Identification of non‐linear stress–strain–time relationship of soils using genetic algorithm

Recognition of non‐linear constitutive rock/soil model from experimental results is often multi‐modal in the large parameter space. A genetic evolution algorithm is thus proposed for its recognition, including that of structure of the model and coefficients in the model. The structure of the model can be firstly determined according to mechanical mechanism if the mechanism is clearly understood or searched by using evolutionary algorithm. The coefficients to be determined are then searched in global optional space. With the new evolutionary algorithm, the non‐linear stress–strain–time constitutive law to describe strain softening behaviours of diatomaceous soil under consolidated and undrained state was recognized by learning stress–strain–time behaviour of an intact sample under consolidated pressure of σ_c=0.1 MPa and strain velocity of_a=0.175%/min. This model gave reasonable prediction for diatomaceous soils under varying consolidated pressures (0.1–3.5 MPa) and strain velocities (0.0044–1.75%/min). It indicates that the methodology proposed in this paper is robust enough and strongly attractive for recognition of non‐linear constitutive model of soil and rock materials. Copyright © 2002 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.     

Quartz‐in‐garnet and Ti‐in‐quartz thermobarometry: Methodology and first application to a quartzofeldspathic gneiss from eastern Papua New Guinea

Mineral inclusions are ubiquitous in metamorphic rocks and elastic models for host‐inclusion pairs have become frequently used tools for investigating pressure–temperature (P–T) conditions of mineral entrapment. Inclusions can retain remnant pressures () that are relatable to their entrapment P–T conditions using an isotropic elastic model and P–T–V equations of state for host and inclusion minerals. Elastic models are used to constrain P–T curves, known as isomekes, which represent the possible inclusion entrapment conditions. However, isomekes require a temperature estimate for use as a thermobarometer. Previous studies obtained temperature estimates from thermometric methods external of the host‐inclusion system. In this study, we present the first P–T estimates of quartz inclusion entrapment by integrating the quartz‐in‐garnet elastic model with titanium concentration measurements of inclusions and a Ti‐in‐quartz solubility model (QuiG‐TiQ). QuiG‐TiQ was used to determine entrapment P–T conditions of quartz inclusions in garnet from a quartzofeldspathic gneiss from Goodenough Island, part of the (ultra)high‐pressure terrane of Papua New Guinea. Raman spectroscopic measurements of the 128, 206, and 464 cm^?1 bands of quartz were used to calculate inclusion pressures using hydrostatic pressure calibrations (), a volume strain calculation (), and elastic tensor calculation (), that account for deviatoric stress. values calculated from the 128, 206, and 464 cm^?1 bands’ hydrostatic calibrations are significantly different from one another with values of 1.8 ± 0.1, 2.0 ± 0.1, and 2.5 ± 0.1 kbar, respectively. We quantified elastic anisotropy using the 128, 206 and 464 cm^?1 Raman band frequencies of quartz inclusions and stRAinMAN software (Angel, Murri, Mihailova, & Alvaro, 2019,  234 :129–140). The amount of elastic anisotropy in quartz inclusions varied by ~230%. A subset of inclusions with nearly isotropic strains gives an average and of 2.5 ± 0.2 and 2.6 ± 0.2 kbar, respectively. Depending on the sign and magnitude, inclusions with large anisotropic strains respectively overestimate or underestimate inclusion pressures and are significantly different (<3.8 kbar) from the inclusions that have nearly isotropic strains. Titanium concentrations were measured in quartz inclusions exposed at the surface of the garnet. The average Ti‐in‐quartz isopleth (19 ± 1 ppm [2σ]) intersects the average QuiG isomeke at 10.2 ± 0.3 kbar and 601 ± 6°C, which are interpreted as the P–T conditions of quartzofeldspathic gneiss garnet growth and entrapment of quartz inclusions. The P–T intersection point of QuiG and Ti‐in‐quartz univariant curves represents mechanical and chemical equilibrium during crystallization of garnet, quartz, and rutile. These three minerals are common in many bulk rock compositions that crystallize over a wide range of P–T conditions thus permitting application of QuiG‐TiQ to many metamorphic rocks.     

