Soil-pipeline interaction through a frictional interface during earthquakes

In almost all of the existing investigations on the earthquake response of buried pipelines, the slip between pipe and surrounding soil was overlooked. It is now known through bench-scale and field experiments that the slip phenomenon plays an important role during and after earthquakes. Numerous analytical modellings of very small vibrational amplitudes of the shear force acting at the soil-pipe interface were reported in the literature (for example, Toki and Takada,¹ Ugai² and Parnes³. However, no serious analytical modelling of large vibrational amplitudes for such system is possible until a good model of slipping is adopted.

This paper addresses the concept of large vibrational amplitudes in dealing with the interaction of imperfectly bonded soil-pipe system during earthquakes. The friction at the interface is assumed to be of Coulomb mechanism by a viscous friction model having a viscous coefficient developed by Miller⁴ and Akiyoshi⁵. Analysis is first made for steady-harmonic earthquakes (= plane P- and S-waves) and the slip displacement is represented in closed form which involves some earthquake parameters, soil and pipes in which the break-loose condition for slip is compared with Ugai's⁶ solution. The frequency response function is investigated for the earthquakes with the flat acceleration spectra, and then used for the formulation of pipe and soil strains subjected to randomly vibrating earthquakes.

In this study the following assumptions are adopted:

• 1.

  (1) Soil is linear, homogeneous and isotropic infinite medium, and pipes are long elastic rods without joints.

• 2.

  (2) Frictional stress distributes uniformly around the pipe, and slip occurs when the boundary shear stress equals the frictional one.

• 3.

  (3) Earthquake plane P- and S-waves are correlated with the same spectral distributions.