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The dimensionless form of Navier-Stokes equations for two dimensional jet flows are solved using direct numerical simulation. The length scale and the velocity scale of jet flow at the inlet boundary of computational domain are used as two characteristics to define the jet Reynolds number. These two characteristics are jet half-width and centerline velocity. Governing equations are discretized in streamwise and cross stream directions using a sixth order compact finite difference scheme and a mapped compact finite difference method, respectively. Cotangent mapping of is used to relate the physical domain of to the computational domain of . The compact third order Runge-Kutta method is used for time-advancement of the simulation. convective outflow boundary condition is employed to create a non-reflective type boundary condition at the outlet. An inviscid Stuart flow and a completely viscose solutions of Navier Stokes equations are used for the verification of numerical simulations. Results for perturbed jet flow in self-similar coordinates were also investigated which indicate that the time-averaged statistics for velocity, vorticity, turbulence intensities and Reynolds stress distribution tend to collapse on top of each other at flow downstream locations.

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Functionally graded materials have been taken into consideration by many researchers in the last two decades. Gradual changes of mechanical properties in FGMs decrease stress concentration, crack initiation and propagation and delamination. Many of the present and potential applications of FGM contain contact loading.This kind of loading causes surface crack initiation which is followed by subcritical crack propagation.Thus, propagation of surface cracks is one of the most important failure mechanisms in FG structures. In this article two dimensional sliding contact of a rigid flat punch on a homogeneous substrate with an FGM coating is studied. Plane strain condition is considered in this problem. The Properties of the substrate and the FGM layer are assumed to be elastic and the Poisson’s ratio is assumed to be constant. The modulus of elasticity in the graded layer is calculated based on TTO model approximation. This model defines a parameter q which considers the microstructural interactions. The governing equations are solved by Finite Difference method by means of MATLAB software. The influence of different parameters such nonhomogeneity,q, the dimensions of the punch, the thickness of the graded layer and the coefficient of friction on the mode I and II stress intensify factors are investigated.

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The cone-penetration test (CPT) is a well-established in situ test in geotechnical engineering for soil classification and estimation of soil properties. In a CPT, a cone shaped penetrometer is pushed into the ground at a constant rate. The resistance on the cone tip is measured and is then related to soil classification and soil properties. In this research, the finite difference analysis of large deformations for the cone penetration testing (CPT) in the cohesive soil have been conducted using FLAC 2D Software. In this modeling, interface elements between penetrometer and soil are considered and it is assumed that the penetrometer materials show rigid behavior in reaction to the soil materials. FLAC provides interfaces that are characterized by Coulomb sliding and/or tensile separation. Interfaces have the properties of friction, cohesion, dilation, normal and shear stiffness, and tensile strength there is an in-situ state of stress in the ground, before any excavation or construction is started. In FLAC 2D, an attempt is made to reproduce this in-situ state by setting initial conditions. Ideally, information about the initial state comes from field measurements. Boundary conditions are modeled as axesymmetry. Horizontal and vertical direction at the bottom boundary and horizontal direction at the vertical boundary of soil model are fixed. Soil behavior follows full elastic–plastic model and Mohr-Coulomb failure criterion. Numerical model is analyzed to achieve mesh convergency at the various grids. The values of cone and frictional resistance have been obtained through software calculations and then compared with the results obtained from cone penetration test at the aluminum melt factory in Lamard, Fars Province. Stress and displacement contours are related for evaluation of the penetration process. Steady state is considered to achieve steady stress range in which the hole diameter is equal with the CPT hole. The numerical modeling results of CPT test by FLAC 2D software shows good agreement with the field tests results. Furthermore, the results have been discussed by using Robertson Chart 1986 and Eslami- Felonious Chart 1997. Charts almost show same profile with the field test results at the aluminum melt factory site.

