Establishing derailment profiles by position for corridor shipments of dangerous goods

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  • Establishing derailment profiles by position for corridor shipments of dangerous goods

    F. F. SACCOMANNO Departtnetlt of Civil Engineering, University of Waterloo, Waterloo, Ont., Canada N2L 3G1

    AND

    S . M. EL-HAGE Transportation Planning, Mars/~all Macklin Monaghan, 80 Cornmerce Valley Drive East,

    Thorrthill, Ont., Canada W T 7N4

    Received November 15, 1989

    Revised manuscript accepted July 11, 1990

    The position of railcars carrying dangerous goods in a train can affect their involvement in a derailment. A model is presented, which minimizes the number of cars carrying dangerous goods derailing for different marshalling strategies and rail corridor conditions. An application of the model to the Sarnia-Toronto rail corridor is presented. The results of this analysis suggest that marshalling strategies for cars carrying dangerous goods need to be sensitive to corridor conditions that affect the causes of train derailments. Current Canadian Transport Commission directives governing the placement of cars carrying dangerous goods along a train were found to be ineffective in reducing their derailment probability when compared to a low-cost unregulated option. Effective marshalling strategies can substitute for speed controls on the shipment of danger- ous goods, resulting in a similar or improved derailment profiles and lower operating costs.

    Key words: dangerous goods, derailment, rail, marshalling, railcars.

    La position des wagons transportant des marchandises dangereuses peut avoir une influence sur leur comportement en cas de dkraillement. Un modkle qui limite le dkraillement de wagons de marchandises dangereuses selon diverses stratkgies de formation des trains et de conditions h l'intkrieur des corridors est prksentk. L'application de ce modkle au corridor Sarnia-Toronto est discutke. Les rksultats de l'analyse indiquent que les stratkgies de formation des trains transportant des matikres dangereuses doivent tenir compte de conditions du corridor ayant un impact sur les causes d'un dkraillement. Les lignes directrices actuelles de l'Office national des transports concernant la formation des trains comportant des wagons de marchandises dangereuses se sont rkvklkes inefficaces h rkduire les probabilitks de dkraillement en comparaison d'une option non rkglementke h faible co0t. Des stratkgies de formation des trains efficaces peuvent se substituer aux contrales de vitesse et entrainent des profils de dkraillement semblables ou amkliorks et des cotits d'exploitation plus faibles.

    Mots cle's : marchandises dangereuses, dkraillement, raille, formation des trains, wagons. [Traduit par la rkdaction]

    Can. J . Civ. Eng. 18, 67-75 (1991)

    Introduction For a given set of rail corridor conditions, the risks

    associated with the derailment of trains carrying dangerous goods (DG) can be reduced in two ways: (i) reducing the prob- ability that any railcar carrying DG is involved in the derail- ment block, and (ii) reducing the opportunity of incompatible DG being involved in the same derailment block.

    The involvement of DG cars in a derailment block is influenced by the position of these cars along a given train con- sist and by the placement of non-DG car buffers separating incompatible materials. Effective marshalling and buffering strategies seek to assign DG cars to points along the train that are less likely to derail in an accident situation. If such a derailment were to take place, these strategies seek to reduce the opportunity that incompatible materials are involved in the same derailment block. Incompatible materials situated close to one another in the same derailment block can increase the potential threat posed by the derailment. For example, in the 1979 Mississauga derailment, the major concern for emer- gency response personnel was the presence of three potentially explosive propane tankers in the same derailment block with a 90 t tank car carrying highly toxic chlorine. An explosion of

    NOTE: Written discussion of this paper is welcomed and will be received by the Editor until June 30, 1991 (address inside front cover). Printed in Canada / Imprime au Canada

    any one of the propane cars could have caused a rupture of the neighboring chlorine car, with potentially catastrophic effects for the neighboring population.

