2ND INTL SYMP ON GEOMECHANICS AND APPLICATIONS FOR SUSTAINABLE DEVELOPMENT

Plastic deformation and failure of structural integrity in materials are frequently accompanied by acoustic emission (AE). AE is a multi-scale phenomenon, defined as stress waves generated within the material due to (micro)structure changes (usually linked with structural defects dynamics), ranging from earthquakes and landslides to collective dislocation motion on micron scales. Recently, AE measurements performed on bulk as well as miniaturized samples (micropillars) revealed that the motion of dislocations resembles a stick-and-slip process, which may even develop in a series of unpredictable local strain bursts with a scale-free size distribution, e.g. in single crystals. Despite of fundamental differences in the mechanism as well as length and timescales, dislocation avalanches and earthquakes can be, from the point of view of AE, described in a similar way.
The talk will cover an introduction to the AE technique, followed by discussion of several applications, from fundamentals of defect dynamics to a couple of topics in geology and materials engineering.

In geo-engineering, hydraulic fracturing (HF) is used to improve the oil/gas production and optimize well stimulation in low permeability reservoirs. To design HF treatments, it is necessary to predict the pattern of fracture geometry as a function of treatment parameters. Present day HF simulators used in the industry are based on rather old approaches, relying on questionable assumptions about fracture geometry and disregarding hydro-mechanical coupling when dealing with fluid pressure evolution. As a consequence, most of the commercial codes fail in the reproduction of the complex intricate fracture patterns shown by the field acoustic measurements [1].
In this contribution we present the application of a recently developed model of brittle damage of confined rock masses to simulate HF treatments. The model is based on the explicit micromechanical construction of connected patterns of parallel equi-spaced cracks, by extending to saturated porous media the dry multi-scale brittle damage model firstly introduced in [2]. A relevant feature of the model is that the fracture patterns are not arbitrary, but their inception, orientation and spacing follow from energetic consideration. The capability of the model to predict the mechanical response of brittle rocks and the related porosity and permeability evolution has been presented in [3] and [4].
The model, based on the Terzaghi effective stress concepts, has been implemented into a coupled hydro-mechanical finite element code, where the linear momentum and the fluid mass balance equations are numerically solved via a staggered approach. The coupled code is used to simulate laboratory and field scale fracturing processes induced by an increase in pore pressure, as in hydraulic fracturing jobs for reservoir stimulation. A reference case, based on typical data of a HF process, has been used to ascertain the influence of different operational parameters on the outcomes of the process. In particular, with reference to a simple geometry, a parametric study is performed by varying the number of wellbore perforations, the number of fracking processes, the distance between the different perforation slots, the wellbore deviation from the minimum principal stress direction axis, fluid pressure, fluid density, and proppant size.
The examples show the capability of the model in reproducing three-dimensional multiscale complex fracture patterns and permeability enhancement in the damaged porous medium.

Non-Extensive Statistical Physics (NESP) is based on a generalization of the standard Boltzmann-Gibbs expression of the entropy. It was introduced a few decades ago by Tsallis [1] in an attempt to describe and enlighten phenomena with “anomalous” behaviour for which the statistical mechanical concepts of the Boltzmann-Gibbs approach have been proven inadequate. A typical class of such phenomena are the ones involving long-range interactions and memory effects. Given that fracture is characterized by both long-range interactions and memory effects [2], it is reasonable to examine whether the mechanical response of brittle building materials at load levels approaching these causing fractures could be described in terms of concepts based on NESP. The challenge is to detect proper and clear indicators that could be considered as early warning signals of the upcoming entrance of the system (loaded specimen or structure) into its “critical stage”, i.e., that of impending fracture. In this direction, advantage is taken of experimental data gathered from a long series of experimental protocols with specimens made of brittle building materials submitted to a variety of loading schemes (direct tension, uniaxial compression, three-point bending, shear) either monotonic or stepwise. The protocols include both elementary and structural tests. The study is carried out in terms of characteristic parameters of the Acoustic Emissions detected during loading. It is concluded that the time evolution of the entropic parameters of NESP provide reliable pre-failure indicators, in good agreement to the respective ones obtained from completely different analyses of the acoustic activity (as it is, for example, the F-function [3] or the Ib-value) or even from different monitoring tools (as it is, for example, the Pressure Stimulated Currents technique [4]).

