Experimental study and constitutive modelling of elasto‐plastic damage in heat‐treated mortar

This study investigates the effect of a heat‐treatment upon the thermo‐mechanical behaviour of a model cement‐based material, i.e. a normalized mortar, with a (w/c) ratio of 0.5. First, a whole set of varied experimental results is provided, in order to either identify or validate a thermo‐mechanical constitutive model, presented in the second paper part. Experimental responses of both hydraulic and mechanical behaviour are given after different heating/cooling cycling levels (105, 200, 300, 400^°C). The reference state, used for comparison purposes, is taken after mass stabilization at 60^°C. Typical uniaxial compression tests are provided, and original triaxial deviatoric compressive test responses are also given. Hydraulic behaviour is identified simultaneously to triaxial deviatoric compressive loading through gas permeability K_gas assessment. K_gas is well correlated with volumetric strain evolution: gas permeability increases hugely when ε_v testifies of a dilatant material behaviour, instead of contractile from the test start. Finally, the thermo‐mechanical model, based on a thermodynamics approach, is identified using the experimental results on uniaxial and triaxial deviatoric compression. It is also positively validated at residual state for triaxial deviatoric compression, but also by using a different stress path in lateral extension, which is at the origin of noticeable plasticity. Copyright © 2009 John Wiley & Sons, Ltd.     

From micron-sized needle-shaped hydrates to meter-sized shotcrete tunnel shells: micromechanical upscaling of stiffness and strength of hydrating shotcrete

Knowledge on the stresses in shotcrete tunnel shells is of great importance, as to assess their safety against severe cracking or failure. Estimation of these stresses from 3D optical displacement measurements requires shotcrete material models, which may preferentially consider variations in the water–cement and aggregate–cement ratios. Therefore, we employ two representative volume elements within a continuum micromechanics framework: the first one relates to cement paste (with a spherical material phase representing cement clinker grains, needle-shaped hydrate phases with isotropically distributed spatial orientations, a spherical water phase, and a spherical air phase; all being in mutual contact), and the second one relates to shotcrete (with phases representing cement paste and aggregates, whereby aggregate inclusions are embedded into a matrix made up by cement paste). Elasticity homogenization follows self-consistent schemes (at the cement paste level) and Mori–Tanaka estimates (at the shotcrete level), and stress peaks in the hydrates related to quasi-brittle material failure are estimated by second-order phase averages derived from the RVE-related elastic energy. The latter permits upscaling from the hydrate strength to the shotcrete strength. Experimental data from resonant frequency tests, ultrasonics tests, adiabatic tests, uniaxial compression tests, and nanoindentation tests suggest that shotcrete elasticity and strength can be reasonably predicted from mixture- and hydration-independent elastic properties of aggregates, clinker, hydrates, water, and air, and from strength properties of hydrates. At the structural level, the micromechanics model, when combined with 3D displacement measurements, predicts that a decrease of the water–cement ratio increases the safety of the shotcrete tunnel shell.     

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.     

A New Three–Dimensional Superstructure in Bafertisite

A new superstructure was found in bafertisite [(Ba0.98Na0.02)1.00(Fe1.71Mn0.26Mg0.01)1.98 TiO[(Si1.82Ti0.04Al0.03Cr0.01)1.90O7](OH1.40F0.53Cl0.03)1.96] from Donghai County, Jiangsu Province, China. The occurrence of the superstructure reflections were observed by single crystal diffraction using a SMAR APEX CCD. The a*, b*and c* axis directions revealed extra weak reflection spots of the superstructure. The apparent 2a, 2b and 2c superstructure is monoclinic with unit cell a＝10.6502(15)?, b＝13.7233(19)?, c＝21.6897(3)?, α＝90o, β＝94.698(3)o, γ＝90o,space group Cm,Z=16. If c* extra weak reflections are ignored, the secondary supercell gave a cell a＝10.6548(15)?, b＝13.7284(19)?, c＝11.6900(17)?, α＝90o, β＝112.322(28)o, γ＝90o,space group Cm,Z=8. The basic subcell was obtained by ignoring all extra weak reflection spots and gave: a＝5.3249(17)?, b＝6.8669(22)?, c＝10.8709(36)?, α＝90o, β＝94.740(62)o, γ＝90o,space P21/m,Z=2. The superstructure has been refined to R = 0.063 for 7805 [R(int) = 0.0266] unique reflections I>2δ(I). The structure consists of an octahedra (O) sheet sandwiched between two heteropolyhedral (H) sheets. These sheets consist of Ti–octahedra and twin tetrahedral disilicate groups [Si2O7]. The O sheet comprises (Fe,Mg)O4 octahedra. The large Ba cation is located in the interlayer area. The refined structure shows Fe, Mg are partly ordered. The shifting of the TiO6 octahedron and SiO4 tetrahedron sites in the sheet may be a consequence of the superstructure.     