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Most of the research has been concentrated on the effects of the horizontal components of near-field earthquakes on the dynamic behavior of the embankment dams. In this paper, the effects of the vertical components will be considered. One of the important characteristics of the near-field ground motions, is the noticeable vertical component with the high frequency content that can exceed considerably, in many cases, the horizontal component of the same earthquake. So far, few studies have been done in this area. In order to investigate the effect of the vertical ground motion on the dynamic behavior of embankment dams, a two dimensional numerical model of the Alborz dam is analyzed by using finite difference method which is used in FLAC2D code. It should be noted that the Alborz dam is a rockfill type with clay core and a maximum height of 78 m located on the Babol River in the north of Iran. The Mohr Coulomb elastic perfectly plastic constitutive model was used to simulate the stress-strain behavior of the dam body and its foundation during the static and dynamic loading. Steps of modeling are as follow: At first stage, construction was carried out in 16 layers. At this step, coupling analysis were done in order to simulate the consolidation and build up of pore pressure in clayey core, with respect to the real time of construction for each layer. Then the analyses were continued to modeling of the impounding. So at this stage the reservoir was raised to the normal water level and the model were analyzed to the steady state seepage condition. Records of near-field and far-field were selected from the same earthquake to provide better and more accurate comparison. Before applying the earthquake records to the base of the foundation in the model, they must be modified. So deconvolution analyses were done by using SHAKE2000 code in order to get the target motion with peak ground acceleration of 0.52g at the surface of the foundation (maximum credible earthquake level at the site of Alborz dam). In addition filtering process, baseline correction and conversion the acceleration time history to the stress time history were done. Results of analysis show that the vertical component of near-field ground motion has considerable effect on the magnitude of strains and deformations including: increasing the settlement of the dam crest to about 45 percent, increasing the deformation of the horizontal axis of the dam, reduction of the magnification factor of the dam crest and especially in the case of near-fault, which the occurrence of near-field earthquakes is more probable. Therefore, this issue should be considered in locating the embankment dams regarding the seismic potential and the distance from the fault, and in the design of them.

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Simultaneous Heat and Water Model (SHAW) is based on the assimilation rate of melting and/or freezing of the accumulated snow as well as melting of ice in soil. The main objective of this study was to evaluate applicability of SHAW Model in determining maximum depth of frost penetration in soils in some typical climates of Iran. To this end, the daily data of air temperature, soil temperatures at different depths, duration of bright sunshine, and air humidity were collected for the period of 1992-2003 for four meteorological stations of Iran including Shahr-e- Kord, Urumia, Sanandaj, and Yazd. Then, the maximum soil frost penetration depth (SFPD) for each year in the above mentioned stations was determined based on both the measured temperatures at different layers of soil and the calculated values using SHAW Model. Results of the analyses indicated that there was a significant linear relationship between the observed and the calculated values of maximum SFPD. The obtained coefficients of linear correlation between the observed and the calculated values for meteorological stations of Shahr-e-Kord, Urumia, Sanandaj and Yazd were 0.90, 0.77, 0.84 and 0.94, respectively, all being significant at one percent level. According to the results, it was concluded that, with the yearly records of weather parameters and soil conditions, a reliable estimate of the maximum annual depth of soil frost penetration can be made in similar regions of Iran by application of SHAW Model.

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Lateral ground displacement due to liquefaction causing damages to major infrastructures like buildings, bridges, pipe, shore line utilities etc. When the surface slope is mild, a common mode of failure is lateral spreading with surface displacements that can exceed several meters. Considering the widespread use of pile foundations, their safety in the occurrence of earthquake has a special importance. Studies after the earthquake have shown that both the force due to structure and the Kinematics interaction between the pile foundations and the soil play an important role in mechanical behavior of piles. Since the effect of the superstructure on the pile-soil interaction analysis is significant; the analysis should be done based on the interaction axis of pile-soil-structure. In this study, finite difference method (FDM) has been used to investigate the effect of the thickness of liquefied layer, slope of liquefied layers and the underground water level on behavior of pile foundations. Results indicate that with an increase in the slope of liquefied layers, the maximum bending moment raises but the slope of this graph for low underground water level (near the surface) is higher. This type of behavior also is observed in the shear force created in the pile foundation.

