Large-strain Consolidation Model Research Articles

Application of a one-dimensional large-strain consolidation model to a full-scale tailings storage facility

The objective of this study was to evaluate applicability of a commercially-available, one-dimensional (1-D) large-strain consolidation model to predict mine tailings consolidation in a full-scale tailings storage facility (TSF). Data pertaining to tailings production, cyclone operation time, impoundment height, and impoundment volume were made available for a full-scale copper mine TSF. A numerical model was applied to predict tailings consolidation for two considerations: Design Assessment – based on design estimates, and Operation Assessment – based on actual operational data. Comparison between actual average tailings dry density (ρd) during the first 4 yr of operation and predicted ρd yielded coefficients of determination (R2) as high as 0.81 for the Operation Assessment and 0.93 for the Design Assessment. Predictions of tailings height for both assessments also agreed well with actual impoundment heights for the first 6 yr of operation. A procedure was developed to predict average ρd of a full-scale TSF that includes (i) estimating TSF volume based on predicted impoundment height and (ii) using TSF volume with dry tailings mass to compute ρd. The main finding was that the modeling of gradual tailings deposition via a 1-D large-strain consolidation model can provide a reliable prediction of tailings height and capacity during TSF operation.

One-Dimensional Model for Large-Strain Consolidation in a Bench-Scale Centrifuge

We present a mathematical model for large-strain consolidation in a bench-scale centrifuge, which is not based on scaling laws. The model allows for different boundary condition setups at the base of the sample: free outflow, imposed head or containment. Constitutive relationships for effective stress and permeability both in terms of void ratio are required inputs. A numerical algorithm is proposed to solve the constructed mathematical model based on the method of lines. Example numerical problems are discussed, and solution strategies are proposed to deal with anomalies in the numerical solution. A limited experimental test was performed to test the feasibility of the approach. The outcome of the test was positive for preconsolidated grounds. For a slurry, vibration effects appear to be present in the used centrifuge, which are not included in the model.

CS3: Large Strain Consolidation Model for Layered Soils

AbstractA numerical model, called CS3, is presented for one-dimensional, large strain consolidation of layered soils. The algorithm accounts for vertical strain, soil self-weight, conventional constitutive relationships, changing material properties during consolidation, unload/reload, time-dependent loading and boundary conditions, an externally applied hydraulic gradient, and multiple soil layers with different material properties. CS3 can accommodate equilibrium and nonequilibrium profiles for the initial void ratio as well as variable profiles for preconsolidation stress and applied stress increment. Verification checks show excellent agreement with available analytical and numerical solutions. Several numeric examples are used to illustrate the capabilities of CS3 and highlight errors that may occur when multilayer systems are modeled as a single layer with average properties. Finally, settlement estimates obtained using CS3 are in good agreement with field measurements for the Gloucester test fill.

Evaluation of Data Analysis Methods for the CRS Consolidation Test

AbstractThe constant rate-of-strain (CRS) laboratory consolidation test is used to measure consolidation properties of fine-grained soils. Although the CRS test offers many advantages over the conventional incremental-loading consolidation test, uncertainties associated with the method of data analysis have presented an obstacle to more widespread use of the CRS test in practice. This paper presents results from a numerical investigation of the accuracy of linear and nonlinear data analysis methods for the CRS consolidation test. Numerical simulations were conducted using a validated large strain consolidation model for CRS loading conditions, published material properties for two reconstituted clay soils, and three applied strain rates. Based on the numerical results, recommendations are provided for analysis of CRS consolidation data, including changes to the ASTM D4186 equations for nonlinear data analysis. The most appropriate analysis method for soils with linear compressibility is the current ASTM D...