Evidence for high temperature and 18O‐enriched fluids in the Arab‐D of the Ghawar Field,Saudi Arabia

Using the clumped isotope method, the temperature of dolomite and calcite formation and the oxygen isotopic composition (δ¹⁸O_w) of the diagenetic fluids have been determined in a core taken from the Arab‐D of the Ghawar field, the largest oil reservoir in the world. These analyses show that while the dolomites and limestones throughout the major zones of the reservoir recrystallized at temperatures between ca 80°C and 100°C, the carbonates near the top of the reservoir formed at significantly lower temperatures (20 to 30°C). Although the δ¹⁸O values of the diagenetic fluids show large variations ranging from ca <0‰ to ca +8‰, the variations exhibit consistent downhole changes, with the highest values being associated with the portion of the reservoir with the highest permeability and porosity. Within the limestones, dolomites and dolomites associated with the zone of high permeability, there are statistically significant different trends between the δ¹⁸O_w values and recrystallization temperature. These relationships have different intercepts suggesting that fluids with varying δ¹⁸O_w values were involved in the formation of dolomite and limestone compared to the formation of dolomite associated with the zone of high permeability. These new data obtained using the clumped isotope technique show how dolomitization and recrystallization by deep‐seated brines with elevated δ¹⁸O_w values influence the δ¹⁸O values of carbonates, possibly leading to erroneous interpretations unless temperatures can be adequately constrained.     

Settlement‐time behaviour of granular embankments

Creep settlements are the main cause of deterioration of road pavement and impervious elements of dams, and therefore a method to calculate them is needed. Viscoelastic models (e.g. the standard linear solid) have been chosen to represent the creep of granular materials (Figure 1). Finite element calculations show that quasi‐oedometric conditions exist near the centre of embankments. Explicit expressions for one‐dimensional viscoelastic settlements of an embankment during and after construction have been obtained for any loading law and drawn for a linear load. The three viscoelastic parameters, E_o, R_c and T_r can be determined through laboratory or field testing, and the results can be adjusted by using settlement records. Good agreement has been found between measured and calculated settlements at several dams. Copyright © 2000 John Wiley & Sons, Ltd.     

Petrogenesis and geotectonic setting of early Svecofennian arc cumulates in the Roslagen area,east‐central Sweden

