Constriction Size Distribution Research Articles

Constriction size retention criterion for calcium alginate microcapsules in granular materials

Microcapsules have demonstrated to self-heal cementitious materials. However, their prospect in granular materials and other porous cemented materials remains to be tested. An initial challenge to tackle is to ensure the microcapsules retention in open, interconnected porous media. The purpose of this study is to investigate the retention of microcapsules in gravel under the influence of seepage. This scheme largely coincides with the intention of geotechnical filters to prevent the excessive washout of base soils. A mathematical model previously designed for cohesionless soil is used to establish an initial retention criterion based on the constriction size distribution of gravel (the minimum pore opening size distribution formed by various gravel packings) and, the particle size distribution of microcapsules (made of calcium alginate/polydimethylsiloxane) and an equivalent control material (glass beads). The proposed model is verified experimentally by washout tests on microcapsules-gravel and glass beads-gravel mixtures. Optical microscopy is used to assess the integrity of microcapsules after testing. The lower washout of microcapsules compared with cohesionless glass beads could be attributed to their adhesive nature. By incorporating the influence of size change of microcapsules during drying, which is an intrinsic property of the microcapsules, a modified empirical equation is presented for soft and adhesive microcapsules, demarcating the boundary between effective and ineffective retention for microcapsules-gravel mixtures. • Constriction size is used to design microcapsules - granular materials mixtures. • Permeability/washout of glass beads/microcapsules in gravel mixtures are monitored. • Washout of glass beads and microcapsules depend on constriction size of gravel. • Loss of microcapsules is minor due to their adhesion-prone and swelling nature.

Recent developments in design criteria for granular and geotextile filters

Granular and geotextile filters are commonly provided in several hydrological infrastructures to limit soil erosion and allow unimpeded water seepage. The success of a filter depends on forming a bridging structure, which is governed by the grain size distribution of soil and the constriction size distribution of filter. Currently, the retention requirement is satisfied considering representative grain and opening size, whereas the hydraulic conductivity requirement is satisfied considering empirical factors for avoiding excessive clogging. In this paper, the design criteria for granular and geotextile filters are reviewed, and improved design criteria are presented. A probabilistic retention criterion is developed, considering the grain size and constriction size as random variables. The influence of filter thickness is incorporated into the criterion by considering the number of constrictions in a filtration path. A hydraulic conductivity criterion is developed theoretically based on governing flow equations and the expected partial clogging of geotextiles. The limit states for the developed criteria are evaluated based on the wide range of experimental data. The developed design criteria are applicable to granular and nonwoven geotextiles, which offers an improvement in design compared to the existing criteria in practice.

Improved design criteria for nonwoven geotextile filters with internally stable and unstable soils

In geotextile filtration, the soil fines are either accumulated near the interface, clogged, or washed out, which primarily depends on the grain size distribution (GSD) of soil and the constriction size distribution (CSD) of geotextile. Also, the movement of fines significantly affects the flow capacity of geotextile. Currently, the retention requirement is satisfied based on representative grain and opening sizes, whereas the hydraulic conductivity and clogging requirements are satisfied considering the properties of virgin geotextile. This paper presents a probabilistic retention criterion considering the grain and constriction sizes as random variables. The influence of geotextile thickness is incorporated into the criterion by considering the number of geotextile constrictions in a filtration path. A theoretical approach to predict CSD is presented if the measured data is unavailable. For hydraulic conductivity and clogging requirements, a criterion is presented considering the expected partial clogging of geotextile, which is predicted based on the semi-analytical approach. The limit states for the developed criteria are evaluated based on the wide range of experimental data from the current study and published literature. The developed design criteria are applicable to internally stable and unstable soils, which offers an improvement in design compared to the existing criteria in practice.

Flow dependent constriction-size distribution in gap-graded soils: a statistical inference

The clogging–unclogging process in gap-graded soils is a result of the migration of seepage-driven fines, which subsequently induces measurable changes in the local hydraulic gradients. This process can be temporally observed in the variations of Darcy's hydraulic conductivity (K). The current study proposes an integrated statistical Monte Carlo approach combining the discrete-element method and two-dimensional computational fluid dynamics simulations to estimate the flow-dependent constriction-size distribution (CSD) for a gap-graded soil. The computational inferences were supported with experimental results using an internally stable soil, which was subjected to one-dimensional flow stimulating desired hydraulic loadings: a hydraulic gradient lower than the critical gradient applied as a multi-staged loading pattern. The 35th percentile size of the flow-dependent CSD (Dc35) for both internally stable and unstable gap-graded soils becomes approximately equal to Dc35 at steady state. However, a greater variation of larger constrictions persists for the unstable soils. This pilot study has shown the applicability of the proposed method to estimate flow-dependent CSD for a wide range of experimentally observed K values.

