On the safety level of the SOLAS 29 damage stability rules for RoPax vessels Hendrik Dankowski ), Prof. Stefan Krüger ) Institute of Ship Design and Ship Safety, Hamburg University of Technology Hamburg, Hamburg, Germany Abstract Heading The new probabilistic damage stability rules in SOLAS 29 and their impact on the safety of the ship subdivision design have been widely discussed. Especially the safety level of RoPax designs are considered for further investigations. This paper describes a methodology to compare the safety provided by different damage stability regulations for a certain ship design. The determination of the damage cases probabilities are based on a Monte Carlo simulation for the damage distributions. The damage cube itself is modeled by distribution functions retrieved from statistics based on the HARDER project. This gives a very elegant, fast and direct approach of damage calculations. Together with the calculation of the survivability of all damage cases, this allows to identify and compare the safety level indices of different damage stability standards. The method has been used in the "EMSA Study on Damage Stability of ROPAX vessels". The theory of the simulation methodology and some extracts of the results of the EMSA study will be presented in the following. It has been shown in the study that for the investigated RoPax designs the new SOLAS 29 rules are less stringent than the old, deterministic rules according to the Stockholm agreement. This means that especially the old water-on-deck requirement results in more severe designs and that the required index of the new damage rules is too low for the investigated RoPax vessel designs. Keywords Damage stability, SOLAS 29, Stockholm, Monte Carlo simulation, Water on deck, Safety level Introduction The new probabilistic based damage stability rules have been introduced by the new SOLAS 29 standard based on concepts first introduced by Wendel in the 96 s (Wendel, 96). This probabilistic approach gives more freedom for the designer but requires also more sophisticated methods to perform the calculations. The general idea is to create damage cases, determine their probabilities to occur based on damage statistics provided by the IMO, compute the probabilities to survive these cases and retrieve an attained index A. This calculation has to be performed on three specified drafts for both sides of the ship. The sum over all drafts gives the total attained index, which represents the probability of a certain ship design to survive any damaging of the ship and has to exceed an accepted required index R depending on the ship size and the number of persons to carry. In this paper a computational method is presented, which is applicable to both probabilistic and deterministic based damage stability rules. This Monte Carlo simulation based method generates the required damage cases by drawing a sufficient number of damage cubes of a certain size and location based on incident statistics, virtually penetrating the ships structure with this cube and counting the number of hits for each generated case. The damage probability of each combination is simply the number of hits divided by the total number of virtual damages. In the limit of infinite drawings the analytical probability is reached, but in practice a sufficient number of drawings amount to about,. The hydrostatics for each case together with the stability criteria of the selected rule gives the corresponding survival index s i. In addition, an extension of this method is presented, which allows comparing arbitrary damage stability standards. A so-called safety index for a certain ship design can be computed by looking at all possible damages, i.e. removing the limitation in damage size defined in the rules. Looking at the subsets defined by damage cases included and excluded by a certain standard, reveals hidden safety potentials. In the following, this method is applied to certain example RoPax ship designs according to SOLAS 29 to compare the new SOLAS 29 standard with the old SOLAS 9, deterministic standard together with the Stockholm agreement applicable to RoRo passenger ferries. The presented results reveal a clear picture: Each presented design gives a higher safety index for the new
