ABSTRACT
Using a high safety factor in construction without precise calculations imposes high costs on the execution project. Using a low safety factor exposes the project to a high risk of failure. Therefore, determining the impact of uncertain parameters greatly aids in designing with the least possible risk. The contribution of each parameter to uncertainty can be identified through sensitivity analysis. This paper considers the impact of the uncertainty of three parameters—elastic modulus, pipe thickness, and pipe diameter—on the buckling of a marine pipeline, as these three parameters significantly influence the geometry of the pipeline. Two analyses, First Order Second Moment (FORM) and Second Order Reliability Order (SORM), are employed for the sensitivity analysis of the pipeline parameters. The First Order Second Moment analysis provides four importance vectors, while the Second Order Reliability Order analysis yields only one importance index. The results indicate that the pipe diameter has a greater impact compared to the other two parameters. The smallest difference is observed between the elastic modulus and pipe thickness, suggesting that these two parameters have a similar level of sensitivity. The reliability index values in FORM and FOSM are distinct yet close to each other, with FOSM yielding a lower value.
 

INTRODUCTION

Submarine pipelines are subjected to various forces of different natures during installation and operation, such as hoop stress, axial force, and so on. The high temperature and pressure gradient between the well and the terminal (platform or refinery) in gas transmission lines generates significant axial force in the pipeline. If the mentioned forces exceed a certain threshold, despite the friction of the seabed and the weight of the submerged pipeline, they can cause large deformations in the pipeline or, in other words, lead to pipeline buckling. The DNV-F-110 standard (DET NORSKE VERITAS) classifies this type of buckling as global buckling, which can be categorized into horizontal and vertical buckling based on the deformation mode (Shabani et al., 2017). Global
buckling is a common and likely phenomenon that can occur during the operation of a pipeline. This phenomenon can lead to defects such as failure, bending, and so on in the pipeline (Karampour and Albermani, 2014). As accessible oil fields are depleted, the need for drilling at greater depths has increased, resulting in higher temperatures and pressures due to the transportation of hydrocarbon products. Consequently, the likelihood of global buckling occurring in deep waters has increased. Due to the lower critical temperature for lateral buckling compared to the critical temperature for vertical buckling, non-buried pipelines often face lateral buckling (Karampour et al., 2013). The presence of an initial vertical defect in a non-buried submarine pipeline makes the occurrence of vertical buckling possible.

MATERIALS AND METHODS

The marine pipeline studied in this research has a diameter of 0.816 meters, a thickness of 0.0242 meters, and a length of 40 meters. The Poisson's ratio of the pipeline is considered to be 0.3, and the thermal expansion coefficient is taken as 1.5 × 10^-6. The residual stress from the installation of the pipeline is not considered in this study due to its insignificance compared to other forces affecting the axial force. Horizontal compressive forces are considered with a high conservative coefficient.

RESULTS

Three parameters E, t, and D are geometric parameters of the underwater pipeline subjected to buckling. Among the three parameters mentioned, parameters of pipeline thickness and diameter are resistance variables, and elasticity modulus is the load resistance variable. The results show that the pipeline diameter is the most important among the mentioned parameters and the modulus of elasticity is the least important. In the analysis of FORM and FOSM, there are reliability indicators for both of them, which are the basic part of reliability evaluation by the two mentioned analyses. The reliability index values in FORM and FOSM are distinct but close values, which are lower in FOSM. According to Figure (2), the pipeline diameter is the most important variable of the defined limit state function. As it is clear, the smallest difference is between E and t, in other words, these two parameters are close to each other in terms of sensitivity, with the difference that one is a load variable and the other is a resistance variable. Also, this point can be concluded that the values elated to the importance index κ have a big difference with other importance indices and the rest of the importance indices have close values.

DISCUSSION AND CONCLUSION

Among the three mentioned parameters, the thickness and diameter of the pipeline are variables affecting resistance, while the modulus of elasticity is a variable affecting load resistance. The diameter of the pipeline holds the greatest importance among the mentioned parameters, while the modulus of elasticity is of lesser significance. The reliability index values in FORM and FOSM are distinct yet close to each other, with FOSM yielding a lower value. The approximate equality of the reliability index in the two analyses can be expressed by the difference in the importance vectors in the two analyses, and as the importance of the variables decreases, the difference becomes more pronounced. The values related to the importance index Kappa show a significant difference compared to other importance indices, while the remaining importance indices have values that are close to each other.