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1.
In this paper, the effects of specimen size and geometry on the apparent mode I fracture toughness (K c) of an Iranian white marble (Neyriz) are studied. A number of fracture tests were conducted on center-cracked circular disk (CCCD) specimens with different radii to investigate the size effects on K c. The experimental results demonstrate that the apparent fracture toughness increases in bigger specimens. In order to explain the experimental results, the modified maximum tangential stress (MMTS) criterion is used, where higher order terms of the Williams’ series expansion are included in the maximum tangential stress criterion. It is shown that the MMTS criterion provides good estimates for the apparent fracture toughness of Neyriz marble, obtained from fracture tests of edge-cracked triangular specimens. It is, therefore, concluded that the proposed criterion is able to account for the size and geometry effects on the fracture resistance of rocks simultaneously.  相似文献   

2.
The petrography, mineral chemistry and petrogenesis of a sample from the Weissenstein eclogite, Bavaria, Germany, has been investigated. The total mineral assemblage comprises garnet, clinopyroxeneI+II, quartz, amphiboleI+II, rutile, phengite, epidote/allanite, plagioclase, biotite, apatite, pumpellyite, titanite (sphene), zircon, alkali feldspar and calcite. Textural observations combined with geothermobarometry (Fe/Mg distribution between clinopyroxene/garnet and phengite/garnet; jadeite-content of omphacite, Si-content of phengite, and An-content of plagioclase) provide indications of two different stages in the metamorphic evolution of the rock. The main phengitequartz-eclogite mineral equilibration occurred at minimum P=13–17kbar, minimum T=620±50° C; the retrograde symplectite stage (clinopyroxeneII, amphiboleII, biotite, plagioclase) occurred at P total between 12 and 8.5 kbar. Reactions of the symplectite stage are:
  1. phengite (core) + Na2Oaq + CaOaq=phengite (rim) + biotite + plagioclase + K2Oaq + H2O
  2. phengite (core) + clinopyroxeneI + Na2Oaq=phengite (rim + biotite + plagioclase + amphiboleII + SiO2 + K2Oaq + CaOaq + H2O
  3. clinopyroxeneI + SiO2 + K2Oaq + H2O=clinopyroxeneII + plagioclase+amphiboleII + Na2Oaq + CaOaq
The phengite decomposition produces H2O, whereas the clinopyroxene decomposition consumes H2O. The estimated P-T-conditions for the Weissenstein eclogite are in the same order of magnitude as those for other eclogite bodies from the Alps and Caledonides believed to be related to subduction processes.  相似文献   

3.
Numerical and experimental investigation of symmetric fracture bifurcation (Kalthoff, 1972), has shown that for forks with small branch angles α<αc, where αc is approximately 14°, the propagation of the branches tends to enlarge the angle. For forks with larger branch angles, α>αc, the propagation of the branches tends to diminish the angle. Forks with the critical angle αc will propagate in their original direction. Kalthoff theorized that the branch angle changes as a function of KI/KII, where KI and KII are the stress intensity factors for tensile and shear (sliding) modes, respectively, and KI is considerably larger than KII. In this study I test the hypothesis that this fracture mechanic theory applies to the analysis of fault bifurcation in the crust, particularly in cases of rapid fracture.Fractures produced during the 1968 earthquake at the Coyote Creek fault in California are intensively branched and an example of rapid rupture. The angular behaviour of the branching ruptures in eight forks follows Kalthoffs theory unusually well. This implies that fracture at the surface was dominated by the tensile mode. Additional observations that support this implication are: series of prominent ruptures which show openings (of 20–30 mm per rupture), the symmetrical and bilateral forking, the high-intensity and angular shapes of individual branches, the opening of grabens associated with several bifurcations, lack of bifurcation in the southern break of the Coyote Creek fault, and the patterns of en echelon fractures which reflect mixed mode surfacial rupture.Hence, contrary to previous interpretations, according to field evidence and fracture mechanic theory, the fault bifurcation and opening along the Coyote Creek fault are not compatible with local tension caused by the primary shear. Fracture probably occurred by different mechanical modes at depth and at the surface. While faulting may have originated by shear at depth, rupture at the surface was dominated by far-field tension associated with NE-SW extension in South California. The present model predicts the directions of fracture propagation along the fault.  相似文献   

