Analysis of Tunnel Liner-Packing Systems

A method is developed for analysis of cylindrical tunnel liner-packing systems subjected to transient loads. The continuous system is replaced by a discrete model consisting of axially deformable straight bars connected by flexible joints. The packing material is replaced by a radial spring at each joint. Force-deformation equations are derived for elastic and inelastic behavior of all elements. An averaging process is used to permit determination of the interaction of thrusts and bending moments in the inelastic range. The equations of motion for each point mass are solved by numerical integration. A computer program which utilizes the procedure is described. A procedure for selecting the time interval for numerical integration is given. Typical results for various numbers of mass points in the model are presented.