Experimental evaluation and extension of a simple critical state model for sand

This paper presents an experimental evaluation of a simple critical state model and its extension in modelling the stress-strain behaviour of sand under a wide range of confining pressures and initial void ratios under both drained and undrained loading conditions. The critical state model concerned is known as CASM developed by Yu [1,2] and CASM is a relatively simple model as it only requires seven model constants, five of which are the same as those used in the modified Cam clay model. All these constants have clear physical meanings and can be easily determined from the results of triaxial tests as demonstrated in this paper. A key advantage of CASM over many other existing critical state models lies on its unified nature as it can be used to model the behaviour of both clay and sand. In addition, the paper also shows how CASM can be further extended in order to simulate a particular undrained behaviour of loose sand, which is the reappearance of hardening after the material experiences a peak shear stress followed by a softening response.     

A simple non-associated flow model for sand

 This paper proposes a simple non-associated plasticity model for sand. The yield surface is taken to be a member of a recently derived family of yield loci, requiring the specification of a single parameter in addition to the stress ratio at the peak value of deviatoric stress on the yield surface in deviatoric:mean effective stress space. This simple equation, can easily be fitted to given sand data. The flow rule also has a simple equation, such that the critical state is not at the top of the yield locus in stress space. The equation of the flow rule requires the specification of the critical state dissipation constant, plus one additional parameter. This permits realistic modelling of the undrained behaviour of sand in states looser and denser than critical. The parameter controlling the flow rule can, for convenience, be taken to be equal to the parameter governing the shape of the yield surface. However, since the two parameters are not required to be equal, the flow rule can easily be adjusted to model more accurately the rate of change of direction of the plastic strain increment vector with changing stress ratio around the yield surface. The model resembles more complex models based on the mathematical theory of envelopes, but the equations of the yield loci and flow rules are much simpler. The contribution in this paper is therefore to provide a model similar to those derived based on micro mechanical considerations, but which is more useful to geotechnical engineers, in that the number of parameters is kept to a minimum, the constitutive equations are simple, and the flow rule can easily be controlled. The model is easy to apply in geotechnical analysis, and would be easy to implement in a finite element program. Received: 11 January 2002     

Soil mechanics: breaking ground

In soil mechanics, student's models are classified as simple models that teach us unexplained elements of behaviour; an example is the Cam clay constitutive models of critical state soil mechanics (CSSM). 'Engineer's models' are models that elaborate the theory to fit more behavioural trends; this is usually done by adding fitting parameters to the student's models. Can currently unexplained behavioural trends of soil be explained without adding fitting parameters to CSSM models, by developing alternative student's models based on modern theories?Here I apply an alternative theory to CSSM, called 'breakage mechanics', and develop a simple student's model for sand. Its unique and distinctive feature is the use of an energy balance equation that connects grain size reduction to consumption of energy, which enables us to predict how grain size distribution (gsd) evolves-an unprecedented capability in constitutive modelling. With only four parameters, the model is physically clarifying what CSSM cannot for sand: the dependency of yielding and critical state on the initial gsd and void ratio.     

On the problem of cavity expansion in unsaturated soils

The problem of cavity expansion in unsaturated soils is investigated. A unified constitutive model formulated in a critical state framework using the concepts of effective stress and bounding surface plasticity theory is adopted. Consideration is given to the effects of suction and particle crushing in the definition of the critical state and the evolution of the bounding surface. The model accurately captures stress-strain behaviour for a range of load paths encompassing that experienced by soils during cavity expansion. Specifically, the similarity technique is used to solve the cavity expansion problem in speswhite kaolin and Kurnell sand. Eight governing equations are defined and solved simultaneously as an initial value problem including an equilibrium equation for stresses around the cavity. Cylindrical and spherical cavities are considered, as are constant suction and constant moisture content conditions. Substantial differences in the stress-strain response of saturated and unsaturated soils surrounding expanding cavities are observed. The paper highlights the major influence of suction and the importance of accounting for this when using cavity expansion theory to interpret results of the cone penetration and pressuremeter tests.     

A bounding surface plasticity model for cyclic loading of granular soils

A constitutive model for describing the stress–strain behaviour of granular soils subjected to cyclic loading is presented. The model is formulated using bounding surface theory within a critical state framework. A single set of material parameters is introduced for the complete characterization of the constitutive model. The shape of the bounding surface is based on experimental observations of undrained stress paths for loose samples. A mapping rule which passes through stress reversal points is introduced to depict the stress–strain behaviour during unloading and reloading. The effect of particle crushing is considered through a modified critical state line. Essential features of the model are validated using several experimental data from the literature. Both drained and undrained loading conditions are considered. The characteristic features of behaviour in granular soils subjected to cyclic loading are captured. Copyright © 2005 John Wiley & Sons, Ltd.     

