Gradient‐Enhancement of a Rock Model Applied to Numerical Simulations of Tunnel Advance. Issue 1 (17th December 2018)

• Record Type: Journal Article
• Authors: Schreter, Magdalena; Neuner, Matthias; Hofstetter, Günter
• Other Names: Müller G. guestEditor.; Ulbrich M. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 18:Issue 1(2018)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2018-12-17
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201800056
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: Rock is classified as a frictional cohesive material characterized by nonlinear stress‐strain relations including softening leading to structural failure. To describe the mechanical behavior of rock comprising the accumulation of irreversible strains, strain hardening, and the degradation of stiffness and strength, an isotropic damage plasticity model for intact rock and rock mass was proposed in [1]. In the context of numerical simulations of tunneling, considering strain softening of rock allows to predict the formation of shear bands emanating from the tunnel surface due to the excavation process, which is crucial for engineers to forecast potentially dangerous situations related to failure. To ensure objective results in the softening regime upon mesh refinement, in the aforementioned rock model the concept of the crack band approach by Bažant and Oh was adopted. As a remedy of known deficiencies related to this regularization approach, the rock model is extended by the over‐nonlocal implicit gradient‐enhancement proposed in [2]. Accordingly, a nonlocal field of the damage‐driving variable, implicitly defined as the solution of a Helmholtz‐like partial differential equation, is introduced yielding a fully coupled system of second‐order PDEs. In the present contribution, the over‐nonlocal gradient enhancement of the rock model is presented and applied together with a linear‐elastic material model for shotcrete to finite element simulations of a deep tunnel constructed by the New Austrian Tunneling Method. Based on this real example, objectivity of the results with respect to the finite element discretization is discussed.