Gioacchino Viggiani

Advances in X-ray Tomography for Geomaterials

A thorough quantitative analysis of strain localization of axisymmetric triaxial sand specimens is presented. Computed tomography technique was used to acquire detailed 3-D images of a series of Ottawa sand specimens subjected to Conventional Triaxial Compression (CTC) conditions at very low effective stresses in microgravity and terrestrial laboratories. Analysis tools were developed to track the onset, propagation, thickness and inclination angle of shear bands, and calculate the variation of void ratio within and outside shear bands. It has been found that shear bands initiate in the post-peak strength regime in CTC specimens, where a rather complex pattern of shear bands develops such that behavior is highly influenced by large-scale kinematics of the specimen. Four main deformation patterns were identified and their contribution to the overall volume change of the specimens was quantified.

A review of two different approaches to hypoplasticity

Non-linearity and irreversibility are striking features of soil behavior, affecting the response of any geotechnical “structure”, be it, for example, a foundation, an excavation, an earth dam, or a natural slope. From a mathematical viewpoint (i.e., at the constitutive level), different strategies have been proposed to deal with such features of soil behavior, including:

Ground movements around excavations in granular soils: a few remarks on the influence of the constitutive assumptions on FE predictions

Two different approaches for modelling soil non-linearity (hardening plasticity and hypoplasticity) are compared with reference to the analysis of soil–structure interaction in an excavation in dense dry sand, supported by a propped diaphragm wall. The analysis focuses on the prediction of wall and soil movements. A commercial FE code has been used for the elastoplastic analyses, in order to assess the performance of a readily available design tool in current geotechnical engineering practice as compared to the predictions of a more advanced research tool. Although obtained for an idealized scheme, the results allow a number of more general conclusions to be drawn on the influence of the constitutive assumptions. Copyright

Monitoring Fracture Propagation in a Soft Rock (Neapolitan Tuff) Using Acoustic Emissions and Digital Images

Sudden and unexpected collapses of underground cavities below the city of Naples (Italy) represent a serious safety hazard. The collapses occur due to the detachment of large blocks from the cavity roofs, walls and pillars, often a long time after the original quarry excavation has been completed. It is recognised that existing discontinuities, e.g., fractures, play an important role in the failure process by inducing local stress-concentrations and reducing the overall material strength. The larger fractures, which ultimately lead to collapse occur through interaction, propagation and coalescence of these discontinuities. This paper presents recent results of experiments carried out on natural, dry specimens of Neapolitan fine-grained tuff to investigate the mechanisms involved in sample failure. A better understanding of fracture development and rock bridge behaviour is gained through a combination of AE and photographic monitoring in an experimental program considering samples with artificial pre-existing heterogeneities, which simulate the in situ discontinuities. For a range of rock bridge geometries the mechanisms and timing of different stages of the failure process are identified and characterised. The results show that, in general, a classical description of failure, for samples without artificial flaws or with only a single flaw, is followed: (1) crack closure; (2) linear stress-strain response and crack initiation with stable crack growth; (3) crack damage and unstable crack growth leading to failure. For samples with two artificial pre-existing flaws the third phase is split into two parts and failure of the sample occurs only after both the unstable propagation of external wing cracks and coalescence of the internal cracks in the bridge. In terms of the timing and duration of each phase, it is seen that phases 1 and 2 have little dependence on the flaw configuration but phase 3 seems to depend directly on this. In particular the angle in rock bridge between the inner tips of the pre-existing flaws, β, plays a key role: phase 3 is shorter for β = 120° than for β = 105°. These differences are due to the different modes of coalescence in the rock bridge. For β = 105° the total failure is preceded by bridge rotation, which appears to take longer than the simpler mode of failure for β = 120°. It has only been possible to determine the time ranges of interest using the AE signatures, whilst the photographs allow the fracture geometry evolution to be described. Additionally the frequency character of AE events is investigated and shown to have significant potential for characterisation of AE source types and thus failure processes.

Loss of uniqueness and bifurcation vs instability: some remarks

ABSTRACT The present work is an attempt to clarify the different notions of bifurcation and loss of stability. Although these notions have been already discussed by many authors, we believe that they still deserve some discussion. In fact, many different “definitions” of stability exist. This is not a problem for conservative systems, for which it turns out that all these definitions do coincide. Nor is this a problem if the system incorporates some viscous dissipation. However, for other cases, e.g. non conservative systems incorporating dry friction dissipation, which are of relevance in geomechanics, this is very important, because different definitions may yield different results. We recall first the definition of Lyapunov stability, which is related to the dynamic study of the influence of initial conditions on the solution of the mechanical equations. In this framework, we have a look at the linearization of the equations and its consequences. Then we go back to Hills work and try to give the basis of the so-called “Hill stability criterion”. Finally, we “define” an other stability criterion which has been criticized by Hill in some early paper. Through the study of a very simple mechanical system, we exhibit some differences between all these notions, showing that a system can be stable according to one criterion but unstable according to other criteria. It is necessary to mention which definition of stability is used. Any existing stability criterion has to be thought of as an heuristic method. On the contrary, bifurcation or loss of uniqueness is a more clear concept. Shear band localization, controlability, and invertibility can be actually seen as particular cases of bifurcation. However, bifurcation criteria have to be considered carefully, since they almost always incorporate linearization, which in most cases is not strictly justified. Some examples are given of general results which have been obtained without the use of any linearization procedure.