水泥砂浆固化粉质黏土分离式Hopkinson压杆试验与分析

为研究掺砂量（与干土的质量比）对水泥粉质黏土冲击压缩强度及能量吸收特征的影响,采用Φ 50 mm分离式Hopkinson压杆（Split Hopkinson pressure bar,SHPB）试验装置对不同掺砂量的水泥粉质黏土进行了0.4 MPa冲击气压下的冲击压缩试验。结果表明：普通水泥粉质黏土（未掺砂）动态应力-应变曲线大致分为弹性阶段、屈服硬化阶段及破坏阶段,而随着掺砂量的逐渐增加,水泥砂浆固化粉质黏土动态应力-应变曲线中屈服阶段愈加不明显,出现了理想的塑性阶段;水泥砂浆固化粉质黏土的冲击压缩强度随掺砂量的增大而先增大后减小,在掺砂量为10%时达到最大平均动强度9.56 MPa,较普通水泥土强度提高9.79%;水泥砂浆固化粉质黏土的吸收能随冲击压缩强度的增大而增大,两者具有较好的指数关系。     

结构性软黏土的修正剑桥模型

天然软黏土普遍受到土结构性的影响,如何在土体本构模型中反映这一影响显得非常重要。该文从修正剑桥模型出发,引入结构屈服应力参数表征受土结构性影响的天然土初始屈服面的形状;引入各向异性参数描述天然土体初始各向异性引起的屈服面旋转。基于土结构性突变屈服破坏机理,屈服前结构性软黏土呈现弹性的力学性质,屈服后土结构性的影响完全丧失,采用同修正剑桥模型一致的硬化规律和流动法则。根据一致性连续条件,推导增量型的应力-应变关系,建立适用于结构性软黏土的弹塑性本构模型。选取国外已有的天然沉积Bothkennar软黏土,对比典型应力路径下的试验实测结果与模型计算结果,显示了该文模型模拟结构性软黏土受力变形特性的优越性。     

Design of clay/cement mixtures for extruded building products

In this work, ternary mixes of sand, cement and kaolin are studied in order to design extruded building products with reduced environmental impact. Firstly, the amount of water required to reach the extrusion rheological criterion and the immersed mechanical strength are studied. Results lead to a compressive strength prediction tool (derived from Feret model) which provides the compressive strength of a given ternary mix. Then, the dimensional and immersion stabilities of ternary mixes are studied. It shows that for mixes containing more kaolin volume than cement volume, mechanical strength is largely influenced by the saturation state. Finally, collected data show that cement stabilized clay blocks and high content cement substitution concrete can be designed with clay/cement mixes.     

On the investigation of acid and surfactant modification of natural clay for photocatalytic water remediation

In this study, a series of mineral and organic acids are introduced to natural clay modification. Several analytical techniques are employed to identify the physical and chemical changes in clay. The effect of surfactants on these properties is also investigated. The samples are prepared using simple acid treatment without filtration. The alteration in surface morphology is proportional to the acid strength as evident from SEM and XRD analyses. Therefore, the treatment with mineral acid and organic acid/HNO₃ results in the formation of new layers by surface modification as depicted in SEM images, and a higher degree of suppression in characteristic XRD reflections of clay is noticed. However, the treatment with organic acids modifies the existing interlayer spacing of clay, and therefore, the XRD characteristic reflections of clay are less affected. These observations are also supported by FT-IR analysis. The surface area of modified clay is dependent on the acid strength, composition and size of counter-anion of acid. An increase in surface area and porosity is noticed after surfactant modification of HNO₃-treated clay, where the change is more prominent at the concentration higher than their respective critical micelle concentration. Thermal stability is dependent on the chemical composition and surface area of clay materials. A relatively higher absorbance is observed for modified clay materials compared with untreated clay during DRS analysis. The catalytic efficiency of modified clay materials in Eriochrome Black T degradation has been demonstrated.     

New models for yield strength of polymer/clay nanocomposites

In this paper, a new and simple model is presented for tensile yield strength of polymer/clay nanocomposites assuming the plate-like shape of silicate layers. Moreover, the accuracy of Pukanszky model which is initially developed for polymer composites filled with quasi-spherical particles is improved for silicate layered nanocomposites based on the suggested model. Many nanocomposites are provided from valid literature to estimate the accuracy of the proposed models and to calculate “k₁” and “B₁” parameters in the suggested equation and improved Pukanszky model, respectively. Furthermore, the developed models are joined to approximate the critical values of parameters which show the strengthening of polymer nanocomposites by nanoclay platelets. The large efficiency of the proposed approaches is confirmed, when the experimental data are compared with the calculations.     

