A general semi-analytical solution for consolidation around an expanded cylindrical and spherical cavity in modified Cam Clay

This paper presents a general semi-analytical solution for undrained cylindrical and spherical cavity expansion in Modified Cam Clay (MCC) and subsequent consolidation. The undrained cylindrical and spherical cavity expansion response in MCC model is obtained through the similarity solution technique. Then, the subsequent consolidation process around the cavity is governed by the classical partial differential equation for consolidation. Finite Difference Method (FDM) is selected for solving the consolidation equation numerically. The proposed semi-analytical solution is validated by comparing the prediction of the dissipations of the pore pressure with Randolph’s closed-form solution for elastic-perfectly plastic soil. Parametric study shows that G₀/p₀′, R and M have significant influence on the cavity wall excess pore pressure dissipation curve, while it is not sensitive to the value of ν′. It is also found that the negative pore pressure generates around the expanded cylindrical and spherical cavity wall during the consolidation process when R > 5 for typical Boston blue clay. The developed solution has potential applications in geotechnical problems, such as the pile foundation, in-situ test, tunnel construction, compaction grouting, and so forth.     

Critical state framework for liquefaction of fine grained soils

A consistent methodology based on the critical state framework to characterize the different regimes of fine-grained soil behavior under earthquake loads is put forward. Shear strength and deformation behavior of soils depend in a major way on the combination of volume and confining stress. Depending on their combination, a soil aggregate may fracture into clastic debris, fail with fault planes, or yield plastically. This characterization of the class of limiting soil behavior is used to analyze the potential for large deformation and liquefaction in fine grained soils. The central piece of the proposed characterization is the (η, LI₅) stability diagram where η = q/p′ and LI₅ = LI + 0.5 log (p′/5). This diagram captures the effects of soil plasticity through liquidity index LI, confinement through mean normal effective stress p′, and shear stress q through the stress ratio η. The three regions of behavior; fracture, fault, and fold/yield are identified. Soils become susceptible to liquefaction when they shift into the fracture zone (LI₅ ≤ 0.4), or if they plot outside of the stable yielding region.Under earthquake loading, the initial soil states will migrate into different regions in the stability diagram depending on their initial location, shear stress increment, and, pore pressure response. The final position of the soil state would dictate the type of limiting behavior expected in the field; fracture, rupture or yield. The final states which fall into the fracture region have the potential for catastrophic failures including “liquefaction”; the ones which fall onto the rupture region would experience the attainment of a peak stress ratio followed by softening along failure planes; the ones in the yield region would continue to yield in a stable manner. The latter two types of deformations while resulting in large deformation may not be of a catastrophic nature. The proposed characterization is used to examine the liquefaction susceptibility of fine grained soils from China, Taiwan, and Turkey. Use of simplified empirical criteria based on parameters such as plasticity index and fines contents may not capture the true nature of the type of undrained limiting behavior of fine grains soils in the field including liquefaction.     

压力控制的圆孔扩张数值模拟分析

受沉积历史的影响,实际工程中土体的初始应力往往呈各向异性,此时传统圆孔扩张理论的假定条件不再成立,故其适用性也受到限制。借助于FLAC有限差分数值软件,建立了以压力为圆孔扩张边界的二维圆孔扩张模型,从圆孔的变形、孔周土屈服范围、圆孔扩张产生的超静孔水压力分布等方面进行分析,获得在初始应力各向异性的条件下压力控制圆孔扩张过程土体响应规律。计算分析结果表明,初始应力各向异性时,压力控制的圆孔扩张孔口径向位移、塑性区分布、超静孔隙水压力影响范围各个方向不相等;塑性区的分布具有明显的方向性,塑性区最大半径位于孔周土体初始大主应力方向上,并且其值比在相同的扩张压力作用下各向同性初始应力条件下的塑性区半径大,因此传统的初始等应力条件下位移控制的圆孔扩张理论用于分析各向异性初始应力的工程是偏于不安全的。     

Bearing of plate geometry and rheology on shallow-focus mega-thrust seismicity with special reference to 26 December 2004 Sumatra event