    The Canadian Transport Commission (CTC 1982) recog- nized the importance of position in railcar derailments by tabling in 1981 a special DG marshalling order. The major restrictions included in this order are summarized in Table 1. The most frequently applied restriction states that when train length permits, cars carrying DG must not be nearer than the 6th position from the locomotives block, occupied caboose, or any occupied car in the train. The central focus of this direc- tive is to provide a sufficient distance between derailed DG cars and operating train personnel. The term "when train length permits" in the CTC marshalling directive refers to any train consist having a sufficient number of non-DG railcars to provide a minimum 5-car separation where required. When train length does not permit, the CTC recommends that DG railcars must be placed near the middle of the train, and under no circumstances nearer than the 2nd position from the locomotive block.

    A number of important concerns are raised by these restric- tions regarding their consistency of application and their effectiveness in reducing DG derailments. A major factor con- trolling the placement of DG railcars along a train is the actual length of the train (no. of cars), a feature that is generally governed by traffic patterns along the corridor and by carrier

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  • CAN. J. CIV. ENG. VOL. 18. 1991

    TABLE 1. Position in freight o r mixed trains of cars containing dangerous commodities (CTC 1982)

    (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) Restriction o n position of D G c a r s t

    Placard Type of car group* A B C D E F G H I J K

    Any car 1 x x x x x x x x x x Tank car 2 x x x x x x $ x$ x x $ x All other 2 x x x Tank car 3 x x x x X X X X X X All other 3 X x X X X X X x Any car 4 x x x x x Tank car 5 X $ X $

    *Group 1 consists of explosives 1.1 and 1.2. Group 2 consists of explosives 1.3, 1.4, 1.5; flammable gases 2.1; nonflammable gases 2.2; poison gases 2.3; flammable solids 4.1,4.2,4.3; oxidisers 5.1, 5.2; poisons 6.1, 6.2 and corrosives. Group 3 consists of special commodities of the division 2.3. Group 4 consists of radio active materials. Group 5 consists of flammable liquids 3.3 and "empty placarded cars".

    fAn x entry denotes that restriction on position applies. Restriction A: When train length permits, DG cars must not be nearer than 6th from engine, occupied

    caboose, or occupied car. B: When train length does not permit, DG cars must be near middle of train but not nearer than

    2nd from engine, occupied caboose, or occupied car. C, D, E, and F: DG cars must not be placed next to car in placard groups 1 , 2 , 3, and 4, respec-

    tively. G: DG cars must not be placed next to engine. H: DG cars must not be placed next to caboose. I: DG cars must not be placed next to open-top car when lading protudes beyond car or when

    lading above car end is liable to shift. J: DG cars must not be placed next to any car piggyback or container with automatic heating

    or refrigeration, lighted heaters, stoves, lanterns, or internal combustion engines. K: DG cars must not be placed next to loaded flat car.

    +Except when train consists only of placarded tank cars. Except trailer-on-flat-car, container-on-flat-car, tri-level and bi-level cars, and any other car specially

    equipped with tie down devices for handling vehicles. Permanent end bulk head flat cars considered the same as an open-top car (column 13).

    scheduling restrictions. Given this dependence on train length, marshalling regulations for DG cars can be applied arbitrarily. Railcars carrying the same materials along the same corridor may be placed at different positions along the train, depending on car availability. In general, current regulations in Canada appear to have been developed without a clear understanding of the relationship between positions and derailment probabil- ity, a relationship that is complicated by the effect of speed and accident cause.

    This paper presents an approach for marshalling DG railcars that, for a given set of corridor conditions, minimizes their involvement in a derailment. The results of an application of the approach to the transport of DG along the Sarnia-Toronto rail corridor are discussed. This corridor application focuses on an evaluation of alternative marshalling strategies for an

    tional derailment probabilities, given the occurrence of a train derailment. This probability is a function of the train derailing at a specific point along its length, and having a certain number of cars involved in the derailment block. A position is subject to derailment only if it is situated in the critical block of cars following the initial point of derailment.

