Implicit nonlinear FEM for steel sets in tunnels

• Published in: Science China. Technological sciences 2023-03, Vol.66 (3), p.771-783
• Main Authors: Kong, Ci, Xiao, Ming, Yuan, QingTeng
• Format: Article
• Language: English
• Subjects: Algorithms; Aluminum; Computer simulation; Elastoplasticity; Engineering; Finite element method; Iterative methods; Mathematical models; Mechanical properties; Nonlinear analysis; Steel construction; Stiffness; Strain; Stress-strain relationships; Tunnels
• ISSN: 1674-7321; 1869-1900
• DOI: 10.1007/s11431-022-2177-2

Steel sets are widely used in tunnels with unfavorable geological conditions. Such steel sets always have small dimensions and are densely installed on the excavation surface, which is why performing nonlinear analysis on steel sets in actual engineering is a challenging task. Therefore, an implicit nonlinear finite element method (FEM) for steel sets in tunnels was proposed. First, considering the mechanical characteristics of the steel set, a mathematical model of the steel set was proposed, which can accurately reflect the arch effect of the steel set. Then, the stress-strain relationship of the steel set was divided into the linear elastic stage, the first yield platform stage, the nonlinear hardening stage, and the second yield platform stage. In combination with the mixed hardening model, a nonlinear mechanical model of the steel set was established, and its rationality was verified by a thick aluminum ring example. Thirdly, for the convenience of engineering applications, steel sets were implied into rock elements, and their elastoplastic stiffness was superimposed into rock elements to reflect their supporting action. Furthermore, a stress update algorithm for the steel sets in the nonlinear iterative process and a method to simulate their fracture failure were provided. These models were incorporated into a self-developed FEM program to conduct nonlinear analysis for steel sets in tunnels. Finally, the proposed method was applied in a cross-fault hydraulic tunnel. The results proved its rationality, and some conclusions of interest were obtained. This method does not need to establish a complex solid model for steel sets, has no influence on the meshes of rock elements, and can simulate the whole process of steel sets from the linear elastic stage to the nonlinear hardening stage and finally to the fracture failure stage. Thus, it may be a convenient method of simulating steel sets in tunnels.