GHS BULLETIN
Probabilistic Damage: The IMO Subdivision Index for Cargo Ships

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"Probabilistic damage" refers to a method for computing a measure of probable damage survivability which takes into account not only the vessel's stability when certain subdivisions of the ship are damaged but assigns probabilities to various extents of damage as well as to the survivability when so damaged. The products of these probabilities are summed over the various possible combinations of flooding which could occur from a single breach of the hull, and the result is called the "Attained Subdivision Index".

In GHS terminology, a subdivision of the ship is called a "division". A division is a collection of one or more adjacent tanks/compartments.

In essence, the procedure is as follows:

1) A certain load condition is set for the ship (weight and CG, possibly including loaded tanks).

2) An accumulator variable A (the Attained Index) is initialized to zero.

3) For a given subdivision of the ship, a probability of damage (P) is determined by the size and location of the division. (The longer the division, relative to the length of the ship, the higher its probability of damage).

4) A probability of survival (S) relative to the division is determined by examining the damaged stability characteristics with the division flooded.

5) The product, P*S is added to the attained index: A <-- A + P*S

6) Steps 3 through 5 are repeated for each division.

7) Steps 1 through 6 are repeated for additional load condition(s) and the attained indices for each are averaged.

A certain minimum average Attained Index is required by the rules, based on the size of the ship.

The actual procedure is somewhat more complicated since it can look at fractions of a division being flooded independently as well as multiple divisions being flooded together.

Note that it is inherent in this procedure that all subdivisions of the vessel need not be included in the analysis as long as the Attained Index reaches the minimum required value.

How to Compute a Subdivision Index with GHS

The first step is to define the division geometry, since GHS needs to know what are considered divisions. It does not assume that each tank and compartment is an independent division. Normally, each double bottom tank should be included with at least one other compartment, rather than being a division by itself.

For defining divisions, use the command
```    DIVISION (n) = TankList [/WING:b] [/HBHD:v]
```
which assigns a unique number n to the division which involves those tanks listed by name. If the division includes a wing tank, then the /WING parameter should be used along with the wing breadth b as defined in the IMO rule. If a horizontal bulkhead is present above the waterline and capable of limiting the flooding when not damaged, its height relative to the baseline can be indicated with the /HBHD parameter.

When performing the probabilistic damage procedure, GHS sorts the divisions into order according to their forward longitudinal locations. It then proceeds to use the divisions from bow to stern. After completing the survivability analysis using the first (forwardmost) division, it takes the next division which starts at or after the aft end of the present division. Hence any overlapping division will be ignored.

For this purpose, the nominal forward and aft ends of the division are used. The nominal ends are the same as the actual ends taken from the geometry unless the /FWD and /AFT parameters are used with the DIVISIONS command to set nominal ends at other locations. By this means, divisions which do overlap can be made acceptable. See the DIVISIONS command in the GHS User's Manual for more details.

After all of the divisions have been defined, the Attained Subdivision Index in the current loading condition may be obtained by the command
```  DAMSTAB [(DivList)]  [/L: L1,L2] [/B: B] [/H: Hmax] /SDIC
```
which computes and displays the probability of damage and probability of survival for each damage case as well as the attained index. If DivList is present, it specifies the divisions used; otherwise all of the defined divisions are used. If the /L parameter is present, it specifies the terminal points of the Subdivision Length; otherwise, the overall model length is used. If the /B parameter is present, it specifies the Subdivision Breadth; otherwise, the maximum breadth of the model is used. If the /H parameter is present, it specifies the "maximum possible vertical extent of damage above the baseline"; otherwise the same is computed as a function of the Subdivision Length.

Following is an example of a subdivision index Run File.

```    PROJECT CARGO1
REPORT
```
```    DIV(1) workspc.c, fwctk.c, apt.c /AFT:107.3
DIV(2) no2dot.s, btmineng.c, enginrm.c /FWD:82.9
DIV(3) hold5.c, no4wbt.s, void5.s /AFT:82.2 /FWD:69.6
DIV(4) fwt.s, void4.s, no4wbt.s, hold4.c /AFT:69.6 /FWD:56.3 /WING:3.0
DIV(5) no3wbt.s, no2wing.s, void3.s, hold3.c /AFT:56.3 /FWD:43. /WING:3.0
DIV(6) no3wbt.s, no1wing.s, void2.s, hold2.c /AFT:43. /FWD:29.7 /WING:3.0
DIV(7) no2wbt.s, void1.s /AFT: 29.7 /FWD:20.6
DIV(8) hold1.c, no1wbt.c, no2wbt.s, void1.s /AFT:20.6 /FWD:9.4
DIV(9) thrstrm.c DIV(10) fpt.c /FWD:-4.80 DIV
```
```    MACRO case
TRIM = 0
HEEL = 0
DRAFT = %1
VCG = %2
SOLVE WEIGHT, LCG
DAMSTAB /SDIC
/
```
```    .case 6.5, 7.13
.case 4.684, 6.564
```
```    QUIT
```

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