    In Canada, all train accidents having damages exceeding $850 are reportable to the Canadian Transport Commission (CTC) and have been included in this data base. The CTC rail accident data base used in this analysis consists of 805 train derailments covering the period 1983 - 1985 inclusive. Approximately 40 % of these derailments involve some type of dangerous material. Each accident record in the CTC data base includes information on train length, point of derailment, number of cars derailing, and causes of each derailment acci-

    assumed mix of material shipments and train consists. dent. While the involvement of a dangerous material in the total derailment block was indicated by the CTC in the data,

    Methodology the number of DG railcars actually derailing was not reported.

    As illustrated in Fig. 1, the methodology adopted in this study consists of four components: (i) establishing a relation- ship between the cause of the accident and the beginning of the derailment block; (ii) establishing a relationship between train speed, accident cause, and the number of cars involved in the derailment block; (iii) establishing a derailment probability distribution for each accident cause based on the position of the railcar along the train; and (iv) evaluating specific mar- shalling strategies for a given mix of dangerous and non- dangerous railcars and a set of rail corridor conditions.

    The basic thrust of this analysis is the estimation of posi-

    Point of derailment In this study, the initial point of derailment (POD) is

    assumed to depend on the cause of each train accident. For example, initial points of derailment associated with roadbed or track defects are assumed more likely to occur nearer to the front of the train than derailments associated with defects in the rolling stock (e.g., wheels, axle, and journal bearing failures). These latter derailments are more randomly dis- tributed throughout the train length. In this analysis, CTC rail accident data have been used to assess the statistical validity of this assertion.

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  • SACCOMANNO AND EL-HAGE

    I PROBABlLlN DISTRIBUTION OF POINT OF DERAILMENT I

    FOR A GIVEN TRAlN CONSIST AND POD

    BUFFERING DATA (DIFFERENT REGULATIONS

    DERAILMENT PROBABlLlN OF EVERY CAR IN A GIVEN TRAlN CONSIST. TRAlN SPEED,

    t

    NUMBER OF DC CARS DERAILING FOR A GIVEN MARSHALLING REGULATION. A N D A

    SPECIFIC RAlL CORRIDOR

    POSITION OF DC CARS IN A GIVEN TRAIN CONSIST AND MARSHALLING REGULATION

    EXPECTED NUMBER OF DC CARS DERAILING FOR A GIVEN TRAlN CONSIST A N D ACCIDENT SITUATION

    EVALUATION AND COMPARISON O F THE DIFFERENT BUFFERING A N D MARSHALLING REGULATIONS

    ~r

    ACCIDENT PROBABlLlN BY CAUSE OF DERAILMENT O N A

    SPECIFIC RAlL CORRIDOR

    FIG. 1. Model flow chart. (DC = dangerous commodity.)

    1

    -

    In obtaining a probability distribution for the POD, the dis- tribution of train lengths in the accident data base needs to be considered. Positions near the front of the train tend to be overrepresented in the accident data base, since these positions are available for short as well as for long trains. Positions further back in the train, however, are only available if the total number of cars in the train is sufficient to include these positions.

    The 1983- 1985 CTC accident data base provides a distri- bution of derailments for different train lengths. Visual inspec- tion of these data suggest a grouping of train length into two

    I categories: trains with fewer than 50 cars and trains with 50 or more cars. This grouping serves as a crude adjustment for total train length in the analysis of points of derailment.

    I Within each of these train length categories, car positions along the train were expressed in percentile form (NPOD). For example, in a 50-car train the 5th position was assigned the 10th percentile interval (0.1). The CTC accident data base was then classified by NPOD, train length, and accident cause.

    Analyses of variance techniques were used to assess the statistical effect of accident cause and train length on the normalized point of derailment. The results summarized in

    v

    Table 2 indicate that, while cause of derailment has a signifi- cant effect on NPOD, the effect of train length (alone or acting interactively with cause) was not significant. Accordingly, in the subsequent analysis, NPOD probabilities were estimated ignoring the effect of train length.

