Time-varying ultimate strength of aging tanker deck plate considering corrosion effect

Transcription

1 Time-varying ultimate strength of aging tanker deck plate considering corrosion effect Jinting Guo a,b,*, Ge Wang a, Lyuben Ivanov a, Anastassios N. Perakis b a. American Bureau of Shipping, Houston, TX 77060, USA b. Department of Naval Architecture & Marine Engineering, University of Michigan, Ann Arbor, MI 48109, USA Originally published in the Journal of Marine Structures, Vol. 1 Nos. 4, October 008, pp , Elsevier and reprinted with their kind permission. Abstract This paper presents a semi-probabilistic approach to assess the time-varying ultimate strength of aging tanker deck plate considering corrosion wastage. The procedure includes 1) defining the limit state function of deck plate failure, ) determining the time-varying probability density function of corrosion wastage and values for selected severity levels of corrosion, 3) calculating the time-varying ultimate strength of deck plates corresponding to the selected levels of corrosion wastage, 4) determining the time-varying maximum nominal stress, 5) calculating when the deck plate reaches the ultimate strength limit state, and 6) determining the inspection intervals based on the risk of ultimate strength failure. A nonlinear corrosion model was proposed for deriving the time-varying probability density function of deck plates corrosion wastage. The probability density function was determined based on a statistical analysis of the American Bureau of Shipping (ABS) corrosion wastage database [Wang G, Spencer J, Sun HH. Assessment of Corrosion Risks to Aging Oil Tankers In:nd International Conference on Offshore Mechanics and Arctic Engineering, Cancun, Mexico, 8 13 June 00].To simplify the calculations of ultimate strength, a semi-probabilistic model was adopted. Three levels of corrosion severity were considered, and the corresponding values of corrosion wastage were used instead of the probability density function. The increasing nominal stresses as ships age were also taken into account considering the loss of global hull girder section modulus. The loads of still-water-induced and wave-induced bending moments were treated as deterministic values. The ultimate strength calculation was based on the latest International Association of Classification Societies (IACS) - Common Structure Rule (CSR) formula [Common Structural Rules for Double Hull Oil Tankers, 007]. Deck failure was defined as deck plate s ultimate strength becoming lower than the maximum nominal stress. An inspection should be conducted before such failure takes place. A total of nine sample tankers, designed in 1970s, 1980s and 1990s were selected for demonstrating this approach. Time to deck plate s failure by ultimate strength varies widely, depending on the initial designs and corrosion severity at both local plate and global hull girder levels. Keywords: Corrosion wastage, Semi-probabilistic approach, Ultimate strength, Reliability-based approach, Time-varying reliability, Risk-based inspection, Aging tankers Time-Varying Ultimate Strength of Aging Tanker Deck Plate Considering Corrosion Effect 177

2 1. Introduction Plates, stiffeners and main supporting members of ship hulls may fail by yielding, buckling or fatigue. Many ship casualties, especially in older ships, can be attributed to age-related structural degradations, i.e., corrosion wastage, fatigue or brittle fracture. Over the past several years, there has been increasing interest in research of aging ships [3-6]. Risk-based approaches have been more and more applied in the inspection planning [7,8]. One of the major challenges of the inspection planning is predicting the structural conditions of aging ships. There exist many uncertainties in the determination of loads, operation, and structural degradation. Many investigations are severely limited by lack of data. This paper presents a semi-probabilistic approach to assess the time-varying ultimate strength of aging tanker s deck plate by considering corrosion wastage. The objective is to develop and illustrate an easy-to-use procedure. This procedure involves the following steps: defining the limit state function of deck plate failure, determining the time-varying probability density function of corrosion wastage and values for selected severity levels of corrosion, calculating the time-varying ultimate strength of deck plates corresponding to the selected levels of corrosion wastage, determining the time-varying maximum nominal stress, calculating when the deck plate reaches the ultimate strength limit state, and determining the inspection intervals based on the risk of ultimate strength failure. A total of nine sample tankers in Table 1 were selected for demonstrating this approach. Table 1 Sample tankers analyzed in this paper Year built 1970s 1980s 1990s Ship ID 70-A 70-B 70-C 80-A 80-B 80-C 90-A 90-B 90-C Ship type SHT SHT SHT SHT SHT SHT DHT DHT DHT Ship length (m) Deadweight (Tonne) Deck plate material HT 3 HT 3 HT 36 HT3 HT 3 Mild HT 3 HT 3 Mild Deck plate thickness(mm) Longitudinal spacing (mm) Frame spacing (mm) Section Modulus as built / IACS requirement Notes: SHT Single Hull Tanker; DHT Double Hull Tanker; HT High Tensile. Ultimate limit state of deck plate The limit state function of ultimate strength failure of deck plates is derived from the following equation: M T g( t) = σ u () t σ () t = σ u () t < 0 (1) SM deck () t where σ u (t) is the ultimate strength of the deck plate at year t; σ (t) is the nominal stresses of the deck plate at year t; M T represents the total bending moment, which equals the sum of still water bending moment M S and wave-induced bending moment M W, and the lateral load such as green water on the deck is assumed not to contribute to M T ; SM deck (t) represents hull girder section modulus (HGSM) to the deck at year t. It is determined by taking into account the corrosion wastage information known in every location of the hull structures. It is highly unlikely that in the first few years of operation the deck plate will fail the limit state function (1). However, during the ship s service life, deterioration in the form of metal corrosion reduces the safety margin. It is assumed when the demand σ (t) exceeds the structural capacity σ u (t), failure occurs. 3. Ultimate strength of deck plate The behavior of plate panels under predominantly compressive loads is schematically shown in Fig. 1. A plate panels usually undergoes five stages: pre-buckling, buckling, post-buckling, collapse (ultimate strength) and post-collapse. In the pre-buckling stage, the plate s response to load follows the Hooke s Law where its load displacement relationship is linear. When compressive loads reach the critical buckling load of the plate, buckling occurs. Buckling strength can be defined as the end stress when the buckling profile of the plate (usually in the form of half-waves of approximately equal length) is first observed during incremental loading. Thin plates usually show elastic buckling, while thick plates usually exhibit inelastic buckling. A plate having buckled in the elastic region will eventually collapse, 178 Time-Varying Ultimate Strength of Aging Tanker Deck Plate Considering Corrosion Effect

