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.     

P–T–t estimation of deformation in low‐grade quartz‐feldspar‐bearing rocks using thermodynamic modelling and 40Ar/39Ar dating techniques: example of the Plan‐de‐Phasy shear zone unit (Briançonnais Zone,Western Alps)

Pressure–Temperature–time (P–T–t) estimates of the syn‐kinematic strain at the peak‐pressure conditions reached during shallow underthrusting of the Briançonnais Zone in the Alpine subduction zone was made by thermodynamic modelling and ⁴⁰Ar/³⁹Ar dating in the Plan‐de‐Phasy unit (SE of the Pelvoux Massif, Western Alps). The dated phengite minerals crystallized syn‐kinematically in a shear zone indicating top‐to‐the‐N motion. By combining X‐ray mapping with multi‐equilibrium calculations, we estimate the phengite crystallization conditions at 270 ± 50 °C and 8.1 ± 2 kbar at an age of 45.9 ± 1.1 Ma. Combining this P–T–t estimate with data from the literature allows us to constrain the timing and geometry of Alpine continental subduction. We propose that the Briançonnais units were scalped on top of the slab during ongoing continental subduction and exhumed continuously until collision.     

Metamorphic history of a syn‐convergent orogen‐parallel detachment: The South Tibetan detachment system,Bhutan Himalaya

The South Tibetan detachment system (STDS) in the Himalayan orogen is an example of normal‐sense displacement on an orogen‐parallel shear zone during lithospheric contraction. Here, in situ monazite U(–Th)–Pb geochronology is combined with metamorphic pressure and temperature estimates to constrain pressure–temperature–time (P–T–t) paths for both the hangingwall and footwall rocks of a Miocene ductile component of the STDS (outer STDS) now exposed in the eastern Himalaya. The outer STDS is located south of a younger, ductile/brittle component of the STDS (inner STDS), and is characterized by structurally upward decreasing metamorphic grade corresponding to a transition from sillimanite‐bearing Greater Himalayan sequence rocks in the footwall with garnet that preserves diffusive chemical zoning to staurolite‐bearing Chekha Group rocks in the hangingwall, with garnet that records prograde chemical zoning. Monazite ages indicate that prograde garnet growth in the footwall occurred prior to partial melting at 22.6 ± 0.4 Ma, and that peak temperatures were reached following c. 20.5 Ma. In contrast, peak temperatures were reached in the Chekha Group hangingwall by c. 22 Ma. Normal‐sense (top‐to‐the‐north) shearing in both the hangingwall and footwall followed peak metamorphism from c. 23 Ma until at least c. 16 Ma. Retrograde P–T–t paths are compatible with modelled P–T–t paths for an outer STDS analogue that is isolated from the inner STDS by intervening extrusion of a dome of mid‐crustal material.     

The effective stress concept and the evaluation of changes in pore air pressure under jacketed isotropic compression tests for dry sand based on the 2‐phase porous theory

The effective stress concept for solid‐fluid 2‐phase media was revisited in this work. In particular, the effects of the compressibility of both the pore fluid and the soil particles were studied under 3 different conditions, i.e., undrained, drained, and unjacketed conditions based on a Biot‐type theory for 2‐phase porous media. It was confirmed that Terzaghi effective stress holds at the moment when soil grains are assumed to be incompressible and when the compressibility of the pore fluid is small enough compared to that of the soil skeleton. Then, isotropic compression tests for dry sand under undrained conditions were conducted within the triaxial apparatus in which the changes in the pore air pressure could be measured. The ratio of the increment in the cell pressure to the increment in the pore air pressure, m, corresponds to the inverse of the B value by Bishop and was obtained during the step loading of the cell pressure. In addition, the m values were evaluated by comparing them with theoretically obtained values based on the solid‐fluid 2‐phase mixture theory. The experimental m values were close to the theoretical values, as they were in the range of approximately 40 to 185, depending on the cell pressure. Finally, it was found that the soil material with a highly compressible pore fluid, such as air, must be analyzed with the multi‐phase porous mixture theory. However, Terzaghi effective stress is practically applicable when the compressibilities of both the soil particles and the pore fluid are small enough compared to that of the soil skeleton.     

