Dynamics of unsaturated poroelastic solids at finite strain     

Ryosuke Uzuoka  Ronaldo I. Borja 《国际地质力学数值与分析法杂志》2012,36(13):1535-1573

We derive the governing equations for the dynamic response of unsaturated poroelastic solids at finite strain. We obtain simplified governing equations from the complete coupled formulation by neglecting the material time derivative of the relative velocities and the advection terms of the pore fluids relative to the solid skeleton, leading to a so‐called u^s ? p^w ? p^a formulation. We impose the weak forms of the momentum and mass balance equations at the current configuration and implement the framework numerically using a mixed finite element formulation. We verify the proposed method through comparison with analytical solutions and experiments of quasi‐static processes. We use a neo‐Hookean hyperelastic constitutive model for the solid matrix and demonstrate, through numerical examples, the impact of large deformation on the dynamic response of unsaturated poroelastic solids under a variety of loading conditions. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

Outburst floods from glacial Lake Missoula     

G. K. C. ClarkeW. H. Mathews  R. T. Pack 《Quaternary Research》1984,22(3):289-299

The Pleistocene outburst floods from glacial Lake Missoula, known as the “Spokane Floods”, released as much as 2184 km³ of water and produced the greatest known floods of the geologic past. A computer simulation model for these floods that is based on physical equations governing the enlargement by water flow of the tunnel penetrating the ice dam is described. The predicted maximum flood discharge lies in the range 2.74 × 10⁶−13.7 × 10⁶ m³ sec⁻¹, lending independent glaciological support to paleohydrologic estimates of maximum discharge.  相似文献   

Evolution model for substellar objects     

A. I. Pisarenko  A. A. Yatsenko  V. A. Zakhozhay 《Astronomy Reports》2007,51(8):605-614

A new model for the evolution of substellar objects is proposed, which enables computation of their internal structure and evolution in an adiabatic approximation without allowance for axial rotation, magnetic fields, and nuclear reactions. The basic set of differential equations in the model contains a new equation for the gradient of the electron degeneracy parameter and adiabatic coefficients of the new type. The results of numerical simulations of evolutionary sequences of hydrogen (X = 1), helium (Y = 1), and hydrogen-helium (X = 0.75, Y = 0.25) substellar objects with masses M < 0.08 M _⊙ during the evolutionary stage 10⁶ yr < t < 10¹⁰ yr are reported. Luminosity-effective temperature, mass-radius, radius-time, central temperature-central density, and central temperature-age relations are analyzed for the indicated chemical composition.  相似文献   

A numerical model of the evolution of ocean sulfate and sedimentary sulfur during the last 800 million years     

《Geochimica et cosmochimica acta》1986,50(10):2289-2302

A reservoir model describing the time evolution of the sedimentary cycle of sulfur over the past 800 my has been developed. As a first approximation, the ocean sulfate concentration is assumed to be time-independent. With this assumption, the model is integrated backward in time and a new initialization procedure is derived in order to calculate the present state of the system which must be compatible with both observational data and model equations. The effects of a variation of the present state of the cycle on its past evolution are investigated. It is found that, when the present gypsum reservoir content is too low or when the weathering rate constants are too high, no acceptable solution can be obtained for the evolution of the cycle, since one reservoir is forced to depletion. The sensitivity of the model to the mean isotopic composition of the sedimentary system and to the fractionation factor during pyrite formation is also studied.Moreover, a model with time-dependent ocean sulfate concentration was developed. The existence of an acceptable solution appears to be linked to the steady state hypothesis for ocean sulfate, since a model with no acceptable steady state solution may be integrated until t = −800 my without any problem of reservoir depletion when the time-dependent equations are used.A tentative evolution of the ocean sulfate concentration is calculated. It is shown that this concentration is negatively correlated to the δ³⁴S of seawater sulfate. The carbon cycle is modelled in order to compare the calculated δ¹³C of carbonate deposits to the observational data.  相似文献   

The molar volume of FeO–MgO–Fe2O3–Cr2O3–Al2O3–TiO2 spinels     

Emily A. Hamecher  Paula M. Antoshechkina  Mark S. Ghiorso  Paul D. Asimow 《Contributions to Mineralogy and Petrology》2013,165(1):25-43