SOLAS 29 rules compared to the old deterministic rules including the Stockholm addendum. This means that the RoPax designs are judged as safer by the new rules compared to the old standard. Basics of the simulation The Monte Carlo approach If damaging of ships is considered as a statistical process, the assumed damage cube is defined by distribution functions of its degrees of freedom. These distributions (also called cumulative distribution function CDF) are derived from damage statistics. For the development of the new SOLAS 29 rules, these distributions were derived and suggested by the EU research project HARDER, 23. The principle of the Monte Carlo simulation is simply to regenerate the damage statistics by using a uniform random number generator and taking the inverse of the distributions. This random number represents a probability leading to an event, for example a certain damage length. This is illustrated in Fig., showing distribution functions for the damage length according to different standards. Other distribution functions for the remaining degrees of freedom of the damage cube (location, penetration and height) can be found in HARDER, 23 or can be directly derived from the rules. Geometric or statistical interdependency of two or more degrees of freedom are taken into account by either truncating the values (as implemented in SOLAS 29) or redrawing until a valid cube is generated. probability random number.9.8.7.6.5.4.3.2. Distributions of damage length for different rules resulting length..2.3.4.5.6.7.8.9 damage length/subdivision length Solas 4 R8 Solas 9 B HARDER Fig. : Different distributions of the damage length and the drawing of one random number Generation of damage cases With this approach the generation of damage cases simplifies to the generation of a sufficient amount of uniformly distributed random numbers and selecting the corresponding damage extends and its locations from the known distribution models. This damage cube breaches a certain combination of ship compartments. Counting the number of hits for each combination and dividing it by the total number leads to the encountered probability of damaging this combination. The damage generation process can be summarized as follows: - Drawing the damage cube from the damage distributions - Finding the corresponding compartment combination - Integrating the hits for each combination - After a sufficient number of hits, the frequency for each combination is simply the fraction of hits to the total number of samples. The advantages of this method can be outlined as follows: - The generation is independent of the ships internal subdivision, since the view is from the damage and not from the ships perspective. Even very complicated geometries can be investigated. - Since the simulation is completely automatic, more combinations can be found compared to a manual method like the zone approach described in the Explanatory Notes for the new SOLAS 29 rules (IMO, 28). In the limit, even all possible damage cases can be found. - Sorting the cases according to the probabilities gives direct access to the most important ones for the subdivision design. This immediately shows the designer, which compartment combinations are the most relevant ones for the subdivision index. - This method can be applied to both types, probabilistic and deterministic based rules. For the deterministic rules one can for example simply take unit distributions to model the damage cube and to generate all possible damage cases according to the assumed deterministic damage extension. Implementation aspects The damage stability method is completely integrated in the ship design environment E4 developed at our institute. The whole process of hull form and subdivision definition, damage cases generation and the hydrostatic evaluations of the stability criteria is performed using well tested algorithms in one system. The quality of the random number generator influences the convergence to the underlying distributions. In this case a Mersenne-Twister generator is used (Matsumoto, 998). An accurate and fast geometric algorithm was developed to determine which compartment combination was hit by a certain random damage cube. This damage calculation method is very fast: The three drafts times the two sides require about 2-3 minutes to be computed, including the generation of damage cases and the hydrostatic evaluation of the stability criteria. The damage cases generation part takes only one or two minutes. This means, it can be used as a very useful tool at the early design stage, even the optimization of GMmin/KGmax curves is possible and actually implemented as an additional method in the E4 software system.