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In the present study the problem of a two-layered model for an unsteady and pulsatile flow of blood through a stenosed artery is numerically simulated. The model consists of a core layer of suspension of erythrocytes and a peripheral plasma layer. The core is assumed to be represented using a micropolar fluid and the plasma layer using a Newtonian fluid. The artery is considered to be elastic and the geometry of the stenosis is taken as time-dependent, however a comparison has been made with the rigid ones. The shape of the stenosis in the arterial lumen is chosen to be axially non-symmetric but radially symmetric in order to improve resemblance to the in-vivo situations. By applying a suitable coordinate transformation, the stenosed artery turns into a rectangular and rigid artery. The Navier-Stokes equations of motion of the blood flow, subjected to a pulsatile pressure gradient are solved numerically using the finite difference scheme. Dynamical characteristics of the blood flow such as the velocity profile, the volumetric flow rate and the resistance to flow are obtained and the effects of the wall motion and the severity of the stenosis on these flow characteristics are discussed. The results are found to be in good agreement with the available analytical results.

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Anchors play a special role in geotechnical structures such as excavations. The anchor section in soil is generally divided into five zones including reinforcement element, grout, grout and surrounding soil mixture, shear zone and soil media. The main objective of the present research is to determine the soil-anchor interaction parameters for numerical modeling of anchored wall using FLAC2D software. Basically, the injection area determining is the main challenge in the anchor force nomination. According to the proposed method, the diameter of the injected area is determined based on the injection pressure, grout volume, porosity and shear zone thickness. It is shown that the diameter of the injected area is approximately increased by 40% relatively to the drilling diameter. The diameter of the injected area in rock media, however, is equal to the drilling diameter. The other parameters are determined using equalization of rock media formulas for soil media. In order to ensure the validity of the proposed method, the pull-out test is numerically simulated in FLAC2D software. The numerical results have been then verified with anchor tension results in an excavation project. The results indicate that ultimate load of anchor calculated from the numerical model is comparable with equations proposed by many researches. Also, there is a negligible difference between the displacement obtained in numerical simulation and pull-out test results. This method is therefore can be used in numerical modeling of anchored wall in soil media with high precision. Anchors play a special role in geotechnical structures such as excavations. The anchor section in soil is generally divided into five zones including reinforcement element, grout, grout and surrounding soil mixture, shear zone and soil media. The main objective of the present research is to determine the soil-anchor interaction parameters for numerical modeling of anchored wall using FLAC2D software. Basically, the injection area determining is the main challenge in the anchor force nomination. According to the proposed method, the diameter of the injected area is determined based on the injection pressure, grout volume, porosity and shear zone thickness. It is shown that the diameter of the injected area is approximately increased by 40% relatively to the drilling diameter. The diameter of the injected area in rock media, however, is equal to the drilling diameter. The other parameters are determined using equalization of rock media formulas for soil media. In order to ensure the validity of the proposed method, the pull-out test is numerically simulated in FLAC2D software. The numerical results have been then verified with anchor tension results in an excavation project. The results indicate that ultimate load of anchor calculated from the numerical model is comparable with equations proposed by many researches. Also, there is a negligible difference between the displacement obtained in numerical simulation and pull-out test results. This method is therefore can be used in numerical modeling of anchored wall in soil media with high precision.

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In this article bubbly flow under the specified axial pressure gradient in a curved channel is studied numerically. To do so, a second order parallelized front-tracking/finite-difference method based on the projection algorithm is implemented to solve the governing equations including the full Navier-Stokes and continuity equations in the cylindrical coordinates system using a uniform staggered grid well fitted to the geometry concerned. In the absence of gravity the mid-plane parallel to the curved duct plane, which is the symmetry plane in the single fluid flow inside the curved duct, separates the bubbly flow into two different flow regions not interacting with each other. Twelve bubbles with diameters of 0.125 wall units are distributed in the equally spaced distances from each other. The numerical results obtained indicate that for the cases studied here, the bubbles reach the statistical steady state with an almost constant final orbital motion path due to the strong secondary field. Furthermore, the effects of different physical parameters such as Reynolds number, and curvature ratio on the flow field at the no slip boundary conditions, are investigated in detail.

