An anisotropic elastic–viscoplastic model for soft clays

Experimental evidences have shown deficiencies of the existing overstress and creep models for viscous behaviour of natural soft clay. The purpose of this paper is to develop a modelling method for viscous behaviour of soft clays without these deficiencies. A new anisotropic elastic–viscoplastic model is extended from overstress theory of Perzyna. A scaling function based on the experimental results of constant strain-rate oedometer tests is adopted, which allows viscoplastic strain-rate occurring whether the stress state is inside or outside of the yielding surface. The inherent and induced anisotropy is modelled using the formulations of yield surface with kinematic hardening and rotation (S-CLAY1). The parameter determination is straightforward and no additional experimental test is needed, compared to the Modified Cam Clay model. Parameters determined from two types of tests (i.e., the constant strain-rate oedometer test and the 24 h standard oedometer test) are examined. Experimental verifications are carried out using the constant strain-rate and creep tests on St. Herblain clay. All comparisons between predicted and measured results demonstrate that the proposed model can successfully reproduce the anisotropic and viscous behaviours of natural soft clays under different loading conditions.     

Rheological determination of peptizing agents in bentonite clays

This paper presents the results of an evaluation of the rheological properties of commercial bentonite suspensions made from peptized and unpeptized clay samples collected over a six year time span. The rheological properties of these suspensions were measured between shear rates of 5.11 to 1022 s^–1 at concentrations of 15, 30, 45, 64.2 and 70 kg/m³. Bingham, power-law and Casson models were then fitted to the shear stress and shear rate values. Parameters derived from these models were then subjected to further analyses. Four rheological methods (termed peptization index tests) were developed to differentiate between peptized and unpeptized bentonite samples.     

On the behavior of fine mud suspensions

Flows of natural mud-water mixtures are of great interest for industrial and civil engineering. But there is still no general agreement about the methods for determining the main rheological characteristics of these systems. We propose here an accurate rheological study of some natural mud-water mixtures. We first discuss the possible effects of changing various parameters such as temperature, pH, electrolyte concentration, solid concentration, clay type. The behavior of these muds appears to be very sensitive to most of these parameters and to be hardly predictable from a knowledge of their components. Then, we show that a Herschel-Bulkley model fits very well steady flow experimental data for a very large range of shear rates. We also suggest physical explanations of this model in agreement with our observations of behavior changes when some parameters change. The yield stress value of this model provides a good estimation of real yield stress which is a key parameter for mixture behavior. These considerations are very useful to characterize, predict, and compare various mud flows.     

Elastoplastic model describing cyclic creeping behaviour of soft clays

The elastoplastic model in the deviatoric stress space is constructed to describe the cyclic undrained creeping behaviour of soft clays under cyclic stress by using Mises yield criterion and the concept of a field of hardening moduli. Furthermore, the effect of model parameters on the deformation is studied, and a method is given to determine quantitatively model parameters from results of cyclic triaxial tests of the saturated soft clay. The project supported by National Natural Science Foundation of China and Tianjin Twenty-one Century Youth Science Foundation     

An investigation of squeeze flow as a viable technique for determining the yield stress

A systematic study of squeeze flow (SF) was performed on different concentrations of Carbopol with varying yield stresses. A sample of constant volume was placed between two parallel plates and a series of constant force steps applied, following the plate separation as a function of time. Precise rheological measurements of the model yield stress fluids were performed in addition to the well-controlled SF tests. These rheological measurements were used in conjunction with the SF equations to determine the time-dependent plate separation, allowing a direct comparison of theory and experiment throughout the entire test. The limiting height achieved during constant force SF reveals information about the yield stress of the fluid as predicted by the theory. It appears that by carefully controlling the experimental conditions of the squeeze test one can obtain yield stress values that agree with the rheological measurements within 10%. Additionally, the validity of the lubricational theory was tested; not only for the determination of the yield stress but throughout the flow as well.     

