Finite deformation model of simple shear of fault with microrotations: apparent strain localisation and en-echelon fracture pattern

Strain localisation is a widespread phenomenon often observed in shear and compressive loading of geomaterials, for example, the fault gouge. It is believed that the main mechanisms of strain localisation are strain softening and mismatch between dilatancy and pressure sensitivity. Observations show that gouge deformation is accompanied by considerable rotations of grains. In our previous work as a model for gouge material, we proposed a continuum description for an assembly of particles of equal radius in which the particle rotation is treated as an independent degree of freedom. We showed that there exist critical values of the model parameters for which the displacement gradient exhibits a pronounced localisation at the mid-surface layers of the fault, even in the absence of inelasticity. Here, we generalise the model to the case of finite deformations characteristic for the gouge deformation. We derive objective constitutive relationships relating the Jaumann rates of stress and moment stress to the relative strain and curvature rates, respectively. The model suggests that the pattern of localisation remains the same as in the linear case. However, the presence of the Jaumann terms leads to the emergence of non-zero normal stresses acting along and perpendicular to the shear layer (with zero hydrostatic pressure), and localised along the mid-line of the gouge; these stress components are absent in the linear model of simple shear. These additional normal stresses, albeit small, cause a change in the direction in which the maximal normal stresses act and in which en-echelon fracturing is formed.

Desenvolvimento de um sistema misto de pasta à base de geopolímero e cimento portland para correção de perda de circulação

The materials engineering includes processes and products involving several areas of engineering, allowing them to prepare materials that fulfill the needs of various new products. In this case, this work aims to study a system composed of cement paste and geopolymers, which can contribute to solving an engineering problem that directly involves the exploitation of oil wells subject to loss of circulation. To correct it, has been already proposed the use of granular materials, fibers, reducing the drilling fluid or cement paste density and even surface and downhole mixed systems. In this work, we proposed the development of a slurry mixed system, the first was a cement-based slurry and the second a geopolymer-based slurry. The cement-based slurry was formulated with low density and extenders, 12.0 ppg (1.438 g/cm ³), showing great thixotropic characteristics. It was added nano silica at concentrations of 0.5, 1.0 and 1.5 gps (66.88, 133.76 and 200.64 L/m3) and CaCl2 at concentrations of 0.5, 1, 0 and 1.5%. The second system is a geopolymer-based paste formulated from molar ratios of 3.5 (nSiO2/nAl2O3), 0.27 (nK2O/nSiO2), 1.07 (nK2O/nAl2O3) and 13.99 (nH2O/nK2O). Finally, we performed a mixture of these two systems, for their application for correction of circulation lost. To characterize the raw materials, XRD, XRF, FTIR analysis and titration were performed. The both systems were characterized in tests based on API RP10B. Compressive strength tests were conducted after curing for 24 hours, 7 and 28 days at 58 °C on the cement-based system and the geopolymer-based system. From the mixtures have been performed mixability tests and micro structural characterizations (XRD, SEM and TG). The results showed that the nano silica, when combined with CaCl2 modified the rheological properties of the cement slurry and from the concentration of 1.5 gpc (200.64 L / m³) it was possible to obtain stable systems. The system mixture caused a change in the microstructure of the material by favoring the rate of geopolymer formation to hinder the C3S phase hydration, thus, the production of CSH phases and Portlandite were harmed. Through the mixability tests it can be concluded that the system, due to reduced setting time of the mixture, can be applied to plug lost circulation zones when mixed downhole

Influence de la taille et de la gradation des particules sur la résistance au cisaillement et le comportement dilatant des matériaux granulaires

