J. Ocean Univ. China (Oceanic and Coastal Sea Research) DOI 10.1007/s11802-015-2368-8 ISSN 1672-5182, 2015 14 (1): 75-83 http://www.ouc.edu.cn/xbywb/ E-mail:xbywb@ouc.edu.cn Nonlinear Contact Between Inner Walls of Deep Sea Pipelines in Buckling Process MA Weilin 1) , YU Jianxing 1) , ZHOU Qingji 1), * , XIE Bin 2) , CAO Jing 2) , and LI Zhibo 1) 1) State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, P. R. China 2) CNOOC Research Institute, Beijing 100027, P. R. China (Received April 17, 2013; revised June 18, 2013; accepted December 1, 2014) © Ocean University of China, Science Press and Springer-Verlag Berlin Heidelberg 2015 Abstract In order to study buckling propagation mechanism in deep sea pipelines, the contact between pipeline’s inner walls in buckling process was studied. A two-dimensional ring model was used to represent the pipeline and a nonlinear spring model was adopted to simulate the contact between inner walls. Based on the elastoplastic constitutive relationship and the principle of virtual work theory, the coupling effect of pipeline’s nonlinear large deformation and wall contact was included in the theoretical analysis with the aid of MATLAB, and the application scope of the theoretical model was also discussed. The calculated results show that during the loading process, the change in external pressure is closely related to the distribution of section stress, and once the walls are contacting each other, the external pressure increases and then remains stable after it reaches a specific value. Without fracture, the pipeline section will stop showing deformation. The results of theoretical calculations agree well with those of numerical simula- tions. Finally, in order to ensure reliability and accuracy of the theoretical results, the collapse pressure and propagation pressure were both verified by numerical simulations and experiments. Therefore, the theoretical model can be used to analyze pipeline’s buckling deformation and contact between pipeline’s inner walls, which forms the basis for further research on three-dimensional buckling propagation. Key words deep sea pipeline; buckling propagation; nonlinear contact; collapse pressure; propagation pressure 1 Introduction The subsea pipeline plays an important role in the off- shore oil and gas exploration. Its structural safety is of great concern for engineers. Because hydrostatic pressure increases with water depth, even a small initial defect of the pipeline can easily lead to local buckling collapse or buckling propagation and result in a wide range of struc- tural damage in the deep ocean. Buckling experiments of full-scale pipelines were carried out in a deepwater pres- sure laboratory (Fig.1) and the contact between inner walls due to buckling collapse and the related buckling propagation were observed and studied in these experi- ments (Fig.2). Fabian (1977) analyzed the nonlinear buckling re- sponse of pipelines under combined forces of bending moment and axial tension. Chen and Shao (1979) con- ducted experiments on buckling of stiffened cylindrical shells under hydrostatic pressure in three different geo- metric scales, followed by large deflection analysis and small deflection calculations using the plastic flow theory and the small elasto-plastic deformation theory, respec- tively. Kyriakides and Babcock (1981) proposed a con- * Corresponding author. E-mail: zhouqingji2008@126.com tinuous mechanical model for a large ring deformation under hydrostatic pressure. Based on a three-dimensional cylindrical shell model, Kyriakides and Arikan (1983) utilized both experiments and numerical simulations to study the buckling problem of pipelines under bending moment, axial force and hydrostatic pressure, and ana- lyzed the effects of radius-thickness ratio, material prop- erty, initial ovality and loading path on pipeline local buckling. Estefen (1999) evaluated the ultimate strength of intact pipelines under external hydrostatic pressure and bending moment, and the resident strength of damaged pipelines. Gong et al. (2012) studied defective thick- walled steel pipes with model tests and numerical simula- tions, and found that the larger the material hardening coefficient is, the greater the collapse pressure of pipes becomes. Ji et al. (2012) researched on the buckling be- havior of pipelines for strain-based design by means of numerical simulations as the supplement to full scale bending tests. Li et al. (2012) analyzed the collapse of deep sea pipes by adopting a combined method with nu- merical simulations and full-scale experiments, and cal- culated the structural reliability index of deep sea pipes with the J-C method. Cui and Zhang (2012) analyzed the nonlinear pipe buckling with ABAQUS, and conducted the sensitivity analysis of diameter-thickness ratio, initial ovality, axial force and bending moment. Using various