LP/HT metamorphism as a temporal marker of change of deformation style within the Late Palaeozoic accretionary wedge of central Chile

A Late Palaeozoic accretionary prism, formed at the southwestern margin of Gondwana from Early Carboniferous to Late Triassic, comprises the Coastal Accretionary Complex of central Chile (34–41°S). This fossil accretionary system is made up of two parallel contemporaneous metamorphic belts: a high‐pressure/low temperature belt (HP/LT – Western Series) and a low pressure/high temperature belt (LP/HT – Eastern Series). However, the timing of deformation events associated with the growth of the accretionary prism (successive frontal accretion and basal underplating) and the development of the LP/HT metamorphism in the shallower levels of the wedge are not continuously observed along this paired metamorphic belt, suggesting the former existence of local perturbations in the subduction regime. In the Pichilemu region, a well‐preserved segment of the paired metamorphic belt allows a first order correlation between the metamorphic and deformational evolution of the deep accreted slices of oceanic crust (blueschists and HP greenschists from the Western Series) and deformation at the shallower levels of the wedge (the Eastern Series). LP/HT mineral assemblages grew in response to arc‐related granitic intrusions, and porphyroblasts constitute time markers recording the evolution of deformation within shallow wedge material. Integrated P–T–t–d analysis reveals that the LP/HT belt is formed between the stages of frontal accretion (D₁) and basal underplating of basic rocks (D₂) forming blueschists at c. 300 Ma. A timeline evolution relating the formation of blueschists and the formation and deformation of LP/HT mineral assemblages at shallower levels, combined with published geochronological/thermobarometric/geochemistry data suggests a cause–effect relation between the basal accretion of basic rocks and the deformation of the shallower LP/HT belt. The S₂ foliation that formed during basal accretion initiated near the base of the accretionary wedge at ~30 km depth at c. 308 Ma. Later, the S₂ foliation developed at c. 300 Ma and ~15 km depth shortly after the emplacement of the granitoids and formation of the (LP/HT) peak metamorphic mineral assemblages. This shallow deformation may reflect a perturbation in the long‐term subduction dynamics (e.g. entrance of a seamount), which would in turn have contributed to the coeval exhumation of the nearby blueschists at c. 300 Ma. Finally, ⁴⁰Ar–³⁹Ar cooling ages reveal that foliated LP/HT rocks were already at ~350 °C at c. 292 Ma, indicating a rapid cooling for this metamorphic system.     

Metamorphic evolution of sapphirine‐ and orthoamphibole‐cordierite‐bearing gneiss,Okanogan dome,Washington, USA

Gneiss domes are commonly cored by quartzofeldspathic rocks that provide little information about the pressure–temperature–fluid history of the domes. Three northern Cordilleran migmatite domes (Thor‐Odin and Valhalla/Passmore, British Columbia, Canada; Okanogan, Washington, USA), however, contain Mg–Al‐rich orthoamphibole‐cordierite gneiss as layers and lenses that record metamorphic conditions and pressure–temperature (P–T) path information not preserved in the host migmatite. These Mg–Al‐rich rocks are therefore a valuable archive of metamorphic conditions during dome evolution, although refractory rocks such as these commonly contain reaction textures that may complicate the calculation of metamorphic conditions. In the Okanogan dome, Mg–Al‐rich layers are part of the Tunk Creek unit, which occurs at the periphery of an underlying migmatite domain. Bulk compositional layers (mm‐ to m‐scale) consist of gedrite‐dominated, hornblende‐dominated and biotite‐bearing layers that contain variable amounts of gedrite, hornblende, anorthite, cordierite, spinel, sapphirine, corundum, kyanite, biotite and/or staurolite. The presence of different compositional layers (some with reaction textures, some without) allows systematic analysis of metamorphic history by a combined petrographic and phase equilibrium analysis. Gedrite‐dominated layers containing relict kyanite preserve evidence of the highest‐P conditions; symplectitic and coronal reaction textures around kyanite indicate decompression at high temperature. Gedrite‐dominated layers lacking these reaction textures contain layers of sapphirine and spinel in apparent textural equilibrium and record a later high‐T–low‐P part of the path. Phase equilibria (pseudosection) analysis for layers that lack reaction textures indicates metamorphic conditions of 720–750 °C at a range of pressures (>8 to <4 kbar) following decompression. Elevated crustal temperatures and concordant structural fabrics in the Tunk Creek unit and underlying migmatite domain suggest that the calculated P–T conditions recorded in Tunk Creek rocks were coeval with anatexis, extension, and dome formation in Palaeocene–Eocene time. In contrast to orthoamphibole‐cordierite gneiss in the other Cordilleran domes, the Tunk Creek unit occurs as a discontinuous km‐scale layer rather than as smaller (m‐scale) pods, is more calcic, and lacks garnet. In addition, kyanite did not transform to sillimanite, and spinel commonly occurs as a blocky matrix phase in addition to vermicules in symplectite. These differences, along with the compositional layering, allow an analysis of bulk composition v. tectonic (P–T path) controls on mineral assemblages and textures. Pseudosection modelling of different layers in the Tunk Creek unit provides a basis for understanding the metamorphic history of these texturally complex, refractory rocks and their host gneiss domes, and other such rocks in similar tectonic settings.     

