonia is 35 ppm, and 10 ppm for chlorine. In estimating the population exposure, we adopt the worst-case approach by assuming least favorable weather conditions, and refer the reader to Arya[33] for all relevant details. To make this explicit, consider that w hazmat railcars are traveling on segment l. Hence, the aggregate concentration level at downwind distance z (since they contain the maximum concentration at any distance from the source)[33] can be calculated as:

  • display math(8)

where Q is the release rate from the ruptured container; u is the wind speed; a, b, c, and d are atmospheric constants; and z is the downwind distance from the hazmat median of the train. For a given IDLH for a hazmat, inline image, Equation (8) will yield the expression for threat zone (or threshold distance), which is:

  • display math(9)

The movement of the danger circle, of radius inline image, along rail segment l will carve out a band, and the number of people within the band is the resulting population exposure. We make use of avenue programming in ArcView GIS environment[34] to estimate the number of people exposed along every segment for the given road and rail network. We refer the reader to Ref. 18 for complete methodological details, and the existing literature for applications of the methodology to realistic size problem instances.[35, 36]

Finally, we make use of ALOHA to efficiently estimate the release rate in Equation (8). ALOHA, a modeling program made available through the Environmental Protection Agency, estimates the threat zones associated with hazardous chemical releases, including toxic gas clouds, fires, and explosions.[37] The computer program, based on both Gaussian plume and dense gas dispersion models, makes use of a set of inputs regarding weather and topographical conditions, container volume, and rupture characteristics to estimate threat zones. It should be evident that since the input parameters will be different for various segments (or transportation corridors), one should expect dissimilar threat zones even when the release volumes are the same. For our problem instances, a conservative rupture diameter of 4 inches was assumed that resulted in the loss of an entire tank car lading within seven minutes, which was considerably less than the anticipated emergency response times. An identical loss scenario was simulated for every hazmat railcar, leading to the determination of aggregate contaminant level in Equation (8), and the threat zone in Equation (9). Finally, information about the threat zone (or threshold distance) for a release scenario on a specific segment was fed into ArcView GIS, both to generate the exposure band and to estimate the number of individuals exposed.

4. COMPUTATIONAL EXPERIMENTS

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. LITERATURE REVIEW
  5. 3. EC FRAMEWORK
  6. 4. COMPUTATIONAL EXPERIMENTS
  7. 5. CONCLUSION
  8. ACKNOWLEDGMENTS
  9. Appendix
  10. REFERENCES

This section is organized under four subsections. The first outlines the details of the different problem instances, which are then solved and analyzed in the following two subsections. Finally, we comment on the limitations of the proposed approach.

4.1. Experimental Setting

In an effort to make general deductions, the EC methodology developed in Section 'EC FRAMEWORK' was applied to study transport risk resulting from road and rail shipments of chlorine and ammonia, which together account for around 70% of the transportation-related risks from toxic by inhalation (TIH) hazmat in North America. A total of 36 problem instances were generated using the North American Free Trade Area (NAFTA) transportation corridor,[38] as depicted in Fig. 3. It was important that not only the relevant transportation infrastructure for both modes existed between each OD pair, but also that the routes presented varying geographical and geometric attributes. To that end, we were able to identify six distinct transportation corridors from Fig. 3, and their attributes for the two transportation modes are listed in Tables II and III. For expositional purposes, we introduce labels for each corridor. For example, the corridor from Chicago to Memphis (shaded) will be referred to as Corridor C.

Table II. Railroad Attributes for the Six Corridors
SegmentsLength (Miles)Track ClassMax Speed (mph)
A: Montreal–Albany–New York
First240460
Second141580
B: Vancouver–Seattle–Portland–Eugene
First157460
Second187580
Third123580
C: Chicago–Carbondale–Memphis
First309580
Second219460
D: Portland–Sacramento
First647460
E: Chicago–St. Louis–Little Rock–Dallas
First284580
Second490580
Third217460
F: Sunset Limited: Los Angeles–Yuma
First251460
image

Figure 3. Corridors with road and rail network.

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On each corridor, the problem instances entail shipping 3 million gallons of (i) chlorine and (ii) ammonia. For each hazmat, the decisionmaker can either use 9,000-gallon truck tankers,[39] or 30,000-gallon rail tank cars.[40] This implies that a total of 100 rail tank cars or approximately 333 truck tankers would be needed to meet the demand for each hazmat. It is important to note that any shipment cannot be split between the two modes. Finally, the decisionmaker has the choice of three different types of trains: (i) 10 trains each with 10 hazmat railcars, (ii) four trains each with 25 hazmat railcars, and (iii) a single hazmat-unittrain with 100 hazmat railcars, which will leave the origin yard for the destination yard with the entire hazmat cargo and not make any intermediate stops. It should be clear that 36 problem instances, for each transportation mode, would have to be solved to make general deductions and gain robust managerial insights.

