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Governing Equations (governing + equation)
Selected AbstractsOn the Governing Equations and Model Assumptions for Multiphase Flow in Porous MediaGROUND WATER, Issue 4 2000Amir Gamliel No abstract is available for this article. [source] Numerical simulation of two-dimensional transient water driven non-Newtonian fluid flow in porous mediaINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 4 2002Zuojin Zhu Abstract Numerical simulation of two-dimensional transient water driven non-Newtonian fluid flow in porous media has been performed. The hyperbolic non-Newtonian fluid model was used to describe the characteristics of non-Newtonian fluid flow. Governing equations were first approximated by implicit finite difference, and then solved by a stabilized bi-conjugate gradient (Bi-CGSTAB) approach. A comparison of the numerical results for the case of water driven Newtonian fluid was made to validate the numerical method. For water driven Newtonian fluid flow, it was found that the numerical results are satisfactorily consistent with those obtained by commercial software VIP which is the abbreviation of vector implicit procedure for numerical simulation of Newtonian fluid flow in porous media. The maximum deviation for average pressure is less than 1.5 per cent; the distribution of water saturation is almost the same as that obtained by VIP. For water driven non-Newtonian fluid flow in porous media, it was found that the factor of pressure gradient of the non-Newtonian fluid has significant effects on the process of oil recovery. The correction of numerical simulation based on the global mass balance plays an important role in oil reservoir simulation. Copyright © 2002 John Wiley & Sons, Ltd. [source] Critical damping of structures with elastically supported visco-elastic dampersEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 2 2002Yujin Lee Abstract This paper presents a new formulation for critical damping of structures with elastically supported visco-elastic dampers.Owing to the great dependence of damper performance on the support stiffness, this model is inevitable for reliable modelling of structures with visco-elastic dampers. It is shown that the governing equation of free vibration of this model is reduced to a third-order differential equation and the conventional method for defining the critical damping for second-order differential equations cannot be applied to the present model. It is demonstrated that the region of overdamped vibration is finite in contrast to that (semi-infinite) for second-order differential equations and multiple critical damping coefficients exist. However, it turns out that the smaller one is practically meaningful. Copyright © 2001 John Wiley & Sons, Ltd. [source] The boundary element method for solving the Laplace equation in two-dimensions with oblique derivative boundary conditionsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2007D. Lesnic Abstract In this communication, we extend the Neumann boundary conditions by adding a component containing the tangential derivative, hence producing oblique derivative boundary conditions. A variant of Green's formula is employed to translate the tangential derivative to the fundamental solution in the boundary element method (BEM). The two-dimensional steady-state heat conduction with the imposed oblique boundary condition has been tested in smooth, piecewise smooth and multiply connected domains in which the Laplace equation is the governing equation, producing results at the boundary in excellent agreement with the available analytical solutions. Convergence of the normal and tangential derivatives at the boundary is also achieved. The numerical boundary data are then used to successfully calculate the values of the solution at interior points again. The outlined test cases have been repeated with various boundary element meshes, indicating that the accuracy of the numerical results increases with increasing boundary discretization. Copyright © 2006 John Wiley & Sons, Ltd. [source] P-wave and S-wave decomposition in boundary integral equation for plane elastodynamic problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2003Emmanuel Perrey-Debain Abstract The method of plane wave basis functions, a subset of the method of Partition of Unity, has previously been applied successfully to finite element and boundary element models for the Helmholtz equation. In this paper we describe the extension of the method to problems of scattering of elastic waves. This problem is more complicated for two reasons. First, the governing equation is now a vector equation and second multiple wave speeds are present, for any given frequency. The formulation has therefore a number of novel features. A full development of the necessary theory is given. Results are presented for some classical problems in the scattering of elastic waves. They demonstrate the same features as those previously obtained for the Helmholtz equation, namely that for a given level of error far fewer degrees of freedom are required in the system matrix. The use of the plane wave basis promises to yield a considerable increase in efficiency over conventional boundary element formulations in elastodynamics. Copyright © 2003 John Wiley & Sons, Ltd. [source] PC cluster parallel finite