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1.
Property and behaviour of sand–pile interface are crucial to shaft resistance of piles. Dilation or contraction of the interface soil induces change in normal stress, which in turn influences the shear stress mobilised at the interface. Although previous studies have demonstrated this mechanism by laboratory tests and numerical simulations, the interface responses are not analysed systematically in terms of soil state (i.e. density and stress level). The objective of this study is to understand and quantify any increase in normal stress of different pile–soil interfaces when they are subjected to loading and stress relief. Distinct element modelling was carried out. Input parameters and modelling procedure were verified by experimental data from laboratory element tests. Parametric simulations of shearbox tests were conducted under the constant normal stiffness, constant normal load and constant volume boundary conditions. Key parameters including initial normal stress ( $ \sigma_{{{\text{n}}0}}^{\prime } $ ), initial void ratio (e 0), normal stiffness constraining the interface and loading–unloading stress history were investigated. It is shown that mobilised stress ratio ( $ \tau /\sigma_{\text{n}}^{\prime } $ ) and normal stress increment ( $ \Updelta \sigma_{\text{n}}^{\prime } $ ) on a given interface are governed by $ \sigma_{{{\text{n}}0}}^{\prime } $ and e 0. An increase in $ \sigma_{{{\text{n}}0}}^{\prime } $ from 100 to 400 kPa leads to a 30 % reduction in $ \Updelta \sigma_{\text{n}}^{\prime } $ . An increase in e 0 from 0.18 to 0.30 reduces $ \Updelta \sigma_{\text{n}}^{\prime } $ by more than 90 %, and therefore, shaft resistance is much lower for piles in loose sands. A unique relationship between $ \Updelta \sigma_{\text{n}}^{\prime } $ and normal stiffness is established for different soil states. It can be applied to assess the shaft resistance of piles in soils with different densities and subjected to loading and stress relief. Fairly good agreement is obtained between the calculated shaft resistance based on the proposed relationship and the measured results in centrifuge model tests.  相似文献   

2.
The objective of the paper is to derive the strength and modulus properties of rockmass as a function of intact rock strength and joint factor. The joint factor reflects the combined effect of joint frequency, joint inclination and joint strength. A study for the strength and deformation characteristics of jointed rock is done by conducting standard laboratory tests on cylindrical specimens of plaster of Paris after introducing artificial joints. The specimens having one to four joints at different inclinations which vary from 0° to 90° were tested at different confining conditions. The test results were examined to understand the effect of joint frequency and joint inclination on the strength and deformation behaviour of rock mass. Empirical correlations were developed for prediction of the uniaxial compressive strength and elastic modulus of jointed rocks. Results are compared with the earlier work on jointed specimens covering a wide variety of rocks. So, knowing the intact rock properties and the joint factor, the jointed rock properties can be estimated. These relations can be used for developing an equivalent continuum model for rock mass for handling boundary value problems. A failure criterion as proposed by Ramamurthy (1993 Ramamurthy, T. 1993. “Strength and modulus response of anisotropic rocks”. In Comprehensive rock engineering, Edited by: Hudson, J.A. Vol. 1, 313–329. Oxford: Pergamon Press.  [Google Scholar]) has been validated from these experimental results.  相似文献   