Analysis of the rules in general Introduction The new probabilistic based damage stability rules have to be applied to new ships after st January 29 and are published in the new SOLAS consolidated edition 29, Chapter II-, Part B-. These rules are simply called SOLAS 29 in the following. They still contain a deterministic part to take into account some minor side damages with a penetration limited to B/ (or.75m, whichever is larger) together with a compartment status according to the old SOLAS 9. Bottom damages have to be taken into account if the double bottom height is less than 2m (or B/2, whichever is less). The old deterministic rules have been valid since the 99 s for passenger ships. The most recent consolidated edition of the SOLAS containing these rules in Chapter II- Regulation 8 was published 24. The Stockholm agreement for RoPax ferries were established after the ESTONIA accident (994) as an addendum to the damage rules. It specifies an additional amount of water on the freeboard deck depending on the freeboard of the assumed damage and the operating sea area. The water on deck has to be taken into account for the calculation of the resulting lever arms in the damage situation for all damage cases defined by the deterministic damage rules. In addition the freeboard deck may not be submerged in the final condition. These rules will be called SOLAS 9 and Stockholm in the following. Further details of the different rules can be found in Valanto, 29. The damage sets and the safety index concept For the comparison of different damage stability rules, the evaluation of a safety index was developed. This index is very useful to tell if one design is declared to be safer according to one rule compared to another rule. In detail, the safety index of the new SOLAS 29 rules will be compared to the old deterministic rule including the Stockholm agreement. One has clearly to distinguish between safety index and safety level. The safety index represents a value to compare different damage stability rules, as outlined in the following. It shows how safe a certain ship design is judged by a certain standard, i.e. how stringent a certain damage rule is. In contrast, the safety level is the real ability of the ship to withstand damages, which total amount is unknown. At first, the statistical basis for the different damage standards has to be the same, because every standard limits the maximum size of the possible damages. This means that each standard uses only a subset of all possible damages as listed in Tab.. The statistical material defined by the HARDER project is considered as the total set of all possible damages. By removing this limit, it can be depicted how many damages are taken into account by a certain standard. Tab. : Damage limits Max. damage SOLAS 9 SOLAS 29 Length m or 3m+.3L, 6m or.33l one or two compartment status Penetration B/5 B/2 This question is answered in Fig. 2, where the sizes of the damage sets depending on the subdivision length are shown. In addition, the old, probabilistic standard for cargo ships is shown as well. The new SOLAS 29 (blue line) includes around 92 percent of all damages for ships below 2m length. The old SOLAS 9 standard (green line) includes only a much smaller amount, which is in addition quickly decreasing with increasing subdivision length. The idea of the total safety index concept is now to distinguish between damage cases included in a certain standard and cases which are excluded by the damage limits of that standard. For both sets the attained indices are computed on all required drafts and the port and starboard side. Weighting these two indices by their percentage size of all damages gives the total safety index. It should be stressed that a higher safety index in this context does not mean that the ship has a better ability to withstand damage cases! It is only evaluated by the applied damage stability standard to be safer, i.e. the standard is less stringent then a one with a lower safety index. An application in the EMSA project presented in the following will clarify this concept. included in rule [%] 8 6 4 2 2 3 4 5 subdivision length LS [m] Fig. 2: Subsets of damages contained in a rule The EMSA project Introduction Subsets of all damages Solas 4 B Solas 4 R8 Solas 9 B As a subcontractor of the Hamburg Ship Model Basin (HSVA) the Institute of Ship Design and Ship Safety of the Hamburg University of Technology (in the following TUHH) performed the damage stability calculations for a research project of the European Maritime Safety Agency (EMSA) (Valanto, 29). The aim of this project was to evaluate with the help of simulation methods and model tests the safety level of current ships