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In this paper a mathematical model of pulsatile, unsteady and non-Newtonian blood flow through elastic tapered artery with overlapping stenosis is proposed. The blood flow has been assumed to be non-Linear, fully developed, laminar, axisymmetric, two-dimensional. The non-Newtonian model chosen is characterized by Sisko model for discribe the rheology of blood. The artery has been assumed to be elastic and time-dependent stenosis is considered. Due to the blood flow depends on the pumping action of the heart, the blood flow has been assumed pulsate. The stenosed artery change in to a rectangular and rigid artery, using a radial coordinate transformation on the continuity and the nonlinear momentum equations and boundary conditions. The discretization of the continuity and the non-linear momentum equations and boundary conditions are obtained by finite difference scheme. The radial and axial velocity profiles are obtained and the blood flow characteristics such a resistive impedances and volumetric flow rate and the severity of the stenosis are discussed. The volumetric flow rate is minimum in the case of converging tapered arteries and the resistive impedances is maximum in the case of converging tapered arteries by effect of tapering angle.

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Abstract: Saturated granular soils are possible liquefied when subjected to earthquake loading. This phenomenon is result from generation of excess water pore pressure because of non enough time to water drainage and govern non- Consolidated Condition. When liquefaction is occurred, many forces are generated and undergrounds structures are affected. In this research numerical analysis on buried pipelines in FLAC 2D software are performed and verified duration a comparative process with experimental result from ASCE organization. In present research surveyed effects of various parameters on liquefaction occurrence and probable damages to buried pipelines as dilatancy and friction angle of soil, relative density of back fill around the pipe, diameter and buried depth of pipe and underground water level. Results indicated that uplift of pipe decrease when dilatancy and friction angle of soil increased in constant relative density condition. This result is different for varied relative density. In low and medium relative density by increasing of dilatancy angle, uplift of pipe increase, reach to pick and decrease. But floating decrease with increasing dilatancy angle for high relative density always. Buried pipe in depth trench and increase of dead load result from back fill on pipeline and usage of pipes with small diameter, decrease uplift the pipe in liquefaction occurrence too. Of course don’t expect perform this subjects in all conditions. for example conflict ion to other underground installation, necessary hydraulic gradient for fluids flow or excavation in region with up underground level, don’t make to excavation of deep conduits. The analysis demonstrate that vertical displacement and damages to pipe is decrease if around installed pipe in conduit back fill with non- liquefied soils. In this new analysis all physical properties of soil and pipe in model are without any change except the cohesion and friction angle of soil around the pipe. Cohesion soils are low potential to liquefaction. For this reason we increase this coefficient from zero to 30 kpa and reach the friction angle to 30 degree. Results are demonstrated in a graph that show uplift versus thickness of non- liquefied soil normalized with diameter of pipe. Final parameter that surveyed in this research is effect of underground water level on floating buried pipeline. Results show decrease of underground water level cause to decrease of floating and damages to pipeline. For this purpose add a new water level to base model and run the analysis. In next steppes the underground water level is lesser and results are show in a graph that explain variation of vertical displacement versus water level normalized by thickness of soil model. This work possible by excavation of drainage shaft and drop down water level nearby the pipeline. Of course, look this work isn’t economical proposal for long transmission pipelines as petroleum or water conveyance. But in limit industrial sites as refineries this proposal is an improvement work to prevent any damage and and continual service of lifelines duration of unpredictable phenomenon. Keywords: Liquefaction, buried pipelines, FLAC, finite difference method, Finn’s model. Liquefaction, buried pipelines, FLAC, finite

