Collision damage statistics and probabilistic damage stability calculations in preliminary ship design

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COLLISION DAMAGE STATISTICS

AND

PROBABILISTIC DAMAGE STABILITY CALCULATIONS IN PRELIMINARY SHIP DESÏGN

3. lUNCHER JENSEN, L BAATRUP & P. ANDERSEN Departthent of Ocean Engineering

Technical University of Denmark,

Building 101 E, DK-2800 Lyngby, DENMARK

ABSTRACT

The recent 1MO Resolution MSC 19(58) points towards. a more rational way of obtaining subdivisiöns in ships to ensure a sufficient stability in damaged conditions.

In the prelimiñary phase of ship design it is important to know how the attained subdivision index and the possible oil outflow in a collision are influenced by the actual positions of the watertight bulkheads This information should be given in form of sensitivity factors yielding the change in attained index, subdivision and oil outflow for specified changes in the position of userdefined bulkheads.

In the paper such a procedure will be described. The formûlation is quite general implying that ftitur improvements in the damage stability regulatiöns cari be easily implemented.. Furthermore, infôrmation of oil outflow from damaged cargo tanks is included. By that, both the probability of zero outflow, average hypothetical oil outflow as well as mean local outflow are presented The procedure can thus be used to compare the environmental damage to be expected from different type of oil tankers in. a given collision scenario.

INTRODUCTION

Recently the assessment of damage stability of ships has received a great deal of attentiondue to the tragic losses of sevèral Ro-Ro ferries: the "EurbpaflGateway" (1982), the "Herald of

Free Enterprise" (1987)and the "Estonia" (1994). Of course the international maritime society

is seriously concerned and. puts substantial effort in both deriving rational procedures for

assessing the residual stability Of a damaged ship and setting up reasonable minimum

requirements.

A significant development in the rules and regulations for damage stability assessment can be foreseen in the next few years, most certainly within the framework of a probabilistic description of the dathagés a ship may suffer in a grounding or a collision accident.

The probabilistic daínage stability regulations for thy cargo ships of length greater than 100 m issued by the International Maritime Organization (1MO) in 1990 [1] provide the most updated, generally accepted version of such a procedure. Whereas the probabilistic, concept is simple and gives a single measure öf the probability of surviving a collision accidént its implementation in actual design poses a number of problems.. The main problems are:

Establishment of realistic probability distributions for the location and extent of damages.

Extension to cover damage statistics for grounding.

Definition of the probability of damage of a given. compartment or group of compartments.

Realistic criteria for the probability of surviving a given daiiage. (y) Definition of suitable loading conditions.

Proper account of openings, downflooding points and crossflöoding pipes. Specification of realistic permeabilities of flooded compartments.

Definition of minimum requirements taking into account the number Of people. on board and the possible damage to the environment (oil outflow).

Proper account of the water ingress process.

Some of the problems are neglected in the present regulations [1] by simply demanding for example specific loading conditions and permeabilities. Other problems are covered by other regulations: grounding and oil outflow. Thç remaining items are treated in a more or less rigorous manner, allowing for some ambiguity in the application of the régulations.This

is a very undesirable situation as the resulting safety measure, the attained subdivision index, should be. the same for a given ship, irrespective of the design office or computer software

doing the calculations Therefore 1MO has released an explanatory note, 1MO Resolution A.684(17), [2] which eliminates some of the ambiguity, but still accepts different modelling of the damaged compartments.

In this paper an outline will be given of a computer program package for ship design including a probabilistic datflage stability module iñ accordance with [f], but so versatile that improvements in the regulations can. easily be accòmnmodated. In addition the expected oil outflow in a collision is determined, using the procedure described in [3]. Te computer software is especially intended fôr use in the preliminary design phase where the compartment layout cari still be changed, Therefore, the procedure includes a sensitivity analysis for the attained subdivision index with respect to the vertical centre of gravity and on selected bulkhead and deck positions.

The designer may from these results relatively easily determine a compartment layout satisfying the requirement to the attained subdivision index.

In the next section a short description of the geometry definition of the hull and

compartment layout in the present procedure is given The following sections discuss some of the pertinent aspects in the probabilistic damage calcúlations and a possible extension to

oil outflow estimation. The final section deals with an application of the procedure in

preiminaiy ship design.

GEOMETRY DEFINiTION

The first part in the description of the geometry is the definition, of the outer hull. In the computer program package used in the present study the hull is defined by a number of two-and three dimensional curves. The available curves are station curves, contour cUrves, water lines, knUckle lines, buttocks and generic curves. A wireframe model of the outer hull surface can easily be defined using these curves. Both symmetrical and asymmetrical hulls can be represented. It is important tO notice that the wirefratne model is a connected wireframe, i.e.

the curves are "glued " together at the intersectiOn points. This forces e.g. a water line

intersecting a station to change shape if the shape of the station curve is modified.