Rheology modification of montmorillonite dispersions by colloidal silica

We have studied the effect of additions of both anionic and cationic spherical silica colloids of different sizes on the rheology of dispersions of a well-characterised montmorillonite clay, SWy-2. The systems have been studied above and below the critical hydrodynamic overlap concentration, c*, of the clay. For dispersions at c < c* on replacement of ～10 % w/w of the clay content by silica, it was found that whereas a cationic silica additive transformed a liquid-like, non-gelling montmorillonite dispersion into a substantial gel, anionic silica destroyed any nascent structure in the fluids, reducing the effective viscosity and virtually eliminating the rheological hysteresis characteristic of structured fluids. On the other hand, in the regime of c > c*, replacement of ～10 % w/w of the clay content by silica leads to enhancements of all the rheological parameters characteristic of a gelling system, for the addition of both anionic and cationic silica. A simple tentative microstructural model for this complex behaviour is presented. This work, alongside our previous studies, confirms significant rheological modification by the addition of small quantities of nanoparticles as a general phenomenon of clay-colloid systems. It further suggests that viscosity enhancement and control of the rates of sol-gel transitions for product applications can be achieved using relatively low-cost, commercially available materials, such as silica nanoparticles and natural clays of different mineralogy.     

Use of ram extruder as a combined rheo-tribometer to study the behaviour of high yield stress fluids at low strain rate

We propose in this work to provide an efficient and simple extruder device able to evaluate the rheological and tribological behaviour of high yield stress fluids, such as extrudible materials. An extruder able to measure simultaneously both the friction force acting on the extruder wall and the total extrusion force is developed. Based on previous studies, an efficient and accurate method of data analysis is then proposed and applied in order to obtain both a flow curve and a tribological law. Experimental tests are performed on soft modelling clay, kaolin paste and cement-based materials. Results are compared to conventional rheometry measurements. This comparison helps to evaluate the accuracy of the proposed experimental device and procedure.     

Studies in the rheology of clay-water systems

Summary The rheological properties of sodium Attapulgite sols and gels have been studied as a function of clay concentration, etc.; and the effects of peptising and coagulating electrolytes on these properties have been investigated. These systems show similar properties to those of mixed calcium-sodium Montmorillonite (and Hectorite) clays of equivalent exchangeable sodium content. The intrinsic viscosity and viscosities of the heterocoagulated sols are low, despite the high anisometry of the individual Attapulgite laths (or needles), since disaggregation is incomplete: these sols set to gels of moderate strength. Heterocoagulation is eliminated (as in other clays) by adsorption of peptisors (polyphosphates, etc.) onto the positively charged edges of the dispersed clay particles.Coagulation of the sols dispersed in sodium carbonate solution by electrolytes leads to the formation of highly dissymmetric structures with high viscosity and yield stress. The peptised sols are more stable to electrolyte; and when coagulated, the particle-particle aggregation and structure formation is very much reduced.The previous paper (4) in Soil Science (1957) will henceforth be considered as Part 4 of this series.     

Influence of relative humidity on fracture toughness of rock: Implications for subcritical crack growth

Information relating to the fracture toughness of geomaterials is critical to our understanding of tensile fracturing, and in particular in geological and rock engineering projects that are subjected to elevated moisture levels. In this study, we conducted a comprehensive set of fracture toughness tests on a suite of key rock types in air under different relative humidities and at constant temperature in order to investigate the influence of relative humidity on fracture toughness. Three sandstones and two igneous rocks were chosen for this purpose. We show that the value of fracture toughness decreases with increasing relative humidity. In addition, we find that the decrease in fracture toughness was more significant when the expansive clay such as smectite was included in rock. Since smectite is prone to expanding in the presence of water, the strength and thus crack growth resistance decrease when relative humidity is high. Therefore, we interpret the decreasing fracture toughness upon the degradation of expansive clays with increasing water content. It was also shown that the decrease of the fracture toughness with increasing humidity is less significant than the concomitant decrease in the measured value of the subcritical stress intensity factor. This was likely as a result of stress corrosion having little influence on the fracture toughness. We conclude that crack growth in rock is affected by humidity, and that clay content is an important contributing factor to changes in fracture toughness and subcritical stress intensity factor.     

