Luan Carlos de S. M. Ozelim

Cellular Automata and X-Ray Microcomputed Tomography Images for Generating Artificial Porous Media

AbstractProblems involving fluid flow in porous media are of great interest in many scientific and technological areas. The development of numerical methods at the pore level allows simulating such phenomena considering characteristics and heterogeneities of the medium normally ignored in the macroscopic approach. To achieve the computational implementation of those numerical methods, it is necessary to initially define the domain (porous media) in which the simulations will be held. In this study, a simple, yet powerful methodology of representing a porous medium by means of cellular automata (CA) and microcomputed tomography is presented. Two parameters are proposed to link the tomographic images with those generated by CA. The first one considers the porosity, whereas the second one takes into account void alignment inside the image. The methodology computes the parameters in every automata image generated in a time range and compares them with the parameters of the tomographic image until certain user...

Novel Approach to Consolidation Theory of Structured and Collapsible Soils

AbstractConsolidation is one of the most important concepts in geotechnics. The pioneer ideas of both Terzaghi and Biot, and its attendant phenomena have been shown to be widely applicable to a wide variety of soils. However, when structured and collapsible soils are taken into account, the standard consolidation theory ultimately requires complementary considerations to correctly predict a soil’s behavior. In particular, indirect determination of permeability by means of the consolidation coefficient, cv, tends to highly underestimate the real hydraulic behavior for these types of soil. In the present paper, a modification in the understanding of the consolidation process is proposed to adjust the prevailing theory to the reality of both structured and collapsible soils. In short, it is considered that every soil may suffer microcollapses that increase pore-water pressure momentarily during the consolidation process. The mathematical basis for the new theory is developed and a new parameter, the collapsi...

ANALYTICAL SOLUTIONS FOR ALTERNATE DEPTHS

ABSTRACT Triangular, parabolic rectangular and trapezoidal sections are practical open channel sections. For rectangular channel section it is possible to express the alternate depths analytically. For other sections the alternate depths are presently obtained by trial and error procedure. In this paper exact analytical solutions of alternate depths for exponential and trapezoidal open channel sections have been obtained in the form of fast converging infinite series and algebraic equations.

On the iota-delta function: a link between cellular automata and partial differential equations for modeling advection---dispersion from a constant source

Describing complex phenomena by means of cellular automata (CAs) has shown to be a very effective approach in pure and applied sciences. Most of the applications, however, rely on multidimensional CAs. For example, lattice gas CAs and lattice Boltzmann methods are widely used to simulate fluid flow and both share features with two-dimensional CAs. One-dimensional CAs, on the other hand, seem to have been neglected for modeling physical phenomena. In the present paper, we demonstrate that some one-dimensional CAs are equivalent to a stable linear finite difference scheme used to solve advection–diffusion partial differential equations (PDEs) by relying on the so-called iota-delta representation. Consequently, this work shows an important link between continuous and discrete models in general, and PDEs and CAs more in particular.

Analytical Slope Stability Analysis Based on Statistical Characterization of Soil Primary Properties

The role of statistical tools in the modeling of slope stability has been increasingly studied in the last decades. Mainly, this growth can be related to the availability of fast computational routines which enable massive-repetition numerical algorithms such as Monte Carlo simulations. On the other hand, analytical approaches to this problem, in the majority of cases, rely on considering the random variables of interest being normally distributed. This latter assumption tends to provide incorrect results while dealing with skewed data since normal distribution is symmetric about its mean value. In order to address this issue, a complete statistical study of a set of porosities data is undertaken. A total of seven well-known statistical distributions are adjusted to such data, showing that normal distribution is the worst possible fit for the considered data set. By means of an empirical correlation between strength properties and porosity, the probability density function of the factor of safety of a hypothetical slope is analytically derived based on a Mohr-Coulomb failure criterion. This way, it is shown that the probability of failure can be explicitly obtained by means of solely the distribution of a primary property of the material in study, namely, its porosity. Also, the results obtained by considering the porosity data normally distributed are compared to the ones hereby developed showing considerable differences.

Integral and Closed-Form Analytical Solutions to the Transport Contaminant Equation Considering 3D Advection and Dispersion

AbstractEven though numerical procedures have been tremendously enhanced over the last years, analytical closed-form solutions are of special interest to water resources scientists. In general, these solutions are used to check the consistency and validate numerical routines. Bibliographical research reveals that up-to-date analytical solutions only take into account one-dimensional (1D) advection, even when three-dimensional (3D) dispersion is considered. This assumption creates an axis dependency because the flux is assumed to be parallel to one of the three possible orthogonal directions, which does not apply to all practical situations in which diagonal advection is present. In this work an analytical solution is derived for the 3D advective-dispersive equation (ADE) by means of Fourier and Laplace integral transforms. The solution allows the contaminant plume to move angularly with respect to the coordinate axes.