Sedimentation Consolidation Research Articles

The Influence of Soil Saturation on the Geotechnical Test Results

The consistency limits are important properties of soil. The fall cone test method has a good repeatability, and the operator’s judgement has little effect on the results. This paper presents a new sample preparation method, in which the sedimentation method and consolidation test are combined, to prepare the saturated specimens for fall cone test for determining the consistency limits, and the sample prepared by this new method can be considered completely saturated. For the specimens prepared by the previous sample preparation method, the decrease in the water content leads to a decrease in the degree of saturation of soil. The test results show that the specimens prepared by this new method can reach a low water content, and the minimum penetration depths are as low as 2 mm, and the plastic limit could be obtained directly. In addition, the van shear test results show that the unsaturated specimens have larger values of undrained shear strength than the saturated specimens at the same water content, which could explain the difference of consistency limits obtained from different specimen preparation methods.

Convergence of H(div)-conforming schemes for a new model of sedimentation in circular clarifiers with a rotating rake

A macroscopic model is introduced for simulating the sedimentation–consolidation of solid particles in an incompressible fluid under the effect of gravity and in the presence of a slowly rotating arm assisting the removal of sediment on the bottom of clarifier–thickener units. The governing model is an initial–boundary value problem for the Navier–Stokes equations describing the flow of the mixture coupled with a nonlinear parabolic equation describing the volume fraction of solids. The rotating structure is accounted for by suitable drag laws on the momentum balance of the mixture and on the mass balance of the solid phase. An H(div)-conforming method for the coupled problem is proposed, a rigorous proof of convergence is provided, and the validity of the new model and the performance of the scheme are demonstrated numerically by several computational tests.

Geological and geophysical studies of the Agoudal impact structure (Central High Atlas, Morocco): New evidence for crater size and age

AbstractSince the discovery of shatter cones (SCs) near the village of Agoudal (Morocco, Central High Atlas Mountains) in 2013, the absence of one or several associated circular structures led to speculation about the age of the impact event, the number, and the size of the impact crater or craters. Additional constraints on the crater size, age, and erosion rates are obtained here from geological, structural, and geophysical mapping and from cosmogenic nuclide data. Our geological maps of the Agoudal impact site at the scales of 1:30,000 (6 km2) and 1:15,000 (2.25 km2) include all known occurrences of SCs in target rocks, breccias, and vertical to overturned strata. Considering that strata surrounding the impact site are subhorizontal, we argue that disturbed strata are related to the impact event. Three types of breccias have been observed. Two of them (br1‐2 and br2) could be produced by erosion–sedimentation–consolidation processes, with no evidence for impact breccias, while breccia (br1) might be impact related. The most probable center of the structure is estimated at 31°59′13.73ʺN, 5°30′55.14ʺW using the concentric deviation method applied to the orientation of strata over the disturbed area. Despite the absence of a morphological expression, the ground magnetic and electromagnetic surveys reveal anomalies spatially associated with disturbed strata and SC occurrences. The geophysical data, the structural observations, and the area of occurrence of SCs in target rocks are all consistent with an original size of 1.4–4.2 km in diameter. Cosmogenic nuclide data (36Cl) constrain the local erosion rates between 220 ± 22 m Ma−1 and 430 ± 43 m Ma−1. These erosion rates may remove the topographic expression of such a crater and its ejecta in a time period of about 0.3–1.9 Ma. This age is older than the Agoudal iron meteorite age (105 ± 40 kyr). This new age constraint excludes the possibility of a genetic relationship between the Agoudal iron meteorite fall and the formation of the Agoudal impact site. A chronolgy chart including the Atlas orogeny, the alternation of sedimentation and erosion periods, and the meteoritic impacts is presented based on all obtained and combined data.

A posteriori error estimation for an augmented mixed-primal method applied to sedimentation–consolidation systems

In this paper we develop the a posteriori error analysis of an augmented mixed-primal finite element method for the 2D and 3D versions of a stationary flow and transport coupled system, typically encountered in sedimentation–consolidation processes. The governing equations consist in the Brinkman problem with concentration-dependent viscosity, written in terms of Cauchy pseudo-stresses and bulk velocity of the mixture; coupled with a nonlinear advection – nonlinear diffusion equation describing the transport of the solids volume fraction. We derive two efficient and reliable residual-based a posteriori error estimators for a finite element scheme using Raviart–Thomas spaces of order k for the stress approximation, and continuous piecewise polynomials of degree ≤k+1 for both velocity and concentration. For the first estimator we make use of suitable ellipticity and inf–sup conditions together with a Helmholtz decomposition and the local approximation properties of the Clément interpolant and Raviart–Thomas operator to show its reliability, whereas the efficiency follows from inverse inequalities and localisation arguments based on triangle-bubble and edge-bubble functions. Next, we analyse an alternative error estimator, whose reliability can be proved without resorting to Helmholtz decompositions. Finally, we provide some numerical results confirming the reliability and efficiency of the estimators and illustrating the good performance of the associated adaptive algorithm for the augmented mixed-primal finite element method.