3 resulting in a rapid decrease in in-plane stiffness. On the other hand, if buckling occurs in the inelastic region, plates normally reach the ultimate limit state immediately. In other words, the buckling and ultimate strength of the plate are equal in the inelastic range. There are a few approaches developed for assessing ultimate strength of aging ship hull structures taking corrosion and fatigue into account [3,9,10]. Because of the high variation of corrosion wastage, a probabilistic assessment of timevarying ultimate strength is still needed [11]. Deck plates are chosen for this study because deck failure is one of the most critical. Traditionally, the inelastic buckling strength of plate panels is calculated by a correction for plasticity applied to the Euler buckling strength [1]. This approach tends to conservatively predict the buckling/ultimate strength. ε Theoretical Elastic Behavior Ultimate Strength Fig. 1. Typical stress-strain behavior The Von Karman et al. s (193) effective width concept has been widely used [8]. Approximately, this effective width is an estimate of the ultimate strength of plate panels. Recently, IACS CSR introduced a formula for predicting the ultimate strength of plate panels []. The IACS S11 method, ABS SafeHull [13] and IACS CSR criteria are compared in Table and Fig.. Table Buckling / ultimate strength of plate panels IACS S11 ABS SafeHull IACS CSR Terminology Critical Buckling Effective Width Critical Stresses Strength σ cr =Cσ y σ u =Cσ y σ cr =Cσ y σ C stress of t u n : ultimate strength; the material; : net plate thickness ; 3.6 for β.68 β β 1 for β < σ :actual nominal stress; β : slenderness ratio = 1/ ( σ E) E : Young's Modulus; y β β 1 σ cr s/t ; for β 1.5 for β < 1.5 :critical compressive stress; n s :spacing of Thick Plate Thin Plate σ β β 1 longitudinals or stiffeners; for β 1.58 for β < 1.58 σ : specified minimum yield y Time-Varying Ultimate Strength of Aging Tanker Deck Plate Considering Corrosion Effect 179