4.
The observed fractal nature of both fault length distributions and earthquake magnitude-frequency distributions suggests that there may be a relationship between the structure of active fault systems and the resulting seismicity. In previous theoretical work, a positive correlation between the exponent D from the fracture length distribution, and the seismic or acoustic emission (AE) b-value has been inferred from a simple dislocation model of the seismic source. Here, we present the first experimental evidence for a correlation between D and b from a series of tensile fracture mechanics tests on crystalline rock, carried out in different environmental conditions, both air-dry and water-saturated, and at ambient temperature and pressure. The microseismic acoustic emissions were monitored during subcritical crack growth under controlled conditions of constant stress intensity, KI, and quantitative analyses of the resulting fracture patterns were carried out on the same specimens. It is found that AE b-values, ranging from 1.0 to 2.3, correlate negatively with the normalized stress intensity KI/KIC, where KIC is the fracture toughness of the specimen. The microcrack length distribution exponent D, ranges from 1.0 to 1.7. Fluid presence has a first-order influence on both the AE and structure produced in these experiments. For experiments at low stress intensity or high fluid content, the activation of the stress corrosion mechanism for KI < KIC leads to a greater relative proportion both of small cracks and of low amplitude acoustic emissions, reflected in higher values of D and b. The exponent D is found to correlate positively with the AE b-value.  相似文献   

5.
华文  董世明  徐积刚 《岩土力学》2016,37(3):753-758
岩石断裂韧度表征其抵抗裂纹起裂和扩展的能力,作为其力学性能的一个重要指标,在岩石力学理论研究与岩体工程应用中有着不可替代的作用。由于岩石结构的复杂性,其破坏形式大多呈现为复合型断裂破坏,研究复合型加载条件下岩石断裂韧度具有重要的意义。为了研究锈岩的断裂力学性能,以便其在建筑工业中得到更为广泛的应用,通过18个中心裂纹圆盘（CSTBD）试件径向受压试验,进行了复合型加载条件下锈岩断裂韧度的试验研究。测得了锈岩在纯I型,纯II型以及复合型加载时的断裂韧度,并将试验结果与基于广义最大周向应力（GMTS）准则的理论值进行了对比分析,结果表明：锈岩的纯I型断裂韧度为1.01 MPa?m0.5,而纯II型断裂韧度为1.51 MPa?m0.5,是纯I型断裂韧度的1.49倍,这与基于GMTS准则的理论值1.34非常接近,而比基于最大周向应力（MTS）准则的理论值0.87大很多。裂纹尖端附近的T应力及断裂过程区裂纹尖端的临界距离rc对岩石类材料的开裂路径以及复合型断裂韧度都有较大的影响。考虑了T应力的广义最大周向应力（GMTS）准则能很好的预测试验结果。  相似文献   

6.
In situ X-ray diffraction measurements of KAlSi3O8-hollandite (K-hollandite) were performed at pressures of 15–27 GPa and temperatures of 300–1,800 K using a Kawai-type apparatus. Unit-cell volumes obtained at various pressure and temperature conditions in a series of measurements were fitted to the high-temperature Birch-Murnaghan equation of state and a complete set of thermoelastic parameters was obtained with an assumed K′300,0=4. The determined parameters are V 300,0=237.6(2) Å3, K 300,0=183(3) GPa, (?K T,0/?T) P =?0.033(2) GPa K?1, a 0=3.32(5)×10?5 K?1, and b 0=1.09(1)×10?8 K?2, where a 0 and b 0 are coefficients describing the zero-pressure thermal expansion: α T,0 = a 0 + b 0 T. We observed broadening and splitting of diffraction peaks of K-hollandite at pressures of 20–23 GPa and temperatures of 300–1,000 K. We attribute this to the phase transitions from hollandite to hollandite II that is an unquenchable high-pressure phase recently found. We determined the phase boundary to be P (GPa)=16.6 + 0.007 T (K). Using the equation of state parameters of K-hollandite determined in the present study, we calculated a density profile of a hypothetical continental crust (HCC), which consists only of K-hollandite, majorite garnet, and stishovite with 1:1:1 ratio in volume. Density of HCC is higher than the surrounding mantle by about 0.2 g cm?3 in the mantle transition zone while this relation is reversed below 660-km depth and HCC becomes less dense than the surrounding mantle by about 0.15 g cm?3 in the uppermost lower mantle. Thus the 660-km seismic discontinuity can be a barrier to prevent the transportation of subducted continental crust materials to the lower mantle and the subducted continental crust may reside at the bottom of the mantle transition zone.  相似文献   