Résumé : Cette étude examine l'impact de la taille et de la gradation de particules sur les corrélations théoriques et empiriques existantes les plus connues entre la résistance au cisaillement et le comportement dilatatant des matériaux granulaires en condition de déformation plane et en compression triaxiale drainée. À cette fin, 276 tests de cisaillements symétriques directs et 35 tests de compressions triaxiales drainées ont été menés sur des échantillons composés de billes de basalte (particules rondes), et de sables constitués de particules angulaires (sable de Péribonka et sable d'Eastmain) sur une échelle de 63 µm à 2000 µm afin d'évaluer leur résistance au cisaillement et leur comportement de dilatance sur une vaste échelle de pressions normales et de densités relatives initiales. Premièrement, la fiabilité et l'applicabilité des limites de mesure à l’aide de tests physiques de cisaillements symétriques directs dans l'interprétation de la résistance au cisaillement frictionnel en déformation plane des matériaux granulaires ont été discutées et confirmées par l'usage du code informatique DEM, SiGran. L'accent a été particulièrement mis sur la validation du modèle DEM au moyen de comparaison des résultats des simulations DEM avec leurs équivalents physiques à une échelle macro. Les résultats virtuels DSA sont abordés du point de vue de la coaxialité entre les principales tensions et les principales directions des paliers de pression ainsi que de la déviation de la direction d'extension nulle à partir de la direction horizontale. Les résultats numériques fournissent également des données quantitatives sur les différentes formes d'énergie consommées durant le cisaillement confirmées par d'autres résultats physiques et numériques publiés. Sur la base des postulats précédents, un examen minutieux des résultats des essais de cisaillements directs et de données issues de la littérature a été accompli afin d'évaluer la fiabilité des formules empiriques bien connues de Bolton et Collins et al. avec leurs constantes couramment employées en condition de déformation plane. L'étude montre qu'une application des relations empiriques de force-dilatation de cisaillement avec les constantes proposées par Bolton (1986) et Collins et al. (1992) aux sables ayant une distribution de taille de particules différente peut conduire à surestimer leurs valeurs en terme de force de cisaillement. Dans cette étude, les coefficients des équations de Bolton et Collins et al. ont donc été ajustée afin de prendre en compte les caractéristiques des particules, en particulier le diamètre médian, D50. De manière analogue, les effets microstructuraux imposés par la géométrie interne des particules (par exemple la taille, la forme et la gradation des particules) sur la relation tension-dilatation très connue, celle de Rowe (1962), et son ajustement empirique en condition triaxiale drainée ont été examinés dans cette étude. Une comparaison des prédictions des formules proposées avec les données de force de cisaillement issues de la littérature fournit de nombreuses preuves en faveur des contraintes mises en place au sein des relations existantes de force-dilatation de cisaillement en condition de déformation plane et triaxiale. Ces comparaisons prouvent également que la prise en compte de la taille des grains conduit à des résultats plus tangibles que lorsque la taille de la particule n'est pas considérée. Les formules de force-dilatation ajustées peuvent se révéler avantageuses pour évaluer indépendamment la cohérence des forces de cisaillement déterminées expérimentalement et pour introduire des lois d’écoulement plus précises dans les analyses géotechniques analytiques et numériques.

Stability of Granular Base Course Materials Containing Bituminous Admixtures

This report concerns the stabilization of three crushed limestones by an ss-1 asphalt emulsion and an asphalt cement, 120-150 penetration. Stabilization is evaluated by marshall stability and triaxial shear tests. Test specimens were compacted by the marshall, standard proctor and vibratory methods. Stabilization is evaluated primarily by triaxial shear tests in which confining pressures of 0 to 80 psi were used. Data were obtained on the angle of internal friction, cohesion, volume change, pore water pressure and strain characteristics of the treated and untreated aggregates. The MOHR envelope, bureau of reclamation and modified stress path methods were used to determine shear strength parameters at failure. Several significant conclusions developed by the authors are as follows: (1) the values for effective angle of internal friction and effective cohesion were substantially independent of asphalt content, (2) straight line MOHR envelopes of failure were observed for all treated stones, (3) bituminous admixtures did little to improve volume change (deformation due to load) characteristics of the three crushed limestones, (4) with respect to pore water characteristics (pore pressures and suctions due to lateral loading), bituminous treatment notably improved only the bedford stone, and (5) at low lateral pressures bituminous treatments increased stability by limiting axial strain. This would reduce rutting of highway bases. At high lateral pressures treated stone was less stable than untreated stone.

Laboratory study on the performance of recycled concrete aggregates blended with reclaimed asphalt pavement as pavement granular material

Production of recycled concrete aggregates (RCA) from construction and demolition (C&D) waste has become popular all over the world since the availability of land spaces are limited to dispose. Therefore it is important to seek alternative applications for RCA. The use of RCA in base and sub-base layers in granular pavement is a viable solution. In mechanistic pavement design, rutting (permanent deformation) is considered as the major failure mechanisms of the pavement. The rutting is the accumulation of permanent deformation of pavement layers caused by the repetitive vehicle load. In Queensland, Australia, it is accepted to have the maximum of 20% of reclaimed asphalt pavement (RAP) in RCA and therefore, it is important to investigate the effect of RAP on the permanent deformation properties of RCA. In this study, a series of repeated load triaxial (RLT) tests were conducted on RCA blended with different percentage of RAP to investigate the permanent deformation and resilient modulus properties of RCA. The vertical deformation and resilient modulus values were used to determine the response of RCA for the cyclic loading under standard pressure and loading conditions.

Dense granular flow down an inclined plane A comparison between the hard particle model and soft particle simulations

The granular flow down an inclined plane is simulated using the discrete element (DE) technique to examine the extent to which the dynamics of an unconfined dense granular flow can be well described by a hard particle model First, we examine the average coordination number for the particles in the flow down an inclined plane using the DE technique using the linear contact model with and without friction, and the Hertzian contact model with friction The simulations show that the average coordination number decreases below 1 for values of the spring stiffness corresponding to real materials, such as sand and glass, even when the angle of inclination is only 10 larger than the angle of repose Additional measures of correlations in the system, such as the fraction of particles with multibody contact, the force ratio (average ratio of the magnitudes of the largest and the second largest force on a particle), and the angle between the two largest forces on the particle, show no evidence of force chains or other correlated motions in the system An analysis of the bond-orientational order parameter indicates that the flow is in the random state, as in event-driven (ED) simulations V Kumaran, J Fluid Mech 632, 107 (2009), J Fluid Mech 632, 145 (2009)] The results of the two simulation techniques for the Bagnold coefficients (ratio of stress and square of the strain rate) and the granular temperature (mean square of the fluctuating velocity) are compared with the theory V Kumaran, J Fluid Mech 632, 107 (2009), J Fluid Mech 632, 145 (2009)] and are found to be in quantitative agreement In addition, we also conduct a comparison of the collision frequency and the distribution of the precollisional relative velocities of particles in contact The strong correlation effects exhibited by these two quantities in event-driven simulations V Kumaran, J Fluid Mech 632, 145 (2009)] are also found in the DE simulations (C) 2010 American Institute of Physics doi 10 1063/1 3504660]