The drying of clay minerals and mixed clay minerals

In natural plastic clays used on ceramic compositions, the presence of certain minerals is frequently observed in the mineralogical composition. In this study, the drying ability of five different clay minerals was examined. All experiments were conducted under steady-state drying conditions. The sorption isotherm of the samples was determined by measurement of the mass of water absorbed at a fixed temperature versus the relative partial water pressure. The shrinkage of pastes was measured under the same experimental conditions. From the experimental data the heat of water sorption was calculated using a model which comes from the interpretation of a sorption reaction. The specific behaviour of the five clay minerals studied was observed; this can explain the behaviour of common plastic clays during the drying process. In particular, some investigations were conducted on mixed minerals. The results should support the possibility of obtaining a correlation between the heat of water sorption of certain clay raw materials and their mineralogical composition.     

Analytic solution of phreatic surface in the slope of reservoir bank

In most cases, the slope stability of reservoir bank is analyzed on the premise that the location of phreatic surface is obtained. But many designers generalize a line as the phreatic surface through their experience to analyze the stability, which is unsafe in the project. To find a solution to the phreatic surface which is convenient to put into use and in accordance with the practice, the article, based on Boussinesq equation, infers analytic solutions suitable to the water level at different ratio and achieves the expression of analytic solution through fitting curves. The correctness of the expression is also proved by the experiments of sand and sand-clay models and the inaccuracy of empirical generalization is analyzed quantitatively. The calculation results show that the inaccuracy through the method of experiential generalizing is so large that the designers should be awake to it.     

Investigation on the competing effects of clay dispersion and matrix plasticisation for polypropylene/clay nanocomposites. Part II: crystalline structure and thermo-mechanical behaviour

In view of the structure–property relationship, the mechanical property enhancement of polypropylene (PP)/clay nanocomposites can also be associated with the alterations of their crystalline structures and behaviour in addition to the general interpretation of intercalation/exfoliation level and uniform dispersion of more rigid clay platelets with higher aspect ratios in the PP matrix. Wide-angle X-ray diffraction (WAXD) was utilised to evaluate the effects of clay content, maleated PP (MAPP) content (MAPP as the compatibiliser) on PP crystalline structures of nanocomposites. Furthermore, the melting and crystallisation behaviour of PP/clay nanocomposites was also investigated by conducting differential scanning calorimetry (DSC). The thermo-mechanical properties were characterised via dynamic mechanical thermal analysis (DMTA). It is observed that enhancement of mechanical properties are mainly affected by the preferred orientation of PP crystals, the growth of α-PP phase and effective nucleating agent role of additional clay while the excessive amount of MAPP becomes detrimental to these crucial aspects, which is also evidently revealed in DMTA measurements.     

A method to model realistic particle shape and inertia in DEM

A simple and fast original method to create irregular particle shapes for the discrete element method using overlapping spheres is described. The effects of its parameters on the resolution of the particle shape are discussed. Overlapping spheres induce a non-uniform density inside the particle leading to incorrect moments of inertia and therefore rotational behaviour. A simple method to reduce the error in the principal moments of inertia which acts on the individual densities of the spheres is also described. The pertinence of the density correction is illustrated by the case of free falling ballast particles forming a heap on a flat surface. In addition to improve behaviour, the correction reduces also computational time. The model is then used to analyse the interaction between ballast and geogrid by simulating pull-out tests. The pulling force results show that the model apprehends better the ballast geogrid interlocking than models with simple representation of the shape of the particles. It points out the importance of modelling accurately the shape of particles in discrete element simulations.     

Procedure to determine the impact of the surface film resistance on the hygric properties of composite clay/fibre plasters

The experimental determination of dynamic mass transfer properties of porous materials such as eco-efficient clay plasters is greatly influenced by the convective conditions at the surface of the material during the test. The measurement of the intrinsic vapour permeability of highly porous materials has shown to present wide discrepancies when the surface film resistance is not known. Therefore, a proper assessment of the hygric properties of clay plasters requires the determination of such resistance to vapour flow. An adapted experimental procedure was used to determine intrinsic water vapour permeability taking into account the influence of the surface film resistance. The moisture buffering test was used to measure dynamic exchange behaviour. The results gave evidence on the thickness of the active layer in the material and the impact of surface resistance on the exchange behaviour. A 1D mass transfer model was used to verify the validity of corrected vapour permeability by the surface film resistance and discuss its nature and influence on dynamic results.     

Removal of Pb(II) from aqueous solution using modified and unmodified kaolinite clay

Modified kaolinite clay with 25% (w/w) aluminium sulphate and unmodified kaolin were investigated as adsorbents to remove Pb(II) from aqueous solution. The results show that amount of Pb(II) adsorbed onto modified kaolin (20 mg/g) was more than 4.5-fold than that adsorbed onto unmodified kaolin (4.2 mg/g) under the optimized condition. In addition, the linear Langmuir and Freundlich models were used to describe equilibrium isotherm. It is observed that the data from both adsorbents fitted well to the Langmuir isotherm. The kinetic adsorption of modified and unmodified kaolinite clay fitted well to the pseudo-second-order model. Furthermore, both modified and unmodified kaolinite clay were characterized by X-ray diffraction, Fourier transform infrared (FT-IR) and scanning electron microscope (SEM). Finally, both modified and unmodified kaolinite clay were used to remove metal ions from real wastewater, and results show that higher amount of Pb(II) (the concentration reduced from 178 to 27.5 mg/L) and other metal ions were removed by modified kaolinite clay compared with using unmodified adsorbent (the concentration reduced from 178 to 168 mg/L).     