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Subsurface drainage systems are used to control the depth of the water table and to reduce or prevent soil salinity. Water flow in these systems is described by the Boussinesq Equation, and the Advection-Dispersion Equation coupled with the Boussinesq Equation is used to study the solute transport. The objective of this study was to propose a finite difference solution of the Advection-Dispersion Equation using a lineal radiation condition in the drains. The equations’ parameters were estimated from a methodology based on the granulometric curve and inverse problems. The algorithm needs the water flow values, which were calculated with the Boussinesq Equation, where a fractal radiation condition and variable drainable porosity were applied. To evaluate the solution descriptive capacity, a laboratory drainage experiment was used. In the experiment, the pH, temperature, and electric conductivity of drainage water were measured to find the salt’s concentration. The salts concentration evolution was reproduced using the finite difference solution of the Advection-Dispersion Equation, and the dispersivity parameter was found by inverse modelling. The numerical solution was used to simulate the leaching of saline soil. The result showed that this solution could be used as a new tool for the design of agricultural drainage systems, enabling the optimal development of crops according to their water needs and the degree of tolerance to salinity.

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In this study, the hybrid Lattice Boltzmann - Finite difference - Immersed Boundary method has been used for investigation of problems with heat transfer. For this purpose, mass and momentum conservation equations are solved by the Immersed Boundary- Lattice Boltzmann method and finite difference method has been used for solving energy conservation equation. The effect of Immersed Boundary has been shown as force and external energy source term in equations and therefor flow and heat transfer around circular cylinder and also the effect of how to move cylinder in heating of fluid inside the cavity has been studied. for this purpose four kinds of movements: circular reciprocating, normal circular, diagonal amplitude and horizontal amplitude have been considered for the cylinder and in all cases, the changes of force coefficients and Nusselt number have been discussed. It has been showed that the circular reciprocating movement has more effect on heating of fluid inside the cavity, which indeed this movement reduces the time of fluid heating about 20 percent in comparison with normal circular and diagonal amplitude movement and approximately 37 percent in comparison with horizontal amplitude movement. In all of the studied problems, the efficiency of hybrid method has been proved.

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Soil reinforcement is a new technique to improve the mechanical properties of soil. Geosynthetic reinforced soil walls are usually designed based on limit equilibrium methods, ignoring the effects of foundation, reinforcement stiffness, facing, and other parameters. However, design procedures do not consider the deformation of the walls explicitly. Recently, numerical methods are used for the design and analysis of reinforced soil walls, and the programs written on this basis are used. Usually in limit methods, design of reinforced soil structures control for external stability or total stability or internal stability. After design of reinforcement elements, the overall stability of wall, i.e. overturning, sliding, and bearing capacity should be controlled. But in numerical methods, stress distribution and deformation can be achieved in reinforced soil walls. In this study, the finite difference method is used to perform analysis. According to the deformation manner of the wall and boundary conditions imposed on the structure in the reference study, so that the wall is joint at the heel (wall cannot slide) and taken into account its foundation in the rigid (insufficient bearing capacity does not happen), it can be said that obtained results of this modeling are used only for the overturning mode. In this numerical study, the effect of various system parameters on the performance of the wall, especially the maximum tensile force in the reinforcements and the horizontal displacement of the wall, is merely investigated for the external overturning instability mode. The important parameters of reinforced soil wall structure were studied including the reinforcement stiffness (J), the backfill soil friction angle (∅), the elasticity modulus of backfill soil (Es), the facing wall rigidity (EI), the reinforcement length (L), and wall height (H). Among investigated parameters, the most important parameters effective on the amount of deformation of the wall and maximum tensile force in reinforcements are reinforcement stiffness (J) and backfill soil friction angle (∅) regarding the material properties, respectively; other parameters do not have significant effect on the cases studied. The effect of stiffness on the maximum tensile force in the reinforcements is minimal and negligible. In the wall geometry which includes the reinforcement length (L) and wall height (H), the reinforcement length was the most effective and the most important factor to design reinforced soil walls. Based on the numerical results, the best range of L/H ratio to design reinforced soil walls is between 0.5 and 0.8 since for L/H ratio equal to 0.8 and more, the horizontal displacement of the wall is considered almost the same. Due to the importance of the project and the cost, it is suggested to consider L/H equal to 0.7. In this numerical study, curves are provided for predicting the maximum horizontal displacement of the wall and the maximum tensile force in the reinforcements. The numerical analyses show that there is a particular pattern between the maximum horizontal displacements of the walls and maximum tensile forces in the reinforcements. The results are presented in the form of graphs; using these graphs, the maximum horizontal displacement of the facing wall and the maximum tensile force in the reinforcement for walls with different heights can be predicted.