We propose a model pertaining to the generation of 26th December 2004 off Sumatra mega-event in the backdrop of other similar type earthquakes along subduction zones around the world. Reconstructions of Benioff trajectories through the hypocenters of historical earthquakes including six mega-earthquakes indicate (i) confinement of hypocenters right within the descending lithosphere, and (ii) natural coincidence of foci of the mega-events around the zones of plate flexing. These observations are discussed in detail with special emphasis on the Sumatra margin considering the role of rheological anomaly across the cross-section of the descending lithosphere; yield strength envelope and residual stress accumulation through time. The intraplate origin of shallow mega-thrust earthquakes allowed us to advocate the ‘zone of flexing’ along the profiles of the subducting plates as nodal area for stress concentration. We propose here that at elevated confining pressure and temperature, loading of unidirectional cyclic stress on time-average bending stress enhanced the material yield strength (i.e., strain-hardening), and leads the semi-brittle portion of the lithosphere into near-brittle condition through rheological transformation. Under subsequent rise in neutral surface and increase in compressive stress field, non-coaxial deformation triggered shear failure on 26th December 2004 preferably at the rheological interface between strain-hardened near-brittle layer and deformed ductile layer within the sub-oceanic mantle.A two-stage fracture mechanism viz. a slow (～1.1 km/s) bilateral initiation in an essentially strain-hardened near-brittle domain and a follow-up very rapid progression (3.3 km/s) in the brittle, crustal domain was mainly involved in the generation of 2004 off Sumatra mega-event. Estimation shows an amount of 3.38 × 10²² to 4.50 × 10²² N m seismic moment (M_o) and 8.95–9.03 moment magnitude (M_w) for the southern part of the 1300 km extended rupture i.e. between the North Andaman to the north and the Sumatra at its south. The study necessitates the reassessment of other shallow-focus mega-thrust earthquakes along the subduction margins around the globe.     

Synthesis and characterization of polycrystalline KAlSi3O8 hollandite [liebermannite]: Sound velocities vs. pressure to 13 GPa at room temperature

A polycrystalline specimen of liebermannite [KAlSi₃O₈ hollandite] was synthesized at 14.5 GPa and 1473 K using glass starting material in a uniaxial split-sphere apparatus. The recovered specimen is pure tetragonal hollandite [SG: I4/m] with bulk density of within 98% of the measured X-ray value. The specimen was also characterized by Raman spectroscopy and nuclear magnetic resonance spectroscopy. Sound velocities in this specimen were measured by ultrasonic interferometry to 13 GPa at room T in a uniaxial split-cylinder apparatus using Al₂O₃ as a pressure marker. Finite strain analysis of the ultrasonic data yielded K_S0 = 145(1) GPa, K₀′ = 4.9(2), G₀ = 92.3(3) GPa, G₀′ = 1.6(1) for the bulk and shear moduli and their pressure derivatives, corresponding to V_P0 = 8.4(1) km/s, V_S0 = 4.9(1) km/s for the sound wave velocities at room temperature. These elasticity data are compared to literature values obtained from static compression experiments and theoretical density functional calculations.     

Pressure-induced dehydration of dioptase: A single-crystal X-ray diffraction and Raman spectroscopy study

We present a synchrotron-based, single-crystal X-ray diffraction and Raman spectroscopy study of natural green dioptase (Cu₆Si₆O₁₈·6H₂O) up to ∼30 GPa at room temperature. The lattice parameters of dioptase exhibit continuous compression behavior up to ∼14.5 GPa, whereupon a structural transition is observed. Pressure–volume data below 14.5 GPa were fitted to a second-order Birch–Murnaghan equation of state with V₀ = 1440(2) ų and K₀ = 107(2) GPa, with K₀′ = 4(fixed). The low-pressure form of dioptase exhibits anisotropic compression with axial compressibility β_a > β_c in a ratio of 1.14:1.00. Based on the diffraction data and Raman spectroscopy, the new high-pressure phase could be regarded as a dehydrated form of dioptase in the same symmetry group. Pressure-induced dehydration of dioptase contributes broadly to our understanding of the high-pressure crystal chemistry of hydrous silicates containing molecular water groups.     

