10 In the design process of oﬀshore platforms in Indonesia, random variables of load and material 11 strength must be taken into account. To cover this uncertainty, the industry standard in Indonesia is 12 to use the American Petroleum Institute Recommended Practice 2A-LRFD (API RP2A-LRFD) load factor. 13 To further assess the reliability of the structure, a structural design analysis was carried out according 14 to the provisions of API RP2A-LRFD, and the Monte Carlo method was used to determine the reliability 15 index of the structure. This would help to determine whether the structural design is conservative or not 16 according to the LRFD load factor. Additionally, four important members of the structure were selected 17 to assess the reliability of the structure against the random variables of load and material strength. With 18 the reliability index, it will be possible to have an overview of the structural design and ensure that the 19 structure is safe and secure against environmental conditions in Indonesia. 20 1 Introduction 21 Oﬀshore platforms are used in oil and gas exploration and production and can be ﬁxed to the seabed or 22 ﬂoat (Qiu, 2007). This project uses a four-legged jacket type structure ﬁxed to the Java Sea seabed, with a 23 water depth of 100ft from the mean sea level (m.s.l.). The structure must meet the American Petroleum 24 Institute Recommended Practice 2A-LRFD (API RP2A-LRFD) criteria (Turner et al., 1994), and therefore three 25 analyses must be conducted: an in-place analysis, a seismic analysis, and a fatigue analysis (Shittu et al., 26 2021). In the In-place analysis, Cross-sectional optimization is carried out on the structure, and a Reliability 27 analysis is conducted to assess the structure’s probability of failure (Pf)with the given load and structural 28 resistance (Qiu, 2007). This approach provides an initial indication of the API RP2A-LRFD design load factor 29 in the Java Sea, and the structural members’ reliability index (β)would be obtained. 30 In this study, structural modeling was conducted using the Bentley Structural Analysis Computer System 31 (SACS) Oﬀshore Structure software to account for the structure, equipment, and environmental load. This 32 software has proven to be used successfully to analyze and design oﬀshore structures in various places 33 in the world (e.g. Karimi et al., 2017; Ozkul et al., 2021; Lakhani and Panchal, 2022; Raheem et al., 2022; 34 Tran et al., 2022). Furthermore, the design process was completed based on in-place analysis criteria and 35 seismic and fatigue analysis (Turner et al., 1994). Member stress checks, joint punching shears, and pile 36 capacity checks were carried out. If there was a structural failure, a cross-section redesign was imple- 37 mented to meet the API RP2A-LRFD design criteria (Turner et al., 1994). In addition, reliability analysis was 38 conducted on four important members, each representing the four main parts of the structure. To this 39 end, data on signiﬁcant wave height from generated sea-ﬁne was used as the random variable load, and 40 the yield strength of degenerated steel based on ISO 19902 parameters were used as the random variable 41 strength. The Monte Carlo method was then employed to calculate the reliability index value (β), which 42 is the condition of the member stress performance in in-place analysis (Turner et al., 1994; ISO 19902, 43 2007; Barthelmie et al., 2016). Figure 1 summarizes the overall stages of this project. This study analyzed 44 an oﬀshore platform structure with a four-legged jacket type. It was installed in the waters of the Java 45 Sea, located at coordinates 108.671389◦E,6.3375◦S. This location is in the northern part of Cirebon and 46 1 the east of Indramayu (Figure 2). The water depth at this location is 100 ft from the datum m.s.l to the 47 seabed. 48 Figure 1: Project ﬂowchart. Figure 2: Platform location oﬀ the coast of the Java Sea (red dot). This map was rendered using PyGMT (Wessel et al., 2019; Uieda et al., 2023). The bridge structure has three decks: 49 •main deck at +45 ft, 50 •mezzanine deck at +31 ft, 51 2 •cellar deck at +25 ft. 52 The working point is at +15 ft elevation, and the jacket walkway is at +10 ft elevation. Figure 3 illustrates 53 the structure of the bridge. Environmental data such as wind, current, and wave were used to perform the 54 analysis. Table 1 shows the wind data used in the process. Since the ﬂow data above is a single dataset on 55 the water surface ( 0m.s.l.), the current data must be distributed to generate distributed ﬂow data (Table 56 2). 