element analysis of sloshing problem by earthquake using different network environmentsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2002Kazuo Kashiyama Abstract This paper presents a parallel finite element method for the analysis of the sloshing problem caused by earthquakes. The incompressible Navier,Stokes equation based on Arbitrary Lagrangian,Eulerian description is used as the governing equation. The SUPG/PSPG formulation is employed to improve the numerical stability and the accuracy. Parallel implementation of the unstructured grid based formulation was carried out on a PC cluster. The present method was applied to analyse the sloshing problem of a rectangular tank and an actual reservoir. The effect of parallelization on the efficiency of the computations was examined using a number of different network environments. Copyright © 2002 John Wiley & Sons, Ltd. [source] Numerical calculations of erosion in an abrupt pipe contraction of different contraction ratiosINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2004M. A. Habib Abstract Erosion predictions in a pipe with abrupt contraction of different contraction ratios for the special case of two-phase (liquid and solid) turbulent flow with low particle concentration are presented. A mathematical model based on the time-averaged governing equations of 2-D axi-symmetric turbulent flow is used for the calculations of the fluid velocity field (continuous phase). The particle-tracking model of the solid particles is based on the solution of the governing equation of each particle motion taking into consideration the effect of particle rebound behaviour. Models of erosion were used to predict the erosion rate in mg/g. The effect of Reynolds number and flow direction with respect to the gravity was investigated for three contraction geometries considering water flow in a carbon steel pipe. The results show that the influence of the contraction ratio on local erosion is very significant. However, this influence becomes insignificant when the average erosion rates over the sudden contraction area are considered. The results also indicate the significant influence of inlet velocity variations. The influence of buoyancy is significant for the cases of low velocity of the continuous flow. A threshold velocity below which erosion may be neglected was indicated. Copyright © 2004 John Wiley & Sons, Ltd. [source] Stability and accuracy of a semi-implicit Godunov scheme for mass transportINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2004Scott F. Bradford Abstract Semi-implicit, Godunov-type models are adapted for solving the two-dimensional, time-dependent, mass transport equation on a geophysical scale. The method uses Van Leer's MUSCL reconstruction in conjunction with an explicit, predictor,corrector method to discretize and integrate the advection and lateral diffusion portions of the governing equation to second-order spatial and temporal accuracy. Three classical schemes are investigated for computing advection: Lax-Wendroff, Warming-Beam, and Fromm. The proposed method uses second order, centred finite differences to spatially discretize the diffusion terms. In order to improve model stability and efficiency, vertical diffusion is implicitly integrated with the Crank,Nicolson method and implicit treatment of vertical diffusion in the predictor is also examined. Semi-discrete and Von Neumann analyses are utilized to compare the stability as well as the amplitude and phase accuracy of the proposed method with other explicit and semi-implicit schemes. Some linear, two-dimensional examples are solved and predictions are compared with the analytical solutions. Computational effort is also examined to illustrate the improved efficiency of the proposed model. Copyright © 2004 John Wiley & Sons, Ltd. [source] Spatially varied flow in non-prismatic channels.IRRIGATION AND DRAINAGE, Issue 1 2002II: numerical solution, experimental verification canal d'irrigation; modélisation; écoulement spatialement varié; équation de transfert; analyse numérique; expérimentation Abstract A new governing equation was proposed for the spatially varied flows with increasing discharge, which affects the position and the depth of the control section as well as the entire water surface profile within the channel. This paper presents the use of the Newton-Raphson method in the solution process. The results of the computational model were compared with experimental data and with the output of the traditional equation. It was indicated that because of incorporating the expansion factor of the non-prismatic channels, the proposed equation is able to represent the experimental data very well and hence is superior to the traditional equation for design purposes. Copyright © 2002 John Wiley & Sons, Ltd. RÉSUMÉ Une nouvelle éeuation a été purposée pour l'écoulement varié spatialement sous la condition de l'augmentation du débit. Cette équation considére la situation et la profondeue de coupe de contrôle et aussi calcule le profil de niveau de l'eau. La solution numérique utilise la méthode de Newton-Raphson. On a comparé les résultata obtenus par ce modéle avec les données expérimentales et la méthode traditionnelle. Cette comparison montre que grâce à l'incorporation du facteur d'expansion d'un cour d'eau irrégulier, la méthode proposée est