Two-dimensional analytical analysis of equilibrium shape of inflated geomembrane tube resting on rigid foundation with arbitrary shape

Geomembrane tubes are used as an alternative to old methods for flood protection and may be considered as inflatable structures. These tubes can be filled with air and/or water and placed on ground, or any foundation. In this paper, a new analytical method is developed to determine the equilibrium shape of a geomembrane tube filled with air and resting on rigid foundations of an arbitrary shape. Geometric and equilibrium relations of a tube element are used to obtain the equilibrium shape of tube in an explicit (closed) form. The material of the tube is assumed to be inextensible and its bending stiffness is neglected. Using the closed form solution presented in this paper, the equilibrium shape of geomembrane tubes resting on foundations with different shapes and with different internal pressures, can be easily determined and there is no need to solve the problem numerically. The validity of the present analytical approach is confirmed by comparing the results with selected references. The results of comparison show that the presented analytical formulation provides the same level of accuracy with less numerical effort.