Large-strain elastic viscoplastic consolidation analysis of very soft clay layers with vertical drains under preloading

A very soft clay layer is highly compressible and exhibits significant creep under loading. The classical linearly elastic constitutive relationship and small-strain assumption are not suitable for the consolidation analysis of very soft clays. This paper presents a new large-strain consolidation model that incorporates the Yin–Graham elastic viscoplastic (EVP) constitutive equation for use in studying the consolidation of very soft clay layers with vertical drains under preloading. First, the large-strain fluid continuity equation and the EVP constitutive equation are incorporated into a quadratic differential equation of pore-water pressure and its integral terms. Second, the alternating-direction implicit (ADI) method and virtual node method are adopted to obtain the finite difference solution. A computer program named “BSSDS” is developed for large-strain EVP consolidation analysis of clay layers with vertical drains, taking into account the complicated in situ conditions, such as resistance of vertical drains, smear effects, variation of permeability with void ratio, and multilayered soils. Third, the new large-strain numerical method is applied to the consolidation modeling of very soft clay layers with vertical drains under preloading at a site that is part of the Hong Kong – Shenzhen Western Corridor Link Project. It is found that the foundation settlements of the new large-strain EVP consolidation model have good agreement with the measured data. Finally, three different consolidation models are used to calculate the average degree of consolidation and settlements of the clay layers. The analysis shows that it is essential to consider both large-strain compression and creep effects in the analysis of very soft clay layers with vertical drains under loading.

Model for large strain consolidation under constant rate of strain

SUMMARYA numerical model, called CCRS1, is presented for one‐dimensional large strain consolidation under constant rate of strain loading conditions. The algorithm accounts for vertical strain, general constitutive relationships, relative velocity of fluid and solid phases, changing compressibility and hydraulic conductivity during consolidation, and an externally applied hydraulic gradient acting across the specimen. Soil compressibility is rate independent, and as such, the current model is most appropriate for less‐structured clays. Verification checks show excellent agreement with analytical and numerical solutions for small and large strain conditions. A series of numeric examples indicates that compressibility and hydraulic conductivity constitutive relationships can have an important effect on constant rate of strain consolidation response. Results also indicate that analytical solutions obtained using small strain theory can be in significant error for large strain conditions with changing coefficient of consolidation. Copyright © 2012 John Wiley & Sons, Ltd.

Enhanced CS2 Model for Large Strain Consolidation

AbstractSince original publication in 1997, the CS2 numerical model has been widely used for consolidation analysis and has formed the basis for several more advanced consolidation models. In this paper, an enhanced version of the CS2 model is presented along with simulations to illustrate its new capabilities. The algorithm includes features of the original model with the addition of time-dependent loading, an external hydraulic gradient, and unload/reload effects. Verification checks show excellent agreement with analytical solutions for time-dependent loading under small strain conditions. A variety of numerical examples indicates that the new capabilities describe important considerations for consolidation analysis. The simulations also indicate that failure to correctly account for compressibility and hydraulic conductivity constitutive relationships and self-weight of the soil in particular can lead to significant errors.

Model for Large Strain Consolidation by Centrifuge

A numerical model, called CC1, is presented for one-dimensional large strain consolidation in a geotechnical centrifuge. The model includes all the capabilities of a previous large strain consolidation code, CS2, written for surcharge loading under normal gravity conditions. In addition, CC1 accounts for variation of acceleration factor N over the depth of a centrifuge test specimen. The development of CC1 is first presented, followed by a comparison of simulated time–settlement curves with experimental measurements for Singapore marine clay and a parametric study illustrating the effects of nonuniform N distribution on centrifuge consolidation behavior. Simulations indicate that the effect of spatially varying N is most strongly controlled by the ratio of specimen height to centrifuge arm length and that the error associated with the assumption of constant N is relatively small if this ratio is 0.2 or less. Finally, CC1 is used to calculate the optimal location within a centrifuge specimen of Singapore m...

Determination of consolidation behaviour of Haliç dredged material by using a seepage‐induced consolidation test

PurposeTo establish relationships between effective vertical stress‐void ratio and hydraulic conductivity‐void ratio on high water content dredged clays, which are then used to predict the field consolidation behavior.Design/methodology/approachThe large strain consolidation model is used for numerical modeling of large‐strain self‐weight consolidation. Material parameters determined from seepage‐induced consolidation tests provided satisfactory predictions of field compression behavior.FindingsIt is shown that realistic estimates of self‐weight consolidation behavior of dredged sea bottom sediments stored on land can be made by using a seepage‐induced consolidation test system and an appropriate consolidation model such as CS2, which is very important in storage capacity design and reclamation planning of such storage areas.Originality/valueIn this paper, the findings are presented of an experimental investigation of the consolidation behavior of Golden Horn dredge material using a seepage‐induced testing system. The experimentally determined consolidation properties have yielded useful relationships for the variation of void ratio with effective stress and coefficient of permeability with void ratio, and use of these has enabled a realistic prediction of the observed behavior.