Adsorption Mechanism and Kinetic Characterization of Bituminous Coal under High Temperatures and Pressures in the Linxing‐Shenfu Area

The majority of coalbed methane(CBM) in coal reservoirs is in adsorption states in coal matrix pores. To reveal the adsorption behavior of bituminous coal under high-temperature and high-pressure conditions and to discuss the microscopic control mechanism affecting the adsorption characteristics, isothermal adsorption experiments under hightemperature and high-pressure conditions, low-temperature liquid nitrogen adsorption-desorption experiments and CO2 adsorption experiments were performed on coal samples. Results show that the adsorption capacity of coal is comprehensively controlled by the maximum vitrinite reflectance(Ro, max), as well as temperature and pressure conditions. As the vitrinite reflectance increases, the adsorption capacity of coal increases. At low pressures, the pressure has a significant effect on the positive effect of adsorption, but the effect of temperature is relatively weak. As the pressure increases, the effect of temperature on the negative effect of adsorption gradually becomes apparent, and the influence of pressure gradually decreases. Considering pore volumes of pores with diameters of 1.7-100 nm, the peak volume of pores with diameters 10-100 nm is higher than that from pores with diameters 1.7-10 nm, especially for pores with diameters of 40-60 nm, indicating that pores with diameters of 10-100 nm are the main contributors to the pore volume. The pore specific surface area shows multiple peaks, and the peak value appears for pore diameters of 2-3 nm, indicating that this pore diameter is the main contributor to the specific surface area. For pore diameters of 0.489-1.083 nm, the pore size distribution is bimodal, with peak values at 0.56-0.62 nm and 0.82-0.88 nm. The adsorption capability of the coal reservoir depends on the development degree of the supermicroporous specific surface area, because the supermicroporous pores are the main contributors to the specific pore area. Additionally, the adsorption space increases as the adsorption equilibrium pressure increases. Under the same pressure, as the maximum vitrinite reflectance increases, the adsorption space increases. In addition, the cumulative reduction in the surface free energy increases as the maximum vitrinite reflectance increases. Furthermore, as the pressure increases, the surface free energy of each pressure point gradually decreases, indicating that as the pressure increases, it is increasingly difficult to adsorb methane molecules.     

Petrogenetic relations among titanium‐rich minerals in an anatectic high‐P mafic granulite

