Inverse Variational Principle Based Coupled
Modeling Of Underground Structures
Author(s)
P. Procházka
Abstract
In some previous papers of the author coupled numerical–experimental modeling
of tunnels embedded in surrounding rock was based on minimization of a certain
functional describing the steepest descend mode of differences of measured and
computed values of stresses or displacements at selected points. The idea
consisted of a choice of subdomains (patches), the eigenstrains in which were
introduced using the unit impulse technique. Influence matrices were generated
and the linear hull of eigenstrain effects together with the optimization problem
lead to the identification of plastic stresses inside the domain describing the
surrounding rock. Consequently, a nonlinear model in numerical analysis can be
improved using eigenparameters as design parameters in optimization. The only
problem remaining is how to select the patches. In this paper inverse variational
principles are applied to help solve this principal problem. The 2D problem is
solved with moving patches (support subdomains) with uniformly introduced
eigenstrains.
Keywords: coupled modeling, tunnel face stability, Inverse variational
principles, Desai’s model.
1 Introduction
Using a very powerful tool, a combination of Transformation field analysis
(TFA) and a certain plasticity rule (possibly softening included), back analysis of
structures can be regarded as seeking the optimal distribution of eigenparameters
(eigenstrains or eigenstresses) in the domain describing undeformed rock in a
certain sense. For the first time the TFA was applied to optimization of
prestressing of composite structures, [1]. The eigenparameters can represent
many phenomena (not only prestress), and also the influence of plastic
Keywords
coupled modeling, tunnel face stability, Inverse variational
principles, Desai’s model.
Related Book
Other papers in this volume
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