7.
A new synchrotron X-ray diffraction study of chromium oxide Cr2O3 (eskolaite) with the corundum-type structure has been carried out in a Kawai-type multi-anvil apparatus to pressure of 15 GPa and temperatures of 1873 K. Fitting the Birch–Murnaghan equation of state (EoS) with the present data up to 15 GPa yielded: bulk modulus (K 0,T0), 206 ± 4 GPa; its pressure derivative K′0,T , 4.4 ± 0.8; (?K 0,T /?T) = ?0.037 ± 0.006 GPa K?1; a = 2.98 ± 0.14 × 10?5 K?1 and b = 0.47 ± 0.28 × 10?8 K?2, where α 0,T  = a + bT is the volumetric thermal expansion coefficient. The thermal expansion of Cr2O3 was additionally measured at the high-temperature powder diffraction experiment at ambient pressure and α 0,T0 was determined to be 2.95 × 10?5 K?1. The results indicate that coefficient of the thermal expansion calculated from the EoS appeared to be high-precision because it is consistent with the data obtained at 1 atm. However, our results contradict α 0 value suggested by Rigby et al. (Brit Ceram Trans J 45:137–148, 1946) widely used in many physical and geological databases. Fitting the Mie–Grüneisen–Debye EoS with the present ambient and high-pressure data yielded the following parameters: K 0,T0 = 205 ± 3 GPa, K′0,T  = 4.0, Grüneisen parameter (γ 0) = 1.42 ± 0.80, q = 1.82 ± 0.56. The thermoelastic parameters indicate that Cr2O3 undergoes near isotropic compression at room and high temperatures up to 15 GPa. Cr2O3 is shown to be stable in this pressure range and adopts the corundum-type structure. Using obtained thermoelastic parameters, we calculated the reaction boundary of knorringite formation from enstatite and eskolaite. The Clapeyron slope (with \({\text{d}}P/{\text{d}}T = - 0.014\) GPa/K) was found to be consistent with experimental data.  相似文献   

8.
Thermal equation of state of an Al-rich phase with Na1.13Mg1.51Al4.47Si1.62O12 composition has been derived from in situ X-ray diffraction experiments using synchrotron radiation and a multianvil apparatus at pressures up to 24 GPa and temperatures up to 1,900 K. The Al-rich phase exhibited a hexagonal symmetry throughout the present pressure–temperature conditions and the refined unit-cell parameters at ambient condition were: a=8.729(1) Å, c=2.7695(5) Å, V 0=182.77(6) Å3 (Z=1; formula weight=420.78 g/mol), yielding the zero-pressure density ρ0=3.823(1) g/cm3 . A least-square fitting of the pressure-volume-temperature data based on Anderson’s pressure scale of gold (Anderson et al. in J Appl Phys 65:1534–543, 1989) to high-temperature Birch-Murnaghan equation of state yielded the isothermal bulk modulus K 0=176(2) GPa, its pressure derivative K 0 ′ =4.9(3), temperature derivative (?K T /?T) P =?0.030(3) GPa K?1 and thermal expansivity α(T)=3.36(6)×10?5+7.2(1.9)×10?9 T, while those values of K 0=181.7(4) GPa, (?K T /?T) P =?0.020(2) GPa K?1 and α(T)=3.28(7)×10?5+3.0(9)×10?9 T were obtained when K 0 ′ was assumed to be 4.0. The estimated bulk density of subducting MORB becomes denser with increasing depth as compared with earlier estimates (Ono et al. in Phys Chem Miner 29:527–531 2002; Vanpeteghem et al. in Phys Earth Planet Inter 138:223–230 2003; Guignot and Andrault in Phys Earth Planet Inter 143–44:107–128 2004), although the difference is insignificant (<0.6%) when the proportions of the hexagonal phase in the MORB compositions (～20%) are taken into account.  相似文献   