Evaluation of Combined Base Soil Erodibility and Granular Filter Efficiency

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 hydraulic conductivity leads to an estimation of the filter performance which provides a more quantifiable and realistic criterion. The results indicate that even existing criteria were not met; the tested filters remain efficient as regards to experimental data. An analytical approach based on constrictions size distribution was used and pore reduction was matched with experimental results.

Determination of the opening size of granular filters

AbstractGranular filters are used in hydraulic earthen structures as a natural barrier to protect base soils from erosion under seepage conditions. Their performance is greatly dependent on the pore space connectivity that provides transport pathways for migrating fine particles. Traditional filter design rules are based on characteristic particle diameters of the involved materials, which do not explicitly reflect the pore structure dimensions. Even though the literature offers some mathematical tools that can be used to characterize the opening size of granular filters, the underlying physical fundamentals are still not sufficiently understood. Therefore, this study aims to provide a plausible physical framework for determining the filter opening size by means of numerical simulations using the discrete element method. From the investigation of particle transport processes in polydisperse packings of spheres, the opening sizes associated to these numerical filters are defined on the basis of their constriction size distribution. A mathematical procedure is then introduced to determine the effective opening size of the filter and subsequently, a revised retention criterion for granular filters is proposed and validated with experimental data from the literature. The study findings can offer a valuable perspective for erosion assessment methods in both new and existing earthen structures.

Assessment of permeability of granular drainage layer considering particle size and air void distribution

Granular drainage layers are utilized in the permeable pavement structure to temporarily store the infiltrated water and to gradually penetrate it into the underlying layer or the subsurface drainage system. The selected particle size distribution (PSD) of aggregate and consequently the size of air voids distributed between particles inherently affect the drainage capability of drainage course. In the present study, the effect of distribution of pores between aggregate along with the general properties of characterized gradation curve on the permeability of this granular porous media is assessed by establishment of various PSDs. For this purpose, large-scale constant head permeability test is carried out on distinct gradations of coarse-sized aggregate derived from three different rock types. A well-established analytical procedure is utilized to determine the constriction size distribution characterizing the interconnectivity of pores. A probabilistic approach is employed to estimate the distribution of size of air voids based on the captured two-dimensional images from prepared specimens. Obtained results confirm nonlinear relationship between the flow velocity and the applied hydraulic gradient especially for specimens comprised of more uniform size range. Also, the developed relationship based on the power law between the hydraulic conductivity and the characteristic pore size can effectively describe the permeability of coarse-sized aggregate used as drainage layer. Furthermore, establishment of gradation with higher uniformity coefficient leads to smaller-sized pores between particles and consequently lower hydraulic conductivity coefficient. Finally, the extended regression model based on the characterized properties can effectively predict the permeability of aggregate specimen.

A coupled CFD–DEM investigation of internal erosion considering suspension flow

The influence of two-phase flows containing suspension particles, which are common in nature, on internal erosion with coupling effect of clogging remains unclear. This paper presents a three-dimensional coupled computational fluid dynamics and discrete element method (CFD–DEM) analysis of internal erosion considering different concentrations of suspension C (i.e., mass of the suspended particles in unit volume of fluid) in gap-graded granular soils with different fine fraction Fc (i.e., the percentage by mass of the fine particles in the gap-graded sample). The influences of C and Fc on the erosion and clogging behavior of soils are investigated from both the macroscopic and microscopic perspectives. It is found that for gap-graded samples being underfilled with Fc = 15%, the suspension flow (i.e., influent fluid with suspending particles) decreases the cumulative eroded fine particle loss and the increasing rate of soil hydraulic conductivity due to clogging at the top of the sample. The degree of clogging is found to jointly be determined by both constriction size distribution and the suspension concentration. Clogging in a local area usually occurs with the formation of the clusters, which have a high resistance to the drag force applied by the fluid flow.