4 110% 100% 90% 80% % σy 70% 60% 50% 40% IACS S11 ABS SafeHull IACS CSR 30% β Fig.. Comparison of different formula of buckling / ultimate strength of plate panels 4. Corrosion wastage of deck plate The International Association of Classification Societies (IACS) has established guidelines and recommendations for inspection and repair of corroded ship hulls. According to the mechanics, corrosion is categorized as general pitting, grooving and weld metal corrosion. It is noted that the corrosion rate of ship hull is influenced by many factors, including the corrosion protection system and various operational parameters [14]. 4.1 Previous research on corrosion wastage model The conventional corrosion models assumed a constant corrosion rate and a linear relationship between the material lost and time. Starting with a linear equation proposed by Southwell et al. [15] to estimate the corrosion wastage thickness, nonlinear models (Fig. 3) were used and have become widely accepted to predict the corrosion wastage [6,16-19]. Corrosion Wastage Corrosion Progression (Alternatives) No Corrosion Constant Corrosion Rate Southwell et al Guedes Soares & Garbatov 1998 Coating Life 3 4 Qin & Cui 00 Paik et al. 1998, Ivanov 004 Transition Exposure Period Fig. 3. Schematic corrosion wastage models in previous literature Fig. 3 summarizes the existing corrosion wastage models. Normally, the corrosion protection system was considered, except the Southwell s model. We ignored the differences in assumed coating life and assumed that all models except 1 st have the same coating life and the corrosion rate becomes zero at the same exposure period for the nd and 3 rd models. From the nd model, the time-variant corrosion wastage is divided into three different phases. The first phase is assuming no corrosion due to the corrosion protection system. After the corrosion protection is damaged, the second phase is 180 Time-Varying Ultimate Strength of Aging Tanker Deck Plate Considering Corrosion Effect

5 initiated and a decrease in the thickness of the plate starts. The third phase corresponds to a stop in the corrosion process because the corroded material stays on the plate surface protecting it from contact with the corrosive environment. As for the 3 rd model, it is assumed that the coating protection system deteriorates gradually, then the pitting leads to early corrosion. In the last stage, the corrosion rate becomes zero. In the 4 th model, a second transition stage between the breakdown of the corrosion protection system and the start of the corrosion is introduced and assumed to follow a lognormal distribution. A concave, convex or linear curve could be the corrosion loss curve for the third phase. The 5 th model assumed that the second phase is a gradual acceleration of corrosion after the coating breaks down, and the corrosion rate reaches its maximum in the final phase. Although the nd model was used in a number of papers for the estimation of ship corrosion wastage, there is no corrosion science theoretical justification for this particular model. Also, because of the difficulty of simulating the real seawater condition in the laboratory, reliable corrosion data will be the only way to justify the models in real life. 4. Existing corrosion wastage dataset Because corrosion is affected by many variables and uncertainties, it is not straightforward to develop a corrosion model solely based on theory. A statistically derived corrosion model is considered practical and reasonable. So far, there are a couple of databases of corrosion wastage in the public domain (Table 3). The Tanker Structure Co-operative Forum (TSCF) (199) published results of corrosion data from 5 oil tankers [0]. Yamamoto and Ikegami (1998) introduced a database of 50 bulk carriers [11]. Paik et al. developed a probabilistic corrosion rate estimation model based on the measurements of 44 bulk carriers (1998) and more than 100 oil tankers (003) [6] [1]. Harada et al. (001) collected a database from 197 oil tankers []. ABS has developed a database based on 140 oil tankers [1]. Table 3 The summary of available corrosion wastage databases [1] Wang et al. [1] TSCF [0] Harada et al. [] Paik et al. [6] Ship type Single hull oil tankers Single hull tankers Single hull tankers Single hull tankers Data sources SafeHull Condition Assessment Owner, class Gauging records Gauging reports Vessels >100 Gauging reports 157 Not known 346 Not known Thick. measurements 110,08 Not known > 50,000 33,80 Girder section modulus > 000 sections No No No Ship size 168 ~ 401 meters > 150, 000 DWT 100 ~ 400 meters Not known Service years 1 ~ 6, 3 years ~ 5 years ~ 3 years 1 ~ 6 years Class ABS, LR, NK, DnV, KR ABS, DnV, LR, NK NK KR, ABS Ship built Mostly 1970 s, some 1980 s 1960s ~ 1980s Not known Not known Ship measured Not known Not known Not known It appears that the dataset shows a very high level of scatter. As shown in Fig. 4(a), (b) [1], the mean and standard deviation of the deck plates of cargo tanks and ballast tanks vary in a range. With aging, the corrosion wastage of tankers becomes more and more severe. Corrosion wastage measurements spread over a wide range. The mean value and standard deviation fluctuate with ship age. The maximum corrosion wastage is much higher than the average. The maximum corrosion wastage seems to be higher in cargo tanks than in ballast tanks. Time-Varying Ultimate Strength of Aging Tanker Deck Plate Considering Corrosion Effect 181