Interaction of U(VI) with Äspö diorite: A batch and in situ ATR FT-IR sorption study

Pristine diorite drill cores, obtained from the Äspö Hard Rock Laboratory (HRL, Sweden), were used to study the retention properties of fresh, anoxic crystalline rock material towards the redox-sensitive uranium. Batch sorption experiments and spectroscopic methods were applied for this study. The impact of various parameters, such as solid-to-liquid ratio (2–200 g/L), grain size (0.063–0.2 mm, 0.5–1 mm, 1–2 mm), temperature (room temperature and 10 °C), contact time (5–108 days), initial U(VI) concentration (3 × 10⁻⁹ to 6 × 10⁻⁵ M), and background electrolyte (synthetic Äspö groundwater and 0.1 M NaClO₄) on the U(VI) sorption onto anoxic diorite was studied under anoxic conditions (N₂). Comparatively, U(VI) sorption onto oxidized diorite material was studied under ambient atmosphere (pCO₂ = 10^−3.5 atm). Conventional distribution coefficients, K_d, and surface area normalized distribution coefficients, K_a, were determined. The K_d value for the U(VI) sorption onto anoxic diorite in synthetic Äspö groundwater under anoxic conditions by investigating the sorption isotherm amounts to 3.8 ± 0.6 L/kg which corresponds to K_a = 0.0030 ± 0.0005 cm (grain size 1–2 mm). This indicates a weak U sorption onto diorite which can be attributed to the occurrence of the neutral complex Ca₂UO₂(CO₃)₃(aq) in solution. This complex was verified as predominating U species in synthetic Äspö groundwater by time-resolved laser-induced fluorescence spectroscopy (TRLFS). Compared to U sorption at room temperature under anoxic conditions, U sorption is further reduced at decreased temperature (10 °C) and under ambient atmosphere. The U species in aqueous solution as well as sorbed on diorite were studied by in situ time-resolved attenuated total reflection Fourier-transform infrared (ATR FT-IR) spectroscopy. A predominant sorbing species containing a UO₂(CO₃)₃⁴⁻ moiety was identified. The extent of U sorption onto diorite was found to depend more on the low sorption affinity of the Ca₂UO₂(CO₃)₃(aq) complex than on reduction processes of uranium.     

Characterization of the CO2 fluid adsorption in coal as a function of pressure using neutron scattering techniques (SANS and USANS)

Small angle neutron scattering techniques have been applied to investigate the phase behavior of CO₂ injected into coal and possible changes in the coal pore structure that may result from this injection. Three coals were selected for this study: the Seelyville coal from the Illinois Basin (R_o = 0.53%), Baralaba coal from the Bowen Basin (R_o = 0.67%), and Bulli 4 coal from the Sydney Basin (R_o = 1.42%). The coals were selected from different depths to represent the range of the underground CO₂ conditions (from subcritical to supercritical) which may be realized in the deep subsurface environment. The experiments were conducted in a high pressure cell and CO₂ was injected under a range of pressure conditions, including those corresponding to in-situ hydrostatic subsurface conditions for each coal. Our experiments indicate that the porous matrix of all coals remains essentially unchanged after exposure to CO₂ at pressures up to 200 bar (1 bar = 10⁵ Pa). Each coal responds differently to the CO₂ exposure and this response appears to be different in pores of various sizes within the same coal. For the Seelyville coal at reservoir conditions (16 °C, 50 bar), CO₂ condenses from a gas into liquid, which leads to increased average fluid density in the pores (ρ_pore) with sizes (r) 1 × 10⁵ ≥ r ≥ 1 × 10⁴ Å (ρ_pore ≈ 0.489 g/cm³) as well as in small pores with size between 30 and 300 Å (ρ_pore ≈ 0.671 g/cm³). These values are by a factor of three to four higher than the density of bulk CO₂ (ρ_CO2) under similar thermodynamic conditions (ρ_CO2 ≈ 0.15 g/cm³). At the same time, in the intermediate size pores with r ≈ 1000 Å the average fluid density is similar to the density of bulk fluid, which indicates that adsorption does not occur in these pores. At in situ conditions for the Baralaba coal (35 ^OC, 100 bar), the average fluid density of CO₂ in all pores is lower than that of the bulk fluid (ρ_pore / ρ_CO2 ≈ 0.6). Neutron scattering from the Bulli 4 coal did not show any significant variation with pressure, a phenomenon which we assign to the extremely small amount of porosity of this coal in the pore size range between 35 and 100,000 Å.     

