Reliability functions for buried submarine pipelines in clay subjected to upheaval buckling

This paper presents the reliability analyses for studying and quantifying the variation of the reliability index (β) with the main parameters involved during the upheaval buckling of submarine buried pipes caused by high pressure and temperature conditions (HPHT). The analyses correspond to typical geotechnical and operational conditions of pipelines installed in the Bay of Campeche, offshore Mexico. The parameters that mainly control the vertical uplift capacity of pipe-soil system and considered as uncertain are: the undrained shear strength of soils (S_u) and the soil cover height (H). Driving vertical loading depends mainly on the levels on temperature and pressure combined with vertical imperfections (δ), therefore those parameters were also considered as uncertain. Model errors for both capacity and driving vertical force were estimated and applied in the analyses.The limit state function was established by comparing the uplift pipe-soil capacity with the vertical driving loading. Parameter uncertainty was covered based on literature reviews, information of the proper conditions for pipelines operating in the Bay of Campeche and numerical analyses.A lower-bound capacity of the pipe-clayey soil system was included in the reliability analysis and is a novelty of this work. Lower-bound capacity is the smallest possible physical limit of the uplift pipe-soil capacity and its effect on the reliability is studied. Furthermore, finite element analyses were executed to evaluate the uplift capacity of the pipe-soil system and determine the analytical model error for estimating the capacity.The reliability indices (β) of the pipe-soil system under upheaval phenomena were evaluated by means of directional simulations. Consequently, the reliability functions β- δ and β- H/ D (ratio cover height over pipe diameter) were quantified. It was found that the inclusion of the lower-bound capacity by means of a left-censored distribution possibly increases β in comparison to the estimations using conventional distributions, the maximum increments observed are in the range of 22-34%.