Next, we list the pertinent features collected using publicly available information and published peer-reviewed works. Table II lists the route attributes for railroad for the six corridors. As outlined in Section 'Train Derailment', derailment probabilities for different segments require information on length and track class. For example, Corridor A that runs between Montreal and New York consists of two rail segments, each of which has a distinct track class with a specified maximum speed limit. It should be clear from Table II that the derailment probability will be unique for each segment lengthtrack class combination, which in turn will have a bearing on transport risk.

Table III lists the highway attributes for the six corridors including classifying road segments based on whether they are interstate or regular highways, since each has distinctive features. The last two columns indicate the accident rate and conditional release probabilities associated with hazmat shipments on the highways. These values, reported by Harwood et al.,[41] are the weighted average of data from three states (California, Illinois, and Michigan) in the United States. To the best of our knowledge, there has not been any subsequent work in this domain, and hence we use the numbers proposed in Ref. 41.

Table III. Highway Attributes for the Six Corridors
     Conditional Release
Corridors (Segments)Length (Miles)Road ClassRoad TypeAccident Rate/MileProbability
Note
  1. I refers to interstate, and A to autoroute. L refers to limited access, and M to multilane divided.

A: Montreal–Albany–New York
First36.22A-15L0.640 × 10−60.090
Second333.49I-87M0.215 × 10−50.082
B: Vancouver–Seattle–Portland–Eugene
First423I-5M0.215 × 10−50.082
C: Chicago–Carbondale–Memphis
First532I-55, I-57M0.215 × 10−50.082
D: Portland–Sacramento
First580I-5M0.215 × 10−50.082
E: Chicago–St. Louis–Little Rock–Dallas
First1,003I-55, I-44, I-35M0.215 × 10−50.082
F: Sunset Limited: Los Angeles–Yuma
First327I-5, I-8M0.215 × 10−50.082

4.2. Solution

In this subsection, we will discuss the solution for the various problem instances. For expositional reasons, we have organized the subsection into two parts: the first contains the discussion for rail, while the second will focus on road. Furthermore, in an effort to ensure the flow of text, we have chosen to place most of the details pertaining to calculations in the Appendix, but will refer to them in the text.

4.2.1. Rail Transportation

Table IV depicts the EC values for the 36 problem instances (i.e., six on each transportation corridor), when rail was the mode of transportation. As indicated earlier, three different types of train make-up options have been considered. For example, the first option entailed using 10 trains each of which carried 10 hazmat railcars to meet the demand, whereas the third scenario implied using a hazmat-unittrain. We next provide the details associated with determining the EC on the first track segment in Corridor A (i.e., italicized), which runs from Montreal to Albany, and note that other risk numbers could be determined similarly.

Table IV. Expected Consequence for Rail
 Train Type
 ChlorineAmmonia
Corridors1st2nd3rd1st2nd3rd
A3.591.49 + 0.561.220.790.460.28
B5.513.081.751.120.620.36
C9.725.393.031.971.090.62
D10.105.843.592.051.180.73
E14.217.814.322.881.580.88
F1.500.870.530.300.180.11
4.2.1.1. Derailment probability for position i

Probability of train derailment, inline image, on the first track segment in Corridor A (Table II) was determined using the technique outlined in Section 'Train Derailment' On the basis of the existing literature,[29] we assumed that approximately 25% of all derailments can be classified as train-mile caused, and the remaining as car-mile caused. We also know from Table II that the length of this segment is 240 miles, and that it belongs to track class 4. The latter lets us estimate RC and RT from Table I. Finally, we assume a 100-railcar train, and replace the various terms in Equation (5) with the respective parameters to get 0.000172 as the probability of train derailment on this segment.

Probability of point of derailment starting at position i, inline image, is estimated using the best-fit distributions from Bagheri et al.,[17] and, as outlined in Section 'Point of Derailment', Fig. 4 depicts the resulting point of derailment probabilities for each of the 100 railcar positions for the track section between Montreal and Albany, and their exact values are indicated in Table AI. For example, the probability that point of derailment starts at the very first position is 0.0432, which together with the train derailment probability is fed into Equation (4) to determine the probability of derailment of the first slot in the train, that is, inline image.

image

Figure 4. inline image for the first segment of Corridor A.