Geometrical method for assessing the internal stability against suffusion of cohesionless soils based on controlling constriction size

Suffusion is an internal erosion mechanism which can occur in cohesionless soils composed of a bimodal structure, where a sufficient seepage force leads to the detachment of loose finer particles and their transport through the constrictions formed by the primary coarser skeleton. The assessment of the susceptibility of cohesionless soils to suffusion is based on the evaluation of their capacity to filter erodible particles. Compared to models based on the grain size distribution analysis of soil, the approaches focused on the constriction size distribution are most suitable to provide a physical description of soil retention capacity. However, some important soil parameters are not taken explicitly in these models. In this research work and on the basis of the results of an experimental study conducted on mixtures of sands (dmax = 2 mm) and fines (dfmax = 100 μm) under different testing conditions, the main parameters that can influence the soil’s response to erosion were identified. Considering the contribution of these parameters to the suffusion development probability, new empirical formula has been proposed to calculate a control diameter characterizing the soil coarser fraction. This control diameter will be compared with the characteristic diameter of the loose finer fraction to assess the soil stability against suffusion. The application of the proposed model to the tested soils gives a good stability assessment as compared to other models.

NO EROSION CRITERION FOR GRANULAR FILTERS BASED ON CONSTRICTION SIZE – AN EXPERIMENTAL STUDY

Filters are provided in embankments in order to arrest the eroded soil particles that are carried by the seepage water .Current design method of graded filters was developed by Terzaghi which is based on the particle size distribution of the filter material and the base material. This paper presents an attempt to develop filter design criteria in relation to constriction size in gravel filters. It is an alternative approach from the conventional filter design criteria of Terzaghi, which is based on the particle size distribution of the filter media and base material. In his study a criterion for filter to prevent erosion is proposed based on the constriction size distribution of the filter media. The proposed constriction size-based criterion, C10/d95 2 directly compares the controlling constriction size (C10) with the specific representative base size (d95) defines the effectiveness of filters, hence it is a more effective method compared to the Terzaghi criterion (D15 /d85<5) which is based purely on particle size. This ratio explains the behavior of filters more clearly and is proved by a number of tests on various base-filter combinations. When compared to Terzaghi criteria, constriction size distribution criterion proves to be more effective.

Laboratory study of retention and clogging performance of no-fines concretes

No-fines concrete (NFC) relief well screens function similarly to filters; thus, the retention and clogging performance of NFC should be accurately assessed. The Silveira model was adopted to predict the constriction size distribution for NFC, and the results were compared with those of slicing tests. The flow in NFC was also tested, and it was proved to be a non-Darcy flow that was well matched with the Slepicka formula. With quartz sand injection into pores seven times, the permeability of NFC changed from sharp decline to gradual stabilisation; whereas, it could be largely recovered after high-pressure water flushing. Uniform sand, continuously graded sand and discontinuously graded quartz sand were applied as base soils in a series of horizontal seepage tests in the model box, with the protection of various NFC specimens. It was found that the retention effectiveness of NFC was determined by the stability of the self-filtration layer, which was related to the interfacial ratio, soil gradation, soil density and hydraulic condition. Moreover, to prevent clogging, the hydraulic gradient should be restricted in the base soil.

Influence of the coefficient of uniformity on the size and frequency of constrictions in sand filters

Constrictions between voids control the filtration and permeability properties of granular materials. This study uses high-resolution microcomputed tomography images and discrete-element modelling to analyse two important characteristics of constrictions in granular filters: (a) the constriction size distribution (CSD) and (b) the constriction density per unit volume. The results demonstrate the importance of the particle size distribution (PSD) and void ratio of the granular material in determining the constriction density, with more widely graded materials having more densely spaced constrictions. The PSD is shown to be the main determinant of the CSD, in agreement with previous studies. The data are used to examine proposed approaches to estimate constriction spacing or void size.

Merging criteria for defining pores and constrictions in numerical packing of spheres

The void space of granular materials is generally divided into larger local volumes denoted as pores and throats connecting pores. The smallest section in a throat is usually denoted as constriction. A correct description of pores and constrictions may help to understand the processes related to the transport of fluid or fine particles through granular materials, or to build models of imbibition for unsaturated granular media. In the case of numerical granular materials involving packings of spheres, different methods can be used to compute the pore space properties. However, these methods generally induce an over-segmentation of the pore network and a merging step is usually applied to mitigate such undesirable artifacts even if a precise delineation of a pore is somewhat subjective. This study provides a comparison between different merging criteria for pores in packing of spheres and a discussion about their implication on both the pore size distribution and the constriction size distribution of the material. A correspondence between these merging techniques is eventually proposed as a guide for the user.

