Subsea pipelines buried in the seabed may undergo large lateral displacement under environmental, operational, and accidental loads at different interaction rates and hence different drainage conditions. The undrained shear strength is commonly used in practice to assess the pipe-soil interaction assuming a sufficiently high displacement rate. This approach neglects consolidation effects and the rate-dependent response of the soil and may significantly underestimates the lateral resistance for a pipeline moving slowly relative to the ground. In this study, a coupled large deformation finite element (LDFE) framework is developed via a remeshing and interpolation technique with small strain (RITSS). A Modified Cam-Clay (MCC) model with efficient numerical integration is used. The proposed coupled LDFE framework is verified against selected physical model tests. Effects of the interaction rate and hence drainage condition on the p-y curve, excess pore pressure generation and dissipation, and failure mechanisms are discussed. An empirical relationship between the ultimate resistance and the normalized velocity of the pipe (denoting the drainage condition) is proposed, which may be applied for the integrity and safety analysis of buried pipes in landslide or fault-crossing regions.