The petrogenetic relations among Ti‐rich minerals in high‐grade metabasites is illuminated here through a detailed petrological investigation of an anatectic garnet–clinopyroxene granulite from the Grenville Province, Ontario, Canada containing rutile, titanite and ilmenite in distinct microtextural settings. Garnet porphyroblasts exhibit zoned Ti concentrations (up to 0.15 wt% TiO₂ in their cores), as well as a variety of rutile inclusion types, including clusters of small, variably elongate grains and thin (≤1 μm) oriented needles. Calcite inclusions in garnet, commonly observed surrounding garnet cores containing quartz and clinozoisite, indicate the presence of evolving C–O–H fluids during garnet growth and suggest that the rutile clusters may have formed from subsequent Ti diffusion and rutile precipitation within existing fluid inclusions. Titanite forms large subhedral crystals and typically occurs where the primary garnet–clinopyroxene assemblage is in contact with leucosome containing megacrystic hornblende, silvialitic scapolite and calcic plagioclase. Many titanite crystals exhibit marginal subgrains that correspond with sharp changes in their major and trace element composition, likely related to a dissolution–precipitation or recrystallization process following primary crystallization. Clinopyroxene–ilmenite symplectite coronas surround titanite in most locations, likely forming from reaction with the hornblende‐plagioclase matrix (±fluids/melt). Integration of multi‐equilibria thermobarometry and Zr thermometry in rutile and titanite with phase equilibrium modelling allows definition of a clockwise P–T path evolving to peak pressures of ~1.5 GPa at ~750°C during garnet and rutile growth, followed by peak temperature conditions of ~1.2 GPa and ~820–880°C associated with melt‐present titanite growth, and finally cooling and decompression to regional amphibolite facies conditions (~1.0 GPa and ~750°C) associated with the formation of clinopyroxene–ilmenite symplectites surrounding titanite. P–T pseudosections calculated for the pristine (leucosome‐ and titanite ‐free) metabasite bulk composition reproduce much of the prograde phase relations, but predict rutile as the stable Ti‐rich mineral at the peak thermal conditions associated with melt‐present titanite growth. The P–M(CaO) and T–M(CaO) models show that bulk CaO concentrations have a significant effect on the stability ranges of titanite and rutile. Increased bulk CaO tends to stabilize titanite to higher pressure and temperature at the expense of rutile, with a ≥15% increase in CaO producing the observed titanite‐bearing assemblage at high‐P granulite facies conditions. Thus, the model results are consistent with the textural observations, which suggest that titanite stability is associated with a chemical exchange between the host metabasite and a Ca‐rich melt.     

Numerical analysis of a one‐dimensional infiltration problem in unsaturated soil by a seepage–deformation coupled method

A multiphase coupled elasto‐viscoplastic finite element analysis formulation, based on the theory of porous media, is used to describe the rainfall infiltration process into a one‐dimensional soil column. Using this framework, we have numerically analyzed the generation of pore water pressure and deformations when rainfall is applied to the soil. A parametric study, including rainfall intensity, soil–water characteristic curves, and permeability, is carried out to observe their influence on the changes in pore water pressure and volumetric strain. From the numerical results, it is shown that the generation of pore water pressure and volumetric strain is mainly controlled by material parameters α and n′ that describe the soil–water characteristic curve. A comparison with the laboratory results shows that the proposed method can describe very well the characteristics observed during the experiments of one‐dimensional water infiltration into a layered unsaturated soil column. Copyright © 2010 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.     

A window into the Early to mid‐Cretaceous infrastructure of the Yukon‐Tanana terrane recorded in multi‐stage garnet of west‐central Yukon,Canada

Amphibolite facies metasedimentary schists within the Yukon‐Tanana terrane in the northern Canadian Cordillera reveal a two‐stage, polymetamorphic garnet growth history. In situ U‐Th‐Pb Sensitive High Resolution Ion Microprobe dating of monazite provide timing constraints for the late stages of garnet growth, deformation and subsequent decompression. Distinct textural and chemical growth zoning domains, separated by a large chemical discontinuity, reveal two stages of garnet growth characterized in part by: (i) a syn‐kinematic, inclusion‐rich stage‐1 garnet core; and (ii) an inclusion‐poor, stage‐2 garnet rim that crystallized with syn‐ to post‐kinematic staurolite and kyanite. Phase equilibria modelling of garnet molar and compositional isopleths suggest stage‐1 garnet growth initiated at ~600 °C, 8 kbar along a clockwise P–T path. Growth of the compositionally distinct, grossular‐rich, pyrope‐poor inner portion of the stage‐2 overgrowth is interpreted to have initiated at higher pressure and/or lower temperature than the stage‐1 core along a separate P–T loop, culminating at peak P–T conditions of ~650–680 °C and 9 kbar. Stage‐2 metamorphism and the waning development of a composite transposition foliation (S_T) are dated at c. 118 Ma from monazite aligned parallel to S_T, and inclusions in syn‐ to post‐S_T staurolite and kyanite. Slightly younger ages (c. 112 Ma) are obtained from Y‐rich monazite that occurs within resorbed areas of both stage‐1 and stage‐2 garnet, together with retrograde staurolite and plagioclase. The younger ages obtained from these texturally and chemically distinct grains are interpreted, with the aid of phase equilibria calculations, to date the growth of monazite from the breakdown of garnet during decompression at c. 112 Ma. Evidence for continued near‐isothermal decompression is provided by the presence of retrograde sillimanite, and cordierite after staurolite, which indicates decompression below ~4–5 kbar prior to cooling below ~550 °C. As most other parts of the Yukon‐Tanana terrane were exhumed to upper crustal levels in the Early Jurassic, these data suggest this domain represents a tectonic window revealing a much younger, high‐grade tectono‐metamorphic core (infrastructure) within the northern Cordilleran orogen. This window may be akin to extensional core complexes identified in east‐central Alaska and in the southeastern Canadian Cordillera.     