    Based on the CTC accident data base, point of derailment probabilities were estimated for each NPOD interval and derailment cause. The results of this analysis are summarized in Table 3. For roadbed defects, there is a 26% probability of initial derailment in the first 10 positions of the train, com- pared with a 10.9% probability for the same position when derailment is caused by wheel, axle, and journal failures.

    In establishing the probability distribution of derailment by position, only those cars located after the point of derailment need to be considered, since positions preceding the point of derailment are unlikely to be involved in the subsequent derail- ment block. This assertion is supported by the CTC accident data where nearly all derailments for the period 1983 - 1985 were characterized by a consistent front-to-rear progression beginning at the POD and ending at the rear of the train. Only two exceptions were found in the data base, both dealing with rear-end collision taking place in railyards.

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  • CAN. J. CIV. ENG. VOL. 18. 1991

    TABLE 2. Analysis of variance (effect of train length and cause of derailment)

    Source Sum of squares DF* Mean square F-ratio P t

    Train length 0.000 1 0.000 0.001 0.979 Cause of derailment 2.104 6 0.351 4.424 0.000 Length x cause 0.299 6 0.050 0.629 0.707 Error 41.208 520 0.079

    NOTE: Coefficient of determination = 0.244. *DF = degrees of freedom. t P = tolerance level.

    TABLE 3. Relative frequency of derailments by cause of derailment and train section (%)

    Range of normalized point of derailment

    Cause of derailment 0-0.1 0.1-0.2 0.2-0.3 0.3-0.4 0.4-0.5 0.5-0.6 0.6-0.7 0.7-0.8 0.8-0.9 0.9-1.0

    Roadbed defects Track geometry defects Rail and joint bar defects Frogs, switches, and track

    appliances General car defects

    (mechanical and electrical) Axles and journal bearings

    and defective wheels Miscellaneous, operations, and

    all other causes All causes

    0 20 40 60 80 100 120 140 Number of cars derailing Train speed (km/h)

    FIG. 3. Frequency histograms for number of cars derailing. (-, FIG. 2. Number of cars derailing versus speed. (+, geometric roadbed defects; , vehicle failures.)

    model; m, A. D. Little Model; -, observed data.)

    Number of cars derailing A report prepared by A. D. Little Inc. (1983) established a

    statistical relationship between train speed and the mean number of cars derailing:

    where N is the mean number of cars derailing; S is the mean speed of the train on derailment; and a and b are calibration constants (2.416 and 0.3 10 respectively).

    The A. D. Little expression ([I]) was fitted to the CTC acci- dent data to yield values of 2.416 for the parameter a and 0.310 for b . This curve-fitting exercise produced inconclusive results, with very high residuals observed at higher derailment speeds (Fig. 2). Frequency histograms of cars derailing as a

    function of speed indicated that there were as many single-car derailments at higher speeds as at lower speeds, a result that appears to be counter-intuitive. From the A. D. Little expres- sion, one would expect a lower percentage of single-car derail- ments at higher speeds. These results suggest that in addition to speed, other factors may be acting to bias the reliability of the A. D. Little expression. One such factor considered in this analysis was the cause of the derailment.

    Using the U.S. Federal Railway Association (FRA) classifi- cation system, all CTC rail accidents were grouped into seven classes of derailments by cause. Figure 3 illustrates the rela- tionship between the number of cars derailing and their cumulative frequency of occurrence in the data base for two FRA causes: roadbed defects and wheel, axle, and journal failures. In general, this observed relationship follows a nega-

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  • SACCOMANNO AND EL-HAGE 7 1

    tive exponential function similar to the A. D. Little expres- sion. The shape and position of each distribution, however, is sensitive to the cause of derailment. For example, derailments caused by wheel, axle, and journal failures reflect a highly peaked relationship with a disproportionately large number of single-car incidents, whereas derailments caused by roadbed defects are more representative of multiple car involvements.

