Formulation of a unified constitutive model for clays and sands

This paper presents a new generalized effective stress model, referred to as MIT-S1, which is capable of predicting the rate independent, effective stress–strain–strength behaviour of uncemented soils over a wide range of confining pressures and densities. Freshly deposited sand specimens compressed from different initial formation densities approach a unique condition at high stress levels, referred to as the limiting compression curve (LCC), which is linear in a double logarithmic void ratio, e, mean effective stress space, p′. The model describes irrecoverable, plastic strains which develop throughout first loading using a simple four-parameter elasto-plastic model. The shear stiffness and strength properties of sands in the LCC regime can be normalized by the effective confining pressure and hence can be unified qualitatively, with the well-known behaviour of clays that are normally consolidated from a slurry condition along the virgin consolidation line (VCL). At lower confining pressures, the model characterizes the effects of formation density and fabric on the shear behaviour of sands through a number of key features: (a) void ratio is treated as a separate state variable in the incrementally linearized elasto-plastic formulation: (b) kinematic hardening describing the evolution of anisotropic stress–strain properties: (c) an aperture hardening function controls dilation as a function of ‘formation density’; and (d) the use of a single lemniscate-shaped yield surface with non-associated flow. These features enable the model to describe characteristic transitions from dilative to contractive shear response of sands as the confining pressure increases. This paper summarizes the procedures used to select input parameters for clays and sands, while a companion paper compares model predictions with measured data to illustrate the model capability for describing the shear behaviour of clays and sands. Copyright © 1999 John Wiley & Sons, Ltd.     

Modified Structured Cam Clay: A generalised critical state model for destructured,naturally structured and artificially structured clays

This paper presents a generalised constitutive model for destructured, naturally structured and artificially structured clays that extends the Structured Cam Clay (SCC) model. This model is designated as “Modified Structured Cam Clay (MSCC) model”. The influence of structure and destructuring on the mechanical behaviour of clay can be explained by the change in the modified effective stress, which is the sum of the current mean effective stress and the additional mean effective stress due to structure (structure strength). The presence of structure increases the modified mean effective stress and yield surface, enhancing the cohesion, peak strength and stiffness. The destructuring begins when the stress state is on the virgin yield surface. After the failure (peak strength) state, the abrupt destructuring occurs as the soil–cementation structure is crushed; hence the strain softening. The soil structure is completely removed at the critical state when the yield surface becomes identical to the destructured surface. The destructuring law is proposed based on this premise. In the MSCC model, the yield function is the same shape as that of the Modified Cam Clay (MCC) model. A plastic potential is introduced so as to account for the influence of structure on the plastic strain direction for both hardening and softening behaviours. The required model parameters are divided into those describing destructured properties and those describing structured properties. All the parameters have physical meaning and can be simply determined from the conventional triaxial tests. Thus, the MSCC model is a useful tool for geotechnical practitioners. The capability of the model is verified by the test results of destructured, natural structured and artificially structured clays.     

Modelling of anisotropic damage in brittle rocks under compression dominated stresses

A new model for describing induced anisotropic damage in brittle rocks is proposed. Although phenomenological, the model is based on physical grounds of micromechanical analysis. Induced damage is represented by a second rank tensor, which is related to the density and orientation of microcracks. Damage evolution is related to the propagation condition of microcracks. The onset of microcrack coalescence leading to softening behaviour is also considered. The effective elastic compliance of the damaged material is obtained from a specific form of Gibbs potential. Irreversible damage‐related strains due to residual opening of microcracks after unloading are also captured. All the model's parameters could be determined from conventional triaxial compression tests. The proposed model is applied to a typical brittle rock. Comparison between test data and numerical simulations shows an overall good agreement. The proposed model is able to describe the main features related to induced microcracks in brittle geomaterials. Copyright © 2002 John Wiley & Sons, Ltd.     

An Orthotropic Cosserat Elasto-Plastic Model for Layered Rocks

Summary Modelling the behaviour of rock masses consisting of a large number of layers is often necessary in mining applications (e.g. coal mining). Such a modelling can be carried out in a discontinuum manner by explicit introduction of joints. When the number of rock layers is large, it is advantageous to devise a continuum-based model in which case the joints are considered to be virtually smeared across the mass. In this study, a fully elasto-plastic equivalent continuum model suitable for describing the behaviour of such layered rock masses is considered. The model is based on the Cosserat continuum theory and incorporates the moment stresses in its formulation. In contrast to the earlier Cosserat models, the possibility of rock layer plasticity is considered. The accuracy of the developed Cosserat model is verified against analytical and experimental results. Received October 15, 2000; accepted July 30, 2001 Published online August 2, 2002     

Modelling of the physical behaviour of clay barriers close to water saturation

The physical properties of bentonite-based buffer materials for nuclear waste repositories have been investigated by a number of different laboratory tests. These tests have yielded a material model that is valid for conditions close to water saturation and is useful for describing: (a) the stress, strain and volume change behaviour; (b) the pore pressure and flow of water; and (c) the thermal and thermomechanical response.

