Probabilistic Damage: The IMO Subdivision Index for Cargo Ships
"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
Following is an example of a subdivision index Run File.
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
TRIM = 0
HEEL = 0
DRAFT = %1
VCG = %2
SOLVE WEIGHT, LCG
.case 6.5, 7.13
.case 4.684, 6.564
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