Several intrusions of ultrabasic to basic composition occur in the Roslagen area of east‐central Sweden in close spatial and temporal association with the surrounding 1.90–1.87 Ga old early orogenic Svecofennian granitoids. An imprecise Sm‐Nd WR errorchron yields an age of 1895 ± 71 Ma. In spite of the penetrative deformation in the granitoids, the basic–ultrabasic rocks mostly appear undeformed and largely preserve magmatic textures with plagioclase, olivine (in some rock types), orthopyroxene and clinopyroxene, and amphibole as major constituents. The plagioclase is typically very anorthitic (ca. An₉₀). The Roslagen intrusions range in composition from primitive to evolved (Mg# 80 to 49) but contain only 40–50 wt% SiO₂. Many samples are highly elevated in Al₂O₃ (up to 30 wt%), CaO (up to 16 wt%) and Sr (up to 800 ppm), with strongly positive Eu and Sr anomalies, in line with being plagioclase cumulates. Although masked by cumulus effects, the relative trace element contents indicate a volcanic arc signature. The initial Nd isotope composition is homogeneously ‘mildly depleted’, with ε_Nd of +0.3 to +1.1, and the initial Sr isotope composition ‘mildly enriched’, with ε_Sr of +8 to +15. Non‐cumulus rocks with small Eu and Sr anomalies can be used to deduce the composition of the parental magma. This LILE‐ and LREE‐enriched and HFSE‐depleted high‐alumina basalt magma, with Mg# of ca. 50–60 and Ca# of ca. 80, most likely formed by partial melting of mantle material, enriched by fluids in a subduction environment, at 1.9 Ga. The cumulate rocks apparently crystallized from a somewhat more evolved water‐rich magma with Mg# of ca. 40. Crystallization was followed by the development of late‐magmatic to post‐magmatic coronas between olivine and plagioclase in the presence of H₂O‐rich fluids. The subduction‐related setting would make these intrusions Palaeoproterozoic counterparts of Alaskan‐type ultramafic intrusions, but they differ from those in being plagioclase enriched, possibly reflecting different levels of exposure. Copyright © 2012 John Wiley & Sons, Ltd.     

Metabolic effects on stable carbon isotopic composition of freshwater bivalve shell Corbicula fluminea

The stable isotopic composition of the bivalve shell has been widely used to reconstruct the pa-laeo-climate and palaeo-environment. The climatic and environmental significance of carbon isotopic composition of the bivalve shell is still in dispute, and incorporation of metabolic carbon can obscure carbon isotope records of dis-solved inorganic carbon. This study deals with freshwater bivalve, Corbicula fluminea aragonite shell. The results indicated that the δ13C values of bivalve shells deposited out of equilibrium with the host water and showed an onto-genic decrease, indicating that there are metabolic effects and more metabolic carbon is incorporated into larger shells. The proportion of metabolic carbon of shells varies between 19.8% and 26.8%. However, δ13CS can still be used as qualitative indicators of δ13CDIC and environmental processes that occurred during shell growth.     

Internally consistent data for sulphur‐bearing phases and application to the construction of pseudosections for mafic greenschist facies rocks in Na2O–CaO–K2O–FeO–MgO–Al2O3–SiO2–CO2–O–S–H2O

The Holland and Powell internally consistent data set version 5.5 has been augmented to include pyrite, troilite, trov (Fe_0.875S), anhydrite, H₂S, elemental S and S₂ gas. Phase changes in troilite and pyrrhotite are modelled with a combination of multiple end‐members and a Landau tricritical model. Pyrrhotite is modelled as a solid solution between hypothetical end‐member troilite (trot) and Fe_0.875S (trov); observed activity–composition relationships fit well to a symmetric formalism model with a value for w_trot?trov of ?3.19 kJ mol^?1. The hypothetical end‐member approach is required to compensate for iron distribution irregularities in compositions close to troilite. Mixing in fluids is described with the van Laar asymmetric formalism model with a_ij values for H₂O–H₂S, H₂S–CH₄ and H₂S–CO₂ of 6.5, 4.15 and 0.045 kJ mol^?1 respectively. The derived data set is statistically acceptable and replicates the input data and data from experiments that were not included in the initial regression. The new data set is applied to the construction of pseudosections for the bulk composition of mafic greenschist facies rocks from the Golden Mile, Kalgoorlie, Western Australia. The sequence of mineral assemblages is replicated successfully, with observed assemblages predicted to be stable at X(CO₂) increasing with increasing degree of hydrothermal alteration. Results are compatible with those of previous work. Assemblages are insensitive to the S bulk content at S contents of less than 1 wt%, which means that volatilization of S‐bearing fluids and sulphidation are unlikely to have had major effects on the stable mineral assemblage in less metasomatized rocks. The sequence of sulphide and oxide phases is predicted successfully and there is potential to use these phases qualitatively for geobarometry. Increases in X(CO₂) stabilized, in turn, pyrite–magnetite, pyrite–hematite and anhydrite–pyrite. Magnetite–pyrrhotite is predicted at temperatures greater than 410 °C. The prediction of a variety of sulphide and oxide phases in a rock of fixed bulk composition as a function of changes in fluid composition and temperature is of particular interest because it has been proposed that such a variation in phase assemblage is produced by the infiltration of multiple fluids with contrasting redox state. The work presented here shows that this need not be the case.     