6 a Data Mean Mean+Stdv Mean+Stdv 7.00 Corrosion Wastage (mm) Age of Vessels (Year) b Data Mean Mean+Stdv Mean+Stdv 7.00 Corrosion Wastage (mm) Age of Vessels (Year) Fig. 4. Scatter plot of corrosion wastage to the deck of single hull tankers (a)cargo oil tanks; and (b) ballast tanks. The following equation is assumed for the corrosion wastage at t years old. This assumption is commonly applied [6] [11] [] [3] [4] [5] [6]. β C ( t ) = α ( t t 0) () where C(t) is the corrosion wastage at age t; t 0 is the year when thickness of the plates starts to deviate from the as-built condition; α and index β are constants that can be determined according to the measurement data. The age when the corrosion starts, t 0, is itself a random variable. It can follow some distribution, like the Log-normal distribution [11], the Normal distribution [7], and the Weibull distribution [10]. And t 0 can vary in a wide range. It is generally acknowledged that coating breakdown starts to take place in certain places when a ship is between and 10 years old. Therefore, it can be expected that t 0 varies from to 10 years. 18 Time-Varying Ultimate Strength of Aging Tanker Deck Plate Considering Corrosion Effect

7 It does not seem very meaningful to attempt to create a curve fitting all data points. The number of data points varies from year to year, as there are more data points in some years than in others. The following were considered in deriving formulae for the mean values and standard deviations by best fitting the data set: The mean value of corrosion wastage increases with ships age. The standard deviation of corrosion wastage also increases with ships age. The trends are better revealed or presented by ship with more data points. The coating life t 0 is assumed to be a constant value. The estimated equations cover the most severe investigated data due to the conservative consideration. Table 4 lists a set of equations which t 0 are assumed to be 6.5 years when calculating C μ and 5 years when calculating C μ+σ which were used in [6]. Fig. 5(a) and Fig. 5(b) show the derived equations in comparison to the measurement data. Table 4 Mean values and standard deviations of corrosion wastage in deck plate of single hull tankers Mean (μ) Mean + Standard Deviation (μ + σ) Standard Deviation (σ) Cargo oil tanks C μ (t)=0.15(t-6.5) /3 When t >6.5 year C μ+σ (t)=0.349(t-5) 3/4 When t >5 year C σ (t)=c μ+σ (t)-c μ (t) When t >6.5 year Ballast tanks C μ (t)=0.18(t-6.5) /3 When t >6.5 year C μ+σ (t)=0.35(t-5) 3/4 When t >5 year C σ (t)=c μ+σ (t)-c μ (t) When t >6.5 year Fig. 6 and 7 show the histograms of corrosion wastage of selected ship ages. Clearly, there does not exist a consistent probability distribution function that can fit equally well with all ship ages. This again demonstrates the high variation of corrosion wastage. a 3.50 Mean Mean+Stdv 3.00 Estimated Mean Estimated Mean+Stdv.50 Corrosion Wastage (mm) ( t ) /3 Cμ = ( t ) 3/4 Cμ+ σ= Age of Vessels (Year) Time-Varying Ultimate Strength of Aging Tanker Deck Plate Considering Corrosion Effect 183

8 b 3.50 Mean Mean+Stdv 3.00 Estimated Mean Estimated Mean+Stdv Corrosion Wastage (mm) ( t ) 3/4 Cμ+ σ= ( ) /3 Cμ = 0.18 t Age of Vessels (Year) Fig. 5. The derived equations of mean value and standard deviation of corrosion wastage with the current database (a) cargo oil tanks: and (b) ballast tanks Goodness of fit 1 st Exponential nd Weibull 3 rd Gamma Percent (a) Corrosion wastage of deck plate at age 18 cargo oil tanks (mm) Goodness of fit 1 st Weibull nd Lognormal 3 rd Exponential Percent (b) Corrosion wastage of deck plate at age 0 cargo oil tanks (mm) Fig. 6. Histogram of corrosion wastage of deck plates at selected age in cargo oil tanks with best fit distribution 184 Time-Varying Ultimate Strength of Aging Tanker Deck Plate Considering Corrosion Effect

9 Goodness of fit 1 st Gamma nd Lognormal 3 rd Weibull Percent (a) Corrosion wastage of deck plate at age 19 ballast tanks (mm) Goodness of fit 1 st Weibull nd Gamma 3 rd Lognormal Percent (b) Corrosion wastage of deck plate at age ballast tanks (mm) Fig.7. Histogram of corrosion wastage of deck plates at selected age in ballast tanks with best fit distribution However, the Weibull distribution appears to be a good candidate for representing the corrosion wastage over a ship s life. It is assumed that corrosion wastage at t years old follows a Weibull distribution or probability density function: k 1 k pdf ( C; k, λ) = ( k / λ)( C / λ) exp( ( C / λ) ) (3) where k and λ are the shape and scale parameters, respectively, which are functions of ships age. Given the values of the mean and standard deviation in Table 4, the following parameters of Weibull distribution function were calculated. Equations were also derived for the Weibull shape and scale parameters as functions of time: k = + t t for cargo oil tanks (4) 6.30 λ = t t k = + t t for ballast tanks (5) λ = t t Examples of the probability density function of corrosion wastage at selected ship age are listed in Table 5 and Fig. 8(a), (b). For both cargo oil tanks and ballast tanks, the shape parameter increases from the beginning about 19 years old, remains almost constant until 1 years old and then slightly decreases. The scale parameter increases continuously with time. Table 5 Time-Varying Ultimate Strength of Aging Tanker Deck Plate Considering Corrosion Effect 185