All the curves in the wireframe are represented by Ferguson splines [4] which is an interpolating spline containing the offset points.

---

I---Figure 1: General arrangement of a Ro-Ro ship (student's exercise).

The wireframe model of the outer hull is defined interactively in the program package. It is possible to monitor important hydrostatic data such as displacement, center of buoyancy

and center of flotation during definition and modification of the model.

When the wireframe model is completed the topology of the hull can be established automatically and a surface model using N-sided patches is generated. Usually the surface model is only used for visual presentation of the hull while the hydrostatic properties are calculated using a longitudinal integration technique. However, a panel integration procedure is also available, [5]. The wireframe model can be transferred to any CADICAE package able to read points and B-splines from an IGES file. The drawing on Figure 1, showing the Ro-Ro ship used as an example in final section, is made by a transfer to AutoCAD.

The internal subdivision of the hull is described by compartments, modeffing all closed volumes e.g. cargo holds, engine room, water ballast tanks and void spaces. A compartment is a collection of volumes with each volume defined by two transverse bulkheads, a number of longitudinal surfaces and of course the outer hull. The longitudinal surfaces are defined by a number of transverse polygons representing the shape of the surface at given longitudinal positions. These transverse polygon curves form a skeleton which is skinned to give the exact shape of the surface. By this approach rather complicated volumes and hence compartments can be defined. For each compartment an intact and a damage volume permeability are given.

This allows the designer to use correct peimeabilities whenever applicable. It is assumed that the fluid contents in a compartment can mQve freely between all volumes used to define the compartment. It should be mentioned that the entire internal subdivision is semi parametric allOwing the designer to make major changes with limited effort.

The loaning conditions are defined by a combination, of fixed masses and liquid content in user-selected compartments. This ensures correct values for the center of gravity and free surface effects.

PROBABILISTIC DAMAGE STABILITY CALCULATIONS

The damage statistics applied in [1] is based on recorded data fOr 296 rammed ships. A quite extensive discussion of this damage statistics is given in [2], but the actual derivation of it is omitted. However, it may easily be shown, [6] that it is derived using a joint probability dnsity function f(x,y) in the form

a(x)

= a(x)é(y)

where x and y are the dimensionless longitudinal position and extent, respectively of the damage. The functions a(x), c(y) are

ÍO.4+1.6x; Ox1/2

11.2

;

1/2x1

c(Y)=_(1_t);YJm

(3)

and it is readily verified that Eq. (2) and Eq. (3) fit reasonably well with the damagestatistics shown in [2] using J 0.24.

The probability p that only the compartment bounded by x1 and x2 (x1< X2) is damaged

rna4T,T) x2-yfl

f

c(y)

_f

a(x) dxdy (4)

O

where J = x2 - x1. Performing the integrations th results uoted in [i] are exactly obtalned except for compartments bounded by either the forward or aft end of the ship, where p is calculated slightly differently, [4]. For instance

max(JJ,) _j...

=

f c(y) f

a(x) dxdy +

f

c(y)

f

a(x) dxdy

(5)

O O O _J72

for the aft compartment. The first integral is seen to include damages aft of the aft end which seems strange, but could be argued with the need to inchde sonie damages to the stem nót included in the damage location parameter x. Integration of Eq. () yields exactly the resifit.

quoted iii [1].

A more rational calculation of p would be to apply Eq. (4) alsO, for the fore ad aft

ëompartrnents. Thereby, c(y) should be normalized such that

Ji11 _1-y/2

f c(y)

_f.

a(x) d.tdy =

O y!2 yielding

c(Y)=C(i_'t)

where

i

C=

0.8

OJz

lJm

3

The fact that a more rational approach could be followed indicates, that future changes in the daxúage statistics are very likely. Improvements in the d2rnge statistics for the 'transverse penetration and for the vertical extent of damage are even more urgently needed as the present formulas in [1] can result in negative probabilities or ship designs which may suffer

(6)

a catastrophic accident if rammed by a ship with a bow height larger than the stipulated minimum bow height of the ramming ship.

Therefore, the current wrk taking place in a Ñordic Project on Safety of PassengerlRoRo Vessels should be followed with great attention. Some preliminary results indicate that using the theories outlined in [9], reasonable collision damage statistics may be Obtained for ships sailing in specific routes. This is a very important development as it points toward. a rationái proèedure for estimating the côllision. damage statistis Withoùt releying solely On actual

recorded colusión events. The procedure takes into account the ship traffic in the area,

navigational aids and the structural layout of the shps and thus gives the ship designer and the maritime administratiôns a tool able to estimate the benefit of various changes in the ship structures and in the operational profile.