The tectono‐metamorphic evolution of the very low‐grade hangingwall constrains two‐stage gneiss dome formation in the Montagne Noire (Southern France)

The Montagne Noire in the southernmost French Massif Central is made of an ENE‐elongated gneiss dome flanked by Palaeozoic sedimentary rocks. The tectonic evolution of the gneiss dome has generated controversy for more than half a century. As a result, a multitude of models have been proposed that invoke various tectonic regimes and exhumation mechanisms. Most of these models are based on data from the gneiss dome itself. Here, new constraints on the dome evolution are provided based on a combination of very low‐grade petrology, K–Ar geochronology, field mapping and structural analysis of the Palaeozoic western Mont Peyroux and Faugères units, which constitute part of the southern hangingwall of the dome. It is shown that southward‐directed Variscan nappe‐thrusting (D₁) and a related medium‐P metamorphism (M₁) are only preserved in the area furthest away from the gneiss dome. The regionally dominant pervasive tectono‐metamorphic event D₂/M₂ largely transposes D₁ structures, comprises a higher metamorphic thermal gradient than M₁ (transition low‐P and medium‐P metamorphic facies series) and affected the rocks between c. 309 and 300 Ma, post‐dating D₁/M₁ by more than 20 Ma. D₂‐related fabrics are refolded by D₃, which in its turn, is followed by dextral‐normal shearing along the basal shear zone of both units at c. 297 Ma. In the western Mont Peyroux and Faugères units, D₂/M₂ is largely synchronous with shearing along the southern dome margin between c. 311 and 303 Ma, facilitating the emplacement of the gneiss dome into the upper crust. D₂/M₂ also overlaps in time with granitic magmatism and migmatization in the Zone Axiale between c. 314 and 306 Ma, and a related low‐P/high‐T metamorphism at c. 308 Ma. The shearing that accompanied the exhumation of the dome therefore was synchronous with a peak in temperature expressed by migmatization and intrusion of melts within the dome, and also with the peak of metamorphism in the hangingwall. Both, the intensity of D₂ fabrics and the M₂ metamorphic grade within the hangingwall, decrease away from the gneiss dome, with grades ranging from the anchizone–epizone boundary to the diagenetic zone. The related zonation of the pre‐D₃ metamorphic field gradients paralleled the dome. These observations indicate that D₂/M₂ is controlled by the exhumation of the Zone Axiale, and suggest a coherent kinematic between the different crustal levels at some time during D₂/M₂. Based on integration of these findings with regional geological constraints, a two‐stage exhumation of the gneiss dome is proposed: during a first stage between c. 316 and 300 Ma dome emplacement into the upper crust was controlled by dextral shear zones arranged in a pull‐apart‐like geometry. The second stage from 300 Ma onwards was characterized by northeast to northward extension, with exhumation accommodated by north‐dipping detachments and hangingwall basin formation along the northeastern dome margin.     

Non‐linear consolidation analysis of soil with variable compressibility and permeability under cyclic loadings

In this paper, a simple semi‐analytical method has been developed to solve the one‐dimensional non‐linear consolidation problems by considering the changes of compressibility and permeability of the soil layer, subjected to complicated time‐dependent cyclic loadings at the ground surface. The solution presented here takes into account e ～ lg k_v and e ～ lg σ′ linear responses. With c_k the slope of the e ～ lg k_v line and c_c as the slope of the e ～ lg σ′ line, the identified parameter c_c/c_k is found to control the rate of consolidation. Using the solutions obtained, some diagrams are prepared and the relevant behaviours of one‐dimensional non‐linear consolidation of saturated soft soil under cyclic loadings are discussed. The method in this paper does not require any special data; conventional oedometer data can be used. Therefore, the method is particularly efficient and convenient for engineering practice. Copyright © 2006 John Wiley & Sons, Ltd.     