10 Time-variant Weibull parameters for deck corrosion in single hull tankers Cargo Oil Tanks Ballast Tanks 10 years old 15 years old 0 years old 5 years old Shape parameter Scale parameter Shape parameter Scale parameter a 4 10 year year 3 0 year 5 year Corrosion Wastage (mm) b 4 10 year year 3 0 year 5 year Corrosion Wastage (mm) Fig. 8. Probability density functions (Weibull) of corrosion wastage of deck plate (a) cargo tanks; and (b) ballast tanks As ship ages, the probability density function of corrosion wastage becomes flatter and wider. This means that when ships become older, the deck plate thickness varies in an ever wider range and the uncertainties associated with corrosion wastage increase. 4.3 Slight, moderate and severe levels of corrosion wastage The corrosion wastage of deck plate was ranked in three levels, slight, moderate and severe, which corresponds to the mean (µ), mean plus a standard deviation (µ +σ) and mean plus two standard deviation (µ +σ)of corrosion wastage. Examples of the corrosion wastage at selected ship age are listed in Table 6. Table shows the ultimate strength of deck plate will decrease only if the plate thickness decreases due to the corrosion, because E, σ y and s are assumed to be constant for the specified material and hull structure. Fig. 9(a), (b) show the lifetime change of deck plate ultimate strength for a selected single hull tanker according to these three different ranks. The ultimate strength of the deck plate is assessed by IACS CSR formulae in this paper. 186 Time-Varying Ultimate Strength of Aging Tanker Deck Plate Considering Corrosion Effect

11 Table 6 Time-variant corrosion wastage for deck plate in single hull tankers corresponding to different corrosion severity levels (mm) Tanks Cargo Oil Tanks Ballast Tanks Corrosion severity Level 10 years old 15 years old 0 years old 5 years old 30 years old Slight Moderate Severe Slight Moderate Severe Hull girder section modulus to the deck The hull girder section modulus is an important design parameter. HGSM is viewed as the primary measure of the strength of a hull girder. This is true as ships are designed to operate within the material elastic range of their steel structure. As the corrosion takes place on the structure, HGSM decreases over time and so does the hull girder strength. IACS has established harmonized rules to guide ship designs. Further, IACS specifies that ships in services should maintain their HGSM to at least 90% of that required as a new build. These IACS requirements have become the industry standard, as the same requirement was adopted by the International Maritime Organization (IMO) as Resolutions MSC.105 (73) and MSC.145 (77) for tankers and bulk carriers, respectively. A statistical study for the loss of HGSM was performed by Wang, et al. [6]. The dataset demonstrated a high variation of HGSM that changes over time, and the mean value and standard deviation of HGSM loss were derived as functions of time, which are described in Table 7. As an example, the lifetime change of HGSM of sample tanker SHT 80-B is listed in Table 8. Table 7 Equations for predicting the mean values and standard deviations of HGSM loss Mean value Mean value + Standard deviation Standard deviation Loss of HGSM (deck) as compared with as-built condition R m (t) = 0.6 (t-6.5) 0.67 / 100, when t > 6.5 year R m+σ (t) = 0.80 (t-5) 0.75 / 100, when t > 5 year R σ (t) = R m+σ (t) - R σ (t) when t > 6.5 year Table 8 Time-variant HGSM of a selected single hull tanker SHT 80-B with as-built HGSM according to different corrosion level Corrosion Level 10 years old 15 years old 0 years old 5 years old 30 years old Slight 99.3% 98.1% 97.% 96.3% 95.6% Moderate 98.0% 96.% 94.6% 93.1% 91.7% Severe 96.8% 94.% 9.0% 89.8% 87.8% Extreme 95.5% 9.3% 89.4% 86.6% 83.9% Time-Varying Ultimate Strength of Aging Tanker Deck Plate Considering Corrosion Effect 187