    Prior to fitting a mathematical expression to the cars derail- ing expression, it was necessary to adjust the relationship by "residual train length." Residual train length here refers to the number of cars following the point at which derailment is initiated. As the residual length is reduced, the number of cars derailing is also reduced proportionately, since fewer cars are available for derailment.

    From the CTC data, residual train length was found to vary exponentially with the number of cars derailing. A probability distribution for number of cars derailing was established based on a modified geometric distribution. The geometric distribu- tion was adjusted for definition over a practical car derailment range from a minimum of one car to a maximum number equal to the residual train length. In the modified geometric, the sum of derailment probabilities from the POD to the end of the train is equal to one. The conditional probability of x cars derailing, given that a derailment started at a specific car in a train, is defined as

    where x = 1, 2, 3, . . . , RL; RL = number of cars in the residual train length; and PN(x) = probability of exactly x cars derailing for a given POD. The mean number of cars derailing in the above expression is given as

    [3] MEAN = 1

    P( l - PIRL

    The parameter p in [2] and [3] is expressed as a logistic function of train speed, cause of derailment, and residual train length,

    where

    in which cause;, i = 1, 2, . . . , in [5] are dummy variables which take on a value of 1 if the cause is in effect or 0 otherwise.

    Maximum likelihood techniques were applied to the product function of [2] for all observed values of cars derailing to yield values for the coefficients in [5]. The summary statistics for this maximum likelihood calibration exercise are given in Table 4 for the 1983- 1985 CTC accident data base.

    A comparison of residuals between the recalibrated A. D. Little and the geometric models favors the geometric model. These results are illustrated in Fig. 2 for all causes of derail- ment in the CTC data. Since casual inputs are considered directly in the geometric expression, the estimated cars derail- ing are unique to each derailment profile. The A. D. Little model, on the other hand, is based on a more aggregate rela- tionship between mean cars derailing and mean speed, and thereby lacks sensitivity to unique causal factors in each acci-

    dent profile. Both models suggest that the number of cars derailing increases exponentially with speed, at a decreasing rate. The number of cars involved in the derailment block seems to dissipate forces acting on subsequent cars along the train. This in turn reduces their likelihood of being derailed. Hence, the decreasing rate expression for the number of cars derailing obtained from our analysis appears to be intuitive.

    Probability distribution for derailment by position This section of the paper focuses on a procedure for estimat-

    ing the probability that, given a train derailment, a car occupy- ing the ith position is derailed.

    Assuming that a train has iz cars, the probability of a derail- ment starting at the jth position is given as POD(j) and the corresponding probability of having x cars derailing in the block is given as PN(x) ([2]). Given that a derailment occurred on a train, the corresponding conditional probability that a railcar in the ith position derails can be obtained from the expression:

    The term i - j + 1 in [6] represents the number of cars avail- able between the point of derailment at the jth position (POD(j)) and the ith position being considered. The term n - j + 1 represents the residual train length following the point of derailment. The summation term for PN(x) reflects the probability that at least i - j + 1 cars have derailed, given that the derailment started at the jth position. The probability of the ith car derailing is obtained by summing the product of the probabilities for all cars following the point of derailment (POD(j)), in this case, the jth car in the train.

    The probability that any one position in the train is occupied by a DG car depends on the availability of both DG and non- DG cars in the consist and on overriding marshallinglbuffer- ing restrictions. In this analysis, combinatorial mathematics was used to obtain such a probability for an assumed set of train parameters and marshallinglbuffering strategies. For this analysis, a minimum buffer of five non-DG cars was used to separate different classes of dangerous goods along the same train consist. A more detailed discussion of this procedure is available in El-Hage (1988).

    Corridor analysis of marshalling regulations Corridor features

    The Sarnia-Toronto rail corridor, to which the above model is applied, represents a major artery for dangerous goods traffic in Ontario. This corridor links the major petrochemical producers at Sarnia (i.e., DOW Chemical, CIL, Polisar) with the Toronto industrial base. Sarnia is also a major transborder crossing point for dangerous goods traffic to and from the United States. Both Canadian National (CN) and Canadian Pacific (CP) rail lines were considered in the analysis, although most DG are routed to the northern branch of CN line using the Macmillan yard in Toronto (Wade et al. 1988). A scaled railroad map of the Sarnia-Toronto corridor is provided in Fig. 4.

