Extended CFD–DEM for free‐surface flow with multi‐size granules

Computational fluid dynamics and discrete element method (CFD–DEM) is extended with the volume of fluid (VOF) method to model free‐surface flows. The fluid is described on coarse CFD grids by solving locally averaged Navier–Stokes equations, and particles are modelled individually in DEM. Fluid–particle interactions are achieved by exchanging information between DEM and CFD. An advection equation is applied to solve the phase fraction of liquid, in the spirit of VOF, to capture the dynamics of free fluid surface. It also allows inter‐phase volume replacements between the fluid and solid particles. Further, as the size ratio (SR) of fluid cell to particle diameter is limited (i.e. no less than 4) in coarse‐grid CFD–DEM, a porous sphere method is adopted to permit a wider range of particle size without sacrificing the resolution of fluid grids. It makes use of more fluid cells to calculate local porosities. The developed solver (cfdemSolverVOF) is validated in different cases. A dam break case validates the CFD‐component and VOF‐component. Particle sedimentation tests validate the CFD–DEM interaction at various Reynolds numbers. Water‐level rising tests validate the volume exchange among phases. The porous sphere model is validated in both static and dynamic situations. Sensitivity analyses show that the SR can be reduced to 1 using the porous sphere approach, with the accuracy of analyses maintained. This allows more details of the fluid phase to be revealed in the analyses and enhances the applicability of the proposed model to geotechnical problems, where a highly dynamic fluid velocity and a wide range of particle sizes are encountered. Copyright © 2015 John Wiley & Sons, Ltd.     

Numerical approximation of water–air two-phase flow by the mixed finite element method

A new model for two-phase flow of water and air in soil is presented. This leads to a system of two mass balance equations and two equations representing conservation of momentum of fluid and gas, respectively. This paper is concerned with the verification of this model for the special case of a rigid soil skeleton by computational experiments. Its numerical treatment is based on the Raviart–Thomas mixed finite element method combined with an implicit Euler time discretization. The feasibility of the method is illustrated for some test examples of one- and two-dimensional two-phase flow problems.     

Modelling the flow of self‐compacting concrete

A Lagrangian particle‐based method, smooth particle hydrodynamics (SPH), is used in this paper to model the flow of self‐compacting concretes (SCC) with or without short steel fibres. An incompressible SPH method is presented to simulate the flow of such non‐Newtonian fluids whose behaviour is described by a Bingham‐type model, in which the kink in the shear stress vs shear strain rate diagram is first appropriately smoothed out. The viscosity of the SCC is predicted from the measured viscosity of the paste using micromechanical models in which the second phase aggregates are treated as rigid spheres and the short steel fibres as slender rigid bodies. The basic equations solved in the SPH are the incompressible mass conservation and Navier–Stokes equations. The solution procedure uses prediction–correction fractional steps with the temporal velocity field integrated forward in time without enforcing incompressibility in the prediction step. The resulting temporal velocity field is then implicitly projected on to a divergence‐free space to satisfy incompressibility through a pressure Poisson equation derived from an approximate pressure projection. The results of the numerical simulation are benchmarked against actual slump tests carried out in the laboratory. The numerical results are in excellent agreement with test results, thus demonstrating the capability of SPH and a proper rheological model to predict SCC flow and mould‐filling behaviour. Copyright © 2010 John Wiley & Sons, Ltd.     

Efficient reliability method for implicit limit state surface with correlated non‐Gaussian variables

In contrast to the traditional approach that computes the reliability index in the uncorrelated standard normal space (u‐space), the reliability analysis that is simply realized in the original space (x‐space, non‐Gaussian type) would be more efficient for practical use, for example, with the Low and Tang's constrained optimization approach. On the other hand, a variant of Hasofer, Lind, Rackwits and Fiessler algorithm for first‐order reliability method is derived in this paper. Also, the new algorithm is simply formulated in x‐space and requires neither transformation of the random variables nor optimization tools. The algorithm is particularly useful for reliability analysis involving correlated non‐Gaussian random variables subjected to implicit limit state function. The algorithm is first verified using a simple example with closed‐form solution. With the aid of numerical differentiation analysis in x‐space, it is then illustrated for a strut with complex support and for an earth slope with multiple failure modes, both cases involving implicit limit state surfaces. Copyright © 2015 John Wiley & Sons, Ltd.     