Study of the sedimentation and self-weight consolidation behavior of seafloor sediments using a radioisotope densitometer

ABSTRACTIn this study, settling tests were conducted to investigate the sedimentation and self-weight consolidation behavior of seafloor sediments from Isahaya Bay, Ariake Sea, Japan. During the tests, the density variations with depth and time were measured by a gamma-ray transmission radioisotope densitometer. The test results show that the settling process of the seafloor sediments can be classified into the flocculation stage, settling stage, and consolidation stage. The settling rate of the seafloor sediments in the settling stage is dependent on the temperature and initial water content, while the settling rate in the consolidation stage is independent of the temperature and initial water content. The density profile changes from a constant density profile to a linear density profile when the sedimentation process transitions to the self-weight consolidation process. The relations between the void ratio (e) and effective vertical stress (p’) at very low pressures can be calculated from the measured density values, and this can be used for the analysis of the self-weight consolidation of seafloor sediments. For the seafloor sediments tested in this study, the undrained shear strength (su) values are almost the same when the density values are less than 1.14 g/cm3, and the su values increase linearly with an increase in density when the density values are in the range of 1.14–1.2 g/cm3.

Discontinuous traveling wave entropy solutions for a sedimentation–consolidation model

This paper deals with a mathematical model of gravitational sedimentation–consolidation processes, for which the existence of discontinuous traveling wave entropy solutions is established by using the phase plane analysis method.

A mixed-primal finite element approximation of a sedimentation–consolidation system

This paper is devoted to the mathematical and numerical analysis of a strongly coupled flow and transport system typically encountered in continuum-based models of sedimentation–consolidation processes. The model focuses on the steady-state regime of a solid–liquid suspension immersed in a viscous fluid within a permeable medium, and the governing equations consist in the Brinkman problem with variable viscosity, written in terms of Cauchy pseudo-stresses and bulk velocity of the mixture; coupled with a nonlinear advection — nonlinear diffusion equation describing the transport of the solids volume fraction. The variational formulation is based on an augmented mixed approach for the Brinkman problem and the usual primal weak form for the transport equation. Solvability of the coupled formulation is established by combining fixed point arguments, certain regularity assumptions, and some classical results concerning variational problems and Sobolev spaces. In turn, the resulting augmented mixed-primal Galerkin scheme employs Raviart–Thomas approximations of order [Formula: see text] for the stress and piecewise continuous polynomials of order [Formula: see text] for velocity and volume fraction, and its solvability is deduced by applying a fixed-point strategy as well. Then, suitable Strang-type inequalities are utilized to rigorously derive optimal error estimates in the natural norms. Finally, a few numerical tests illustrate the accuracy of the augmented mixed-primal finite element method, and the properties of the model.

Discontinuous finite volume element discretization for coupled flow–transport problems arising in models of sedimentation

The sedimentation–consolidation and flow processes of a mixture of small particles dispersed in a viscous fluid at low Reynolds numbers can be described by a nonlinear transport equation for the solids concentration coupled with the Stokes problem written in terms of the mixture flow velocity and the pressure field. Here both the viscosity and the forcing term depend on the local solids concentration. A semi-discrete discontinuous finite volume element (DFVE) scheme is proposed for this model. The numerical method is constructed on a baseline finite element family of linear discontinuous elements for the approximation of velocity components and concentration field, whereas the pressure is approximated by piecewise constant elements. The unique solvability of both the nonlinear continuous problem and the semi-discrete DFVE scheme is discussed, and optimal convergence estimates in several spatial norms are derived. Properties of the model and the predicted space accuracy of the proposed formulation are illustrated by detailed numerical examples, including flows under gravity with changing direction, a secondary settling tank in an axisymmetric setting, and batch sedimentation in a tilted cylindrical vessel.

Studies on parameter estimation and model predictive control of paste thickeners

Paste thickeners have attracted significant interest from mining industry due to its higher dewatering ability as compared to conventional or high rate thickeners. However, the underflow solids concentration, which is an important process variable of thickeners, is often poorly regulated. In this article, a dynamic model based on sedimentation–consolidation theory is adopted and validated using industrial plant data. Based on this model, control studies have been carried out to explore approaches to address a number of difficulties in current industrial operation. An extended Kalman filter is developed to estimate the compressibility parameter of the feed (coal tailing). As a key process parameter, coal tailing compressibility plays a significant role in thickener dynamics, but is time-varying and difficult to measure. Potential improvements of process operation by implementing model predictive control (MPC) are investigated. Simulation studies show that the proposed control can deliver a higher underflow solids concentration and a better regulated underflow removal rate than the existing operation. It is also demonstrated that taking into account the “future” time-varying input constraints in the MPC algorithm can help overcome the current control difficulty caused by co-disposal of coal tailing and coarse reject.

