• Geomechanics and Engineering
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• v.15 no.1
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• pp.645-657
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• 2018

The paper aims to analyze the behaviour of torsional type surface waves propagating through fluid saturated inhomogeneous porous media clamped between two inhomogeneous anisotropic media. We considered three types of inhomogeneities in upper anisotropic layer which varies exponentially, quadratically and hyperbolically with depth. The anisotropic half space inhomogeneity varies linearly with depth and intermediate layer is taken as inhomogeneous fluid saturated porous media with sinusoidal variation. Following Biot, the dispersion equation has been derived in a closed form which contains Whittaker's function and its derivative, for approximate result that have been expanded asymptotically up to second term. Possible particular cases have been established which are in perfect agreement with standard results and observe that when one of the upper layer vanishes and other layer is homogeneous isotropic over a homogeneous half space, the velocity of torsional type surface waves coincides with that of classical Love type wave. Comparative study has been made to identify the effects of various dimensionless parameters viz. inhomogeneity parameters, anisotropy parameters, porosity parameter, and initial stress parameters on the torsional wave propagation by means of graphs using MATLAB. The study has its own relevance in connection with the propagation of seismic waves in the earth where fluid saturated poroelastic layer is present.

• Structural Engineering and Mechanics
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• v.59 no.6
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• pp.951-972
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• 2016

The purpose of this study is to illustrate the propagation of the shear waves (SH-waves) in a prestressed hetrogeneous orthotropic media overlying a pre-stressed anisotropic porous half-space with self weight. It is considered that the compressive initial stress, mass density and moduli of rigidity of the upper layer are space dependent. The proposed model is solved to obtain the different dispersion relations for the SH-wave in the elastic-porous medium of different properties. The effects of compressive and tensile stresses along with the heterogeneity, porosity, Biot's gravity parameter on the dispersion of SH-wave are shown numerically. The wave analysis further indicates that the technical parameters of upper and lower half-space affect the wave velocity significantly. The results may be useful to understand the nature of seismic wave propagation in geophysical applications and in the field of earthquake and material science engineering.

• Earthquakes and Structures
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• v.14 no.4
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• pp.313-322
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• 2018

The present study is dedicated to investigate the SH body-as well as Love-waves propagation effects in porous media with uncertain porosity and permeability. A unified formulation of the governing equations for one-dimensional (1-D) wave propagation in anisotropic porous layered media is presented deterministically. The uncertainties around the above two cited parameters are taken into account by random fields with the help of Monte Carlo Simulations (MCS). Random samples of the porosity and the permeability are generated according to the normal and lognormal distribution functions, respectively, with a mean value and a coefficient of variation for each one of the two parameters. After performing several thousands of samples, the mathematical expectation (mean) of the solution of the wave propagation equations in terms of amplification functions for SH waves and in terms of dispersion equation for Love-waves are obtained. The limits of the Love wave velocity in a porous soil layer overlaying a homogeneous half-space are obtained where it is found that random variations of porosity change the zeros of the wave equation. Also, the increase of uncertainties in the porosity (high coefficient of variation) decreases the mean amplification function amplitudes and shifts the fundamental frequencies. However, no effects are observed on both Love wave dispersion and amplification function for random variations of permeability. Lastly, the present approach is applied to a case study in the Adapazari town basin so that to estimate ground motion accelerations lacked in the fast-growing during the main shock of the damaging 1999 Kocaeli earthquake.

• Journal of the Chungcheong Mathematical Society
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• v.19 no.4
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• pp.335-347
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• 2006

The homogenization of non-stationary Navier-Stokes equations on anisotropic heterogeneous media is investigated. The effective coefficients of the homogenized equations are found. It is pointed out that the resulting homogenized limit systems are of the same form of non-stationary Navier-Stokes equations with suitable coefficients. Also, steady Stokes equations as cell problems are identified. A compactness theorem is proved in order to deal with time dependent homogenization problems.