We define and calibrate a new model of molar volume as a function of pressure, temperature, ordering state, and composition for spinels in the supersystem (Mg, Fe²⁺)(Al, Cr, Fe³⁺)₂O₄ ? (Mg, Fe²⁺)₂TiO₄. We use 832 X-ray and neutron diffraction measurements performed on spinels at ambient and in situ high-P, T conditions to calibrate end-member equations of state and an excess volume model for this system. The effect on molar volume of cation ordering over the octahedral and tetrahedral sites is captured with linear dependence on Mg²⁺, Al³⁺, and Fe³⁺ site occupancy terms. We allow standard-state volumes and coefficients of thermal expansion of the end members to vary within their uncertainties during extraction of the mixing properties, in order to achieve the best fit. Published equations of state of the various spinel end members are analyzed to obtain optimal values of the bulk modulus and its pressure derivative, for each explicit end member. For any spinel composition in the supersystem, the model molar volume is obtained by adding excess volume and cation order-dependent terms to a linear combination of the five end-member volumes, estimated at pressure and temperature using the high-T Vinet equation of state. The preferred model has a total of 9 excess volume and order-dependent parameters and fits nearly all experiments to within 0.02 J/bar/mol, or better than 0.5 % in volume. The model is compared to the current MELTS spinel model with a demonstration of the impact of the model difference on the estimated spinel-garnet lherzolite transition pressure.  相似文献   

A model for the explosive synthesis of p nuclei     

E. M. Babishov  I. V. Kopytin 《Astronomy Reports》2006,50(7):569-578

A model for the synthesis of p nuclei during a supernova explosion of a 25 M _⊙ star is presented. Its main distinguishing feature is the requirement that the yield of s nuclei after the explosion fully correspond to the observed solar-system abundances. A fully self-consistent system of kinetic equations including (n, γ), (p, γ), (α, γ), (p, n), (α, n), and (α, p) reactions and their reverse reactions was solved for the mass fractions of various nuclei, taking into account the dynamics of the propagation of the supernova shock. The absolute abundances of the p nuclei are calculated, and the role of helium layers in the supernova in the synthesis of r nuclei is analyzed. The calculated abundances of p nuclei are in overall good agreement with observations. This makes it possible to synthesize ¹¹³In, ¹³⁸La, and some other problematic isotopes, although the problem of synthesizing molybdenum and ruthenium remains.  相似文献   

A three-scale model for pH-dependent steady flows in 1:1 clays     

Sidarta Araújo de Lima  Márcio A. Murad  Christian Moyne  Didier Stemmelen 《Acta Geotechnica》2008,3(2):153-174

A new three-scale model to describe the coupling between electro-chemistry and hydrodynamics in non-swelling kaolinite clays in steady-state conditions is proposed. The medium is characterized by three separate nano-micro and macroscopic length scales. At the pore (micro)-scale the portrait of the clay consists of micro-pores saturated by an aqueous solution containing four monovalent ions (Na⁺, H⁺, Cl⁻, OH⁻) and charged solid particles surrounded by thin electrical double layers. The movement of the ions is governed by the Nernst–Planck equations and the influence of the double layers upon the hydrodynamics is modeled by a slip boundary condition in the tangential velocity governed by the Stokes problem. To capture the correct form of the interface condition we invoke the nanoscopic modeling of the thin electrical double layer based on Poisson–Boltzmann problem with varying surface charge density ruled by the protonation/deprotonation reactions which occur at the surface of the particles. The two-scale nano/micro model is homogenized to the macroscale leading to a precise derivation of effective governing equations. The macroscopic model is discretized by the finite volume method and applied to numerically simulate desalination of a clay sample induced by an external electrical field generated by the placement of electrodes. Numerical results indicate strong pH-dependence of the electrokinetics.  相似文献   

Calculations of activity-composition relations in multi-site solid solutions: the example of AB2O4 spinels     

Jean Lehmann  Jacques Roux 《Contributions to Mineralogy and Petrology》1984,87(4):328-336