3.
The flow rule used in the high-cycle accumulation (HCA) model proposed by Niemunis et al. (Comput Geotech 32: 245, 2005) is examined on the basis of the data from approximately 350 drained long-term cyclic triaxial tests (N = 105 cycles) performed on 22 different grain-size distribution curves of a clean quartz sand. In accordance with (Wichtmann et al. in Acta Geotechnica 1: 59, 2006), for all tested materials, the “high-cyclic flow rule (HCFR)”, i.e., the ratio of the volumetric and deviatoric strain accumulation rates \(\dot{\varepsilon}_{\rm{v}}^{{\rm acc}}/\dot{\varepsilon}_{\rm{q}}^{{\rm acc}}\) , was found dependent primarily on the average stress ratio η av = q av/p av and independent of amplitude, soil density and average mean pressure. The experimental HCFR can be fairly well approximated by the flow rule of the modified Cam-clay (MCC) model. Instead of the critical friction angle \(\varphi_{\rm{c}}\) which enters the flow rule for monotonic loading, the HCA model uses the MCC flow rule expression with a slightly different parameter \(\varphi_{\rm{cc}}\) . It should be determined from cyclic tests. \(\varphi_{\rm{cc}}\) and \(\varphi_{\rm{c}}\) are of similar magnitude but not always identical, because they are calibrated from different types of tests. For a simplified calibration in the absence of cyclic test data, \(\varphi_{\rm{cc}}\) may be estimated from the angle of repose \(\varphi_{\rm{r}}\) determined from a pluviated cone of sand (Wichtmann et al. in Acta Geotechnica 1: 59, 2006). However, the paper demonstrates that the MCC flow rule with \(\varphi_{\rm{r}}\) does not fit well the experimentally observed HCFR in the case of coarse or well-graded sands. For an improved simplified calibration procedure, correlations between \(\varphi_{\rm{cc}}\) and parameters of the grain-size distribution curve (d 50,   C u) have been developed on the basis of the present data set. The approximation of the experimental HCFR by the generalized flow rule equations proposed in (Wichtmann et al. in J Geotech Geoenviron Eng ASCE 136: 728, 2010), considering anisotropy, is also discussed in the paper.  相似文献   

4.
This study investigates a simple constitutive model based on the critical state framework and bounding surface (BS) plasticity that is suitable for reconstituted clays over a wide range of overconsolidation ratios under monotonic loading. For heavily overconsolidated (OC) clays, rather than using the conventional Hvorslev line, an empirical surface is introduced into the model formulation based on two image points on the BS. The peak strength and the dilatancy of heavily OC clays can thus be predicted satisfactorily. Comparisons with triaxial test data show that the model well captures the peak strength and the dilatancy of heavily OC clays under monotonic loading.  相似文献   

5.
Kong  Yuxia  Zhou  Annan  Shen  Feifan  Yao  Yangping 《Acta Geotechnica》2019,14(6):1871-1881
  相似文献   

6.
Micro-mechanical failure analysis of wet granular matter   总被引：1，自引：1，他引：0  
We employ a novel fluid–particle model to study the shearing behavior of granular soils under different saturation levels, ranging from the dry material via the capillary bridge regime to higher saturation levels with percolating clusters. The full complexity of possible liquid morphologies Scheel et al. (Nat Mater 7(3):189–193, 2008. doi: 10.1038/nmat2117) is taken into account, implying the formation of isolated arbitrary-sized liquid clusters with individual Laplace pressures that evolve by liquid exchange via films on the grain surface Melnikov et al. (Phys Rev E 92(022):206, 2015. doi: 10.1103/PhysRevE.92.022206). Liquid clusters can grow in size, shrink, merge and split, depending on local conditions, changes of accessible liquid and the pore space morphology determined by the granular phase. This phase is represented by a discrete particle model based on contact dynamics Brendel et al. (Contact dynamics for beginners. Wiley-VCH, Weinheim, 2005. doi: 10.1002/352760362X.ch14), where capillary forces exerted from a liquid phase add to the motion of spherical particles. We study the macroscopic response of the system due to an external compression force at various liquid contents with the help of triaxial shear tests. Additionally, the change in liquid cluster distributions during the compression due to the deformation of the pore space is evaluated close to the critical load.  相似文献   

7.
The compressibility behaviour of loose and contracting granular assemblies, normally consolidated and overconsolidated, under isotropic drained compression is investigated in this paper. Short cylindrical samples of water-saturated monodisperse glass beads, initially assembled in loose state by moist-tamping technique, are isotropically compressed in a classical axisymmetric triaxial machine. Very loose glass bead samples experience numerous unexpected events, sometimes cascading, under undetermined triggered effective isotropic stress in loading and in unloading, while the classical compressibility behaviour of granular material is recovered once these events ignored. Each event, resembling the stick–slip instability during shear in triaxial compression, is characterized by a transient dynamic phase I with very fast drop of effective isotropic stress \(\sigma ^{'}\) due to an excess pore pressure development at nearly constant volume and constant axial strain, followed by a quasi-static phase II with gradual increase in axial \(\varepsilon _\mathrm{a}\) (contraction) and volumetric \(\varepsilon _\mathrm{v}\) (compaction) strain, and a full progressive recovery of \(\sigma ^{'}\) to the previous level before event. A short-lived liquefaction with null \(\sigma ^{'}\) measured in the first phase I results in a local collapse state. Collapse events also happen on unsaturated moist and dry states. Rare events even occur during the unloading of subsequent isotropic compression cycles. The effects of triggered isotropic stress are discussed, the instability characteristics measured, the comparison with stick–slip instability made and the hypothesis of micro-structural instability with local collapse of contact networks and rapid micro-structural rearrangement argued.  相似文献   