capable de représenter trés bien les données expérimentales et peut être beaucoup plus efficace pour le motif de dessin par rapport à la méthode traditionnele Copyright © 2002 John Wiley & Sons, Ltd. [source] Frequency response analysis of slot coatingAICHE JOURNAL, Issue 9 2010Takeaki Tsuda Abstract Frequency responses to the slot die coating process is analyzed using empirical modal analysis to predict the effects of periodic process disturbances such as gap oscillation and variations in vacuum pressure, web velocity, and flow rate. A type of empirical modal analysis known as an experimental modal approach was used, and an oscillator basis model was assumed by using a linearized governing equation, and the coefficient of the basis model was determined by curve-fitting. By completing the process, we were able to decompose each mode, during which process it was found that the modes are of two types: a squeeze mode related to viscous characteristics and sinuous modes that are identical to capillary waves. Observation of the meniscus shapes of each mode revealed, in the third mode near the lip edge, significant fluctuations that can induce other coating defects. © 2010 American Institute of Chemical Engineers AIChE J, 2010 [source] The particular solutions for thin plates resting on Pasternak foundations under arbitrary loadingsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2010Chia-Cheng Tsai Abstract Analytical particular solutions of splines and monomials are obtained for problems of thin plate resting on Pasternak foundation under arbitrary loadings, which are governed by a fourth-order partial differential equation (PDEs). These analytical particular solutions are valuable when the arbitrary loadings are approximated by augmented polyharmonic splines (APS) constructed by splines and monomials. In our derivations, the real coefficient operator in the governing equation is decomposed into two complex coefficient operators whose particular solutions are known in literature. Then, we use the difference trick to recover the analytical particular solutions of the original operator. In addition, we show that the derived particular solution of spline with its first few directional derivatives are bounded as r , 0. This solution procedure may have the potential in obtaining analytical particular solutions of higher order PDEs constructed by products of Helmholtz-type operators. Furthermore, we demonstrate the usages of these analytical particular solutions by few numerical cases in which the homogeneous solutions are complementarily solved by the method of fundamental solutions (MFS). © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010 [source] An Improved LES on Dense Particle-Liquid Turbulent Flows Using Integrated Boltzmann EquationsTHE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 2 2007Xuelin Tang Abstract An improved large eddy simulation (LES) using a dynamic second-order subgrid stress (SGS) model has been developed for simulating dense particle-liquid two-phase turbulent flows. The governing equations of each phase are obtained from a microscopic point of view, using the kinetic theory of molecular gas. They are derived by multiplying the Boltzmann equation of each phase by property parameters and integrating over the velocity space. An inter-particle collision term is included in the governing equation of the particle phase. Assuming a Maxwellian distribution of the velocity for particle-phase, an inter-particle collision term is derived. On a amélioré la simulation des grands tourbillons (LES) à l'aide d'un modèle de contraintes dans les mailles inférieures (SGS) de second ordre dynamique afin de simuler des écoulements turbulents diphasiques particules-liquide. Les équations gouvernantes de chaque phase sont obtenues d'un point de vue microscopique, au moyen de la théorie cinétique du gaz moléculaire. Elles sont calculées en multipliant l'équation de Boltzmann de chaque phase par des paramètres de propriétés et en intégrant sur l'intervalle des vitesses. Un terme de collision inter-particulaire est inclus dans l'équation gouvernante de la phase des particules. [source] Computer programs for estimating substrate flux into steady-state biofilms from pseudoanalytical solutionsCOMPUTER APPLICATIONS IN ENGINEERING EDUCATION, Issue 1 2002Chetan T. Goudar Abstract Fixed-film processes employing microorganisms attached to an inert surface (biofilms) are widely used for biological treatment of municipal and industrial wastewater. For optimal design and analysis of these processes, mathematical models are necessary that describe the dynamics of contaminant transport within these biofilms and the associated contaminant utilization by the microorganisms. However, these governing equations that typically involve Fickian diffusion for contaminant transport and Monod kinetics for contaminant utilization are inherently nonlinear and have no closed form solutions except under special conditions. This can restrict their use in the classroom as cumbersome numerical techniques must be used for their solution. This problem is well documented in the literature and several authors have presented pseudoanalytical solutions that replace numerical solutions with algebraic equations. In the present study, we present pseudoanalytical solution-based computer programs for estimating