A New Numerical Procedure for Calculating Societal Risk from Road Transport of Dangerous Substances. P. Leonelli and G. Spadoni, Department of Chemical, Mining Engineering and Environmental Technologies, University of Bologna, IT
INTRODUCTION
The importance of assessing risks in transportation of
dangerous goods has been shown by several historical analyses [1]
which pointed out how their magnitude is, in many cases, quite
similar to that one resulting from chemical and process
industries. Consequently the quantitative risk analysis (QRA)
must be considered an important tool to support activities of
land-use planning and safety control, not only for process
industries, but for all types of transportation too.
In order to obtain a global picture of the risk to which a
population living in a territory is subjected, the societal risk,
represented by F/N curves, is usually evaluated. The societal
risk requires, above all, a realistic modelling of the population
distribution, besides careful modelling of accidents which
characterise the transport vector. As a matter of fact,
population may be off-road or on-road, distributed (different
densities for different land uses) or aggregated in centres (e.g.
schools, hospitals, ...) and large differences may result in the
cumulated annual frequencies F of accidental events responsible
for N or more fatalities if this distribution is not properly
taken into account.
In this paper the attention is focused on road transport of
dangerous goods and a numerical procedure is briefly described
which is able to overlapping vulnerability maps of the possible
accidents of a tanker on the user defined impact area. This
procedure allows to evaluate, by an efficient mathematical
algorithm the contribution of all people categories (population
on-road, distributed or aggregated) to the total number N of
people affected from each accidental scenario. Tests are
performed to compare the new procedure with a translation
procedure previously proposed [2] in order to highlight
improvements in result accuracy and computer time effectiveness.
VULNERABILITY MAPS
The identification of possible accidental scenarios due to a
material release after an accident and the assessment of the
corresponding consequences depend on the design characteristic of
the tanker and on the properties of the conveyed dangerous
substance. Typical accidental release cases for road transport of
flammable and toxic substances may be identified and the
characterisation of their accidental scenarios -- regarding
likelihood and size of breakage; rate, physical aspect and
duration of the release -- may be carried out by using
engineering judgement, literature information [3], proper
simulation models. Consequences models enable to calculate the
spatial distribution of the physical effects (toxic gas
concentration, thermal radiation and blast overpressure) in the
impact area, under the assumption of typical weather conditions.
Lastly probit models allow to translate physical effects in
vulnerability maps.
It is worth noticing that the vulnerability maps of all the
accidental scenarios which characterise the point risk source
(the vehicle travelling on the road), do not depend on the
population distribution and may be conveniently stored. In this
procedure a scenario is represented by a vulnerability
distribution on a 
Cartesian reference frame, whose origin is the
vehicle, 
being the downwind direction (Fig. 1). Its vulnerability data are
stored in a matrix which represents the distribution, calculated
once and for all, on a non uniform grid in the plane. The Cartesian
axes can be rotated and translated on the area of interest in
order to describe both the changes in the wind direction and the
vehicle motion.
POPULATION DISTRIBUTION
As far as population modelling is concerned, the user
describes: -the distributed population by partitioning the impact
area into rectangular subareas, where population density may be
considered uniform, - the on-road population by means of lines,
with a specific traffic, - the aggregated population by means of
points, i.e. Centres of Aggregated Population (CAP's: school,
hospitals, ...). In order to better describe changes in
population density, in this way taking into account its
dependence on time, the year may be subdivided in more periods
(seasons, day-night distribution, ...). For each periods the
procedure evaluates accident occurrence frequencies and people
involved in each scenario.
MATHEMATICAL ALGORITHM
The evaluation of societal risk can be performed through the
following steps. First of all, for each accidental scenario
located in a generic point of the road, the frequency of
occurrence per unit road length (accidents year-1 km-1)
f and the number of fatalities N are evaluated, by
recalling vulnerability values stored for the point risk source.
Then the frequency function per unit road length, for a fixed
number of people involved, fN is integrated on
the line (road) simulating a sort of travelling accident. Lastly
the frequencies (events year-1) of events causing N or
more fatalities are added to determine the cumulated curve F/N.
Number of fatalities
Once the point risk source is located on population map and
the
plane is oriented taking into account wind direction, the
fatalities N due to each scenario are evaluated resorting to the
following equation:
 |
(1) |
where nl, nA and nC are
respectively the numbers of fines, rectangles and CAP's on the
population map; 
the corresponding people density, NC the
number of persons in a CAP; x1, xA and xC
the probability of being outdoor. In equation 1 vp and
are
respectively the vulnerability and the mitigation factor,
deriving from being indoors, stored in vulnerability maps. In
order to perform the integration steps, continue functions for vp
and
are obtained by a linear interpolation of vulnerability matrixes.