A plasticity model for multiaxial cyclic loading and ratchetting

Summary The nonlinear behavior of metals when subjected to monotonic and cyclic non-proportional loading is modeled using the proposed hardening rule. The model is based on the Chaboche [1], [2] and Voyiadjis and Sivakumar [3], [4] models incorporating the bounding surface concept. The evolution of the backstress is governed by the deviatoric stress rate direction, the plastic strain rate, the backstress, and the proximity of the yield surface from the bounding surface. In order to ensure uniqueness of the solution, nesting of the yield surface with the bounding surface is ensured. The prediction of the model in uniaxial cyclic loading is compared with the experimental results obtained by Chaboche [1], [2]. The behavior of the model in multiaxial stress space is tested by comparing it with the experimental results in axial and torsional loadings performed by Shiratori et al. [5] for different stress trajectories. The amount of hardening of the material is tested for different complex stress paths. The model gives a very satisfactory result under uniaxial, cyclic and biaxial non-proportional loadings. Ratchetting is also illustrated using a non-proportional loading history.     

Simulation of serrated yielding with noise effects included

The phenomenon of repeated yield drops is extensively studied using computer simulation. The basic input is the Cottrell-Bilby model for dislocation drag, used in conjunction with a suitable scenario for work hardening. Stochastic effects associated with dislocation velocity and density are built in via multiplicative noise. Using the above scheme for modelling the plastic response and assuming first that the yielding is homogeneous, the machine equation is solved for successive time steps to obtain complete stress-strain curves, similar to those obtained in laboratory experiments. Real-life patterns are well simulated, including several detailed features observed in diverse experiments. The role of noise in the region of marginal stability is explored. The simulation study is next extended to the case of inhomogeneous yielding where, in addition to the model earlier proposed by Penning, we explore one which takes some account of dislocation flow across the sample. Attention is then drawn to similarities observed in the flow of sand in a sand pile. Finally, some suggestions are made for further work.     

Error behaviour in explicit integration algorithms with automatic substepping

This paper studies the behaviour of the error incurred when numerically integrating the elasto‐plastic mechanical relationships of a constitutive model for soils using an explicit substepping formulation with automatic error control. The correct update of all the variables involved in the numerical integration of the incremental stress–strain relationships is central to the computational performance of the integration scheme, and, although often missed in the literature, all variables (including specific volume) should be explicitly considered in the algorithmic formulation. This is demonstrated in the paper by studying, in the context of the Cam clay formulations for saturated soils, the influence that the updating of the specific volume has on the accuracy of the numerical solution. The fact that the variation of the local error with the size of the integrated strain depends on the order of local accuracy of the numerical method is also used in the paper to propose a simple and powerful strategy to verify the correctness of the implemented mathematical formulation. Copyright © 2016 John Wiley & Sons, Ltd.     

Internal-variable constitutive model for rate-independent plasticity with hardening saturation surface

Summary An elastic-plastic material model with internal variables and thermodynamic potential, not admitting hardening states out of a saturation surface, is presented. The existence of such a saturation surface in the internal variables space — a consequence of the boundedness of the energy that can be stored in the material's internal micro-structure — encompasses, in case of general kinematic/isotropic hardening, a one-parameter family of envelope surfaces in the stress space, which in turn is enveloped by a limit surface. In contrast to a multi-surface model, noad hoc rules are required to avoid the intersection between the yield and bounding/envelope surface. The flow laws of the proposed model are studied in case of associative plasticity with the aid of the maximum intrinsic dissipation theorem. It is shown that the material behaves like a standard one as long as its hardening state either is not saturated, or undergoes a desaturation from a saturated hardening state, whereas, for saturated hardening states not followed by desaturation, it conforms to a combined yielding law in which the static internal variable rates obey a nonlinear hardening rule similar to that of analogous models of the literature. Additionally, the material is shown to behave as a perfectly plastic material for a class of (critical) saturated hardening states for which the stress state is on the limit surface. For nonassociative material models, it is shown that, under a special choice of the plastic and saturation potentials and through a suitable parameter identification, the well-known Chaboche model is reproduced. A few numerical examples are presented to illustrate the associative material response under monotonic and cyclic loadings.Dedicated to Prof. Dr. Dr. h. c. Franz Ziegler on the occasion of his 60th birthday