Dynamic response of an elastic and viscoelastic full-space to a spherical source

The dynamic response due to a spherical source of radius a embedded in an elastic and viscoelastic full-space is investigated at a distance R from the source. Previous solutions to the elastic case are extended to incorporate realistic source pressure functions. The elastic solution is then cast in a scale independent form in order to generalize the application. The results show that the near-field of the spherical source may be defined by R/a < 5. For this region the particle velocity and displacement decrease as R^?2, and the risetime decreases as R^?1. However. in the far-field region (R/a > 5) the particle velocity and displacement decrease as R^?1, and the risetime is independent of R. A non-constant Q model is developed to model viscoelastic attenuation and a complete analytical solution for wave propagation is obtained by cascading the separate mechanisms of geometric attenuation and viscoelastic attenuation. A comparison of our analytical model with the results of dynamic finite element modelling shows excellent agreement. This suggests that the method of cascading the separate transfer functions is a valid approach for wave propagation in viscoelastic media.     

Micromechanical model of weakly‐cemented sediments

Experiments indicate that the bulk stiffness of weakly‐cemented granular materials increases significantly with the applied load, a nonlinearity which is not captured by most micromechanical models. Here, we study the deformation of weakly‐cemented materials through grain‐scale simulations. We show that the frequently‐made assumption of linear‐elastic cement and intergranular contact area which varies according to a Hertzian‐type model cannot explain the observed nonlinearity of the bulk response. We introduce the micromechanical effect of mechanisms such as closure and opening of microcracks, granular cement and material heterogeneity through an effective contact stiffness which depends on the local deformation. We find that an exponential dependence between the effective stiffness and the local deformation, with a high exponent value, provides bulk stiffness which is in good agreement with experimental data. The inability of models with weaker intergranular stiffness‐deformation dependence to reproduce the experimental data demonstrates the highly‐nonlinear nature of the intergranular deformation. Our results highlight the importance of accounting for grain‐scale mechanisms in modeling granular materials, and provide a plausible explanation for the nonlinear behavior of weakly‐cemented sediments. Copyright © 2012 John Wiley & Sons, Ltd.     

Empirical Relationships Between the Elastic Settlement of Rigid Rectangular Foundations and the Settlement of the Respective Flexible Foundations

The problem of settlement of shallow foundations is among the most important ones in classical soil mechanics. And while for the settlement of flexible foundations elastic solutions are widely used, for rigid rectangular foundations where the actual contact pressure distribution is still unknown, the problem is approximated either analytically assuming a contact pressure distribution or semi‐empirically combining the theory of elasticity with experimental and/or numerical results. A third and often attractive choice is the use of simple empirical relationships or relevant tabulated values relating the elastic settlement of rigid foundations (ρ_R) with the settlement of the respective flexible foundations (e.g. at the center, ρ_Ce). Reviewing the relathionships of this third approach, the author revealed serious lack of consesous between the various sources; for example, according to the literature, ρ_R ranges between 68 and 125% of ρ_Ce, the time when it is well-known that ρ_R?<?ρ_Ce. In this paper, comparison of the settlement of 210 rigid foundation cases derived from 3D elastic finite element analysis, with the settlement of the respective flexible foundations derived from the theory of elasticity, led to simple empirical relationships between ρ_R and ρ_Ce as well as between ρ_R and ρ_Av (ρ_Av?=?average settlement of the flexible foundation) with coefficient of determination (R²) almost unity. The analysis showed that these relationships are largely independent of the aspect ratio of foundations and the thickness and Poisson’s ratio (ν) of the compressible medium, although separate relationships are given for ν?=?0.5, slightly increasing R². Finally, a correction factor for foundation rigidity is given exploting the known linear relationship that exists between the relative stiffness factor of foundations and settlement.