Coupled bonded particle and lattice Boltzmann method for modelling fluid–solid interaction

This paper presents a two‐dimensional coupled bonded particle and lattice Boltzmann method (BPLBM) developed to simulate the fluid–solid interactions in geomechanics. In this new technique, the bonded particle model is employed to describe the inter‐particle movement and forces, and the bond between a pair of contacting particles is assumed to be broken when the tensile force or tangential force reaches a certain critical value. As a result the fracture process can be delineated based on the present model for the solid phase comprising particles, such as rocks and cohesive soils. In the meantime, the fluid phase is modelled by using the LBM, and the immersed moving boundary scheme is utilized to characterize the fluid–solid interactions. Based on the novel technique case studies have been conducted, which show that the coupled BPLBM enjoys substantially improved accuracy and enlarged range of applicability in characterizing the mechanics responses of the fluid–solid systems. Indeed such a new technique is promising for a wide range of application in soil erosion in Geotechnical Engineering, sand production phenomenon in Petroleum Engineering, fracture flow in Mining Engineering and fracture process in a variety of engineering disciplines. Copyright © 2016 John Wiley & Sons, Ltd.     

Experimental identification of CO2–water–rock interactions caused by sequestration of CO2 in Westphalian and Buntsandstein sandstones of the Campine Basin (NE-Belgium)

Geological sequestration of CO₂ is one of the options studied to reduce greenhouse gas emissions. Although the feasibility of this concept is proven, apart from literature data on modelling still little is known about the CO₂–water–rock interactions induced by CO₂-injection.To evaluate the effect of CO₂–water–rock interactions on three sandstone aquifers in NE-Belgium an experimental setup was built. Eighteen experiments were performed in which sandstones were exposed to supercritical CO₂. CO₂–water–rock interactions were deduced from the evolution of aqueous concentrations of 25 species and a thorough characterisation of the sandstones before and after treatment. The results show that dissolution of ankerite/dolomite and Al-silicates could enhance porosity/permeability. The observed precipitation of end-member carbonates could increase storage capacity if it exceeds carbonate dissolution. Precipitation of the latter and of K-rich clays as observed, however, can hamper the injection.     

Studying the effect of non‐spherical micro‐particles on Hoek–Brown strength parameter mi using numerical true triaxial compressive tests

The strength parameter m_i in the Hoek–Brown strength criterion is empirical and was developed by trial and error. To better understand the fundamental relationship between m_i and the physical characteristics of intact rock, this paper presents a systematic study of m_i by representing intact rock as a densely packed cemented particle material and simulating its mechanical behavior using particle flow modeling. Specifically, the three‐dimensional particle flow code (PFC3D) was used to conduct numerical true triaxial compression tests on intact rock and to investigate the effect of non‐spherical micro‐particle parameters on m_i. To generate numerical intact rock specimens containing non‐spherical micro‐particles, a new genesis process was proposed, and a specific loop algorithm was used based on the efficiency of the process and the acceptability of generated specimens. Four main parameters—number, aspect ratio, size, and shape—of non‐spherical micro‐particles were studied, and the results indicated that they all have great effect on m_i. The strength parameter m_i increases when the number, aspect ratio, or size is larger or the shape becomes more irregular, mainly as a result of the higher level of interlocking between particles. This confirms the observations from engineering experience and laboratory experiments. To simulate the right strength parameter m_i, it is important to use appropriate non‐spherical micro‐particles by controlling these four parameters. This is further demonstrated by the simulation of two widely studied rocks, Lac du Bonnet granite and Carrara marble. Copyright © 2014 John Wiley & Sons, Ltd.     

