Time Dependent Reliability Assessment

RESULT AND DISCUSSION

4.4 Time Dependent Reliability Assessment

In time dependent reliability assessment, the jacket platform has been evaluated and the probability of failure of the jacket platform is expected. The limit state function is incorporated with First Order Reliability Method(FORM) to induce the result of probability of failure. The FERUM has been used to conducted the FORM.

In this section, the RSR, probability of failure, Pf and Reliability Index, RI is presented.

The RSR are obtained from the pushover analysis and tabulated in the table 4.2. The Pf and RI are the result from the FORM method and tabulated in the table 4.2.

Probability of failure represent the tendency of the undesirable performance of the jacket platform. The results of the Probability of failure is shown below;

Table 4.2: Result of FORM Analysis

Time Load Direction RSR Probability of Failure Reliability Index

1 4.888 9.4369E-16 7.9469E+00

2 2.526 8.3823E-09 5.6425E+00

3 4.927 8.3267E-16 7.9671E+00

4 4.889 9.4369E-16 7.9474E+00

5 4.999 6.1062E-16 8.0036E+00

6 4.886 9.4369E-16 7.9460E+00

7 4.728 1.9429E-15 7.8603E+00

8 4.556 4.2744E-15 7.7598E+00

1 4.884 9.9920E-16 7.9448E+00

2 3.059 6.5153E-11 6.4268E+00

3 4.946 7.7716E-16 7.9769E+00

4 4.890 9.4369E-16 7.9479E+00

5 5.002 6.1062E-16 8.0051E+00

6 4.886 9.4369E-16 7.9460E+00

7 4.354 1.1602E-14 7.6316E+00

8 4.523 4.9960E-15 7.7397E+00

1 4.895 9.4369E-16 7.9506E+00

2 3.036 7.9029E-11 6.3974E+00

3 4.957 7.2164E-16 7.9825E+00

4 4.890 9.4369E-16 7.9479E+00

5 4.808 1.3323E-15 7.9043E+00

6 4.889 9.4369E-16 7.9474E+00

7 4.141 3.6526E-14 7.4823E+00

8 4.145 3.5694E-14 7.4854E+00

1 4.895 9.4369E-16 7.9506E+00

2 2.426 2.2719E-08 5.4683E+00

3 4.968 6.6613E-16 7.9880E+00

4 4.890 9.4369E-16 7.9479E+00

5 4.816 1.2768E-15 7.9086E+00

6 4.889 9.4369E-16 7.9476E+00

7 4.148 3.5194E-14 7.4871E+00

8 4.144 3.5971E-14 7.4842E+00

1 4.895 9.4369E-16 7.9506E+00

2 2.426 2.2719E-08 5.4683E+00

3 4.968 6.6613E-16 7.9880E+00

4 4.890 9.4369E-16 7.9479E+00

5 4.816 1.2768E-15 7.9086E+00

6 4.889 9.4369E-16 7.9476E+00

7 4.148 3.5194E-14 7.4871E+00

8 4.144 3.5971E-14 7.4842E+00

1 4.895 9.4369E-16 7.9506E+00

2 2.426 2.2719E-08 5.4683E+00

3 4.968 6.6613E-16 7.9880E+00

4 4.890 9.4369E-16 7.9479E+00

5 4.816 1.2768E-15 7.9086E+00

6 4.889 9.4369E-16 7.9476E+00

7 4.148 3.5194E-14 7.4871E+00

8 4.144 3.5971E-14 7.4842E+00

Table 4.2 showed the relationship between the RSR and time, Pf and Time as well as Reliability Index and time in every load direction. As discussed before, the RSR value is decreased over time and proved that the capacity of the jacket platform is degraded over time. Overall, based on the table 4.2, the probability of failure of the structure showed the upward trends in which the probability of failure increased over time. This proved that likelihood of the structure to fail is higher as the time passes. As the RSR value decreased over time, the Pf increased over time. Hence, the Pf is inversely related to the RSR. Figure 4.4 – 4.11 showed relationship between Pf and time in every different direction.