The material model is based on the Drucker-Prager Plasticity model and a Porous Elastic Model. The effective stress concept and Darcy's law are applied and the swelling/consolidation and thermomechanical processes are coupled according to the separate mechanical properties of the pore water, the solids and the clay skeleton. The model can be used by the finite-element program ABAQUS.

The model has been tested in several laboratory and field verification tests. Comparison between measured and calculated behaviour shows that the general behaviour is described properly and several calculations of different scenarios have been made for the Swedish KBS 3 concept. However, certain processes, like the hysteresis effect at consolidation/swelling, the curved stress-strain relation at shearing, and the curved failure envelope, are not modelled in a perfectly accurate way and an improved material model is proposed here. It combines the behaviour of the Cam-clay model on the wet side with the more relevant plastic behaviour of a modified Drucker-Prager model with a curved failure envelope and the possibility to introduce strain softening after failure.

The paper presents some laboratory results that are the basis of the first model. It also shows the application of the model to finite-element calculations of some laboratory tests. Comparisons between the calculations and measured results expose some disadvantages of the model and a concept for an improved model is suggested.     

易破碎粒状材料本构研究

粒状材料被广泛地应用到土木工程的各个领域。大部分粒状材料在外力作用下较容易产生颗粒破碎,颗粒破碎对材料的力学性能有很大的影响。为了更好地描述易破碎粒状材料的力学特性,基于弹塑性力学和临界状态土力学开发了一种能够考虑颗粒破碎效应的本构模型。此本构模型能够考虑在剪应力和压应力作用下引起的颗粒破碎对粒状材料力学性能的影响。为了考虑颗粒破碎的影响,基于对Cambria 砂的高压试验,得出了临界状态线位置与消耗塑性功之间的关系,并称之为“破碎方程”。此本构模型拥有双屈服面,分别考虑剪切和等向压缩产生的塑性变形。通过试验结果与数值计算结果的对比得出,新的本构模型能较好地描述易破碎粒状材料的力学特性     

Constitutive modelling of aggregate interlock in concrete

A model for formed cracks in concrete is presented. The model can be used in isolation for existing cracks or linked with other damage or plasticity models and applied once a crack has fully formed. It can be applied directly to interface finite elements or used to control the behaviour of crack planes in more general constitutive models that are applied to 2D and 3D continuum elements. The focus of the present development is on aggregate interlock and crack closing behaviour, which is examined from available experimental data. A contact function is derived and is used to differentiate between three contact states. These states are named open, where there is no contact, interlock, for which the stresses depend upon the nearest distance to the contact surface and closed, for which the stresses depend upon the relative displacements directly. The model is developed within an elasto‐plastic framework using effective stresses, which are related to the total stresses via a contact proportion function. The relationship between the effective normal and shear yield stresses is found to be parabolic and the yield shear stress to be dependent upon the opening and embedment displacements. The performance of the model is assessed against experimental data from shear‐normal tests and it is concluded that the model is able to represent the key characteristics of the behaviour of formed cracks in concrete. Copyright © 2002 John Wiley & Sons, Ltd.     

New Viscoplastic Model for Design Analysis of Tunnels in Squeezing Conditions

Summary  This paper is intended to describe the SHELVIP (Stress Hardening ELastic VIscous Plastic) model, a new viscoplastic constitutive law which has been developed to incorporate the most important features of behaviour observed in tunnels excavated in severe to very severe squeezing conditions. This model couples the elastoplastic and time-dependent behaviour by using a plastic yield surface, as frequently adopted in tunnel design analysis, and the definition of a state of overstress referred to a viscoplastic yield surface. The model is formulated in all its detailed aspects. The related analytical closed-form solution for representing triaxial creep deformations is developed. Also developed is an incremental numerical solution for describing the triaxial stress–strain behaviour under constant strain rate conditions. The model is shown to fit very satisfactorily the results of creep tests on clay shales and relaxation tests on coal specimens, as recently performed for design analysis of tunnels in squeezing conditions. Correspondence: D. Debernardi, Department of Structural and Geotechnical Engineering, Politecnico di Torino, Torino, Italy     

Application of a Hill-Climbing technique to the formulation of a new cyclic nonlinear elastic constitutive model

In the field of constitutive modelling of soil behaviour, optimisation techniques have been mostly employed as a calibration tool, particularly when several model parameters lack clear physical meaning. In this paper, however, a procedure based on a Hill-Climbing optimisation algorithm is presented as a form of improving the performance of constitutive models. Specifically, a simple cyclic nonlinear elastic model, which is shown to be unable to simulate adequately the damping ratio measured under small and large strain amplitudes, is modified by applying the Hill-Climbing technique to the determination of a new relationship describing the unloading/reloading behaviour of soil under cyclic loading. The performance of the proposed model is assessed by evaluating its parameters based on three distinct sets of empirical damping ratio curves and computing the corresponding error in their simulation. It is shown that the introduction of the new unloading/reloading expression formulated based on the outcome of the optimisation procedure increases substantially the precision of the constitutive model.     