substrate flux and biofilm thickness for a steady-state biofilm. Depending upon the intended end use, these programs can either partially or totally automate the solution process. In the partial automation mode, they can serve to enhance student understanding of important concepts related to steady-state biofilms, while complete automation can help bring more challenging and realistic problems associated with steady-state biofilms into the classroom. The programs have been tested on MATLAB version 5.0 and are available as freeware for educational purposes. © 2002 Wiley Periodicals, Inc. Comput Appl Eng Educ 10: 26,32, 2002; Published online in Wiley InterScience (www.interscience.wiley.com.); DOI 10.1002/cae.10017 [source] Numerical modelling method for wave propagation in a linear viscoelastic medium with singular memoryGEOPHYSICAL JOURNAL INTERNATIONAL, Issue 2 2004Jian-Fei Lu SUMMARY A numerical modelling method for wave propagation in a linear viscoelastic medium with singular memory is developed in this paper. For a demonstration of the method, the Cole,Cole model of viscoelastic relaxation is adopted here. A formulation of the Cole,Cole model based on internal variables satisfying fractional relaxation equations is applied. In order to avoid integrating and storing of the entire history of the variables, a new method for solving fractional differential equations of arbitrary order based on a set of secondary internal variables is developed. Using the new method, the velocity,stress equations and the fractional relaxation equations are reduced to a system of first-order ordinary differential equations for the velocities, stresses, primary internal variables as well as the secondary internal variables. The horizontal spatial derivatives involved in the governing equations are calculated by the Fourier pseudo-spectral (PS) method, while the vertical ones are calculated by the Chebychev PS method. The physical boundary conditions and the non-reflecting conditions for the Chebychev PS method are also discussed. The global solution of the first-order system of ordinary differential equations is advanced in time by the Euler predictor,corrector methods. For the demonstration of our method, some numerical results are presented. [source] Stochastic Study of Solute Transport in a Nonstationary MediumGROUND WATER, Issue 2 2006Bill X. Hu A Lagrangian stochastic approach is applied to develop a method of moment for solute transport in a physically and chemically nonstationary medium. Stochastic governing equations for mean solute flux and solute covariance are analytically obtained in the first-order accuracy of log conductivity and/or chemical sorption variances and solved numerically using the finite-difference method. The developed method, the numerical method of moments (NMM), is used to predict radionuclide solute transport processes in the saturated zone below the Yucca Mountain project area. The mean, variance, and upper bound of the radionuclide mass flux through a control plane 5 km downstream of the footprint of the repository are calculated. According to their chemical sorption capacities, the various radionuclear chemicals are grouped as nonreactive, weakly sorbing, and strongly sorbing chemicals. The NMM method is used to study their transport processes and influence factors. To verify the method of moments, a Monte Carlo simulation is conducted for nonreactive chemical transport. Results indicate the results from the two methods are consistent, but the NMM method is computationally more efficient than the Monte Carlo method. This study adds to the ongoing debate in the literature on the effect of heterogeneity on solute transport prediction, especially on prediction uncertainty, by showing that the standard derivation of solute flux is larger than the mean solute flux even when the hydraulic conductivity within each geological layer is mild. This study provides a method that may become an efficient calculation tool for many environmental projects. [source] Modeling of a Deep-Seated Geothermal System Near Tianjin, ChinaGROUND WATER, Issue 3 2001Zhou Xun A geothermal field is located in deep-seated basement aquifers in the northeastern part of the North China Plain near Tianjin, China. Carbonate rocks of Ordovician and Middle and Upper Proterozoic age on the Cangxian Uplift are capable of yielding 960 to 4200 m3/d of 57°C to 96°C water to wells from a depth of more than 1000 m. A three-dimensional nonisothermal numerical model was used to simulate and predict the spatial and temporal evolution of pressure and temperature in the geothermal system. The density of the geothermal water, which appears in the governing equations, can be expressed as a linear function of pressure, temperature, and total dissolved solids. A term describing the exchange of heat between water and rock is incorporated in the governing heat transport equation. Conductive heat flow from surrounding formations can be considered among the boundary conditions. Recent data of geothermal water production from the system were used for a first calibration of the numerical model. The calibrated model was used to predict the future changes in pressure and temperature of the geothermal water caused by two pumping schemes. The modeling results indicate that both pressure and temperature have a tendency to decrease with