Interaction of Soil Static and Dynamic Stiffness and Buried Pipeline Under Harmonic Vibration

Abstract

Problem statement: When earthquake is occur, many damages were occurred in pipelines that San Francisco (1906) and Manson (1908), Kobe (Japan) and ate are samples of this topic. So many researchers studied on the pipelines and dynamic forces. Approach: Determine static and dynamic performance parameters of the pipeline and the surrounding soil such as static stiffness, dynamic stiffness, damping and additional mass share of soil which take part with pipe mass in dynamic performance. In the static case relationship between friction forces and joint deflections in a buried element pipe had be calculated and with using of some experimental results and results are compared together. For dynamic cases, Dynamic equilibrium equation of pipeline element axial vibration in continuous system, with neglecting the effect of soil mass share which participates in producing vibration and with considering of it were abstained and values of displacement and forces were calculated. In continuous, these formulations were process for many cases and were drawn in graphs for comparison. Results: Stiffness for ω/ω_n<1 doesn't change much but for the values more than 1 it increase rising. when ω/ω_n<1 the ratio of dynamic stiffness to the static stiffness is less than unique except in big amount of damping ratio (ρ>0.5) which the ratio becomes more than 1. Finally for ω/ω_n>1, the ratio of dynamic to static stiffness rises rapidly and by increasing the additional mass, the value of dynamic stiffness in case of ω/ω_n>1 would increase highly. Conclusion: The static performance between soil and pipe is nonlinear in axial direction and when the hysteric dominates grows, the value of force dominates between soil and pipe and dynamic stiffness would ascend. Also by increasing damping ratio, the dynamic stiffness would increase too however it depends on the static to dynamic stiffness ratio and the damping ratio.