8.
In this paper, we develop a multiscale model reduction technique that describes shale gas transport in fractured media. Due to the pore-scale heterogeneities and processes, we use upscaled models to describe the matrix. We follow our previous work (Akkutlu et al. Transp. Porous Media 107(1), 235–260, 2015), where we derived an upscaled model in the form of generalized nonlinear diffusion model to describe the effects of kerogen. To model the interaction between the matrix and the fractures, we use Generalized Multiscale Finite Element Method (Efendiev et al. J. Comput. Phys. 251, 116–135, 2013, 2015). In this approach, the matrix and the fracture interaction is modeled via local multiscale basis functions. In Efendiev et al. (2015), we developed the GMsFEM and applied for linear flows with horizontal or vertical fracture orientations aligned with a Cartesian fine grid. The approach in Efendiev et al. (2015) does not allow handling arbitrary fracture distributions. In this paper, we (1) consider arbitrary fracture distributions on an unstructured grid; (2) develop GMsFEM for nonlinear flows; and (3) develop online basis function strategies to adaptively improve the convergence. The number of multiscale basis functions in each coarse region represents the degrees of freedom needed to achieve a certain error threshold. Our approach is adaptive in a sense that the multiscale basis functions can be added in the regions of interest. Numerical results for two-dimensional problem are presented to demonstrate the efficiency of proposed approach.  相似文献   

9.
The ‘average’ interdiffusion coefficient ( \(\bar D\) ) for NaSi—CaAl exchange in plagioclase for the interval from An0 to An26 was estimated from experimentally determined homogenization times for peristerite exsolution lamellae. The average spacing between adjacent (unlike) lamellae is 554±77 Å. Dry heating in air at 1,100°C for 98 days produced no change in the exsolution microstructure; thus \(\bar D\) (dry)<10?17 cm2/s. This limit is consistent with the recently reported ‘average’ \(\bar D\) (dry) values for the Huttenlocher interval (An70–90) at this temperature. At 1.5 GPa with about 0.2 weight percent water added the ‘average’ diffusion coefficient from 1,100°C to 900°C is given by: \(\bar D\) (wet)=18 ?15 +108 (cm2/s) exp (?97±5 (kcal/mol)/RT), where R is the gas constant, and T is °K. This \(\bar D\) (wet) at 1,100°C is more than three orders of magnitude greater than \(\bar D\) (dry) for Na- and Ca-rich plagioclases.  相似文献   

10.
Pressuremeter modulus (\(E_{M}\)) and limit pressure (\(P_{L}\)) are used for the calculation of the settlement and bearing capacity of foundation respectively. As the determination of these parameters from pressuremeter test (PMT) is relatively time-consuming and expensive, various empirical correlations have been proposed to correlate the \(E_{M}\) and \(P_{L}\) to other soil parameters. For the existing equations are incapable of estimating these PMT parameters well, in present research group method of data handling type neural network is used to estimate the \(E_{M}\) and \(P_{L}\) of clayey soils. The \(E_{M}\) and \(P_{L}\) were modeled as a function of three variables including the moisture content (\(\omega\)), plasticity index and corrected SPT blow counts (\(N_{60}\)). A database containing 51 data sets have been used for training and testing of the models. The performances of proposed models are compared with those of existing empirical equations. The results demonstrate that appreciable improvement with respect to the other correlations has been achieved. At the end, sensitivity analysis of the obtained models has been performed to study the influence of input parameters on model outputs and shows that the \(N_{60}\) is the most influential parameter on the PMT parameters.  相似文献   