9.
Wadeite-type K2Si4O9 was synthesized with a cubic press at 5.4 GPa and 900 °C for 3 h. Its unit-cell parameters were measured by in situ high-T powder X-ray diffraction up to 600 °C at ambient P. The T–V data were fitted with a polynomial expression for the volumetric thermal expansion coefficient (αT = a 0 + a 1 T), yielding a 0 = 2.47(21) × 10?5 K?1 and a 1 = 1.45(36) × 10?8 K?2. Compression experiments at ambient T were conducted up to 10.40 GPa with a diamond-anvil cell combined with synchrotron X-ray radiation. A second-order Birch–Murnaghan equation of state was used to fit the P–V data, yielding K T = 97(3) GPa and V 0 = 360.55(9) Å3. These newly determined thermal expansion data and compression data were used to thermodynamically calculate the P–T curves of the following reactions: 2 sanidine (KAlSi3O8) = wadeite (K2Si4O9) + kyanite (Al2SiO5) + coesite (SiO2) and wadeite (K2Si4O9) + kyanite (Al2SiO5) + coesite/stishovite (SiO2) = 2 hollandite (KAlSi3O8). The calculated phase boundaries are generally consistent with previous experimental determinations.  相似文献   

10.
A lower amphibolite Alpine shear zone from the Fibbia metagranite (Gotthard Massif, Central Alps) has been studied to better understand the parameters controlling strain localization in granitic rocks. The strain gradient on the metre‐scale shows an evolution from a weakly deformed metagranite (QtzI–KfsI–AbI–BtI ± PlII–ZoI–PhgI–Grt) to a fine banded ultramylonite (QtzII–KfsII–AbII–PlII–BtII–PhgII ± Grt–ZoII). Strain localization is coeval with dynamic recrystallization of the quartzofeldspathic matrix and a modal increase in mica, at the expense of K‐feldspar. The continuous recrystallization of plagioclase during deformation into a very fine‐grained assemblage forming anastomosed ribbons is interpreted as the dominant process in the shear zone initiation and development. The shear zone initiated under closed‐system conditions with the destabilization of metastable AbI–ZoI porphyroclasts into fine‐grained (20–50 μm sized) AbII–PlII aggregates, and with minor crystallization of phengite at the expense of K‐feldspar. The development of the shear zone requires a change in state of the system, which becomes open to externally derived fluids and mass transfer. Indeed, mass balance calculations and thermodynamic modelling show that the ultramylonite is characterized by gains in CaO, FeO and H2O. The progressive input of externally derived CaO drives the continuous metamorphic recrystallization of the fine‐grained AbII–PlII aggregate into a more PlII‐rich and finer aggregate. Input of water favours the crystallization of phengite at the expense of K‐feldspar to form an interconnected network of weak phases. Thus, recrystallization of 50% of the bulk rock volume would induce a decrease of the strength of the rock that might contribute to the development of the shear zone. This study emphasizes the major role of metamorphic reactions and more particularly plagioclase on strain localization process. Plagioclase represents at least one‐third of the bulk rock volume in granitic systems and forms a stress‐supporting framework that controls the rock rheology. Therefore, recrystallization of plagioclase due to changes in P–T conditions and/or bulk composition must be taken into account, together with quartz and K‐feldspar, in order to understand strain localization processes in granites.  相似文献   

11.
Subcritical crack growth plays an important role in evaluating the long-term stability of structures in rocks. By applying the constant-displacement-relax method, two groups of test specimens that one immersed in groundwater and the other in air were tested to get the parameters of subcritical crack growth in double torsion test. The relations of the stress intensity factor K I versus the subcritical crack growth velocity V were obtained under the two different environments, and the behavior of subcritical crack growth was also analyzed. The results showed: the relations of lg K I  ? lg V accorded with linear rules, which is in good agreement with Charles theory; Compared with specimens in nature state, the lg K I  ? lg V curves of saturated water specimens locate top left comer of those of air specimens. The slope of curve is smaller, and the intercept is bigger, which shows that the water–rock interaction speeds up the subcritical crack growth. And A increases 2.9 × 1018 folds but n decreases from 85.12 to 40.83 because of the water–rock interaction. Meanwhile, the fracture toughness K IC also decreases obviously from 2.55 in air to 2.26 in water due to water rock interaction. The testing results provide a basis for time-dependence of rock engineering stability.  相似文献   

