Weaker Matrix Research Articles

Identifying uncertainty in estimates of bimrocks volumetric proportions from 2D measurements

Chaotic geological bodies composed of rock inclusions of different lithology and size enclosed in a weaker matrix are often referred to as bimrocks (block-in-matrix rocks). When dealing with these challenging and widespread geomaterials, a major concern for geopractitioners is the estimation of block content, which has been demonstrated to strongly affect the overall mechanical behaviour of bimrocks. Since the estimation of this parameter is not a simple matter, stereological principles are generally applied to infer 3D block contents from 1D or 2D measurements. However, they are often fraught with a high magnitude of error.In this study, a statistical approach was developed to determine the uncertainties associated with estimates of the 3D block proportions from 2D measurements. A Matlab code was implemented to generate heterogeneous models with a size distribution typical of bimrocks. An uncertainty factor is provided related to the size of the outcrop area investigated and the 2D block content to adjust the initial 2D estimates. It was found that a larger investigation area increases the reliability of the 2D measurements and as actual volumetric block proportion increases, the uncertainty decreases.The results obtained through this procedure were subsequently compared with previous findings from the literature concerning the uncertainty in estimates of the VBP from 1D measurements. The outcome of this comparison highlights the strength of the procedure described in this paper.

Bio-Inspired Laminates of Different Material Systems

Abstract Helicoidal laminates mimicking the laminar structure of the exoskeleton of crustaceans have been reported to resist higher out-of-plane loads than the common cross-ply and quasi-isotropic fiber-reinforced laminates. Some have reported that smaller inter-ply angle improves strength of helicoidal laminates but others have reported the opposite. A few important material parameters that dictate the failure mechanism of helicoidal laminates have recently been proposed based on proof-of-concept carbon fiber-reinforced laminates, which is not the best material system to benefit from a helicoidal configuration. This study investigates the out-of-plane loading performance of helicoidal laminates with various inter-ply angles, ply thicknesses, and materials. Result shows that the failure mechanism is dictated by the competition between spiraling matrix split and delamination followed by fiber breakage regardless of the laminate material system. Spiraling matrix split resistance decreases as pitch (ratio of inter-ply angle to ply thickness) and matrix toughness decreases. This study provides guidelines for the optimization of helicoidal laminates. Coexistence of spiraling matrix split and fiber damage is often seen on the failed laminate with the highest peak load. The optimal inter-ply angle provides the optimal spiraling matrix split resistance; so, neither spiraling matrix split nor fiber/delamination damage becomes dominant. Since resistance to spiraling matrix split decreases as pitch or matrix toughness decreases, the optimal inter-ply angle will increase for laminates with weaker matrix or thicker plies and vice versa.

ENGINEERING GEOLOGICAL CHARACTERISATION OF BLOCK-IN-MATRIX ROCKS

Block-in-matrix rocks (“bimrocks”) are complex, mixed and heterogeneous formations of competent blocks embedded in weaker matrix. The inherent difficulty of sampling and consequently, laboratory testing of bimrocks leads to considerable challenging in geotechnical design and assessment of their engineering behaviour. An approach for the characterisation of “bimrocks” is the use of stereological analysis that extrapolates one-dimensional or two dimensional data to estimate the block volumetric proportion. This has been an established approach of dealing with bimrocks and melanges for the last two decades. This paper presents the parameters that are considered important for the engineering characterisation of such complex formations, while a case study from a bimrock in NW Greece is discussed.

ENGINEERING GEOLOGICAL BEHAVIOUR OF HETEROGENEOUS AND CHAOTIC ROCK MASSES

The engineering characterization of heterogeneous and complex geological formations for estimating their rock mass strength and deformability characteristics constitutes a challenge to geo-scientists and engineers dealing with the design and construction of slopes and tunnels. Mélanges and similar heterogeneous mixtures of hard blocks in weaker matrix, known as “bimrocks”, present an overall strength significantly greater than the matrix strength, because the presence of rock blocks, above a threshold volumetric proportion, influences the mechanical characteristics and the behaviour of these rock masses. Moreover, recent studies have shown that the strength and mechanical behaviour of heterogeneous and composite rock masses such as flysch and molasses consisting of alternating layers of competent and incompetent rocks are governed by the presence and volumetric percentage of the interlayers of the weaker rocks.