砂土中桩土侧向相互作用的应变楔模型修正

提出了砂土中水平受荷单桩的修正应变楔方法。从3个方面对应变楔模型进行了修正,首先假设三维被动土楔后桩身的水平位移呈非线性变化,从而使得楔形体内的水平应变不再是一常量,而是沿深度变化。其次引入了两个双曲线型的模型分别用以模拟楔形体中土体的水平应力增量-应变关系和桩-土界面处桩侧剪应力-位移关系。然后通过算例验证了修正方法的有效性,模拟结果与实测结果吻合较好。最后分析了各个修正因素对计算结果影响,结果显示,非线性位移假设的引入对原应变楔模型计算的水平承载力偏高有明显地改善,新的水平应力增量-应变关系和桩侧剪应力-位移关系的引入使得应变楔方法更加简便有效。     

Modelling the pre-failure instabilities of sand

A simple incremental model describing the pre-failure behaviour of granular soils is presented. The model describes both the dry/fully drained and undrained response. It takes into account an initial anisotropy of soil and an initial state defined as either contractive or dilative. A physically sound definition of loading/unloading is assumed, which differs from elasto-plastic approaches. The model is based on extensive empirical data and gives predictions conformable with experimental results. It also describes pre-failure instabilities of granular soils, both dry/fully drained and undrained. The Hill’s criterion was used to examine stability. It was shown that this condition can be formulated either in terms of the effective stresses or by the total stresses. In the extreme cases of either dry/fully drained or undrained conditions, these alternative formulations are equivalent. This is not so in the case of partial drainage of pore water and associated volumetric deformations as well as pore pressure changes. The model describes the pre-failure instabilities well, and additionally allows for analytical derivation of the instability line. It was shown that the second order work, appearing in the Hill’s condition, is equivalent to the entropy source.     

Modification of strain wedge method for lateral soil-pile interaction in sandEI北大核心CSCD

A modified strain wedge (SW) method for analyzing the behavior of laterally loaded single piles in sand is proposed. The modified model assumes that the lateral displacements of a pile behind the three-dimensional passive soil wedge are nonlinear, which makes the horizontal soil strain variable with depths instead of a constant value in the original strain wedge model, and also employs two different hyperbolic models, one for describing horizontal stress increment-strain behavior of soil in the wedge, and the other for describing the shear stress-displacement property at the interface between soil and pile shafts. An example is analyzed to demonstrate the effectiveness of the modified method, and a good agreement is obtained. Finally, the effects of modifications on the lateral bearing capacity of pile shafts are discussed. The results show that the problem of overestimating the lateral bearing capacity of piles with strain wedge method can be ameliorated by introducing the assumption of nonlinear lateral displacements of piles. It makes the SW method more convenient and effective in analyzing the behavior of laterally loaded piles by introducing the new relationships of horizontal stress increment-strain and shear stress-displacement.     

Revisiting the thermodynamics of hardening plasticity for unsaturated soils

A thermodynamically consistent extension of the constitutive equations of saturated soils to unsaturated conditions is often worked out through the use of a unique ‘effective’ interstitial pressure, accounting equivalently for the pressures of the saturating fluids acting separately on the internal solid walls of the pore network. The natural candidate for this effective interstitial pressure is the space averaged interstitial pressure. In contrast experimental observations have revealed that, at least, a pair of stress state variables was needed for a suitable framework to describe stress–strain–strength behaviour of unsaturated soils. The thermodynamics analysis presented here shows that the most general approach to the behaviour of unsaturated soils actually requires three stress state variables: the suction, which is required to describe the invasion of the soil by the liquid water phase through the retention curve; two effective stresses, which are required to describe the soil deformation at water saturation held constant. However a simple assumption related to the plastic flow rule leads to the final need of only a Bishop-like effective stress to formulate the stress–strain constitutive equation describing the soil deformation, while the retention properties still involve the suction and possibly the deformation. Commonly accepted models for unsaturated soils, that is the Barcelona Basic Model and any approach based on the use of an effective averaged interstitial pressure, appear as special extreme cases of the thermodynamic formulation proposed here.     

