A variationally consistent hyperstatic reaction method for tunnel lining design

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