TeraHertz phonons are produced in solids and fluids by mechanical instabilities at the nano-scale (fracture and cavitation). They present a frequency that is close to the resonance frequency of the atomic lattices and an energy that is close to that of thermal neutrons. A series of fracture experiments on natural rocks and the systematic monitoring of seismic events have demonstrated that TeraHertz phonons are able to induce fission reactions on medium-weight elements (in particular, iron and calcium) with neutron and/or alpha particle emissions. The same phenomenon appears to have occurred in several different situations and to explain puzzles related to the history of our planet, like the primordial carbon pollution (and correlated iron depletion) or the ocean formation (and correlated calcium depletion), as well as scientific mysteries, like the so-called cold fusion or the correct radio-carbon dating of organic materials. Very important applications to earthquake precursors, climate change, and energy production are likely to develop in the next future.
Three different forms of energy might be used as earthquake precursors. At the tectonic scale, Acoustic Emission (AE) prevails, as well as Electro-Magnetic Emission (EME) at the meso-scale, and Neutron Emission (NE) at the nano-scale. The three fracto-emissions tend to anticipate the next seismic event with an evident and chronologically ordered shifting: high frequencies and neutron emission about one week before, then lower frequencies and electromagnetic and acoustic waves. The experimental observations reveal a strong correlation between the three fracto-emission peaks and the major earthquakes occurring in the closest areas.
Regarding cold fusion, despite the great amount of experimental results, the comprehension of these phenomena still remains unsatisfactory. On the other hand, as reported by most of the articles devoted to cold fusion, one of the principal features is the appearance of micro-cracks on the electrode surfaces after the experiments. A mechanical explanation is proposed as a consequence of hydrogen embrittlement of the electrodes during electrolysis. The preliminary experimental activity was conducted using a Ni-Fe anode and a Co-Cr cathode immersed in a potassium carbonate solution. Emissions of neutrons and alpha particles were measured during the experiments as well as evident chemical composition changes of the electrodes revealing the effects of fission reactions occurring in the host lattices. The symmetrical fission of Ni appears to be a clear evidence. Such reaction would produce two Si atoms or two Mg atoms with alpha particles and neutrons as additional fragments. In order to confirm the preliminary investigation, further electrolytic tests have been conducted using Pd and Ni electrodes. As for the early experiments, relevant compositional changes and the appearance of ligther elements previously absent have been observed. The most relevant process emerging from the experiments is the primary fission of palladium (decrement of 30%) into iron and calcium. Then, secondary fissions appear in turn producing oxygen atoms, alpha particles, and neutrons. The chemical composition changes were confirmed by four repetitions of the same experiment. An extensive evaluation of the heat generation has been carried out showing a positive energy balance in correspondence to the major neutron emission peaks.

This paper is focused on numerical analysis of the coupled hydro-mechanical response of geomaterials that contain pre-existing or newly developing zones of localized deformation, such as faults, macrocracks, shear bands, etc. In terms of mechanical response, the existence of discontinuities results in the reduction of material strength that is triggered by sliding/separation along the defects. In addition, the pre-existing cracks act as stress concentrators prompting the formation of new macrocracks that may propagate through the domain. In terms of flow properties, the hydraulic conductivity is also strongly affected by the fracture pattern and displays anisotropy at the macroscale.
The numerical analysis of flow through fractured porous media is usually conducted by employing the Extended Finite Element Method (XFEM). The approach typically involves the assumption that the fluid pressure is continuous across the discontinuity, while the pressure gradient is discontinuous. Such formulation allows for the transport and storage of fluid inside the crack. The jump in the pressure gradient is achieved by partitioning the pressures at both sides of the discontinuity by a signed distance function. Although the approach is accurate, it is computationally very inefficient. The latter stems from incorporation of enriched DOSs, i.e. additional degrees of freedom that account for the presence of discontinuities, as well the need for partitioning of the domain with triangular sub-elements for the Gaussian integration scheme.
Given the problems inherent to XFEM approach, a new formulation is developed here that employs the averaging of the field operators within the referential volume adjacent to macrocrack. This leads to an enriched form of Darcy’s law, which incorporates the notion of equivalent conductivity. The latter is defined as a symmetric second-order tensor whose components are function of hydraulic properties of constituents (viz. intact material and fractured region) as well as the internal length parameter. Such an approach does not require any additional degrees of freedom to account for the presence of discontinuities, which significantly improves the computational efficiency as compared to XFEM.
The mechanical analysis incorporates an enhanced embedded discontinuity approach, which is conceptually similar to that employed for specification of equivalent hydraulic conductivity. It employs the same ‘characteristic dimension’ related to geometry of fractures and enables a discrete tracing of the propagation of new cracks.
The formulation is illustrated by a number of examples. In particular, a series of compression tests on pre-fractured rock-like samples is simulated. Various geometric configurations of pre-existing as well as new propagating cracks are considered and the results are compared with the experimental data. In addition, a steady-state flow through the fractured domain under a prescribed hydraulic gradient is examined for different geometries of fractures. Finally, a coupled problem is considered involving a transient flow under constant traction boundary conditions.

