Development of Equivalent Lattice Beam Model for Support System in Tunnels and Caverns Using FEM Analysis

Abstract

In recent years architects and designers make the extensive use of two- and three-dimensional lattice structures. The lightweight, ease of construction, and freedom of structural shape in lattice structures offer many advantages to the creative designer. Although lattice girder truss elements can model such structures in any finite element package, an equivalent continuum approach is beneficial as in the input of the geometry is much simpler, the number of degrees of freedom reduces drastically, for simple structures like beams or plates, explicit expressions for the deflections and the stress resultants are available in textbooks, and the structural behavior of the equivalent continuum model can be understood more easily. The objective of this paper is to use these methods for the determination of equivalent stiffness of rectangular lattice beam, which is a primary rock support system employed in tunnels and caverns. The equivalent stiffness of lattice beam rectangular in shape was determined by four continuum modeling techniques, namely, an equivalent moment of area based on simply supported condition or fixed end condition, method of parallel axis theorem, Burgardt and Cartraud’ method, and direct energy approach method. The equivalent stiffness so obtained was used as an input parameter in numerical analysis tool STRAND7 for analysis of equivalent rectangular lattice beam. The maximum deflection and bending stress at the center of equivalent lattice beam were calculated and compared with central deflection and bending stress in case of original lattice girder using this analysis tool STRAND7.