designed for the new SOLAS 29 standard. This project will simply be called EMSA in the following. The first ship design EMSA The first investigated design is a small RoPax ferry of approximate 8m length and a passenger capacity of 3 persons according to SOLAS 29. The required index R for this design amounts to.7. As an initial guess for the required GM values for the SOLAS 29, the resulting values from the intact criteria were used, calculated physically correct with free trimming. The attained index was beyond.75, therefore it was decided to compute the intact stability curve on the basis of a fixed trim. According to many administrations this was allowed in the past. Nowadays this is no longer valid according to the new Intact Stability Code 28. Considering free trim, the resulting attained index for SOLAS 29 amounts to.73, which is still beyond the required index. It should further be noted that the damage stability requirements are governed by the deterministic addendum of minor side damages for this particular design and not by the probabilistic part of the regulations. Already at this point, it can be concluded that the safety requirements according to the new SOLAS 29 are lower for this ship compared to the old SOLAS 9 standard, since the damage stability of this design is restricted by the deterministic part of the SOLAS 29. But that part actually assumes smaller damage penetrations (B/) than the old rules (B/5) did, where the stability requirements are about the same. This means that the new deterministic part cannot be more stringent if a smaller amount of lost buoyancy is assumed, even without any additional water on the vehicle deck. A slight increase of the number of persons above 4 would change the required compartment status from one to two, where most of these two compartment cases would not be survived. On the other hand, this leads only to a minor increase of the required index to.77. The safety index according to SOLAS 29 Now the safety index for EMSA is evaluated with the prescribed method. The new standard includes about 92 percent of all possible damages cases; the remaining 8 percent are not covered by the standard. Tab. 2: Attained Indices of all HARDER damages in- and exclude in SOLAS 29 Draft Included Excluded Total 92% Total 8% Light.795.73.635.52 Partial.72.662.549.45 Deepest.679.624.524.43 To get the index contribution to the total safety index, the values of each set has to be weighted by its percentage amount. The results are given in Tab. 2 and visualized in Fig. 3. Even though the amount of damages not included in the standard is low, about 5-6 percent of these damages are survived as well. Safety index.9.8.7.6.5.4.3.2. Safety index according to SOLAS 29 B Contribution from all Damages not in SOLAS 29 Contribution from all SOLAS 29 B Damages 22 225 23 235 24 245 25 255 26 Deplacement in t All HARDER damages Damages covered by SOLAS 29 B Fig. 3: The overall safety index of the EMSA design according to SOLAS 29 In this context, it should also be mentioned that the overall safety index, and also the related safety level, decreases with increasing draft, whereas a deterministic standard requires (at least within the assumptions of such standard) the same safety level on all drafts. The safety index according to SOLAS 24 As a next step, the total safety index of the ship according to the SOLAS 9 standard for a one compartment status is determined. This results in a total amount of 5.4 percent of all possible damages covered by the standard. To fulfill this standard as well, all of these damages have to be survived according to the stability criteria defined in the rules, which is the case for this design. The detailed results are not listed here but may be found in Valanto, 29. Most interesting is the fact, that a huge number of cases, which were not included in the damage set, are survived as well. This means on the other hand that the most critical cases are already covered by the standard, even though its total amount is quite small. The overall safety index is significantly lower compared to SOLAS 29. Further comparison of the total safety index follows. The safety index according to Stockholm The additional water on deck requirements lead to an additional, significant drop of the safety index. This RoPax design, which fulfills easily the probabilistic and also the deterministic part of the new SOLAS 29 rules does clearly not fulfill the Stockholm Agreement, since several damage cases included in the SOLAS 9 standard are not survived. Especially for the deepest draft, the loss in the safety index is about 23 percent, as many damage cases including those with a high probability of occurrence are not survived. In most of these cases, the critical criterion is the submerging of the freeboard deck. But this margin line criterion was removed in the new SOLAS 29 rules. Comparison of the different standards Required Index The overall safety indices of all three standards investigated are summarized in Tab. 3 and Fig. 4. As it can be seen in Fig. 4, the safety gap between the different standards is very large.