The gradient approach is applied to discuss disintegration and size effects in cavities and deep level tunnels in geomechanics. Previous results of classical theories are revisited and further extended by adjusting the newly introduced gradient coefficient which multiplies the gradient term and accounts for nonlocality and underlying microstructural heterogeneity. Qualitative comparison with related observations is discussed.

It is known that the classical elastic beam model fails in the indentation analysis of an elastic beam by a rigid indenter. A simple higher-order beam model developed based on the Kerr-type differential relation between the indentation pressure and the deflection of pressured surface of the beam is applied to study the indentation of an elastic beam by a rigid circular cylinder. The proposed method is validated by comparing its predicted results with known data, and the merit of the proposed model is demonstrated by some new easy-to-use explicit formulas and numerical results. In particular, the present model confirms that the contact zone becomes two separate strips when its width increases and exceeds a certain critical value. It is expected that this simple higher-order beam model could be found useful in the mechanical indentation analysis of some elastic beam problems for which the classical beam model fails.

Granular materials are ubiquitous in nature and industry. From landslides to extrusion of animal feed, particulate materials are relevant for all aspects of human life. Despite our frequent exposure to these materials, their handling still confronts us with unique engineering challenges. Notably the flow behavior of these materials is spatiotemporally heterogeneous and non-local in nature, both of which present both experimental and theoretical complexities. Granular materials however also present us with an opportunity to systematically investigate this behavior, as we are nowadays uniquely capable of tuning particle properties to a great extent, and can study their mechanical behavior in ever greater detail. We foresee that studying granular materials thus offers a window on the behavior of a broad range of classes of materials that display heterogeneous behavior. In my talk I will discuss the latest experimental developments on granular flow measurements and related modeling attempts.

We present recent advances in the modelling and simulation of fracture in heterogeneous materials, either natural, such as geomaterials, or manmade, such as aerospace and energy materials.
We discuss how imaged microstructures can be used to model the macroscopic behaviour of engineering structures used in various areas of engineering.
The main directions discussed include:
- acceleration of multi-scale methods
- machine-learning-enhanced model order reduction
- applications in chemistry, engineering, materials and medicine
- stochastic approaches for uncertainty quantification
We show how recent developments are used in practice and transferred to companies and start-ups and discuss innovation and knowledge transfer in the field of computational methods for engineering and sciences.

We present recent advances in the modelling and simulation of fracture in heterogeneous materials, either natural, such as geomaterials, or manmade, such as aerospace and energy materials. We discuss how imaged microstructures can be used to model the macroscopic behaviour of engineering structures used in various areas of engineering. The main directions discussed include: acceleration of multi-scale methods, machine-learning-enhanced model order reduction, applications in chemistry, engineering, materials and medicine, and stochastic approaches for uncertainty quantification. We show how recent developments are used in practice and transferred to companies and start-ups and discuss innovation and knowledge transfer in the field of computational methods for engineering and sciences.

