and, finally, it presents the application of the theory for studying strain localization in solids. Some aspects related to shear band thickness, mesh dependency and higher order continua are also briefly discussed.
The third chapter, “Material Instability and Strain Localization Analysis”, covers the principles of strain localization analysis as applied to geomaterials. The conditions for the formation of different types of deformation bands are given and an extension of the analysis to fluid-saturated porous media is presented.
The fourth chapter, “Experimental Investigation of the Emergence of Strain Localization in Geomaterials”, focuses on strain field measurements of strain localization. Full field methods, imaging tools and experimental loading apparatus have evolved considerably over the past 15 years. This chapter presents recent developments on the characterization of the strain localization process and introduces the methods that are most frequently used.
The fifth chapter, “Numerical Modeling of Strain Localization”, gives the basic concepts of numerical modeling of the post-localization regime of strain softening geomaterials. For this purpose, two higher-order continua with microstructure are presented. This type of continuum is used to regularize the ill-posed mathematical problem of strain-softening materials and to enable the modeling of progressive localization of deformation in zones of intense shearing that eventually leads to failure.
The sixth chapter, “Numerical Modeling of Bifurcation: Applications to Borehole Stability, Multilayer Buckling and Rock Bursting”, presents typical boundary value problems of bifurcation theory in applications related to the petroleum industry, mining and structural geology. The formulation of the bifurcation problem is described and the governing equations are integrated numerically using higher-order continua with microstructure, such as the Cosserat continuum.
The seventh chapter, “Numerical Modeling of Multiphysics Couplings and Strain Localization”, focuses on the numerical modeling of localized phenomena induced by multiphysical couplings. To deal with interactions that occur between the different phases of porous media, a regularization technique based on the second gradient model is used.
The next two chapters, “Multiphysics Couplings and Strain Localization in Geomaterials” and “On the Thermo-poro-mechanics of Chemically Active Faults”, provide a review of research regarding the effects of temperature, pore pressure, chemical reactions and microstructure on strain localization in geomaterials. Examples have been given in relation to seismic slip in outcrops, core drillings on active faults and compaction banding.
The last chapter, “Theoretical and Numerical Analysis of Softening and Instabilities in Faults”, focuses on the Cosserat continuum, strain-localization and thermo-hydro-mechanical couplings. The interplay of different length and time scales is shown and the role of the size of the microstructure is emphasized.
We would like to thank all of the contributors of this volume and we hope that the chapters provide a valuable introduction to bifurcation theory and stability in geomechanics, covering the state of the art of theoretical, experimental and numerical developments in the field.
This volume is dedicated to the memory of late Professor Ioannis Vardoulakis (1949–2009) on the 10th anniversary of his death, in recognition of his contributions and achievements in mechanics, geomechanics and bifurcation theory.
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Multiphysics Role in Instabilities in Geomaterials: a Review
Tomasz HUECKEL
Duke University, Durham, USA
Multiphysical nature is characterized by complex phenomena involved in instabilities, strain localization and bifurcation in landslides, borehole instability in nuclear waste disposal and drying cracking, as seen in situ and in the laboratory. The multiphysics includes the effect of heat generated during precursor creep in the development of landslides, as well as the effect of geochemical reactions, the effect of heat on inducing possible failure through pressurization of pore water, the effect of evaporation-induced suction and air entry during drying and subsequent cracking of soils. The phenomena illustrated with specific natural or engineered events are interpreted as scenarios of processes that are either simultaneous or sequential, and that are coupled or result from an accumulation of dissipative processes. As pointed out by Terzaghi (1950), the causes of the instabilities are often long-term phenomena, rather than single events, such as major rainfalls, which are contributing factors. The need for a proper description of these long-term phenomena and their coupling with variable mechanical properties of soil and rock is emphasized.
1.1. Introduction
The engineering practice in all branches of geomechanics is now at an interesting stage of development, when the customary tools of evaluation of the margin of safety, such as “admissible stress” and “factors of safety”, are felt to lead to an oversimplification of what we are capable of saying about a sample, soil/rock mass or structure. This is mainly because of the developed computational capabilities of contemporary engineering, as well as experimentally supported modeling capabilities, including coupled fields, through which soil and rock behavior is mathematically described. In the statement above I have adapted the words of Giulio Maier, with which he opens the foreword to a fascinating book by Davide Bigoni (2012) on bifurcation and material instabilities. While the book refers to bifurcations in a larger class of materials than just geomaterials, the above pronouncement catches the situation exactly: we can predict much more in detail than we could a few years ago: the stress field evolution, together with strain and/or damage progress along a process of loading following multiple scenarios of coupling with temperature; concentration of ions; salts or reaction progress field. It potentially includes patterns related to failure/instability and their precursors. However, how this information could/should be utilized to quantify “the distance from failure” or “factor of safety” (FOS) often remains an open question.
The purpose of this chapter is to provide an overview of a series of phenomena in geomechanics which qualify as instabilities/failures of various kinds. The use of this less-than-strictly defined term is intentional, as we want to encompass the widest possible class of phenomena for which the criteria are not necessarily within a single type of definition, but which correspond in loose terms to Lyapunov’s definition: an unlimited response to a limited solicitation. Solicitation refers to a trigger of any sort: mechanical, hydraulic, thermal or chemical. We shall start with classical phenomena associated with purely mechanical loading induced instabilities and their criteria and implications to expand into an array of non-classical multiphysics instability phenomena. Current observations and understanding of geomechanical processes indicate a critical role of non-mechanical variables, whereas the conceptual base is lagging behind. Material (local) and field (global) instabilities based on the actual instability events leading to failure are both discussed.
1.2. General remarks
As we started with a promise to be wide open and inclusive, we have to issue several warnings in order to try to wave off an inevitable confusion that the subject brings, despite the appearance of a strictly rigorous approach.
To start with, in a geoengineering/geophysics context, instability or, better, loss of stability may mean instability of a material per se (at a point), instability of a soil/rock mass, or speaking mathematically of a boundary value problem. In other terms, we speak of a local or global stability. A local loss of stability at at least a single point of the continuum is considered a necessary (but far from sufficient) condition for global instability. Similarly, a local instability in a volume around a tunnel opening may