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It is clear from Fig. 4 (and Table AI) that the third quarter of the train has the lowest derailment probabilities, and hence may be the safest position to place the hazmat railcars. Note that this observation is consistent with another work in the area,[12] and hence we choose this train-quarter to place the hazmat railcars under the first and the second make-up plans. More specifically, for a 100-railcar train, hazmat railcars would be placed starting at the 51st slot and until the 75th under the second plan, and until the 60th under the first. This implies that for the problem instance being analyzed, all the 25 hazmat railcars are placed in the third quarter of the train, while the other slots contain regular freight.

4.2.1.2. Consequence for position i

Recall that consequence associated with any position in a train would require information on conditional probability of derailment of hazmat railcars, conditional probability of derailed hazmat railcars releasing, and the population exposure associated with the number of railcars releasing. We next outline the computation of each term for the problem instance being analyzed. For expositional reasons, we focus on the computation for the first slot in the train, and note that values for other slots can be determined similarly.

Probability that a given number of railcars will derail given that the derailment started at the first position (i.e., inline image) was estimated using the technique proposed in Saccomanno and El-Hage,[30] and outlined in Section 'Number of Railcars Derailed' Fig. 5 depicts the respective probabilities for a given number of railcars derailing when derailment starts at the first position of the train, and the values range from a high of 0.0292 to a low of 0.0017 (Table AII). Note that there is no hazmat risk if less than 51 railcars derail—since hazmat railcars are in the 51st through the 75th slots. On the other hand, hazmat risk will accrue if the number of railcars derailed exceeds 50, and that all the hazmat railcars will pose a risk if inline image. Furthermore, and as highlighted in Table AII, the probability that the first hazmat railcar will derail is 0.0071—which is the probability that m = 51—whereas the probability of all hazmat railcars derailing is 0.0036 or less.

image

Figure 5. inline image for the first segment of Corridor A.

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As indicated in Section 'Number of Derailed Railcars Releasing', we intend to take advantage of the FRA database containing the rail accident records from 1997 to 2006. Hence, we assume a conditional release probability of 0.0903 given that a hazmat railcar has derailed. Furthermore, given that the conditional release probability from each hazmat railcar is independent of each other, the probability that j = 2 is 0.008649 (i.e., 0.0903 × 0.0903), and so on for other values of j.

Population exposure was estimated using the technique outlined in Section 'Population Exposure' To that end, two pieces of information were required, that is, the number of hazmat railcars releasing, and the quantity of hazmat released from each railcar. The first issue was addressed by building scenarios where the number of railcars releasing ranged from the minimum to the maximum possible value for the given setting. For example, for the problem instance being analyzed, j will range from 1 to 25—since each derailed hazmat may or may not release. The second element was estimated based on the existing literature that specified loss of entire lading within 10 minutes, which was less than the anticipated response time for emergency service providers.[12] Given the response time, this assumption is reasonable since it is not possible to contain (or stop) hazmat release from ruptured containers in less than 10 minutes. For each value j can assume, the atmospheric parameters—likely to result in the worst case scenario—were fed into ALOHA to generate the release rate from the ruptured hazmat containers, followed by the substitution of resulting values into Equation (8) for aggregate concentration level estimation. The IDLH level for chlorine (i.e., 10 ppm), as specified by the Centers for Disease Control and Prevention,[32] was used to estimate the threat zone (or evacuation distance) using Equation (9)—which in turn was used in ArcView GIS to generate exposure bands around the transport segment. Finally, avenue programming in ArcView GIS was used to estimate the number of people inside the band, which is the value of population exposure for the given number of hazmat railcars releasing. For example, 50,801 individuals were exposed along the track segment from Montreal to Albany if one railcar containing chlorine released, while 84,278 if two railcars released. Table AIII reports the conditional release probabilities and population exposure numbers for all possible values j can assume on this track segment.

As indicated earlier, and given that the derailment starts at the first train slot, at least 51 railcars have to derail to pose any hazmat risk. For this setting, Table AIII lists the conditional probabilities of inline image, conditional probabilities that inline image, population exposure, and the consequence associated with each j. For instance, the conditional probability that 51 railcars would derail is 0.0072; the conditional probability of release from the only derailed hazmat railcar is 0.0903, which in turn will expose 50, 801 individuals along this segment. Hence, inline image=inline image inline image, and associated consequence is inline image On the other hand, if 52 railcars derail then both hazmat railcars pose a risk—and hence one needs to take this additional situation into consideration. To that end, the conditional probability of release (i.e., 0.008649) and the associated population exposure from two hazmat railcars (84, 278) would also be used, which will yield a consequence value of inline image Similarly, we can compute the consequence associated with each position in the train given that derailment started at the first train slot, and the resulting value is inline image (Table AIII). As evident in Table AIII, the total consequence was determined by summing over possible values of j. Note that although the fourth train-quarter does not contain any hazmat railcars, transport risk would still accrue if the number of railcars derailed is more than 75—because such a derailment would involve all the hazmat railcars placed in the third train-quarter.