Plio-Quaternary stress states in NE Iran: Kopeh Dagh and Allah Dagh-Binalud mountain ranges

NE Iran, including the Kopeh Dagh and Allah Dagh-Binalud deformation domains, comprises the northeastern boundary of the Arabia–Eurasia collision zone. This study focuses on the evolution of the Plio-Quaternary tectonic regimes of northeast Iran. We present evidence for drastic temporal changes in the stress state by inversion of both geologically and seismically determined fault slip vectors. The inversions of fault kinematics data reveal distinct temporal changes in states of stress during the Plio-Quaternary (since ～ 5 Ma). The paleostress state is characterized by a regional transpressional tectonic regime with a mean N140 ± 10°E trending horizontal maximum stress axis (σ₁). The youngest (modern) state of stress shows two distinct strike-slip and compressional tectonic regimes with a regional mean of N030 ± 15°E trending horizontal σ₁. The change from the paleostress to modern stress states has occurred through an intermediate stress field characterized by a mean regional N trending σ₁. The inversion analysis of earthquake focal mechanisms reveals a homogeneous, transpressional tectonic regime with a regional N023 ± 5°E trending σ₁. The modern stress state, deduced from the youngest fault kinematics data, is in close agreement with the present-day stress state given by the inversions of earthquake focal mechanisms. According to our data and the deduced results, in northeast Iran, the Arabia–Eurasia convergence is taken up by strike-slip faulting along NE trending left-lateral and NNW trending right-lateral faults, as well as reverse to oblique-slip reverse faulting along NW trending faults. Such a structural assemblage is involved in a mechanically compatible and homogeneous modern stress field. This implies that no strain and/or stress partitioning or systematic block rotations have occurred in the Kopeh Dagh and Allah Dagh-Binalud deformation domains. The Plio-Quaternary stress changes documented in this paper call into question the extrapolation of the present-day seismic and GPS-derived deformation rates over geological time intervals encompassing tens of millions of years.     

Hierarchy of earthquakes in the Baikal rift system: implications for lithospheric stress

We investigated space-time lithospheric stress patterns of the Baikal rift system according to the hierarchy of earthquakes using mechanisms of 265 K_P ≥ 10 events recorded from 1950 to 1998 and seismic moments of 802 K_P ≥ 11 events from 1968 to 1994. The lithosphere of the region was confirmed to undergo rifting with mostly normal-slip events, while local areas of frequent strike-slip and reverse motions may record stress heterogeneity. The dominance of rifting, although being evident in the stress dynamics, is unstable, which is indicated by increase in strike-slip and reverse motions to as many as normal slip events in the latest 1980s–earliest 1990s. The lithospheric stress patterns inferred from seismic-moment data are generally consistent with those derived from the classical focal mechanism method. The suggested approach of seismic zoning according to earthquake slip geometry may provide a more reliable background for successful mitigation of seismic hazard in the region.     

Pan-African metamorphic evolution in the southern Yaounde Group (Oubanguide Complex,Cameroon) as revealed by EMP-monazite dating and thermobarometry of garnet metapelites

Garnet-bearing micaschists and paragneisses of the Yaounde Group in the Pan-African Central African Orogenic Belt in Cameroon underwent a polyphase structural evolution with the deformation stages D₁–D₂, D₃ and D₄. The garnet-bearing assemblages crystallized in course of the deformation stage D₁–D₂ which led to the formation of the regional main foliation S₂. In X_Ca–X_Mg coordinates one can distinguish several zonation trends in the garnet porphyroblasts. Zonation trends with increasing X_Mg and variably decreasing X_Ca signalize a garnet growth during prograde metamorphism. Intermineral microstructures provided criteria for local equilibria and a structurally controlled application of geothermobarometers based on cation exchange and net transfer reactions. The syndeformational P–T path sections calculated from cores and rims of garnets in individual samples partly overlap and align along clockwise P–T trends. The P–T evolution started at ～450 °C/7 kbar, passed high-pressure conditions at 11–12 kbar at variable temperatures (600–700 °C) and involved a marked decompression toward 6–7 kbar at high temperatures (700–750 °C). Th–U–Pb dating of metamorphic monazite by electron microprobe (EMP-CHIME method) in eight samples revealed a single period of crystallization between 613 ± 33 Ma and 586 ± 15 Ma. The EMP-monazite age populations between 613 ± 33 Ma enclosed in garnet and 605 ± 12 Ma in the matrix apparently bracket the high temperature–intermediate pressure stage at the end of the prograde P–T path. The younger monazites crystallized still at amphibolite-facies conditions during subsequent retrogression. The Pan-African overall clockwise P–T evolution in the Yaounde Group with its syndeformational high pressure stages and marked pressure variations is typical of the parts of orogens which underwent contractional crustal thickening by stacking of nappe units during continental collision and/or during subduction-related accretionary processes.     