     

Bond rolling resistance and its effect on yielding of bonded granulates by DEM analyses

A discrete element modelling of bonded granulates and investigation on the bond effect on their behaviour are very important to geomechanics. This paper presents a two‐dimensional (2‐D) discrete element theory for bonded granulates with bond rolling resistance and provides a numerical investigation into the effect of bond rolling resistance on the yielding of bonded granulates. The model consists of mechanical contact models and equations governing the motion of bonded particles. The key point of the theory is that the assumption in the original bond contact model previously proposed by the authors (55th CSCE‐ASCE Conference, Hamilton, Ont., Canada, 2002; 313–320; J. Eng. Mech. (ASCE) 2005; 131 (11):1209–1213) that bonded particles are in contact at discrete points, is here replaced by a more reliable assumption that bonded particles are in contact over a width. By making the idealization that the bond contact width is continuously distributed with the normal/tangential basic elements (BE) (each BE is composed of spring, dashpot, bond, slider or divider), we establish a bond rolling contact model together with bond normal/tangential contact models, and also relate the governing equations to local equilibrium. Only one physical parameter β needs to be introduced in the theory in comparison to the original bond discrete element model. The model has been implemented into a 2‐D distinct element method code, NS2D. Using the NS2D, a total of 86 1‐D, constant stress ratio, and biaxial compressions tests have been carried out on the bonded granular samples of different densities, bonding strengths and rolling resistances. The numerical results show that: (i) the new theory predicts a larger internal friction angle, a larger yielding stress, more brittle behaviour and larger final broken contact ratio than the original bond model; (ii) the yielding stress increases nonlinearly with the increasing value of β, and (iii) the first‐yield curve (initiation of bond breakage), which define a zone of none bond breakage and which shape and size are affected by the material density, is amplified by the bond rolling resistance in analogous to that predicted by the original bond model. Copyright © 2006 John Wiley & Sons, Ltd.     

A packing generation scheme for the granular assemblies with 3D ellipsoidal particles

This paper introduces a new generator algorithm and computer program for 3-D numerical simulation of packing configuration in a granular assemblies composed of ellipsoidal particles of different a/b aspect ratios. Each ellipsoidal particle is approximated by the revolution of an ellipse, formed by four connected arcs, about the major axis passing through its centroid. The centroid co-ordinates, major axis direction and lengths of the major and minor axes are the essential data for the packing generation and associated contact detection. The domain to be filled with particles can be a polyhedron of any shape. The packing program was coded based on a newly proposed scheme which obeys the no interpenetration kinematics of solid bodies. New contact detection algorithms for any two ellipsoids in the packing space were developed. Though simple, these algorithms effectively determine the contact condition and contact point without solving the simultaneous equations of the two ellipsoidal surfaces. Each particle's packing location, contact-point co-ordinates, and three-dimensional graphs can be created using the packing domain given boundaries, along with numbers, and geometrical information of particles to be generated. Simulation results show that this new algorithm provides an effective packing model as a required initial input for analysing the mechanics of granular material. This generation scheme potentially can explore the complex 3-D behaviours of material composed of discrete particles. Copyright © 1999 John Wiley & Sons, Ltd.     

Porphyroclast systems as kinematic indicators

Porphyroclasts of relatively strong minerals in mylonites commonly have an internal monoclinic shape symmetry defined by tails of dynamically recrystallized material. The geometry of a porphyroclast and its tails, called a ‘porhyroclast system’, can serve as a valuable indicator of the sense of vorticity. Porphyroclast systems have been divided into σ- and δ-types on the basis of the geometry of the tails. σ-Types have wedge-shaped recrystallized tails whose median lines lie on opposite sides of a reference plane parallel to the tails and containing the symmetry axis for the system. σ-Types are further subdivided into a σ_a-types, in which the porphyroclast is isolated in a relatively homogeneous matrix, and σ_b-types, in which the porphyroclast system is associated with a shear band foliation in the matrix. δ-Types typically have narrow recrystallized tails whose median lines cross the reference plane adjacent to the porphyroclast. Consequently, embayments of matrix material occur adjacent to the porphyroclasts and the tails display characteristic bends.A porphyroclast system in a mylonite develops when the relatively weak dynamically recrystallized grain aggregate in the porphyroclast mantle changes its shape due to non-coaxial flow in the adjacent matrix. This behaviour has been modelled in shear box experiments. Passive marker lines around rigid cylinders embedded in silicone putty were subjected to simple shear. The experiments were modified to simulate a change in recrystallization rate (R) with respect to rate of deformation (γ) by decreasing the diameter of the rigid cylinder during deformation at variable rates. The ratio R/γ appears to be one of the most important factors in determining which porphyroclast system will develop. At high R/γ values, flow of recrystallized material away from the porphyroclast is continuously appended by the production of new grains and wedge-shaped σ_a-type tails develop. At low R/γ values, relatively few new grains are added to the tails which become thinned and deflected by drag due to the spinning motion of the porphyroclast. In addition, most porphyroclast systems at low shear strains are of σ_a-type or lack monoclinic symmetry, whereas δ-types are only developed at high shear strain values. Complex porphyroclast systems, characterized by two generations of tails, are observed in many of the natural and model shear zones studied and may form due to fluctuating R/γ. Conditions that allow isolated σ_a- and δ-type porphyroclast systems to be used as sense of vorticity indicators are: the systems should have a monoclinic shape symmetry; matrix grain size should be small with respect to porphyroclast size; matrix fabric should be homogeneous; deformation history should be simple, and observations should be made on sections normal to the inferred bulk vorticity vector for the mylonite.     

