Issue 49

A. Guillalet alii, Frattura ed Integrità Strutturale, 49 (2019) 341-349; DOI: 10.3221/IGF-ESIS.49.34 345 evaluation of failure probability can be optimized when using probabilistic methods. Use of worst case input parameters can be avoided so on very pessimistic estimations. The reliability analyses were performed using Importance Sampling at the design point method. This method is based on crude Monte Carlo method, were the sampling is focused on important regions in order to save computational resources and time consuming. Regions of importance during reliability analysis can be considered as failure domain precisely region with the highest probability density among all realizations in the failure region. Fig. 3 shows the design point in the normal space witch accomplish the criterion of highest probability density. This point is situated on the limit state function and has the smallest distance to the origin of normal space [15]. The key aspect of the method is to define the design point using First Order Reliability Method “FORM”. This design point is then used to have an importance sampling density function, the new density function is used to generate samples and calculate failure probability. Figure 3 : Design point in the normal space A PPLICATION AND RESULTS Case of study a. Material parameters he main design parameter involved in this study is fracture toughness where the considered material is API X 80 steel. This latter is a high strength steel characterized by high strength and toughness, Guillal [16] made a review about development of high strength steel and the effect of local brittle zone on weld joints toughness. It was concluded that Carbon content reduction and a better management of alloying elements, enhance mechanical properties in developed API 5L grade steel. Estimation of Fracture toughness is based on Charpy V notch test from [17] and the used correlation to convert Charpy data to facture toughness presented in Eqn. (5) as fallow: 12 * IC K CVN  (6) b. Geometrical parameters Fig. 2 illustrate pipeline dimension with a crack on the surface where its geometries are dimension on pipeline. The scatter in diameter and thickness of pipe is due pipe manufacturing and fabrication process. Cracks are generally characterized by NDT inspection tools. For purpose of our study, defect size is varied to cover a wide range of deep and shallow cracks. The used geometrical configuration is a pipeline with 1219.2 mm of diameter and 12.1 mm of wall-thickness. Random distribution of diameter and thickness of pipeline are presented in Tab. 1. c. loading parameters Larger pipe diameters and high pressure are known to be the most economical solutions in oil and gas transportation. New constructed pipelines reach a diameter of 56” and service pressure of 11-12 MPa. In our case, an API grade X80 steel is chosen to reflect used API modern steel in many projects. Maximum operating pressure and it random propriety are presented in Tab. 1. T