A model to calculate activities in multisite solutions like spinels, from a general expression of the Gibbs free energy is developped. The free energy is written as that of a solution with ideal mixing of cations on each sublattice corrected by any suitable higher order terms. It is shown that activities of i^th end-member can be simply written: $${\text{act (}}i{\text{) = (}}\gamma _i {\text{/}}\gamma _i^{\text{0}} {\text{)}}\mathop \prod \limits_j (N_j /N_j^0 )^{P(j,{\text{ }}i)} .$$ N _j are site occupancy fractions; the γ _i are equal to one for the ideal multisite model and depend only on the higher order corrections to this model; ⁰ indicate values for the i ^th end member. The exponents in the matrix P are integers and constants. The activities cannot be expressed explicitly as function of the macroscopic composition. The site occupancy fractions which minimize the Gibbs free energy must be calculated first solving a set of non linear equations which define the internal equilibrium conditions. The (Fe²⁺, Mg) (Al, Cr, Fe³⁺) spinel are used to illustrate these calculations. For multicomponent AB₂O₄ spinels activity expressions derived for the reference ideal multisite mixing model are: $${\text{act (AB}}_{\text{2}} {\text{O}}_{\text{4}} {\text{) = }}\frac{{({\text{A}})[{\text{B}}]^2 }}{{({\text{A}})_0 [{\text{B}}]_0^2 }}$$ (A): fraction of tetrahedral sites occupied by A²⁺; [B]: fraction of octahedral sites occupied by B³⁺. Because the site occupancy fractions at equilibrium are not independent (but related by the internal equilibrium relations) many equivalent expressions of the activities can be obtained. Finally approximations proposed in the literature to obtain simple explicit activity-concentration relationships are discussed.  相似文献   

Kinematic models for non‐coaxial granular materials. Part I: theory     

M. J. Jiang  D. Harris  H. S. Yu 《国际地质力学数值与分析法杂志》2005,29(7):643-661

The purpose of this paper is to present a physically based plasticity model for non‐coaxial granular materials. The model, which we shall call the double slip and rotation rate model (DSR² model), is a pair of kinematic equations governing the velocity field. The model is based on a discrete micro‐analysis of the kinematics of particles in contact, and is formulated by introducing a quantity called the averaged micro‐pure rotation rate (APR) into the unified plasticity model which was proposed by one of the authors. Our macro–micro mechanical analysis shows that the APR is a non‐linear function of, among other quantities, the macro‐rotation rate of the major principal axis of stress taken in the opposite sense. The requirement of energy dissipation used in the double‐sliding free‐rotating model appears to be unduly restrictive as a constitutive assumption in continuum models. In the DSR² model the APR tensor and the spin tensor are directly linked with non‐coaxiality of the stress and deformation rate tensors. We also propose a simplified plasticity model based on the DSR² model for a class of dilatant materials, and analyse its material stability. Copyright © 2005 John Wiley & Sons, Ltd.  相似文献   

Gravitational radiation during coalescence of neutron stars     

A. G. Aksenov  V. M. Chechetkin 《Astronomy Reports》2013,57(7):498-508

The coalescence of components of a binary star with equal masses (M ₁ = M ₂ = M _⊙) and moving in circular orbits is considered. The equation of state for degenerate neutrons is used, leading to the equation of state for an ideal gas. The initial model has zero temperature, corresponding to a polytrope with n = 1.5. To reduce the required computational time, the initial close binary is constructed using the self-consistent field method. The computations use Newtonian gas dynamics, but the back reaction of the gravitational radiation is taken into account in a PN2.5 post-Newton approximation, obtained using ADM formalism. This makes it possible to apply previous experienceof constructing high-order Godunov-type difference schemes, which are suitable for end-to-end calculations of discontinuous solutions of the gas-dynamics equations on a fixed Eulerian grid. The Poisson equations were solved using an original spherical-function expansion method. The 3D computations yielded the parameters of the gravitational signal. Near the radiation maximum, the strain amplitude is rh ～ 4 × 10⁴ cm, the power maximum is 4 × 10⁵⁴ erg/s, and the typical radiation frequency is ?1 kHz. The energy carried away by gravitational waves is ?10⁵² erg. These parameters are of interest, since they form an inherent part of a rotational mechanism for the supernova explosion. They are also of interest for the planning of gravitational-wave detection experiments.  相似文献   