time and pumping. The current withdrawal rates and a pumping period of five months followed by a shut-off period of seven months are helpful in minimizing the degradation of the geothermal resource potential in the area. [source] Research on the thermal corridor of a hypersonic vehicleHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 4 2008Ling Jin Abstract The establishment of a reasonable physical model and an effective solution scheme for the thermal corridor is very important to thermal protection structure design, trajectory selection, aerodynamic configuration optimization design, etc. The concept of a thermal corridor for a hypersonic vehicle was analyzed and a physical model was proposed in this paper. Furthermore, the governing equations and the corresponding algorithm for the thermal corridor were discussed. The envelopes of the height,velocity curves at typical positions of the vehicle X43 were calculated, the characteristics of the thermal corridor were summarized, the effect of the thermal protection material on the thermal corridor was discussed, and the emission coefficient of the thermal protection material was defined. The results indicate that the thermal corridor depends on the emission coefficient of the surface material, the flow conditions, and turbulence transition position. © 2008 Wiley Periodicals, Inc. Heat Trans Asian Res, 37(4): 218,223, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20203 [source] Mixed convection in a horizontal square duct with local inner heatingHEAT TRANSFER - ASIAN RESEARCH (FORMERLY HEAT TRANSFER-JAPANESE RESEARCH), Issue 3 2005Koichi Ichimiya Abstract Numerical analyses were performed for the effect of local inner heating on the mixing flow in a horizontal square duct. Three-dimensional governing equations were solved for Re = 100,Pr = 0.72, and six kinds of inner heating sizes in a duct, with insulated walls or uniform temperature walls. Local inner heating induced the local buoyancy force and produced four recirculating flows across a section in a thermally insulated duct. In a horizontal square duct with uniform wall temperature, the interaction of the buoyancy-induced flows by temperature difference between the fluid and the local inner heating, and between the fluid and the walls reduced the maximum intensity of the secondary flow. Two recirculating flows were generated in a downward region. Heat transfer was locally enhanced or depressed corresponding to the flow situation. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(3): 160,170, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/htj.20056 [source] Axisymmetric interaction of a rigid disc with a transversely isotropic half-spaceINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 12 2010Amir Aabbas Katebi Abstract A theoretical formulation is presented for the determination of the interaction of a vertically loaded disc embedded in a transversely isotropic half-space. By means of a complete representation using a displacement potential, it is shown that the governing equations of motion for this class of problems can be uncoupled into a fourth-order partial differential equation. With the aid of Hankel transforms, a relaxed treatment of the mixed-boundary value problem is formulated as dual integral equations, which, in turn, are reduced to a Fredholm equation of the second kind. In addition to furnishing a unified view of existing solutions for zero and infinite embedments, the present treatment reveals a severe boundary-layer phenomenon, which is apt to be of interest to this class of problems in general. The present solutions are analytically in exact agreement with the existing solutions for a half-space with isotropic material properties. To confirm the accuracy of the numerical evaluation of the integrals involved, numerical results are included for cases of different degrees of the material anisotropy and compared with existing solutions. Further numerical examples are also presented to elucidate the influence of the degree of the material anisotropy on the response. Copyright © 2009 John Wiley & Sons, Ltd. [source] Wave propagation in an inhomogeneous cross-anisotropic mediumINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 7 2010Cheng-Der Wang Abstract Analytical solutions for wave velocities and wave vectors are yielded for a continuously inhomogeneous cross-anisotropic medium, in which Young's moduli (E, E,) and shear modulus (G,) varied exponentially as depth increased. However, for the rest moduli in cross-anisotropic materials, , and ,, remained constant regardless of depth. We assume that cross-anisotropy planes are parallel to the horizontal surface. The generalized Hooke's law, strain,displacement relationships, and equilibrium equations are integrated to constitute governing equations. In these equations, displacement components are fundamental variables and, hence, the solutions of three quasi-wave velocities, VP, VSV, and VSH, and the wave vectors, , and , can be generated for the inhomogeneous cross-anisotropic media. The proposed solutions and those obtained by Daley and Hron, and Levin correlate well with each other when the inhomogeneity parameter, k, is 0. Additionally, parametric study results indicate that the magnitudes and directions of wave velocity are markedly affected by (1) the inhomogeneous parameter, k; (2) the