1. Paris, March 2011
Probabilistic Damage Stability Rules for cargo ships and SPS (Part B – SOLAS 2009)
Marine Technical Department Stability Section (DT5)

2. CONTENTS Probabilistic concept Stability criteria to be satisfied
Parameters to be considered
Concepts for simplified analysis
Openings, controls & escape routes
Bottom damage
Minimum required GM
SOLAS 92 and SOLAS 2009

3. APPLICATION SOLAS PART B – 1
MSC.281(85) : Explanatory notes to SOLAS CH II-1
Dry  cargo ships with type B freeboard
L > 80 m, if constructed on or after 1 January 2009
L is the length as defined in the ICLL in force
For SPS : MSC.266(84) : application depending on
flag requirements.

4. PROBABILISTIC CONCEPT
What is the basis of the probabilistic concept?
The probabilistic concept is based on the probability of survival after collision (damaged ship condition)
This probability of survival is expressed by the attained index A
The attained index A is obtained from the summation of the partial indices As, Ap, Al
For which values of attained index A do we consider a ship as surviving?
The requirement for the survivability of the ship is set by the required index R
Therefore, the attained index A is to be compared with the required index R

5. STABILITY CRITERIA TO BE SATISFIED
Four criteria need to satisfied for cargo ships/SPS
As ≥ 0.5R/0.9R, and
Ap ≥ 0.5R/0.9R, and
Al ≥ 0.5R/0.9R, and
A ≥ R
Partial attained index
As : corresponds to the deepest subdivision draught ds
Ap :corresponds to the partial subdivision draught dp
Al : corresponds to the lightest subdivision draught dl

6. REQUIRED INDEX R FOR CARGO SHIPS
Where:
Ro = R as calculated for Ls > 100 m

7. REQUIRED INDEX R FOR PASSENGER SHIPS/SPS
N= N1+ 2 N2 with
N1, number of persons for whom lifeboats are provided and
N2, number of persons the ship is permitted to carry in excess of N1
N can be reduced to a minimum of N1+N2 subject to the agreement of the flag

8. ATTAINED INDEX A
Each partial attained index is a summation of the contribution from all damage cases taken into consideration, using the following formula:
Where:
i : damaged zone or group of compartments under consideration
c : the considered loading condition

9. FACTORS OF PROBABILITY
Example:
p(j=3) : represents the probability that only zone number 3 will be flooded taking into account the transverse subdivision (factors r1, r2, r3)

10. FACTORS OF PROBABILITY
Example 1:
Calculation of damage cases
Vertical limit: v1
Penetration: r1
Select the case which
gives the smallest value
for s:
MIN {s3;s32;s321}
Case Nr
Damaged spaces
Transverse extent (r)
Vertical extent (v)
s-factor 1 3 r1 v1 s3 2
3+2
s32
3+2+1
s321

11. FACTORS OF PROBABILITY
Example 2:
Calculation of damage cases
Vertical limit: v2 = 1
Penetration: r1
Select the case which
gives the smallest value
for s:
MIN{s34;s342;s3421}
Case Nr
Damaged spaces
Transverse extent (r)
Vertical extent (v)
s-factor 4
3+4 r1
1 - v1
s34 5
3+4+2
s342 6
s3421

12. FACTORS OF PROBABILITY
Example 3:
Calculation of damage cases
Vertical limit: v1
Penetration: r2
Case 6a or 6b depending on
B/2 exceeding the CL or not
Select the case which
gives the smallest value
for s:
MIN{s36;s3625;s36251/s362518}
Case Nr
Damaged spaces
Transverse extent (r)
Vertical extent (v)
s-factor 4
3+6
1 - r1 v1
s36 5
s3625 6a
s36251 6b
s362518