For the complex compartment layout in actual ships, some simplifications must be. done in order to determine the probability of damaging a single compartment or group of compart ments. The explanatory notes [2] deal very extensively with this matter, but also demonstrate that various approaches, yielding different results, all are in accordance with the regulations

From a computational point of view the most convenient of the acceptable procédures is to divide each compartment into fictitious, rectangular boxes. Thereby, the designer does not need .to specify the transverse depth of a compartment which may be difficult, as shown in

Fürthermore, the use of fictitious compartments usually leads to the largest value of the attained subdivision index as beneficial effects of all kinds of recesses are taken into account., The computer module for probabilistic damage stability implemented in the present program therefore makes use of an automatic subdivision into fictitious rectangular boxes.

The most time consuming part of the probabilistic damage stability calculation is deter-mination of the GZ-curve for each damage corfiguration. As the same damage configuration can appear many times when fictitious compartments are used the GZ-curve is of course

stored when first calculated. In the preliminary design phase the vertical center of gravity is often not known precisely and therefore damage stability results for different values of the intact GM are useful. Such results are easily obtained Without the need for further damage stability calculations as

GZ(8) = G'Z(0) + GG' sin o

(9) The sensitivity of the attained subdivision index to user-selected re-positions of bulkheads is calculated automatically. Thereby, the designer is guided towards bulkhead locations satisfying the requirements in [1]. Also some additional local requirements as discussed in [7] may be considered.

Proper account of openings and pipe connections between compartments are extremely important and may be the most tedious point to deal with due to the complexity of the piping system in ships. As mentioned in [8], the bilge piping system effectively connects a large

number of tanks in a damage condition, where a number of pipes are dmged. In the

preliminary design phase the topology of the ship is seldom documented in such detail as to automatically extract information of these openings and the designer must therefore carefully either define such openings for a compartment or specify a probability of survival equal to zero for any damage conditions involving that compartment.

Nearly as important as the openings are the permeabilities assigned to the flooded

compartments. These values are fixed in the regulations [1], but as discussed in e.g. [6), [8] more accurate values should be aimed at including both volumetric andsurface permeabiities. Finally, the number of loading conditions may need some extension. Today only full loading and partial loading must be analysed. This seems to be too few and may lead to designs which are overly safe in one condition and disproportionately below the average requirement in the other condition. An extension to three loading conditions may be better. In this context one may also look at the specification of these loading conditions. It seems much more relevant to use actual loading conditions including liquid cargo content in tanks,

rather than fictitious loading conditions based solely on the hydrostatics of the ship.

PROBABILISTIC ASSESSMENT OF OIL OUTFLOW

The present regulations concerning prevention of oil outflow are given in Regulation 13F of Annex 1 of MARPOL73/78. For purposes of comparison between different tanker designs three outflow parameters are defined: Probability of zero outflow, mean outflow and extreme

(local) outflow. A weighted single, so-called Pollution Index E, can be defined from these parameters and used. .for overall assessment of a given design relative to a reférence double hull design.

The danage statistics applied is specified sçparately for collision and grounding. For collision the damage statistics used in the MARPOL. regulations differs quite significantly frrri the damage statistics applied in the damage stability regulations [1]. From a rational point, of view such differences Must be expected. to diminish in future modifications of the

regulations, although some çorrelati'on of the damage statistics with ship type may be

included.

The cirrent damage statistics used in oil outflow calculations for collisions can yield a negative probability for damaging a group of cómpartments fOr certain compartthent layouts. This Cn asi1y bé demonstrated by examples. The same is true with the damage. statistics for

damage stability calculations, but to a much lessér degree. In both cases this is due tO

approximations in the forrriulas for the damage Statistics, and future modificatiöns shoüld remove this undesirable phenomena.

A similar development of a rational procedure. as mentioned for collision damage. statiStics may also be expected for grounding accidents and this may be the way to remove the Inconsistencies in the current. regulations.'

In the program package, the dam ge statistics specified in [1] for dathage stability

analysis is also applied for prediction of oil outflow. This procedure has previously been suggested, [3].. However, other damage statistics may quite easily be. implemented as well.