Multistage centrifugation method for determination of filtration and consolidation properties of mineral and biological suspensions using the analytical photocentrifuge

The article describes a new method of multistage centrifugation (MC) for determination of filterability (local filtration and consolidation properties) of mineral and biological suspensions. The method comprises centrifugal compression–permeability and sedimentation–consolidation experiments, performed with the help of analytical photocentrifuge at different centrifugal rotation speeds. The experimental procedure implies determination of the analytical centrifugation curves: dependencies of (i) sediment height on centrifugal acceleration in sedimentation–consolidation experiments and (ii) permeate volume and filter cake dryness on centrifugation time and centrifugal acceleration in filtration–consolidation experiments. The combined analysis of these curves yields the pressure dependencies of local cake dryness, specific cake resistance, and consolidation coefficient in the wide range of solid pressure (5×103–5×105Pa). Application of MC requires a relatively small quantity of suspension (about 2ml).The method was tested for suspensions with different filterabilities and compressibilities: calcium carbonate, kaolin and yeast suspensions. The pressure dependencies of cake dryness, specific cake resistance, and consolidation coefficient, determined by MC, were in correspondence with those determined in the series of conventional constant pressure dead-end filtration–consolidation experiments.

Modelling sedimentation–consolidation in the framework of a one-dimensional two-phase flow model

A one-dimensional vertical two-phase flow model for sedimentation–consolidation process is presented. The model is based on solving the continuity and momentum equations for both fluid and solid phases. In the non-cohesive case, the momentum transfer between the two phases is reduced to the drag force around a single particle modified to take the hindrance effects into account. In the cohesive case, Darcy–Gersevanov's law is used for the closure of the momentum transfer between the two phases and the concept of “effective stress” is introduced to take into account the bed structuring. These closure laws are validated against high-resolution experimental data in terms of settling curves and concentration profiles. The reliability of the model is illustrated from an analysis of the momentum balances at different stages during the process. Finally, the proposed closure laws and numerical algorithms are shown to be able to quantitatively reproduce sedimentation of non-cohesive and sedimentation–consolidation of cohesive sediments, including mud.

Sedimentation–consolidation modeling with an interaction coefficient

This paper examines the use of an interaction coefficient to couple sedimentation and consolidation phenomena with the conventional finite strain consolidation theory. A specific continuous interaction function was implemented and the resulted model was examined. The model was found to able to capture proper sedimentation–consolidation features. It was also determined that the structural and maximum suspension void ratios are the major factors controlling the shape of the void ratio profile. The model was compared with experimental data and other numerical models and qualitatively good agreement was obtained.

Steady-state, control, and capacity calculations for flocculated suspensions in clarifier–thickeners

A spatially one-dimensional model for the behaviour of flocculated suspensions in clarifier–thickeners is studied. This model combines a theory of sedimentation–consolidation processes of flocculated suspensions, which leads to a strongly degenerate diffusion equation, with the discontinuous flux appearing in the recently analyzed clarifier–thickener (CT) setup. This setup includes both clarification and thickening zones of clarifier–thickener units, while the earlier ideal continuous thickener (ICT) concept explicitly models the thickening zone only. The construction of steady-state concentration profiles attainable in a continuously operated CT is described. This construction incorporates an entropy principle, which implies that only those steady states are admissible for which the solids concentration is increasing downwards. Numerical examples of steady-state profiles and their applications to comparisons between both modes of operation, to the control of sediment height through selection of the clarification/thickening split ratio of the feed flux, and for capacity calculations are presented. A numerical example illustrates the use of a numerical method for the full (time-dependent) model to compare several fill-up strategies.

Sedimentation–consolidation of a double porosity material

This paper studies the sedimentation–consolidation of a double porosity material, such as lumpy clay. Large displacements and finite strains are accounted for in a multidimensional setting. Fundamental equations are derived using a phenomenological approach and non-equilibrium thermodynamics, as set out by Coussy [Coussy, Poromechanics, Wiley, Chichester, 2004]. These equations particularise to three non-linear partial differential equations in one dimensional context. Numerical implementation in a finite element code is currently being undertaken.

On an upwind difference scheme for strongly degenerate parabolic equations modelling the settling of suspensions in centrifuges and non-cylindrical vessels

We prove the convergence of an explicit monotone finite difference scheme approximating an initial-boundary value problem for a spatially one-dimensional quasilinear strongly degenerate parabolic equation, which is supplied with two zero-flux boundary conditions. This problem arises in a model of sedimentation–consolidation processes in centrifuges and vessels with varying cross-sectional area. We formulate the definition of entropy solution of the model in the sense of Kružkov and prove the convergence of the scheme to the unique BV entropy solution of the problem. The scheme and the model are illustrated by numerical examples.