Neotethys closure history of Anatolia: insights from 40Ar–39Ar geochronology and P–T estimation in high‐pressure metasedimentary rocks

The multiple high‐pressure (HP), low‐temperature (LT) metamorphic units of Western and Central Anatolia offer a great opportunity to investigate the subduction‐ and continental accretion‐related evolution of the eastern limb of the long‐lived Aegean subduction system. Recent reports of the HP–LT index mineral Fe‐Mg‐carpholite in three metasedimentary units of the Gondwana‐derived Anatolide–Tauride continental block (namely the Afyon Zone, the Ören Unit and the southern Menderes Massif) suggest a more complicated scenario than the single‐continental accretion model generally put forward in previous studies. This study presents the first isotopic dates (white mica ⁴⁰Ar–³⁹Ar geochronology), and where possible are combined with P–T estimates (chlorite thermometry, phengite barometry, multi‐equilibrium thermobarometry), on carpholite‐bearing rocks from these three HP–LT metasedimentary units. It is shown that, in the Afyon Zone, carpholite‐bearing assemblages were retrogressed through greenschist‐facies conditions at c. 67–62 Ma. Early retrograde stages in the Ören Unit are dated to 63–59 Ma. In the Kurudere–Nebiler Unit (HP Mesozoic cover of the southern Menderes Massif), HP retrograde stages are dated to c. 45 Ma, and post‐collisional cooling to c. 26 Ma. These new results support that the Ören Unit represents the westernmost continuation of the Afyon Zone, whereas the Kurudere–Nebiler Unit correlates with the Cycladic Blueschist Unit of the Aegean Domain. In Western Anatolia, three successive HP–LT metamorphic belts thus formed: the northernmost Tav?anl? Zone (c. 88–82 Ma), the Ören–Afyon Zone (between 70 and 65 Ma), and the Kurudere–Nebiler Unit (c. 52–45 Ma). The southward younging trend of the HP–LT metamorphism from the upper and internal to the deeper and more external structural units, as in the Aegean Domain, points to the persistence of subduction in Western Anatolia between 93–90 and c. 35 Ma. After the accretion of the Menderes–Tauride terrane, in Eocene times, subduction stopped, leading to continental collision and associated Barrovian‐type metamorphism. Because, by contrast, the Aegean subduction did remain active due to slab roll‐back and trench migration, the eastern limb (below Southwestern Anatolia) of the Hellenic slab was dramatically curved and consequently teared. It therefore is suggested that the possibility for subduction to continue after the accretion of buoyant (e.g. continental) terranes probably depends much on palaeogeography.     

A general viscous‐spring transmitting boundary for dynamic analysis of saturated poroelastic media

A time‐domain viscous‐spring transmitting boundary is presented for transient dynamic analysis of saturated poroelastic media with linear elastic and isotropic properties. The u–U formulation of Biot equation in cylindrical coordinate is adopted in the derivation. By this general viscous‐spring boundary, the effective stress and pore fluid pressure on the truncated boundary of the computational area are replaced by a set of continuously distributed spring and dashpot elements, of which the parameters are defined assuming an infinite permeability and considering the two dilatational waves. Numerical examples demonstrate good absorption of both the two cylindrical dilatational waves by the proposed ‘drained’ boundary. For general two‐dimensional wave propagation problems, acceptable accuracy can still be achieved by setting the proposed boundary relatively far away from the scatter. Numerical comparison shows that the results obtained by using this boundary are more accurate for all permeability values than those by the traditional viscous‐spring or viscous boundaries established for u–U formulation. Copyright © 2015 John Wiley & Sons, Ltd.     