Analytical approach for time‐dependent groundwater inflow into shield tunnel face in confined aquifer

Prediction of time‐dependent groundwater inflow into a shield tunnel is a significant task facing engineers. Published literature shows that there is no available method with which to predict time‐dependent groundwater inflow into a tunnel. This paper presents a prediction approach for time‐dependent groundwater inflow into a tunnel in both anisotropic and isotropic confined aquifers. The proposed solution can predict groundwater inrush from the tunnel cutting face. To obtain the time‐dependent groundwater flow quantity, the concept of a horizontal‐well pumping test based on the theory of a point source is adopted. Multiple factors, eg, drawdown, thickness of aquifer, conductivities, and specific storage, are taken into account. Both groundwater inflow to the cross section of a tunnel face in the y‐z plane and total tunnel inflow are obtained. Based on the proposed approach, the time‐dependent groundwater inflow to a tunnel can be classified as either a uniform or non‐uniform flow. The proposed approach is applied to analyse groundwater inflow of 2 field cases: (1) Metro line No. 7, Guangzhou City and (2) an underground tunnel in Huizhou, Guangdong Province. Results show that the proposed method can predict the measured values, and drawdown‐related curves are also derived. In addition, the calculated results also reveal that the effect of hydraulic conductivity k_z on the total groundwater inflow differs from that of hydraulic conductivities k_x and k_y and the thickness of the aquifer.     

Minerals at high pressure. Mechanics of compression from quantum mechanical calculations in a case study: the beryl (Al<Subscript>4</Subscript>Be<Subscript>6</Subscript>Si<Subscript>12</Subscript>O<Subscript>36</Subscript>)

The Bader topological analysis has been applied to ab initio computed electron densities of beryl, in order to clarify its mechanism of compression. Full structural optimization and total energy (E) calculations were performed at different cell volumes (V _c). The pressure at each volume and the equation of state were estimated from the first and second derivatives of the resultant E(V _c) curve. The total (negative) potential energy of the crystal, sum of both attractive and repulsive electrostatic terms, was found to systematically decrease (i.e., it moved to more negative values) up to the highest pressure considered (28.4 GPa), indicating that interelectronic and internuclear repulsions are not the only terms controlling the compressibility, at least in the pressure range investigated. Electronic kinetic energy increases as the cell volume is reduced, leading to a parallel increase of the total energy. Both structure at equilibrium and compressibility are therefore due to the balance between the opposing kinetic and potential energy terms. The Bader theory has been used to identify the topological atoms within the structure and to calculate their properties, with particular attention to the forces driving the structural relaxation at high pressure. On a qualitative basis, the obtained results are expected to be transferable to the discussion of compressibility of other mineral phases.     

Molecular Structure of Kerogen in the Longmaxi Shale: Insights from Solid State NMR,FT‐IR,XRD and HRTEM