Figure 4.4: Graph of Pf Vs Time from Direction 1

9.4000E-16 9.5000E-16 9.6000E-16 9.7000E-16 9.8000E-16 9.9000E-16 1.0000E-15 1.0100E-15

0 10 20 30 40 50 60

P

Time, Year

P

Vs Time from Direction 1

Figure 4.5: Graph of Pf Vs Time from Direction 2

Figure 4.6: Graph of Pf Vs Time from Direction 3

0.0000E+00 5.0000E-09 1.0000E-08 1.5000E-08 2.0000E-08 2.5000E-08

0 10 20 30 40 50 60

P

Time, Year P

Vs Time from Direction 2

0.0000E+00 1.0000E-16 2.0000E-16 3.0000E-16 4.0000E-16 5.0000E-16 6.0000E-16 7.0000E-16 8.0000E-16 9.0000E-16

0 10 20 30 40 50 60

P

Time, Year

P

Vs Time from Direction 3

Figure 4.7: Graph of Pf Vs Time from Direction 4

Figure 4.8: Graph of Pf Vs Time from Direction 5

0.0000E+00 1.0000E-16 2.0000E-16 3.0000E-16 4.0000E-16 5.0000E-16 6.0000E-16 7.0000E-16 8.0000E-16 9.0000E-16 1.0000E-15

0 10 20 30 40 50 60

P

Time, Year P

Vs Time from Direction 4

0.0000E+00 2.0000E-16 4.0000E-16 6.0000E-16 8.0000E-16 1.0000E-15 1.2000E-15 1.4000E-15

0 10 20 30 40 50 60

P

Time, Year

P

Vs Time from Direction 5

Figure 4.9: Graph of Pf Vs Time from Direction 6

Figure 4.10: Graph of Pf Vs Time from Direction 7

0.0000E+00 1.0000E-16 2.0000E-16 3.0000E-16 4.0000E-16 5.0000E-16 6.0000E-16 7.0000E-16 8.0000E-16 9.0000E-16 1.0000E-15

0 10 20 30 40 50 60

P

Time, Year P

Vs Time from Direction 6

0.0000E+00 5.0000E-15 1.0000E-14 1.5000E-14 2.0000E-14 2.5000E-14 3.0000E-14 3.5000E-14 4.0000E-14

0 10 20 30 40 50 60

P

Time, Year

P

Vs Time from Direction 7

Figure 4.11: Graph of Pf Vs Time from Direction 8

0.0000E+00 5.0000E-15 1.0000E-14 1.5000E-14 2.0000E-14 2.5000E-14 3.0000E-14 3.5000E-14 4.0000E-14

0 10 20 30 40 50 60

P

Time, Year

P

Vs Time from Direction 8

Table 4.3: Failure of Member During Pushover Analysis Load direction 2

Member 534-528 530-524 528-518

0 year

Load Factor 4.00 x Storm load 4.00 x Storm load 3.90 x Storm load

Length (m) 3.450 3.450 3.450

Displaced Length (m) 3.459 3.440 3.461

Diameter (m) 50.8 50.8 50.8

Thickness (m) 0.98 0.98 2.00

10 years

Load Factor 4.00 x Storm load 4.00 x Storm load 3.90 x Storm load

Length (m) 3.450 3.450 3.450

Displaced Length (m) 3.447 3.438 3.434

Diameter (m) 50.608 50.608 50.608

Thickness (m) 0.854 0.854 1.904

20 years

Load Factor 4.00 x Storm load 4.00 x Storm load 3.90 x Storm load

Length (m) 3.450 3.450 3.450

Displaced Length (m) 3.447 3.437 3.441

Diameter (m) 50.478 50.478 50.478

Thickness (m) 0.789 0.789 1.839

30 years

Load Factor 4.00 x Storm load 4.00 x Storm load 3.90 x Storm load

Length (m) 3.450 3.450 3.450

Displaced Length (m) 3.473 3.435 3.459

Diameter (m) 50.472 50.472 50.472

Thickness (m) 0.786 0.786 1.836

Since the RSR and probability of failure of load direction 2 showed unexpected variation, assumption has been made to explain the undesirable result. Table 4.3 shows that the state of three members of the jacket platform before fail during pushover analysis. The three member denoted as 534-528, 530-524 and 528-518. The state of members is observed in 0 year, 10 years, 20 years and 30 years. The load factor for members of 534-528 and 530-524 are constant in which 4.00 x storm load. However, the load factor for member 528-518 is 3.90 x storm load as the member is completely failed before reach load factor 4.00 x storm load. The length of the members observed is constant in which 3.450m. The red part of the member shows that the segment of the member is 100% in plastic state which the member is completely yielded. The purple part illustrates the segment of the member 75% in plastic state. The yellow part displays that the member is 50% yielded, the blue part shows that the segment of the member is 25% in plastic state whereas the green part displays that the member is still in elastic state. For the member 534-528 in 0 year, some of the segments of the whole length of member is completely yielded or in plastic state. However, the same segments of member analyzed in 10 and 20 years illustrated green color which the segments are not yield. The same pattern also can be seen in member 