Discrete element method analysis of non‐coaxial flow under rotational shear

This study focuses on non‐coaxial flow behavior of cohesionless soil undergoing cyclic rotational shear, with a special interest in the effects of particle‐scale characteristics. To this end, we perform a series of 2D discrete element simulations with various particle shapes, inter‐particle coefficient of friction, initial density, and stress ratios. The validity and efficacy of the numerical model is established by systematically comparing numerical simulation results with existing laboratory testing results. Such comparison shows that the numerical simulations are capable of capturing mechanical behavior observed in laboratory testing under rotational shear. We further demonstrate and quantify a strong yet simple relationship between the deviatoric part of the normalized strain increment and the non‐coaxial angle, denoted by and ψ, respectively. This quantitative correlation between ψ and is independent of applied stress ratio, initial and current void ratio, and the number of cycles applied, but dependent on the principal stress orientation and particle‐scale characteristics. At the same , specimens with higher inter‐particle friction angle or smaller particle aspect ratio show greater non‐coaxial angles. A simple model is able to fit this ψ‐ relationship well, which provides a useful relationship that can be exploited in developing constitutive models for rotational shearing. Copyright © 2014 John Wiley & Sons, Ltd.     

Non‐coaxiality and stress–dilatancy rule in granular materials: FE investigation within micro‐polar hypoplasticity

This paper deals with FE investigations of shear localization in dilatant granular bodies. The calculations were carried out with a hypoplastic constitutive law enhanced by micro‐polar terms to properly model the shear zone evolution. The behaviour of an initially medium dense sand specimen with very smooth and very rough horizontal boundaries was analyzed during a plane strain compression test. A stochastic distribution of the initial void ratio was assumed to be spatially correlated. Attention was focused on the non‐coaxiality of the directions of the principal strain increments and principal stresses in the shear zone and on the stress–dilatancy rule. Copyright © 2008 John Wiley & Sons, Ltd.     

Facies model of a mixed clastic–carbonate,wave‐dominated open‐coast tidal flat (Tithonian–Berriasian,north‐east Spain)

Detailed logging and analysis of the facies architecture of the upper Tithonian to middle Berriasian Aguilar del Alfambra Formation (Galve sub‐basin, north‐east Spain) have made it possible to characterize a wide variety of clastic, mixed clastic–carbonate and carbonate facies, which were deposited in coastal mudflats to shallow subtidal areas of an open‐coast tidal flat. The sedimentary model proposed improves what is known about mixed coastal systems, both concerning facies and sedimentary processes. This sedimentary system was located in an embayed, non‐protected area of a wide C‐shaped coast that was seasonally dominated by wave storms. Clastic and mixed clastic–carbonate muds accumulated in poorly drained to well‐drained, marine‐influenced coastal mudflat areas, with local fluvial sandstones (tide‐influenced fluvial channels and sheet‐flood deposits) and conglomerate tsunami deposits. Carbonate‐dominated tidal flat areas were the loci of deposition of fenestral‐laminated carbonate muds and grainy (peloidal) sediments with hummocky cross‐stratification. Laterally, the tidal flat was clastic‐dominated and characterized by heterolithic sediments with hummocky cross‐stratification and local tidal sandy bars. Peloidal and heterolithic sediments with hummocky cross‐stratification are the key facies for interpreting the wave (storm) dominance in the tidal flat. Subsidence and high rates of sedimentation controlled the rapid burial of the storm features and thus preserved them from reworking by fair‐weather waves and tides.     

A numerical study of particle motion and two‐phase interaction in aeolian sand transport using a coupled large eddy simulation – discrete element method

Wind‐blown sand movement, considered as a particle‐laden two‐phase flow, was simulated by a new numerical code developed in the present study. The discrete element method was employed to model the contact force between sand particles. Large eddy simulation was used to solve the turbulent atmospheric boundary layer. Motions of sand particles were traced in the Lagrangian frame. Within the near‐surface region of the atmospheric boundary layer, interparticle collisions will significantly alter the velocity of sand. The sand phase is quite dense in this region, and its feedback force on fluid motion cannot be ignored. By considering the interparticle collision and two‐phase interaction, four‐way coupling was achieved in the numerical code. Profiles of sand velocity from the simulations were in good agreement with experimental measurements. The mass flux shows an exponential decay and is comparable to reported experimental and field measurements. The turbulence intensities and shear stress of sand particles were estimated from particle root‐mean‐square velocities. Distributions of slip velocity and feedback force were analysed to reveal the interactions between sand particles and the continuous fluid phase.     