Rheology for deposition control of polymer-amended oil sands tailings

Mineral slurries may be dewatered to the point that they manifest non-Newtonian behavior. Many such slurries exhibit both thixotropic and hysteric behavior in their rheology, which has important implications for managing their deposition in tailings impoundments. This paper characterizes the rheology of a mineral slurry with relatively high clay content, which is treated with a high molecular weight anionic polymer to induce flocculation. The rheology exhibits viscosity bifurcation behavior similar to pure clay, including shear history-dependent apparent yield stress values. Rheometry results are presented including stress growth, controlled stress tests, and oscillatory rheometry, all using a vane fixture. The measured rheology is modeled using a previously published viscosity bifurcation model that accounts for hysteresis in the apparent yield stress. The rheology results are used semi-quantitatively to explain deposition rate-dependent behavior seen in flume tests. The geometry of tailings in flume tests with relatively slow deposition is affected by the presence of deposited tailings that have come to rest sufficiently to manifest the yield stress of initially fully structured material, rather than the lower value yield stress that characterizes when the material first comes to a stop. This full recovery of the yield stress seems to be particularly important to managing surface deposition, as zones of tailings that have stopped moving substantially steepen the slope of deposits near the deposition point.     

Micromechanical analysis of kinematic hardening in natural clay

This paper presents a micromechanical analysis of the macroscopic behaviour of natural clay. A microstructural stress–strain model for clayey material has been developed which considers clay as a collection of clusters. The deformation of a representative volume of the material is generated by mobilizing and compressing all the clusters along their contact planes. Numerical simulations of multistage drained triaxial stress paths on Otaniemi clay have been performed and compared the numerical results to the experimental ones in order to validate the modelling approach. Then, the numerical results obtained at the microscopic level were analysed in order to explain the induced anisotropy observed in the clay behaviour at the macroscopic level. The evolution of the state variables at each contact plane during loading can explain the changes in shape and position in the stress space of the yield surface at the macroscopic level, as well as the rotation of the axes of anisotropy of the material.     

Rheological properties of suspensions of the green microalga Chlorella vulgaris at various volume fractions

A systematic study of the rheological properties of solutions of non-motile microalgae (Chlorella vulgaris CCAP 211-19) in a wide range of volume fractions is presented. As the volume fraction is gradually increased, several rheological regimes are observed. At low volume fractions (but yet beyond the Einstein diluted limit), the suspensions display a Newtonian rheological behaviour and the volume fraction dependence of the viscosity can be well described by the Quemada model (Quemada, Eur Phys J Appl Phys 1:119–127, 1997). For intermediate values of the volume fraction, a shear thinning behaviour is observed and the volume fraction dependence of the viscosity can be described by the Simha model (Simha, J Appl Phys 23:1020–1024, 1952). For the largest values of the volume fraction investigated, an apparent yield stress behaviour is observed. Increasing and decreasing stress ramps within this range of volume fractions indicate a thixotropic behaviour as well. The rheological behaviour observed within the high concentration regime bears similarities with the measurements performed by Heymann and Aksel (Phys Rev E 75:021505, 2007) on polymethyl methacrylate suspensions: irreversible flow behaviour (upon increasing/decreasing stresses) and dependence of the flow curve on the characteristic time of forcing (the averaging time per stress values). All these findings indicate a behaviour of the microalgae suspensions similar to that of suspensions of rigid particles. A deeper insight into the physical mechanisms underlying the shear thinning and the apparent yield stress regime is obtained by an in situ analysis of the microscopic flow of the suspension under shear. The shear thinning regime is associated to the formation of cell aggregates (flocs). Based on the Voronoi analysis of the correlation between the cell distribution and cell sizes, we suggest that the repulsive electrostatic interactions are responsible for this microscale organisation. The apparent yield stress regime originates in the formation of large-scale cell aggregates which behave as rigid plugs leading to a maximally random jammed state.     