12 a 100% 95% 90% Ultimate Strength / Yielding Stress 85% 80% 75% 70% 65% 60% Slight corrosion wastage Moderate corrosion wastage Severe corrosion wastage 55% 50% Age of Vessel (Year) b 100% 95% 90% Ultimate Strength / Yielding Stress 85% 80% 75% 70% 65% 60% Slight corrosion wastage Moderate corrosion wastage Severe corrosion wastage 55% 50% Age of Vessel (Year) Fig. 9. Lifetime change of deck plate ultimate strength for a sample tanker 80-B (a) cargo oil tanks; and (b) ballast tanks 6. Loads and maximum stresses of the deck plate The total bending moment M T can be divided into two components, namely still water load and wave-induced load. Strictly speaking, these two components influence each other and the two random variables are statistically dependent. However, practically they are treated as statistically independent variables. In this paper, the total bending moment is calculated as the linear summation of the class-permissible still water bending moment and the design wave-induced bending moment. The wave-induced bending moment is a stochastic process and may be described by either short-term or long-term statistics. To simplify the procedure, the IACS formula (A-1) is applied and intended to provide an estimate of the wave-induced bending moment for a vessel. Thus, it is an extreme rather than an average or a point in time value. From Eq. (1), the maximum nominal stresses of deck plate will increase with the decrease of HGSM to the deck due to the corrosion. Fig. 10 shows the lifetime change of the maximum deck stresses of sample tankers SHT 80-B according to the different corrosion levels. 188 Time-Varying Ultimate Strength of Aging Tanker Deck Plate Considering Corrosion Effect

13 100% 95% 90% Max. Deck Stress / Yielding Stress 85% 80% 75% 70% 65% 60% 55% Slight corrosion (Global) Moderate corrosion (Global) Severe corrosion (Global) Extrem corrosion (Global) 50% Age of Vessel (Year) Fig. 10. Lifetime change of the maximum deck stresses of a sample tanker 80-B There is no correlation between the corrosion severities of a local deck plate and that of a global hull girder (Fig. 11). For example, a deck plate can be severely wasted while the overall wastage of the entire hull section may remain at a very low level. Therefore, corrosion wastage of local plate and wastage of hull girder section modulus are treated independently. No Corrosion Actual Corrosion by Local Investigation Mean Corrosion for Global Analysis As-built Deck Plate Corroded Deck Plate Fig. 11. Schematic differences between actual deck plate actual corrosion and assumed corrosion 7. Likely failure & RBI As a ship ages, the local carrying capacity of its structural components decreases and the uncertainties associated with its strength grows. It is no longer adequate to consider the uncertainties determined at the time of construction. It is therefore important to establish the capacity of a vessel at any year with a certain level of confidence be able to predict. The existing renewal criteria of classification societies require maintaining certain levels of remaining thickness. This does not explicitly measure the remaining strength of hull structure. A more rational way of determining inspection interval is schematically depicted in Fig. 1. An inspection has to be conducted before the predicted ultimate strength failure takes place. It is noted that only the ultimate strength but not fatigue or brittle fracture is covered in this research. Likewise, only corrosion effects but not fatigue cracks are considered in this procedure. Following Eq. (1), this failure occurs when the curve of strength crosses the curve of maximum nominal stresses. Time-Varying Ultimate Strength of Aging Tanker Deck Plate Considering Corrosion Effect 189

14 Stress Ultimate strength of deck plate Decreasing HGSM (Global) Maximum nominal stresses Increasing corrosion of deck plate (Local) Inspection time t time Fig. 1. Schematic time-variant reliability of deck plate failure Three levels of corrosion severity were considered, and the corresponding values of corrosion wastage were used instead of the probability density function. The increasing nominal stresses as ship ages were also taken into account in the same manner by considering the loss of global hull girder section modulus for selected levels of corrosion severity. The required inspection intervals for all the sample tankers were described in Table 9. Table 9 Required inspection interval (year) for a sample tanker SHT 80-B cargo oil tanks local corrosion level slight moderate Severe global corrosion level mean mean+stdv mean+stdv slight mean >30 > moderate mean+stdv > severe mean+stdv > extreme mean+3stdv > Discussions The required inspection interval for double hull tankers can be carried out by assuming that the corrosion estimation of the single hull tankers remains the same for the double hull tankers. The responding required inspection intervals for the sample tankers are provided in Appendix B. All the sample tankers in Table 1 were analyzed using the presented approach. By comparing the results of selected tankers from 1970s~1990s, we can draw the following conclusions: The deck plates of the selected 70 s tankers are usually much thicker than those of the selected 80 s tankers. According to the results, it s hard to tell whether the corrosion problem of 80 s tankers is more critical than that of the 90 s tankers. Time to when deck plates fail by ultimate strength varies in a wide range depending on the initial designs and corrosion severity at both local plate and global hull girder. 9. Conclusion This paper presents a semi-probabilistic approach to assess the time-varying ultimate strength of aging tanker s deck plate considering corrosion wastage. The procedure includes: 1) defining the limit state function of deck plate failure, ) determining the time-varying probability density function of corrosion wastage and determining wastage values for selected severity levels of corrosion, 3) calculating the time-varying ultimate strength of deck plates corresponding to the selected levels of corrosion wastage, 4) determining the time-varying nominal stress, 5) predicting when the deck plate reaches the ultimate strength limit state, and 6) determining the inspection intervals based on the risk of ultimate strength failure. 190 Time-Varying Ultimate Strength of Aging Tanker Deck Plate Considering Corrosion Effect