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In the present study, properties of unsteady blood flow through an stenosed artery is investigated. The study has a tapered artery stenosed and asymmetric elastic walls is considered. The flow of blood is assumed to be incompressible, laminar and fully developed. To consider the effect of suspended particles in the blood, fluid model is used to describe micropolar Eringen. Governing equations are extracted and Mild stenosis approximation is applied to simplify. Also, an suitable converted is applied to momentum equations, initial and boundary conditions, the cosine shape mesh grid to regular mesh grid by utilizing suitable transformation. Non-slip boundary condition equations using finite difference method is solved numerically. To investigate the graphical shapes in the study, the effect of parameters related to flow and tapered angle has been the matter of into rest to investigate the Axial and rotational velocity profiles, the volumetric flow rate, Wall shear stress and the resistance to flow. Characteristics of elastic and non-elastic artery are compared and the results confirm the importance of elastic assumed artery. To confirm the accuracy results, these are compared the results of previous literature.

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In this paper, an open-source software framework named “Chesmeh” for numerical solution of the fluid dynamics equations is introduced. The data structure is designed in a way that the software framework supports structured grids on arbitrary number of spatial dimensions. The software has the ability to decompose the numerical grid into several smaller grids for parallel processing. Furthermore, using some functions, the complexity of the parallel programming is considerably made easier for the user. The software is developed using the new features of the C++ programming language, specially the template metaprogramming feature. In addition to the linear finite difference schemes, which can be simply implemented, the nonlinear schemes such as essentially non-oscillatory shock capturing schemes are implemented. Using the software, it is also possible to use compact finite difference schemes, which lead to a tridiagonal system of equations. Defining and applying different kinds of boundary conditions are also predicted in the software. In addition, utilities are considered for file input and output. Using several test cases of compressible and incompressible flows and viscous and inviscid flows, the capabilities of the software are demonstrated.

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In this paper, a sandwich beam of a SMP material which have a corrugated core is studied. The corrugated core is from a polymeric material. Structures with corrugated profiles show higher stiffness-to-mass ratio in the transverse to corrugation direction compared to flat structures. As a result, the beam with corrugation along the transverse direction is stiffer than the one with corrugation along the beam length. The flexural behavior of the composite corrugated beam is studied employing a developed constitutive model for SMP and the Euler-Bernoulli beam theory. The constitutive model utilized is in integral form and is discretized employing finite difference scheme. To verify the results of the Euler-Bernoulli beam theory and finite difference method, finite element models of different corrugated sections have been simulated in a 3D finite element program. The results demonstrate that the developed model for the composite beam presented in this study predicts the behavior of the beam successfully. The sandwich beam with different corrugated cores (triangular, sinusoidal and trapezoidal shapes) are compared with each other. Also, results show that the shape fixity is decreased a little, like any other reinforcing method. This decrease in shape fixity results in increase of load capacity in composite beams. The stress-free strain recovery and constrained stress-recovery cycles are both studied.