12.
High pressure in situ synchrotron X-ray diffraction experiment of strontium orthophosphate Sr3(PO4)2 has been carried out to 20.0 GPa at room temperature using multianvil apparatus. Fitting a third-order Birch–Murnaghan equation of state to the P–V data yields a volume of V 0 = 498.0 ± 0.1 Å3, an isothermal bulk modulus of K T  = 89.5 ± 1.7 GPa, and first pressure derivative of K T ′ = 6.57 ± 0.34. If K T ′ is fixed at 4, K T is obtained as 104.4 ± 1.2 GPa. Analysis of axial compressible modulus shows that the a-axis (K a  = 79.6 ± 3.2 GPa) is more compressible than the c-axis (K c  = 116.4 ± 4.3 GPa). Based on the high pressure Raman spectroscopic results, the mode Grüneisen parameters are determined and the average mode Grüneisen parameter of PO4 vibrations of Sr3(PO4)2 is calculated to be 0.30(2).  相似文献   

13.
The thermo-elastic behaviour of Be2BO3(OH)0.96F0.04 (i.e. natural hambergite, Z = 8, a = 9.7564(1), b = 12.1980(2), c = 4.4300(1) Å, V = 527.21(1) Å3, space group Pbca) has been investigated up to 7 GPa (at 298 K) and up to 1,100 K (at 0.0001 GPa) by means of in situ single-crystal X-ray diffraction and synchrotron powder diffraction, respectively. No phase transition or anomalous elastic behaviour has been observed within the pressure range investigated. P?V data fitted to a third-order Birch–Murnaghan equation of state give: V 0 = 528.89(4) Å3, K T0 = 67.0(4) GPa and K′ = 5.4(1). The evolution of the lattice parameters with pressure is significantly anisotropic, being: K T0(a):K T0(b):K T0(c) = 1:1.13:3.67. The high-temperature experiment shows evidence of structure breakdown at T > 973 K, with a significant increase in the full-width-at-half-maximum of all the Bragg peaks and an anomalous increase in the background of the diffraction pattern. The diffraction pattern was indexable up to 1,098 K. No new crystalline phase was observed up to 1,270 K. The diffraction data collected at room-T after the high-temperature experiment showed that the crystallinity was irreversibly compromised. The evolution of axial and volume thermal expansion coefficient, α, with T was described by the polynomial function: α(T) = α 0 + α 1 T ?1/2. The refined parameters for Be2BO3(OH)0.96F0.04 are: α 0 = 7.1(1) × 10?5 K?1 and α 1 = ?8.9(2) × 10?4 K ?1/2 for the unit-cell volume, α 0(a) = 1.52(9) × 10?5 K?1 and α 1(a) = ?1.4(2) × 10?4 K ?1/2 for the a-axis, α 0(b) = 4.4(1) × 10?5 K?1 and α 1(b) = ?5.9(3) × 10?4 K ?1/2 for the b-axis, α 0(c) = 1.07(8) × 10?5 K?1 and α 1(c) = ?1.5(2) × 10?4 K ?1/2 for the c-axis. The thermo-elastic anisotropy can be described, at a first approximation, by α 0(a):α 0(b):α 0(c) = 1.42:4.11:1. The main deformation mechanisms in response to the applied temperature, based on Rietveld structure refinement, are discussed.  相似文献   

14.
Orthorhombic post-perovskite CaPtO3 is isostructural with post-perovskite MgSiO3, a deep-Earth phase stable only above 100 GPa. Energy-dispersive X-ray diffraction data (to 9.4 GPa and 1,024 K) for CaPtO3 have been combined with published isothermal and isobaric measurements to determine its P–V–T equation of state (EoS). A third-order Birch–Murnaghan EoS was used, with the volumetric thermal expansion coefficient (at atmospheric pressure) represented by α(T) = α0 + α1(T). The fitted parameters had values: isothermal incompressibility, $ K_{{T_{0} }} $  = 168.4(3) GPa; $ K_{{T_{0} }}^{\prime } $  = 4.48(3) (both at 298 K); $ \partial K_{{T_{0} }} /\partial T $  = ?0.032(3) GPa K?1; α0 = 2.32(2) × 10?5 K?1; α1 = 5.7(4) × 10?9 K?2. The volumetric isothermal Anderson–Grüneisen parameter, δ T , is 7.6(7) at 298 K. $ \partial K_{{T_{0} }} /\partial T $ for CaPtO3 is similar to that recently reported for CaIrO3, differing significantly from values found at high pressure for MgSiO3 post-perovskite (?0.0085(11) to ?0.024 GPa K?1). We also report axial P–V–T EoS of similar form, the first for any post-perovskite. Fitted to the cubes of the axes, these gave $ \partial K_{{aT_{0} }} /\partial T $  = ?0.038(4) GPa K?1; $ \partial K_{{bT_{0} }} /\partial T $  = ?0.021(2) GPa K?1; $ \partial K_{{cT_{0} }} /\partial T $  = ?0.026(5) GPa K?1, with δ T  = 8.9(9), 7.4(7) and 4.6(9) for a, b and c, respectively. Although $ K_{{T_{0} }} $ is lowest for the b-axis, its incompressibility is the least temperature dependent.  相似文献   