15 It is expected that this procedure can be easily applied to assist the risk based inspection. Time to when deck plates fail by ultimate strength varies in a wide range depending on the initial designs and corrosion severity at both local plate and global hull girder. A few assumptions were made while the research was carried out, such as the loads of still-water-induced and waveinduced bending moments were treated as deterministic values, coating life was assumed as a constant value, and the effects of fatigue cracks were not included for deriving the inspection intervals of the aging tankers. In future research, one of the aims would be to modify the methodology applied in order to eliminate some of the assumptions mentioned in this report and to generate a more realistic approach to the ultimate strength failure prediction. Acknowledgements The authors appreciate the valuable input from many colleagues, including C. Lee, G. Chang, H. Sun, J. Speed, A.Lee, C. Serratella and R. Basu. Appendix A: IACS design wave-induced bending moment [1] M w 3 190CL BCb 10 (kn-m), for hogging = CL B( Cb + 0.7) 10 (kn-m), for sagging (A-1) where L < L m C = < L 350 m 1.5 L L > 350 m 150 LB=, ship length and beam in meters, C b = block coefficient at summer load waterline Appendix B: Calculations of required inspection interval for sample tankers Table B-1 Required inspection intervals (years) for sample tankers cargo oil tanks ballast tanks Ship local corrosion level slight moderate severe slight moderate severe ID global corrosion level (mean) (mean+stdv) (mean+stdv) mean (mean+stdv) (mean+stdv) slight (mean) >30 >30 >30 >30 >30 >30 SHT moderate (mean+stdv) >30 >30 >30 >30 >30 >30 70-A severe (mean+stdv) >30 >30 >30 >30 >30 >30 extreme (mean+3stdv) >30 >30 >30 >30 >30 >30 slight (mean) >30 >30 >30 >30 >30 >30 SHT moderate (mean+stdv) >30 >30 >30 >30 >30 >30 70-B severe (mean+stdv) >30 >30 >30 >30 >30 >30 extreme (mean+3stdv) >30 >30 >30 >30 >30 >30 SHT slight (mean) >30 >30 >30 >30 >30 >30 Time-Varying Ultimate Strength of Aging Tanker Deck Plate Considering Corrosion Effect 191

