A variationally consistent hyperstatic reaction method for tunnel lining design

• Published in: International journal for numerical and analytical methods in geomechanics Vol. 46; no. 1; pp. 205 - 217
• Main Authors: Bui, Hoang‐Giang, Ninić, Jelena, Do, Ngoc‐Anh, Dias, Daniel, Meschke, Günther
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01.01.2022
• Subjects: Aquatic reptiles; consistent linearization; Design; FEM; hyperstatic reaction method; Iterative algorithms; Iterative methods; Linearization; lining design; Nonlinear response; Nonlinear systems; Soil; Stiffness; Tunnel linings; Tunnels
• ISSN: 0363-9061; 1096-9853
• DOI: 10.1002/nag.3288

In this technical note, a consistent finite element formulation of the Hyperstatic Reaction Method (HRM) for tunnel linings design is proposed by introducing a variational consistently linearized formulation. It permits to consider a nonlinear interaction between a lining structure and the surrounding ground. Recent advances of the HRM in regard to the consideration of the nonlinear response of the segmented tunnel lining exposed to design loads use an iterative algorithm for solving the nonlinear system of equations. In the proposed Variationally consistent Hyperstatic Reaction Method (VHRM), a distributed nonlinear spring model representing the interaction between the lining and the ground soils is considered in a variationally consistent format. Computing the tangential spring stiffness via consistent linearization, and using Newton‐Raphson iteration, requires significantly smaller number of iterations as compared to the original HRM model based on nodal springs. Furthermore, the method is applicable for simulations using solid finite elements (2D and 3D), as well as beam or finite shell elements, respectively.