11.
Seismic source parameters of small to moderate sized intraplate earthquakes that occurred during 2002–2009 in the tectonic blocks of Kachchh Rift Basin (KRB) and the Saurashtra Horst (SH), in the stable continental region of western peninsular India, are studied through spectral analysis of shear waves. The data of aftershock sequence of the 2001 Bhuj earthquake (\(M_{w}\) 7.7) in the KRB and the 2007 Talala earthquake (\(M_{w}\) 5.0) in the SH are used for this study. In the SH, the seismic moment (\(M_{o})\), corner frequency \((f_{c})\), stress drop (\(\varDelta \sigma \)) and source radius (r) vary from \(7.8\times 10^{11}\) to \(4.0\times \)10\(^{16}\) N-m, 1.0–8.9 Hz, 4.8–10.2 MPa and 195–1480 m, respectively. While in the KRB, these parameters vary from \(M_{o} \sim 1.24 \,\times \, 10^{11}\) to \(4.1 \times 10^{16}\) N-m, \(f_{c }\sim \) 1.6 to 13.1 Hz, \(\varDelta \sigma \sim 0.06\) to 16.62 MPa and \(r \sim 100\) to 840 m. The kappa (K) value in the KRB (0.025–0.03) is slightly larger than that in the SH region (0.02), probably due to thick sedimentary layers. The estimated stress drops of earthquakes in the KRB are relatively higher than those in SH, due to large crustal stress concentration associated with mafic/ultramafic rocks at the hypocentral depths. The results also suggest that the stress drop value of intraplate earthquakes is larger than the interplate earthquakes. In addition, it is observed that the strike-slip events in the SH have lower stress drops, compared to the thrust and strike-slip events.  相似文献   

12.
Extensive laboratory model tests have been carried out on a strip footing resting over dry sand bed subjected to eccentrically inclined load to determine the ultimate bearing capacity (Patra et al. in Int J Geotech Eng 6(3):343–352, 2012a.  https://doi.org/10.3328/IJGE.2012.06.03.343-352, Int J Geotech Eng 6(4):507–514, b.  https://doi.org/10.3328/IJGE.2012.06.04.507-514). Similarly, lower bound calculations based on finite element method were performed to compute the bearing capacity of a strip footing subjected to an eccentric and inclined load lying over a cohesionless soil with varying embedment depth and relative density (Krabbenhoft et al. in Int J Geomech ASCE, 2014.  https://doi.org/10.1061/(ASCE)GM.1943-5622.0000332). The load may be applied in two ways namely, towards the center line and away from the center line of the footing. Based on the results (both experimental and numerical analyses), a neural network model is developed to predict the reduction factor that will be used in computing the ultimate bearing capacity of an eccentrically inclined loaded strip footing. This reduction factor (RF) is the ratio of the ultimate bearing capacity of the footing subjected to an eccentrically inclined load to the ultimate bearing capacity of the footing subjected to a centric vertical load. A thorough sensitivity analysis is carried out to evaluate the parameters affecting the reduction factor. Based on the weights of the developed neural network model, a neural interpretation diagram is developed to find out whether the input parameters have direct or inverse effect on the output. A prediction model equation is framed with the trained weights of the neural network as the model parameters. The predictions from ANN, and those from other approaches, are compared with the results computed from both experimentation and FEM analyses. The ANN model results are found to be more accurate and well matched with other results.  相似文献   