16 70-C SHT 80-A SHT 80-B SHT 80-C DHT 90-A DHT 90-B DHT 90-C moderate (mean+stdv) >30 >30 >30 >30 >30 >30 severe (mean+stdv) >30 >30 >30 >30 >30 >30 extreme (mean+3stdv) >30 > >30 >30 >30 slight (mean) > >30 > moderate (mean+stdv) > >30 > severe (mean+stdv) > >30 7. extreme (mean+3stdv) slight (mean) >30 > >30 >30 >30 moderate (mean+stdv) > >30 > severe (mean+stdv) > >30 > extreme (mean+3stdv) > > slight (mean) > > moderate (mean+stdv) > > severe (mean+stdv) extreme (mean+3stdv) slight (mean) >30 >30 >30 >30 >30 >30 moderate (mean+stdv) >30 > >30 >30 >30 severe (mean+stdv) >30 > >30 >30 >30 extreme (mean+3stdv) >30 > >30 >30 >30 slight (mean) > >30 >30 >30 moderate (mean+stdv) > >30 >30 7 severe (mean+stdv) > > extreme (mean+3stdv) > > slight (mean) >30 > >30 >30 >30 moderate (mean+stdv) > >30 > severe (mean+stdv) > >30 >30 6 extreme (mean+3stdv) > > References [1] Wang G, Spencer J, Sun HH. Assessment of corrosion risks to aging oil tankers. In: nd international conference on offshore mechanics and arctic engineering, Cancun, Mexico, 8-13 June 00. [] Common structural rules for double hull oil tankers, Available from: [3] Akpan UO, Koko TS, Ayyub B, Dunbar TE. Risk assessment of aging ship hull structures in the presence of corrosion and fatigue. Marine Structures 00; 15: [4] Ivanov L, Spencer J, Wang G. Probabilistic evaluation of hull structure renewals for aging ships. The eighth international marine design conference (IMDC), Athens, Greece, 5-8 May 003. [5] Ivanov LD, Wang Ge, Seah AK. Evaluating corrosion wastage and structural safety of aging ships. In: Pacific international maritime conference, Sidney, Australia, -5 Feb 004. [6] Paik JK, Wang G, Thayamballi AK, Lee JM. Time-variant risk assessment of aging ships accounting for general/pit corrosion, fatigue cracking and local dent damage. In: SNAME annual meeting, San Francisco, USA, 003. [7] Ku A, Spong RE, Serratella C, Wu S, Basu R, Wang G. Structural reliability application in risk-based inspection plans and their sensitivities to different environmental conditions. In: Offshore technology conference (OTC 05), Houston, USA, -5 May 005. [8] Lee A, Serratella C, Basu R, Wang G, Spong RE. Flexible approaches to risk-based inspection of FPSOs. In: Offshore technology conference (OTC 06), Houston, USA, 1-4 May 006. [9] Guedes Soares C, Garbatov Y. Reliability of maintained, corrosion protected plates subjected to non-linear corrosion and compressive loads. Marine Structures 1999; 1: [10] Sun H, Bai Y. Time-variation reliability assessment of FPSO s hull girders. Marine Structures 003;7: [11] Yamamoto N, Ikegami K. A study on the degradation of coating and corrosion of ship s hull based on the probabilistic approach. Journal of Offshore Mechanics and Arctic Engineering 1998, 10:11-8. [1] IACS (International Association of Classification Societies) UR S11. Longitudinal strength standard, Rev.5, January 006. [13] ABS. Rules for building and classing steel vessels. ABS; 007. Part 5C. [14] Hu Y, Cui W, Pedersen PT. Maintained ship hull girder ultimate strength reliability considering corrosion and fatigue. Marine Structures 004; 17: [15] Southwell CR, Bultman JD, Hummer Jr CW. Estimating of service life of steel in seawater, seawater corrosion handbook., New Jersey, USA: Noyes Data Corporation; 1979, [16] Garbatov Y, Guedes Soares C, Wang G. Nonlinear time dependent corrosion wastage of deck plates of ballast and cargo tanks of tankers. In: 5th international conference on offshore mechanics and arctic engineering, Halkidiki, Greece, 1-17 June 005. [17] Paik JK, Kim SK, Lee SK. Probabilistic corrosion rate estimation model for longitudinal strength members of bulk carries. Ocean Engineering 1998; 5: [18] Melchers RE. Development of new applied models for steel corrosion in marine applications including shipping. In: 10th international symposium on practical design of ships and other floating structures, Houston, USA, Sept. 30-Oct. 5, 007. [19] Qin SP, Cui WC. Effect of corrosion models on the time-variant reliability of steel plated elements. Marine Structures 003;16: [0] TSCF (Tanker Structure Co-operative Forum). Condition evaluation and maintenance of tanker structures. London: Witherby & Co. Ltd; 199. [1] Paik JK, Kim SK, Yang SH, Thayambali AK. Ultimate strength reliability of corroded ship hulls, RINA Transactions 1998; Time-Varying Ultimate Strength of Aging Tanker Deck Plate Considering Corrosion Effect

17 [] Harada S, Yamamoto N, Magaino A, Sone H. Corrosion analysis and determination of corrosion margin. Part 1and, IACS discussion paper, 001. [3] Wang G, Spencer J, Elsayed T. Estimation of corrosion rates of oil tankers. In: nd international conference on offshore mechanics and arctic engineering, Cancun, Mexico, 8-13 June 00. [4] Gardiner CP, Melchers RE. Bulk carrier corrosion modeling. In: International offshore and polar engineering conference, Stavanger, Norway, (IV) pp , 001. [5] Sun H, Guedes Soares C. A corrosion model and reliability-based inspection for ship-type FPSO hulls. Journal of Ship Research 006. [6] Wang G, Lee AK, Ivanov LD, Lynch TJ, Serratella C, Basu R. A statistical investigation of time-variant hull girder strength of aging ships and coating life. Marine Structures 008; 1: [7] Paik JK, Kim DH. An analytical method for predicting ultimate compressive strength of stiffened panels. Journal of the Research Institute of Industrial Technology 1997; 5(6): [8] Von Karman T, Sechler EE, Donnel LH. Strength of thin plates in compression. Transactions of the ASME 193; 54. Time-Varying Ultimate Strength of Aging Tanker Deck Plate Considering Corrosion Effect 193