Modification of fluid inclusions in quartz by deviatoric stress. III: Influence of principal stresses on inclusion density and orientation

Extraction of useful geochemical, petrologic and structural information from deformed fluid inclusions is still a challenge in rocks displaying moderate plastic strain. In order to better understand the inclusion modifications induced by deviatoric stresses, six deformation experiments were performed with a Griggs piston-cylinder apparatus. Natural NaCl–H₂O inclusions in an oriented quartz crystal were subjected to differential stresses of 250–470 MPa at 700–900 °C and at 700–1,000 MPa confining pressure. Independently of the strain rate and of the crystallographic orientation of the quartz, the inclusions became dismembered and flattened within a crystallographic cleavage plane subperpendicular to σ ₁. The neonate (newly formed) inclusions that result from dismemberment have densities that tend towards equilibrium with P _fluid = σ ₁ at T _shearing. These results permit ambiguities in earlier deformation experiments on CO₂–H₂O–NaCl to be resolved. The results of the two studies converge, indicating that density changes in neonate inclusions are promoted by high differential stresses, long periods at high P and high T, and fluid compositions that maximize quartz solubility. Neonates spawned from large precursor inclusions show greater changes in density that those spawned from small precursors. These findings support the proposal that deformed fluid inclusions can serve as monitors of both the orientation and magnitude of deviatoric stresses during low-strain, ductile deformation of quartz-bearing rocks.     

Influences of loading direction and intermediate principal stress ratio on the initiation of strain localization in cross-anisotropic sand

Since cross-anisotropic sand behaves differently when the loading direction or the stress state changes, the influences of the loading direction and the intermediate principal stress ratio (b = (σ ₂ ? σ ₃)/(σ ₁ ? σ ₃)) on the initiation of strain localization need study. According to the loading angle (angle between the major principal stress direction and the normal of bedding plane), a 3D non-coaxial non-associated elasto-plasticity hardening model was proposed by modifying Lode angle formulation of the Mohr–Coulomb yield function and the stress–dilatancy function. By using bifurcation analysis, the model was used to predict the initiation of strain localization under plane strain and true triaxial conditions. The predictions of the plane strain tests show that the major principal strain at the bifurcation points increases with the loading angle, while the stress ratio decreases with the loading angle. According to the loading angle and the intermediate principal stress ratio, the true triaxial tests were analyzed in three sectors. The stress–strain behavior and the volumetric strain in each sector can be well captured by the proposed model. Strain localization occurs in most b value conditions in all three sectors except for those which are close to triaxial compression condition (b = 0). The difference between the peak shear strength corresponding to the strain localization and the ultimate shear strength corresponding to plastic limit becomes obvious when the b value is near 0.4. The influence of bifurcation on the shear strength becomes weak when the loading direction changes from perpendicular to the bedding plane to parallel. The bifurcation analysis based on the proposed model gives out major principal strain and peak shear strength at the initiation of strain localization; the given results are consistent with experiments.     

Multi-surface Cyclic Plasticity Sand Model with Lode Angle Effect

A Drucker-Prager J ₂ multi-surface-plasticity sand model is modified to employ the Lade-Duncan failure criterion as the yield function. This function includes the first and third stress invariants to account for the dependence of cyclic shear stress–strain behavior on confining pressure and the Lode angle. Related modifications to the flow rule and hardening rule are described. Dependence of dilatancy on confinement is also included. Salient features of the model performance are presented under general three-dimensional (3D) loading conditions, where the yield function provides a more accurate representation of nonlinear shear response. Dynamic response analyses of a mildly inclined infinite slope are performed to illustrate the influence of excitation direction on the accumulation of liquefaction-induced lateral ground deformation.     

Joint development normal to regional compression during flexural-flow folding: the Lilstock buttress anticline,Somerset, England

Alpine inversion in the Bristol Channel Basin includes reverse-reactivated normal faults with hanging wall buttress anticlines. At Lilstock Beach, joint sets in Lower Jurassic limestone beds cluster about the trend of the hinge of the Lilstock buttress anticline. In horizontal and gently north-dipping beds, J₃ joints ( 295–285° strike) are rare, while other joint sets indicate an anticlockwise sequence of development. In the steeper south-dipping beds, J₃ joints are the most frequent in the vicinity of the reverse-reactivated normal fault responsible for the anticline. The J₃ joints strike parallel to the fold hinge, and their poles tilt to the south when bedding is restored to horizontal. This southward tilt aims at the direction of σ₁ for Alpine inversion.Finite-element analysis is used to explain the southward tilt of J₃ joints that propagate under a local σ₃ in the direction of σ₁ for Alpine inversion. Tilted principal stresses are characteristic of limestone–shale sequences that are sheared during parallel (flexural-flow) folding. Shear tractions on the dipping beds generate a tensile stress in the stiffer limestone beds even when remote principal stresses are compressive. This situation favors the paradoxical opening of joints in the direction of the regional maximum horizontal stress. We conclude that J₃ joints propagated during the Alpine compression caused the growth of the Lilstock buttress anticline.     