13. PARAMETERS TO BE CONSIDERED
Watertight bulkheads and decks
Weathertight bulkheads and decks
Doors (watertight, weathertight of sufficient tightness and strength to restrict the flow
Air pipes
Ventilators
Piping systems
Horizontal evacuation routes
Vertical escape hatches
Controls: operation of watertight doors, equalisation arrangements, valves on piping or ventilation ducts, etc.)
Permeability of spaces

14. PARAMETERS TO BE CONSIDERED
Spaces
Permeability
at draught ds
at draught dp
at draught dl
Appropriated to stores
0.60
Occupied by accommodation
0.95
Occupied by machinery
0.85
Void spaces
Intended for liquids
0 or 0.95 *
Dry cargo spaces
0.70
0.80
Container spaces
Ro-ro spaces
0.90
Cargo liquids
* whichever results in the more severe
Other figures for permeability may be used if substantiated by calculation

15. Specific requirements for SPS

16. CONCEPTS FOR SIMPLIFYING THE ANALYSIS
V-lines concept
Important factors for the calculation of the s-value:
θe : Equilibrium heel angle
θv : Angle where GZ < 0 or submersion of unprotected openings (downflooding point: openings cannot be closed weathertight)

17. CONCEPTS FOR SIMPLIFYING THE ANALYSIS
V-lines concept
The envelope curve of worst waterlines after damage for all the damage cases giving positive contribution to the attained index A
Type of V-lines
“Watertight V-lines” derived from equilibrium heel angle (final or intermediate stages of flooding)
“Weathertight V-lines” derived from positive range (of GZ-curve)
Input for the calculation of the V-lines
Bulkheads limiting the boundary of damage under consideration
Decks limiting the boundary of damage under consideration

18. CONCEPTS FOR SIMPLIFYING THE ANALYSIS
V-lines concept
Construction
Scantling calculation (sufficient strength to resist flooding loads)
Machinery
Position of ventilators, air pipes
Electricity
Control of watertight doors, valves, etc.
Safety
Horizontal evacuation routes
Vertical escape hatch
Escape routes, etc.
Stability
Verification of progressive flooding
V-lines from positive range
V-lines from equilibrium
No immersion of openings
Weathertight
openings
Watertight openings

19. CONCEPTS FOR SIMPLIFYING THE ANALYSIS
Safe Area concept
Area far away from side shell (damage)
Probability (r-factor) to have damage to area close to CL is very small
Piping system as much as possible positioned close to the CL
Maximum penetration is the boundary of the safe area (r2) instead of CL
Way to simplify the investigation of progressive flooding
Negligible impact on attained index A: r3 = 1 – r2 is very small

20. CONCEPTS FOR SIMPLIFYING THE ANALYSIS
No Safe Area
Investigation on progressive flooding for each damage case giving positive contribution to the attained index A
Fitting of valves to prevent progressive flooding
Maximum penetration is CL (or B/2)

21. CONCEPTS FOR SIMPLIFYING THE ANALYSIS
Shadow of Tank concept CL CL
Damage case:
Damage in zone 1
Consequences:
Damage in space 1
Damage of pipe
Progressive flooding of space 3 3 1 2

22. CONCEPTS FOR SIMPLIFYING THE ANALYSIS
Shadow of Tank concept
Damage case:
Damage in zone 1
Consequences:
Damage in space 1
(No damage of pipe)
(No progressive flooding of space 3) CL CL 3 1 2

23. CONCEPTS FOR SIMPLIFYING THE ANALYSIS
Shadow of Tank concept
Damage case:
Damage in zone 2, up to r
Consequences:
Damage in space 2
Damage of pipe
Progressive flooding of space 3 CL CL 3 1 r 2

24. CONCEPTS FOR SIMPLIFYING THE ANALYSIS
Shadow of Tank concept
Damage case:
Damage in zone 2
Consequences:
up to r1: damage in space 2 (no damage of pipe, no progressive flooding of space 3)
up to r2: damage in space 2, space 3 and pipe CL CL 1 3 r1 r1 r2 2