Boudinage and folding as an energy instability in ductile deformation

AbstractWe present a theory for the onset of localization in layered rate‐ and temperature‐sensitive rocks, in which energy‐related mechanical bifurcations lead to localized dissipation patterns in the transient deformation regime. The implementation of the coupled thermomechanical 2‐D finite element model comprises an elastic and rate‐dependent von Mises plastic rheology. The underlying system of equations is solved in a three‐layer pure shear box, for constant velocity and isothermal boundary conditions. To examine the transition from stable to localized creep, we study how material instabilities are related to energy bifurcations, which arise independently of the sign of the stress conditions imposed on opposite boundaries, whether in compression or extension. The onset of localization is controlled by a critical amount of dissipation, termed Gruntfest number, when dissipative work by temperature‐sensitive creep translated into heat overcomes the diffusive capacity of the layer. Through an additional mathematical bifurcation analysis using constant stress boundary conditions, we verify that boudinage and folding develop at the same critical Gruntfest number. Since the critical material parameters and boundary conditions for both structures to develop are found to coincide, the initiation of localized deformation in strong layered media within a weaker matrix can be captured by a unified theory for localization in ductile materials. In this energy framework, neither intrinsic nor extrinsic material weaknesses are required, because the nucleation process of strain localization arises out of steady state conditions. This finding allows us to describe boudinage and folding structures as the same energy attractor of ductile deformation.

Shape of pinch and swell structures as a viscosity indicator: Application to lower crustal polyphase rocks

Pinch and swell structures occur where a more competent layer in a weaker matrix is subjected to layer-parallel extension. In this contribution, we use numerical models to explore the use of pinch and swell structure shape symmetry and asymmetry as a determinant of relative viscosity between layers. Maximum asymmetry is attained when the matrix viscosity on one side is subtly weaker than the competent layer, while the other side is significantly weaker.Our numerical results are directly applied to asymmetrically developed pinch and swell structures in exposed lower continental crust. Here, shape geometries observed in a shear zone comprised of plagioclase-dominated, garnet-dominated and mixed amphibole-plagioclase-dominated bands, reveals that the plagioclase-dominated band is the most competent band and is marginally stronger (2×) and significantly stronger (10–40×) than the fine grained garnet-dominated and mixed amphibole-plagioclase-dominated band, respectively. Based on the experimentally determined viscosity of a plagioclase-dominated material and quantitative microstructural analysis, the viscosity range of the natural rock bands is 2.8 × 1015 to 1.1 × 1017 Pa s. Consequently, the assumption that the experimentally-derived plagioclase flow law is an appropriate proxy for the middle to lower continental crust may lead to a viscosity over-estimation by up to forty times.

Effect of Various Fillers on Mechanical Properties of Glass Fiber Reinforced Polymer Composites: A Review

Filler materials are the inert materials which are used in glass fiber reinforced polymer (GFRP) composites for modifying the chemical and physical properties of the matrix polymers to reduce material costs, to improve processability, to improve product performance or to simply act as extenders or matrix diluents. Some of the commonly used fillers are carbon black, calcium carbonate, clay, alumina tri-hydrate, magnesium hydroxide, bone powder, coconut powder, hematite powder, TiO2, SiO2,ZnS, graphite, etc. Effect of these fillers on mechanical properties like tensile strength, flexural strength, inter laminar shear strength (ILSS), tensile modulus, impact strength, hardness were tested by various methods experimentally. Some of the authors also discussed the effect of filler size on the above mechanical properties. KeywordsFillers, glass fiber reinforced polymer composites (GFRP), Mechanical properties Introduction Filler materials are generally the inert materials which are used in composite materials to reduce material costs, to improve mechanical properties to some extent, in some cases to improve processability and to improve product performance. Two or more materials with different material properties are combined together they will form a composite material. Fibers when embedded with weaker matrix materials comprise of strong load carrying capacity.The fibers in the composite materials will improve the mechanical properties such as tensile strength, flexural strength, impact strength, stiffness and matrix will transfer stresses between the reinforcing fibers. Fiber reinforced polymer composites are also called as fibrous composites because they consists of fibers as the reinforcing materials. The applications of composite materials are in automotive, marine, aerospace, etc. because of having properties such as high specific strength and stiffness. The types of composite materials are metal matrix composites, ceramic matrix composites and polymer matrix composites. When the matrix material is taken as ceramic it is called as ceramic matrix composite. The properties of ceramic matrix composites are better toughness, high strength, hardness, high temperature properties and better wear resistance.When the polymer resin is used as a matrix material then it is called as polymer matrix composite. These materials are having properties such as low density, good thermal and electrical insulator, ease of fabrication and low cost. The properties of polymer matrix composites mainly depend upon types of reinforcement that is particles and fibers, the type of polymer used and interface which is used between them. Polymers are classified into thermoplastics and thermosets. Thermoplastic materials are reversible and reshaped by