The present paper deals with the opposite natural trends in composite systems: catastrophe and chaos arising from simple nonlinear rules, as well as order and structure emerging from heterogeneity and randomness.
Part I deals with Nonlinear Fracture Mechanics models (in particular, the Cohesive Crack Model to describe strain localization both in tension and in compression) and their peculiar consequences: fold catastrophes (post-peak strain-softening and snap-through instabilities) or cusp catastrophes (snap-back instabilities) in plain or reinforced structural elements. How can a relatively simple nonlinear constitutive law, which is scale-independent, generate a size-scale dependent ductile-to-brittle transition? Constant reference is made to Dimensional Analysis and to the definition of suitable nondimensional brittleness numbers that govern the transition. These numbers can be defined in different ways, according to the selected theoretical model. The simplest way is that of directly comparing critical LEFM conditions and plastic limit analysis results. This is an equivalent way --although more effective for finite-sized cracked plates-- to describe the ductile-to-brittle size-scale transition, if compared to the traditional evaluation of the crack tip plastic-zone extension in an infinite plate. In extremely brittle cases, the plastic zone or process zone tends to disappear and the cusp catastrophe conditions prevail over the strain-softening ones and tend to coincide with the LEFM critical conditions in the case of initially cracked plates.
Part II deals with the occurrence of self-similar and fractal patterns in the deformation, damage, fracture, and fragmentation of heterogeneous disordered materials, and with the consequent apparent scaling in the nominal mechanical properties of the same materials. Such a scaling is negative (lacunar fractality) for tensile strength and fatigue limit, whereas it is positive (invasive fractality) for fracture energy, fracture toughness, and fatigue threshold. At the same time, corresponding fractal (or renormalized) quantities emerge, which are the true scale-invariant properties of the material. They appear to be the constant factor (the universal property) in the power-law relating the nominal canonical quantity to the size-scale of observation. When the reference sets from self-similar become self-affine, we obtain Multi-fractal Scaling Laws, which are asymptotic and present a decreasing fractality for increasing structural sizes. They reproduce the experimental data very consistently. On the other hand, Critical Phenomena are always associated with the emergence of self-similar or self-affine patterns, to fractal (renormalized) or multi-fractal quantities, and to spontaneous self-organization. Typical examples are represented by: phase transformations, laminar-to-turbulent fluid flow transitions, avalanches in granular media, earthquakes, micro-cracking, and fracture in structural materials. In a fractal framework, it is then possible to define a scale-invariant constitutive law: the so-called Fractal Cohesive Crack Model, in which stress and strain are defined over lacunar fractal sets and the fracture energy in an invasive fractal set, which is the Cartesian product of the two previous sets.

Traveltimes due to compressional (P) and shear (S) waves have been proven essential in many applications of earthquake seismology. Therefore, an accurate and efficient traveltime computation approach for P and S waves is essential for successful applications. However, construction of a solution to the Eikonal equation with a complex velocity field in an anisotropic medium is challenging. The Eikonal equation is a first-order, hyperbolic, nonlinear partial differential equation (PDE) that represents a high-frequency approximation of the wave equation.
The fast marching method (FMM) and the fast sweeping method (FSM) are the most accepted techniques due to their efficiency for the solution of the Eikonal equation. However, these methods tend to suffer from numerical accuracy in the presence of anisotropic media with sharp heterogeneity, irregular surface topography and complex velocity fields. In order to overcome these difficulties, this study presents a solution method to the Eikonal equation by employing the peridynamic differential operator (PDDO) [1-3]. The PDDO provides the nonlocal form of the Eikonal equation by introducing an internal length parameter (horizon) and a weight function with directional nonlocality. It is immune to discontinuities and invokes the direction of information travel in a consistent manner. It enables numerical differentiation through integration; thus, the field equations are valid everywhere regardless of the presence of discontinuities. The weight function controls the degree of association among points within the horizon. Also, it enables directional nonlocality based on the knowledge of characteristic directions along which information travels. Solutions are constructed in a consistent manner without special treatments through simple discretization. The capability of this approach is demonstrated by considering different types of Eikonal equations with a complex velocity field in anisotropic media. Numerical stability is ensured and solutions compare well with the reference solutions.

A statistical study of precursor activity in rain- as well as earthquake-induced landslides by means of spring block models enhanced with displacement gradients and stochasticity is performed. This way, a robust 2D model can be formulated for studying triggered landslides. A cellular automaton is utilized, in order to examine the dynamic behavior and the stability of rock/soil slopes due to neighboring heavy rainfall or earthquake activity. The type and nature of the failure plane, as well as the triggering mechanism is studied. Moreover, the different dynamic evolution modes of the slope can be mapped to specific shape parameters of the corresponding distributions of the incremental displacements. These parameters are calibrated through comparison with statistical data on landslides events available in the literature. The calibrated model can then be used as a means for understanding, predicting and mitigating the impact of catastrophic landslides and its theoretical predictions are compared with the respective predictions of alternative techniques for studying slope stability.

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