Water Retention Behaviour Explored by X-Ray CT Analysis

This study aims to experimentally characterise the link between partial water saturation and suction in a sand sample at the micro scale. The paper presents the first results of an experimental study in which high resolution (7.5μm/px) X-ray tomography has been performed on a small (10×10mm) cylindrical sample of Hostun HN31 sand at several different levels of imposed suction. A specialised cell allowing X-ray scanning as well as fine control of suction (imposed both by negative water pressure as well as by positive air pressure) has been developed for this study and is described herein. The 3D images resulting from X-ray tomography are treated in order to define each voxel in the image as either air, water or grain. From these “trinarised” 3D images, local and global values of porosity and degree of saturation are then measured. This method enables the study of water retention behaviour of sand at the grain scale, all the while allowing characterisation of water retention in the sample as a whole.

An assessment of plasticity theories for modeling the incrementally nonlinear behavior of granular soils

The objective of this paper is to assess the predictive capability of different classes of extended plasticity theories (bounding surface plasticity, generalized plasticity and generalized tangential plasticity) in the modeling of incremental nonlinearity, which is one of the most striking features of the mechanical behavior of granular soils, occurring as a natural consequence of the particular nature of grain interactions at the microscale. To this end, the predictions of the various constitutive models considered are compared to the results of a series of Distinct Element simulations performed ad hoc. In the comparison, extensive use is made of the concept of incremental strain-response envelope in order to assess the directional properties of the material response for a given initial state and stress history.

Shear bands as bottlenecks in force transmission

The formation of shear bands is a key attribute of degradation and failure in soil, rocks, and many other forms of amorphous and crystalline materials. Previous studies of dense sand under triaxial compression and two-dimensional analogues from simulations have shown that the ultimate shear band pattern may be detected in the nascent stages of loading, well before the bands known nucleation point (i.e., around peak stress ratio), as reported in the published literature. Here we construct a network flow model of force transmission to identify the bottlenecks in the contact networks of dense granular media: triaxial compression of Caicos ooid and Ottawa sand and a discrete element simulation of simple shear. The bottlenecks localise in the nascent stages of loading —in the location where the persistent shear band ultimately forms. This corroborates recent findings on vortices that suggest localised failure is a progressive process of degradation, initiating early in the loading history at sites spanning the full extent, yet confined to a subregion, of the sample. Bottlenecks are governed by the local and global properties of the sample fabric and the grain kinematics. Grains with large rotations and/or contacts having minimal load-bearing capacities per se do not identify the bottlenecks early in the loading history.

Mechanics of natural solids

Sand as an archetypical natural solid.- The Physics of Granular Mechanics.- Are we there yet? Following the energy trail in cohesionless granular solids.- Micromechanical alternatives to phenomenological hardening plasticity.- Mechanisms of localized deformation in geomaterials: an experimental insight using full-field measurement techniques.- Two-dimensional Distinct Element Method (DEM) modeling of tectonic fault growth in mechanically layered sequences.- When geophysics met geomechanics: Imaging of geomechanical properties and processes using elastic waves.- Fracture of Ice and other Coulombic Materials.- Experimental studies of the viscoplasticty of ice and snow.- Discontinuities in granular materials: Particle-level mechanisms.- Grain Crushing, Pore Collapse and Strain Localization in Porous Sandstone.- Long term behaviour and size effects of coarse granular media.- Nature - A Very Clever Experimentalist.

Experimental evidence of "Granulence"

We present an experimental study of velocity fluctuations in quasistatic flow of a 2D granular material deformed in a shear apparatus named 1γ2e [1]. Radjai and Roux [2] revealed systematic similarities between velocity fluctuations observed in discrete element simulations of quasistatic flow of granular material and turbulent flows in fluids. The character of these velocity fluctuations - named granulence by [2] - manifests as a non-Gaussian broadening of the probability density function of the fluctuations as the length of the analyzed shear-window is decreased, and exhibits some space and time scaling. The experiments presented are simple shear tests on granular samples composed of about 2000 wooden rods. The kinematics of the rod centers was followed by means of 2D Particle Image Tracking (PIT) technique applied to a sequence of 24 Mpixels digital pictures acquired throughout the duration of the loading at a frequency of 0.08 image/s. This analysis confirms the existence of granulence features in a real experimental test, which is comparable to that previously observed in numerical simulations of [2]. The experimental results obtained open up a new avenue for further studies on fluctuations in granular materials. (Less)