Two-Dimensional Vibrations of Inflated Geosynthetic Tubes Resting on a Rigid or Deformable Foundation

Abstract

Geosynthetic tubes have the potential to replace the traditional flood protection device of sandbagging. These tubes are manufactured with many individual designs and configurations. A small number of studies have been conducted on the geosynthetic tubes as water barriers. Within these studies, none have discussed the dynamics of unanchored geosynthetic tubes.

A two-dimensional equilibrium and vibration analysis of a freestanding geosynthetic tube is executed. Air and water are the two internal materials investigated. Three foundation variations are considered: rigid, Winkler, and Pasternak. Mathematica 4.2 was employed to solve the nonlinear equilibrium and dynamic equations, incorporating boundary conditions by use of a shooting method.

General assumptions are made that involve the geotextile material and supporting surface. The geosynthetic material is assumed to act like an inextensible membrane and bending resistance is neglected. Friction between the tube and rigid supporting surface is neglected. Added features of viscous damping and added mass of the water were applied to the rigid foundation study of the vibrations about the freestanding equilibrium configuration.

Results from the equilibrium and dynamic analysis include circumferential tension, contact length, equilibrium and vibration shapes, tube settlement, and natural frequencies. Natural frequencies for the first four mode shapes were computed. Future models may incorporate the frequencies or combinations of the frequencies found here and develop dynamic loading simulations.