Повышение качества поверхности при обработке волоконно-армированного композита фрезой с встречно расположенными лезвиями на основе sph моделирования

Unidirectional fiber-reinforced composite workpieces are often machined in practice. During such cutting process stronger fibers are bended more than weaker matrix and an interfacial debonding between them is occurred under machined surface. It deteriorates working properties of composite and so debonding reduction is a vital technological problem. One of the perspective ways to diminish such debonding is to substitute the orthogonal cutting by the oblique one. This decision is confirmed by known practice of milling cutter design. Milling cutters with the continuous helix edges and with interrupted ones with a large tool cutting edge angle are often used. In this case fiber deformations in a cutting zone are significant. To diminish such deformations the hypothesis about efficient use of opposite cutting edges location with a large tool cutting edge inclination is assumed. This hypothesis is checked by using of SPH method with micro-simulation of cutting of metal-matrix composites (steel fibers and aluminum alloy matrix). Johnson-Cook approach is used for both materials. Obtained qualitative deformation pictures confirm this hypothesis. On this basis a new milling cutter design with tool major cutting edges located as a chevron on a cylindrical surface with alternate arrangement is suggested. Computer simulation of such edges operation shows minimal fibers deformations in cutting zone. At the same time, undesired excessive chip packing in a zone between the adjacent cutting edges is not observed. The obtained results are preliminary considering the limited computer model size and no experiment verification made.

Localised folding in general deformations

One control on the buckling of a layer (or layers) embedded in a weaker matrix is the reaction force exerted by the deforming matrix on the layer. If the system is linear and this force is a linear function of the layer deflection, as for linear elastic and viscous materials, the resulting buckles can be sinusoidal or periodic. However if the system is geometrically nonlinear, as in general non-coaxial deformations, or the matrix material is nonlinear, as for nonlinear elastic, non-Newtonian viscous and plastic materials, the buckling response may be localised so that individual packets of folds form; the resulting fold profile is not sinusoidal. These folds are called localised folds. Most natural folds are localised. One view is that irregularity derives solely from initial geometrical perturbations. We explore a different view where the irregular geometry results from a softening material or geometrical nonlinearity without initial perturbations. Localised folds form in a fundamentally different way than the Biot wavelength selection process; the concept of a dominant wavelength does not exist. Folds grow and collapse sequentially rather than grow simultaneously. We discuss the formation of localised folds with recent considerations of constitutive behaviour at geological strain rates for general three-dimensional deformations.

The transition from single layer to foliation boudinage: A dynamic modelling approach

Foliation boudinage is a deflection of foliation in the vicinity of a central discontinuity in foliated rocks, mostly filled with vein material. It shows evidence for brittle deformation and void-opening during ductile flow. We used a two-dimensional visco-elastic spring model based on a discrete element approach to study the dynamic development of foliation boudinage and the behaviour of anisotropic visco-elastic material deformed under pure shear conditions. The anisotropies are set by defining rheological heterogeneities in the models with (1) a single layer in a weaker matrix; (2) multi-layers with different elastic properties and (3) random-distributed “micas”, rows of horizontally aligned elements with the same elastic properties. The models show the nucleation and propagation of fractures during ductile deformation and flow perturbation and localization in the vicinity of fractures. Voids localize along extension fractures, at intersections of conjugate shear fractures and in small pull-apart structures along shear fractures, which look identical to boudin necks in isolated stiff layers. Results show that strain localization is strong in models with lower elastic constants and anisotropy whereas it is distributed in the models with higher elastic constants and anisotropy in which asymmetric and complex geometries develop. The models successfully show the development of and transitions between a single layer, multi-layer and foliation boudinage that are common structures in high strain zones.