type and degree of geomaterial anisotropy (E/E,, G,/E,, and ,/,,); and (3) the phase angle, ,. Consequently, one must consider the influence of inhomogeneous characteristic when investigating the behaviors of wave propagation in a cross-anisotropic medium. Copyright © 2009 John Wiley & Sons, Ltd. [source] Equal strain consolidation for stone columns reinforced foundationINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 15 2009Kang-He Xie Abstract Column consolidation and deformation are considered by assuming that the quantity of water flowing through the disturbed soil zone into the column is not equal to that flowing out from the column and the difference between them is equal to the volume change of the column. In addition, three patterns of distribution of the horizontal permeability of soil in the disturbed zone are also considered to account for the disturbance effect of columns construction on the surrounding soil. These three patterns include the constant distribution pattern (Pattern I), the linear distribution pattern (Pattern II) and the parabolic distribution pattern (Pattern III). By incorporating the aforementioned characteristics into the analyses, the governing equations containing two variables (i.e. the average excess pore-water pressures within the column and within the entire foundation at any depth) for the consolidation of a composite foundation are derived. The solutions of the governing equations are then obtained using a new initial condition derived from the assumption of equal strain and the equilibrium condition. On the basis of the solutions for excess pore-water pressures, the average degree of consolidation of a composite foundation is obtained and discussed. Finally, a comparison is made of some available solutions. Copyright © 2009 John Wiley & Sons, Ltd. [source] Vertical dynamic response of a rigid foundation embedded in a poroelastic soil layerINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 11 2009Y. Q. Cai Abstract A simplified analytical method is presented for the vertical dynamic analysis of a rigid, massive, cylindrical foundation embedded in a poroelastic soil layer. The foundation is subjected to a time-harmonic vertical loading and is perfectly bonded to the surrounding soil in the vertical direction. The soil underlying the foundation base is represented by a single-layered poroelastic soil based on rigid bedrock while the soil at the side of the foundation is modeled as an independent poroelastic layer composed of a series of infinitesimally thin layers. The behavior of the soil is governed by Biot's poroelastodynamic theory and its governing equations are solved by the use of Hankel integral transform. The contact surface between the foundation base and the soil is smooth and fully permeable. The dynamic interaction problem is solved following standard numerical procedures. The accuracy of the present solution is verified by comparisons with the well-known solutions obtained from other approaches for both the elastodynamic interaction problem and poroelastodynamic interaction problem. Numerical results for the vertical dynamic impedance and response factor of the foundation are presented to demonstrate the influence of nondimensional frequency of excitation, soil layer thickness, poroelastic material parameters, depth ratio and mass ratio on the dynamic response of a rigid foundation embedded in a poroelastic soil layer. Copyright © 2008 John Wiley & Sons, Ltd. [source] Dynamics of unsaturated soils using various finite element formulationsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 5 2009Nadarajah Ravichandran Abstract Unsaturated soils are three-phase porous media consisting of a solid skeleton, pore liquid, and pore gas. The coupled mathematical equations representing the dynamics of unsaturated soils can be derived based on the theory of mixtures. Solution of these fully coupled governing equations for unsaturated soils requires tremendous computational resources because three individual phases and interactions between them have to be taken into account. The fully coupled equations governing the dynamics of unsaturated soils are first presented and then two finite element formulations of the governing equations are presented and implemented within a finite element framework. The finite element implementation of all the terms in the governing equations results in the complete formulation and is solved for the first time in this paper. A computationally efficient reduced formulation is obtained by neglecting the relative accelerations and velocities of liquid and gas in the governing equations to investigate the effects of fluid flow in the overall behavior. These two formulations are used to simulate the behavior of an unsaturated silty soil embankment subjected to base shaking and compared with the results from another commonly used partially reduced formulation that neglects the relative accelerations, but takes into account the relative velocities. The stress,strain response of the solid skeleton is modeled as both elastic and elastoplastic in all three analyses. In the elastic analyses no permanent deformations are predicted and the displacements of the partially reduced formulation are in between those of the reduced and complete formulations. The frequency of vibration of the complete formulation