Direct search solution of an inverse problem in elastoplasticity: Identification of cohesion, friction angle and in situ stress by pressure tunnel tests

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Abstract
The identification (or ‘calibration’ or ‘inverse’) problem with in this paper, can be outlined as follows. The ‘real system’ is a deep rock formation which can be regarded as isotropic and elastoplastic. A mathematical‐numerical model, intended for the analysis of its response to excavations, rests on the assumption of an elastic‐perfectly plastic Mohr–Coulomb constitutive law and of a homogeneous isotropic initial (in situ) stress state. The values of cohesion, friction angle and initial stress to be introduced in this model are identified by minimizing a measure of the discrepancy (error) between theoretical and experimental relationship (pressure vs. average diameter increase), concerning a standard pressure tunnel test carried out well inside the nonlinear range. For the error minimization process, two very general ‘search techniques’ are adopted and discussed from the computational standpoint: the flexible polyhedron (modified simplex) strategy and the alternating variable strategy in the Rosenbrock version. Both are found to be adequate for solving this inverse problem, when the mathematical model has to be use as a ‘black box’ in a purely numerical identification process.

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