• Smart Structures and Systems
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• v.18 no.5
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• pp.911-930
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• 2016

The main purpose of this paper is to study the effects of initial stress, gravity, anisotropy and porosity on the propagation of shear wave (SH-waves) in a fiber-reinforced layer placed over a porous media. The frequency equations in a closed form have been derived for SH-waves by applying suitable boundary conditions. The frequency equations have been expanded and approximated up to $2^{nd}$ order of Whittaker's function. It has been observed that the SH-wave velocity decreases as width of fiber-reinforced layer increases. However, with the increase of initial stress, gravity parameter and porosity, the phase velocity increases. The results obtained are in perfect agreement with the standard results investigated by other relevant researchers.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.5 no.1
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• pp.55-78
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• 2001

Given the anisotropic Poisson equation $-{\nabla}{\cdot}{\mathcal{K}}{\nabla}p=f$, one can convert it into a system of two first order PDEs: the Darcy law for the flux $u=-{\mathcal{K}{\nabla}p$ and conservation of mass ${\nabla}{\cdot}u=f$. A very natural mixed finite volume method for this system is to seek the pressure in the nonconforming P1 space and the Darcy velocity in the lowest order Raviart-Thomas space. The equations for these variables are obtained by integrating the two first order systems over the triangular volumes. In this paper we show that such a method is really a standard finite element method with local recovery of the flux in disguise. As a consequence, we compare two approaches in analyzing finite volume methods (FVM) and shed light on the proper way of analyzing non co-volume type of FVM. Numerical results for Dirichlet and Neumann problems are included.

• Tunnel and Underground Space
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• v.13 no.6
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• pp.465-475
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• 2003

Groundwater inflow into the caverns constructed in fractured rock mass was simulated by numerical modeling, NAPSAC (DFN, discrete fracture network model) and NAMMU (CPM, continuous porous media model), a finite-element software package for groundwater flow in 3D fractured media developed by AEA Technology, UK. The input parameters for modeling were determined on surface fracture survey, core logging and single hole hydraulic test data. In order to predict the groundwater inflow more accurately, the anisotropic hydraulic conductivity was considered. The anisotropic hydraulic conductivities were calculated from the fracture network properties. With a minor adjustment during model calibration, the numerical modeling is able to reproduce reasonably groundwater inflows into cavern and the travel length and times to the ground surface along the flow paths in the normal, dry and rainy seasons.

• Geomechanics and Engineering
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• v.9 no.4
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• pp.465-481
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• 2015

Three-dimensional simulation of flow through dam foundation is performed using finite element (Seep3D model) and artificial neural network (ANN) models. The governing and discretized equation for seepage is obtained using the Galerkin method in heterogeneous and anisotropic porous media. The ANN is a feedforward four layer network employing the sigmoid function as an activator and the back-propagation algorithm for the network learning, using the water level elevations of the upstream and downstream of the dam, as input variables and the piezometric heads as the target outputs. The obtained results are compared with the piezometric data of Shahid Abbaspour's Dam. Both calculated data show a good agreement with available measurements that demonstrate the effectiveness and accuracy of purposed methods.

• Proceedings of the KSME Conference
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• 2008.11b
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• pp.2540-2543
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• 2008

Liquid crystal displays (LCD's) are continuously coated with some chemicals in the clean room of a factory. Spreading of these chemicals is causing serious problems both in controlling clean room quality as well as to the workers inside the factory. It is required to alleviate or properly control the offensive odor which is mainly composed of propylene glycol mono ethyl acetate, novolak resin and photo active compound. The control strategy employed is to bleed the offensive odor gas out the clean room. A full scale 3D CFD model was created with anisotropic porous media, chemical species transport with no volumetric reaction, and thermal diffusion with propane gas (tracer gas) to simulate the odor spreading. A segregated implicit solver with standard k-$\varepsilon$ model is employed. The detailed CFD analysis made it possible to develop an effective method of ventilating the coater room and optimizing their capacities.

• Nuclear Engineering and Technology
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• v.36 no.6
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• pp.559-570
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• 2004

A computational fluid dynamics model for predicting moderator circulation inside the Canada deuterium uranium (CANDU) reactor vessel has been developed to estimate the local subcooling of the moderator in the vicinity of the calandria tubes. The buoyancy effect induced by the internal heating is accounted for by the Boussinesq approximation. The standard $k-{\varepsilon}$ turbulence model with logarithmic wall treatment is applied to predict the turbulent jet flows from the inlet nozzles. The matrix of the calandria tubes in the core region is simplified to a porous media in which the anisotropic hydraulic impedance is modeled using an empirical correlation of pressure loss. The governing equations are solved by DFX-4.4, a commercial CFD code developed by AEA technology. The resultant flow patterns of the constant-z slices containing the inlet nozzles and the outlet port are "mined-type", as observed in the former 2-dimensional experimental investigations. With 103% full power for conservatism, the maximum temperature of the moderator is $82.9^{\circ}C$ at the top of the core region. Considering the hydrostatic pressure change, the minimum subcooling is $24.8^{\circ}C$.