Discriminating between pore‐filling load and bed‐structure load: a new porosity‐based method,exemplified for the river Rhine

Sediments contained in the river bed do not necessarily contribute to morphological change. The finest part of the sediment mixture often fills the pores between the larger grains and can be removed without causing a drop in bed level. The discrimination between pore‐filling load and bed‐structure load, therefore, is of practical importance for morphological predictions. In this study, a new method is proposed to estimate the cut‐off grain size that forms the boundary between pore‐filling load and bed‐structure load. The method evaluates the pore structure of the river bed geometrically. Only detailed grain‐size distributions of the river bed are required as input to the method. A preliminary validation shows that the calculated porosity and cut‐off size values agree well with experimental data. Application of the new cut‐off size method to the river Rhine demonstrates that the estimated cut‐off size decreases in a downstream direction from about 2 to 0·05 mm, covariant with the downstream fining of bed sediments. Grain size fractions that are pore‐filling load in the upstream part of the river thus gradually become bed‐structure load in the downstream part. The estimated (mass) percentage of pore‐filling load in the river bed ranges from 0% in areas with a unimodal river bed, to about 22% in reaches with a bimodal sand‐gravel bed. The estimated bed porosity varies between 0·15 and 0·35, which is considerably less than the often‐used standard value of 0·40. The predicted cut‐off size between pore‐filling load and bed‐structure load (D_c,p) is fundamentally different from the cut‐off size between wash‐load and bed‐material load (D_c,w), irrespective of the method used to determine D_c,p or D_c,w. D_c,w values are in the order of 10^?1 mm and mainly dependent on the flow characteristics, whereas D_c,p values are generally much larger (about 10⁰ mm in gravel‐bed rivers) and dependent on the bed composition. Knowledge of D_c,w is important for the prediction of the total sediment transport in a river (including suspended fines that do not interact with the bed), whereas knowledge of D_c,p helps to improve morphological predictions, especially if spatial variations in D_c,p are taken into account. An alternative to using a spatially variable value of D_c,p in morphological models is to use a spatially variable bed porosity, which can also be predicted with the new method. In addition to the morphological benefits, the new method also has sedimentological applications. The possibility to determine quickly whether a sediment mixture is clast‐supported or matrix‐supported may help to better understand downstream fining trends, sediment entrainment thresholds and variations in hydraulic conductivity.     

Early Last Interglacial palaeoenvironments in the western Baltic Sea: benthic foraminiferal stable isotopes and diatom‐based sea‐surface salinity

Knudsen, K. L., Jiang, H., Kristensen, P., Gibbard, P. L. & Haila, H. 2011: Early Last Interglacial palaeoenvironments in the western Baltic Sea: benthic foraminiferal stable isotopes and diatom‐based sea‐surface salinity. Boreas, 10.1111/j.1502‐3885.2011.00206.x. ISSN 0300‐9483. Stable isotopes from benthic foraminifera, combined with diatom assemblage analysis and diatom‐based sea‐surface salinity reconstructions, are used for the interpretation of changes in bottom‐ and surface‐water conditions through the early Eemian at Ristinge Klint in the western Baltic Sea. Correlation of the sediments with the Eemian Stage is based on a previously published pollen analysis that indicates that they represent pollen zones E2–E5 and span ～3400 years. An initial brackish‐water phase, initiated c. 300 years after the beginning of the interglacial, is characterized by a rapid increase in sea‐surface and sea‐bottom salinity, followed by a major increase at c. 650 years, which is related to the opening of the Danish Straits to the western Baltic. The diatoms allow estimation of the maximum sea‐surface salinity in the time interval of c. 650–1250 years. After that, slightly reduced salinity is estimated for the interval of c. 1250–2600 years (with minimum values at c. 1600–2200 years). This may be related to a period of high precipitation/humidity and thus increased freshwater run‐off from land. Together with a continuous increase in the water depth, this may have contributed to the gradual development of a stratified water column after c. 1600 years. The stratification was, however, particularly pronounced between c. 2600 and 3400 years, a period with particularly high sea‐surface temperature, as well as bottom‐water salinity, and thus a maximum influence of Atlantic water masses. The freshwater run‐off from land may have been reduced as a result of particularly high summer temperatures during the climatic optimum.     