57 Figure 3: Four-legged jacket type structural model in Bentley SACS. condition wind speed (ft/sec.) wave Hmax(ft) wave Tmax(sec.) wave speed (ft/sec.) 1-year operating 42.19 14.83 8 2.07 100-year extreme 56.14 20.87 9.1 2.56 Table 1: Environmental data. 3 Z(ft) operating UZ(ft/sec.) storm UZ(ft/sec.) 0 0 0 10 1.49 1.842 20 1.645 2.034 30 1.743 2.155 40 1.816 2.246 50 1.875 2.319 60 1.924 2.38 70 1.967 2.433 80 2.005 2.48 90 2.039 2.522 100 2.07 2.56 Table 2: Current distribution. 2 Structural analysis 58 2.1 In-place analysis 59 The in-place analysis in the design process included member stress checks, joint punching shear inspec- 60 tions, and pile axial capacity checks based on the API RP2A-LRFD criteria. Two loading conditions were 61 considered: Operating and Storm. Unity Check (UC) values were calculated, and a safe design criterion 62 of UC less than 1was applied. For the pile capacity inspection, the load on the pile must be below the 63 factored pile capacity, with a factor of 0.7for operating conditions and 0.8for storm conditions (Turner 64 et al., 1994; Mangiavacchi et al., 2005; Digre and Zwerneman, 2012). The results of the in-place analysis for 65 the respective operating and storm conditions are presented in Tables 3 to 6. All load values were below 66 the factored capacity value, indicating that the structure meets the design criteria for both operating and 67 storm conditions. Therefore, the overall structural design examination based on the in-place analysis was 68 successful. 69 location member group property UC min. UCmax. main deck M397-M030 MA2 W24 ×68 0.851 0.85 cellar deck C024-C029 CL4 C 8 ×11.5 0.574 0.576 mezzanine deck Z037-Z016 ME2 L4 ×41/4 0.963 0.964 deck leg 603L-C003 DL1 OD30” ×1”WT 0.394 0.396 deck brace C002-M015 TR1 OD10.75” ×0.365”WT 0.685 0.678 jacket leg 0026-0038 LG2 OD34” ×0.5”WT 0.375 0.363 jacket brace 304L-403L DG2 OD16” ×0.375”WT 0.582 0.605 pile 301P-401P PL1 OD30” ×1”WT 0.377 0.357 Table 3: UC member operating. location member group property UC min. UCmax. main deck M054-M057 MA3 W16 ×21 0.734 0.727 cellar deck C132-C133 CL1 C16 ×67 0.927 0.927 mezzanine deck 0092-Z027 ME2 L4 ×41/4 0.664 0.663 deck leg 602L-C002 DL1 OD30” ×1”WT 0.418 0.412 deck brace C002-M015 TR1 OD10.75” ×0.365”WT 0.623 0.614 jacket leg 0025-0037 LG2 OD34” ×0.5”WT 0.483 0.483 jacket brace 304L-403L DG2 OD16” ×0.375”WT 0.818 0.842 pile 301P-401P PL1 OD30” ×1”WT 0.555 0.537 Table 4: UC member storm. 4 operating condition storm condition joint UC min. UCmax. joint UC min. UCmax. 403L 0.630 0.704 304L 0.481 0.481 402L 0.569 0.554 303L 0.395 0.389 304L 0.492 0.492 302L 0.359 0.364 Table 5: UC joint can. pile joint capacity (QD) 0.8 (QD)operating storm water water water water level max. level min. level max. level min. (Kips) (Kips) (Kips) (Kips) (Kips) (Kips) (Kips) 001P 1500.4 1200.32 690.5 711.5 787.3 806.4 002P 1506.2 1204.96 690.5 521.8 400 402.5 003P 1500.4 1200.32 599.8 611.6 723.2.3 733.4 004P 1506.2 1204.96 790.4 805.4 758.4 772.1 Table 6: pile capacity 2.2 Seismic analysis 70 Dynamic analysis was used to assess the seismic conditions of the structure. The structure’s natural period 71 was determined to be 2.03sec., with 90% of the mass participation in the 12th mode. Table 7 displays the 72 value of each Pseudo Spectrum (PSV) of the two earthquake loads; Strength Level Earthquake (SLE, PGA 73 = 0.159g) and Ductility Level Earthquake (DLE, PGA = 0.239g). 74 period PSV SLE(in/s/g) PSV DLE(in/s/g) 0.03 1.845 1.845 0.05 3.075 3.075 0.125 15.238 15.238 0.5 54.714 60.952 5 54.714 60.952 10 23.357 30.476 Table 7: Response spectra. Tables 8 to 10 display the results of the member stress UC, joint punching shear, and pile capacity checks for 75 the SLE and DLE earthquake conditions. The pile capacity met both operating and storm conditions for each 76 maximum and minimum water level, as the working load was below the factored capacity value. Based 77 on the seismic analysis, it can be concluded that the structure has met the design criteria for SLE and DLE 78 earthquake conditions. This evidence is supported by the ﬁndings of Khatibi et al. (2014), which determined 79 that structures must satisfy the design criteria for seismic conditions to remain safe and secure. 