Safety index.9.8.7.6.5.4.3.2. Saf ety index acc. to SOLAS 29 B Safety index acc. to all Standards Saf ety index acc. to SOLAS Reg. 8 + Stockholm Safety gap SOLAS 29 - Reg. 8 Saf ety index acc. to SOLAS Reg. 8 Safety gap Stockholm 22 225 23 235 24 245 25 255 26 Deplacement in t SOLAS 29 B SOLAS Reg. 8 + Stockholm SOLAS Reg. 8 Fig. 4: The overall safety index of the EMSA design according to all standard On the largest draft the safety index according to Stockholm is even halved compared to SOLAS 29. Tab. 3: Comparison of the safety indices of all standards Draft SOLAS SOLAS Stockholm 29 24 Light.782.698.574 Partial.77.559.5 Deepest.667.55.39 Status Fulfilled Fulfilled Not Fulfilled Conclusion for the safety level of the EMSA design The following can be concluded from this first investigation: The requirements of the probabilistic part of SOLAS 29 are for this particular ship less stringent compared to the deterministic standard SOLAS 9. This is shown by the fact that SOLAS 29 attains by far the highest total safety index for this ship. As the deterministic part of SOLAS 29 is per definition less stringent than the deterministic standard according to SOLAS 9, it clearly represents a generally lower safety level. So whenever this deterministic part of SOLAS 29 becomes the governing damage stability requirement for a specific ship design, it is obvious that the overall safety level is lower than according to SOLAS 9. If the calculation of the water-on-deck criterion, as required by the Stockholm Agreement, is regarded as a useful contribution to the safety of RoRo passenger ships, it was found for this particular ship that the safety level represented by the SOLAS 29 lies significantly below the requirements of the SOLAS 9 in conjunction with the Stockholm Agreement. Even for the one compartment flooding, the difference in the loss of the safety index is tremendous. A slight increase of the number of persons beyond 4 leading to a two compartment status is discussed as a design option in the next section. Concluded, for the ship design EMSA no reason has been found to assume that the safety level represented by the new SOLAS 29 standard would be equivalent to or higher than the SOLAS 9 standard in conjunction with the Stockholm Agreement requirements. On the contrary, all calculations show that the safety clearly drops down to a significantly lower level. The remaining open question is of course whether this safety level is still sufficient or if the current damage stability rules require a revision. This is also discussed in the following, where the effect of additional water-on-deck is studied in more detail. Design option for EMSA A reasonable design option of increasing the number of persons beyond 4 was theoretically considered. This would have the following impact on the damage stability characteristics: - The ship would with minor alterations fulfill the probabilistic part of SOLAS 29. This design option would result in a two compartment status for the deterministic part of SOLAS 29. These damage cases would not be survived. The GM-required curve for the total SOLAS 29 would then only be on the basis of its deterministic part. - The SOLAS 9 two compartment status would then clearly not be achieved, as the deterministic standard requires an si value of one for all cases, where SOLAS 29 requires only a value of si=.9. - The requirements of the Stockholm Agreement would in that case never be met, as most of the twocompartment flooding cases would not have any chance to survive with additional water on the freeboard deck. A short test on the deepest draft showed that the percentage of Stockholm cases survived drops down to 45 percent, which was about 65 percent before. The effect of additional water-on-deck It has further been investigated whether or not the Stockholm addendum considering an additional amount of water on the freeboard deck is a reasonable criterion to increase the overall safety level of the ship design. For this purpose a specific damage case is selected for which the water-on-deck criterion has the largest impact and is considered to be safe by the new SOLAS 29 and the SOLAS 9 rules (without Stockholm). This case No. includes the Engine Room, the RoRo Cargo Hold and the Void Space. The resulting lever arm curve shown in Fig. 5 is significantly reduced by the water on the vehicle deck. No stability requirement of the SOLAS 9 is fulfilled. Righting lever [m].3.25.2.5..5 -.5 -. -.5 -.2 -.25 -.3 GM at Equilib.:.658 m Without water on deck Including water on deck 2.5 5 7.5 2.5 5 7.5 2 22.5 25 27.5 3 Heeling angle [deg] Fig. 5: Righting levers of case with and without wateron-deck according to the Stockholm Agreement