Size-dependent mechanical behavior of an intergranular bond revealed by an analytical model

The size of intergranular bonds significantly affects the macroscopic mechanical properties of geomaterials. A size-dependent bond contact model is desired in the distinct element method (DEM) for geomaterials formed by aggregates of bonded particles. This paper proposes an analytical solution of highly-precise stress fields of a biconcave bond between two identical disc-shaped particles under different loading paths based on Dvorkin’s solution. The Unified Strength theory is then introduced to obtain the initial failure domain in the bond. The proposed solution is consistent with results predicted by finite element simulations and experimental observations. The functions of bond stiffness with respect to all influencing parameters, i.e. bond width/thickness, particle radius and elastic parameters of bond material, are provided by the solution and empirically formulated by fitting a large number of analytical results. Additionally, the failure criterion or envelope under different combined loads is formulated for typical brittle bonds. The resulting failure criterion, approximated as an ellipsoid, depends on the size and material properties of the bonds. The proposed solution and equation can be implemented into a bond contact model used in DEM simulations of a geomaterial, where variation of bond sizes is significant and size-dependent contact model is important.     

Pressure solution at grain-to-grain contacts

Whereas much petrographic evidence for pressure solution, in sedimentary rocks has been accumulated since Sorby's work, its thermodynamic justification has never been clearly established, and has been challenged by some authors. Difficulties disappear when it is recognized that in the most general case migration of chemical components proceeds down chemical-potential gradients rather than down concentration gradients. Along a grain contact a chemical-potential gradient is produced by variations in contact pressure and by local variations in Helmholtz energy of the solid. For example, in a sand made up of even-sized spherical grains buried 500 m, the ratio of the diameter (D) of the grains to that of a spherical elastic contact circle (a) is D/a ～- 26. The chemical potential at the center of such an elastic contact is ～- 14kcal mol^?1 higher than in surrounding pore water saturated with respect to quartz. For comparison, at a temperature of 30°C, saturation with respect to amorphous silica rather than quartz raises the chemical potential by only 1.6 kcal mol^?1. If the diameter of the contact circle has enlarged to e.g. a = D/5, the chemical potential at its center is still 0.5 kcal mol ^?1 greater than that of free quartz under hydrostatic pressure. The corresponding potential gradients are the driving force of pressure solution. The concept of pressure solution thus does not contradict any thermodynamic principle; in particular, it does not require that the chemical component of the solid have a smaller partial volume in solution than in the solid state. Petrographic and experimental evidence can therefore be accepted without reservation.     