13.
A new experimental model has been designed to simulate the influence of a natural fracture network on the propagation geometry of hydraulic fractures in naturally fractured formations using a tri-axial fracturing system. In this model, a parallel and symmetrical pre-fracture network was created by placing cement plates in a cubic mold and filling the mold with additional cement to create the final testing block. The surface of the plates will thus be weakly cemented and form pre-fractures. The dimension and direction of the pre-fractures can be controlled using the plates. The experiments showed that the horizontal differential stress $\Updelta \sigma$ and the angle $\Updelta \theta$ between the maximum horizontal principal in situ stress and the pre-fracture are the dominating factors for the initiation and propagation of hydraulic fractures. For $\Updelta \theta = 90^\circ$ and $\Updelta \sigma \ge 2{\text{ MPa}}$ or $\Updelta \theta = 60^\circ$ and $\Updelta \sigma \ge 4{\text{ MPa}}$ , the direction of the initiation and propagation of the hydraulic fractures are consistent with or deviate from the normal direction of the pre-fracture. When the hydraulic fractures approach the pre-fractures, the direction of the hydraulic fracture propagation will be consistent with the normal direction of the pre-fracture. Otherwise, the hydraulic fracture will deflect and perpendicularly cross the parallel and symmetric pre-fracture network. For $\Updelta \theta = 90^\circ$ and $\Updelta \sigma < 2{\text{ MPa}},\,\Updelta \theta = 60^\circ$ , and $\Updelta \sigma < 4{\text{ MPa}}$ or $\Updelta \theta = 45^\circ$ and $\Updelta \sigma = 4 - 8{\text{ MPa}}$ , before the hydraulic fracture and the pre-fractures intersect, the direction of the hydraulic fracture propagation remains unchanged, and the pre-fractures open or dilate when the hydraulic fracture propagates to the intersection point, forming a complicated hydraulic fracture network with the propagation region of the overall hydraulic fracture network taking the shape of an ellipse. In this condition, the complexity level of the hydraulic fracture is controlled by the net pressure, the compressive normal stress acting on the pre-fractures, the shearing strength and the cohesion strength of the planes of weakness. The conclusions of this research are inconsistent with the formulation of the approach angle that has been widely accepted by previous studies. The principle of hydraulic fracture propagation is that it follows the least resistance, the most preferential propagation, and the shortest propagation path.  相似文献   

14.
Seasonal changes in phytoplankton biomass and production, total zooplankton biomass, and biomass and potential production rates of the two dominant copepods, Acartia hudsonica (formerly called Acartia clausi) and Acartia tonsa are described for several stations in Narragansett Bay, R.I. Plankton in the bay behaved as a single population with simultaneous changes occurring at the upper bay (Station 5) and the lower bay (Station 1). Phytoplankton biomass was higher in the upper bay ( \(\bar x\) =16.95 mg chl a·m?3) than in the lower bay ( \(\bar x\) =6.37 mg chl a·m?3) and these 0269 0101 V differences in biomass were reflected in the phytoplankton production rates. The zooplankton, which was dominated by A. hudsonica in the spring and early summer and A. tonsa during summer and fall, showed no such consistent differences between the stations. Mean A. hudsonica biomass (St 1, \(\bar x\) ;=82.7 mg dry wt·m?3; St 5, _ \(\bar x\) ;=95.2 mg dry wt·m?3) exceeded that of A. tonsa (St 1, \(\bar x\) ;=56.7 mg dry wt·m?3; St 5, \(\bar x\) ;=60.0 mg dry wt·m?3). Potential production rates of the two Acartia 0269 0101 V spp. were strongly temperature dependent. Despite the higher biomass levels of A. hudsonica, low temperatures resulted in lower potential production rates ( \(\bar x\) ; St 1=7.25 mg C·m?3 day?1; \(\bar x\) ; St 5=10.77mg C·m?3 day?1) and biomass doubling times of up to 9.6 days. Potential production rates of A. tonsa at summer temperatures were high ( \(\bar x\) ; St 1=19.0 mg C·m?3 day?1; \(\bar x\) ; St 5=22.9 mg C·m?3 day?1) and biomass doubling times were generally less than one day.  相似文献   

15.
The hydrogen isotope (deuterium- $ \delta D $ ) composition at natural abundance levels of xylem water, soil water, groundwater, river water, and rainwater was used to evaluate whether adult plant species use groundwater and to detect seasonal shifts (dry/wet season) in water sources for plants growing in a semi-arid coal-mining area (located at the frontier of the Mu Us Desert). A direct inference approach and the IsoSource mixing model were used to estimate the contributions of different sources to the plant xylem water. The results showed that (1) the $ \delta D $ values of rainfall fluctuated considerably, while those of groundwater were generally constant during the experimental period; (2) the $ \delta D $ patterns in plant xylem water suggest that groundwater was a significant source of water for transpiration in the dry season, while all five selected species reduced dependence on groundwater sources in the wet season; and (3) soil water from the deep layer (50–100 cm) was used largely by adult species possibly because of interspecific competition. These results indicated that coal mining would significantly affect plant growth by reducing the water supply if it leads to a water table decrease. Therefore, it is necessary to protect groundwater resources during the coal mining operations in the region.  相似文献   

16.
In this paper, we study on a history matching approach that consists of finding stable approximations to the problem of minimizing the weighted least-squares functional that penalizes the misfit between the reservoir model predictions G(u) and noisy observations y η . In other words, we are interested in computing an approximation to the minimizer of $\frac {1}{2}\vert \vert \Gamma ^{-1/2}(y^{\eta }-G(u))\vert \vert _{Y}^{2} $ where Γ is the measurements error covariance, Y is the observation space, and X is a set of admissible parameters. This is an ill-posed nonlinear inverse problem that we address by means of the regularizing Levenberg–Marquardt scheme developed by Hanke (Inverse Probl. 13:79–95, 1997; J. Integr. Equ. Appl. 22(2):259–283, 2010). Under certain conditions on G, the theory of Hanke (Inverse Probl. 13:79–95, 1997; J. Integr. Equ. Appl. 22(2):259–283, 2010) ensures the convergence of the scheme to stable approximations to the inverse problem. We propose an implementation of the regularizing Levenberg–Marquardt scheme that enforces prior knowledge on the geologic properties. In particular, the prior mean $\overline {u}$ is incorporated in the initial guess of the algorithm, and the prior error covariance C is enforced through the definition of the parameter space X. Our main goal is to numerically show that the proposed implementation of the regularizing Levenberg–Marquardt scheme of Hanke is a robust method capable of providing accurate estimates of the geologic properties for small noise measurements. In addition, we provide numerical evidence of the convergence and regularizing results predicted by the theory of Hanke (Inverse Probl. 13:79–95, 1997; J. Integr. Equ. Appl. 22(2):259–283, 2010) for a prototypical oil–water reservoir model. The performance for recovering the true permeability with the regularizing Levenberg–Marquardt scheme is compared to the typical approach of computing the maximum a posteriori (MAP) estimator. In particular, we compare the proposed application of the regularizing Levenberg–Marquardt (LM) scheme against the standard LM approach of Li et al. (SPE J. 8(4):328–340, 2003) and Reynolds et al. (2008) for computing the MAP. Our numerical experiments suggest that the history matching approach based on iterative regularization is robust and could potentially be used to improve further on various methodologies already proposed as effective tools for history matching in petroleum reservoirs.  相似文献   

17.
Earthquake source parameters and crustal \(Q_{0}\) values for the 138 selected local events of (\(\hbox {M}_{\mathrm{w}}{:}2.5{-}4.4\)) the 2001 Bhuj earthquake sequence have been computed through inversion modelling of S-waves from three-component broadband seismometer data. SEISAN software has been used to locate the identified local earthquakes, which were recorded at least three or more stations of the Kachchh seismological network. Three component spectra of S-wave are being inverted by using the Levenberg–Marquardt non-linear inversion technique, wherein the inversion scheme is formulated based on \(\omega ^{2}\) source model. SAC Software (seismic analysis code) is being utilized for calculating three-component displacement and velocity spectra of S-wave. The displacement spectra are used for estimating corner frequency (in Hz) and long period spectral level (in nm-s). These two parameters play a key role in estimating earthquake source parameters. The crustal \({Q}_{0}\) values have been computed simultaneously for each component of three-component broadband seismograph. The estimated seismic moment (\(M_{0}\)) and source radius (r) using S-wave spectra range from 7.03E+12 to 5.36E+15 N-m and 178.56 to 565.21 m, respectively. The corner frequencies for S-wave vary from 3.025 to 7.425 Hz. We also estimated the radiated energy (\(E_{S}\)) using velocity spectra, which is varying from 2.76E+06 to 4.07E+11 Joules. The estimated apparent stress drop and static stress drop values range from 0.01 to 2.56 and 0.53 to 36.79 MPa, respectively. Our study also reveals that estimated \(Q_{0}\) values vary from 119.0 to 7229.5, with an average \(Q_{0}\) value of 701. Another important parameter, by which the earthquake rupture process can be recognized, is Zuniga parameter. It suggests that most of the Kachchh events follow the frictional overshoot model. Our estimated static stress drop values are higher than the apparent stress drop values. And the stress drop values are quite larger for intraplate earthquakes than the interplate earthquakes.  相似文献   