A Method for Rapid Determination of Re and Os Isotope Compositions Using ID‐MC‐ICP‐MS Combined with the Sparging Method

A simple, rapid method for the determination of Re and Os concentrations and isotope compositions using isotope dilution multi‐collector inductively coupled plasma‐mass spectrometry (ID‐MC‐ICP‐MS) combined with Carius tube digestion and sparging introduction of Os was developed. For Os measurement, four channeltron ion counters to detect different Os isotopes were used simultaneously, which led to a drastic reduction in the measurement time. Rhenium isotopes were measured by means of eight Faraday cups with solution nebulisation and an ultrasonic membrane desolvator. The representative ¹⁸⁸Os count rate of an Os standard solution containing 50 pg of total Os was approximately 110000–120000 cps at the onset of measurement; the Re intensity of our in‐house 10 pg g^?1 standard solution reached 1820 V/μg g^?1 with a sample uptake rate of 95–99 μl min^?1. These values indicate that the sensitivity of the method was sufficient even for samples with low Re and Os concentrations, such as chert. As the temporal variations of the amplification efficiency of the ion counters differed from one another, we adopted a sample‐calibrator bracketing method to correct the measured Re and Os isotope ratios. The Re and Os concentrations via the isotope dilution method and the ¹⁸⁷Os/¹⁸⁸Os ratios of two sedimentary rock reference materials (JMS‐2 and JCh‐1) on the basis of the isotope ratios determined by the MC‐ICP‐MS and by negative thermal ionisation mass spectrometry (N‐TIMS) were comparable within their ranges. Based on Os isotope measurement of the IAG reference material [Durham Romil Os (DROsS)], the average difference from the recommended value and precision of Os isotope measurements by the sparging method in combination with multi‐ion‐counters were 0.72% and 0.76% [1RSD (%), n = 29], respectively. The precisions in the ¹⁸⁷Os/¹⁸⁸Os ratios [1RSD (%)] of JMS‐2, JCh‐1 and DROsS were 0.35–0.71, 1.56–3.31 and 0.99–1.28%, respectively, which depended on their Os ion intensities. No systematic difference was observed between the Re and Os geochemical compositions of JCh‐1 and JMS‐2 obtained by means of digestion with inverse aqua regia and CrO₃‐H₂SO₄ solutions, suggesting that either acid solution can be used for the sparging method of sedimentary rock samples. As CrO₃‐H₂SO₄ solution is believed to liberate predominantly the hydrogenous Re and Os fraction from organic‐rich sediment, the sparging method combined with CrO₃‐H₂SO₄ digestion and multi‐ion‐counters in the mass spectrometry is expected to be a powerful tool for reconstructing the secular change in marine Os isotope compositions with high sample throughput.     

Three‐dimensional numerical analysis of concrete‐faced rockfill dam using dual‐mortar finite element method with mixed tangential contact constraints

Concrete‐faced rockfill dam (CFRD) is a popular alternative to traditional dam types in the last two decades. The modelling of CFRD involves complex multi‐body contact and strong geometry and material nonlinearities. We present a numerical approach for the modelling of CFRDs in this paper. Based on the dual‐mortar finite element method, the presented approach considers different parts of rockfill and all concrete slabs as independent deformable continuum. The multi‐body contacts are modelled using Lagrange multipliers with a weak form segment‐to‐segment contact strategy. To alleviate instability induced by strong geometry nonlinearity in the slab–slab contact, we propose a mixed type of constraints for the tangential contact. A general transformation scheme is introduced to simplify the implementation of contact constraints. Three‐dimensional analysis of Tianshengqiao‐1 CFRD is performed. The nonlinear and time‐dependent deformation of the rockfill is considered. We study the influence of the rockfill deformation on the reliability of the concrete face. Three major concerns of the face, that is, the axial compression, the slab–slab separation and the face‐rockfill separation, are discussed in detail. The numerical results are compared with data from in‐situ observation. Copyright © 2016 John Wiley & Sons, Ltd.     