Flow behaviour of tailings paste for surface disposal

Surface disposition of mine tailings in paste form is a new disposal technique, and to achieve a desired depositional geometry, it is necessary to characterize the paste's flow properties. This study investigates how water content affects the flow behaviour and depositional geometry of tailings and kaolinite pastes, which are shear-thinning, high solids content, mineral pastes. A stress-controlled rheometer and a strain-controlled viscometer with vane fixtures were used to characterize the yield behaviour of the pastes, and three types of yield stress were determined. A flume apparatus was used to simulate paste deposition under laboratory conditions. The depositional angle, determined from the flume tests, and the yield stresses, determined from the rheometers, decreased as the water content increased. For each type of yield stress, a linear relationship was found between the depositional angle and the Sofra–Boger dimensionless group (τ_y′Fr/Re), with the linear coefficient depending on paste type.     

Olivine as an in situ piezometer in high pressure apparatus

The deviatoric stress produced in a large-volume, high-pressure apparatus of the girdle-anvil type has been estimated from the density of free dislocations induced in natural olivine single crystals (initial density of 2×10⁶ cm^?2). Experiments at maximum pressure P=40 kbar and temperature T=1050°C for t=1 h in NaCl cell assemblies and various P-T paths yield specimens whose dislocation densities are unchanged from this initial value, implying that the deviatoric stress was less than 140 bar. In BN cell assemblies, the recovered specimen from high P-T experiments exhibit much higher densities of dislocations (～10⁹ cm^?2) which have been produced by steady-state plastic deformation of the olivine crystals under a deviatoric stress of ～3 kbar. This value of deviatoric stress in BN has been corroborated by observations of the subgrain size and recrystallized grain size in specimens of longer run duration (3 h).     

Numerical investigation of hydraulic fracture network propagation in naturally fractured shale formations

Hydraulic fracture network (HFN) propagation in naturally fractured shale formations is investigated numerically using a 3D complex fracturing model based on the discrete element method. To account for the plastic deformation behavior of shales, the Drucker–Prager plasticity model is incorporated into the fracturing model. Parametric studies are then conducted for different Young's moduli, horizontal differential stresses, natural fracture (NF) properties, injection rates, and number and spacing of perforation clusters. Numerical results show that horizontal differential stress primarily determines the generation of a complex HFN. The plastic deformation of shale can reduce the stimulated reservoir volume; this is more obvious with Young's modulus of less than 20 GPa. In addition, a higher injection rate could largely increase the fracture complexity index (FCI). Moreover, increasing perforation cluster numbers per fracturing stage is beneficial for increasing the FCI, but it also increases the potential merging of neighboring fractures, which may lead to non-uniform development of HFN in far-wellbore regions. To achieve uniform development of HFN within a fracturing stage, the distribution of NFs should be fully considered. The results presented here may provide improved understanding of HFN generation and are favorable for optimizing fracturing treatment designs for shale formations.     

Simple shear of isotropic elasto–plastic soil

The implications of assuming isotropic elasto–plasticity to model the behaviour of soil under simple shear conditions are considered. For small strains, use of such a model implies the following three consequences: (1) strains and strain increments at any stage of shearing may be expressed as the sum of elastic and plastic components; (2) principal directions of stress and of plastic strain increment are collinear; (3) principal directions of stress increment and of elastic strain increment are collinear. These consequences are used in order to establish relationships between the stresses, stress increments and strains which develop in a simple shear test. No additional assumptions with regards the form of the yield function, the flow rule or the hardening function are required for this development. By defining the ratio of the plastic to the total shear strain increment on the horizontal plane (the plane of zero extension) as λ, it is possible to define the horizontal normal stress σ_x in terms of λ and other stresses and strains which are normally known during simple shear loading. As a result, all components of the stress tensor in the simple shear plane may be defined. Results of some direct simple shear tests on soft clay have been interpreted using the model and found to be generally consistent with some of the observations reported in the literature from tests in which boundary stresses were measured.     