    In a recent report, Saccomanno et al. (1988) compiled data from different producers and from the railways (CN and CP) to obtain estimates of annual liquified propane gas (LPG), chlorine, and sulfuric acid shipment volumes along the Sarnia- Toronto corridor. Total tonnage shipped on each link of the

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  • CAN. J. CIV. ENG. VOL. 18, 1991

    TABLE 4a. Maximum likelihood summary statistics for the geometric distribution

    Source DF Sum of squares Mean square F-test

    Regression 9 29477.4510 3275.2723 81.2851 Residual 43 1 17366.5490 40.2936 Uncorrected total 440 46844 .OOOO Corrected total 439 28564.6909

    TABLE 46. Summary statistics for derailment causes

    Asymptotic 95 % interval

    Asymptotic Student Parameter* Estimate std. error T-test Lower Upper

    -

    Intercept, A Speed effect, B, Roadbed, B, Track geometry, B, Railbar Switches, B, General car, B4 Axles/wheels, B, All other, B, Residual length, C,

    -

    1.6741 0.3342 5.0099 1.0173 2.3309 -0.5755 0.0818 7.0358 -0.7363 -0.4147

    0.6479 0.1438 4.5052 0.3652 0.9306 0.3824 0.0942 4.0605 1.1973 0.5676

    (No parameter) 0.4702 1.4246 0.3301 -2.3298 3.2703 1.6722 0.3228 5.1809 1.3078 2.3066 1.5105 0.1283 11.7714 1.2583 1.7627 1.3292 0.2611 5.0913 0.8161 1.8424

    -0.6381 0.0538 11.8549 -0.7439 -0.5323

    *Response function, Z = A + B, X log(speed) + C, X log (residual train length) + (B,, for roadbed defect) + (B,, if cause of derailment is track geometry) + (B,, for railbar defect) + (B,, if cause of derailment is switch defects) + (B,, for general car) + (B,, if cause of derailment is other causes).

    RAILROAD MAP

    SOUTHERN ONTARIO

    FIG. 4. Railroad map of the Sarnia-Toronto corridor.

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  • SACCOMANNO AND EL-HAGE

    TABLE 5. Dangerous commodity flows on the Sarnia-Toronto corridor links

    Dangerous commodity type

    LPG Chlorine sulfuric acid Total Total NO. NO. of DG Distance freight of trains trains

    From To (km) Cars (%) Cars (%) Cars (%) (cars) per year per year

    Sarnia Kornoka London Brantford Lynden Copetown Hamilton Burlington Burlington Malton Thornlea

    Komoka London Brantford Lynden Copetown Hamilton Burlington CN bend Malton Thornlea Pickering

    corridor was translated into car movements using average bulk tanker carrying capacities for these three types of dangerous goods. For the purpose of this application, DG traffic on the Sarnia-Toronto rail corridor was confined to these three representative commodities (LPG, chlorine, and sulfuric acid), all of which are assumed to be transported in rail bulk tankers. Information on total freight movement was available only for the national rail network. Estimates of total car move- ments on individual links of the Sarnia-Toronto corridor were extrapolated from these national published statistics.

    As reported by Swoveland (1987), a freight train in Canada consists-on average of 76 rail cars. ~ s s u m i n ~ a uniform train length for all trains on the Sarnia-Toronto corridor, the total number of trains carrying dangerous goods (LPG, chlorine and sulfuric acid) was estimated (Table 5).