Correlation between optical, chemical and micro-structural parameters of high-rank coals and graphite

In order to identify the parameters that best characterize the chemical and structural evolution of organic matter during coalification, the relationships between optical, chemical and micro-structural parameters in high-rank coals and natural graphite were studied. The samples include anthracites from Peñarroya–Belmez–Espiel Basin (Spain), Douro Basin (Portugal), and Alto Chicama Basin (Peru); and natural graphite from Canada, Mozambique, and Austria.Correlations between the following optical parameters were assessed: vitrinite random reflectance (R_r), Reflectance Indicating Surfaces (RIS) axis (R_MAX, R_INT and R_MIN), and RIS parameters (R_am, R_ev and R_st), as well as B_w and AI anisotropy parameters. Furthermore, the chemical parameters used were chosen according to their significant variation in coals, namely volatile matter, carbon, and hydrogen contents calculated in dry ash free basis (VM_daf, C_daf, H_daf), as well as the H/C atomic ratio. Structural organization was characterized by micro-Raman spectroscopy and XRD. Raman parameters used were the full width at half maximum (FWHM) and position of G and D1 bands on the first-order Raman spectrum, and the ID1/IG intensity area ratio. The selected XRD parameters were interlayer spacing d₀₀₂, and crystallite sizes L_a and L_c.Results show that: (i) R_MAX RIS axis seems to correlate best with chemical and micro-structural parameters; (ii) for the majority of studied samples, H_daf and H/C atomic ratio are the only chemical parameters with significant correlations with R_MAX; (iii) the FWHM of the G band of Raman spectrum shows good linear correlation with the XRD parameter d₀₀₂; and, (iv) structural organization of carbon materials, as measured by trends in their optical and crystalline parameters, is influenced by their hydrogen content (daf basis) and therefore by the H/C atomic ratio.     

Ensemble smoothing of land subsidence measurements for reservoir geomechanical characterization

Geomechanical models are often used to predict the impact on land surface of fluid withdrawal from deep reservoirs, as well as investigating measures for mitigation. The ability to accurately simulate surface displacements, however, is often impaired by limited information on the geomechanical parameters characterizing the geological formations of interest. In this study, we employ an ensemble smoother, a data assimilation algorithm, to provide improved estimates of reservoir parameters through assimilation of measurements of both horizontal and vertical surface displacement into geomechanical model results. The method leverages the demonstrated potential of remote sensing techniques developed in the last decade to provide accurate displacement data for large areas of the land surface. For evaluation purposes, the methodology is applied to the case of a disk‐shaped reservoir embedded in a homogeneous, isotropic, and linearly elastic half space, subject to a uniform change in fluid pressure. Multiple sources of uncertainty are investigated, including the radius, R, the thickness, h, and the depth, c, of the reservoir; the pore pressure change, Δp; porous medium's vertical uniaxial compressibility, c_M, and Poisson's ratio, ν, and the ratio, s, between the compressibilities of the medium during loading and unloading cycles. Results from all simulations show that the ensemble smoother has the capability to effectively reduce the uncertainty associated with those parameters to which the variability and the spatial distribution of land surface displacements are most sensitive, namely, R, c, c_M, and s. These analyses demonstrate that the estimation of these parameters values depends on the number of measurements assimilated and the error assigned to the measurement values. Copyright © 2014 John Wiley & Sons, Ltd.     

A PACKING GENERATION SCHEME FOR THE GRANULAR ASSEMBLIES WITH PLANAR ELLIPTICAL PARTICLES

In this paper, a new generator algorithm and a computer program PG2D is introduced for 2D numerical simulation of packing configuration in a granular material composed of elliptical particles of different a/b aspect ratios. Each elliptical particle is approximated by four connected arcs. The centre co-ordinates and radius of each arc and co-ordinates of connecting points can be determined from the formulae derived by entering the major axis length, 2a, and the eccentricity. The domain to be filled with particles can be a polygon of any shape. Given the size of the packing domain, geometrical information and numbers of particles to be generated, the packing location of each particle and the co-ordinates of contact points along with contact normal rose diagram can be generated as outputs. Simulation results show that this new algorithm can provide quite a reasonable packing model in accordance with the initial input required for the analysis of the mechanics of granular material. This generation scheme has the potential to cover packing generation and behaviour analysis of 3D sphere or ellipsoidal shaped granular materials. © 1997 by John Wiley & Sons, Ltd.     