80 location member group property UC SLE. UCDLE. main deck M021-M001 MA2 W24 ×68 0.503 0.555 cellar deck C057-C085 CL4 C8 ×11.5 0.460 0.556 mezzanine deck 0092-Z027 ME2 L4 ×41/4 0.519 0.532 deck leg 602L-C002 DL1 OD30” ×1”WT 0.310 0.406 deck brace C003-M008 TR1 OD10.75” ×0.365”WT 0.416 0.558 jacket leg 0026-0038 LG2 OD34” ×0.5”WT 0.253 0.342 jacket brace 304L-403L DG2 OD16” ×0.375”WT 0.463 0.685 pile 301P-401P PL1 OD30” ×1”WT 0.332 0.444 Table 8: UC member values. 5 joint UC SLE UCDLE 304L 0.688 0.688 303L 0.421 0.421 401L 0.386 0.386 204L 0.334 0.334 Table 9: UC joint can values. pile capacity (QD) 0.7 (QD) DLE load SLE load joint (Kips) (Kips) (Kips) (Kips) 001P 1432.35 1002.645 701.06 569.19 002P 1432.35 1002.645 370.47 328.88 003P 1432.35 1002.645 587.23 450.26 004P 1432.35 1002.645 778.38 637.39 Table 10: Pile capacity. 2.3 Fatigue analysis 81 Fatigue analysis is a critical stage of the design analysis process. It helps determine the service life of a 82 joint structure by analyzing the eﬀect of cyclic environmental loads on it. The analysis involves providing 83 the system with diﬀerent wave heights, wave periods, and directions (eight directions) (Bai, 2003a; Chen 84 et al., 2016; Plodpradit et al., 2019; Sánchez et al., 2019). The fatigue analysis output is the joint structure’s 85 service life, which is determined by the damage value of the design upon its exposure to cyclic loads. 86 The fatigue analysis results for the joint structure are presented in Tables 11 and 12. The damage value 87 for the joint structure was above 1, indicating that further assessment of the jacket bracing members is 88 necessary to survive the desired service life of 52years (Lee et al., 2023). Table 12 displays the fatigue life 89 values for the other joints below 1. 90 joint member group damage fatigue life (year) 0006 102L-0006 BR3 1.67 31 Table 11: Fatigue life (damage >1). joint member group damage fatigue life (year) 003P 003P-103P PL1 0.85 61.11 304L 202L-304L DG3 0.64 81.27 304L 0032-304L LG1 0.54 96.57 604L 504L-604L PL1 0.53 98.06 0163 0165-0163 HR3 0.28 184.40 303L 303L-304L HR1 0.21 248.80 Table 12: Fatigue life (damage <1). 3 Reliability analysis 91 Reliability analysis is a crucial step in this study. Based on the criteria presented in Table 13, four main members were selected for the analysis. Reliability is deﬁned as the probability of success (Ps)that meets the performance criteria expressed in the performance function as follows, Z=g(X1, X2,···, Xn) (1) , where Xideﬁnes a random variable related to load and capacity parameters. Two random variables, structural strength and load, were selected to determine the performance failure parameters. Therefore, 6 the performance function used was, g(R, Q) =R−Q (2) , where Rdeﬁnes the parameter of the strength of the structure, and Qis the parameter of the structure’s 92 load. The structure’s failure probability is when g(R, Q)<0. 93 location factored unfactored main beammean 0.5917 mean 0.3753 standard error 0.0044 standard error 0.0029 COV 0.0525 COV 0.0540 deck legmean 0.3197 mean 0.2006 standard error 0.0024 standard error 0.0016 COV 0.0524 COV 0.0547 jacket legmean 0.2615 mean 0.1784 standard error 0.0029 standard error 0.0021 COV 0.0764 COV 0.0826 pilemean 0.2552 mean 0.1662 standard error 0.0029 standard error 0.0021 COV 0.0790 COV 0.0875 Table 13: UC statistical parameters The structural strength parameter selected was the yield stress of the structural material (Fy), and the load parameter was a wave load with signiﬁcant wave height and period. Monte Carlo simulation (Alpers, 1983; Guo et al., 2012; Clarindo et al., 2021; Görmüş et al., 2022) was used as the reliability analysis method, with50simulations carried out. To generate the wave data, 59years of signiﬁcant wave data from the Java Sea was used to determine the wave data distribution. Kolmogorov-Smirnov (K-S) method (Massey Jr., 1951) was used to carry out the distribution test, which results are shown in Figure 4, with the log normal distribution having the smallest Dnvalue (Dn= 0.0612) . This method was then used to generate 50 wave data pairs with parameters: Hmax= 16.22ft, mean = 3.45ft, and standard deviation = 2.53ft. The wave period was determined through a linear regression of the wave period, obtaining the relationship of Tto Has, T= 0.5409Hs+ 3.843. (3) Figure 4: Hswave K-S test results. A period value was determined for every 50wave heights generated. In order to generate yield stress data 94 for the material, it is necessary to determine the statistical parameters used. ISO 19902 (2007) recommends 95 the log normal distribution with the mean bias parameter = 1.1266 and standard deviation = 0.0572 . The 96 7 locationLRFD unfactored λUC ζUC β λ UC ζUC β main deck -0.53 0.05 10.03 -0.98 0.05 18.20 deck leg -1.14 0.05 21.80 -1.61 0.05 29.44 jacket -1.34 0.08 17.62 -1.73 0.08 20.94 pile -1.37 0.08 17.35 -1.80 0.09 20.59 βaverage 17.70 βaverage 22.29 Table 14: UC statistical parameters normal mean Fy= 36 Ksi is also used. The generated waveform and yield stress data are then paired as 97 input to the Bentley SACS software. The results of the simulation yield 50UC values for each representative 98 member and for each pair of wave height and yield stress data generated. 