Study of the soil–atmosphere moisture exchanges through convective drying tests in non‐isothermal conditions

This paper deals with the moisture exchanges occurring between soils and the surrounding atmosphere. Convective drying tests are performed on Awans silts at different drying temperatures and air relative humidities in order to reproduce the natural drying conditions. The experiments improve the understanding of the vapour transfers kinetics between the soil samples and the atmosphere. The experimental results are analysed assuming that the transfers take place in a boundary layer existing at the surface of the porous medium. The influence of the thermal conditions on the evaporation is also taken into account. In our model, coupled vapour and energy exchanges are controlled by mass and heat transfer coefficients characterizing the boundary layer. These coefficients are determined from the drying experiments. The modelling of the drying tests in non‐isothermal conditions is performed in order to validate the formulation of the vapour and heat exchanges. The numerical results present a good agreement with the kinetic of the materials desaturation determined during the tests. The analysis of the moisture transport mechanisms into the sample and at the boundary shows that at the beginning of the test, the drying is first achieved by the transport of moisture in its liquid form and its evaporation at the sample outer boundary in contact with the atmosphere. In a second step, vapour diffusion becomes predominant into the sample and it corresponds to the most important decrease of relative humidity. Copyright © 2009 John Wiley & Sons, Ltd.     

The origin of chloritoid – 3‐mica pseudomorph growth in staurolite–muscovite schist,Bangriposi (Eastern India)

At Bangriposi, variable stages in replacement of staurolite by chloritoid – Na–K–Ca mica shimmer aggregates in muscovite schists provides insight into the complex interplay between fluid flow, mass transfer, and dissolution–precipitation during pseudomorph growth. Idioblastic chloritoid growing into mica caps without causing visible deformation, and monomineralic chloritoid veins (up to 300 μm wide) within shimmer aggregates replacing staurolite attest to chloritoid nucleation in fluid‐filled conduits along staurolite grain boundaries and crystallographic planes. The growth of shimmer aggregates initiated along staurolite margins, and advanced inwards into decomposing staurolite along networks of crystallographically controlled fluid‐filled conduits. Coalescence among alteration zones adjacent to channel fills led to dismemberment and the eventual demise of staurolite. Mass balance calculation within a volume‐fixed, silica‐conserved reference frame indicate the shimmer aggregates grew via precipitation from fluids in response to mass transport that led to the addition of H₂O, K₂O, Na₂O and CaO in the reaction zone, and Al₂O₃ was transported outward from the inward‐retreating margin of decomposing staurolite. This aided precipitation of chloritoid in veins and in the outer collars, and as disseminated grains in the shimmer aggregates at mid‐crustal condition (~520 ± 20 °C, 5.5 ± 2.0 kbar). Computation using one‐dimensional transport equation suggests that staurolite decomposition involved advection dominating over diffusive transport; the permeation of externally derived H₂O caused flattening of chemical potential gradients in H₂O and aqueous species, for example, and , computed using the Gibbs method. This suggests that staurolite decomposition was promoted by the infiltration of a large volume of H₂O that flattened existing chemical potential gradients. In the initial stages of replacement, chloritoid super‐saturation in fluid caused preferential nucleation and growth of chloritoid at staurolite grain boundaries and in crystallographic planes. As reaction progressed, further chloritoid nucleation was halted, but chloritoid continued to grow as the 3‐mica aggregates continued to replace the remaining staurolite in situ, while the chloritoid‐compatible elements were transported in the water‐rich phase facilitating continued growth of the existing chloritoid grains.     