Localized and chaotic folding: the role of axial plane structures

Most natural fold systems are not sinusoidal in profile. A widely held view is that such irregularity derives solely from inherited initial geometrical perturbations. Although, undoubtedly, initial perturbations can contribute to irregularity, we explore a different (but complementary) view in which the irregular geometry results from some material or system softening process. This arises because the buckling response of a layer (or layers) embedded in a weaker matrix is controlled in a sensitive manner by the nature of the reaction forces exerted by the deforming matrix on the layer. In many theoretical treatments of the folding problem, this reaction force is assumed to be a linear function of some measure of the deformation or deformation rate. This paper is concerned with the influence of nonlinear reaction forces such as arise from nonlinear elasticity or viscosity. Localized folds arising from nonlinearity form in a fundamentally different way than the Biot wavelength selection process. As a particular example of nonlinear behaviour, we examine the influence of axial plane structures made up of layers of different mineralogy formed by chemical differentiation processes accompanying the deformation; they are referred to as metamorphic layering. The alternating mineralogical composition in the metamorphic layers means that the embedding matrix exerts a reaction force on the folded layers that varies not only with the deflection or the velocity of deflection of the layer, but also in a periodic manner along the length of the folded layers. The influence of this spatially periodic reaction force on the development of localized and chaotic folding is explored numerically.

Reconciliation of contrasting theories for fracture spacing in layered rocks

Natural and man-made brittle layers embedded in a weaker matrix and subjected to layer-parallel extension typically develop an array of opening-mode fractures with a remarkably regular spacing. This spacing often scales with layer thickness, and it decreases as extension increases until fracture saturation is reached. Existing analytical one-dimensional (1-D) ‘full-slip’ models, which assume that interfacial slip occurs over the entire length of the fracture-bound blocks, predict that the ratio of fracture spacing to layer thickness at saturation is proportional to the ratio of layer tensile to interface shear strength ( T/τ). Using 2-D discontinuum mechanical models run for conditions appropriate to layered rocks, we show that fracture spacing at saturation decreases linearly with decreasing T/τ ratio, as predicted by 1-D models. At low T/τ ratios (ca. <3.0), however, interfacial slip is suppressed and the heterogeneous 2-D stress distribution within fracture-bound blocks controls further fracture nucleation, as predicted by an existing 2-D ‘fracture infill criterion’. The applicability of the two theories is hence T/τ ratio dependent. Our models illustrate that fracture spacing in systems permitting interfacial slip is not necessarily an indicator of fracture system maturity. Fracture spacing is expected to decrease with increasing overburden pressure and decreasing layer tensile strength.

Porphyroblast rotation versus nonrotation: Conflict resolution!

Data on foliation intersection and/or inflection axes preserved in porphyroblasts (FIAs) indicate that no rotation occurs during ductile deformation relative to spatial coordinates. This contrasts with 99% of investigations of rigid objects in non-coaxially deforming media where the objects rotate. When anastomosing shear zone formation around relatively strong objects in a weaker matrix is modeled, no porphyroblast rotation occurs. Formation of these anastomosing zones controls the development of this phenomenon, called gyrostasis. If such zones are absent, porphyroblasts rotate. In weak materials the gyrostatic situation arises because the superposition of simple shearing deformation normal to initial coaxial shortening results in only small rotations of principal axes of stress. Since shear zones are controlled by the orientations of principal axes of stress, initial anastomosing zones retain their orientations and positions during subsequent non-coaxial deformation. The porphyroblast is isolated from the embedding non-coaxially deforming matrix, but this material close to the continues to deform coaxially; no local rotation occurs. This has major tectonic significance because, allowing for the effects of rotation due to brittle deformation, porphyroblasts can now be routinely used to access lengthy structural and/or metamorphic histories destroyed in the matrix by reactivation such as movement directions, shear senses, and extended pressure-temperature-time paths.