It has been found in Valanto, 29 that the ship will statically capsize in this case even with a very small additional amount of water on the cargo deck. But the si-value according to SOLAS 29 amounts still to about.4 including the additional heeling moments, considering this case to be, at least partially, safe. Additional numerical simulations and model tests were carried out by the HSVA. The numerical simulation depicts a limiting wave height of about.2m, in the model test the survival of this case is limited by a wave height of around 3m. This underestimation of numerical simulations has been further discussed in Valanto, 29. However, in all cases the assumed wave height of 4m according to the Stockholm agreement is not survived. In the referenced EMSA project, further cases have been investigated with similar results: These cases gain a si-value between and according to SOLAS 29, but lead to an unsafe condition in rough seaway conditions and therefore considered to not fulfill the Stockholm requirements. Concluding remarks for the EMSA design It has been shown, that it is possible to create a valid RoPax design according to SOLAS 29 which does in about 7 percent of all possible damage cases not fulfill the Stockholm agreement, i.e. sinks or capsizes in rough sea conditions. The reason for this is the insufficient level of stability in general. In the past, almost every RoPax design was governed by the damage stability requirements. With the new SOLAS 29, the design is now limited by the intact requirements according to the IS Code. It has been put forward by several authors (e.g. Kluwe (2)) in the past (also by TUHH and FSG ), that the actual intact stability limit is too low for those types of ships which are characterized by flared hull forms. This observation made it necessary to develop additional criteria for dynamic stability. However, this was not regarded as a serious problem in the past, because the minimum stability requirement was anyway determined by the deterministic damage stability codes. To illustrate the lack of general static stability, the lever arm curve on a fixed trim and on a (real physics) free trim basis are shown in Fig. 6. Righting lever [m].8.6.4.2.8.6.4.2 GM at Equilib.:.642 m Fixed Trim Free Trim -.2-2 3 4 5 6 7 Heeling angle [deg] Fig. 6: Righting levers for the intact condition It can immediately be depicted from both lever arm curves, that this ship cannot withstand very large heeling moments. That is the reason why a small amount of water on the cargo deck yields to an immediate loss of stability in the damaged condition. Therefore the following arguments connected to the total safety regime can be forwarded to explain the drastic reduction in the safety level of the EMSA design: - The new damages stability rule lead into the situation, in which there is no need to increase the stability beyond the values which are attained by the intact criteria. - The level of safety is exactly reduced to that one which is represented by the intact stability criteria, which appears to be too low for this particular ship. Based on the findings of the investigation of the ship design EMSA, the following actions might be considered:. A water-on-deck requirement shall be worked into the stability regulations to ensure that this failure mode is represented correctly. 2. An equivalent level of safety for the RoPax ship type compared to SOLAS 9 without water-ondeck shall be achieved on all drafts. 3. The level of safety provided by the intact stability criteria shall be large enough that the provided safety in the intact condition must not be artificially lifted up by the damage stability requirements. The second ship design EMSA2 The second investigated ship is a 2m RoPax ferry with a large lower hold bounded by a B/ double hull designed to carry 6 persons on short international voyage. The probabilistic part of the SOLAS 29 damage rules is fulfilled, where the limiting stability criteria are the deterministic minor side damages, even though the lower hold is protected by the B/ double hull. The requirements resulting from the intact criteria, namely the weather criterion and a maximum GZ beyond 25 degrees heel, are for most of the draft range of this design stricter than the new damage stability standard. For example, the required GM for the intact criteria on the lightest draft amounts to about 6.2m while the GM values required to barely fulfill the probabilistic part of the SOLAS 29 are 4.m on the lightest and partial draft. The curve of required GM values is shown in Fig. 7. Only the deepest draft in question is limited by the SO- LAS 29 damage stability rules and especially its deterministic addendum. The required index amounts to.722, which is almost equal to the attained index with the mentioned GM values. For this design, the limiting damage criteria are the intermediate stages of several damage cases, due to the flooding of the lower hold in these cases. Flensburger Schiffbau Gesellschaft
