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Showing 12 results for Analytical Solution

Sabagh Yazdi S.r., Mohammad Zadeh Qomi M.,
Volume 2, Issue 2 (6-2004)

A numerical model is introduced for solution of shallow water flow equations with negligible physical dissipations due to canal roughness and turbulence effects. Two-dimensional velocity distribution and water depth of the flow field are computed by solving the depth average equations of continuity and motion. The equations are converted to discrete form using cell vertexfinite volume method on triangular unstructured mesh. The formulation of the added numericalviscosity is chosen in such a way that preserves the accuracy of numerical results. The accuracy ofthe model is assessed by computing the challenging case of inviscid frictionless flow in a canal with a 1800 bend. The computed results are compared with analytical solution which is obtainedfrom potential flow theory. Simulation of frictionless free surface flow in a constant width meandering sinusoidal canal is considered as an application of the model. The algorithm produced encouraging results.
M.b. Javanbarg, A.r. Zarrati, M.r. Jalili, Kh. Safavi,
Volume 5, Issue 1 (3-2007)

In the present study a quasi 2-D numerical model is developed for calculating air concentration distribution in rapid flows. The model solves air continuity equation (convection diffusion equation) in the whole flow domain. This solution is then coupled with calculations of the free surface in which air content in the flow is also considered. To verify the model, its results are compared with an analytical solution as well as a 2-D, numerical model and close agreement was achieved. The model results were also compared with experimental data. This comparison showed that the decrease in air concentration near the channel bed in an aerated flow could be well predicted by the model. The present simple numerical model could therefore be used for engineering purposes.
A. Ghanbari, M. Ahmadabadi,
Volume 8, Issue 2 (6-2010)

Inclined retaining walls with slopes less than perpendicular are appropriate candidates in several

engineering problems. Yet, to the knowledge of authors, only a few analytical solution for calculation of active earth

pressure on such walls, which will be usually smaller than the same pressure on vertical ones, has been presented

neither in research papers nor in design codes. Considering limit equilibrium concept in current research, a new

formulation is proposed for determination of active earth pressure, angle of failure wedge and application point of

resultant force for inclined walls. Necessary parameters are extracted assuming the pseudo-static seismic coefficient

to be valid in earthquake conditions. Moreover, based on Horizontal Slices Method (HSM) a new formulation is

obtained for determining the characteristics of inclined walls in granular and or frictional cohesive soils. Findings of

present analysis are then compared with results from other available methods in similar conditions and this way, the

validity of proposed methods has been proved. Finally according to the results of this research, a simplified relation

for considering the effect of slope in reduction of active earth pressure and change in failure wedge in inclined

retaining walls has been proposed.

Hasan Ghasemzadeh, Ms. Esmat Akbari Jalalabad,
Volume 9, Issue 3 (9-2011)

In this study compressive strength of carbon nanotube (CNT)/cement composite is computed by analytical method. For this purpose representative elementary volume (REV) as an indicator element of composite is chosen and analyzed by elasticity relationships and Von mises' criterion applied to it. It is assumed that carbon nanotubes are distributed uniformly in the cement and there is perfect bonding in the interface of cement and nanotube. At first for simplicity of computations, carbon nanotubes ( CNTs) are assumed to have unidirectional orientation in the cement matrix. In following, the relations are generalized to consider random distribution of nanotubes in cement, and a new factor suggested for random orientation of fibers in the CNT/cement composite. The results of analytical method are compared with experimental results.