Age and Tectonic Setting of Mesothermal Magmatic Hydrothermal Vein‐Type Pb–Zn–(Ag) Mineralization in the Xiaohongshilazi Deposit,Central Jilin Province,Northeast China

The Xiaohongshilazi deposit located in central Jilin Province, Northeast China, is a newly discovered and medium‐scale Pb–Zn–(Ag) deposit with ore reserves of 34,968 t Pb, 100,150 t Zn, and 158 t Ag. Two‐stage mineralization has been identified in this deposit. Stratiform volcanic‐associated massive sulfide (VMS) Pb–Zn mineralization interbedding with the marine volcanic rocks of the Late Carboniferous–Early Permian Daheshen Formation was controlled by the premineralization E–W‐trending faults. Vein‐type Pb–Zn–(Ag) mineralization occurs within or parallel to the granodiorite and diorite porphyries controlled by the major‐mineralization N–S‐trending faults that cut the stratiform mineralization and volcanic rocks. To constrain the age of vein‐type Pb–Zn–(Ag) mineralization and determine the relationship between mineralization and magmatism, we conducted LA–ICP–MS U–Pb dating on zircon from the ore‐bearing granodiorite and diorite porphyries and Rb–Sr dating on metal sulfide. Granodiorite and diorite porphyries yield zircon U–Pb weighted‐mean ²⁰⁶Pb/²³⁸U ages of 203.6 ± 1.8 Ma (Mean Standard Weighted Deviation [MSWD] = 1.8) and 225.6 ± 5.1 Ma (MSWD = 2.3), respectively. Sulfides from four vein‐type ore samples yield a Rb–Sr isochron age of 195 ± 17 Ma (MSWD = 4.0). These results indicate a temporal relationship between the granodiorite porphyry and vein‐type Pb–Zn–(Ag) mineralization. The granodiorite associated with vein‐type mineralization has high SiO₂ (68.99–70.49 wt.%) and Na₂O (3.9–4.2 wt.%; Na₂O/K₂O = 1.07–1.10) concentrations, and A/CNK values of 0.95–1.04; consequently, the intrusion is classified as a high‐K, calc‐alkaline, metaluminous I‐type granite. The granodiorite porphyry is enriched in large‐ion lithophile elements (e.g. Rb, Th, U, and K) and light REE and is depleted in high‐field‐strength elements (e.g. Nb, Ta, P, and Ti) and heavy REE, indicating that it represents a subduction‐related rock that formed at an active continental margin. Furthermore, the granodiorite porphyry has Mg# values of 31–34, indicating a lower crustal source. Based on petrological and geochemical features, we infer that the ore‐bearing granodiorite porphyry was derived from the partial melting of the lower crust. In summary, mineralization characteristics, cross‐cutting relationships, geochronological data, and regional tectonic evolution indicate that the region was the site of VMS Pb–Zn mineralization that produced stratiform orebodies within the Late Carboniferous–Early Permian marine volcanic rocks of the Daheshen Formation, followed by mesothermal magmatic hydrothermal vein‐type Pb–Zn–(Ag) mineralization associated with granodiorite porphyry induced by the initial subduction of the Paleo‐Pacific Plate beneath the Eurasia Plate during the Late Triassic–Early Jurassic.     

Lateral and vertical juxtaposition of matrix‐rich and matrix‐poor lithologies caused by particle settling in mixed mud–sand deep‐marine sediment suspensions

Sandy sedimentary rocks rich in detrital matrix (>10% silt/clay) have long been recognized in the ancient sedimentary record, and nowhere more commonly than in deep‐marine turbidite systems. Despite this, their depositional mechanisms remain poorly understood, in part because these rocks, which are enriched in fine‐grained sediment, are often poorly exposed in outcrop or are confined to observation in core. Matrix‐rich strata in the Neoproterozoic Windermere Supergroup, in contrast, are very well‐exposed and show systematic changes in lithofacies over distances of several tens to a few hundreds of metres along‐strike. Notably, these strata are observed in both basin floor and continental slope deposits, suggesting that their occurrence and systematic lithological arrangement is related to mechanistic, rather than palaeogeographic, controls. Specifically, the facies transect consists of structureless, clayey sandstone that transforms along‐strike to a two‐layer deposit with the development of an upper, planar‐based, markedly more matrix‐rich layer. Further along‐strike, the basal clayey sandstone thins and eventually pinches out, leaving only the (upper) sandy claystone layer, which in turn thins along‐strike and then pinches out. These systematic changes in lithology, but more specifically the distribution of clay, is interpreted to form a depositional continuum related to particle settling in a horizontally advecting, high concentration particle suspension formed along the margins of an avulsion‐related high‐energy turbulent suspension.     