For the track segment between Montreal and Albany in Corridor A, the EC risk associated with the first train slot is inline image. Similarly, EC risk for all other slots can be computed, and they are listed in Table AIV. For the second train make-up plan, the EC risk from a single train is 0.3716. Since four trains of this type are needed to meet the demand, the EC risk from the second train make-up plan is inline image (i.e., boldfaced in Table IV). The proposed assessment approach was used similarly to estimate the equivalent for the second segment of Corridor A (i.e., from Albany to New York), and also the other values in Table IV.

4.2.1.3. Other risk measures

In the interest of providing general conclusions, we also report results using two other most popular measures of hazmat transport risk. Table V depicts the solutions for the 36 problem instances when population exposure was the measure of risk, wherein the assessment methodology as proposed in Verma and Verter[18] was followed. For instance, around 34.8 million people would be exposed in Corridor A, if the second train make-up plan would be used to meet the demand for chlorine. It is important to note that, for any given corridor, population exposure risk is the highest under the first train make-up plan and the lowest under the third. This is resulting from the nonlinearity of the aggregate concentration curve (i.e., Equations (8) and (9)), and favors sending fewer but larger over more frequent but smaller hazmat loads. On the other hand, results using the incident probability approach as proposed in Bagheri et al.[17] are reported in Table VI, which for the corridor in question was 1.15 × 10−4. Since consequence is being captured using a simple binary variable, there is a single value for each train make-up plan for both chlorine and ammonia. Furthermore, the incident probability risk for a single train is the lowest for the first train make-up plan, since fewer number of hazmat railcars in a train imply fewer sources of risk—and there are no nonlinear curves to be exploited.

Table V. Population Exposure for Rail
 Train Type
 ChlorineAmmonia
Corridors1st2nd3rd1st2nd3rd
A45,701,83034,838,45222,713,9499,270,1487,066,6234,607,292
B8,781,3616,694,0214,364,3631,781,2091,357,814885,266
C11,687,8088,909,6025,808,8762,370,7521,807,2221,178,271
D8,291,2606,320,4184,120,7821,681,7971,282,032835,858
E12,790,0339,749,8286,356,6862,594,3271,977,6531,289,389
F3,260,2372,485,2751,620,348661,306504,113328,671
Table VI. Incident Probability for Rail
 Train Type
Corridors1st2nd3rd
A0.46 × 10−41.15 × 10−43.95 × 10−4
B0.53 × 10−41.31 × 10−44.44 × 10−4
C0.61 × 10−41.51 × 10−45.15 × 10−4
D0.85 × 10−42.11 × 10−47.40 × 10−4
E1.13 × 10−42.80 × 10−49.49 × 10−4
F0.33 × 10−40.81 × 10−42.87 × 10−4
4.2.2. Road Transportation

Equivalent values, using the three measures of risk, for road transportation of both chlorine and ammonia in the six corridors are depicted in Table VII. Note that these values are just for a single truck. For example, each truck departing Montreal for New York with 9,000 gallons of chlorine poses an EC risk of 0.57, which was determined as follows. There are two road segments in Corridor A (Table III), with Albany as the junction between the two. A danger circle corresponding to the IDLH level for chlorine was drawn at Albany, which resulted in an exposure of 9,316 people. Hence, using the values specified in Table III, the EC risk for the first segment is inline image. Similarly, EC risk for the second segment is 0.5477, which would add up to 0.57. Assuming that 333 identical trucks would be used to meet the demand, the total transport risk for Corridor A will be 188.89. Results from the other two measures could be interpreted as outlined in Section 'Other risk measures' Finally, for the same volume, transportation risk for chlorine is higher than that for ammonia, which in most part is because of the lower threshold level of the former (i.e., 10 ppm vs. 35 ppm). It is reasonable to expect that the lower exposure limit would entail exposure of further away population centers to airborne chlorine contaminants, which in turn will result in higher risk values compared to airborne ammonia contaminants.

Table VII. Three Risk Measures for Road (One Truck)
 ChlorineAmmoniaBoth
 ECPEECPEIP
Corridors(People)(People)(People)(People)(Per Mile)
A0.57200,7740.1656,0820.6088 × 10−4
B1.5647,2450.4413,1970.7457 × 10−4
C2.8447,8200.7913,3580.9379 × 10−4
D1.6337,7830.4510,5541.0225 × 10−4
E3.0963,3340.8617,6911.7683 × 10−4
F0.3416,0250.104,4760.5765 × 10−4

4.3. Analysis

In this subsection, we highlight the values for Corridor A (Table VIII) to compare the hazmat transport risk for the two modes, using the three measures, and highlight any deviations or exceptions in other corridors.