Effect of sludge water from ready-mixed concrete plant on properties and durability of concrete

Besides the increasing disposal cost, sludge water, a wastewater washout from ready-mixed concrete plant, has caused environmental impact problems. This paper investigates the utilization and recycling of sludge water as mixing water for concrete production. The basic properties of sludge water were obtained according to ASTM standards. The properties of dry sludge powder such as chemical compositions and physical properties were investigated. The properties of fresh concrete studied were unit weight, slump, and temperature rise. The mechanical properties of concrete, such as compressive strength and modulus of elasticity, were studied. The durability aspects, such as drying shrinkage and weight loss due to acid attack, were investigated. For parametric study, sludge water was used as a replacement of tap water varying from 0% to 100% by weight. The water-to-cement ratios were 0.5, 0.6, and 0.7, respectively. In this study the sludge water tested has a high alkalinity and the total solids content exceeding the limit of ASTM C94, contributing to the more porous and weaker matrix. As a result, when increasing the percentage of sludge water in mixing water, the drying shrinkage and weight loss due to acid attacks increased, and the slump and strength decreased. However, the unit weight and temperature of fresh concrete were not affected by the use of sludge water.

Syntectonic melt pathways in granitic gneisses, and melt-induced transitions in deformation mechanisms

Partial melting of granodioritic gneisses in the contact aureole of the Bergell Pluton (Central Alps) occurred during regional deformation. Melting occurred in the presence of water, which was released from the pluton. The presence of melt is evidenced by local segregations of granite in shear zones, veins and dykes, and by grain-scale interstitial films of K-feldspar and quartz that do not occur in the unmelted protolith. These films are oriented parallel, as well as perpendicular to the foliation plane. In contrast, on the outcrop scale, cm-wide leucosome veins are oriented almost exclusively parallel to the foliation plane, indicating foliation-parallel flow. The partially molten granitic rocks contain dm-long clasts of restitic, well-foliated gneiss, showing a higher competence than their granitic matrix. K-feldspar is lacking in these clasts, the microstructure of which is characterized by elongate aggregates of quartz and feldspar, both dynamically recrystallized. In contrast, the granitic matrix is characterised by a random distribution of minerals, whith a shape preferred orientation defining a weak foliation. These microstructures are indicative of granular flow, whereas the microstructures of the clasts indicate dislocation creep involving dynamic recrystallization. The presence of K-feldspar controls the onset of melting and thus the transition from dislocation creep to granular flow. The weakening resulting from this transition is indicated by the formation of strong clasts in a weaker matrix.

Ice Stream C, Antarctica, sticky spots detected by microearthquake monitoring

Microearthquakes at the base of slow-moving Ice Stream C occur many times more frequently than at the base of fast-moving Ice Stream B. We suggest that the microearthquake source sites are so-called “sticky spots”, defined as limited zones of stronger Subglacial material interspersed within a weaker matrix. The fault-plane area of the microearthquakes (O(102m2)) is therefore a measure of the size of the sticky spots. The spatial density of the microearthquakes (O(10 km-2)) is a measure of the distribution of sticky spots.The average stress drop associated with these microearthquakes is consistent with an ice-stream bed model of weak subglacial till interspersed with stronger zones that support much or all of the basal shear stress. We infer a weak inter-sticky-spot material by the large distances (O(103m)), relative to fault radius, to which the microearthquake stress change is transmitted.

Ice Stream C, Antarctica, sticky spots detected by microearthquake monitoring

Microearthquakes at the base of slow-moving Ice Stream C occur many times more frequently than at the base of fast-moving Ice Stream B. We suggest that the microearthquake source sites are so-called “sticky spots”, defined as limited zones of stronger Subglacial material interspersed within a weaker matrix. The fault-plane area of the microearthquakes (O (102m2)) is therefore a measure of the size of the sticky spots. The spatial density of the microearthquakes (O (10 km-2)) is a measure of the distribution of sticky spots.The average stress drop associated with these microearthquakes is consistent with an ice-stream bed model of weak subglacial till interspersed with stronger zones that support much or all of the basal shear stress. We infer a weak inter-sticky-spot material by the large distances (O (103 m)), relative to fault radius, to which the microearthquake stress change is transmitted.