The effect of subduction on the sulphur,carbon and redox budget of lithospheric mantle

Subduction of hydrated lithospheric mantle introduces HO, ferric iron, oxidized carbon and sulphur to the subduction zone system. The fate of these components is poorly known, but is intimately linked to the global geochemical cycles of iron, carbon and sulphur, the genesis of arc‐related ore deposits, the temporal evolution of mantle redox state and subduction‐related earthquakes and magmatism. thermocalc is used to provide first‐order constraints on the effect of subduction zone metamorphism on metamorphic redistribution of iron, carbon, sulphur and water in ultramafic rocks via construction of P?T and T‐X(O) pseudosections with open system calculation of the effect of fluid loss. The calculations replicate observed mineral assemblages in high‐P to low‐T ultramafic rocks at P?T conditions consistent with those suggested by other workers. The results are consistent with open system fluid loss without significant fluid infiltration. Water loss is complete by 850 C, the corresponding depth of fluid loss being consistent with that inferred for earthquakes in subducting slabs. Losses of carbon and sulphur are relatively minor, at around <5% and <1%, respectively, so it is envisaged that most carbon and sulphur subducted in ultramafic lithologies is transported to >5 GPa, below the depths of the source zone for arc volcanoes. Oxygen activity for rocks in closed systems that evolve with a fixed redox budget is calculated to change from ΔFMQ ?1 at 350 C to over ΔFMQ +3 at 850 C. This result emphasizes the need to consider redox budget as well as oxygen activity when the results of experiments performed at fixed oxygen activity relative to some buffer are interpreted in the context of natural systems. In open systems, devolatilization is calculated to increase the redox budget and oxygen activity of the residue via loss of methane and HS at the brucite‐out and serpentine‐out reactions respectively. No fluid‐induced mechanism for oxidation of sub‐arc mantle by transfer of redox budget from hydrated ultramafic lithologies to the overlying sub‐arc mantle was identified, although further thermodynamic data on fluid species such as S are required to confirm this.     

Mineralogy,Fluid Inclusions,and Sulfur Isotopes of the Huanzala Deposits,Peru: Early Skarn and Late Polymetallic Replacement Style Mineralizations

Carbonate‐replacement polymetallic mineralization at the Huanzala deposits (9°51′S, 77°00′W) was conducted in two contrasting stages that occurred in almost the same location. Early‐stage mineralization has a relation with a granodiorite porphyry stock, whereas the late‐stage mineralization is genetically associated with quartz porphyry sills. The early stage involved low to intermediate sulfidation Cu–Zn–(Pb) mineralization associated with metasomatic skarn, and the late stage involved high to intermediate sulfidation Cu–Zn–Pb–(Mn) mineralization associated with hydrothermal alteration characterized by paragonitic sericitization. The orebodies are hosted by steeply dipping (approximately 60°NE) Lower Cretaceous carbonate rocks in a relatively narrow range of approximately 4 km in horizontal extent and less than 1 km in depth. The pathway of the early‐stage brine‐derived fluids (300–>400°C, >33 wt% NaCl equivalent) along a plot of log against 1000/T is best explained by the progressive dual decline of the value and the temperature under rock‐buffering conditions; this decline saw the pathway progress through the stability field of pyrrhotite to reach that of pyrite and promoted a decrease in FeS from 14.5 to 1.6 mol% in the sphalerite. In contrast, an explanation for the pathway of the late‐stage fluids (140–290°C, 3–13 wt% NaCl equivalent) is given by an almost isothermal decline at approximately 270°C, with passing through the stability field of pyrite–bornite to reach that of chalcopyrite, promoting an increase in FeS from 0.1 to 1.6 mol% in the sphalerite, suggesting gas‐buffering conditions. The ore formation pressure records in the fluid inclusions illustrate an approximately 2‐km erosion during the roughly 2‐Myr total lifetime of the hydrothermal system.     

Autogenic incision‐backfilling cycles and lobe formation during the growth of alluvial fans with supercritical distributaries