On the dynamic stiffness of circular ring footings on an elastic stratum

Circular ring footings on an elastic stratum are considered. The static and dynamic stiffnesses are calculated using an efficient numerical technique. The results indicate that the static torsional and rocking stiffnesses of a ring footing do not deviate significantly from the corresponding stiffness of the circular footing for values of the inner-radius-to-outer-radius ratio up to about 0.75. The static horizontal and vertical stiffnesses change considerably only for values of this ratio greater than about 0.60. The change in the stiffness and damping coefficients is small for values of the ratio between 0 and 0.5.     

Laboratory Tests on Shotcrete-Rock Joints in Direct Shear, Tension and Compression

Summary. A series of laboratory tests was performed on cemented shotcrete-rock joints to investigate the strength and stiffness of the interfaces, while simulating field conditions as close as possible. The direct shear test formed the core of the experimental work, while the tension and compression tests were complementary. To simulate loading conditions experienced in practical cases the direct shear tests were performed under fairly low normal stresses. In most practical cases when shotcrete is used with rock bolts, the normal load on shotcrete lining seldom exceeds 0.2 to 0.5 MPa. The direct shear test results show that, for such normal load range the shear strength is determined by the bond strength for genuinely bonded shotcrete-rock interfaces. For higher normal stresses (σ_n > 1.0 MPa), which rarely exist at the shotcrete-rock interface, the shear strength is largely influenced by friction resulting in the cohesive strength being less significant. Assessment of the shear surface revealed that the steel fibres in the shotcrete appeared to contribute significantly to the frictional component. The shear and normal stiffnesses of the interface were also determined, which were in principal the stiffnesses of the bond. An interesting observation was the complex interaction at the interface and the mechanisms that controlled the peak shear strength which depended on the surface roughness, the existence of natural flaws and the normal load.     

On the use of discrete element modelling to simulate the viscoelastic deformation behaviour of an idealized asphalt mixture

The use of discrete-element modelling (DEM) to simulate the behaviour of a highly idealized bituminous mixture under uniaxial and triaxial compressive creep tests is investigated in this paper. The idealized mixture comprises single-sized spherical particles (sand) mixed with bitumen and was chosen so that the packing characteristics are known and the behaviour of the mixture is dominated by the bitumen. The bitumen is represented as shear and normal (tensile and compressive) contact stiffnesses. Numerical sample preparation procedures for specimens containing spherical particles or clumps have been developed to ensure that the final specimen is isotropic and has the correct volumetric proportions. An elastic contact was used for the compressive normal contact stiffness and a viscoelastic contact was used for shear and tensile normal contact stiffness. Simulation results show that the idealized mixture is found to dilate when the ratio of compressive to tensile contact stiffness increases as a function of loading time. Uniaxial and triaxial viscoelastic simulations have been performed to investigate the effect of stress ratio on dilation and the numerical results have been verified with experimental data. The effects of introducing a proportion of frictional contacts and a more complex particle shape (clump) on dilation have been examined.     

Granular contact dynamics with elastic bond model

This paper proposes an elastic bond model in the framework of contact dynamics based on mathematic programming. The bond model developed in this paper can be used to model cemented materials. The formulation can be reduced to model pure static problems without introducing any artificial damping. In addition, omitting the elastic terms in the objective function turns the formulation into rigid bond model, which can be used for the modeling of rigid or stiffly bonded materials. The developed bond model has the advantage over the explicit DEM that large time step or displacement increment can be used. The tensile and shear strength criteria of the bond model are formulated based on the modified Mohr–Coulomb failure criterion. The torque transmission of bonds is introduced based on rolling resistance model. The loss of shear or tensile strength, or torque transmission will lead to the breakage of bonds, and turn the bond into purely frictional contact. Three simple examples are first used to validate the bond model. Numerical examples of uniaxial and biaxial compression tests are used to show its potential in modeling cemented geomaterials. Numerical results show that elastic bonds are indeed necessary for the modeling of cemented granular material under static conditions.     