A network model to assess base-filter combinations

Granular filters retain base material within the narrowest constrictions of their void network. A direct comparison of the base material particle size distribution (PSD) and the filter constriction size distribution (CSD) cannot easily be used to assess filter-base compatibility. Here a conceptually simple random-walk network model using a filter CSD derived from discrete element modelling and base PSD is used to assess filter-base compatibility. Following verification using experimental data the model is applied to assess empirical ratios between filter and base characteristic diameters. The effects of filter density, void connectivity and blocking in the first few filter layers are highlighted.

Constriction size distributions of granular filters: a numerical study

The retention capability of granular filters is controlled by the narrow constrictions connecting the voids within the filter. The theoretical justification for empirical filter rules used in practice includes consideration of an idealised soil fabric in which constrictions form between co-planar combinations of spherical filter particles. This idealised fabric has not been confirmed by experimental or numerical observations of real constrictions. This paper reports the results of direct, particle-scale measurement of the constriction size distribution (CSD) within virtual samples of granular filters created using the discrete-element method (DEM). A previously proposed analytical method that predicts the full CSD using inscribed circles to estimate constriction sizes is found to poorly predict the CSD for widely graded filters due to an over-idealisation of the soil fabric. The DEM data generated are used to explore quantitatively the influence of the coefficient of uniformity, particle size distribution and relative density of the filter on the CSD. For a given relative density CSDs form a narrow band of similarly shaped curves when normalised by characteristic filter diameters. This lends support to the practical use of characteristic diameters to assess filter retention capability.

Discussion of “Geometrical Method for Evaluating the Internal Instability of Granular Filters Based on Constriction Size Distribution” by Buddhima Indraratna, Jahanzaib Israr, and Cholachat Rujikiatkamjorn

Discussion of “Geometrical Method for Evaluating the Internal Instability of Granular Filters Based on Constriction Size Distribution” by Buddhima Indraratna, Jahanzaib Israr, and Cholachat Rujikiatkamjorn

Discussion of “Geometrical Method for Evaluating the Internal Instability of Granular Filters Based on Constriction Size Distribution” by Buddhima Indraratna, Jahanzaib Israr, and Cholachat Rujikiatkamjorn

Discussion of “Geometrical Method for Evaluating the Internal Instability of Granular Filters Based on Constriction Size Distribution” by Buddhima Indraratna, Jahanzaib Israr, and Cholachat Rujikiatkamjorn

Closure to “Geometrical Method for Evaluating the Internal Instability of Granular Filters Based on Constriction Size Distribution” by Buddhima Indraratna, Jahanzaib Israr, and Cholachat Rujikiatkamjorn

Closure to “Geometrical Method for Evaluating the Internal Instability of Granular Filters Based on Constriction Size Distribution” by Buddhima Indraratna, Jahanzaib Israr, and Cholachat Rujikiatkamjorn

Probability of Transportation of Loose Particles in Suffusion Assessment by Self-Filtration Criteria

Suffusion occurs when soil particles are loosened, detached, and transported away by seepage flow through a series of pores and pore constrictions. While traditional suffusion assessment methods are often based on particle size distribution analysis only, modern assessment methods are focused on constriction size distributions, which are derived from particle size distributions based on certain assumptions. This paper provides a new assessment method, which employs the probability of loose particles being transported to the next pore. The new approach can introduce the influence of an overlapping zone between the two fractions of loose particles and soil primary fabric. This overlapping zone was often overlooked in prior studies. The constriction size distribution of the primary fabric can be calculated approximately by two-dimensional or three-dimensional methods. The three-dimensional method used in the presented study even offers the opportunity to study the influence of particle arrangements on suffusion. The results of the new assessment methods show satisfactory agreement with experimental results.

Geometrical Method for Evaluating the Internal Instability of Granular Filters Based on Constriction Size Distribution

AbstractInternal instability occurs when the finer fraction from a well-graded granular soil escapes with the infiltrates, rendering a filter ineffective. Thus far, numerous particle size as well as constriction size distribution–based geometrical methods have been proposed to assess potential internal instability. This paper reports the results from hydraulic tests performed on six granular soils (five well-graded sand-gravel mixtures and medium sand) at different uniformity coefficients and compacted at varying relative density. The study facilitated an objective evaluation of some of the well known published methods, leading to a more realistic interpretation of filtration data based on a revised technique, which accurately demarcates the boundary between internally stable and unstable granular soils. A large body of published data and the current laboratory results were used to validate the proposed criterion for the assessment of internal instability, which is also sensitive to the relative density o...