Kerogen plays an important role in shale gas adsorption, desorption and diffusion. Therefore, it is necessary to characterize the molecular structure of kerogen. In this study, four kerogen samples were isolated from the organic-rich shale of the Longmaxi Formation. Raman spectroscopy was used to determine the maturity of these kerogen samples. High-resolution transmission electron microscopy (HRTEM), 13C nuclear magnetic resonance (13C NMR) , X-ray diffraction (XRD) and Fourier transform infrared (FT-IR) spectroscopy were conducted to characterize the molecular structure of the shale samples. The results demonstrate that VReqv of these kerogen samples vary from 2.3% to 2.8%, suggesting that all the kerogen samples are in the dry gas window. The macromolecular carbon skeleton of the Longmaxi Formation kerogen is mainly aromatic (fa’=0.56). In addition, the aromatic structural units are mainly composed of naphthalene (23%), anthracene (23%) and phenanthrene (29%). However, the aliphatic structure of the kerogen macromolecules is relatively low (fal*+falH=0.08), which is presumed to be distributed in the form of methyl and short aliphatic chains at the edge of the aromatic units. The oxygen-containing functional groups in the macromolecules are mainly present in the form of carbonyl groups (fac=0.23) and hydroxyl groups or ether groups (falO=0.13). The crystallite structural parameters of kerogen, including the stacking height (Lc=22.84 ?), average lateral size (La=29.29 ?) and interlayer spacing (d002=3.43 ?), are close to the aromatic structural parameters of anthracite or overmature kerogen. High-resolution transmission electron microscopy reveals that the aromatic structure is well oriented, and more than 65% of the diffractive aromatic layers are concentrated in the main direction. Due to the continuous deep burial, the longer aliphatic chains and oxygen-containing functional groups in the kerogen are substantially depleted. However, the ductility and stacking degree of the aromatic structure increases during thermal evolution. This study provides quantitative information on the molecular structure of kerogen samples based on multiple research methods, which may contribute to an improved understanding of the organic pores in black shale.     

Nonlinear analysis of NATM tunnel construction with the boundary element method

This paper presents a novel approach to the simulation of NATM tunnel construction using the Boundary Element Method (BEM) as principal numerical method. This new approach has the advantage that only the excavation surface, the possible plastic zones and the tunnel lining have to be discretised. The whole rock mass is represented by the BEM whereas the Finite Element Method (FEM) is used to represent the tunnel lining only. Thus, a general coupling strategy for coupling three-dimensional boundary elements with shell finite elements (shotcrete) and beam finite elements (steel arches) is presented. To achieve realistic results the effect of hydration of the shotcrete and yielding of the steel arches is considered in the excavation process. Furthermore, the nonlinear rock behaviour is modelled more realistically by using a powerful hierarchical constitutive model which considers a large range of rock materials. The combination of these ideas results in higher user-friendliness and efficiency. Some verification tests and practical applications in tunnelling are presented.     

An approach to estimate Lower Jurassic seawater oxygen‐isotope composition using δ18O and Mg/Ca ratios of belemnite calcites (Early Pliensbachian,northern Spain)

Palaeotemperature estimates from the oxygen‐isotope compositions of belemnites have been hampered by not knowing ancient seawater isotope compositions well enough. We have tackled this problem using Mg/Ca as a proxy for temperature and here, we present a ~2 Ma record of paired Mg/Ca and δ¹⁸O measurements of Jurassic (Early Pliensbachian) belemnites from the Asturian basin as a palaeo‐proxy of seawater oxygen‐isotope composition. From the combined use of the two approaches, we suggest a δ¹⁸O_w composition of about ?0.1‰ for the Jamesoni–Ibex zones. This value may have been increased by about 0.6‰ during the Davoei Zone due to the effect of waters with a different δ¹⁸O_w composition. These findings illustrate the inaccuracy of using a globally homogeneous ice‐free value of δ¹⁸O_w = ?1‰ for δ¹⁸O_carb‐based palaeotemperature reconstructions. Our data suggest that previous palaeotemperatures calculated in the region from δ¹⁸O values of belemnites may have been underestimated as the seawater oxygen isotopic composition could have been higher.     

Secondary Alterations of the Shell Apatite of Discinisca tenuis from Lüderlitz,Namibia

A collection of subfossil specimens of Discinisca tenuis from Lüderlitz, Namibia was studied by means of the X-ray diffraction (XRD) technique. Using the whole-pattern fitting procedure refined by the authors, the unit cell dimensions, crystallite dimensions, and number of strains were detected. Post-mortality alterations in shell apatite are related to mineral component content ranging from 69 to 82% in subfossil shells, as compared to 68% in shells of living species. It has been established that the lattice parameter a decreases from 9.380 to 9.370 Å, while parameter c is less involved during the decomposition of organic matter. The post-mortality alteration is assumed to proceed by the subsequent recrystallization of shell apatite. Consequently, primarily elongated hexagonal prisms (150 × 370 Å) turn to smaller ones (120 × 260 Å), and the number of strains tends to increase.     

