Optimal topology of eigenstrains in the assessment of tunnel structures

Eigenstresses and eigenstrains act out a very important role in many branches of applied mechanics. The eigenparameters may represent plastic strains, or relaxation stresses (or also prestresses, changes of temperature, etc.), and may also serve as free parameters for improving numerical models to get the computed quantities that should be as close as possible to the real state. A special variational formulation can be formulated, dealing with the minimum variance of differences between measured and computed values. When using a very useful treatment, the generalized transformation field analysis (GTFA), having recently been proposed by Dvorak and Prochazka, and the Disturbed State Concept proposed by Desai, the primary problem leads to a linear system of algebraic equations. First, we briefly introduce an estimation of physically nonlinear behavior of the body by Desai. The eigenparameters will then be introduced in such a manner that the optimal variance of errors from measurement and numerical results are sought. It appears that the number of components of eigenparameters should not exceed the number of data points from measurements either on site or on a scale model, and hence, the number of free eigenparameters is restricted. The main problem remains: how to select the zones with, say, uniformly distributed eigenparameters in order to achieve the minimum deviation of computed and measured results in dependence of the minimum variation of errors from computation and of the topology of the eigenparameters zone. They basically influence the final results from the procedure to be described. The main goal of this paper consists in finding out both the phenomena. While the minimum of the error functional leads to linear algebraic equations, searching for optimal topology of eigenparameters zones brings about a nonlinear problem, which should be solved in some reasonable way. We first concentrate on the optimization of the error functional under the condition that the zones are known and then the zones will be sought.