Dynamic response of buried pipelines in randomly structured soil

Abstract Buried pipelines in soil undergoing ground vibrations respond by simple kinematic interaction and essentially follow the motion of the surrounding ground. More specifically, the strains that develop in the soil are imparted to the outer surface of the pipeline, which is the celebrated Newmark assumption dating from the 1960's that appears in design codes for pipelines. Of course, this assumption is invalid if the pipeline has bends and other geometric discontinuities. Furthermore, there remains the basic question of modeling the surrounding soil, which is a complex, two-phase medium with an inhomogeneous and anisotropic composition. In this work, we examine the dynamic response of a continuous pipeline by employing the waveguide model from classical elastodynamics. This implies that the pipeline is a continuously supported, beam-type structural element with distributed mass undergoing both axial and flexural vibrations. In here, we retain the influence of the axial vibrations on the flexural vibrations and work with a coupled system of two partial differential equations. The end boundaries of the pipeline are assumed to be fixed at a large distance from its center. We first examine the eigenvalue problem and then focus on the transient vibrations of the pipeline to support motion. In order to account for the complex composition of the ground, the soil impedance is converted into a random variable. Assuming uniform, Gaussian and log-normal distributions, we use Monte Carlo simulations to generate sample values for the soil impedance and compute the statistics (mean, variance and skewness) for the eigenvalue problem. Once the statistics of the eigenproperties of the buried pipeline example are recovered, the validity of the assumption that the soil is a deterministic medium is discussed.