Autogenic cycles of channelization, terminal deposit formation, channel backfilling and channel abandonment have been observed in the formation of fans and deltas. In subcritical flow, these terminal deposits are characterized as mouth bars that lead to flow bifurcation, backwater and eventual channel backfilling. Similar, although less well characterized, cycles also take place on supercritical subaerial and submarine fans. This study investigates the hydraulics and morphodynamics of autogenic incision and backfilling cycles associated with supercritical distributive channel flow in alluvial fans. The research questions of the study are: (i) how are supercritical autogenic cycles on alluvial fans different from the subcritical cycles; (ii) what are the hydraulic and sediment transport characteristics at the various stages of autogenic feedback cycles; and (iii) what role do the cycles play in the overall fan evolution? These questions are investigated in the laboratory, and emphasis is placed on measuring the hydraulic and topographic evolution of the systems during the cycles. The cycles arise quasi‐periodically under constant water and sediment discharge. Periods of sheet‐like flow are competent to move sediment () but not competent enough to carry the full imposed load. The net result is preferential deposition near the inlet, resulting in fan steepening and an increase in flow competency with time. At a sediment supply to capacity ratio of , the sheet‐like flow is unstable to small erosional events near the inlet, resulting in the collapse of the distributed flow to a strong channelized state. During channelization, a graded () supercritical (Fr > 1) channel develops and transports eroded and fed sediment up to and through the fan front – extending the fan, initiating a lobe shaped deposit and reducing the local slope. The slopes defined by a sheet‐like flow with and channelized flow with set the maximum and minimum slopes on the fan, respectively. Once formed, graded channels act as bypass conduits linking the inlet with the terminal deposit. On average, deposits are up to six channel depths in thickness and have volumes approximately five times that of the excavated channel. The main distinctive characteristics of the supercritical cycles relate to how the flow interacts with the terminal deposit. At the channel to deposit transition, the flow undergoes a weak hydraulic jump, resulting in rapid sedimentation, dechannelization and lateral expansion of the flow, and deposition of any remaining sediment on top of the channel fill and floodplain. This process often caps the channel as the deposit propagates up channel erasing memory of the excavated channel.     

Activity–composition relations for the calculation of partial melting equilibria in metabasic rocks

A set of thermodynamic models is presented that, for the first time, allows partial melting equilibria to be calculated for metabasic rocks. The models consist of new activity–composition relations combined with end‐member thermodynamic properties from the Holland & Powell dataset, version 6. They allow for forward modelling in the system NaO–CaO–KO–FeO–MgO–AlO–SiO–HO–TiO–FeO. In particular, new activity–composition relations are presented for silicate melt of broadly trondhjemitic–tonalitic composition, and for augitic clinopyroxene with Si–Al mixing on the tetrahedral sites, while existing activity–composition relations for hornblende are extended to include KO and TiO. Calibration of the activity–composition relations was carried out with the aim of reproducing major experimental phase‐in/phase‐out boundaries that define the amphibolite–granulite transition, across a range of bulk compositions, at ≤13 kbar.     

Determination of ultimate capacity of driven piles in cohesionless soil: A Multivariate Adaptive Regression Spline approach

The determination of ultimate capacity (Q) of driven piles in cohesionless soil is an important task in geotechnical engineering. This article adopts Multivariate Adaptive Regression Spline (MARS) for prediction Q of driven piles in cohesionless soil. MARS uses length (L), angle of shear resistance of the soil around the shaft (?_shaft), angle of shear resistance of the soil at the tip of the pile (?_tip), area (A), and effective vertical stress at the tip of the pile as input variables. Q is the output of MARS. The results of MARS are compared with that of the Generalized Regression Neural Network model. An equation has been also presented based on the developed MARS. The results show the strong potential of MARS to be applied to geotechnical engineering as a regression tool. Copyright © 2011 John Wiley & Sons, Ltd.     

Genesis of the Xiuwenghala Gold Deposit in the Beishan Orogen,Northwest China: Evidence from Geology,Fluid Inclusion,and H–O–S–Pb Isotopes