in the elastic analysis is closer to the predominant frequency of the base motion and smaller than the frequencies of vibration of the other two analyses. Proper consideration of damping due to fluid flows in the complete formulation is the likely reason for this difference. Permanent deformations are predicted by all three formulations for the elastoplastic analyses. The complete formulation, however, predicts reductions in pore fluid pressures following strong shaking resulting in somewhat smaller displacements than the reduced formulation. The results from complete and reduced formulations are otherwise comparable for elastoplastic analyses. For the elastoplastic analysis, the partially reduced formulation leads to stiffer response than the other two formulations. The likely reason for this stiffer response in the elastoplastic analysis is the interpolation scheme (linear displacement and linear pore fluid pressures) used in the finite element implementation of the partially reduced formulation. Copyright © 2008 John Wiley & Sons, Ltd. [source] A novel analytical solution for constant-head test in a patchy aquiferINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 12 2006Shaw-Yang Yang Abstract A mathematical model describing the hydraulic head distribution for a constant-head test performed in a well situated at the centre of a patchy aquifer is presented. The analytical solution for the mathematical model is derived by the Laplace transforms and the Bromwich integral method. The solution for the hydraulic head has been shown to satisfy the governing equations, related boundary conditions, and continuity requirements for the hydraulic head and flow rate at the interface of the patch and outer regions. An efficient numerical approach is proposed to evaluate the solution, which has an integral covering an integration range from zero to infinity and an integrand consisting the product and square of the Bessel functions. This solution can be used to produce the curves of dimensionless hydraulic head against dimensionless time for investigating the effect of the contrast of formation properties on the dimensionless hydraulic head distribution. Define the ratio of outer-region transmissivity to patch-region transmissivity as ,. The dimensionless hydraulic head for ,=0.1 case is about 2.72 times to that for ,=10 case at dimensionless large time (e.g. ,,106) when the dimensionless distance (,) equals 10. The results indicate that the hydraulic head distribution highly depends on the hydraulic properties of two-zone formations. Copyright © 2006 John Wiley & Sons, Ltd. [source] Bond rolling resistance and its effect on yielding of bonded granulates by DEM analysesINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 8 2006M. J. Jiang Abstract A discrete element modelling of bonded granulates and investigation on the bond effect on their behaviour are very important to geomechanics. This paper presents a two-dimensional (2-D) discrete element theory for bonded granulates with bond rolling resistance and provides a numerical investigation into the effect of bond rolling resistance on the yielding of bonded granulates. The model consists of mechanical contact models and equations governing the motion of bonded particles. The key point of the theory is that the assumption in the original bond contact model previously proposed by the authors (55th CSCE-ASCE Conference, Hamilton, Ont., Canada, 2002; 313,320; J. Eng. Mech. (ASCE) 2005; 131(11):1209,1213) that bonded particles are in contact at discrete points, is here replaced by a more reliable assumption that bonded particles are in contact over a width. By making the idealization that the bond contact width is continuously distributed with the normal/tangential basic elements (BE) (each BE is composed of spring, dashpot, bond, slider or divider), we establish a bond rolling contact model together with bond normal/tangential contact models, and also relate the governing equations to local equilibrium. Only one physical parameter , needs to be introduced in the theory in comparison to the original bond discrete element model. The model has been implemented into a 2-D distinct element method code, NS2D. Using the NS2D, a total of 86 1-D, constant stress ratio, and biaxial compressions tests have been carried out on the bonded granular samples of different densities, bonding strengths and rolling resistances. The numerical results show that: (i) the new theory predicts a larger internal friction angle, a larger yielding stress, more brittle behaviour and larger final broken contact ratio than the original bond model; (ii) the yielding stress increases nonlinearly with the increasing value of ,, and (iii) the first-yield curve (initiation of bond breakage), which define a zone of none bond breakage and which shape and size are affected by the material density, is amplified by the bond rolling resistance in analogous to that predicted by the original bond model. Copyright © 2006 John Wiley & Sons, Ltd. [source] The modelling of anchors using the material point methodINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 9 2005C. J. Coetzee Abstract The ultimate capacity of anchors is determined using the material point method (MPM). MPM is a so-called meshless method capable of modelling large displacements, deformations and contact