APPLICATION OF THE PROCEDURE

Because the procedure has been developed by , University institute it has been implemented

for two groups of users:

Students doing their first ship design in the institute's cOurse on Ship Design. and Construction,

In the master's programme students are generally taught Ship Design and Construction in their fourth and fifth semester. They have prior to that learned the basics which include intact stability and to a very limited extent damage stability. But they have no or very limited experience with actual ship constructions. Some experience of this they will gain from the literature, mainly journals and periodicals, where they study general arrangements and

descriptions of ships already built. This enables them to make a conceptual design of the ship of the type and size which they are assigned.

In the conceptual phase of design the subdivision of the ship is carried out with consider-ation mainly for the use of various compartments, i.e. engine room, cargo space, tanks, etc.. The experienced naval architect will, however, already in this stage give some thoughts to the damage stability, keeping in mind that positions of bulkheads could be subject to minor modifications in the preliminary stage of design. When the designer has little experience, or is working with a novel arid innovative design it may call for calculations for large number of configurations to establish the optimum subdivision. It is therefore important that the procedure used will help the inexperienced as well as the innovative designer in obtaining an overview of the influence of the positions of watertight subdivisions on the attained sub-division index A thus giving guidelines towards the most favourable subsub-division.

As described previously the damage stability analysis is done for two loading cases (partial and full load) for a series of user-selected values of intact metacentric heights GM. For ships of the type where damage stability is crucial such calculations will put restrictions to the lowest acceptable value of GM in the intact condition and the designer should assess

the most appropriate pair of restrictions on the basis of his knowledge regarding the

operational profile of the ship. It is of course vital that in each of the two loading conditions a suitably safety level is chosen.

1.0

0.5

Figure 2: Attained sub4ivision index A as function of intact metacentric height GM for the partial (Ar) and full load (Ai) conditions.

The output of such an analysis for the two loading conditions is shown in Figure 2. It is now up to the designer to decide for the design çoúditions fulfilling

A=l/2(A+Af)>R

(10)

where R is the required index, [1]. Such calculations must be done for many compartment layouts covering larger as well as smaller modifications in the internal subdivisioi of the ship. The computer ptogam makes such modifications easily possible. 1f for istance the depth of a deck or the height f a double bottom is modifled all compartments involved are aútòmati-cally modified. too. Such a situation is ilïustrated in the follöwing, where a Ro-Ro ship design made by students as an exercise is modified by moving the main deck 0.5 tri upwards. The general arrangement of the ship is shown in Figure i.

The attained subdivision indices (Af, A) as function of intact GM are shown in Figure 2 for the full and the partial load case both before and after the modification of the depth. to the main deck. From these results the designer must select a pair of conditions which fulfll Eq. (10). These combinations are shown in Figure 3.

A

_original

modified

i 2

GM

(m]

original

---i modified

intact req.

A<R

I k

Figure 3: CombInations of metacentric heights för full and partial loadings, GMf and GM, satisyig A = R for both the original and modified 4esjgn.

REFERENCES

Resolution MSC 19(58), "On the Adoption of Amendments to SOLAS ConventiOn, regarding Subdivision and Damage Stability of Cargo Ships", Report of the MSC on its 58th Session, MSC 58125, Minex 2, 1MO, Lofldon, UK. 1990.

Resolution A.684(17), Explanatory Nôtes to the SOLAS Reguafions on Subdivision

and Damage Stability of Cargo Ships of 100 Metres in Length and Qver' 1MO,

LOndon, UK. 1991.

[31

Pawlowski, M., "Oil Spill Prevention with New Ship Types in the Light of the

Probabilistic Concept", Proc. WEMT'95, Copenhagen, Denmark 17-19 May, 1995,

pp 181-209.

Ferguson, J., "Multivariable Curve Interpolation", JA CM, 11/2, pp. 221-228, 1964.

Schaick, S. and aatrup, J. "Hydrostatic Stability Calculations by Pressure Inte-grations", Ocean Engineerzng, Vol. 17, No. 1-2, pp. 155-169, 1990

[6].

Jensen, J. Juncher, "Damage Stability Rules in Relation to Ship Design", Proc.

WEMT'95, Copenhagen, Denmark, 17-19 May, 1995; pp 71-96.

Sen, P. and Gerigk, M.K., "Some Aspects of a Knowledge-Based Expert system for Preliminaiy Ship Subdivision Design for Safety", Proc. FRA DS'92, Vol. 2, pp. 1187-97. Eds. Cäldwell, J.B. and Ward, G., Elsevier Pubi. Ltd. UK., 1992.

Koelman, Hi. "FreedOm is just Another Word for Nothing Left to Loose",, Proc. WEMT'95, Copenhagen, Denmark 17-19 May, 1995, pp 45-56.

Petersen, P. Terndrup. "Collision and Grounding Mechanics", Proc. WEM T'95, Copenhagen, Denmark 17-19 May, 1995, pp 125-157,