Tab. 4: Comparison of the safety indices of all standards for the EMSA2 design Draft SOLAS SOLAS Stockholm 29 24 Light.695.68.636 Partial.748.64.623 Deepest.733.62.583 Status Fulfilled Not Fulfilled Not Fulfilled It should be noted that the lowest safety index for the new SOLAS 29 rules is attained on the lightest draft, caused by the intermediate stages of flooding of the lower hold. As it can be depicted from Fig. 8 the safety gap between the SOLAS 9 plus Stockholm and the new SOLAS 29 is still present, even though the difference is smaller compared to the first investigated design. The gap between SOLAS 9 and Stockholm is quite small, due to the already mentioned influence of the lower hold. Safety index acc. to all Standards.9.8 Saf ety index acc. to SOLAS 29 B Saf ety index acc. to SOLAS Reg. 8 Safety index.7.6.5.4 Saf ety index acc. to SOLAS Reg. 8 + Stockholm Safety gap SOLAS 29 - Reg. 8 Safety gap Stockholm Agreement Fig. 7: Required GM values for the EMSA2 design The in-depth presentation of the safety indices of the different damage stability rules can be found in Valanto, 29. The comparison of the safety indices and a summary of the results are given in the following. Summary of results for EMSA2 As this RoPax ferry is designed for the new SOLAS 29 rules with a double hull on B/ barely fulfilling the requirements, it is of no surprise that it will fail for the old, deterministic SOLAS 9 rules with an assumed damage penetration of B/5. Most of the cases damaging the large lower hold are not survived due to bow trim submerging the margin line, which results in approximate percent of all cases included in SOLAS 9 not fulfilling the stability criteria of this standard. This can be observed on all drafts. The damage set amounts to about 36 percent of all possible damages (see also Fig. 2). Again a very large amount of damage cases (about 5 percent) not covered by the rules are survived as well, giving a large contribution to the total safety index. The additional water-on-deck requirement of the Stockholm addendum reduces, as expected, the attained safety index further. But the reduction is smaller compared to the EMSA design. Most of the greater damage cases are already not survived without water-on-deck, only a few additional cases not penetrating the lower hold do not fulfill the Stockholm addendum. The resulting safety indices attained by the different rules are given in Tab. 4 and Fig. 8..3.2. 6 7 8 9 2 2 22 23 Deplacement in t SOLAS 29 B SOLAS Reg. 8 + Stockholm SOLAS Reg. 8 Fig. 8: The overall safety index of the EMSA2 design according to all standard Conclusion for the EMSA2 design Also for this very different design, compared to the first investigated design EMSA, it can be concluded that the new damage stability regulations are less stringent than the old, deterministic ones, especially in conjunction with the Stockholm agreement. The deterministic addendum, which should actually only take into account minor side damages, is again the governing criterion on the deepest draft. The problem of the ship design EMSA2 has its origin in the situation that whenever the lower hold is flooded, the ship has a general lack of reserve buoyancy, especially when the upper hold is damaged, too. It has been shown by further numerical simulations and model tests that the damaging of the lower hold is crucial for the safety level of the design. In most of these cases the ship immediately sinks or capsizes in rough seaway conditions. Another problem is the relatively small required index. It allows on the deepest draft, which is in fact the main operating condition, to sink or capsize in 35 percent of all SOLAS 29 cases. An increase in the number of
passengers would lead to the situation that also several damage cases resulting from the probabilistic part of SOLAS 29 involving the lower hold would need to be survived. But it should further be noted that a sufficient index of R=.8 is only required for this size of ship when the number of persons carried on short international voyage is increased to 225 persons. To attain this higher index is in fact only possible with an alternative subdivision design and cannot be reached by simply increasing the static stability by lowering the KG value (i.e. increasing the GM). Design option for EMSA2 A new design option for RoPax vessels has been found, to reduce this lack of reserve buoyancy. Since it is allowed according to the new SOLAS 29 rules to submerge the freeboard deck, the reserve buoyancy from the lower hold can be shifted to a double hull fitted on the freeboard deck, providing additional stability when this deck is submerged, This design option was not possible for the old SOLAS 9 regulations, because the freeboard deck was not allowed to be submerged. The small double hull is simply fitted between the existing web frames in the front part of the hold, not reducing any cargo space at a very low additional cost. This leads to a significant increase of the attained index, which now amounts to approximately.8. Especially the gain on the deepest draft is very large. The problem occurring now is that it is not clear how to apply the Stockholm Agreement to cases where the freeboard deck is already