Table VIII. Risk Measures for the Two Modes for Corridor A
 RailRoad
Risk  
MeasuresMakeupChlorineAmmoniaChlorineAmmonia
EC1st3.590.790.570.16
 2nd1.49 + 0.560.46(188.9)(53.28)
 3rd1.220.28  
      
PE1st45,701,8309,270,148200,27456,082
 2nd34,838,4527,066,623(66.7 mn)(18.7 mn)
 3rd22,713,9494,607,292  
      
IP (per trip)1st0.46 × 10−40.6088 × 10−4
 2nd1.15 × 10−4  
 3rd3.95 × 10−4  

The EC from one truck tanker is much less than that from a single hazmat-unittrain, but not less than the risk accruing from one train under the first and second train make-up plans. For example, the EC from a single truck shipment of chlorine was 0.57, while that from a train under the second plan was 0.5113 (italicized in Table VIII). The EC for a single train under this plan on the first segment—as explained in Section 'Solution'—was 0.3716, while that on the second segment was 0.1397. This implies that it is better to send a single train with 25 railcars of chlorine than a single truck with 9,000 gallons. This is significant because a truck carries roughly a third of the volume carried by a railcar, and hence at least 75 trucks would have to be dispatched to deliver the equivalent of the volume shipped on a single train under the second plan. It is reasonable to expect that the difference in the hazmat transport risk would be more pronounced (i.e., 188.9 in Table VIII), if the entire demand is met using 333 trucks—each of which operates under identical conditions. The above result is interesting, but not surprising, since hazmat release from each mode is dictated by the respective accident characteristics. For example, given the nature of train accidents, the probability of multirailcar derailment and release from each derailed car is very small. On the other hand, each truck could release hazmat if it is involved in an accident, and since each truck travels independent of the other trucks, there is a much higher probability of more than one hazmat truck getting involved in accidents, which in turn will have a direct bearing on hazmat transport risk. The above conclusion is based on the assumption that each truck will operate under identical conditions, but since all the trucks will not leave the shipper location in a convoy, one could expect the trucking company to evaluate routing options following a hazmat accident. Note that the option to reevaluate hazmat routing following an accident also exists under the first and the second train make-up plans, but not under the third plan since a single hazmat-unittrain would be used to meet demand.

It was interesting to note that unlike chlorine, dispatching unittrains with ammonia in Corridors B and C resulted in lower hazmat transport risk than from sending a single truck—which could not meet even 1% of the demand. Furthermore, it is important to note that the relative safety of rail over trucks, for moving both chlorine and ammonia, is evident using the other two measures of risk (Tables VII). For example, a single ammonia truck exposes 56,082 people in Corridor A, which translates into 18.7 million people if the entire demand has to be met. On the other hand, the riskiest train make-up plan puts less than half the individuals at risk.

Finally, we would like to comment on the best train make-up plan. The third train make-up plan will yield the lowest hazmat transport risk, when using any of the three measures of risk (Tables IV and V). This is because of the nonlinearity of the aggregate concentration curve for both the EC and population exposure risk measures, which simply means that two hazmat railcars would result in less than twice the risk. It is important to point out that this observation is incremental to the argument in the existing literature that sending larger but fewer hazmat shipments may be preferred by certain stakeholders.[18] This implies that it is perhaps beneficial to make use of a single hazmat-unittrain that can receive priority in being routed and scheduled, than either the other two train make-up plans or using 333 trucks.

In conclusion, irrespective of the risk measure, rail consistently resulted in lower transport risk in each of the six transportation corridors. Table IX highlights that hazmat transport risk from any unit-train make-up plan is significantly lower than that from 333 trucks. Note that the unittrain plan was selected to demonstrate the huge gap in transport risk between the two modes, since rail transport risk is the lowest under this plan. It is important to reiterate that both the remaining train make-up plans and the road alternative implicitly contain the choice to reevaluate routing decisions following an accident, which is not available for unittrains.