    The involvement of DG cars in a derailment block depends on two factors: (i) the prior occurrence of a train accident and (ii) the primary cause of the accident. Train accident rates were estimated based on CTC (1983 - 1985) accident statistics for different classes of track, geographic region, track quality, average subdivision speed, and volume carried. A family of GLIM (generalized linear interactive model) loglinear models was calibrated to establish the statistical significance of these factors and their effect on the mean accident rate from the data base. Depending on track characteristics, the train derailment rates for individual links of the Sarnia-Toronto corridor varied from 1.550 to 3.287 train derailments per billion tonne- kilometre. It is important to note that train speed was one of the significant factors affecting the frequency of train derailments.

    Derailments taking place along the Sarnia-Toronto cor- ridor were extracted from the CTC data base and classified according to their primary cause of derailment (Table 6). The distribution of accidents by cause was found to differ appreci- ably between the Sarnia-Toronto corridor and the national rail network. This suggests that in order to reduce DG derail- ments on a corridor, corridor-specific marshalling strategies need to be considered.

    Combining the train derailment rates with the distribution of derailments by cause provides an estimate of causal train derailment rates per shipment for various unit distances along the corridor.

    Evaluation of alternative marshalling regulations for assumed corridor conditions

    In this analysis, the effects of five alternative marshalling regulations are considered: 1. Current regulations based on the CTC (1982) standing

    order no. 1974-1-Rail. 2. Marshalling DG cars to the front of the train in a single

    block. Approach suggested by CP in a response to the recommendations of the Grange Inquiry (1980) into the 1979 Mississauga derailment (Swoveland 1987).

    3. Marshalling DG cars to the back of the train in a single block. Suggestion contained in the Swoveland (1987) report.

    4. Marshalling DG cars in the middle section of the train. "De facto" regulation when availability of non-DG cars is a problem.

    5. Random marshalling without additional restrictions for DG cars. Option that would realize the lowest marshalling costs for the railways.

    For an assumed set of corridor conditions and train mixes, the number of DG railcars derailing was estimated as a func- tion of train operating speed for each of the five marshalling strategies being considered.

    From Fig. 5, the number of DG railcars derailing increases at a decreasing rate with higher train operating speeds. For all speed classes, end-of-train marshalling has produced the lowest number of DG cars derailing. Current regulations and front-of-train marshalling have produced car derailment rates that do not differ significantly from the unrestricted random option. This suggests that for the Sarnia -Toronto corridor, current regulations governing the placement of DG cars along a train may be ineffective in reducing their derailment over an unrestricted option. Higher derailment values for middle-of- train marshalling reflects the dominance of equipment-related accidents along the Sarnia-Toronto corridor. Equipment- related accidents are more likely to involve middle-of-train points of derailment than accidents caused by track and roadbed defects.

    Differences in the number of DG cars derailing for equip- ment- and track-related accidents are shown in Fig. 6 for the five marshalling strategies under consideration and two train derailment causes, roadbed defects and wheel, axle, and jour-

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  • CAN. 1. CIV. ENG. VOL. 18, 1991

    TABLE 6. Number of derailments by cause for selected corridor and entire network

    Sarnia -Toronto rail corridor National rail network

    No. of No. of Cause of derailment derailments4' % of total derailments? % of total

    Roadbed defects Track geometry defects Tail and joint bar defects Frogs, switches, and track

    appliances General car defects

    (mechanical and electrical) Axles and journal bearings, and

    defective wheels Miscellaneous, operations, and

    other causes Total

    *Based on 1979- 1981 and 1983- 1985 data tBased on 1983- 1985 data.

    - p 1 z I6 26 36 46 56 66 76 86 96 106 116 128 136

    Train speed (krn/h) 0.0 1 I I I I , I I I I I

    0 10 20 30 40 50 60 70 80 90 100 Train s p e e d ( k r n / h )

    FIG. 5 . Number of DG cars derailing for different marshalling strategies for Sarnia-Toronto corridor. (+, current regulation; - -, front-of-train marshalling; . . . , end-of-train marshalling; - - - , middle-section marshalling; 8, random marshalling.)

    nal failures. From these figures, end-of-train marshalling is found to be most effective in reducing derailments for roadbed defect accidents, but reflects only slight improvements over current regulations where wheel, axle, and journal failures cause the derailment.