The Xiuwenghala gold deposit is located in the Beishan Orogen of the southern Central Asian Orogenic Belt. The vein/lenticular gold orebodies are controlled by Northeast‐trending faults and are hosted mainly in the brecciated/altered tuff and rhyolite porphyry of the Lower Carboniferous Baishan Formation. Metallic minerals include mainly pyrite and minor chalcopyrite, arsenopyrite, galena, and sphalerite, whilst nonmetallic minerals include quartz, chalcedony, sericite, chlorite, and calcite. Hydrothermal alterations consist of silicic, sericite, chlorite, and carbonate. Alteration/mineralization processes comprise three stages: pre‐ore silicic alteration (Stage I), syn‐ore quartz‐chalcedony‐polymetallic sulfide mineralization (Stage II), and post‐ore quartz‐calcite veining (Stage III). Fluid inclusions (FIs) in quartz and calcite are dominated by L‐type with minor V‐type and lack any daughter mineral‐bearing or CO₂‐rich/‐bearing inclusions. From Stages I to III, the FIs homogenized at 240–260°C, 220–250°C, and 150–190°C, with corresponding salinities of 2.9–10.9, 3.2–11.1, and 2.9–11.9 wt.% NaCl eqv., respectively. The mineralization depth at Xiuwenghala is estimated to be relatively shallow (<1 km). FI results indicate that the ore‐forming fluids belong to a low to medium‐temperature, low‐salinity, and low‐density NaCl‐H₂O system. The values decrease from Stage I to III (3.7‰, 1.7–2.4‰, and ?1.7 to 0.9‰, respectively), and a similar trend is found for their values (?104 to ?90‰, ?126 to ?86‰, and ?130 to ?106‰, respectively). This indicates that the fluid source gradually evolved from magmatic to meteoric. δ³⁴S values of the hydrothermal pyrites (?3.0 to 0.0‰; avg. ?1.1‰) resemble those of typical magmatic/mantle‐derived sulfides. Pyrite Pb isotopic compositions (²⁰⁶Pb/²⁰⁴Pb = 18.409–18.767, ²⁰⁷Pb/²⁰⁴Pb = 15.600–15.715, ²⁰⁸Pb^/204Pb = 38.173–38.654) are similar to those of the (sub)volcanic ore host, indicating that the origin of ore‐forming material was mainly the upper crustal (sub)volcanic rocks. Integrating evidence from geology, FIs, and H–O–S–Pb isotopes, we suggest that Xiuwenghala is best classified as a low‐sulfidation epithermal gold deposit.     

Evolution of metamorphic fluid recorded in granulite facies metacarbonate rocks from the middle segment of the Mogok metamorphic belt in central Myanmar

The Mogok metamorphic belt of Palaeogene age, which records subduction‐ and collision‐related events between the Indian and Eurasian plates, lies along the western margin of the Shan plateau in central Myanmar and continues northwards to the eastern Himalayan syntaxis. Reaction textures of clinohumite‐ and scapolite‐bearing assemblages in Mogok granulite facies metacarbonate rocks provide insights into the drastic change in fluid composition during exhumation of the collision zone. Characteristic high‐grade assemblages of marble and calcsilicate rock are clinohumite+forsterite+spinel+phlogopite+pargasite/edenite+calcite+dolomite, and scapolite+diopside+anorthite+quartz+calcite respectively. Calculated petrogenetic grids in CaO–MgO–Al₂O₃–SiO₂–H₂O–CO₂ and subsets of this system were employed to deduce the pressure–temperature–fluid evolution of the clinohumite‐ and scapolite‐bearing assemblages. These assemblages suggest higher temperature (>780–810°C) and [=CO₂/(CO₂+H₂O) >0.17–0.60] values in the metamorphic fluid for the peak granulite facies stage, assuming a pressure of 0.8 GPa. Calcite grains commonly show exsolution textures with dolomite particles, and their reintegrated compositions yield temperatures of 720–880°C. Retrograde reactions are mainly characterized by a reaction zone consisting of a dolomite layer and a symplectitic aggregate of tremolite and dolomite grown between clinohumite and calcite in marble, and a replacement texture of scapolite by clinozoisite in calcsilicate rock. These textures indicate that the retrograde reactions developed under lower temperature (<620°C) and (<0.08–0.16) conditions, assuming a pressure of 0.5 GPa. The metacarbonate rocks share metamorphic temperatures similar to the Mogok paragneiss at the peak granulite facies stage. The values of the metacarbonate rock at peak metamorphic stage are, however, distinctly higher than those previously deduced from carbonate mineral‐free paragneiss. Primary clinohumite, phlogopite and pargasite/edenite in marble have F‐rich compositions, and scapolite in calcsilicate rock contains Cl, suggesting a contrast in the halogen compositions of the metamorphic fluids between these two lithologies. The metamorphic fluid compositions were probably buffered within each lithology, and the effective migration of metamorphic fluid, which would have extensively changed the fluid compositions, did not occur during the prograde granulite facies stage throughout the Mogok metamorphic belt. The lower conditions of the Mogok metacarbonate rocks during the retrograde stage distinctly contrast with higher conditions recorded in metacarbonate rocks from other metamorphic belts of granulite facies. The characteristic low conditions were probably due to far‐ranging infiltration of H₂O‐dominant fluid throughout the middle segment of the Mogok metamorphic belt under low‐amphibolite facies conditions during the exhumation and hydration stage.     