Model for large strain consolidation with compressible pore fluid

AbstractA numerical model, called CCPF1 (Consolidation with Compressible Pore Fluid 1), is presented for one‐dimensional large strain consolidation of a saturated porous medium with compressible pore fluid. The algorithm includes all the capabilities of a previous large strain consolidation code, CS2, written for incompressible pore fluid. In addition, fluid density and fluid viscosity are functions of fluid pressure in CCPF1. Generalization of the numerical approach to accommodate these functions requires several modifications to the CS2 method, including phase relationships, intrinsic permeability, pore pressure, fluid potential, and mass flux. Inertial forces are neglected and isothermal conditions are assumed. The development of CCPF1 is first presented, followed by an example that illustrates the effects of pore fluid compressibility on the mechanics of consolidation of saturated porous media. Copyright © 2004 John Wiley & Sons, Ltd.

Field Investigation of Evaporation from Freshwater Tailings

Safe and economical storage of tailings is now a major consideration in the operation of many mining operations. Tailings in slurried form, particularly if they have a significant clay content, can take a very long time to consolidate under the action of self-weight consolidation alone. However, if the operation is located in an area of high potential evaporation, this can be used to accelerate the rate of tailings densification. This paper presents a study of the evaporation behavior of a clayey tailings slurry deposited into an evaporation pond in the southwest of Western Australia. Over a six-month period, the rate of evaporation from the tailings surface was monitored using the Bowen Ratio method and the microlysimeter method. This was compared with the evaporation from a Class A pan located nearby. The tailings underwent very significant cracking as drying proceeded, and it was found that these cracks had a significant influence on the overall rate of evaporation once the top surface of the deposit started to desaturate. A large strain consolidation model was used to model the behavior, and the algorithm used in this model to include the effects of evaporation is shown to provide a reasonable prediction of the observed evaporation behavior.

Consolidation theory applied to the capillary suction time (CST) apparatus

The Capillary Suction Time-method was introduced in 1967, and was designed for establishing the dewaterability of sludge samples. The CST-test was developed as an alternative to the more cumbersome filtration tests using vacuum pumps. Over the years, extensive research has been conducted on models describing the dewatering process in this apparatus. Most of these models have been based on traditional filtration theory, comprising an assumed average cake filtration resistance. An alternative theory which has not been investigated in this respect before is the large-strain consolidation model proposed by Gibson (1967). When this particular consolidation theory is applied to the CST-apparatus, it can be shown that from measurements with the CST-test, conducted on a series of samples of a certain sludge or soil with different initial void ratios (or water contents), the coefficient of consolidation of the soil can be deduced. The benefits of this approach are multifold. By describing the dewatering of a sludge with the consolidation theory, e.g. in a lagoon, filter press, centrifugal pumps and so forth, the dry matter content can be predicted with respect to time using the coefficient of consolidation found with the CST-test. Also, the influence of polyelectrolytes added to the sludge to improve the dewaterability can be measured quantitatively as an increase of the coefficient of consolidation.

Consolidation theory applied to the capillary suction time (CST) apparatus

The Capillary Suction Time-method was introduced in 1967, and was designed for establishing the dewaterability of sludge samples. The CST-test was developed as an alternative to the more cumbersome filtration tests using vacuum pumps.Over the years, extensive research has been conducted on models describing the dewatering process in this apparatus. Most of these models have been based on traditional filtration theory, comprising an assumed average cake filtration resistance. An alternative theory which has not been investigated in this respect before is the large-strain consolidation model proposed by Gibson (1967).When this particular consolidation theory is applied to the CST-apparatus, it can be shown that from measurements with the CST-test, conducted on a series of samples of a certain sludge or soil with different initial void ratios (or water contents), the coefficient of consolidation of the soil can be deduced. The benefits of this approach are multifold. By describing the dewatering of a sludge with the consolidation theory, e.g. in a lagoon, filter press, centrifugal pumps and so forth, the dry matter content can be predicted with respect to time using the coefficient of consolidation found with the CST-test. Also, the influence of polyelectrolytes added to the sludge to improve the dewaterability can be measured quantitatively as an increase of the coefficient of consolidation.