Influence of shotcrete composition on load‐level estimation in NATM‐tunnel shells: Micromechanics‐based sensitivity analyses

Displacement measurement‐based estimations of loads and utilization degrees in shotcrete tunnel shells as part of the New Austrian Tunneling Method (NATM), have become standard tools in tunnel practice; their quality, however, may crucially depend on the knowledge of the actual shotcrete composition after spraying. To shed light on this issue, we here determine, based on experimentally validated micromechanical representations of shotcrete, the hydration degree‐dependent elastic, creep, and strength properties of different shotcretes, characterized by water cement ratios (w/c) between 0.4 and 0.6, aggregate cement ratios (a/c) between 3.5 and 5, and Young's modulus of aggregates (E_agg) between 40 and 80 GPa. These properties are fed into a structural shell model of the Sieberg tunnel, and this model is subjected to displacement fields approximated from daily displacement measurements at five selected points along the shell's inner surface. Resulting stresses and forces in the tunnel shell allow for analyzing the influence of shotcrete composition on load‐level estimation in NATM tunnel shells: The magnitudes of circumferential and longitudinal normal forces increase significantly with decreasing w/c, while a/c and E_agg have the inverse and relatively minor effect. The utilization degree is virtually insensitive to changes in w/c(especially at early ages), and only slightly decreases with decreasing a/c and E_agg. The location of maximum loading is unaffected by the shotcrete composition underlying the analysis. Conclusively, location and magnitude of maximum utilization degrees are very robust estimates (not affected by limited knowledge on the shotcrete composition), whereas realistic estimation of stresses and forces does require more accurate consideration of shotcrete composition. Copyright © 2011 John Wiley & Sons, Ltd.     

Transmission of Elastic P-waves across Single Fractures with a Nonlinear Normal Deformational Behavior

Summary This paper presents a theoretical study on normally incident elastic P-wave transmission across single dry fractures with a nonlinear normal deformational behavior. The effects of nonlinear fracture normal behavior on P-wave transmission are examined without the mixture of fracture shear behavior. The linear displacement discontinuity model for wave propagation across fractures is extended to a nonlinear model – the hyperbolic elastic model (BB model). Numeric solutions of magnitudes of transmission (|T _non|) and reflection (|R _non|) coefficients, for normally incident P-wave transmission across the nonlinear deformable fractures, are obtained and related to the closure behavior of fractures. Parametric studies are conducted to acquire an insight into the effects of the nonlinear fracture normal deformation on P-wave transmission, in terms of initial normal stiffness and the ratio of current maximum closure to maximum allowable closure of the fractures, as well as the incident wave amplitude and frequency. Comparisons between the linear and nonlinear models are presented. It is shown that, |T _lin| and |R _lin| for the linear model are special solutions of |T _non| and |R _non| for the nonlinear model, when the incident wave amplitude is so low that the current maximum closure of fracture incurred during the wave transmission is much smaller, relative to the maximum allowable closure. In addition, the nonlinear fracture behavior gives rise to a phenomenon of higher harmonics during the wave transmission across the fracture. The higher harmonics contribute to the increase of |T _non| from |T _lin|.     

A bonded-particle model for cemented sand

We propose an extension of the Discrete Element Method for the numerical simulation of cemented sands, in which spherical particles are bonded together by elastic beams connecting the centers of the spheres. The parameters of this model are the strengths and stiffnesses of the bonds and particles. For small strains, the elasticity of the bond element is equal to the well-known linear finite-element Timoshenko beam element with reduced integration. The finite rotations are represented by unit quaternions. An efficient way to compute relative rotations and to decompose them into their components is presented.The results of triaxial compression tests on artificially cemented sands are used to verify that the model can capture the macroscopic behavior of such materials. The results show that peak stress mainly depends on the strength of the bonds and the number of initially bonded particles in the material. Results of triaxial tests with different cement contents are reproduced by the analysis. An important parameter of the model is the strength difference between tension and compression of the bond element. This property controls the influence of the confining pressure on peak strength. In the future, the model could be adapted to other types of bonded materials like asphalt or rock.     