Table IX. Summary of Risk Measures for Chlorine
   Road
 Risk  
CorridorMeasureRail1 Truck333 Trucks
AEC1.220.57189.8
 PE22,713,949200,77466.9 mn
 IP3.95 × 10−40.6088 × 10−42.03 × 10−2
BEC1.751.56519.5
 PE4,364,36347,24515.7 mn
 IP4.44 × 10−40.7457 × 10−42.49 × 10−2
CEC3.032.84945.7
 PE5,808,87647,82015.9 mn
 IP5.15 × 10−40.9379 × 10−43.12 × 10−2
DEC3.591.63542.8
 PE4,120,78237,78312.6 mn
 IP7.40 × 10−41.0225 × 10−43.41 × 10−2
EEC4.323.091028.9
 PE6,356,68663,33421.1 mn
 IP9.49 × 10−41.7683 × 10−45.89 × 10−2
FEC0.530.34113.2
 PE1,620,348160255.4 mn
 IP2.87 × 10−40.5765 × 10−41.92 × 10−2

4.4. Uncertainty of Parameters and Limitations

In this subsection, we briefly discuss the uncertainty of parameters, and the possible limitations of the proposed approach.

The proposed approach requires information, among others, about train derailment rates; dispersion modeling inputs such as wind speed, release rate, and atmospheric constants; and the population at risk. First, both the RC and RT in Equation (5) associated with estimating train derailment rate are likely to vary over different time periods even if none of the four inputs change—since the two are determined from the FRA empirical data. Second, the air-dispersion plume model proposed in Equation (8) requires information on wind speed, release rate, and atmospheric constants. Although we have assumed worst-case scenario, it is important that each of the three can assume a range of values within a transportation corridor over a specified time period. Third, ArcView GIS contains residential data, and hence the population exposure calculation assumes that impacted individuals are at home, when in fact it should be a time-varying attribute. For example, if a hazmat train or truck traverses a specific residential segment at night, then it is appropriate to use the GIS database, but pertinent adjustments should be made for other times of the day.

The proposed EC approach has some limitations. First, given that some of the assessment framework inputs are based on empirical data, information about all the relevant parameters would be required for the model to work. For example, estimating RC and RT requires access to past accident data, which may not be available—at the FRA level of detail—in other parts of the world. Second, although GPM was appropriate to model the dispersion of toxic by inhalation hazmat such as chlorine and ammonia (i.e., class 2 hazardous gases)—since it approximately captures the airborne characteristics of the two—a different approach will be required for hazmat that do not become airborne on release. For example, since gasoline forms a puddle and then evaporates, a two-stage diffusion technique may be necessary. Third, although a single network-wide accident rate and conditional probabilities of release was used for trucks, we note that having access to corridor-specific values would strengthen the resulting analysis. However, developing such values would require primary research into hazmat road shipments, which was not the objective of this article. In addition, we do not expect the corridor-specific values to be significantly lower than those depicted in Table III, or very different for each corridor. Finally, it is reasonable to expect that alternate routing options would be considered following an accident, and hence the assumption about identical operating conditions may not hold for both subsequent trucks and trains (under the first and second make-up plans).

5. CONCLUSION

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. LITERATURE REVIEW
  5. 3. EC FRAMEWORK
  6. 4. COMPUTATIONAL EXPERIMENTS
  7. 5. CONCLUSION
  8. ACKNOWLEDGMENTS
  9. Appendix
  10. REFERENCES

Railroad transportation of hazmat has received increasing attention from academic researchers in the past few years, though most of the works have been straightforward extensions of the risk models developed in the highway context—and hence have ignored the distinguishing features of railroads. This article attempts to do two things. First, it proposes an EC assessment methodology that takes into consideration the characteristics of railroad accidents, viz., the probability of train derailment; the conditional derailment and release probability for every position in the train; and the resulting consequence from each release source. Second, the proposed methodology is used—together with two other most popular measures—to both study hazmat transport risk in six distinct transportation corridors in North America, and comment on the modal safety of road and rail for moving chlorine and ammonia—which together account for around 70% of the total transportation risk for toxic by inhalation chemicals.

Through computational experiments on 36 problem instances, we were able to conclude that hazmat transport risk can be reduced by using rail transport to meet the demand for both chlorine and ammonia. It was shown that irrespective of the risk measure and the transportation corridor, rail would be the preferred option because although it carries higher volume, the nature of railroad accidents implies that the probability of release from multiple railcars would be extremely small. On the other hand, in the presence of similar operating conditions, the resulting cumulative transport risk would always be higher for trucks. Three different train make-up plans were used, and it was concluded that using a hazmat-unittrain will result in the lowest transport risk, thereby entailing using larger but fewer hazmat shipments. On the other hand, since a single hazmat-unittrain is being used to meet the entire demand, it was not possible to suspend and/or reroute the subsequent shipments—options available when the decisionmaker uses the other two train make-up plans or the trucks, though trains would be preferred over trucks even under this setting.

