André Luís Brasil Cavalcante

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...

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.

Experimental and Physical Modeling of Bed Load Heterogeneous Sediment Transport

AbstractThe hydraulic deposition process linked to tailings dams normally presents some technical deficiencies mainly because of the lack of control of hydraulic parameters. Problems of instability in tailings dams usually arise from poor management practices, such as poor decant pond control, in addition to the material being placed randomly. Hydraulic parameters, such as the flow rate and concentration of the slurry, play an important role in the formation of hydraulic fills. Grain size, distribution, segregation, and density, and slope inclination are the main characteristics of tailings dams, which are affected by the hydraulic parameters of the slurry. To investigate these factors, an experimental apparatus [hydraulic deposition simulation test (HDST)] was used to simulate the hydraulic deposition process in the laboratory, where all variables that could affect the phenomenon could be controlled carefully. The HDSTs using different flow rates and concentrations were carried out using the iron waste f...

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.

Alternative Solution for Advective-Dispersive Flow of Reagent Solutes in Clay Liners

AbstractAn analytical solution for the advection-dispersion equation, including sorption effects, was first proposed by Akio Ogata and Robert Banks in 1961. This solution allows the computation of the percentage of dissipation of the contamination plume at a given point in space and time. However, environmental engineers generally wish to determine the time period necessary for this dissipation to take place to reach a minimum acceptable level established in environmental laws. This paper presents a simplified solution that closely matches the exact solution but has the advantage of allowing a numerical-analytical computation of the flow time and/or thickness of the clay liner, using a scheme also developed in this paper. The proposed solution is compared with the simplified solution known as first-order approximation. The comparison shows that, contrary to the method proposed here, the first-order approximation does not satisfy the limit case of purely diffusive flow and gives unsafe estimates of the sol...

Efficient Approach to Solving Transient Unsaturated Flow Problems. I: Analytical Solutions

AbstractAlthough the finite-difference method (FDM) has been commonly used to numerically solve Richard’s equation, numerical difficulties are often encountered, even for comparatively simple probl...

Using the Fractional Advection Dispersion Equation to Improve the Scale Effect in the Sampling Process of Column Tests with Lateritic Soils

Breakthrough curves (BTCs) obtained from column tests in heterogeneous soils are not satisfactorily simulated with the advection-dispersion equation (ADE) for some heavy tailed cases. Furthermore, the dispersion coefficient calculated with the ADE for heavy tailed BTCs are scale dependent when simulating columns of soil larger than the original test depth. In this paper we compare the usage of a fractional ADE (FADE) and the classical ADE to fit column tests BTCs made with Brazilian lateritic soils, discussing both contaminant transport theories and underlying stochastic models. The FADE can more accurately simulate heavy tailed BTCs, and when applying the adjusted FADE parameters to longer depths of soil, the FADE also predicts a more realistic scenario of contaminant transport through heterogeneous soil. The addition of fractional calculus in the advection-dispersion equation proves to improve contaminant transport predictions based on column tests over the classical ADE, with the use of a constant fractional dispersion coefficient that is scale independent.