A particular attention has been devoted to obtain accuracy in
integral calculus and short computing time. As far as area
integration is concerned, the calculation is performed by an
algorithm, derived from the circuitation theorem, which allows to
store the results of the line integration in direction
(see Fig. 1) and then to obtain the surface integral through a
line integration in 
direction.
It is worth noticing that the numbers of fatalities depends
strictly on the point risk source position on the population map
and on the wind direction. To obtain a good estimation of the
number of fatalities which the scenarios cause in all directions,
at least 360 wind directions should be considered. To save both
the accuracy and the time consumption, an algorithm has been
implemented able to reduce the number of directions through a
comparison between the values of N evaluated by a linear
interpolation of some significative directions and those ones
given by equation (1). The influence of the position will result
from the travelling accident algorithm which requires the
evaluation of occurrence frequency.
Occurrence frequency and travelling accident algorithm
The scenario frequency per unit road length f is calculated as follows [3]:
 |
(2) |
where 
is the average incident rate (incidents vehicle-1
km-1), pO and pI are
respectively the release and the ignition probability (for
flammable substances only), pW is the probability of a
given wind direction and weather conditions for the accidental
scenario. The term nV xV is the number of
tankers on the road in the chosen period. Each accidental
scenario of the point risk source is now characterised by a
number of fatalities N and a frequency per unit length f,
such frequencies are added for all scenarios involving a specific
user-defined range of fatalities to evaluate fN.
The travelling accident algorithm performs a line integration
along the road of fN values by means of an
adaptive step size Simpson rule allowing to reduce the number of
road points which must be taken into account to describe the
movement of the vehicle along the road. A convergence criterion,
based on the maximum error on fN integral
values, is adopted to ensure calculation accuracy.
TEST
Tests have been performed to compare the new procedure with
TRAT computer code [3] which utilised a semi 'clustered'
approach. In the following a sample significant case, referred to
an ammonia transport, is discussed.
The release scenarios considered are obviously the same; the sample population map consists of a large rectangle characterised by urban density (8 10-3 persons m-2) with different probability to be indoor or outdoor during four year periods. 2000 tankers/year of ammonia, uniformly distributed in the four periods, travel on a road located in the middle of the area. In figure 2 are reported the F/N curves calculated through the two codes. Time consumption is respectively 10 minutes for TRAT code and 1 minute for the new procedure on a PC-Pentium-66 MHz.
The results show a significative difference in the maximum
number of people involved in the scenarios. In fact, TRAT code
gives 700 as maximum numbers of fatalities whereas the
corresponding evaluation of the new code is 300. Note that the
new procedure performs the surface integral of vulnerability and
this guarantees an accuracy greater than that resulting from
clustering the distributed population in the centres of cells.
That is pointed out in F/N curves for large number of fatalities,
because the cumulative procedure reduces the errors for low
number of people involved.
SOME CONCLUSIONS
Societal risk is often used to measure risks to which a
population is subjected owing to the transport of dangerous
substances. The resulting F/N curves may be utilised to
distinguish among cases of negligible risk, of unacceptable risk
or cases where a risk reduction is convenient or required [3][4]
by adopting tolerability curves. They are often based on a risk
aversion principle, which means that the expected cumulative
frequency of events having more serious consequences must
decrease more than proportionally. As a consequence particular
attention must be given to the numerical procedure which performs
calculations, because decisions depend on the accuracy of the
examined curve. The proposed procedure has been studied to reduce
the numerical uncertainties included in evaluating fatalities
number and corresponding frequencies, which can determine really
significative errors particularly in the range of large number of
people involved.
Furthermore it is worth noting that the procedure adopted can
be easily extended to different ways of transportation (railways,
pipelines, inland water-ways), although it has been originally
conceived for transport by road.
REFERENCE
[1] Brockoff, L. H., 'A Risk Management Model
for Transport of Dangerous Goods', EUR 14675EN, JRC, Ispra,
Italy, 1992.
[2] Spadoni, G., Leonelli, P., Verlicchi, P. and Fiore, R.,
'A numerical procedure for assessing risks from road transport of
dangerous substances', J. Loss Prev. Process Ind., 8, n.4,
245-251, 1995.
[3] Health & Safety Commission, 'Major
Hazard Aspects of the Transport of Dangerous Substances', HMSO,
London, 1991.
[4] Dutch National Environmental Policy Plan, 'Premises
for Risk Management - Second Chamber of the States General,
Session 1988-1989', The Netherlands, 1989, 5, 137.