528-518. The certain segments are completely yielded in 0 year during pushover analysis. However, the same segments analyzed in 10 and 20 years displayed different results compared the analysis in 0 year. These segments illustrated the member is still in elastic state or only in 50% plastic state. These results proved that the failure mechanism of the member is random and likely to affect the RSR and probability of failure results. The load transfer to the member parts are random since the failure of the members are random. Assumption made in previous results that the results may induced by different failure mechanism is relevant with this observation of specific members. This assumption may lead to the unexpected variation of the RSR and probability of failure of load direction 2.

CHAPTER 5

CONCLUSION AND RECOMMENDATION

The aim of this project is to acquire the RSR in different reference time. In order to achieve this objective, the static nonlinear collapse analysis is being used to determine the RSR. The RSR is important value for resistance of the structure and the analysis in different reference time is needed. The thickness of structural member platform is adjusted suit to the corrosion model and analysis is took place in different reference time. From the findings, The RSR value from load direction 2 induce a critical result as the lowest RSR compared with other load direction. However, by interpreting all the results from the load direction, it can be concluded that the RSR value decreased over time. The results proved that the capacity of jacket platform is degrade as time passes. Hence, these results validate the problem statement in this project. Then, the RSR value will be used to satisfy the limit state function in term of resistance. The value that exceeded the limit state is considered fail. In this regard, resistance and load model is prepared and the analysis is conducted utilizing FORM method. The storm load is considered in this study and 100 year return period data is utilized. The probability of failure has been predicted until 50 years based on the corrosion model.

From the overall result, the probability of failure of jacket platform is considered increasing over time. This proved that as time passes, the tendency of the undesirable performance of the structure become higher. With the result of probability of failure, the objectives of this study are achieved. To conclude, the resistance or capacity of the platform degraded and probability of failure of the platform increased as time passes.

Hence, the relationship between RSR and probability of failure of the platform has been made as the probability of failure of the platform is inversely related to RSR. As for the recommendation, this study can be extended with the analysis on the component members of the structure and not only limited to structural system and other failure mode such as buckling and member internal stress will be considered. Besides, as the corrosion applied in this structure is limited to splash and immersion zone, the study

can be continued with consider the atmospheric zone. Since the probability of failure showed small reduction, the explanation has been made. The corrosion model is the most vital part in this study. In 50 years, the total corrosion growth is approximately 1.60mm in which the reduction of thickness of the members is very less. The critical corrosion growth is critical during year 1.38 until year 20. At this point, the members of the platform are maintained in which the corrosion protection is starting to be applied to the structure. This small reduction of the thickness is likely to affect the probability of failure. Hence, the reduction probability of failure is likely to be less.

As for recommendation for this situation, the other corrosion model can be used. The latest corrosion model should take into account in order to perform the reliability assessment method.

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APPENDICES

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