Experimental and theoretical investigation on the compression behavior of sand-marine clay mixtures within homogenization framework     

《Computers and Geotechnics》2017

In this paper, the compression behavior of sand-marine clay mixtures was investigated, both experimentally and theoretically. The test data reveal that the Normal Compression Line of a sand-clay mixture depends on both the sand fraction and the initial water content of the clay matrix. The local stress in the clay matrix σ′_c is approximately close to the overall stress of the sand-clay mixture σ′ for a sand mass fraction of 20%. The stress ratio, σ′_c/σ′, falls significantly with increasing overall stress for a sand fraction of 60%, which may be attributed to the formation of clay bridges between adjacent sand particles. A compression model was formulated within the homogenization framework. First, a homogenization equation was proposed, which gives a relationship between the overall stiffness E and that of the clay matrix Ec. Then, a model parameter ξ was incorporated considering the sensitivity of the structure parameter on the volume fraction of the clay matrix. Finally, a simple compression model with three model parameters was formulated using the tangent stiffness. Comparisons between the experimental data and simulations reveal that the proposed model can well represent the compression curves of the sand-marine clay mixtures observed in the laboratory.  相似文献   

A time dependent constitutive model for soils with isotach viscosity   总被引：1，自引：0，他引：1  

Teresa M. Bodas Freitas  David M. Potts  Lidija Zdravkovic 《Computers and Geotechnics》2011

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Exact solutions for one‐dimensional consolidation of single‐layer unsaturated soil     

Zhendong Shan  Daosheng Ling  Haojiang Ding 《国际地质力学数值与分析法杂志》2012,36(6):708-722

Based on the Fredlund consolidation theory of unsaturated soil, exact solutions of the governing equations for one‐dimensional consolidation of single‐layer unsaturated soil are presented, in which the water permeability and air transmission are assumed to be constants. The general solution of two coupled homogeneous governing equations is first obtained. This general solution is expressed in terms of two functions psi₁ and ψ₂, where ψ₁ and ψ₂, respectively, satisfy two second‐order partial differential equations, which are in the same form. Using the method of separation of variables, the two partial differential equations are solved and exact solutions for three typical homogeneous boundary conditions are obtained. To obtain exact solutions of nonhomogeneous governing equations with three typical nonhomogeneous boundary conditions, the nonhomogeneous boundary conditions are first transformed into homogeneous boundary conditions. Then according to the method of undetermined coefficients and exact solutions of homogenous governing equations, the series form exact solutions are put forward. The validity of the proposed exact solutions is verified against other analytical solutions in the literature. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

Ionic diffusion in naturally-occurring aqueous solutions: use of activity coefficients in transition-state models     

David E. Anderson  Donald L. Graf 《Geochimica et cosmochimica acta》1978,42(3):251-262

The model of Lane and Kirkaldy (Can. J. Chem. 43, 1812–1828, 1965; 44, 477–485, 1966) for estimating diffusion coefficients in aqueous electrolyte solutions from limiting ionic conductances is rederived for a system of n salts with a common anion, by utilizing the equations of Miller (J. Chem. Phys. 71, 616–632, 1967b; 71, 3588–3592, 1967c). Salt and water activities are used, and it is of necessity assumed that the diffusion mechanism does not change with concentration.The revised model predicts the on-diagonal D^v_ik of a 3 M solution in NaCl-KCl-H₂O to within 5%, compared with errors of 20–30% for the original model. Errors remain constant or decrease as concentrations increase to 3 M, so that predictions of these D^v_ik at even higher concentrations appear promising. Relatively large errors persist in our estimates of the small, off-diagonal coefficients in this system.Measured diffusion coefficients in MgCl₂-NaCl-H₂O extend over only a limited concentration range and are of only moderate accuracy. Nevertheless, the revised model predicts D^v₁₁D^v₂₂, and D^v₂₁, the larger of the off-diagonal coefficients, with errors of only 5–20%.  相似文献   

http://www.sciencedirect.com/science/article/pii/S1674987112001041   总被引：1，自引：0，他引：1  