First-principles phase diagram calculations for the system NaCl–KCl: The role of excess vibrational entropy

First principles phase diagram calculations were performed for the system NaCl–KCl. Plane-wave pseudopotential calculations of formation energies were used as a basis for fitting cluster expansion Hamiltonians, both with and without an approximation for the excess vibrational entropy (S_VIB). Including S_VIB dramatically improves the agreement between calculated and experimental phase diagrams: experimentally, the consolute point is {X_C = 0.348, T_C = 765 K}_Exp; without S_VIB, it is {X_C = 0.46, T_C ≈ 1630 K}_Calc; with S_VIB, it is {X_C = 0.43, T_C ≈ 930 K}_Calc.     

Elastic constants of single-crystal Pt measured up to 20 GPa based on inelastic X-ray scattering: Implication for the establishment of an equation of state

Phonon velocities and densities for Pt were measured based on inelastic X-ray scattering from ambient pressure to 20 GPa in order to independently determine its equation of state (EOS). Phonon velocities were determined with sine dispersion relations. C_ij values were obtained by fitting phonon velocities and densities to the Christoffel equation. We found that the obtained C_ijs were in good agreement with previously reported C_ijs at ambient condition. Based on the C_ij values in various conditions, experimental pressures were calculated. The EOS of Pt as a primary pressure scale was determined based on the experimental pressures. We report K’ = 5.17 with fixed K_T = 274.1 GPa and V₀ = 60.360 ų for Vinet EOS. Our scale is in good agreement with several previously published scales based on shock experiments and XRD.     

Geochemistry and U–Pb zircon geochronology of the Alvand plutonic complex in Sanandaj–Sirjan Zone (Iran): New evidence for Jurassic magmatism

This paper presents geochemical, Sr–Nd isotopic, and U–Pb zircon geochronological data on the Alvand plutonic complex in Sanandaj–Sirjan zone (SSZ), Western Iran. The gabbroic rocks show a trend of a calc-alkaline magma suite and are characterized by low initial ⁸⁷Sr/⁸⁶Sr ratios (0.7023–0.7037) and positive εNd(t) values (2.9–3.3), which suggest derivation from a moderately depleted mantle source. Geochemical features of the granites illustrate a high-K calc-alkaline magma series, whereas the leucocratic granitoids form part of a low-K series. Granites have intermediate ⁸⁷Sr/⁸⁶Sr ratios (0.707–0.719) and negative εNd_(t) values (−1.0 to −3.4), while leucocratic granitoids have higher initial ⁸⁷Sr/⁸⁶Sr ratio (0.713–0.714) and more negative εNd_(t) values (−3.5 to −4.5). Potential basement source lithologies for the granites are Proterozoic granites and orthogneisses, and those for the leucocratic granites are plagioclase-rich sources such as meta-arkoses or tonalites. The U–Pb dating results demonstrate that all granitoids were exclusively emplaced during the Jurassic instead of being Cretaceous or younger in age as suggested previously. The pluton was assembled incrementally over c. 10 Ma. Gabbros formed at 166.5 ± 1.8 Ma, granites between 163.9 ± 0.9 Ma and 161.7 ± 0.6 Ma, and leucocratic granitoids between 154.4 ± 1.3 and 153.3 ± 2.7 Ma. Granites and leucocratic granitoids show some A-type affinity. It is concluded that the Alvand plutonic complex was generated in a continental-arc-related extensional regime during subduction of Neo-Tethyan oceanic crust beneath the SSZ. The U/Pb zircon age data, recently corroborated by similar results in the central and southern SSZ, indicate that Jurassic granitoids are more areally extensive in this belt than previously thought.     

Numerical analysis of pile response to open face tunnelling in stiff clay

Three-dimensional (3D) finite element analyses have been performed to study the behaviour of a single pile and 3 × 3 and 5 × 5 pile groups during open face tunnelling in stiff clay. Several governing factors, such as tunnelling-induced ground and pile settlement, axial pile force changes and shear transfer mechanism at the pile–soil interface, have been studied in detail. Tunnelling resulted in the development of pile head settlement larger than the free-field soil surface settlement. In addition, axial force distributions along the pile change substantially due to changes in the shear transfer between the pile and the soil next to the pile, which triggers tunnelling-induced tensile forces in the piles with tunnel advancement. It was found that the relative displacements and the normal stresses at the pile–soil interface drastically affected shear transfer. The extent of slip length along a pile increased as the tunnelling proceeded. The apparent allowable pile capacity was reduced by up to approximately 42% due to the development of tunnelling-induced pile head settlement. Shear stress on the pile was increased for most of the pile depth with tunnel advancement, which was associated with changes in soil stresses and ground deformation, and hence, the axial pile force was gradually reduced with tunnel advancement, indicating the development of tunnelling-induced tensile pile force. The maximum tunnelling-induced tensile force on the pile was approximately 0.33P_a, where P_a is the allowable pile capacity applied to the pile head prior to tunnel excavation. The range affected by tunnelling in the longitudinal direction may be identified as approximately −2D ∼ +(1.5–2.0D), where D is the tunnel diameter, from the pile centre (behind and ahead of the pile axis), in terms of pile settlement and axial pile force changes based on the analysis conditions assumed in the current study. Larger pile head settlements and smaller changes in axial pile forces were computed for piles that were part of groups. It has been found that the serviceability of piles experiencing adjacent tunnelling is more affected by pile settlement than by axial pile force changes, in particular for piles inside groups. The magnitude of the tunnelling-induced excess pore pressure was small and may not substantially affect pile behaviour.     

Dilatant plasticity in high-strain experiments on calcite–muscovite aggregates

Torsion experiments were performed on synthetic aggregates of calcite with a 50% volume of muscovite. The tests were performed at 627–727 °C with a confining pressure of 300 MPa at constant shear strain rates of 3 × 10^?5–3 × 10^?4 s^?1 on cylindrical samples with the starting foliation parallel and perpendicular to the cylinder axis. Both the foliation parallel and the foliation perpendicular experiments show similar stress–strain patterns, with an initial hardening stage followed by significant strain weakening (>60%) before a catastrophic rupture. Microstructural analysis shows that in low-strain experiments calcite grains are intensely twinned while muscovite grains appear slightly bent and kinked. Higher strains promote a segregation of the two phases with calcite forming thin layers of fine, dynamically recrystallized grains, which act as localized shear bands, while muscovite grains keep their original size and rotate assuming a strong shape preferred orientation. This strain localization of the calcite from an initially homogeneous rock produced catastrophic failure at moderate bulk shear strains (γ ～ 3). Localization of the strain first involved ductile deformation to produce a new calcite layering with fine dynamically recrystallized grains along which cavities nucleated. The orientation and kinematics of the cavities are comparable to R1 Riedel structures. All experiments on calcite–muscovite mixtures resulted in heterogeneous strain. In these torsion experiments chemical changes and crystallization of new phases (anorthite and kalsilite) are observed at 627 °C. Whereas, samples hot pressed or deformed in compression at 670 °C did not show such reactions or any localization. The effect of stress-field geometry and pore pressure upon mineral reactions is discussed. It is concluded that deformation-induced heterogeneous phase distributions caused local strength differences initiating strain localization in the calcite–muscovite mixtures, eventually leading to plastic failure.     

Multi-stage metamorphic evolution of retrograde eclogite with a granulite-facies overprint in the Zhaigen area of the North Qinling Belt,China