Tectonic overpressure in competent mafic layers and the development of isolated eclogites

Abstract Variation in the state of stress during heterogeneous deformation should be reflected in variation in the effective pressure of metamorphic reactions, whether this is mean stress or the normal stress acting across the reacting interface. The magnitude of this pressure variation will determine whether it is discernible in the preserved metamorphic mineral assemblages of heterogeneously deformed rocks. The magnitude of the mean stress difference across a non‐slipping interface between two materials with viscosity ratio &gt;c. 20:1 is effectively equal to the maximum shear stress for flow in the more viscous material. Progressive shortening of the interface results in a higher mean stress in the more competent material, whereas extension results in a lower mean stress. For high‐P/low‐T eclogite facies conditions, current experimental data indicate that clinopyroxene‐ and garnet‐rich layers of eclogite should be very strong and that pressure differences of up to 800 MPa (8 kbar) between competent layer and weaker matrix may be possible. Such high values can be obtained in widely separated competent layers for values of bulk stress in the overall multilayer that are much lower (by a factor approaching the viscosity ratio). Extrusion of material between more rigid plates, which has been proposed as a regional mechanism of lateral ‘continental escape’for both the Alps and the Himalayas, should also be accompanied by a lateral gradient in effective pressure; otherwise extrusion could not occur. Maximum mean stresses with magnitudes that are many times the maximum shear stress required for plastic flow should develop for deformation zones that are long relative to their width (e.g. around 20 times for a width‐to‐thickness ratio of 10). Tectonic overpressure in progressively shortened competent layers, particularly in regions of extrusion between more rigid plates, might help explain the occurrence of isolated layers and pods of low‐T eclogite (&lt;550°C) with estimated peak pressures markedly in excess of those in the surrounding matrix. It cannot explain the occurrence of isolated high‐T eclogites, because at temperatures &gt;c. 550°C, the dramatic weakening of clinopyroxene in the power‐law creep field precludes the development of significant overpressures in eclogite layers.

Single layer buckle folding in non-linear materials—I. Experimental study of fold development from an isolated initial perturbation

Scale-model experiments, involving pure shear compression of a single layer embedded in a weaker matrix, were carried out to study the influence of a pre-existing isolated perturbation in the shape of an otherwise planar layer on the location and shape of folds. Different grades of paraffin wax were used as analogues for rocks with power-law rheology. The wax used for the matrix flows in steady state with a stress exponent of about 3.8. The layer has a stress exponent of about 3 and strain softens. Viscosity ratios (considered at yield stress for the layer and matrix) of 30:1 and 8:1 were used. Bell-shaped perturbations were introduced into the layer with initial average wavelengths of 8, 16 and 32 times layer thickness and corresponding initial limb dips of 12 °, 5° and 3° respectively. The fold packet develops at the site of the introduced perturbation and spreads slowly along the layer with increasing shortening. The shape of the initial perturbation strongly influences the fold geometry: broader initial perturbations develop broader folds, undergo more layer parallel shortening and develop a wider zone of contact strain. The influence of the introduced perturbation shape is most marked when its average wavelength component is larger than the dominant wavelength (i.e. the wavelength of maximum growth rate). The degree of bonding between layer and matrix also influences fold development. Folds with welded layer—matrix boundaries amplify much more slowly, with a greater proportion of layer parallel shortening, than folds where slip between layer and matrix is promoted.

Interphase behaviour in graphite-thermoplastic monofilament composites

The role of the fibre-matrix interphase in transferring load from the matrix to the fibre in graphite-thermoplastic composites is not well understood. The goal of this work was to alter the interphase of graphite-thermoplastic monofilament composites in a controlled manner by treating the fibre surface, and then correlating fibre surface morphology, fibre surface energy, fibre strength, and matrix properties with interphase behaviour. A monofilament composite system was employed to study the fibre-matrix interphase because fibre-fibre interaction and processing variability are eliminated. A fragmentation method was used to observe the interphase behaviour of the monofilament composites indirectly by measuring the interphase shear stress, a parameter which governs the load transfer from the matrix to the fibre. It was found that the improvement in the ability of the interphase to transfer load from the matrix to the fibre increased with the severity of the treatment and was due primarily to increased micromechanical locking (increased surface roughness). Debonding at the interphase occurred along either the fibre-matrix interphase (in the composites with a tough matrix) or perpendicular to the fibre (in composites with a weaker matrix, and a strong interphase). Thus the matrix properties, by limiting the properties of the composite, strongly influenced the value of improving the interphase properties.