J. Eberhardsteiner, G. Hofstetter, C. Kropik, H.A. Mang:
"Elasto-viscoplastic Three-Dimensional Hybrid BE-FE Stress Analysis of the Excavation of Tunnels";
in: "Boundary Element Techniques in Geomechanics",
G.D. Manolis, T.G. Davis (Hrg.);
Computational Mechanics Publications,
A hybrid boundary element - finite element (BE-FE) method for three-dimensional elasto-viscoplastic stress analysis of the excavation of tunnels is presented. Such an analysis consists of the mathematical simulation of a sequence of excavation increments of the calotte and of the stope of a tunnel, accompanied by the simultaneous securing of the excavation steps by a shotcrete shell. In the FE subdomain an elasto-viscoplastic multi-surface cap model is used for the description of the constitutive behavior of soil and shotcrete. Application of the return mappping algorithm together with tangent moduli, consistent with the applied algorithm, guarantees an efficient numerical treatment of the elasto-viscoplastic constitutive behavior within the framework of an iterative Newton-Raphson solution strategy. Symmetrization of the unsymmetric coupling stiffness matrix, referring to the interface of the BE subregion and the FE subdomain, is identified as the omission of an equilibrium system of node forces on the coupling interface, which must disappear in the limit of finite discretizations. In the vicinity of the coupling interface such a symmetrization may yield poor results. Results from hybrid BE-FE stress analysis of the excavation of a segment of the underground line U3 of Vienna are compared, on the one hand, to corresponding results obtained by the finite element method (FEM) and, on the other hand, to results from BE-FE hybrid stress analysis on the basis of a Drucker-Prager yield surface.
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