Petrogenesis and implications of jadeite‐bearing kyanite eclogite from the Sanbagawa belt (SW Japan)

Jadeite‐bearing kyanite eclogite has been discovered in the Iratsu body of the Sanbagawa belt, SW Japan. The jadeite + kyanite assemblage is stable at higher pressure–temperature (P–T) conditions or lower H₂O activity [a(H₂O)] than paragonite, although paragonite‐bearing eclogite is common in the Sanbagawa belt. The newly discovered eclogite is a massive metagabbro with the peak‐P assemblage garnet + omphacite + jadeite + kyanite + phengite + quartz + rutile. Impure jadeite is exclusively present as inclusions in garnet. The compositional gap between the coexisting omphacite (P2/n) and impure jadeite (C2/c) suggests relatively low metamorphic temperatures of 510–620 °C. Multi‐equilibrium thermobarometry for the assemblage garnet + omphacite + kyanite + phengite + quartz gives peak‐P conditions of ~2.5 GPa, 570 °C. Crystallization of jadeite in the metagabbro is attributed to Na‐ and Al‐rich effective bulk composition due to the persistence of relict Ca‐rich clinopyroxene at the peak‐P stage. By subtracting relict clinopyroxene from the whole‐rock composition, pseudosection modelling satisfactorily reproduces the observed jadeite‐bearing assemblage and mineral compositions at ~2.4–2.5 GPa, 570–610 °C and a(H₂O) >0.6. The relatively high pressure conditions derived from the jadeite‐bearing kyanite eclogite are further supported by high residual pressures of quartz inclusions in garnet. The maximum depth of exhumation in the Sanbagawa belt (~80 km) suggests decoupling of the slab–mantle wedge interface at this depth.     

A new thermodynamic model for sapphirine: calculated phase equilibria in K2O–FeO–MgO–Al2O3–SiO2–H2O–TiO2–Fe2O3

The activity–composition (a–x) relations of sapphirine are re‐evaluated in the light of a recent new internally‐consistent data set of phase end‐members for use in phase equilibria modelling, particularly of ultra‐high‐temperature (UHT) rocks. This is achieved with the aid of relatively oxidized sapphirine+quartz‐bearing granulites from Wilson Lake, Canada. Calculated P–T projections and compatibility diagrams in the K₂O–FeO–MgO–Al₂O₃–SiO₂–H₂O–TiO₂–Fe₂O₃ (KFMASHTO) system are used to illustrate sapphirine+quartz‐bearing phase equilibria in the context of UHT metamorphism. These new a–x relations for sapphirine should allow pseudosection thermobarometry in NCKFMASHTO for estimating peak P–T conditions of sapphirine‐bearing rocks.     

Analytical‐numerical solution for stress distribution around tunnel reinforced by radial fully grouted rockbolts

This paper presents an analytical‐numerical approach to obtain the distribution of stresses and deformations around a reinforced tunnel. The increase in the radial stress of the reinforced tunnel, based on the performance of a bolt, is modeled by a function, which its maximum value is in the vicinity of the bolt periphery and it exponentially decreases in the far distance from the bolt. On the basis of this approach, the shear stiffness between the bolt and the rock mass and the shear stress distribution around the bolt within the rock mass are also analytically obtained. The results are compared with those obtained by the assumption of ‘uniform increase of radial stress’ method, which is made by the previous studies. The analyses show when the bolts' spacing is large, the safety factor must be increased if the ‘uniform increase of radial stress’ method is used for the design. Finally, a procedure is introduced to calculate the non‐equal deformation of the rock mass between the bolts at any radius that can be useful to compute the bending moment in shotcrete layer in New Austrian Tunnelling Method (NATM) approach. Copyright © 2016 John Wiley & Sons, Ltd.