Three‐dimensional nonlinear finite element analysis of pile groups in saturated porous media using a new transmitting boundary

The dynamic behaviour of pile groups subjected to an earthquake base shaking is analysed. An analysis is formulated in the time domain and the effects of material nonlinearity of soil, pile–soil–pile kinematic interaction and the superstructure–foundation inertial interaction on seismic response are investigated. Prediction of response of pile group–soil system during a large earthquake requires consideration of various aspects such as the nonlinear and elasto‐plastic behaviour of soil, pore water pressure generation in soil, radiation of energy away from the pile, etc. A fully explicit dynamic finite element scheme is developed for saturated porous media, based on the extension of the original formulation by Biot having solid displacement (u) and relative fluid displacement (w) as primary variables (u–w formulation). All linear relative fluid acceleration terms are included in this formulation. A new three‐dimensional transmitting boundary that was developed in cartesian co‐ordinate system for dynamic response analysis of fluid‐saturated porous media is implemented to avoid wave reflections towards the structure. In contrast to traditional methods, this boundary is able to absorb surface waves as well as body waves. The pile–soil interaction problem is analysed and it is shown that the results from the fully coupled procedure, using the advanced transmitting boundary, compare reasonably well with centrifuge data. Copyright © 2007 John Wiley & Sons, Ltd.     

Prograde and retrograde metamorphic fabrics – a key for understanding burial and exhumation in orogens (Bohemian Massif)

In the Orlica–?nie?nik Dome (NE Bohemian massif), alternating belts of orthogneiss with high‐pressure rocks and belts of mid‐crustal metasedimentary–metavolcanic rocks commonly display a dominant subvertical fabric deformed into a subhorizontal foliation. The first macroscopic foliation is subvertical, strikes NE–SW and is heterogeneously folded by open to isoclinal folds with subhorizontal axial planes parallel to the heterogeneously developed flat‐lying foliation. The metamorphic evolution of the mid‐crustal metasedimentary rocks involved successive crystallization of chlorite–muscovite–ilmenite–plagioclase–garnet, followed by staurolite‐bearing and then kyanite‐bearing assemblages in the subvertical fabric. This was followed by garnet retrogression, with syntectonic crystallization of sillimanite and andalusite parallel to the shallow‐dipping foliation. Elsewhere, andalusite and cordierite statically overgrew the flat‐lying fabric. With reference to a P–T pseudosection for a representative sample, the prograde succession of mineral assemblages and the garnet zoning pattern with decreasing grossular, spessartine and X_Fe are compatible with a P–T path from 3.5–5 kbar/490–520 °C to peak conditions of 6–7 kbar/～630 °C suggesting burial from 12 to 25 km with increasing temperature. Using the same pseudosection, the retrograde succession of minerals shows decompression to sillimanite stability at ～4 kbar/～630 °C and to andalusite–cordierite stability at 2–3 kbar indicating exhumation from 25 km to around 9–12 km. Subsequent exhumation to ～6 km occurred without apparent formation of a deformation fabric. The structure and petrology together with the spatial distribution of the metasedimentary–metavolcanic rocks, and gneissic and high‐pressure belts are compatible with a model of burial of limited parts of the upper and middle crust in narrow cusp‐like synclines, synchronous with the exhumation of orogenic lower crust represented by the gneissic and high‐pressure rocks in lobe‐shaped and volumetrically more important anticlines. Converging P–T–D paths for the metasedimentary rocks and the adjacent high‐pressure rocks are due to vertical exchanges between cold and hot vertically moving masses. Finally, the retrograde shallow‐dipping fabric affects both the metasedimentary–metavolcanic rocks and the gneissic and high‐pressure rocks, and indicates that the ～15‐km exhumation was mostly accommodated by heterogeneous ductile thinning associated with unroofing of a buoyant crustal root.     

Two formulations for dynamic response of a cylindrical cavity in cross‐anisotropic porous media

Two formulations for calculating dynamic response of a cylindrical cavity in cross‐anisotropic porous media based on complex functions theory are presented. The basis of the method is the solution of Biot's consolidation equations in the complex plane. Employing two groups of potential functions for solid skeleton and pore fluid (each group includes three functions), the u–w formulation of Biot's equations are solved. Difference of these two solutions refers to use of two various potential functions. Equations for calculating stress, displacement and pore pressure fields of the medium are mentioned based on each two formulations. Copyright © 2009 John Wiley & Sons, Ltd.