Saeed Reza Sabbaghyazdi1, Tayebeh Amiri Saadatabadi,
Volume 9, Issue 3 (9-2011)

In this research, a novel numerical algorithm is introduced for computation of temperature-induced before crack steady strainstress field in plane-stress problem. For this purpose, two dimensional heat transfer equation and force equilibrium equations are sequentially solved using Galerkin Finite Volume method on identical unstructured triangular meshes when proper convergence for each field is achieved. In this model, a proper thermal boundary condition that is suitable for unstructured triangular meshes is introduced for analysis. Two test cases are used to assess accuracy of thermal and structural modules of the developed solver and the computed results are compared with theirs analytical solution.First, thermal analysis is performed for a rectangular plate which is connected to a supporting body with constant temperature and expose to surrounding liquid at three edges.Second, structural analysis is performed for a plate under distributed loads in two directions. Having obtained acceptable results from thermal and structural modules, thermal stress analysis is performed for a plate with fixed-end condition at one of edges,due to a uniform temperature field and the computational principle stress contours are compared with the Finite Element method results which have been reported in the literatures.

A. R. Shokoohi, B. Saghafian,
Volume 10, Issue 1 (3-2012)

In almost all of the present mathematical models, the upstream subbasins, with overland flow as the dominant type of flow, are

simulated as a rectangular plane. However, the converging plane is the closest shape to an actual upstream subbasin. The

intricate nature of the governing equations of the overland flow on a converging plane is the cause of prolonged absence of an

analytical or semi analytical solution to define the rising limb of the resulted hydrograph. In the present research, a new

geomorphologic semi analytical method was developed that tries to establish a relationship between the parallel and converging

flows to reduce the complexity of the equations. The proposed method uses the principals of the Time Area method modified to

apply the kinematic wave theory and then by applying a correction factor finds the actual discharge. The correction factor, which

is based on the proportion of the effective drained area to the analytically calculated one, introduces the convergence effect of

the flow in reducing the potentially available discharge in a parallel flow. The proposed method was applied to a case study and

the result was compared with that of Woolhiser's numerical method that showed the reliability of the new method.

J. Nazari Afshar, M. Ghazavi,
Volume 12, Issue 1 (1-2014)

The Stone-column is a useful method for increasing the bearing capacity and reducing settlement of foundation soil. The prediction of accurate ultimate bearing capacity of stone columns is very important in soil improvement techniques. Bulging failure mechanism usually controls the failure mechanism. In this paper, an imaginary retaining wall is used such that it stretches vertically from the stone column edge. A simple analytical method is introduced for estimation of the ultimate bearing capacity of the stone column using Coulomb lateral earth pressure theory. Presented method needs conventional Mohr-coloumb shear strength parameters of the stone column material and the native soil for estimation the ultimate bearing capacity of stone column. The validity of the developed method has been verified using finite element method and test data. Parametric studies have been carried out and effects of contributing parameters such as stone column diameter, column spacing, and the internal friction angle of the stone column material on the ultimate bearing capacity have been investigated.
E. Lotfi, S. Delfan, A. Hamidi, H. Shahir, Gh. Fardi,
Volume 12, Issue 1 (1-2014)

In saturated soils, heating induces thermal expansion of both grains and the pore fluid. Lower thermal expansion coefficient of aggregates results in the increase of pore pressure and reduction of the effective stress besides subsequent volume changes due to the dissipation of pore pressure and heat transfer. Dissipation of thermally induced pore pressure with time is a coupled thermo-hydro-mechanical (THM) phenomenon, involving gradients of pore pressure and temperature, hydraulic and thermal flows within the mass of soil and changes in the mechanical properties with temperature. The objective of this paper is presentation of a numerical method to determine the effect of temperature on consolidation of clays. In this regard, the finite element code, PISA is used for one dimensional THM analysis of porous media. The analysis performed using both linear elastic and elastoplastic Cam clay models. Modified Cam clay model was applied in elastoplastic analysis. Variation of temperature, displacements and pore pressure determined with time and compared with numerical solutions of other researchers. Also it was indicated that implementation of coupled THM analysis yields better results for displacements compared to the hydro mechanical (HM) one. Application of elastoplastic constitutive model instead of linear elastic one indicated that preconsolidation pressure has an important effect on results of analysis.
O. Farzaneh, F. Askari, J. Fatemi,
Volume 12, Issue 4 (12-2014)