Mineralogy,nucleation and growth of dolomite in the laboratory and sedimentary environment: A review

Dolomite [CaMg(CO₃)₂] forms in numerous geological settings, usually as a diagenetic replacement of limestone, and is an important component of petroleum reservoir rocks, rocks hosting base metal deposits and fresh water aquifers. Dolomite is a rhombohedral carbonate with a structure consisting of an ordered arrangement of alternating layers of Ca²⁺ and Mg²⁺ cations interspersed with anion layers normal to the c‐axis. Dolomite has symmetry, lower than the (CaCO₃) symmetry of calcite primarily due to Ca–Mg ordering. High‐magnesium calcite also has symmetry and differs from dolomite in that Ca²⁺ and Mg²⁺ ions are not ordered. High‐magnesium calcite with near‐dolomite stoichiometry (≈50 mol% MgCO₃) has been observed both in nature and in laboratory products and is referred to in the literature as protodolomite or very high‐magnesium calcite. Many dolomites display some degree of cation disorder (Ca²⁺ on Mg²⁺ sites and vice versa), which is detectable using transmission electron microscopy and X‐ray diffractometry. Laboratory syntheses at high temperature and pressure, as well as studies of natural dolomites show that factors affecting dolomite ordering, stoichiometry, nucleation and growth include temperature, alkalinity, pH, concentration of Mg and Ca, Mg to Ca ratio, fluid to rock ratio, mineralogy of the carbonate being replaced, and surface area available for nucleation. In spite of numerous attempts, dolomite has not been synthesized in the laboratory under near‐surface conditions. Examination of published X‐ray diffraction data demonstrates that assertions of dolomite synthesis in the laboratory under near‐ambient conditions by microbial mediation are unsubstantiated. These laboratory products show no evidence of cation ordering and appear to be very high‐magnesium calcite. Elevated‐temperature and elevated‐pressure experiments demonstrate that dolomite nucleation and growth always are preceded by very high‐magnesium calcite formation. It remains to be demonstrated whether microbial‐mediated growth of very high‐magnesium calcite in nature provides a precursor to dolomite nucleation and growth analogous to reaction paths in high‐temperature experiments.     

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.     

Strong correlation between summer temperature and pollen accumulation rates for Pinus sylvestris,Picea abies and Betula spp. in a high‐resolution record from northern Sweden

Highly resolved pollen spectra analysed from a 47 cm peat monolith recovered from a mire in northern Sweden exhibit climatic sensitivity in the pollen accumulation rates (PAR) of boreal treeline species. Robust temporal control, afforded through multiple AMS radiocarbon dating of the post‐atomic‐bomb‐test period (AD 1961–2002), provides a unique opportunity to compare pollen accumulation rates with the instrumental meteorological record. Strong correlations are observed between summer temperature and PAR for Pinus sylvestris, Picea abies and Betula spp. (excluding B. nana). Despite well constrained, contiguous (‘annual’) sampling, the temporal resolution of the pollen signal preserved within each sample appears to be degraded to ca. 3–5 year resolution. This is likely to reflect processes occurring during peat accumulation and pollen deposition, as well as dating uncertainties and the effects of subsampling. These findings identify limitations to the maximum resolution that may realistically be recovered from the peat archive using high‐resolution sampling protocols and AMS ¹⁴C dating. We also identify the need for additional work to quantify the role of climate on peat accumulation and the resultant impact on assemblage‐based palaeoenvironmental reconstructions within mire sequences. The strongest climate association observed for Picea abies (r = 0.53; n = 36) was extended through the monolith beyond the 42 year period of ‘annual’ sampling and the response successfully correlated with the Bottenviken historical instrumental record to AD 1860. Although only presenting data from a single site, and requiring wider replication, we conclude that for sites close to the ecological limits of tree species, where levels of anthropogenic/non‐climatic forcing on pollen production are low, well‐dated records of PAR may potentially provide a proxy for reconstructing past summer temperature variability. Copyright © 2007 John Wiley & Sons, Ltd.     