25. OPENINGS, CONTROLS AND ESCAPE ROUTES
s = 0 (means: ship is not surviving), if position of
Air pipes, ventilators and openings closed by means of weathertight doors or hatch covers through which progressive flooding may take place
Horizontal evacuation route
is below the waterline at final equilibrium
Vertical escape hatch
Controls for the operation of watertight doors, equalisation devices, valves on piping or on ventilation ducts intended to maintain the integrity of watertight bulkheads above the bulkhead deck
Any part of piping or ventilation ducts not fitted with watertight means of closure, carried through a watertight boundary
is below the waterline in intermediate stages or at final equilibrium

26. OPENINGS, CONTROLS AND ESCAPE ROUTES
s not automatically 0 if position of
Air pipes, ventilators and openings closed by means of weathertight doors or hatch covers through which progressive flooding may take place
Horizontal evacuation route and vertical escape hatch
Controls for the operation of watertight doors, equalisation devices, valves on piping or on ventilation ducts intended to maintain the integrity of watertight bulkheads above the bulkhead deck
is above the V-lines
Any part of piping or ventilation ducts carried through a watertight boundary is fitted with valves able to prevent progressive flooding

27. SIMPLIFIED ANALYSIS – SUMMARY
V-lines concept
Safe Area concept
Shadow of Tank concept
Pipes and valves are adjacent to a bulkhead (longitudinal/transverse) or deck
Provision: the separation distance is of the same order as the stiffening structure
Total cross sectional area of pipe < 710 mm2 (where possible)
Otherwise:
Investigation on progressive flooding for each damage case
If pipes and valves are outside the order of the stiffening structure, introduction of a gap or additional zone and investigation of progressive flooding

28. LOCATION OF VALVES AT BULKHEADS
Example: or or

29. SURVIVABILITY FACTORS
sintermediate and smom not applicable to cargo ships but to passenger ships/SPS

30. S intermediate and S mom

31. S intermediate and S mom
→ S intermediate to be calculated for passenger ships only if :
progressive flooding / equalization before cross flooding
greater than > 60 s
Non watertight bulkheads restricting the immediate flow of water such as A class fire bulkheads, incenerator room, refrigerated spaces.

32. S intermediate and S mom

33. S intermediate and S mom

34. S intermediate and S mom

35. S intermediate and S mom

36. Double bottom height [m]
BOTTOM DAMAGE
Double bottom height [m]
Bottom damage
h ≥ MIN{B/20,2}
hmin = 0.76 NO

37. MINIMUM REQUIRED GM
If the attained index A = pr  v  s satisfies the stability criteria of SOLAS 2009, the minimum GM-curve is drawn based on the chosen VCGs
pr, v-factors
s-factor
Geometry of watertight arrangement
Loading condition
VCG
Trim
Operational
trim range ≤ 0.5% Ls
Operational trim
range ≥ 0.5% Ls
p: longitudinal direction
r: transverse direction
v: vertical direction
Light draught
(dl)
VCGl
Actual
Partial draught
(dp)
VCGp
≠0 with steps
≤1% Ls
Deepest draught
(ds)
VCGs

38. MINIMUM REQUIRED GM
Minimum GM-curve = envelope GM-curve covering calculations for different trim values

39. 2. SOLAS 92 and SOLAS 2009 SOLAS 1992 (cargo ships)
Calculations for 2 draughts (deepest & partial)
No partial index requirements
Permeability for cargo holds is constant and equal to 0.70
Damage extent is up to CL
Calculations are performed at even keel (trim = 0)
SOLAS (cargo and passenger ships)
Calculation for 3 draughts (deepest, light service & partial)
Partial indices Ai ≥ 0.5R
Permeability of cargo holds is function of draughts and cargo type
Damage extent is up to B/2
Calculations are performed for several trims if range of operational trims exceed +/- 0.5% Ls (subdivision length)

40. Thank you for your attention