Retrograde eclogite from the central part of the Qinling Complex, Zhaigen area of the North Qinling Belt, was studied using integrated petrology, mineral chemistry, pseudosection modeling, and geochronology. Microstructures and mineral relationships reveal five metamorphic stages and associated mineral assemblages as follows: (1) pre-peak stage M₁, which is recorded by the inner cores of garnets together with mineral inclusions of clinopyroxene (Cpx₁) + amphibole (Am₁) + plagioclase (Pl₁) ± quartz ± rutile, occurred under conditions of 760–770 °C and 11.4–14.0 kbar; (2) eclogite-facies stage M₂, recorded by garnet cores + relic omphacite (with a high jadeite content up to 31%) + rutile + quartz under conditions of > 16.7 kbar and 679–765 °C; (3) high-pressure granulite-facies stage M₃, characterized by clinopyroxene (Cpx₂) + plagioclase (Pl₂) symplectites under conditions of 14.5–15.6 kbar and 800–850 °C; (4) medium-pressure granulite-facies stage M₄, characterized by the growth of plagioclase + orthopyroxene coronas around garnet under conditions of 8.3–10 kbar and 795–855 °C; and (5) retrogressive amphibolite-facies stage M₅, which is represented by amphibole (Am₃) + plagioclase (Pl₃) kelyphitic rims around garnet at conditions of < 4 kbar and < 620 °C. Based on Laser Raman analysis of mineral inclusions, cathodoluminescence images, in situ trace element concentrations from different domains within zircon grains, and LA-ICP-MS and SHRIMP U–Pb dating, the protolith age of the Zhaigen retrograde eclogite is suggested at 786 ± 10 Ma and the eclogite-facies metamorphic age recorded by metamorphic zircon cores is limited within 501–497 Ma. The retrograde zircon rims display ages of 476–447 Ma and 425 Ma that probably reflect the timing of two stages of retrograde metamorphism, respectively. The mineral assemblages, P–T conditions, and zircon U–Pb data define a clockwise P–T–t path for the retrograde eclogite, suggesting that the Neoproterozoic protolith of the retrograde eclogite might evolved into continental subduction and eclogite-facies metamorphism during 501–497 Ma before undergoing retrograde metamorphism during an initial stage of exhumation to middle–upper crust level at 474–447 Ma and subsequent exhumation to shallow upper crust at ~ 420 Ma.     

Quantitative analysis of the shallow crustal tectonic stress field in China mainland based on in situ stress data

The latest hydraulic fracturing and stress relief measurement data in the Chinese mainland were collected. The total of 3856 data entries are measured at 1474 locations. The measured area covers 75–130°E and 18–47°N, and the depth range varies from surface to 4000 meters depth, which generally includes each active tectonic block of China and each segment of North–South seismic belt. We investigated the tectonic stress field by removing the effect of gravity. For this, we assume lateral constraints and Heim’s rule. The gravity contribution is removed by using the assumption of lateral constraint and Heim’s rule. Our results show: (1) the maximum and the minimum horizontal principal stress σ_H, σ_h and the vertical stress σ_V in the shallow crust of China all increase linearly with depth: σ_H = 0.0229D + 4.738, σ_h = 0.0171D + 1.829, σ_V = 0.0272D. Maximum and minimum horizontal tectonic stress varies as a function of depth D linearly 4.738 < σ_T < 0.0139D + 4.738 and 1.829 < σ_t < 0.0162D + 1.829. The horizontal tectonic differential stress is σ_T − σ_t = 0.0058D + 2.912. (2) The intermediate value of σ_T1 (regression value of tectonic stress inferred from the assumption of lateral constraint at 2000 m depth) changes in different areas, the maximum value of which is 45.6 MPa, while the minimum value of which is 26.8 MPa. Horizontal tectonic differential stress σ_T − σ_t increases linearly with depth and the maximum and minimum of σ_T − σ_t is 25.3 MPa and 13.0 MPa, respectively. In general, the stress magnitude is much higher in western than in eastern China. This indicates that the strong Indo-Eurasian collision dominates the present tectonic stress field in Chinese mainland. (3) Compared with other study regions, the northward crustal compression to the Qinghai-Tibet block is relatively lower in magnitude in the shallow subsurface and higher at deeper depth. (4) The orientations of σ_T in China mainland generally form a radial scattering pattern centered in Tibetan Plateau. From western to eastern China, they rotate gradually clockwise from NS to NNE, NE, NEE, and SE, which is consistent with the result of focal mechanism solutions.     