The P–T–X(fluid) evolution of meta‐anorthosites in the Eastern Granulites,Tanzania

Meta‐anorthosite bodies are typical constituents of the Neoproterozoic Eastern Granulites in Tanzania. The mineral assemblage (and accessory components) is made up of clinopyroxene, garnet, amphibole; scapolite, epidote, biotite, rutile, titanite, ilmenite and quartz. Within the feldspar‐rich matrix (70–90% plagioclase), mafic domains with metamorphic corona textures were used for P–T calculations. Central parts of these textures constitute high‐Al clinopyroxene – which is a common magmatic mineral in anorthosites – and is therefore assumed to be a magmatic relict. The clinopyroxene rims have a diopsidic composition and are surrounded by a garnet corona. Locally the pyroxene is surrounded by amphibole and scapolite suggesting that a mixed CO₂–H₂O fluid was present during their formation. Thermobarometric calculations give the following conditions for the metamorphic peak of the individual meta‐anorthosite bodies: Mwega: 11–13 kbar, 850–900 °C; Pare Mountains: 12–14 kbar, 850–900 °C; Uluguru Mountains: 12–14 kbar, 850–900 °C. The P–T evolution of these bodies was modelled using pseudosections. The amount and composition of the metamorphic fluid and <0.5 mol.% fluid in the bulk composition is sufficient to produce fluid‐saturated assemblages at 10 kbar and 800 °C. Pseudosection analysis shows that the corona textures most likely formed under fluid undersaturated conditions or close to the boundary of fluid saturation. The stabilities of garnet and amphibole are dependent on the amount of fluid present during their formation. Mode isopleths of these minerals change their geometry drastically between fluid‐saturated and fluid‐undersaturated assemblages. The garnet coronae developed during isobaric cooling following the metamorphic peak. The cooling segment is followed by decompression as indicated by the growth of amphibole and plagioclase. The estimated of the metamorphic fluid is ～0.3–0.5. Although the meta‐anorthosites have different formation ages (Archean and Proterozoic) they experienced the same Pan‐African metamorphic overprint with a retrograde isobaric cooling path. Similar P–T evolutionary paths are known from the hosting granulites. The presented data are best explained by a tectonic model of hot fold nappes that brought the different aged anorthosites and surrounding rocks together in the deep crust followed by an isobaric cooling history.     

Three dimensional simulation of fluid flow in X‐ray CT images of porous media

A numerical scheme is developed in order to simulate fluid flow in three dimensional (3‐D) microstructures. The governing equations for steady incompressible flow are solved using the semi‐implicit method for pressure‐linked equations (SIMPLE) finite difference scheme within a non‐staggered grid system that represents the 3‐D microstructure. This system allows solving the governing equations using only one computational cell. The numerical scheme is verified through simulating fluid flow in idealized 3‐D microstructures with known closed form solutions for permeability. The numerical factors affecting the solution in terms of convergence and accuracy are also discussed. These factors include the resolution of the analysed microstructure and the truncation criterion. Fluid flow in 2‐D X‐ray computed tomography (CT) images of real porous media microstructure is also simulated using this numerical model. These real microstructures include field cores of asphalt mixes, laboratory linear kneading compactor (LKC) specimens, and laboratory Superpave gyratory compactor (SGC) specimens. The numerical results for the permeability of the real microstructures are compared with the results from closed form solutions. Copyright © 2004 John Wiley & Sons, Ltd.     

Mesozoic to Cenozoic tectono‐metamorphic history of the South Pamir–Hindu Kush (Chitral,NW Pakistan): Insights from phase equilibria modelling,and garnet–monazite petrochronology