Improved rotational hardening rule for cohesive soils and definition of inherent anisotropy

Improved, microfabric‐inspired rotational hardening rules for the plastic potential and bounding surfaces associated with the generalized bounding surface model for cohesive soils are presented. These hardening rules include 2 new functions, f_η and , that improve the simulation of anisotropically consolidated cohesive soils. Three model parameters are associated with the improved hardening rules. A detailed procedure for obtaining suitable values for these parameters is presented. The first 2 parameters affect the simulation of constant stress ratio loading where, because of the presence of f_η, the third parameter is inactive. The second new function, , accelerates the rotation of the plastic potential and bounding surfaces during shearing, which is particularly important for overconsolidated soils tested in extension. This paper also describes the proper manner in which to define the inherent anisotropy. This seemingly straightforward test has rarely been discussed in sufficient detail.     

Discrete element modeling of tool‐rock interaction II: rock indentation

The failure mechanisms induced by a wedge‐shaped tool indenting normally against a rock surface are investigated using the discrete element method (DEM). The main focus of this study is to explore the conditions controlling the transition from a ductile to a brittle mode of failure. The development of a damage zone and the initiation and propagation of a brittle fracture is well captured by the DEM simulations. The numerical results support the conjecture that initiation of brittle fractures is governed by a scaled flaw length Λ, a ratio between the flaw size λ and the characteristic length (where K_Ic is the toughness and σ_c the uniaxial compressive strength). The size of the damage zone agrees well with analytical predictions based on the cavity expansion model. The effects of a far‐field confining stress and the existence of a relief surface near the indenter are also examined.Copyright © 2012 John Wiley & Sons, Ltd.     

On Bagnold's sediment transport equation in tidal marine environments and the practical definition of bedload

Bagnold's sediment transport equation has proved to be important in studying tidal marine environments. This paper discusses three problems concerning Bagnold's transport equation and its practical application:

• 1 Bagnold's suspended-load transport equation and the total-load transport equation with are incorrect from the viewpoint of energy conservation. In these equations the energy loss due to bedload transport has been counted twice. The correct form should be for suspended-load transport and for total-load transport with
• 2 The commonly used Bagnold's transport coefficient K varies as a non-linear function of the dimensionless excess shear stress, which can be represented best by the power law , where the coefficient A and exponent B depend on sediment grain size D. The empirical values of A and B for fine to medium grained sands are determined using Guy et al.'s (1966) flume-experiment data.
• 3 The sediment transport rates predicted from this equation are compared with bedform migration measurements in the flume and the field. This comparison shows that the sediment transport rates measured from bedform migrations are higher than the predicted bedload transport rates, but comparable to the calculated total-load (bedload plus intermittent suspended-load) transport rates. This indicates that bedform migration involves both bedload and intermittent suspended-load transport. As a logical conclusion, bedform migration data should be compared with Bagnold's total-load transport equation rather than with his bedload transport equation. In this respect the term ‘bed material’ might be more appropriate than the term ‘bedload’ for estimating sediment transport rate from bedform migration data.

The sediment transport rates predicted from this modified Bagnold transport equation are in good agreement with field measurements of bedform migration rates in four individual tidal marine environments, which cover a wide range of sediment grain size, flow velocity and bedform conditions (ranging from small ripples, megaripples to sandwaves).     

A novel insight into vertical ground motion modelling in earthquake engineering

Recent observations of failure and damage of buildings and structures under seismic action has led to an increasing interest for an in-depth analysis of the vertical component of site ground motion. In particular, when dealing with saturated soils, the current engineering practice does not usually go beyond the simplified $u$–$p$ formulation of the Biot's equations describing the coupled hydro-mechanical behaviour, thus neglecting some terms of fluid inertial forces, despite the presence of more refined formulations, for example, the $u$–$U$ formulation. Therefore, a theoretical and numerical validation of the $u$–$p$ formulation as compared with the $u$–$U$ formulation is proposed in this work, where the numerical simulations are compared with the analytical solution for the $u$–$p$ formulation, which is also derived and illustrated in this text. The comparison between the two formulations and the analytical solution is provided for different levels of permeability and dynamic actions, which are representative of a wide scenario of site ground properties and seismic hazard in the vertical direction. In particular, the soil response is analysed in terms of acceleration and pore pressure time history, frequency content, acceleration response spectrum, and amplification ratio of acceleration. This study extends the discussion of the limits of applicability of the $u$–$p$ formulation with respect to the rigorous solution of Biot's equations (obtained here with $u$–$U$ formulation) to the context of a complex dynamic regime provided by the vertical components of real earthquake records, and paves the way for further investigations.     