Deaeration of powders in hoppers: a simple linear theory including filling

The deaeration of powder during hopper filling is analysed according to a simple, linear, large-strain consolidation model. The solution is presented in terms of simple dimensionless charts for end of fill air pressures. Post-fill behaviour is predicted by a straightforward finite difference scheme suitable for programming on microcomputers. It is demonstrated that the model agrees well with some previously presented large-scale hopper measurements.

One-dimensional mathematical model for large strain consolidation : Monte, J L Ph D thesis, Northwestern Univ, 1975, 73P

One-dimensional mathematical model for large strain consolidation : Monte, J L Ph D thesis, Northwestern Univ, 1975, 73P

One-dimensional mathematical model for large-strain consolidation. 6F, 4T, 31R : MONTE, JL KRIZEK, RJ GEOTECHNIQUE, V26, N3, SEPT. 1976, P495–510

One-dimensional mathematical model for large-strain consolidation. 6F, 4T, 31R : MONTE, JL KRIZEK, RJ GEOTECHNIQUE, V26, N3, SEPT. 1976, P495–510

One-dimensional mathematical model for large-strain consolidation

A mathematical model is developed to represent the one-dimensional large-strain consolidation of a fully saturated clay. The fluid limit is postulated to be that water content associated with a ‘stress-free’ condition of the soil, and it is taken as the reference state from which strains are measured. Experimental results from a series of permeability tests suggest that the relationship between the logarithm of the coefficient of permeability and the void ratio is not a straight line for the entire range of void ratio considered. In addition, the variation of the constrained modulus as consolidation progresses is taken into account. The resulting boundary value problem involves a non-linear partial differential equation with void ratio as the dependent variable, and the numerical solution is accomplished by a step-by-step procedure combined with a weighted residual technique which leads to a finite element discretization in the spatial variable and a finite difference discretization in the time variable. The mathematical model is applied to four cases (two involving a salt flocculated kaolinite slurry and two involving a dispersed kaolinite slurry) in the stress range within which a ‘slurry’ is transformed to a ‘soil’. For the particular clay (Hydrite 10) investigated it was found that classical small-strain consolidation theory can adequately describe the deformation-time response for all practical purposes after the effective consolidation stress on the slurry had exceeded a value of about 8 lb/in.2 (55 kN/m2). Un modèle mathématique est utilisé pour reprénter la consolidation à une dimension à grande déformation d'une argile totalement saturée. La limite de fluidité est supposée êre la teneur en eau correspondant à une condition de sol sans contrainte et elle est prise comme base de référence à partir de laquelle les déformations sont mesurées. Des résultats expérimentaux obtenus à partir d'une série d'essais de perméabilité montrant que la relation entre le logarithme du coefficient de perméabilité et l'indice des vides n'est pas une ligne droite pour l'ensemble des indices des vides considérés dans cette étude. De plus, on tient compte de la variation du module de déformation en fonction de la consolidation. L'étude du problème résultant de la prise en compte des conditions aux limites aboutit à une équation partielle différentielle non linéaire avec l'indice des vides comme variable dépendante, et la solution numérique est obtenue par approximations successives combinées à une technique de pondération résiduelle qui conduit à une discrétisation d'éléments finis dans la variable espace et une discrétisation de différences finies dans la variable temps. Le modèle mathématique est appliqué à quatre cas (deux concernant un coulis de kaolinite salée floculée et deux concernant un coulis de kaolinite diluée) dans la gamme des contraintes dans laquelle un ‘coulis’ est transformé en un ‘sol’. Pour une argile particulière (Hydrite 10), la recherche a montré aue la théorie classiaue de consolidation à faible déformation est suffisante pour décrire la relation déformation–temps, pour toutes les applications pratiques dès que la contrainte de consolidation effective sur le coulis dépasse une valeur à peu près égale 8 lb/in.2 (55 kN/m2).