flooded. Formally the water level in that compartment would have to be increased by.5m, but it is not quite clear whether this is in line with the physics of the problem. This case was further analyzed by the HSVA with numerical simulations and model tests. The simulation results in a limiting wave height of 6m, the model tests even lead to a height of 6.7m. The reason for a very safe and stable condition in this damage case is simply the fact that the net water ingress on the vehicle deck goes gradually to zero. The very dangerous condition of cumulating water on the vehicle deck is only possible with an initial list or trim or additional heeling moments such as wind or cargo shift. Further investigations of this design option allowing the submerging of the freeboard deck in a damaged case are recommended. Conclusions A fast, elegant and reliable method for damage stability calculations based on Monte Carlo simulations of the damages has been presented. This simulation method gives the ship designer a very useful tool to evaluate the damage stability properties of different subdivision designs at an early design stage. In addition, it allows to compute and to compare arbitrary damage stability standards by the outlined safety index concept. Applied to two new RoPax designs, it has been revealed that the safety level provided by the new SOLAS 29 rules is significantly lower compared to the old damage stability rules SOLAS 9 in conjunction with the Stockholm Agreement. A straightforward idea would be, to apply the Stockholm addendum on the new probabilistic standard as well. But the design option for EMSA2 with a double hull fitted on the vehicle deck shows that this is not directly possible, due to fact that the development of the Stockholm Agreement is based on the deterministic concept of the old SOLAS 9. Another important result was the fact that it is now possible to create RoPax designs easily fulfilling the SOLAS 29 standard, which limiting stability criteria are now the requirements provided by the intact stability code. Another problem revealed is the fact that the deterministic addendum of minor side damages in the SOLAS 29 represents in many cases the limiting criterion for the damage stability. This means, at least for this particular ship type, no real benefit of a probabilistic standard has been gained. The only change is that the typical B/5 wall is shifted to B/, reducing the overall safety level. This leads to the situation that still deterministic borders exist for the subdivision design of new ships, which was indented to be avoided by a new probabilistic damage stability standard. The required index of the SOLAS 29 standard need to be revised for RoPax designs. Its dependency on the ships size and its general level are too low, as it has been shown in the EMSA study. As the Stockholm Agreement has been proven to be a reasonable safety requirement, this regulation should be considered to be adjusted to the new probabilistic standard. The failure mode of accumulating water on large vehicle decks needs to be taken into account for new designs. It is suggested by Valanto, 29 that this new water-on-deck criterion should properly take into account the deck layout and not sanction new design concepts. In addition, the intact stability requirements may also need to be extended by further dynamic criteria, to avoid the situation that only the damage stability standard determines the overall safety level of the ship, which for some designs might not be large enough to guarantee a sufficient level of safety for new ships. Acknowledgements We are particularly grateful to the European Maritime Safety Agency (EMSA) supporting the mentioned research project. References IMO, (29). International Convention for the Safety of Life at Sea, Fifth consolidated edition 29 IMO, (28). Explanatory Notes to the SOLAS Chapter II- Subdivision and Damage Stability Regulations, Resolution MSC.28(85) IMO, (24). International Convention for the Safety of Life at Sea, Fourth consolidated edition 24 HARDER (23). Harmonization of Rules and Design
Rationale. EU Contract No. GDRB CT-998-28, Final Technical Report Kluwe, F. (2), Development of a Minimum Stability Criterion to Prevent Large Amplitude Roll Motions in Following Seas, Dissertation Krüger, S. and Dankowski, H. (29). On the Evaluation of the Safety level of the Stockholm Agreement, Proceedings IMDC 29 Matsumoto, M. and Nishimura T. (998), "Mersenne Twister: A 623-dimensionally equidistributed uniform pseudorandom number generator", ACM Trans. on Modeling and Computer Simulation Vol. 8, No., January pp.3-3 Valanto, P. (29). Research for the Parameters of the Damage Stability including the Calculation of Water-on-deck of Ro-Ro Passenger Vessels, HSVA Report No. 669 Wendel, K. (96). Die Bewertung von Unterteilungen., STG Jahrbuch, Bd. 55 Wendel, K. (96). Die Wahrscheinlichkeit des Überstehens von Verletzungen., Schiffstechnik, Bd. 4