15.
Empirical criteria (K1–K2 > 0 and η–K3 > 0) for predicting the presence of voids in abandoned shallow underground workings in Donetsk city (Ukraine) located in the zone of intensive weathering are proposed. The voids exist when both inequalities K1–K2 > 0 and η–K3 > 0 are satisfied. The statistical analysis has established that the value of criterion K2 is inversely related to rock quality designation (RQD) and that a decrease in RQD leads to a decrease in K1–K2 and, hence, the probability of the void existence is decreased. It is also established that a statistical parameter η in the left-hand part of inequality η–K3 > 0 decreases according to logarithmic law with increasing standard linear intensity of weathering-induced fractures (P10). When the fracture intensity (P10) increases, the probability of the presence of a void is decreased. The proposed criteria confirm that a thick immediate roof and sandstone layers contribute to the existence of voids of unknown stability. On the other hand, the probability of existence of these voids decreases with increasing thickness of alluvium and total thickness of argillites and sandy shale layers in the rock mass which in turn suggests a decreased probability of void migration and surface subsidence in the future as this has likely already occurred. The use of the proposed criteria in engineering practice is discussed.  相似文献   

16.
《Geochimica et cosmochimica acta》1999,63(19-20):3487-3497
The solubility of iron(III) hydroxide as a function of pH was investigated in NaCl solutions at different temperatures (5–50°C) and ionic strengths (0–5 M). Our results at 25°C and 0.7 M in the acidic range are similar to the solubility in seawater. The results between 7.5 to 9 are constant (close to 10−11 M) and are lower than those found in seawater (>10−10) in this pH range. The solubility subsequently increases as the pH increases from 9 to 12. The solubility between 6 and 7.5 has a change of slope that cannot be accounted for by changes in the speciation of Fe(III). This effect has been attributed to a solid-state transformation of Fe(OH)3 to FeOOH. The effect of ionic strength from 0.1 to 5 M at a pH near 8 was quite small. The solubility at 5°C is considerably higher than at 25°C at neutral pH range. The effects of temperature and ionic strength on the solubility at low and high pH have been attributed to the effects on the solubility product and the formation of FeOH2+ and Fe(OH)4−. The results have been used to determine the solubility products of Fe(OH)3, K1Fe(OH)3 and hydrolysis constants, β11, β12, β13, and β14 as a function of temperature (T, K) and ionic strength (I):log K1Fe(OH)3 = −13.486 − 0.1856 I0.5 + 0.3073 I + 5254/T (σ = 0.08)log β11 = 2.517 − 0.8885 I0.5 + 0.2139 I − 1320/T (σ = 0.03)log β12 = 0.4511 − 0.3305 I0.5 − 1996/T (σ = 0.1)log β13 = −0.2965 − 0.7881 I0.5 − 4086/T (σ = 0.6)log β14 = 4.4466 − 0.8505 I0.5 − 7980/T. (σ = 0.2)Both strong ethylenediaminetetraacetic acid and weak (HA) organic ligands greatly affect iron solubility. The additions of ethylenediaminetetraacetic acid and humic material were shown to increase the solubility near pH 8. The higher solubility of Fe(III) in seawater compared to 0.7 M NaCl may be caused by natural organic ligands.  相似文献   

17.
The thermoelastic parameters of synthetic Mn3Al2Si3O12 spessartine garnet were examined in situ at high pressure up to 13 GPa and high temperature up to 1,100 K, by synchrotron radiation energy dispersive X-ray diffraction within a DIA-type multi-anvil press apparatus. The analysis of room temperature data yielded K 0 = 172 ± 4 GPa and K 0 ′  = 5.0 ± 0.9 when V 0,300 is fixed to 1,564.96 Å3. Fitting of P–V–T data by means of the high-temperature third-order Birch–Murnaghan EoS gives the thermoelastic parameters: K 0 = 171 ± 4 GPa, K 0 ′  = 5.3 ± 0.8, (?K 0,T /?T) P  = ?0.049 ± 0.007 GPa K?1, a 0 = 1.59 ± 0.33 × 10?5 K?1 and b 0 = 2.91 ± 0.69 × 10?8 K?2 (e.g., α 0,300 = 2.46 ± 0.54 × 10?5 K?1). Comparison with thermoelastic properties of other garnet end-members indicated that the compression mechanism of spessartine might be the same as almandine and pyrope but differs from that of grossular. On the other hand, at high temperature, spessartine softens substantially faster than pyrope and grossular. Such softening, which is also reported for almandine, emphasize the importance of the cation in the dodecahedral site on the thermoelastic properties of aluminosilicate garnet.  相似文献   

