Analytical Solutions for Filtration Process Based on the Constriction Size Concept (original) (raw)
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Analytical Solutions for Filtration Process Based on Constriction Size Concept
Journal of Geotechnical and Geoenvironmental Engineering, 2013
An analytical model is proposed to describe the filtration process applicable to a base soil-filter system. The Navier-Stokes equations for porous media are used to capture the hydrodynamic behavior, whereas, numerically, a new algorithm is proposed to solve the Navier-Stokes equation in a nonlinear form. The various mixtures of base soil particles eroded and water flow within the system are computed using the workenergy principle incorporating the constriction size of the filter.The model can assess the filtration process through the flowrate and the accumulation and redistribution of fine particles within the filter. By discretizing the base soil and filter domains into discrete elements, the model can predict the time-dependent particle gradation of the filter for each element. Laboratory tests reported in other studies and those conducted by the authors validate the model in relation to other available models.
2018
This study is devoted to filter-constrictions analysis and its application with respect to void and constrictions reduction during soil filtration. The experimental investigation involves combined Hole Erosion-Filtration tests using several soils and filters. The base soils are lean clays and the granular filters are selected according to the usual filtration criteria. The combination of the experimental data for porosity variation and the analytical results from the Constriction Size Distribution (CSD) analysis was used to evaluate the constrictions size reduction subsequent to the filtration process. The filtration depth was also estimated according to the retained soil mass and the porosity reduction deduced from the measured hydraulic conductivity. An analytical model of the CSD was applied to the experimental results in order to assess the constrictions reduction. As regards the obtained results, a nonuniform constriction reduction was suggested according to the effective filtr...
Evaluation of Combined Base Soil Erodibility and Granular Filter Efficiency
Geotechnical and Geological Engineering, 2021
Filters managed in zoned dams are designed according to criteria based on the grain size distribution of both filter and eroded soil. However, the constriction size distribution of the filter is the key parameter which governs the filter retention process of flowing eroded particles. To assess the filter efficiency regarding eroded particles, several filters and base soils are tested in a vertical cell with a configuration coupling erosion and filtration processes. For setting the boundary condition of eroded particles at the filter inlet, hole erosion test (HET) was performed on the base soil. The investigation of the evolution of filter behavior shows that the void ratio and the grain shape are of a great influence on filter efficiency. A new approach of filter clogging was proposed by evaluating a damage index which is affected by various parameters such as the ratio D15/d85 and the size of eroded particles. An approach linking the geometrical parameters (damage index) to the hyd...
Enhanced Criterion for Base Soil Retention in Embankment Dam Filters
Journal of Geotechnical and Geoenvironmental Engineering, 2006
In effective filters, potentially erodible base particles are transported to the filter and retained to form a stable self-filtration layer. At any given time, the mass proportion of the filter and the base materials in this layer depends on the initial porosity of the filter and the subsequent porosity of the self-filtration layer. In this paper, an analytical procedure is given to obtain the particle size distribution ͑PSD͒ of the self-filtration layer by combining the PSDs of the filter and the base soil modified by D c95 , where 95% of filter constrictions are finer than the size denoted by D c95. The assessment of internal stability of the PSD of the self-filtration layer forms a rational model to successfully identify the effective filters from their ineffective counterparts. The proposed model is verified by large-scale laboratory tests carried out by the writers in addition to other published data. The model performance is acceptable in relation to various base and filter materials, and provides an alternative and rigorous design approach by eliminating most limitations of the conventional particle based criteria ͑e.g., D 15 / d 85 ratio͒.
Constriction-Based Retention Criterion for Granular Filter Design
Journal of Geotechnical and Geoenvironmental Engineering, 2007
The filter design criteria in practice are currently based on laboratory tests that were carried out on uniform base soil and filter materials. These criteria mostly involve specific particle size ratios, where the system of base soil and filter is represented by some characteristic particle sizes. Consequently, these criteria have limitations when applied to nonuniform materials. In filters, it is the constriction size rather than the particle size that affects filtration. In this paper, a mathematical procedure to determine the controlling constriction size is introduced, and subsequently, a constriction-based retention criterion for granular filters is presented. The model also incorporates the effect of nonuniformity of base soil in terms of its particle size distribution, considering the surface area of the particles. The proposed retention criterion is verified based on experimental data taken from past studies plus large-scale filtration tests carried out by the authors. The model successfully and distinctly demarcates the boundary between effective and ineffective filters in the case of cohensionless base soils.
Eastern-European Journal of Enterprise Technologies, 2021
Mathematical modeling and computer simulation methods have been used to investigate the extent of influence exerted by bio-clogging on the dynamics of excess head scattering in the soil massif. To this end, the classical equation of filtration consolidation has been modified for the case of variable porosity resulting from changes in the biomass. The numerical solution to the constructed mathematical model in the form of a nonlinear boundary problem was derived by a finite-element method. Numerical experiments were carried out and their analysis was performed. Specifically, this paper shows the charts of pressure differences in the soil array when neglecting bio-clogging and when estimating the effects exerted by bio-clogging at specific points in time. The numerical experiments demonstrated that in two years after the onset of the consolidation process in the neighborhood of the lower limit of the examined soil mass with a thickness of 10 meters, excess heads fall from the initial ...
The importance of permeability in granular filter design and control
Scour and Erosion, 2016
Granular filters are required to perform two basic functions in embankment dams: (a) prevent the migration of base soil particles, and (b) allow drainage of seepage water. Traditionally, retention function (a) has been evaluated using Particle Size Distribution (PSD) and drainage function (b) using Permeability (k f), but usually permeability have been also correlated with PSD, so the permeability criterion have been expressed in terms of D 15b of the base soil and D 15f of the granular filter. Only few authors have used filter permeability for the assessment of retention function and there is no general agreement with them, but permeability should be a very important variable because it takes into account not only the whole PSD of the filter, (instead of just several representative diameters), but also other important characteristic such as compaction, porosity, density and particle shape. Based on a literature review and research experience at the University of Granada, this paper analyses the importance of filter permeability in the design and control of granular filters in embankment dams, even with dispersive base soils.
Simulation of the dynamic behavior of horizontal granular filters
Separation and Purification Technology, 2007
An improved simulator for the transient behavior of horizontal depth filters, based on the one-dimensional simulator published recently by the authors, is developed. The need for a different approach in designing horizontal filters arises from the inherent two-dimensional character of horizontal filtration, since gravity causes a drift of particle motion in a direction normal to the main flow, as opposed to the one-dimensional character of upward or downward filtration. Calculation of horizontal and vertical filtration coefficients is based on a new set of phenomenological equations which take into consideration the two-dimensional character of the particle motion. This approach also considers the motion of particle clusters that become detached from grain surfaces under the effect of local shear stresses, become reentrained, and usually clog downstream and/or downhill pores. Results are given in terms of the evolution of the specific deposit, the directional filter efficiencies, and the directional losses of filter permeability.