between different bodies. A short introduction to MPM is given and the derivation of the discrete governing equations. The analysis of a vertically loaded anchor and one loaded at 45° is presented. The load,displacement curves are compared to that obtained from experiments and the effect of soil stiffness and anchor roughness is investigated. The results of the vertically loaded anchor are also compared to an analytical solution. The displacement of the soil surface above the anchor was measured and compared to the numerical predictions. Convergence with mesh refinement is demonstrated and the effect of mesh size and dilatancy angle on the shear band width and orientation is indicated. The results show that MPM can model anchor pull out successfully. No special interface elements are needed to model the anchor,soil interface and the predicted ultimate capacities were within 10% of the measured values. Copyright © 2005 John Wiley & Sons, Ltd. [source] Experience in calibrating the double-hardening constitutive model MonotINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 13 2003M. A. Hicks The Monot double-hardening soil model has previously been implemented within a general purpose finite element algorithm, and used in the analysis of numerous practical problems. This paper reviews experience gained in calibrating Monot to laboratory data and demonstrates how the calibration process may be simplified without detriment to the range of behaviours modelled. It describes Monot's principal features, important governing equations and various calibration methods, including strategies for overconsolidated, cemented and cohesive soils. Based on a critical review of over 30 previous Monot calibrations, for sands and other geomaterials, trends in parameter values have been identified, enabling parameters to be categorized according to their relative importance. It is shown that, for most practical purposes, a maximum of only 5 parameters is needed; for the remaining parameters, standard default values are suggested. Hence, the advanced stress,strain modelling offered by Monot is attainable with a similar number of parameters as would be needed for some simpler, less versatile, models. Copyright © 2003 John Wiley & Sons, Ltd. [source] Development of a technique for modelling clay liner desiccationINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 6 2003Y. Zhou Abstract This paper presents a model for the analysis of clay liner desiccation in a landfill barrier system due to temperature effects. The model incorporates consideration of fully coupled heat-moisture-air flow, a non-linear constitutive relationship, the dependence of void ratio and volumetric water content on stress, capillary pressure and temperature, and the effect of mechanical deformation on all governing equations. Mass conservative numerical schemes are proposed to improve the accuracy of the finite element solution to the governing equations. The application of the model is then demonstrated by examining three test problems, including isothermal infiltration, heat conduction and non-isothermal water and heat transport. Comparisons are made with results from literature, and good agreement is observed. Copyright © 2003 John Wiley & Sons, Ltd. [source] Numerical solution for consolidation and desiccation of soft soilsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 2 2002Daniel T. C. Yao Abstract The consolidation and desiccation behaviour of soft soils can be described by two time-dependent non-linear partial differential equations using the finite strain theory. Analytical solutions do not exist for these governing equations. In this paper, we develop efficient numerical methods and software for finding the numerical solutions. We introduce a semi-implicit time integration scheme, and show numerically that our method converges. In addition, the numerical solution matches well with the experimental result. A boundary refinement method is also developed to improve the convergence and stability for the case of Neumann type boundary conditions. Interface governing equations are derived to maintain the continuity of consolidation and desiccation processes. This is useful because the soil column can undergo desiccation on top and consolidation on the bottom simultaneously. The numerical algorithms has been implemented into a computer program and the results have been verified with centrifuge test results conducted in our laboratory. Copyright © 2001 John Wiley & Sons, Ltd. [source] Chemically induced deformation of a porous layer coupled with advective,dispersive transport.INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 8 2001Analytical solutions Abstract In this paper a chemically induced deformation of porous material taking place during advective,dispersive transport of a chemical is considered. Linearized governing equations are derived and analytical solutions of 2 one-dimensional problems for a homogeneous layer with drained boundaries are developed. Numerical results for a particular clayey material and a chemical migrating through the layer showing distributions of concentration of chemical, changes in porosity of the material and pore fluid pressure, and evolution of settlement of the layer as functions of time are discussed. Copyright © 2001 John Wiley & Sons, Ltd. [source] | ||||||||||||||||||||||