99 A K-S test was conducted to determine the type of distribution of UC members, with the log normal dis- 100 tribution suitable for each member. PDF-UC factoring conditions, namely the main deck member shown 101 in Figure 5. The probability of member failure can be determined from the PDF-UC curve by calculating 102 the area under the PDF curve with a limit of 1≤UC≤ ∞ . Based on the results of the previous distri- 103 bution, the calculation of the reliability index (β)was done using the following log normal equations, as 104 follows, 105 Pf= 1−Φln (1)−λUC ζUC −ln (0)−λUC ζUC = 1−ΦλUC ζUC (4) , so we get, Pf= 1−Ps Ps= Φ(β).(5) The value of the reliability index can be determined by, β=λAUC ζAUC. (6) Table 13 shows the main statistical parameters of the UC obtained from the simulation results. Table 14 106 shows the results of calculating the reliability index value carried out on each member of the representative 107 structure for LRFD and non-factor loading conditions. The reliability index (β)for LRFD loading conditions 108 is16.70and for conditions without a factor of 22.29. 109 Bai (2003b) recommends Pfand values for a certain security class, as shown in Table 15. The security 110 classes are described as low safety class, normal safety class, and high safety class. The four members that 111 are the main focus of reliability analysis are in the category of high safety class, with the recommended 112 minimum reliability index being 3.72. So, the reliability index value for a factored load of 16.70without a 113 factor of 22.3is still very far from the recommended value range. 114 safety level target (Pf)safety (β) Low 10−22.32 Normal 10−33.09 High 10−43.72 Table 15: Environmental data. From the results of this analysis, it was concluded that the structure of a four-legged jacket-type wellhead 115 platform in the Java Sea, designed according to the design principles of the 1993 API RP2A-LRFD, has a 116 very large reliability index. Further studies are needed to adjust the application of load factors to oﬀshore 117 platforms in Java Sea waters. 118 8 (a) (b) Figure 5: PDF of UC main beam: (a) LRFD and (b) unfactored. 4 Conclusion 119 The analysis of this study resulted in several conclusions. The structure was determined to meet the design 120 criteria for member stress, joint punching shear, and pile capacity according to the 1993 API RP2A-LRFD 121 design criteria. Fatigue analysis revealed one joint in the bracing to be below the desired service life of 31 122 years and, thus, requires optimization by increasing the cross-section. The Monte Carlo simulation method 123 determined the reliability index (β)with50simulations of the four main member representatives using 124 random variables in the form of signiﬁcant waves. The mean value for the LRFD condition was 16.70, and 125 for the unfactored condition was 22.29. It is concluded that using the 1993 API RP2A-LRFD load factor is 126 inadequate for conditions in the Java Sea, and further studies are required to apply the appropriate load 127 factor. 128 There are several suggestions to improve this study, including: 129 •Structure and load data for a more complete and detailed design so that the analysis results are more 130 accurate. 131 •Wave data for reliability analysis should use maximum wave data to get more critical results. 132 •The Monte Carlo simulation is carried out more with a minimum number of 1000 simulations in order 133 to get more accurate simulation results. 134 •Conduct a reliability analysis on the structure of oﬀshore platforms in diﬀerent Indonesian waters to 135 obtain a more comprehensive conclusion regarding the study of the application of the API RP2A-LRFD 136 environmental load factor for Indonesian waters in general. 137 9 Acknowledgements 138 This study was funded by ITB Research, Community Service and Innovation Program (P3MI-ITB). 139