A back analysis program system for geomechanics applications

Abstract

A Back Analysis Program System has been developed for geomechanics applications. The system inherits the developments made in the last two decades and adds new features to establish a multi-purpose back analysis program system to account for elasticity and elastoplasticity both from deterministic and stochastic viewpoints.The contributions made by previous researchers are systematically analyzed to categorize various factors considered in back analysis in geomechanics. A scheme which results from this analysis becomes a Back Analysis Classification Scheme. This scheme identifies seven different types of unknown data category combinations. The thesis uses these seven cases as a guideline to present the discussions.Firstly, the back analysis procedures are discussed for elasticity considering the unknown data categories M (Material), L (Load), and ML (Material and Load), respectively. These three cases deed with the most fundamental aspects of a force-displacement relationship. The use of stress measurements along with displacement measurements is identified as a necessary step to be taken for a stable estimation of load parameters, or simultaneous estimation of Young's moduli and load parameters.Secondly, the three ad hoc back analysis procedures developed for elasticity are extended to account for elasto-plasticity. Numerical examples show that the elasto-plastic versions of the back analysis algorithms work equally well for those cases in which the degree of nonlinearity is relatively mild.https://espace.library.uq.edu.au/js/fckeditor/editor/images/spacer.gifThirdly, the six back analysis algorithms and the two forward analysis modules developed for elasticity and for elasto-plasticity are coupled with Roseribrock's method to form the eight versions of deterministic Direct Search algorithms. By these algorithms, the other four types of unknown categories (G-eometry, GM, GL, and GML) which have not been otherwise accounted for, are covered. Benchmark analyses reveal that problems of all unknown data category types in elasticity and in elasto-plasticity are readily solvable by these Direct Search algorithms. However, practical costs involved remain high especially for a complex problem having unknown parameters in all categories in elasto-plasticity.Having completed a multi-purpose back analysis program system from a deterministic viewpoint, another eight versions of stochastic hybrid back analysis algorithms are added to the system by using the Bayesf method. This completes a brief description of the current form of the back analysis program system CAD AX. A simple scheme with which an efficiency of a measurement pattern may be quantitatively evaluated is introduced as the Measurement Grade System (MGS). To maximize the benefit of the MGS, an economical method of computing measurement efficiency is proposed as the Quick-Co-Variance Method.In addition to the library of the back analysis algorithms formulated for problems involving one load application process, the new algorithm DBAP ! Multiple-Stage is developed for problems involving more than one load application process (in this case, excavation). By this method, in-situ stresses can be determined by measurements taken from an arbitrary stage of excavation. This may be beneficial for those cases in which displacement or stress monitoring cannot be performed in the early stages of excavation due to practical restraints. This multiple-stage algorithm is coupled with general estimation methods to form Direct Search and Bayesian versions of DBAP I Multiple-Stage. These hybrid multiple-stage back analysis procedures are applied to various types of numerical examples in which the MGS and the QCV Method are used to perform comparative studies to evaluate the relative efficiencies of various measurement patterns.A localized investigation is performed with the MGS and the QCV Method to establish the fundamental measurement strategies to accurately estimate the Mohr-Coulomb parameters of a continuum and of a joint plane. The results of this study reveal that recommended orientations of measurements may be identified with respect to the directions of the principal stresses (for a continuum) or a structural feature (for a joint plane). The description of the applied back analysis procedures for elasto-plasticity is concluded by a simulation of the progressive characterization of rock mass properties and in-situ conditions in a staged excavation problem. This numerical example confirms various findings made in the thesis and presents a typical repetitive sequence of strategy establishment, measurement planning, and back analysis required for monitoring a staged excavation problem.The thesis is closed by reviewing the developments made and graphically illustrating those developments with the previous contributions . Figures provided in Chapter 8 show how the back analysis program system CAD AX has inherited the work of previous researchers and added new features to be in the current form. The areas for further improvements, exploration, and fie ld applications are graphically identified by those figures. Four major development directions are identified to conclude the presentation.