    The relationship illustrated in Figs. 5 and 6 are especially meaningful when considered in relation to changes in train operating speeds for trains carrying DG. These results suggest that effective marshalling strategy can be used to offset the adverse effect of higher speeds on the number of cars derail- ing. Assuming an average corridor speed of 60 kmlh, current regulations produce a potential 4.2 DG car derailments per year, as compared to 3.8 derailments per year for an end-of- train strategy (Fig. 5 ) . To accomplish the same number of car derailments subject to current marshalling regulations, aver- age operating speeds on the corridor would have to be reduced by approximately 7 kmlh. Assuming similar train assembly costs, an end-of-train marshalling strategy can result in signifi- cant savings per year for the volun~e of rail shipments moving over the Sarnia-Toronto corridor, indeed over the entire national network.

    0 20 40 60 80 100 Train speed ( k m / h )

    FIG. 6. Effectiveness of marshalling strategies for (a) roadbed defect derailments and (b) wheel, axle, and journal failure derail- ments. (+, current regulation; -, front-of-train marshalling; . . . , end-of-train marshalling; - - - , middle-section marshalling; 8, random marshalling.)

    These results suggest that the marshalling of DG cars along a train is subject to corridor characteristics affecting the nature of derailment. From this analysis, it would be inappropriate to suggest, in accordance with current CTC marshalling regu-

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  • SACCOMANNO AND EL-HAGE 75

    lations, that corridor and traffic conditions are incidental to the problem, and that regulations can be established at the network-wide level.

    Conclusions

    This paper has presented a framework for evaluating the marshalling of DG railcars along a given train consist in terms of derailment potential. The framework is sensitive to certain corridor characteristics affecting the cause of train derailment and the point of derailment.

    The probability of derailment by position in the train depends on the point of derailment and the number of cars derailing. The point of derailment was found to depend on the cause of each train derailment. The number of cars involved in the subsequent derailment block was found to depend on the cause of the accident, the length of the train, and the speed of o~eration at the time of the derailment.

    Application of this model to a typical rail corridor suggests that marshalling regulations for DG cars should be sensitive to corridor conditions. For the Sarnia - Toronto corridor, current CTC regulations governing the placement of DG cars on a train were found to be ineffective in reducing derailments for DG cars over a random marshalling option.

    This analysis has also demonstrated that effective marshall- ing strategies can be used to offset the threat of increased derailments caused by trains operating at higher speeds.

    Acknowledgments This study was funded by the Natural Sciences and Engi-

    neering Research Council of Canada and by the Ontario University Research Incentives Fund.

    A. D. LITTLE INC. 1983. Event probability and impact zones for hazardous material accidents on railroads. Report DOT/FRA/ ORD-83/20, Federal Railway Association, U.S. Department of Transportation, Washington, DC.

    CTC. 1982. Regulations for the transportation of dangerous com- modities by rail. General order no. 1974-1-rail, Canadian Trans- port Commission, Ottawa, Ont.

    EL-HAGE, S. M. 1988. Evaluating train marshalling regulations for railcars carrying dangerous commodities. M.Sc. thesis, University of Waterloo, Waterloo, Ont.

    GRANGE, S. G. M. 1980. Report of Mississauga railway accident inquiry. Ministry of supply and services, Ottawa, Ont.

    SACCOMANNO, F. F., SHORTREED, J. H., and VAN AERDE, M. 1988. Assessing the risks of transporting dangerous goods by truck and rail. Final Report I and 11, Waterloo Research Institute Award No. 11 18801, University of Waterloo, Waterloo, Ont.

    SWOVELAND, C. 1987. Risk analysis of regulatory options for the transport of dangerous commodities by rail. Interfaces, 14: 90-117.

    WADE, PHILIP E. AND ASSOCIATES. 1986. A strategic overview: hazardous goods transportation by rail in Toronto. Final Report prepared for the City of Toronto Planning Department, Toronto, Ont. November.

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