There are a number of research projects arising from the EC approach proposed in this article. The first deals with the placement of hazmat railcars within a block and the train consist. To that end, the questions surrounding the sequence of railcars within a block and the order of blocks to form a train, resulting from the interplay of yard and segment risk, are being investigated. Second, the insights gained from these works would be used to develop an analytical approach to determine railcar routing, hazmat railcar position in a train-consist, and yard activities in a network-level setting.

ACKNOWLEDGMENTS

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. LITERATURE REVIEW
  5. 3. EC FRAMEWORK
  6. 4. COMPUTATIONAL EXPERIMENTS
  7. 5. CONCLUSION
  8. ACKNOWLEDGMENTS
  9. Appendix
  10. REFERENCES

This work was supported in part by a research grant from the Social Sciences and Humanities Research Council of Canada to the third author, and was conducted when the first author was a postdoctoral fellow at Desautels Faculty of Management, McGill University. The second and third authors are members of the Interuniversity Research Centre on Enterprise Networks, Logistics and Transportation (CIRRELT) and acknowledge the research infrastructure provided by the Centre. The authors are grateful to the three anonymous referees and the associate editor whose constructive feedback was helpful in improving the article.

Appendix

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. LITERATURE REVIEW
  5. 3. EC FRAMEWORK
  6. 4. COMPUTATIONAL EXPERIMENTS
  7. 5. CONCLUSION
  8. ACKNOWLEDGMENTS
  9. Appendix
  10. REFERENCES
Table AI.. Probability of Derailment Starting at Position i
Corridor A: Montreal to Albany Segment
iP(POD)iP(POD)iP(POD)
10.0432390.0077770.0082
20.0228400.0077780.0083
30.0187410.0077790.0084
40.0164420.0077800.0085
50.0150430.0076810.0086
60.0139440.0076820.0087
70.0131450.0076830.0088
80.0125460.0076840.0090
90.0119470.0076850.0091
100.0115480.0076860.0093
110.0111490.0075870.0095
120.0108500.0075880.0097
130.0105510.0075890.0099
140.0102520.0075900.0102
150.0100530.0075910.0105
160.0098540.0075920.0108
170.0096550.0075930.0112
180.0094560.0075940.0117
190.0093570.0075950.0124
200.0091580.0075960.0132
210.0090590.0075970.0144
220.0089600.0076980.0161
230.0088610.0076990.0193
240.0087620.00761000.0352
250.0086630.0076  
260.0085640.0076  
270.0084650.0077  
280.0083660.0077  
290.0082670.0077  
300.0082680.0078  
310.0081690.0078  
320.0081700.0078  
330.0080710.0079  
340.0080720.0079  
350.0079730.0080  
360.0079740.0080  
370.0078750.0081  
380.0078760.0082  
Table AII.. Probability that m Railcars Will Derail Given i = 1
Corridor A: Montreal–Albany Segment
mP(m|1)mP(m|1)mP(m|1)
20.0292420.0092820.0029
30.0284430.0090830.0028
40.0275440.0087840.0028
50.0268450.0085850.0027
60.0260460.0082860.0026
70.0253470.0080870.0025
80.0246480.0078880.0025
90.0239490.0076890.0024
100.0232500.0073900.0023
110.0225510.0071910.0023
120.0219520.0069920.0022
130.0213530.0067930.0021
140.0207540.0065940.0021
150.0201550.0064950.0020
160.0195560.0062960.0020
170.0190570.0060970.0019
180.0184580.0058980.0018
190.0179590.0057990.0018
200.0174600.00551000.0017
210.0169610.0054  
220.0164620.0052  
230.0160630.0051  
240.0155640.0049  
250.0151650.0048  
260.0146660.0046  
270.0142670.0045  
280.0138680.0044  
290.0134690.0043  
300.0130700.0041  
310.0127710.0040  
320.0123720.0039  
330.0120730.0038  
340.0116740.0037  
350.0113750.0036  
360.0110760.0035  
370.0107770.0034  
380.0104780.0033  
390.0101790.0032  
400.0098800.0031  
410.0095810.0030  
Table AIII.. Consequence If Derailment Starts at i = 1
Corridor A: Montreal–Albany Segment
