**5. Occurrence frequency of accidents during the transport of explosive materials**

One important input for the calculations is the occurrence frequency of accidents during the transport of explosive material with different transportation means. Information has to be gathered from the competent institutions in the respective country. As an example the approach in Germany is shortly described.

### **5.1. Train accident statistic**

According to the accident statistics of the German Railways there was in Germany in the time frame of 10 years no accident of dangerous goods transports with explosive materials. From the zero-error statistics, there is the expectation value for the current admission rate of accidents in Germany in dangerous goods transports by rail with explosive materials (hUEG,B):

$$h\_{\text{LEG},B} = \frac{1}{2 \cdot 10a} \tag{4}$$

Thus, HUEG,B is defined as

$$H\_{\text{LEG},B} = \frac{h\_{\text{LEG},B}}{L\_{E,B}} \cdot n \cdot l \tag{5}$$

with

134 Nuclear Power – Practical Aspects

with

reached.

with

nuclear power plant,

The occurrence frequency of a detonation is several orders of magnitude lower compared with a deflagration [20]. As far as the distance of the area where the deflagration started has a distance larger than 100 m from the plant under consideration (see safety margins in

In case of accidents with materials with the potential of a detonation (in particular explosives, ammunition, gases exothermically disintegrating) the detonation is expected to occur at the accident location, i.e. at a transport route or a fixed industrial installation. Here

HE,SMZ Annual frequency of a explosion pressure wave by explosives, ammunition or

HU,SMZ Annual frequency of accidents with explosives, ammunition or gases

The deflagration pressure of maximal 10 bar drops over 100 m around a factor 1E04, so that within the power station pressure values within the range of the wind pressures are

In case of explosive gas air mixtures (combustible gases with air; inflammable steams, e.g. also of liquid gas, with air) clouds can appear and a drifting of these clouds from the place

In this situation the deflagration can take place in the area of the plant buildings. The

HE,GLG Annual frequency of an explosion pressure wave by gas air mixtures in the

HU,GLG Annual frequency of accidents with combustible gas in the surroundings of the

WM Conditional probability for the development of an explosive gas air mixture in case

WD Conditional probability for drifting of the gas air mixture to the nuclear power

In a more detailed verification the assumptions introduced can be replaced by plant-specific

proofs, considering the different effects of the determined explosion pressure waves.

gases exothermically disintegrating in the surroundings of the nuclear power plant,

exothermically disintegrating in the surroundings of the nuclear power plant,

WZ Conditional probability of the ignition in case of an accident.

where the accident happened into the direction of the plant is possible.

approach applied for this case is described in the following equation [20]:

plant (as a result of temporal averaging of the arising wind directions), WZ Conditional probability of the ignition at the area of the plant.

surroundings of the nuclear power plant,

of an accident with combustible gas,

*H HW E SMZ U SMZ Z* , , (2)

*H H W WW E GLG U GLG M D Z* , , (3)

accordance with [18]), no endangerment of the plant buildings has to be assumed.

the approach as provided in formula (2) is applied:

HUEG,B yearly frequency of accidents in case of transports of dangerous goods with explosive materials by rail in the vicinity of the nuclear power plant,

LE,B train transport kilometers per year with explosive materials,

n number of transports (trains) per year with an explosive good passing the nuclear power plant,

l section length l along the nuclear power plant (e.g. l = 2 km) which could lead to a hazardous situation for the nuclear power plant.

The section length l can be calculated from

$$l = 2\sqrt{r^2 - a^2} \tag{6}$$

with

a minimum distance of the railway line to the nuclear power plant,


## **5.2. Ship accident statistics**

Ship accidents (provided in Germany by the local Waterways and Shipping Directorate) are provided for a defined time period and the river-km and distinguished by the types of accidents. Information with respect to the participation of gas, liquid gas and ammunition shipments to the accident is usually given. The evaluation is performed according to the procedure in [21].

Probabilistic Assessment of Nuclear Power Plant Protection Against External Explosions 137

An alternative method is to compute the theoretical probability of an explosion event within the radius rP in each scenario the wind direction will move the explosive gas mixture to the plant. The advantage over the lee is that each scenario gives a contribution to the probability

By analogy with transport theory, this procedure is called free flight estimator (ffe) also described in [25]. Depending on the accident coordinate (xi, yi) and the wind direction φi in

( , ) exp 1 / ( , )

*Eii W ii*

where d1(x, φ) and d2(x, φ) are the distances between the accident coordinate and the

The intersection coordinates (xI, yI) of the wind direction φi and the plant area with radius rP

 <sup>2</sup> 2 2 tan( ) ( ) *I i i Ii P x y xx r* 

 <sup>2</sup> tan( ) ( ) *I i i Ii y y xx* 

> 1 <sup>1</sup> <sup>ˆ</sup> (,) *N E Eii i P Px N*

If the forced transition method is used (see, e.g., [26]), the next transition is forced to take

( | ) (| , )

*PX x x X x Fx x x*

\*

1 2 12

1 2 1

2 1 *w Fx Fx* () () . (13)

() ( ) . () ()

*Fx Fx Fx Fx*

*P x v dx*

 

*v dx*

exp 1 / ( , )

1 2

 

(8)

(9)

(12)

. (10)

(11)

 

*W ii*

trial i the probability of an explosion event within the radius rP is given by

intersection of the wind direction and the plant area with radius rP.

place within the area (wind direction, distance, time etc.) of interest.

of occurrence.

are determined by means of

The sample mean probability is

where N = number of trials.

*6.1.3. Biasing techniques in use* 

The modified conditional cdf is

The weight associated to this bias is

and