Andreas Prokoph  Hafida El Bilali  Richard Ernst 《地学前缘(英文版)》2013,4(3):263-276

Large igneous provinces (LIPs) are considered a relevant cause for mass extinctions of marine life throughout Earth’s history. Their flood basalts and associated intrusions can cause significant release of SO₄ and CO₂ and consequently, cause major environmental disruptions. Here, we reconstruct the long-term periodic pattern of LIP emplacement and its impact on ocean chemistry and biodiversity from δ³⁴S_sulfate of the last 520 Ma under particular consideration of the preservation limits of LIP records. A combination of cross-wavelet and other time-series analysis methods has been applied to quantify a potential chain of linkage between LIP emplacement periodicity, geochemical changes and the Phanerozoic marine genera record. We suggest a mantle plume cyclicity represented by LIP volumes (V) of V = ?(350–770) × 10³ km³ sin(2πt/170 Ma) + (300–650) × 10³ km³ sin(2πt/64.5 Ma + 2.3) for t = time in Ma. A shift from the 64.5 Ma to a weaker ～28–35 Ma LIP cyclicity during the Jurassic contributes together with probably independent changes in the marine sulfur cycle to less ocean anoxia, and a general stabilization of ocean chemistry and increasing marine biodiversity throughout the last ～135 Ma. The LIP cycle pattern is coherent with marine biodiversity fluctuations corresponding to a reduction of marine biodiversity of ～120 genera/Ma at ～600 × 10³ km³ LIP eruption volume. The 62–65 Ma LIP cycle pattern as well as excursion in δ³⁴S_sulfate and marine genera reduction suggest a not-yet identified found LIP event at ～440–450 Ma.  相似文献   

Connections between surface complexation and geometric models of mineral dissolution investigated for rhodochrosite     

Owen W Duckworth 《Geochimica et cosmochimica acta》2003,67(10):1787-1801

Mineral dissolution rates have been rationalized in the literature by surface complexation models (SCM) and morphological and geometric models (GM), and reconciliation of these conceptually different yet separately highly successful models is an important goal. In the current work, morphological alterations of the surface are observed in real time at the microscopic level by atomic force microscopy (AFM) while dissolution rates are simultaneously measured at the macroscopic level by utilizing the AFM fluid cell as a classic flow-through reactor. Rhodochrosite dissolution is studied from pH = 2 to 11 at 298 K, and quantitative agreement is found between the dissolution rates determined from microscopic and macroscopic observations. Application of a SCM model for the interpretation of the kinetic data indicates that the surface concentration of >CO₃H regulates dissolution for pH < 7 while the surface concentration of >MnOH₂⁺ regulates dissolution for pH > 7. A GM model explains well the microscopic observations, from which it is apparent that dissolution occurs at steps associated with anisotropic pit expansion. On the basis of the observations, we combine the SCM and GM models to propose a step-site surface complexation model (SSCM), in which the dissolution rates are quantitatively related to the surface chemical speciation of steps. The governing SSCM equation is as follows: R = χ_1/2(k_co + k_ca)[>CO₃H] + χ_1/2(k_mo + k_ma)[>MnOH₂⁺ ], where R is the dissolution rate (mol m⁻² s⁻¹), 2χ_1/2 is the fraction of surface sites located at steps, [>CO₃H] and [>MnOH₂⁺ ] are surface concentrations (mol m⁻²), and k_co, k_ca, k_mo, and k_ma are the respective dissolution rate coefficients (s⁻¹) for the >CO₃H and the >MnOH₂⁺ surface species on obtuse and acute steps. We find k_co = 2.7 s⁻¹, k_ca = 2.1 × 10⁻¹ s⁻¹, k_mo = 4.1 × 10⁻² s⁻¹, k_ma = 3.7 × 10⁻² s⁻¹, and χ_1/2 = 0.015 ± 0.005. The rate coefficients quantify the net result of complex surface step processes, including double-kink initiation and single-kink propagation. We propose that the SSCM model may have general applicability for dissolution far from equilibrium of flat mineral surfaces of ionic crystals, at least those that dissolve by step retreat.  相似文献   

An evaluation of rate equations for calcite precipitation kinetics at pCO2 less than 0.01 atm and pH greater than 8     