Fluorite solubility in hydrous haplogranitic melts at 100 MPa

Fluorite is the most common fluoride mineral in magmatic silicic systems and its crystallization can moderate or buffer fluorine concentrations in these settings. We have experimentally determined fluorite solubility and speciation mechanisms in haplogranitic melts at 800–950 °C, 100 MPa and aqueous-fluid saturation. The starting haplogranite compositions: peraluminous (alumina saturation index, ASI = 1.2), subaluminous (ASI = 1.0) and peralkaline (ASI = 0.8) were variably doped with CaO or F₂O₋₁ in the form of stoichiometric mineral or glass mixtures. The solubility of fluorite along the fluorite–hydrous haplogranite binaries is low: 1.054 ± 0.085 wt.% CaF₂ (peralkaline), 0.822 ± 0.076 wt.% (subaluminous) and 1.92 ± 0.15 wt.% (peraluminous) at 800 °C, 100 MPa and 10 wt.% H₂O, and exhibits a minimum at ASI ∼ 1. Fluorite saturation isotherms are strongly hyperbolic in the CaO–F₂O₋₁ space, suggesting that fluorite saturation is controlled by the activity product of CaO and F₂O₋₁, i.e., these components are partially decoupled in the melt structure. The form of fluorite liquidus isotherms implies distinct roles of fluorite crystallization: in Ca-dominant systems, fluorite crystallization is controlled by the fluorine concentration in the melt only and remains nearly independent of calcium contents; in F-rich systems, the crystallization of fluorite is determined by CaO contents and it does not buffer fluorine concentration in the melt. The apparent equilibrium constant, K, for the equilibrium CaO + cF₂O₋₁ = CaF₂ (+ associates) is log K= − (2.449 ± 0.085)·Al₂O₃^exc + (4.902 ± 0.066); the reaction-stoichiometry parameter varies as follows: c= − (0.92 ± 0.11)·Al₂O₃^exc + (1.042 ± 0.084) at 800 °C, 100 MPa and fluid saturation where Al₂O₃^exc are molar percent alumina in excess over alkali oxides. The reaction stoichiometry, c, changes at subaluminous composition: in peralkaline melts, competition of other network modifiers for excess fluorine anions leads to the preferential alkali–F short-range order, whereas in peraluminous compositions, excess alumina associates with calcium cations to form calcioaluminate tetrahedra. The temperature dependence of fluorite solubility is described by the binary symmetric Margules parameter, W = 36.0 ± 1.4 kJ (peralkaline), 39.7 ± 0.5 kJ (subaluminous) and 32.8 ± 0.7 kJ (peraluminous). The strong positive deviations from ideal mixing imply the occurrence of CaF₂–granite liquid–liquid immiscibility at temperatures above 1258 °C, which is consistent with previous experimental data. These experimental results suggest very low solubilities of fluorite in Ca-rich melts, consistent with the lack of fluorine enrichment in peralkaline rhyolites and calc-alkaline batholiths. On the other hand, high CaO concentrations necessary to crystallize fluorite in F-rich peraluminous melts are not observed in nature and thus magmatic crystallization of fluorite in topaz-bearing silicic suites is suppressed. A procedure for calculating fluorite solubility and the liquidus isotherms for a whole-rock composition and temperature of interest is provided.     

Archaean to Palaeoproterozoic high-grade evolution of the Belomorian eclogite province in the Gridino area,Fennoscandian Shield: Geochronological evidence

The Belomorian eclogite province was repeatedly affected by multiple deformation episodes and metamorphism under moderate to high pressure. Within the Gridino area, high pressure processes developed in a continental crust of tonalite–trondhjemite–granodiorite (TTG) affinity that contains mafic pods and dykes, in which products of these processes are most clearly evident. New petrological, geochemical and geochronological data on mafic and felsic rocks, including PT-estimates, mineral chemistry, bulk rock chemistries, REE composition of the rocks and zircons and U–Pb and Lu–Hf geochronology presented in the paper make it possible to reproduce the magmatic and high-grade metamorphic evolution in the study area. In the framework of the extremely long-lasting geologic history recorded in the Belomorian province (3–1.7 Ga), new geochronological data enabled us to define the succession of events that includes mafic dyke emplacement between 2.87 and 2.82 Ga and eclogite facies metamorphism of the mafic dykes between ~ 2.82 and ~ 2.72 Ga (most probably in the time span of 2.79–2.73 Ga). The clockwise PT path of the Gridino association crosses the granulite- and amphibolite-facies PT fields during the time period of 2.72 Ga to 2.64 Ga. A special aspect of this work concerns the superposed subisobaric heating (thermal impact) with an increase in the temperature to granulite facies conditions at 2.4 Ga. Later amphibolite facies metamorphism occurred at 2.0–1.9 Ga. Our detailed geochronological and petrological studies reveal a complicated Mesoarchaean–Palaeoproterozoic history that involved deep subduction of the continental crust and a succession of plume-related events.