minline imagejinline imageinline imageinline imageinline image
510.007219.0E-0250,8014724.5234.0165
520.006928.6E-0384,2785453.4437.8088
530.006738.0E-04108,4455540.6737.3252
540.006547.5E-05137,7595550.9736.3351
550.006457.0E-06164,7355552.1235.3129
560.006266.5E-07182,7195552.2434.3131
570.006076.0E-08195,5645552.2533.3410
580.005885.6E-09216,9355552.2532.3963
590.005795.2E-10234,5245552.2531.4784
600.0055104.8E-11248,5955552.2530.5866
610.0054114.5E-12270,6005552.2529.7200
620.0052124.2E-13287,1365552.2528.8779
630.0051133.9E-14301,1295552.2528.0597
640.0049143.6E-15317,0415552.2527.2647
650.0048153.4E-16334,1005552.2526.4922
660.0046163.1E-17349,0275552.2525.7416
670.0045172.9E-18362,1985552.2525.0122
680.0044182.7E-19376,6965552.2524.3036
690.0043192.5E-20392,4955552.2523.6150
700.0041202.3E-21406,7135552.2522.9459
710.0040212.2E-22419,5775552.2522.2958
720.0039222.0E-23431,2725552.2521.6641
730.0038231.9E-24447,0575552.2521.0503
740.0037241.8E-25460,9645552.2520.4538
750.0036251.6E-26473,7595552.2519.8743
760.0035    19.3112
770.0034    18.7641
780.0033    18.2324
790.0032    17.7158
800.0031    17.2139
810.0030    16.7262
820.0029    16.2523
830.0028    15.7918
840.0028    15.3444
850.0027    14.9096
860.0026    14.4872
870.0025    14.0767
880.0025    13.6779
890.0024    13.2903
900.0023    12.9138
910.0023    12.5479
920.0022    12.1924
930.0021    11.8469
940.0021    11.5113
950.0020    11.1851
960.0020    10.8682
970.0019    10.5603
980.0018    10.2611
990.0018    9.9704
1000.0017    9.6879
     TOTAL1059.6238
Table AIV.. Expected Consequence for Each Position in the Train
Corridor A: Montreal to Albany Segment
iPiCiRiiPiCiRi
17.4E-061059.60.0079451.3E-064299.60.0056
23.9E-061061.20.0042461.3E-064457.50.0058
33.2E-061094.10.0035471.3E-064622.40.0060
42.8E-061128.10.0032481.3E-064794.80.0062
52.6E-061163.20.0030491.3E-064975.00.0065
62.4E-061199.50.0029501.3E-065163.60.0067
72.3E-061237.00.0028511.3E-065361.10.0069
82.1E-061275.70.0027521.3E-065360.80.0069
92.1E-061315.70.0027531.3E-065360.50.0069
102.0E-061357.10.0027541.3E-065360.10.0069
111.9E-061399.90.0027551.3E-065359.80.0069
121.9E-061444.20.0027561.3E-065359.40.0069
131.8E-061489.90.0027571.3E-065359.00.0069
141.8E-061537.30.0027581.3E-065358.60.0070
151.7E-061586.20.0027591.3E-065358.20.0070
161.7E-061636.90.0028601.3E-065357.70.0070
171.7E-061689.30.0028611.3E-065357.20.0070
181.6E-061743.60.0028621.3E-065356.70.0070
191.6E-061799.70.0029631.3E-065356.10.0070
201.6E-061857.90.0029641.3E-065355.60.0070
211.5E-061918.10.0030651.3E-065354.90.0071
221.5E-061980.40.0030661.3E-065354.30.0071
231.5E-062045.10.0031671.3E-065353.60.0071
241.5E-062112.00.0031681.3E-065352.90.0071
251.5E-062181.40.0032691.3E-065352.10.0072
261.5E-062253.30.0033701.3E-065351.20.0072
271.4E-062327.90.0034711.4E-065350.20.0073
281.4E-062405.30.0034721.4E-065348.30.0073
291.4E-062485.60.0035731.4E-065338.80.0073
301.4E-062568.90.0036741.4E-065261.70.0073
311.4E-062655.40.0037751.4E-064590.60.0064
321.4E-062745.10.0038761.4E-060.00.0000
331.4E-062838.40.0039771.4E-060.00.0000
341.4E-062935.30.0040781.4E-060.00.0000
351.4E-063036.00.0041791.4E-060.00.0000
361.4E-063140.70.0043
371.3E-063249.60.0044
381.3E-063362.80.0045962.3E-060.00.0000
391.3E-063480.70.0046972.5E-060.00.0000
401.3E-063603.50.0048982.8E-060.00.0000
411.3E-063731.40.0049993.3E-060.00.0000
421.3E-063864.60.00511006.1E-060.00.0000
431.3E-064003.50.0053  TOTAL0.3716
441.3E-064148.40.0054    

REFERENCES

  1. Top of page
  2. Abstract
  3. 1. INTRODUCTION
  4. 2. LITERATURE REVIEW
  5. 3. EC FRAMEWORK
  6. 4. COMPUTATIONAL EXPERIMENTS
  7. 5. CONCLUSION
  8. ACKNOWLEDGMENTS
  9. Appendix
  10. REFERENCES
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