William P. Inskeep  Paul R. Bloom 《Geochimica et cosmochimica acta》1985,49(10):2165-2180

We used a reproducible seeded growth technique with a pH-stat to study the kinetics of calcite precipitation at 25°C. We performed different experiments at initial Ca²⁺ and HCO₃^? concentrations ranging from 0.7–2 and 4–7 mmol L^?1, pH values ranging from 8.25 to 8.70, $\text{pCO}{}_2$ values ranging from 0.0006 to 0.01 atm, and ionic strengths ranging from 0.015 to 0.10 mol L^?1. With this experimental data set, we used initial rate measurements and integral methods to test several precipitation rate equations. Rate equations that possess a disequilibrium functional dependence, such as the BURTON et al. (1951) dislocation model, forms of the Davies and Jones (1955) model, and the model used by Reddy and Nancollas (1973), did not adequately describe the kinetics of calcite precipitation at pH greater than 8 and $\text{pCO}{}_2$ less than 0.01 atm. Rate equations that describe independent dissolution and precipitation mechanisms with elementary reactions, such as the equation presented by Plummeret al. (1978), and nancollas and Reddy (1971) were more successful. However, Plummer's model did not adequately describe the rate of all experiments due to the presence of an OH^? surface term in the precipitation rate equation. The elementary reaction of the Nancollas and Reddy model is written in terms of bulk Ca²⁺ and CO₃^? concentrations, and appears to be the most successful model which describes calcite precipitation at pH > 8 and $\text{pCO}{}_2\text{< 0.01}$ atm. The Nancollas and Reddy model, altered to account for varying ionic strengths, adequately described the rate of all experiments and yielded a precipitation rate constant of $\text{118.2 ± 13.9}$ dm⁶ mol^?1 m^?2 s^?1, with an apparent Arrhenius activation energy of 48.1 kJ mol^?1.  相似文献   

δ13C food web analysis of a Texas sand dune community     

Brian Fry  Richard S. Scalan  Patrick L. Parker  John Baccus 《Geochimica et cosmochimica acta》1978,42(8):1299-1302

Stable carbon isotope ratios (δ¹³C) were determined for 31 plant and 16 animal species from a sand dune community on the south Texas coast. Plants and insects had similar δ¹³C values, forming two distinct groups, while herbivorous rodents formed a third intermediate group. This suggests that insects at the study site are specialists which feed on C₃ or C₄ plants, while the rodents are generalists, feeding on plants of both groups.  相似文献   

Modelling the sorption of Mn(II), Co(II), Ni(II), Zn(II), Cd(II), Eu(III), Am(III), Sn(IV), Th(IV), Np(V) and U(VI) on montmorillonite: Linear free energy relationships and estimates of surface binding constants for some selected heavy metals and actinides     

Michael H. Bradbury  Bart Baeyens 《Geochimica et cosmochimica acta》2005,69(4):875-892

In solution thermodynamics, and more recently in surface chemistry, it is well established that relationships can be found between the free energies of formation of aqueous or surface metal complexes and thermodynamic properties of the metal ions or ligands. Such systematic dependencies are commonly termed linear free energy relationships (LFER). A 2 site protolysis non-electrostatic surface complexation and cation exchange (2SPNE SC/CE) model has been used to model “in house” and literature sorption edge data for eleven elements: Mn(II), Co(II), Ni(II), Zn(II), Cd(II), Eu(III), Am(III), Sn(IV), Th(IV), Np(V) and U(VI) to provide surface complexation constants for the strong sites on montmorillonite. Modelling a further 4 sets of sorption isotherms for Ni(II), Zn(II), Eu(III) and U(VI) provided complexation constants for the weak sites. The protolysis constants and site capacities derived for the 2SPNE SC/CE model in previous work were fixed in all of the calculations. Cation exchange was modelled simultaneously to provide selectivity coefficients. Good correlations between the logarithms of strong ^SK_x−1 and weak ^W1K_x−1 site binding constants on montmorillonite and the logarithm of the aqueous hydrolysis constants ^OHK_x were found which could be described by the following equations: Strong (≡S^SOH) sites: