Analysis of geosynthetic tubes filled with several liquids with different densities

Abstract

A two dimensional model of a geosynthetic tube sitting on a rigid horizontal foundation and filled with several separated liquids with different densities is proposed. The material from which the tube is made is a special synthetic fabric which is inextensible, perfectly flexible, and leakproof. Such a model is useful for modeling a consolidations process in the tube filled with a slurry. The equilibrium equations of the model are formulated. Unknown values like the pressure on the top and bottom of the tube, the tension in the geosynthetic fabric, the length of the contact zone between the tube and the rigid foundation are searched with respect to the given perimeter, the volumes and densities of liquids. Such a problem is solved by the Newton’s method. The initial approximation is obtained by solving a simplified problem with one liquid with the average density. The problem is implemented in a MATLAB code for geosynthetic tubes filled with two, three, and four liquids with different densities. The tubes filled with two different liquids are studied in more detail. The graphs of the relations are compared with the graphs for the tube filled with the single liquid whose density is the average of the densities of the liquids. The comparison enables to discuss the influence of the consolidation process on the height, the contact zone, the pressures and the tension of the tube. The results of the proposed model for a tube filled with a single liquid are compared with another model.