Monitoring in situ stress/strain behaviour during plastic yielding in polymineralic rocks using neutron diffraction

Attempts to use rock deformation experiments to examine the elastic and plastic behaviour of polymineralic rocks are hampered by the fact that usually only whole sample properties can be monitored as opposed to the separate contribution of each phase. To circumvent this difficulty, room-temperature, uniaxial compression experiments were performed in a neutron beam-line on a suite of calcite + halite samples with different phase volume proportions. By collecting diffraction data during loading, the elastic strain and hence stress in each phase was determined as a function of load to bulk strains of 1–2%. In all cases, the calcite behaved elastically while the halite underwent plastic yielding. During the fully elastic part of the deformation, the composite elastic properties and the within-phase stresses are well-described both by recent shear lag models and by analyses based on Eshelby's solution for the elastic field around an ellipsoidal inclusion in a homogeneous medium. After the onset of yielding, the halite in situ stress/total strain curve may be reconstructed using the rule of mixtures. At calcite contents of greater than 30%, the in situ halite response may be significantly weaker or stronger than that obtained at lesser calcite contents. The results highlight the potential that such techniques offer for developing an explicitly experimental approach for determining the influence of microstructural variables on the mechanical properties of polymineralic rocks.     

A general modelling of expansive and non-expansive clays

This paper presents an elastoplastic model for saturated expansive and non-expansive clays. The original feature of this model is that a plastic mechanism is introduced during unloading to take into account the irreversible swelling of the macroporosities. These strains are induced by the repulsive stresses which are unbalanced at the scale of the microporosities. Thus two yield surfaces are activated: a classical contact yield surface (F_C) similar to an associated modified Cam-clay approach and a swelling yield surface (F_R−A) based on the non-associated plasticity. The formulation considers that for the normally consolidated stress states, the strains are mainly produced by an increase of the contact stresses. For the overconsolidated stress states, the repulsive stresses balance the external stresses. The rheological parameters are easily determined from the results of either triaxial or oedometer tests. The model is then used in a finite element program, using the classical concepts of plasticity, especially for the loading–unloading criterion based on the sign of the plasticity multiplier. Simulations of the convergence of a gallery (under an earth retaining structure) sunk at great depth in Boom clay are presented. The results are compared with those obtained with the Cam-clay model. Copyright © 1999 John Wiley & Sons, Ltd.     

A J2‐plasticity model based on bounding surface concept

This article presents the development of a J₂ small strain plasticity model based on bounding surface concept, along with numerical examples to demonstrate model behaviors and identification of model parameter using laboratory test data. The model is motivated by the need for simulating permanent deformation accumulation of asphalt concrete mixtures, which leads to rutting in flexible pavements under repeated traffic loading. The proposed model accounts for the observation that rutting is mostly caused by shearing and takes advantage of the fact that bounding surface concept allows for the progressive accumulation of plastic deformation under constant amplitude loading condition. Analytical solutions are given for typical laboratory testing conditions. The model can be calibrated using repeated simple shear test data that are typically available for asphalt concrete mixtures. It is shown that the model is easy to use and provides a promising alternative for modeling permanent deformation accumulation in materials subjected to repetitive (cyclic) loading. Copyright © 2012 John Wiley & Sons, Ltd.     

Plastic deformation of wadsleyite: I. High-pressure deformation in compression

 We have studied the plastic deformation of Mg₂SiO₄ wadsleyite polycrystals. Wadsleyite was synthesized from a forsterite powder in a multianvil apparatus. It was then recovered and placed in a second multianvil assembly designed to induce plastic deformation by compression between two hard alumina pistons. After the deformation experiment, the microstructures are characterized by transmission electron microscopy (TEM) and large-angle convergent beam electron diffraction (LACBED). Deformation experiments have been carried out at 15–19 GPa and at temperatures ranging from room temperature to 1800–2000 °C. Five different dislocation types have been identified by LACBED: [100], 1/2〈111〉, [010], 〈101〉 and [001]. The [001] dislocations result from dislocation reactions and not from activation of a slip system. The [010] dislocations are activated under high stresses at the beginning of the experiments and further relax by decomposition into 1/2〈111〉 dislocations or by dissociation into four 1/4[010] partial dislocations. The following slip systems have been identified: 1/2〈111〉{101}, [100](010), [100](001), [100]{011}, [100]{021}, [010](001), [010]{101} and 〈101〉(010). Received: 15 July 2002 / Accepted: 14 February 2003 Acknowledgements High-pressure experiments were performed at the Bayerisches Geoinstitut under the EU IHP – Access to Research Infrastructures Programme (Contract no. HPRI-1999-CT-00004 to D.C. Rubie). P.C. has benefited from a Congé thématique pour recherche from the University of Lille, and would like to thank warmly all the people in Bayreuth who contributed to this work by daily assistance and discussions: Nathalie Bolfan-Casanova, Daniel Frost, Jed L. Mosenfelder and Brent Poe. The quality of the preparation of the TEM specimens by H. Schultze is greatly appreciated.     