The Karakoram–Hindu Kush–Pamir and adjacent Tibetan plateau belt comprise a series of Gondwana‐derived crustal fragments that successively accreted to the Eurasian margin in the Mesozoic as the result of the progressive Tethys ocean closure. These domains provide unique insights into the thermal and structural history of the Mesozoic to Cenozoic Eurasian plate margin, which are critical to inform the initial boundary conditions (e.g. crustal thickness, structure and thermo‐mechanical properties) for the subsequent development of the large and hot Tibetan–Himalaya orogen, and the associated crustal deformation processes. Using a combination of microstructural analyses, thermobarometry modelling and U–Th–Pb monazite and Lu–Hf garnet geochronology, the study reappraises the metamorphic history of exposed mid‐crustal metapelites in the Chitral region of the South Pamir–Hindu Kush (NW Pakistan). This study also demonstrates that trace elements in monazite (especially Y and Dy), combined with thermodynamical modelling and Lu–Hf garnet dating, provides a powerful integrated toolbox for constraining long‐lived and polyphased tectono‐metamorphic histories in all their spatial and temporal complexity. Rocks from the Chitral region were progressively deformed and metamorphosed at sub‐ and supra‐solidus conditions through at least four distinct episodes from the Mesozoic to the Cenozoic. Rocks were first metamorphosed at ~400–500°C and ~0.3 GPa in the Late Triassic–Early Jurassic (210–185 Ma), likely in response to the accretion of the Karakoram during the Cimmerian orogeny. Pressure and temperature subsequently increased by ~0.3 GPa and 100°C in the Early‐ to Mid Cretaceous (140–80 Ma), coinciding with the intrusion of calcalkaline granitic plutons across the Karakoram and Pamir regions. This event is interpreted as the record of crustal thickening and the development of a proto‐plateau within the Eurasian margin due to a long‐lived episode of slab flattening in an Andean‐type margin. Peak metamorphism was reached in the Late Eocene–Early Oligocene (40–30 Ma) at conditions of 580–600°C and ~0.6 GPa and 700–750°C and 0.7–0.8 GPa for the investigated staurolite schists and sillimanite migmatites respectively. This crustal heating up to moderate anatexis likely resulted in the underthrusting of the Indian plate after a NeoTethyan slab‐break off or to the Tethyan Himalaya–Lhasa microcontinent collision and subsequent oceanic slab flattening. Near‐isothermal decompression/exhumation followed in the Late Oligocene (28–23 Ma) as marked by a pressure decrease in excess of ~0.1 GPa. This event was coeval with the intrusion of the 24 Ma Garam Chasma leucogranite. This rapid exhumation is interpreted to be related to the reactivation of the South Pamir–Karakoram suture zone during the ongoing collision with India. The findings of this study confirm that significant crustal shortening and thickening of the south Eurasian margin occurred during the Mesozoic in an accretionary‐type tectonic setting through successive episodes of terrane accretions and probably slab flattening, transiently increasing the coupling at the plate interface. Moreover, they indicate that the south Eurasian margin was already hot and thickened prior to Cenozoic collision with India, which has important implications for orogen‐scale strain‐accommodation mechanisms.     

Investigation of influence of particle characteristics on the non‐coaxiality of anisotropic granular materials using DEM

As a result of deposition process and particle characteristics, granular materials can be inherently anisotropic. Many researchers have strongly suggested that the inherent anisotropy is the main reason for the deformation non‐coaxiality of granular materials. However, their relationships are not unanimous because of the limited understanding of the non‐coaxial micro‐mechanism. In this study, we investigated the influence of inherent anisotropy on the non‐coaxial angle using the discrete element method. Firstly, we developed a new discrete element method approach using rough elliptic particles and proposed a novel method to produce anisotropic specimens. Secondly, the effects of initial specimen density and particle characteristics, such as particle aspect ratio A _m, rolling resistance coefficient β , and bedding plane orientation δ , were examined by a series of biaxial tests and rotational principal axes tests. Findings from the numerical simulations are summarized as follows: (1) the peak internal friction angle ? _p and the non‐coaxial angle i both increase with the initial density, A _m and β , and they both increase initially and then decrease with δ in the range of 0–90°; (2) among the particle characteristics, the influence of A _m is the most significant; and (3) for anisotropic specimens, the non‐coaxial angle can be calculated using the double slip and rotation rate model. Then, an empirical formula was proposed based on the simulation results to depict the relationship between the non‐coaxial angle and the particle characteristics. Finally, the particle‐scale mechanism of non‐coaxiality for granular materials was discussed from the perspective of energy dissipation. Copyright © 2016 John Wiley & Sons, Ltd.