High to ultrahigh temperature contact metamorphism and dry partial melting of the Tasiuyak paragneiss,Northern Labrador

Contact aureoles of the anorthositic to granitic plutons of the Mesoproterozoic Nain Plutonic Suite (NPS), Labrador, are particularly well developed in the Palaeoproterozoic granulite facies, metasedimentary, Tasiuyak gneiss. Granulite facies regional metamorphism (M_R), c. 1860 Ma, led to biotite dehydration melting of the paragneiss and melt migration, leaving behind biotite‐poor, garnet–sillimanite‐bearing quartzofeldspathic rocks. Subsequently, Tasiuyak gneiss within a c. 1320 Ma contact aureole of the NPS was statically subjected to lower pressure, but higher temperature conditions (M_C), leading to a second partial melting event, and the generation of complex mineral assemblages and microstructures, which were controlled to a large extent by the textures of the M_R assemblage. This control is clearly seen in scanning electron microscopic images of thin sections and is further supported by phase equilibria modelling. Samples collected within the contact aureole near Anaktalik Brook, west of Nain, Labrador, mainly consist of spinel–cordierite and orthopyroxene–cordierite (or plagioclase) pseudomorphs after M_R sillimanite and garnet, respectively, within a quartzofeldspathic matrix. In addition, some samples contain fine‐grained intergrowths of K‐feldspar–quartz–cordierite–orthopyroxene inferred to be pseudomorphs after osumulite. Microstructural evidence of the former melt includes (i) coarse‐grained K‐feldspar–quartz–cordierite–orthopyroxene domains that locally cut the rock fabric and are inferred to represent neosome; (ii) very fine‐ to medium‐grained cordierite–quartz intergrowths interpreted to have formed by a reaction involving dissolution of biotite and feldspar in melt; and (iii) fine‐scale interstitial pools or micro‐cracks filled by feldspar interpreted to have crystallized from melt. Ultrahigh temperature (UHT) conditions during contact metamorphism are supported by (i) solidus temperatures >900 °C estimated for all samples, coupled with extensive textural evidence for contact‐related partial melting; (ii) the inferred (former) presence of osumilite; and (iii) titanium‐in‐quartz thermometry indicating temperatures within error of 900 °C. The UHT environment in which these unusual textures and minerals were developed was likely a consequence of the superposition of more than one contact metamorphic event upon the already relatively anhydrous Tasiuyak gneiss.     

Grain coarsening in contact metamorphic carbonates: effects of second-phase particles, fluid flow and thermal perturbations

Under contact metamorphic conditions, carbonate rocks in the direct vicinity of the Adamello pluton reflect a temperature‐induced grain coarsening. Despite this large‐scale trend, a considerable grain size scatter occurs on the outcrop‐scale indicating local influence of second‐order effects such as thermal perturbations, fluid flow and second‐phase particles. Second‐phase particles, whose sizes range from nano‐ to the micron‐scale, induce the most pronounced data scatter resulting in grain sizes too small by up to a factor of 10, compared with theoretical grain growth in a pure system. Such values are restricted to relatively impure samples consisting of up to 10 vol.% micron‐scale second‐phase particles, or to samples containing a large number of nano‐scale particles. The obtained data set suggests that the second phases induce a temperature‐controlled reduction on calcite grain growth. The mean calcite grain size can therefore be expressed in the form D = C₂ e^Q*/RT(d_p/f_p)^m*, where C₂ is a constant, Q* is an activation energy, T the temperature and m* the exponent of the ratio d_p/f_p, i.e. of the average size of the second phases divided by their volume fraction. However, more data are needed to obtain reliable values for C₂ and Q*. Besides variations in the average grain size, the presence of second‐phase particles generates crystal size distribution (CSD) shapes characterized by lognormal distributions, which differ from the Gaussian‐type distributions of the pure samples. In contrast, fluid‐enhanced grain growth does not change the shape of the CSDs, but due to enhanced transport properties, the average grain sizes increase by a factor of 2 and the variance of the distribution increases. Stable δ¹⁸O and δ¹³C isotope ratios in fluid‐affected zones only deviate slightly from the host rock values, suggesting low fluid/rock ratios. Grain growth modelling indicates that the fluid‐induced grain size variations can develop within several ka. As inferred from a combination of thermal and grain growth modelling, dykes with widths of up to 1 m have only a restricted influence on grain size deviations smaller than a factor of 1.1. To summarize, considerable grain size variations of up to one order of magnitude can locally result from second‐order effects. Such effects require special attention when comparing experimentally derived grain growth kinetics with field studies.