Sample size effect on the dynamic torsional behaviour of the 2A12 aluminium alloy

In order to investigate the effect of sample size on the dynamic torsional behaviour of the 2A12 aluminium alloy. In this paper, torsional split Hopkinson bar tests are conducted on this alloy with different sample dimensions. It is found that with the decreasing gauge length and thickness, the tested yield strength increases. However, the sample inner/outer diameter has little effect on the dynamic torsional behaviour.Based on the finite element method, the stress states in the alloy with different sample sizes are analysed.Due to the effect of stress concentration zone(SCZ), the shorter sample has a higher yield stress.Furthermore, the stress distributes more uniformly in the thinner sample, which leads to the higher tested yield stress. According to the experimental and simulation analysis, some suggestions on choosing the sample size are given as well.     

Magnetorheology in an aging, yield stress matrix fluid

Field-induced static and dynamic yield stresses are explored for magnetorheological (MR) suspensions in an aging, yield stress matrix fluid composed of an aqueous dispersion of Laponite? clay. Using a custom-built magnetorheometry fixture, the MR response is studied for magnetic field strengths up to 1?T and magnetic particle concentrations up to 30?v%. The yield stress of the matrix fluid, which serves to inhibit sedimentation of dispersed carbonyl iron magnetic microparticles, is found to have a negligible effect on the field-induced static yield stress for sufficient applied fields, and good agreement is observed between field-induced static and dynamic yield stresses for all but the lowest field strengths and particle concentrations. These results, which generally imply a dominance of inter-particle dipolar interactions over the matrix fluid yield stress, are analyzed by considering a dimensionless magnetic yield parameter that quantifies the balance of stresses on particles. By characterizing the applied magnetic field in terms of the average particle magnetization, a rheological master curve is generated for the field-induced static yield stress that indicates a concentration–magnetization superposition. The results presented herein will provide guidance to formulators of MR fluids and designers of MR devices who require a field-induced static yield stress and a dispersion that is essentially indefinitely stable to sedimentation.     

K0超固结结构性黏土的本构模型

K₀固结黏土在自然界广泛分布, 其通常同时具有超固结性与天然结构性, 而K₀超固结性又与K₀正常固结性质存在很大差异. 为了有效的描述K₀超固结性质, 在结构性模型基础上, 做了如下三点改进, 使得原模型拓展为同时考虑K₀超固结特性与天然结构性影响的本构模型. (1)引入相对应力比来描述屈服面, 并引入初始各向异性转轴参量ξ来表达初始各向异性对屈服面在p-q空间的位置影响. (2)基于给定的屈服面方程, 推导得到变相应力比参量, 并将变相应力比引入到统一硬化参数中, 利用统一硬化参数可以有效描述初始各向异性固结黏土在剪切加载下的剪缩与剪胀, 应变硬化及软化现象. (3)引入反映结构性胶结强度性质的胶结参量p_e, 并给出p_e随塑性偏应变的衰减演化方程, 利用胶结参量可描述结构性黏土的剪胀特性. 预测与试验结果对比表明, 所提的K₀超固结结构性模型可有效描述K₀超固结黏土的刚度提高效应, 黏土的包辛格效应, 结构性黏土胶结强度的损失现象以及结构性黏土的应变软化现象. 证明了所提模型的适用性以及合理性.      

Bentonite slurries—zeta potential,yield stress,adsorbed additive and time-dependent behaviour

Bentonite clay is a vital ingredient of drilling mud. The time-dependent and high shear thinning yield stress behaviour of drilling mud is essential for maintaining wellbore stability and to remove cuttings, cool and clean the drill bit of debris. As-prepared 3, 5 and 7 wt.% bentonite clay slurries displayed time-dependent behaviour where the yield stress (measured after quick stirring) decreased with time of rest. An equilibrium value is reached after 24 h. Despite the low solids concentration, the yield stress is already relatively high and is displayed at all pH level. The yield stress is maximum at pH 2 and minimum at pH ∼ 7. This yield stress is due to the formation of gel structure by the swelling clay particles. However the addition of phosphate additives such as (PO₃)^19 −, (P₃O₁₀)^5 − and (P₂O₇)^4 − completely dispersed the clay slurries at pH above 6. At pH below 6, yield stress is still present but is 3-folds smaller than that of the pure bentonite slurry. With phosphate additives, the magnitude of the critical zeta potential at the complete dispersion pH is ca 48 mV. However for the pure bentonite, the slurry remained flocculated at zeta potential of >50 mV in magnitude. Interestingly, (P₂O₇)^4 − anions is more effective than the other two phosphate additives in reducing the yield stress at low pH, ∼ 2.0.     