Surface settlement of a finite elastic layer whose modulus increases linearly with depth

An examination has been made of the behaviour of a finite layer of elastic material of constant Poisson's ratio, whose Young's modulus increases linearly with depth, and which rests on a rough rigid base. Values of surface settlement at the corner of a rectangular area of uniform loading are presented for values of Poisson's ratio of \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{1}{2} $\end{document}, \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{1}{3} $\end{document} and 0, and for wide ranges of degree of inhomogeneity and loading breadth to depth ratio.     

Phase equilibria for graphitic metapelite including solution of CO2 in melt and cordierite: implications for dehydration,partial melting and graphite precipitation

When graphite is present, carbon‐bearing species dissolve in the C‐O‐H fluid and lower the activity of water (). Accordingly, metamorphic reactions that involve water, namely dehydration and partial melting reactions, adjust their P–T positions to accommodate the change of . In this modelling study, pseudosections are calculated for graphite‐bearing systems that are either closed or that progressively lose fluid and/or melt. The diagrams incorporate a new model of CO₂ solubility in felsic melts that we derived to be compatible with a recently published melt model. As the result of the lowered in the carbon‐bearing systems, the temperature displacements of the solidus can be as large as 50 °C at low pressures in cordierite‐bearing zones (<4 kbar), but are smaller than 15 °C at mid‐pressure P–T conditions (4–9 kbar). In the supersolidus region, the phase relations among silicate minerals + melt are very close to those in carbon‐free systems. The fluid CO₂ content increases as temperature increases in the supersolidus assemblages. The CO₂‐rich fluid can be stable in granulite facies conditions in an oxidized system. In graphitic systems, melt and/or cordierite dominate the CO₂ budget of high‐grade rocks. During cooling, the fluid that exsolves from such crystalizing melt is CO₂‐rich. In addition to the phase relations, the pseudosections presented in this study enable researchers to quantitatively investigate the evolution of phase modes, including graphite, along specific metamorphic P–T paths. At low pressures in the cordierite stability field, graphite is predicted to precipitate as the pressure increases or temperature decreases in the subsolidus assemblages, or temperature increases in the region of melt + fluid coexistence. On the other hand, the graphite abundance remains nearly constant along the mid‐pressure P–T series, but the graphite mode in the supersolidus region may increase due to residual enrichment if the melt is extracted. The modelling results show that metamorphic processes in closed systems lead to only small changes in graphite mode (a few tenths of a per cent). This strongly suggests that open‐system behaviours are required for large amounts of graphite deposition, including fluid infiltration and mixing or residual enrichment processes in high‐grade rocks. In addition to P–T pseudosections, P/T–X_O diagrams (X_O = O/(H + O) in the fluid) illustrate the thermodynamic features of internal buffering from another perspective, and explore the dependence of phase relations on the externally imposed redox state. If the system is equilibrated with CO₂ or CH₄‐rich infiltrating fluid, the temperature displacements of metamorphic reactions can be larger than 50 °C, compared with carbon‐free systems.     

Numerical determination of the tensile response and the dissipated fracture energy of concrete: role of the mesostructure and influence of the loading rate

At the mesoscopic scale, concrete can be considered as a mix of coarse aggregates with a mortar paste matrix. In this paper, we investigate numerically the influence of aggregates arrangements and loading rate on the tensile response of concrete. Each coarse aggregate is assumed to be circular with six different radiuses following the aggregates size distribution of real gravel. Rate‐independent cohesive elements are used to model failure within the mesostructure. Our results show that the spatial distribution of heterogeneities does not influence the peak strength, while it changes the post‐peak macroscopic response. This implies that our specimen size is large enough for strength computation but that larger mesostructures should be considered to obtain fully reliable toughness predictions. Although the cohesive approach is able to capture the transition from one macro‐crack in quasi‐static to multiple micro‐cracks in fast dynamics, which increases the dissipated fracture energy, our results suggest that the full extent of the high‐rate strengthening of concrete observed experimentally for loading rates greater than 1/s cannot be captured with rate independent constitutive laws.Copyright © 2013 John Wiley & Sons, Ltd.