Contact mechanism of a rock fracture subjected to normal loading and its impact on fast closure behavior during initial stage of fluid flow experiment

Fast closure of rock fractures has been commonly observed in the initial stage of fluid flow experiments at environmental temperatures under low or moderate normal stresses. To fully understand the mechanisms that drive this fast closure, the evolution of local stresses acting on contacting asperities on the fracture surfaces prior to fluid flow tests needs to be evaluated. In this study, we modeled numerically the asperity deformation and failure processes during initial normal loading, by adopting both elastic and elastic–plastic deformation models for the asperities on a real rock fracture with measured surface topography data, and estimated their impact on initial conditions for fluid flow test performed under laboratory conditions. Compared with the previous models that simulate the normal contact of a fracture as the approach of two rigid surfaces without deformations, our models of deformable asperities yielded smaller contact areas and higher stresses on contacting asperities at a given normal stress or normal displacement. The results show that the calculated local stresses were concentrated on the contacts of a few major asperities, resulting in crushing of asperity tips. With these higher contact stresses, however, the predicted closure rates by pressure solution are still several orders of magnitude lower than that of the experimental measurements at the initial stage of fluid flow test. This indicates that single pressure solution may not likely to be the principal compaction mechanism for this fast closure, and that the damages on contacting asperities that occur during the initial normal loading stage may play an important role. Copyright © 2015 John Wiley & Sons, Ltd.     

Reaction rim growth in the system MgO-Al2O3-SiO2 under uniaxial stress

We synthesize reaction rims between thermodynamically incompatible phases in the system MgO-Al₂O₃-SiO₂ applying uniaxial load using a creep apparatus. Synthesis experiments are done in the MgO-SiO₂ and in the MgO-Al₂O₃ subsystems at temperatures ranging from 1150 to 1350 °C imposing vertical stresses of 1.2 to 29 MPa at ambient pressure and under a constant flow of dry argon. Single crystals of synthetic and natural quartz and forsterite, synthetic periclase and synthetic corundum polycrystals are used as starting materials. We produce enstatite rims at forsterite-quartz contacts, enstatite-forsterite double rims at periclase-quartz contacts and spinel rims at periclase-corundum contacts. We find that rim growth under the “dry” conditions of our experiments is sluggish compared to what has been found previously in nominally “dry” piston cylinder experiments. We further observe that the nature of starting material, synthetic or natural, has a major influence on rim growth rates, where natural samples are more reactive than synthetic ones. At a given temperature the effect of stress variation is larger than what is anticipated from the modification of the thermodynamic driving force for reaction due to the storage of elastic strain energy in the reactant phases. We speculate that this may be due to modification of the physical properties of the polycrystals that constitute the reaction rims or by deformation under the imposed load. In our experiments rim growth is very sluggish at forsterite-quartz interfaces. Rim growth is more rapid at periclase-quartz contacts. The spinel rims that are produced at periclase-corundum interfaces show parabolic growth indicating that reaction rim growth is essentially diffusion controlled. From the analysis of time series done in the MgO-Al₂O₃ subsystem we derive effective diffusivities for the Al₂O₃ and the MgO components in a spinel polycrystal as ${\rm D}_{MgO} = 1.4 \pm 0.2 \cdot 10^{-15}$  m²/s and ${\rm D}_{Al_2O_3} = 3.7 \pm 0.6 \cdot 10^{-16}$  m²/s for T?=?1350 °C and a vertical stress of 2.9 MPa.     