AWT IMAGEPresented is a method of two-dimensional analysis of the active earth pressure due to simultaneous effect of both soil weight and surcharge of strip foundation. The study’s aim is to provide a rigorous solution to the problem in the framework of upper-bound theorem of limit analysis method in order to produce some design charts for calculating the lateral active earth pressure of backfill when loaded by a strip foundation. A kinematically admissible collapse mechanism consisting of several rigid blocks with translational movement is considered in which energy dissipation takes place along planar velocity discontinuities. Comparing the lateral earth forces given by the present analysis with those of other researchers, it is shown that the results of present analysis are higher (better) than other researchers’ results. It was found that with the increase in AWT IMAGE, the proportion of the strip load (q) which is transmitted to the wall decreases. Moreover, Increasing the friction between soil and wall ( AWT IMAGE) will result in the increase of effective distance ( AWT IMAGE). Finally, these results are presented in the form of dimensionless design charts relating the mechanical characteristics of the soil, strip load conditions and active earth pressure.

F. Dastjerdy, Dr O.r. Barani, Dr F. Kalantary,
Volume 13, Issue 3 (12-2015)

In this paper, a finite element model is developed for the fully hydro-mechanical analysis of hydraulic fracturing in partially saturated porous media. The model is derived from the framework of generalized Biot theory. The fracture propagation is governed by a cohesive fracture model. The flow within the fracture zone is modeled by the lubrication equation. The displacement of solid phase, and the pressure of wetting and non-wetting phases are considered as the main unknown parameters. Other variables are incorporated into the model using empirical relationships between saturation, permeability and capillary pressure. Zero-thickness element and conventional bulk element are used for propagating fracture and the surrounding media, respectively. The model is validated with respect to analytical solution of hydraulic fracture propagation problem in saturated media and then the problem is solved in semi-saturated media, considering the wetting and non-wetting pore fluid. 

Hossein Rahami, Mohamad Mirhoseini, Ali Kaveh,
Volume 14, Issue 6 (9-2016)

In this paper using the eigenvalues and eigenvectors symmetric block diagonal matrices with infinite dimension and numerical method of finite difference a closed form solution for exact solving of Laplace equation is presented. Moreover, the method of this paper has applications in different states of boundary conditions like Newman, Dirichlet and other mixed boundary conditions. Moreover, with the method of this paper, a mathematical model for the exact solution of the Poisson equation is derived. Since these equations have many applications in engineering problems, in each part examples like water seepage problem through the soil and torsion of prismatic bars are presented. Finally the method is provided for torsion problem of prismatic bars with non-circular and non-rectangular cross sections by using of conformal mapping.

Xilin Lu,
Volume 15, Issue 6 (9-2017)

This paper presents numerical and theoretical studies on the stability of shallow shield tunnel face found in cohesive-frictional soil. The minimum limit support pressure was determined by superposition method; it was calculated by multiplying soil cohesion, surcharge load, and soil weight by their corresponding coefficients. The varying characteristics of these coefficients with soil friction angle and tunnel cover-to-diameter ratio were obtained by wedge model and numerical simulation. The face stability of shallow shield tunnel with seepage was studied by deformation and seepage coupled numerical simulation; the constitutive model used in the analysis was elastic-perfectly plastic Mohr–Coulomb model. The failure mode of tunnel face was shown related to water level. By considering the effect of seepage on failure mode, the wedge model was modified to calculate the limit support pressure under seepage condition. The water head around the tunnel face was fitted by an exponential function, and then an analytical solution to the limit support pressure under seepage condition was deduced. The variations in the limit support pressure on strength parameters of soil and water lever compare well with the numerical results. The modified wedge model was employed to analyze the tunnel face stability of Qianjiang cross-river shield tunnel. The influence of tide on the limit support pressure was obtained, and the calculated limit support pressure by the modified wedge model is consistent with the numerical result.

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