Multifractal analysis, a method to investigate the morphology of materials

Using the multifractal formalism, we discuss the results obtained to characterized the morphology of polymer alloys and granular discontinuous metallic thin films. In the first case we have found a correlation between the multifractality and the mechanical properties of the alloys. In the second case, we have found that it is possible to measure the differences between the morphology of thin films induced by a growth process on a subtrate and that of percolation clusters of the classical theory of percolation.

Large Diameter Triaxial Tests on Geosynthetic-Reinforced Granular Subbases

The estimation of strength and stiffness of reinforced aggregates is very important for the design and construction of reinforced unpaved/paved road sections. This paper presents the experimental results from static and cyclic triaxial tests carried out on granular subbase samples reinforced with multiple layers of geogrid reinforcement. Aggregates of different size ranges were mixed in calculated proportions by weight to obtain the gradation specified for rural roads. Triaxial samples of 300 mm diameter and 600 mm height were prepared using this sampled aggregate. The strength and stiffness characteristics of this aggregate reinforced with geogrids at different elevations were determined from static and cyclic triaxial tests. Triaxial tests were also carried out on geocell encased aggregates, and the results are compared. From the experimental results it is observed that reinforced systems carried more stresses than unreinforced systems at the same strain level. The beneficial effect increased with increase in the quantity of reinforcement, whereas for geocell reinforcement, the advantage was evident only at higher strains. (C) 2014 American Society of Civil Engineers.

Analysis and optimization of stress wave propagation in two-dimensional granular crystals with defects

Granular crystals are compact periodic assemblies of elastic particles in Hertzian contact whose dynamic response can be tuned from strongly nonlinear to linear by the addition of a static precompression force. This unique feature allows for a wide range of studies that include the investigation of new fundamental nonlinear phenomena in discrete systems such as solitary waves, shock waves, discrete breathers and other defect modes. In the absence of precompression, a particularly interesting property of these systems is their ability to support the formation and propagation of spatially localized soliton-like waves with highly tunable properties. The wealth of parameters one can modify (particle size, geometry and material properties, periodicity of the crystal, presence of a static force, type of excitation, etc.) makes them ideal candidates for the design of new materials for practical applications. This thesis describes several ways to optimally control and tailor the propagation of stress waves in granular crystals through the use of heterogeneities (interstitial defect particles and material heterogeneities) in otherwise perfectly ordered systems. We focus on uncompressed two-dimensional granular crystals with interstitial spherical intruders and composite hexagonal packings and study their dynamic response using a combination of experimental, numerical and analytical techniques. We first investigate the interaction of defect particles with a solitary wave and utilize this fundamental knowledge in the optimal design of novel composite wave guides, shock or vibration absorbers obtained using gradient-based optimization methods.

Controlling wave propagation through nonlinear engineered granular systems

We study the fundamental dynamic behavior of a special class of ordered granular systems in order to design new, structured materials with unique physical properties. The dynamic properties of granular systems are dictated by the nonlinear, Hertzian, potential in compression and zero tensile strength resulting from the discrete material structure. Engineering the underlying particle arrangement of granular systems allows for unique dynamic properties, not observed in natural, disordered granular media. While extensive studies on 1D granular crystals have suggested their usefulness for a variety of engineering applications, considerably less attention has been given to higher-dimensional systems. The extension of these studies in higher dimensions could enable the discovery of richer physical phenomena not possible in 1D, such as spatial redirection and anisotropic energy trapping. We present experiments, numerical simulation (based on a discrete particle model), and in some cases theoretical predictions for several engineered granular systems, studying the effects of particle arrangement on the highly nonlinear transient wave propagation to develop means for controlling the wave propagation pathways. The first component of this thesis studies the stress wave propagation resulting from a localized impulsive loading for three different 2D particle lattice structures: square, centered square, and hexagonal granular crystals. By varying the lattice structure, we observe a wide range of properties for the propagating stress waves: quasi-1D solitary wave propagation, fully 2D wave propagation with tunable wave front shapes, and 2D pulsed wave propagation. Additionally the effects of weak disorder, inevitably present in real granular systems, are investigated. The second half of this thesis studies the solitary wave propagation through 2D and 3D ordered networks of granular chains, reducing the effective density compared to granular crystals by selectively placing wave guiding chains to control the acoustic wave transmission. The rapid wave front amplitude decay exhibited by these granular networks makes them highly attractive for impact mitigation applications. The agreement between experiments, numerical simulations, and applicable theoretical predictions validates the wave guiding capabilities of these engineered granular crystals and networks and opens a wide range of possibilities for the realization of increasingly complex granular material design.