Microstructure and fabric development in ice: Lessons learned from in situ experiments and implications for understanding rock evolution

In this contribution we present a review of the evolution of microstructures and fabric in ice. Based on the review we show the potential use of ice as an analogue for rocks by considering selected examples that can be related to quartz-rich rocks. Advances in our understanding of the plasticity of ice have come from experimental investigations that clearly show that plastic deformation of polycrystalline ice is initially produced by basal slip. Interaction of dislocations play an essential role for dynamic recrystallization processes involving grain nucleation and grain-boundary migration during the steady-state flow of ice. To support this review we describe deformation in polycrystalline ‘standard’ water-ice and natural-ice samples, summarize other experiments involving bulk samples and use in situ plane-strain deformation experiments to illustrate the link between microstructure and fabric evolution, rheological response and dominant processes. Most terrestrial ice masses deform at low shear stresses by grain-size-insensitive creep with a stress exponent (n ≤ 3). However, from experimental observations it is shown that the distribution of plastic activity producing the microstructure and fabric is initially dominated by grain-boundary migration during hardening (primary creep), followed by dynamic recrystallization during transient creep (secondary creep) involving new grain nucleation, with further cycles of grain growth and nucleation resulting in near steady-state creep (tertiary creep). The microstructural transitions and inferred mechanism changes are a function of local and bulk variations in strain energy (i.e. dislocation densities) with surface grain-boundary energy being secondary, except in the case of static annealing. As there is a clear correspondence between the rheology of ice and the high-temperature deformation dislocation creep regime of polycrystalline quartz, we suggest that lessons learnt from ice deformation can be used to interpret polycrystalline quartz deformation. Different to quartz, ice allows experimental investigations at close to natural strain rate, and through in-situ experiments offers the opportunity to study the dynamic link between microstructural development, rheology and the identification of the dominant processes.     

Mechanism and numerical simulation of reservoir slope deformation during impounding of high arch dams based on nonlinear FEM

The mechanism of reservoir slope deformation during impounding still lacks a convincing explanation. A generalized effective stress principle for rock masses is presented. A nonlinear iteration algorithm has been proposed and implemented in a 3D FEM program, TFINE. A case study of the Jinping-I high arch dam is then presented, and the calculated values of reservoir slope deformation agree well with the measured values. The results show that the change of the yield surface for the reservoir slope induced by adopting the effective stress principle results in plastic deformation, which is the main reason for slope deformation during impoundment.     

Research on elastoplastic damage constitutive model of intact Q2l loess in northwestern of China

Based on the unsaturated triaxial experiments for the intact fourth period Middle Pleistocene Epoch loess (Q₂l loess), the mechanical characteristic of Q₂l loess is studied. According to the continuum damage mechanics and elastic–plastic theory, the damage potential function and loading function were deduced. Besides, plastic deformation and irreversible damage deformation are supposed to obey Hyushin’s postulate. The elastoplastic damage constitutive model and damage evolution law of the unsaturated intact Q₂ loess are set up. Comparing the experiment curves with the computation result of this model, it is shown that the model can stimulate the mechanics characteristics of Q₂ loess well.     

Plastic deformation of wadsleyite: II. High-pressure deformation in shear

 We have studied the dislocation microstructures that develop in (Mg_0.9Fe_0.1)₂SiO₄ wadsleyite deformed by simple shear at high pressure. The experiments were performed in a multianvil apparatus with the shear assembly designed by Karato and Rubie (1997). The samples were synthesized in a separate experiment from high-purity oxides. The deformation experiments were carried out at 14 GPa and 1300 °C with time durations ranging from 1 to 8 h leading to plastic shear strains of 60 and 73%, respectively. The microstructures investigated by transmission electron microscopy (TEM) show that dislocation glide is activated under these conditions over the whole experimental time. The easy slip systems at 1300 °C involve 1/2<111> dislocations gliding in {101} as well as [100] dislocations gliding in (010) and {011}. Received: 15 July 2002 / Accepted: 14 February 2003 Acknowledgements High-pressure experiments were performed at the Bayerisches Geoinstitut under the EU IHP — Access to Research Infrastructures Programme (Contract no. HPRI-1999-CT-00004 to D.C. Rubie). The quality of the preparation of the TEM specimens by H. Schultze is greatly appreciated.     

Pre-failure behaviour of reconstituted peats in triaxial compression

This paper discusses the results of an experimental programme designed to investigate the deviatoric behaviour of peats. The results are obtained from triaxial experiments carried out on reconstituted peat samples. The interpretation of the experimental results follows a hierarchical approach in an attempt to derive the ingredients that an elastic–plastic model for peats should contain, including the yield locus, the hardening mechanism and the flow rule. The results obtained from stress tests along different loading directions show that purely volumetric hardening is not adequate to describe the deviatoric response of peat and that a deviatoric strain-dependent component should be included. The plastic deformation mechanism also depends on the previous stress history experienced by the sample. Stress and strain path dependence of the interaction mechanisms between the peat matrix and the fibres is discussed as a possible physical reason for the observed behaviour. This work offers a relevant set of data and information to guide the rational development and the calibration of constitutive laws able to model the deviatoric behaviour of peats.