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The soil formation consists of complex and longtime processes in which many different chemical and physical changes occur in soil deposit, or in its original source rock. This processes cause the soil to show nonhomogeneous characteristics and to have spatial variation in its mechanical properties. The spatial variation of soil properties lead to many uncertainties in prediction of soil mechanical behavior; subsequently the design of structure which depend on soil deposits becomes troublesome. For dealing with such problem the probabilistic and statistical tools are proposed as convenient methods for choosing appropriate design soil parameters and estimating the uncertainties in design. The coupled utilization of random field theory and Monte Carlo simulation technique yield probability distribution functions for geotechnical problems in which different cases of soil distribution is assumed for analyses. In such problems the soil properties are distributed into the field according to the assumptions of random field theory by consideration of a probability distribution (with the given mean and standard deviation) and scale of fluctuations. This distribution of soil properties with the use of random field theory is performed repeatedly until a desired statistical distribution for the results is obtained. This distribution can be used as a basis for extracting the statistical characteristics for the problem in hand. In this paper the effect of spatial variability parameters on the bearing capacity of strip foundations on clayey soils were investigated. The soil un-drained shear strength (Cu) was assumed as spatial variable parameter with the use of logarithmic distribution and the so-called coupled random field theory; the Monte Carlo simulation technique was used for obtaining probability distribution of bearing capacity of foundation on nonhomogeneous clayey soil. The Mohr Coloumb elastic perfectly plastic constitutive model and the Finite Difference Method (FDM) were used for modelling soil behavior and calculating the bearing capacity of foundation. The spatial variability of un-drained shear strength was investigated using three parameters: coefficient of variation of un-drained shear strength (Cov(Cu((, and the scale of fluctuation of shear strength in horizontal and vertical directions (x, and y directions). The range of these parameters were chosen such that the results of current research can be generalized to any field problem. The results obtained from this study, were investigated by average and coefficient of variation of NC parameter which is the cohesion factor in classic bearing capacity equations (i.e. as Terzaghi, Meyerhof, Hansen and Vesic bearing capacity equations). It can be interpreted from the results that by increasing the coefficient of variation of soil un-drained shear strength the average bearing capacity decreases and the coefficient of variation of bearing capacity increases; also the average bearing capacity of foundation has an approximately increasing trend with increasing the scale of fluctuations in both horizontal and vertical directions. Finally at the end of this paper two practical simplified equations were suggested using multiple regression method for estimation of average and coefficient of variation of bearing capacity factor NC, given the spatial variation parameters of soil un-drained shear strength. These equations can be implemented by geotechnical experts for applying the variability of cohesion in the design of foundations on nonhomogeneous clayey soil formations.

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Drying is an important method of preservation of wet materials and is applicable to a wide range of industrial and agricultural products. Dried products have limited deterioration rates, due to the low water activity, are easily transported and stored because of the reduced volume, and have no need of refrigeration, representing energy economy. The purpose of the present study was to develop a model to describe the heat and mass transfer during the drying of beetroot. Temperature, moisture content, and shrinkage of a beetroot disc were simulated during drying at three different air temperatures (50, 60, and 70 °C). Simultaneous heat and moisture diffusion equations were solved along with convective boundary conditions, using a simulation language, MATLAB, based on finite difference technique. Shrinkage, variable thermal properties and moisture diffusivity were considered in the simulation. The simulated results matched satisfactorily with measured temperature and moisture content of the beetroot during drying.

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Hamburgers are one of the most widely consumed meat products in the world. The shelf life of this product is rather short, therefore the freezing process is commonly used to reduce water activity and prevent the growth of microorganisms. Accurate temperature prediction during freezing is important in designing optimum cooling procedures and to avoid quality deterioration. Models for predicting freezing times range from relatively simple analytical equations to the more complicated numerical methods which require a lot of computing time and a sophisticated computer. In this research, thermal properties of hamburger, including ice fraction, thermal conductivity and specific heat were determined mathematically and then the freezing process of hamburger patty was investigated by two different numerical models (finite difference& finite element). The results were compared with experimental data and it was found that although both two models could reasonably forecast the temperature of hamburger patties during freezing, the finite element model demonstrated better goodness of fit than finite difference model. This study shows that the use of CFD packages such as COMSOL software can be considered as a suitable option for the estimation of freezing time of meat products.