Effects of smectite, salinity and water content on sedimentation and self-weight consolidation of thoroughly disturbed soft marine clay

Addition of a high-swelling smectite to low-activity-mineral-dominated Leda clay influenced the settling mode, settling/consolidation rates and the final sediment water contents attained when suspensions ranging in water content from 500 to 6000% were allowed to settle under salinity conditions ranging from 30 to 0.5 g/l, and to undergo self-weight consolidation for 14 days. The presence of high-swelling smectite extended the salinity and water content ranges over which consolidation settling and zone settling occurred and the final water content for any initial-water-content/salinity condition increased as the amount of high-swelling smectite increased. The settling and consolidation rate patterns change with time in a manner that is dependent on all of settling mode, water content and salinity. At high-swelling smectite content 10%, the lowest sediment water content is attained at high salinity and the lowest possible initial suspension water content.

Mathematical model and numerical simulation of the dynamics of flocculated suspensions in clarifier–thickeners

We formulate a mathematical model for continuous sedimentation–consolidation processes of flocculated suspensions in clarifier–thickener units. The governing equation of this model is a scalar, strongly degenerate parabolic equation in which both the convective flux and the diffusion term depend on parameters that are discontinuous functions of the depth variable. A simple finite-difference scheme for the numerical solution of the model is introduced. We perform a limited analysis of steady states as desired stationary modes of operation. Finally, numerical examples illustrate that the model realistically describes the dynamics of flocculated suspensions in clarifier–thickeners.

Settling velocities of particulate systems: 13. A simulator for batch and continuous sedimentation of flocculated suspensions

Based on a numerical method introduced by Bürger and Karlsen [J. Eng. Math. 41 (2001) 145], a software was developed for the simulation of batch and continuous thickening. The paper recalls the application of the phenomenological theory of sedimentation–consolidation processes to batch settling and continuous thickening of flocculated suspensions. The software presents two alternatives, one for each of these possibilities. For batch thickening, the initial and critical concentration and the height of the initial suspension must be entered together with the parameters of the flux density function and the effective solid stress. The output is a settling plot showing as many lines of constant concentration as requested and a plot of the concentration profile for selected times. For continuous thickening, only the steady state is simulated. The input is the solid feed flux and the required underflow concentration or volume underflow rate. If the thickener area is known, the capacity and the concentration profile in the equipment can be predicted. On the other hand, if the capacity is known, the required settling area and the resulting concentration profiles are predicted. Several examples show the application.

Existence and Stability for Mathematical Models of Sedimentation–Consolidation Processes in Several Space Dimensions

In this paper, we study several spatially multidimensional initial-boundary value problems modelling sedimentation–consolidation processes of a flocculated suspension. This solid–fluid mixture is considered as two superimposed continuous media differing in density and viscosity. The phenomenological foundation and derivation of the mathematical model are based on the previous work by R. Bürger et al. (2000, Z. Angew. Math. Mech. 80, 79–92). We study the full coupling of the conservation of mass equation and the conservation of linear momentum equation. For different types of regularization, we establish energy estimates. The dissipative nature of the whole system assures the existence as well as the stability (long time asymptotics) of a solution of the system (provided that the viscosities of the fluid are large enough). Moreover, the energy estimates might serve as the foundation for the design of numerical algorithms to simulate the system.

A critical look at the kinematic‐wave theory for sedimentation–consolidation processes in closed vessels

AbstractThe two‐phase flow of a flocculated suspension in a closed settling vessel with inclined walls is investigated within a consistent extension of the kinematic wave theory to sedimentation processes with compression. Wall boundary conditions are used to spatially derive one‐dimensional field equations for planar flows and flows which are symmetric with respect to the vertical axis. We analyse the special cases of a conical vessel and a roof‐shaped vessel. The case of a small initial time and a large time for the final consolidation state leads to explicit expressions for the flow fields, which constitute an important test of the theory. The resulting initial‐boundary value problems are well posed and can be solved numerically by a simple adaptation of one of the newly developed numerical schemes for strongly degenerate convection‐diffusion problems. However, from a physical point of view, both the analytical and numerical results reveal a deficiency of the general field equations. In particular, the strongly reduced form of the linear momentum balance turns out to be an oversimplification. Included in our discussion as a special case are the Kynch theory and the well‐known analyses of sedimentation in vessels with inclined walls within the framework of kinematic waves, which exhibit the same shortcomings. In order to formulate consistent boundary conditions for both phases in a closed vessel and in order to predict boundary layers in the presence of inclined walls, viscosity terms should be taken into account. Copyright © 2001 John Wiley & Sons, Ltd.