18.
Approximately 125 hydrothermal annealing experiments have been carried out in an attempt to bracket the stability fields of different ordered structures within the plagioclase feldspar solid solution. Natural crystals were used for the experiments and were subjected to temperatures of ～650°C to ～1,000°C for times of up to 370 days at \(P_{{\text{H}}_{\text{2}} {\text{O}}} \) =600 bars, or \(P_{{\text{H}}_{\text{2}} {\text{O}}} \) =1,200 bars. The structural states of both parent and product materials were characterised by electron diffraction, with special attention being paid to the nature of type e and type b reflections (at h+k=(2n+1), l=(2n+1) positions). Structural changes of the type C \(\bar 1\) → I \(\bar 1\) , C \(\bar 1\) → “e” structure, I \(\bar 1\) → “e” and “e” structure → I \(\bar 1\) have been followed. There are marked differences between the ordering behaviour of crystals with compositions on either side of the C \(\bar 1\) ? I \(\bar 1\) transition line. In the composition range ～ An50 to ～ An70 the e structure appears to have a true field of stability relative to I \(\bar 1\) ordering, and a transformation of the type I \(\bar 1\) ? e has been reversed. It is suggested that the e structure is the more stable ordered state at temperatures of ～ 800°C and below. For compositions more albite-rich than ～ An50 the upper temperature limit for long range e ordering is lower than ～ 750°C, and there is no evidence for any I \(\bar 1\) ordering. The evidence for a true stability field for “e” plagioclase, which is also consistent with calorimetric data, necessitates reanalysis both of the ordering behaviour of plagioclase crystals in nature and of the equilibrium phase diagram for the albite-anorthite system. Igneous crystals with compositions of ～ An65, for example, probably follow a sequence of structural states C \(\bar 1\) → I \(\bar 1\) → e during cooling. The peristerite, Bøggild and Huttenlocher miscibility gaps are clearly associated with breaks in the albite, e and I \(\bar 1\) ordering behaviour but their exact topologies will depend on the thermodynamic character of the order/disorder transformations.  相似文献   

19.
An empirical model is developed to predict the dissolution rate of calcite in saline solutions that are saturated with respect to dissolved \(\hbox {CO}_2\) over a broad range of both subcritical and supercritical conditions. The focus is on determining the rate of calcite dissolution within a temperature range of 50–100 \(^\circ \hbox {C}\) and pressures up to 600 bar, relevant for \(\hbox {CO}_2\) sequestration in saline aquifers. A general reaction kinetic model is used that is based on the extension of the standard Arrhenius equation with an added, solubility-dependent, pH term to account for the saturated concentration of dissolved \(\hbox {CO}_2\). On the basis of this kinetic model, a new rate equation is obtained using multi-parameter, nonlinear regression of experimental data to determine the dissolution of calcite as a function of temperature, pressure and salinity. Different models for the activity coefficient of \(\hbox {CO}_2\) dissolved in saline solutions are accounted for. The new rate equation helps us obtain good agreement with experimental data, and it is applied to study the geochemically induced alterations of fracture geometry due to calcite dissolution.  相似文献   

20.
The distribution of F between tremolite and talc has been determined in metamorphosed siliceous carbonates from the Grenville Province, Ontario. Wavelength dispersive electron microprobe analyses of contiguous, texturally compatible tremolite-talc pairs indicate that the substitution of F for OH is the most significant deviation from end-member stoichiometry in the samples studied. Mixing of F and OH components has been represented by an ideal solution model for F in tremolite and an asymmetric model for F in talc. Both linear and nonlinear regression techniques have been used to derive activity coefficients for the exchange of one equivalent of OH and F components in talc. The following expressions are the result of nonlinear regression of 32 analyses from coexisting mineral pairs: $$\begin{gathered} \ln \gamma _{TC(OH)} = X_{TC(F)}^2 [2.447 - 2.845X_{TC(OH)} ] \hfill \\ \ln \gamma _{TC(F)} = X_{TC(OH)}^2 [1.024 + 2.845X_{TC(F} ] \hfill \\ \end{gathered} $$ Isobaric \(T - X_{CO_2 } \) sections constructed using these equations show an enhanced stability for the assemblages talc+calcite and phlogopite+quartz+calcite with F substituting for OH. Projection of isothermal invariant points into P-T space predicts a shift in the stability of the assemblage talc-calcite from lower grade into the sillimanite field with increasing substitution of F for OH in talc.  相似文献   

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