Numerical Analysis Of Dynamic Response Of Submarine Pipeline And Seabed Under Seismic Loading

People intensify the exploitation of submarine petroleum and natural gas in recent years because of the needs of energy sources increasing, it makes submarine pipelines applied widely. But submarine pipelines buried in ocean environment usually carry all kinds of loadings, not only wave loading but also seismic loading. The seismic-induced pore water pressure of seabed and internal stress of pipeline are important for people to design submarine pipelines. China is located in the middle of two main earthquake zones of the world (the zone around Pacific Ocean and the zone of middle Asia-Mediterranean Sea) and earthquakes occur easily, particularly in the Bohai Sea which has rich petroleum resources, therefore we must consider the influence of earthquakes when we bury submarine pipelines. In order to evaluate the stability of submarine pipelines under seismic loading correctly, the computation of seismic-induced pore water pressure and effective stresses in saturated seabed is one of main projects for engineers to design submarine pipeline.In this paper, the governing equations of the seabed and pipeline are formulated based on the Biot's consolidation theory and elastic dynamic theory respectively. The model of the seabed-pipeline interaction is established by using the friction contact theory and the FEM analysis method. The distribution of the seismic-induced excess pore water pressure along the pipeline outer surface and the dynamic response of submarine pipeline under seismic loading are studied by virtue of the FEM numerical computations. Through numerical analysis, viscous-elastic artificial boundary is taken into account to simulate the transmission of seismic wave from finite region to infinite region effectively. It actually shows the validity and accuracy of dynamic response of submarine pipeline under seismic loading. Based on the numerical computations, it is found that the viscous-elastic artificial boundary has more superiority than fixed boundary in transient dynamics and the result under viscous-elastic artificial boundary is closer to precise result. The soil characteristic parameters such as deformation modulus and permeability coefficients, the pipeline radius and wall thickness all have some influence on the seismic-induced pore water pressure and radial normal stress as well as shear stress along the pipeline circumferential outer surface and circumferential normal stress along the pipeline circumferential inner surface. The effects of homogeneous seabed and two-layered seabed on the seismic-induced excess pore water pressure along the pipeline circumferential outer surface are remarkable but the effects on internal stresses of pipeline are small. The seismic-induced excess pore water pressure along the pipeline surface decreases with the width of cover layer increasing and increases with the thickness of cover layer increasing, but the tendency of excess pore water pressure with different length and thickness is almost the same.Due to the limitation of equipments, there have no exact expression to describe the building-up pore water pressure which is applicable to seismic cyclic loading so far. In this paper, the advanced soil static and dynamic universal triaxial and torsional shear apparatus is employed to perform cyclic torsional shear tests subjected to cyclic loading. In order to obtain the building-up expression of pore water pressure of seabed under cyclic torsional loading, a series of cyclic torsional tests of different initial effective consolidation pressure (p'm0=100, 200,300kPa) and different initial consolidation ratio (Kc=1.0,1.5,2.0) are performed for saturated Fujian standard sand with relative density of Dr=60%. By the analysis of test results, the stress mode of pore water pressure in saturated sandy seabed under seismic loading is established, the effects of initial effective consolidation pressure and initial consolidation ratio on the pore water pressure are investigated, the generation, increasing processes of pore water pressure in sandy seabed under seismic loading is simulated preferably.According to the boundary value problem of liquefaction around a buried pipeline, the continuity equation for porous medium including accumulative excess pore water pressure source term distribution q in unit control volume of seabed is deduced, two-dimensional dynamic consolidation equation with accumulative excess pore water pressure source term f is established by incorporating with the mode of dynamic increase of excess pore water pressure under undrained conditions gained from tests to equilibrium equation of pore fluid; and it is solved by employing weighted residual method. By numerical computations, the effects of soil characteristic parameters and pipeline geometry on seismic-induced accumulative excess pore water pressure around the pipeline and along the depth of seabed are studied, the accumulation process of pore water pressure and liquefaction potential of seabed soil under seismic loading are evaluated in details.By computations and analysis it is found that the seismic-induced accumulative pore water pressures of seabed increase with the values of soil deformation modulus and Passion's ratio decreasing. The effects of soil permeability coefficient on seismic-induced accumulative pore water pressure ratios of seabed around pipeline are remarkable. The seismic-induced accumulative pore water pressure ratios of seabed increase with the values of the permeability coefficient decreasing, the small reduction of permeability coefficient will lead to significant increment of accumulative pore water pressure ratios of seabed. Otherwise the radius and burial depth of pipeline have some influence on seismic-induced accumulative pore water pressure ratios of seabed around pipeline but they are more complicated. The existence of pipeline only influences the accumulative pore water pressure ratios of seabed nearby the pipeline. The effect of pipeline is very slight and can be neglected in the region of seabed far away from the pipeline.In order to further study dynamic response of submarine pipeline and the seabed around pipeline, a three-dimensional model of the seabed-pipeline interaction including buried pipeline is established based on the FEM analysis method. By using the extending DIANA-SWANDYNE III models, the effects of earthquake loading directions and soil characteristics, such as soil permeability, water depth, seabed depth and pipeline configuration, such as pipeline radius and pipeline buried depth on the seismic-induced excess pore water pressure along the pipeline outer surface and the dynamic response of the pipeline are examined. It can be concluded from numerical results:there is an obvious difference between the distribution of the seismic-induced excess pore water pressure and radial normal stress as well as shear stress along the pipeline circumferential outer surface and circumferential normal stress along the pipeline circumferential inner surface under different seismic loading, the seismic-induced excess pore water pressure around pipeline increases with soil permeability decreasing and pipeline buried depth increasing, radial normal stress as well as shear stress along the pipeline circumferential outer surface decrease with soil permeability decreasing, and increase in some extent at some points with pipeline radius and buried depth increasing.