Soils can rarely be described as ideally elastic or perfectly plastic and yet simple elastic and plastic models form the basis for the most traditional geotechnical engineering calculations. With the advent of cheap powerful computers the possibility of performing analyses based on more realistic models has become widely available. One of the aims of this book is to describe the basic ingredients of a family of simple elastic-plastic models of soil behaviour and to demonstrate how such models can be used in numerical analyses. Such numerical analyses are often regarded as mysterious black boxes but a proper appreciation of their worth requires an understanding of the numerical models on which they are based. Though the models on which this book concentrates are simple, understanding of these will indicate the ways in which more sophisticated models will perform.

Soil Behaviour and Critical State Soil Mechanics

The purpose of this review is to discuss the development and the state of the art in dynamic testing techniques and dynamic mechanical behaviour of rock materials. The review begins by briefly introducing the history of rock dynamics and explaining the significance of studying these issues. Loading techniques commonly used for both intermediate and high strain rate tests and measurement techniques for dynamic stress and deformation are critically assessed in Sects. 2 and 3. In Sect. 4, methods of dynamic testing and estimation to obtain stress–strain curves at high strain rate are summarized, followed by an in-depth description of various dynamic mechanical properties (e.g. uniaxial and triaxial compressive strength, tensile strength, shear strength and fracture toughness) and corresponding fracture behaviour. Some influencing rock structural features (i.e. microstructure, size and shape) and testing conditions (i.e. confining pressure, temperature and water saturation) are considered, ending with some popular semi-empirical rate-dependent equations for the enhancement of dynamic mechanical properties. Section 5 discusses physical mechanisms of strain rate effects. Section 6 describes phenomenological and mechanically based rate-dependent constitutive models established from the knowledge of the stress–strain behaviour and physical mechanisms. Section 7 presents dynamic fracture criteria for quasi-brittle materials. Finally, a brief summary and some aspects of prospective research are presented.

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A Review of Dynamic Experimental Techniques and Mechanical Behaviour of Rock Materials

Dilatancy is often considered a unique function of the stress ratio η = q/p′, in terms of the triaxial stress variables q and p′. With this assumption, the direction of plastic flow is uniquely related to η, irrespective of the material internal state. This obviously contradicts the facts. Consider two specimens of the same sand, one is in a loose state and the other in a dense state. Subjected to a loading from the same η, the loose specimen contracts and the dense one dilates. These two distinctly different responses are associated with a single η but two different values of dilatancy, one positive and the other negative. Treating the dilatancy as a unique function of η has developed into a major obstacle to unified modelling of the response of a cohesionless material over a full range of densities and stress levels (before particle crushing). A theory is presented that treats the dilatancy as a state-dependent quantity within the framework of critical state soil mechanics. Micromechanical analysis is u...

Dilatancy for cohesionless soils

http://www.saetaequina.com/files/1-s2_0-S0950061811006763-main.pdf

A simple review of soil reinforcement by using natural and synthetic fibers

Within the framework of an extended elastoplastic constitutive model for unsaturated soils (loading-collapse (LC) model), an experimental programme was performed in an osmotically controlled suction triaxial apparatus. The laboratory behaviour of a statically compacted silt was studied, and particular attention was given to the volume changes monitored during shear. Isotropic loading tests confirmed the main features of the LC model related to the effect of suction on volume changes, and allowed a direct determination of the LC curve. Constant σ3 and a few constant q shear tests were performed in order to study yielding and plastic flow at various increasing suctions, starting from the as-compacted condition. Several yield criteria were considered, depending on the type of test performed. Some similarities between compacted unsaturated soils and natural soft soils were shown, such as the inclined elliptical form of the yield curve, which results from the anisotropic state of stress prevailing during k0 co...