Electro-chemo-mechanical couplings in saturated porous media: elastic–plastic behaviour of heteroionic expansive clays

Chemically active saturated clays containing several cations are considered in a two-phase framework. The solid phase contains the negatively charged clay particles, absorbed water and ions. The fluid phase, or pore water, contains free water and ions. Electroneutrality is ensured in both phases, which gives rise to electrical fields. Water and ions can transfer between the two phases. In addition, a part of free water diffuses through the porous medium. A global understanding of all phenomena, deformation, transfer, diffusion and electroneutrality, is provided. Emphasis is laid on the electro-chemo-mechanical constitutive equations in an elastic–plastic setting. Elastic chemo-mechanical coupling is introduced through a potential, in such a way that the tangent elastic stiffness is symmetric. Material parameters needed to estimate the coupling are calibrated from specific experiments available in the recent literature. The elastic–plastic behaviour aims at reproducing qualitatively and quantitatively typical experimental phenomena observed on natural clays during chemical and mixed chemo-mechanical loadings, including chemical consolidation and swelling already described in Int. J. Solids Structures (39 (10), 2773–2806) in the simpler context of Na-Montmorillonite clays. Crucially, the successive exposure of a clay to pore solutions with chemical content dominated by a cation already present in the clay or quasi-absent leads to dramatically different volume changes, in agreement with experimental data.     

Quasi-static bubble in a yield stress fluid: elasto-plastic model

The influence of the yield stress of Carbopol® gel dispersions on the behaviour of quasi-static bubbles was investigated. Many fluids, from many different industrial fields, have yield stress behaviour. Most of them contain gas bubbles. To study bubble behaviour in such suspensions, a transparent model fluid (dispersion of Carbopol® in water) was used. The experimental device allowed to quasi-statically increase bubble internal pressure with small pressure step to reach a maximum target internal pressure and the pressure setpoint was inverted to return to the initial pressure. Hysterical behaviour of the bubbles was highlighted as they did not regain their initial shape because of yield stress. We show that the rheological behaviour is related to the internal pressure, bubble geometry and yield stress in quasi-static conditions. A modification of the Laplace law depending on the yield stress of the fluid and bubble sphericity was proposed and validated.     

Rheological studies and optimization of Herschel-Bulkley flow parameters of viscous karaya polymer suspensions using GA and PSO algorithms

Rheological characteristics of gum karaya suspensions which is proposed as a fracturing fluid were investigated with the main objective to determine the yield stress and other rheological parameters using various models. The flow hysteresis confirms the thixotropic behavior of fluid with increased structural breakdown at higher concentration and temperature. An empirical model developed for the studied samples accurately predicts the temperature and polymer concentration sensitivity of the apparent viscosity. The Herschel-Bulkley model showed the best fit to the experimental data; however, the yield stress obtained from some of the samples using nonlinear regression (NL) method reported physically insignificant, negative values. The proposed optimization technique, i.e., “Particle Swarm Optimization” offered the most realistic results with faster convergence over genetic algorithm making it a better choice. The oscillatory study provided more reliable yield stress values and revealed the thermogelation behavior of polymer suspensions making it suitable for high-temperature fracturing application.     

考虑温度影响的软黏土流变固结模型及解析解

基于四元件流变模型,考虑温度影响,建立了宁波软黏土流变固结模型,并利用拉普拉斯变换得到瞬时加载条件下的考虑温度 影响的饱和软黏土流变固结解析解;利用不同温度下软黏土的流变固结试验结果,拟合获得了四元件流变模型参数,进行编程得到理论值, 并与试验值进行对比. 结果表明：该模型能较好反映宁波软黏土流变固结特性,计算结果与试验结果较为吻合.温度的升高导致渗透系数增大,在相同的时间内孔压消散 越快, 固结 越快.