Rheological behaviour effect of non-newtonian fluids on steady and unsteady flow through a porous medium

This paper describes the flow behaviour of certain non-Newtonian fluids through a porous medium. A generalized Bingham rheological model of power-law in the presence of a yield stress has been considered. Several problems of fluid mechanics, which appear currently in oil reservoir engineering, have been investigated and the rheological behaviour effect has been emphasized. The short time solutions have been formulated in terms of a moving boundary problem. The approximate solutions in a closed formwere obtained by means of the integral method. Several dimensionless groups have been found to be relevant in evaluating the rheological effect on the steady and unsteady and unsteady flow behaviour. The deviation from Newtonian flow behaviour has been illustrated using several numerical examples.     

A hypoplastic model for clay and sand

The theory of hypoplasticity was developed initially for non-cohesive soils. However, sand and clay have many common properties; therefore arose the idea to extend the hypoplastic model to clay. The proposed model is able to describe the behaviour of cohesive soils with the incorporation of an appropriate structure tensor into the constitutive equation. This tensor is a stress-like internal parameter, also called back stress. This enables us to describe the behaviour of cohesive soils with the same material parameters for several states of consolidation and also to model barotropy and pycnotropy of sand. Numerical simulations of element tests are performed in order to check the performance of this hypoplastic model. Experimental data obtained with normally and overconsolidated clay and sand specimens with various densities are taken for comparison, and it is shown that the model is capable of describing the material behaviour of clay and sand. The determination of the material constants, the calibration method, is also presented in this paper.     

Towards an understanding of joint roughness

Summary It is argued that the currently available joint models are incapable of accurate predictions of joint shear behaviour without resorting to substantial levels of empiricism. This is because these models fail to adequately quantify joint roughness, or appreciate the importance of scale. A novel approach, which uses fractal geometry to investigate joint roughness, is described. This approach goes beyond describing the symptoms of roughness and seeks to find the cause. In the application of this approach, the concepts of fractal geometry, fractal dimension and self similarity are described and used as a framework to formulate a statistically based and practical model for the characterisation of rock joint roughness. Important relationships between the fractal dimension and the more useful statistical parameters of standard deviation of both asperity angles and asperity heights are derived. These relationships not only provide a useful, working method for quantifying joint roughness, but are also shown to provide a basis for understanding the Barton empirical JRC-JCS model. In addition, the fractal model is able to provide conceptual models for the effects of normal stress on the shear behaviour of joints and the scale-dependence of joints.     

Kinematic hardening of soft clay in simple shear

In a separate paper, the authors have proposed a normalized, non-degrading form of the shear stress–shear strain relationship for undrained, cyclic simple shear of soft clay. This relationship is described in the present paper, and it is seen to include a single fatigue parameter—the mean effective stress. Application of the relationship therefore requires knowledge of the history of the mean effective stress during any loading history. The present paper proposes an effective stress path model which may be used for prediction of this history. The model is developed within the framework of bounding surface kinematic and isotropic hardening plasticity. It incorporates an isotropic hardening bounding surface, and a kinematic hardening yield surface, in which the elastic region vanishes, and so the yield surface reduces to the stress point. The normalized shear stress–shear strain relationship, developed on the basis of Iwan's model, is used to establish the shape of the cap of the bounding surface. A new translation rule is also incorporated in the model, allowing improved prediction of stress path development within the bounding surface during regular or irregular cyclic loading. Use of the proposed model to simulate the behaviour of soft clay in laboratory undrained cyclic simple shear tests shows excellent qualitative agreement, with most of the major features of the actual behaviour being predicted.     

An acoustic emission landslide early warning system for communities in low-income and middle-income countries

Early warning systems for slope instability are needed to alert users of accelerating slope deformation behaviour, enable evacuation of vulnerable people, and conduct timely repair and maintenance of critical infrastructure. Communities exposed to landslide risk in low- and middle-income countries seldom currently instrument and monitor slopes to provide a warning of instability because existing techniques are complex and prohibitively expensive. Research and field trials have demonstrated conclusively that acoustic emission (AE) monitoring can be an effective approach to detect accelerating slope movements and to subsequently communicate warnings to users. The objective of this study was to develop and assess a simple, robust, low-cost AE monitoring system to warn of incipient landslides, which can be widely deployed and operated by communities globally to help protect vulnerable people. This paper describes a novel AE measurement sensor that has been designed and developed with the cost constrained to a few hundred dollars (US). Results are presented from physical model experiments that demonstrate performance of the AE system in measuring accelerating deformation behaviour, with quantifiable relationships between AE and displacement rates. Exceedance of a pre-determined trigger level of AE can be used to communicate an alarm to users in order to alert them of a slope failure. Use of this EWS approach by communities worldwide would reduce the number of fatalities caused by landslides.