Yielding and plastic behaviour of an unsaturated compacted silt

A method to evaluate settlements and rotations of rigid shallow foundations on sand under the combined action of inclined and eccentric loads is presented. Experimental results obtained on a model strip foundation are shown first. Next, a mathematical model is formulated which is based on the hypotheses that (a) the foundation and the soil can be considered as a macro-element for which the loadings act as generalized stress variables while the displacements and rotation of the foundation are the corresponding generalized strain variables; and (b) the constitutive law of the macro-element, that is the relationship between generalized stress and strain rates, is rigid-plastic strain-hardening with a non-associated flow rule. Constitutive functions and parameters are determined by means of simple calibration tests. Predictions of the theory are then compared with experimental results in tests where loadings vary in a complex way up to foundation failure. It is shown that experimental evidence is well matched...

Settlements of shallow foundations on sand

An experimental and theoretical investigation on the behaviour of a calcarenite subjected to various axisymmetric loading programmes is reported. The essential feature of the observed behaviour is the occurrence of a destructuration phase, which marks the transition from rock-like to soil-like behaviour. During this phase the state of stress remains constant, while strains increase steadily. Three phases can be distinguished: an initial elastic, a destructuration phase and a hardening or softening phase which ends on an ultimate state locus which is linear in the p'–q plane. The observed behaviour is more and more ductile for increasing confining pressures. In the softening regime the specimen is unstable. It is shown that by means of a mathematical model based on the theory of strain-hardening plasticity it is possible to describe mathematically the overall behaviour of the calcarenite in various types of triaxial compression test. Qualitative and quantitative accuracy is generally satisfactory, especial...

An experimental and theoretical study of the behaviour of a calcarenite in triaxial compression

Although there is a large number of constitutive models for sand available in the literature it is believed that a fresh approach, striking a balance between complexity and theoretical rigour, is desirable.



The approach here has certain conceptual links with the Cam Clay series of elastic–plastic models, but includes the more general starting assumption that the yield function, plastic potential and failure locus should be given quite distinct mathematical expressions. Possible physical bases for the proposed forms are discussed.



Ways in which the parameters required to define the model may be determined are suggested and the use of the model is then demonstrated. Firstly, it is shown that, where a limited set of experimental data is available, the model is flexible enough to be able to match the test results. Secondly, it is shown that, where a wide range of test results has been produced, it is possible to determine the model constitutive parameters from a small number of tests and proceed to make satisfactory predictionsfor other, quite different, types of test.



The model is developed for sand at a single initial density, but the way in which the constitutive parameters might be expected to vary with density is discussed. The model is described for conditions of triaxial compression, and extension to more general stress states will be needed before it can be put to the test of incorporation in, for example, a finite element program.

A constitutive model for sand in triaxial compression

The mechanical behaviour of bonded geomaterials is described by means of an elastoplastic strain-hardening model. The internal variables, taking into account the ‘history’ of the material, depend on the plastic strains experienced and on a conveniently defined scalar measure of damage induced by weathering and/or chemical degradation.



For the sake of simplicity, it is assumed that only internal variables are affected by mechanical and chemical history of the material. Despite this simplifying assumption, it can be shown that many interesting phenomena exhibited by weathered bonded geomaterials can be successfully described. For instance, (i) the transition from brittle to ductile behaviour with increasing pressure of a calcarenite with collapsing internal structure, (ii) the complex behaviour of chalk and other calcareous materials in oedometric tests, (iii) the chemically induced variation of the stress and strain state of such kind of materials, are all phenomena that can be qualitatively reproduced. Several comparisons with experimental data show that the model can capture the observed behaviour also quantitatively. Copyright © 2003 John Wiley & Sons, Ltd.

Roberto Nova

Papers

Settlements of shallow foundations on sand

An experimental and theoretical study of the behaviour of a calcarenite in triaxial compression

A constitutive model for sand in triaxial compression

A constitutive model for bonded geomaterials subject to mechanical and/or chemical degradation

Conceptual bases for a constitutive model for bonded soils and weak rocks