18.
  相似文献   

19.
The thermal evolution of 10-Å phase Mg3Si4O10(OH)2·H2O, a phyllosilicate which may have an important role in the storage/release of water in subducting slabs, was studied by X-ray single-crystal diffraction in the temperature range 116–293 K. The lattice parameters were measured at several intervals both on cooling and heating. The structural model was refined with intensity data collected at 116 K and compared to the model refined at room temperature. As expected for a layer silicate on cooling in this temperature range, the a and b lattice parameters undergo a small linear decrease, α a  = 1.7(4) 10?6 K?1 and α b  = 1.9(4) 10?6 K?1, where α is the linear thermal expansion coefficient. The greater variation is along the c axis and can be modeled with the second order polynomial c T  = c 293(1 + 6.7(4)10?5 K?1ΔT + 9.5(2.5)10?8 K?2(ΔT)2) where ΔT = T ? 293 K; the monoclinic angle β slightly increased. The cell volume thermal expansion can be modeled with the polynomial V T  = V 293 (1 + 8.0 10?5 K?1 ΔT + 1.4 10?7 K?2 (ΔT)2) where ΔT = T ? 293 is in K and V in Å3. These variations were similar to those expected for a pressure increase, indicating that T and P effects are approximately inverse. The least-squares refinement with intensity data measured at 116 K shows that the volume of the SiO4 tetrahedra does not change significantly, whereas the volume of the Mg octahedra slightly decreases. To adjust for the increased misfit between the tetrahedral and octahedral sheets, the tetrahedral rotation angle α changes from 0.58° to 1.38°, increasing the ditrigonalization of the silicate sheet. This deformation has implications on the H-bonds between the water molecule and the basal oxygen atoms. Furthermore, the highly anisotropic thermal ellipsoid of the H2O oxygen indicates positional disorder, similar to the disorder observed at room temperature. The low-temperature results support the hypothesis that the disorder is static. It can be modeled with a splitting of the interlayer oxygen site with a statistical distribution of the H2O molecules into two positions, 0.6 Å apart. The resulting shortest Obas–OW distances are 2.97 Å, with a significant shortening with respect to the value at room temperature. The low-temperature behavior of the H-bond system is consistent with that hypothesized at high pressure on the basis of the Raman spectra evolution with P.  相似文献   

20.
袁小平  刘红岩  王志乔 《岩土力学》2012,33(6):1679-1688
基于Drucker-Prager（下简称D-P）准则,建立压缩载荷作用下的非贯通节理岩石的弹塑性断裂模型。针对节理岩石小范围屈服翼裂纹尖端塑性区,推导了D-P屈服准则的纯I、纯II及I、II复合型3种翼裂纹无量纲塑性区径长函数,并与Mises准则的塑性区进行对比;结果表明,D-P准则的I型和复合型塑性区较Mises屈服准则的塑性区大,且其II型及I、II复合型塑性区在翼裂纹上下表面不连续。进一步,引入断裂软化因子以表征节理岩石裂隙断裂扩展后的断裂软化规律,考虑非贯通节理岩石复合型断裂软化,是由于节理尖端翼裂纹应变能密度超过最小应变能密度导致其成核扩展引起的,提出用应变能密度的指数函数形式表征断裂软化变量的演化;塑性屈服函数采用Borja等的应力张量3个不变量的硬化/软化函数,反映塑性内变量及应力状态对硬化函数的影响;建立节理岩石的弹塑性断裂本构关系及其数值算法,并用回映隐式积分算法编制了弹塑性断裂模型的程序。以单轴压缩下非贯通节理岩石为例,分析岩石断裂韧度、节理摩擦系数和节理倾角等参数的影响,结果表明,所提出的弹塑性断裂模型与数值和试验结果比较吻合。  相似文献   

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