D Muir Wood

A kinematic hardening constitutive model for sands : The multiaxial formulation

This paper explores the possibility of using well-accepted concepts—Mohr-Coulomb-like strength criterion, critical state, existence of a small strain elastic region, hyperbolic relationship for representing global plastic stress–strain behaviour, dependence of strength on state parameter and flow rules derived from the Cam-Clay Model—to represent the general multiaxial stress–strain behaviour of granular materials over the full range of void ratios and stress level (neglecting grain crushing). The result is a simple model based on bounding surface and kinematic hardening plasticity, which is based on a single set of constitutive parameters, namely two for the elastic behaviour plus eight for the plastic behaviour, which all have a clear and easily understandable physical meaning. In order to assist the convenience of the numerical implementation, the model is defined in a ‘normalized’ stress space in which the stress–strain behaviour does not undergo any strain softening and so certain potential numerical difficulties are avoided. In the first part the multiaxial formulation of the model is described in detail, using appropriate mixed invariants, which rationally combine stress history and stress. The model simulations are compared with some experimental results for tests on granular soils along stress paths lying outside the triaxial plane over a wide range of densities and mean stresses, using constitutive parameters calibrated using triaxial tests. Furthermore, the study is extended to the analysis of the effects induced by the different shapes of the yield and bounding surfaces, revealing the different role played by the size and the curvature of the bounding surface on the simulated behaviour of completely stress- and partly strain-driven tests. Copyright

Source near-field effects and pulse tests in soil samples

Shear modulus measurement using bender elements in laboratory samples has become very popular. However, the test results are hard to interpret. Simple plane wave test models are too coarse and result in substantial measurement uncertainty: near 100% in G0. A possible refinement of the test model is based on Stokess fundamental solution for an isolated source. Near-field effects appear, and they have been regularly quoted as a major source of uncertainty in tests. There are some criteria in use for avoidance of near-field distortions, but they are signal dependent and not always successful. After some consideration of Stokess fundamental solution the authors propose a new frequency domain signal-independent criterion to avoid near-field effects. Time-domain criteria are also given, but they are shown to be signal dependent. Applying this criterion to some experimental results the authors then also show how near-field induced errors are not responsible for much of the observed signal distortion. Uncertain...

An implicit constitutive algorithm for finite strain Cam-clay elasto-plastic model

This work is directed toward the formulation and analysis of the modified Cam-clay critical state model within the framework of isotropic multiplicative finite strains. A suitable energy function, in which the shear modulus is made to depend on the mean pressure, is chosen allowing the hyperelastic response to be energy conserving. As a result of the use of Eulerian logarithmic stretches as strain measures in conjunction with an exponential approximation of the plastic flow rule, the small strain integration algorithms, and the corresponding consistent tangent operators, automatically extend to the finite strain regime. Numerical simulations are provided to demonstrate the stability and good performance of the proposed formulation. Copyright

Experimental observations of behaviour of heterogeneous soils

Triaxial tests have been performed on mixtures of kaolin clay and a coarse uniform sand (d50∼2 mm). Drained and undrained compression tests have been performed on isotropically normally consolidated and overconsolidated samples. It has been found that the mechanical behaviour of the mixture is dominated by the mechanical behaviour of the clay matrix until the clay content falls below 40 per cent and the volume fraction of the granular constituent reaches about 0.45. Pore pressures in undrained tests are unaffected by the presence of the sand. Volumetric strains in the clay matrix in drained tests are virtually identical to those seen in pure clay. Calculations of mechanical response of mixtures have been made using a theoretical analysis, developed for the behaviour of composites: it is found that this analysis overestimates the effect of the granular material. Numerical analyses using a finite element program lie closer to the experimental observations but still overestimate the influence of the sand.

Anisotropic elasticity and yielding of a natural plastic clay

Abstract Simple elastic-hardening plastic constitutive models for soils can be very powerful for bringing together apparently unrelated observations of soil behavior and for predicting the response of geotechnical structures. The model known as modified Cam clay has been widely used for many years, but when yield loci for undisturbed natural soils are studied, it is found to be deficient in the shape of the yield locus that it assumes. However, the framework of critical state soil mechanics, within which the Cam clay model is constructed, can be used to generate anisotropic elastic-plastic constitutive models for soil which match experimental observations more closely.

Mechanical Behaviour of Mixtures of Kaolin and Coarse Sand

Experimental studies have been performed in order to discover the ways in which the presence of different proportions of coarse sand (particle size ∼2mm) affects the mechanical properties of a clay (kaolin). The behaviour of the mixtures can be understood through the use of appropriate volumetric variables. At one extreme, if the coarse particles do not interact then the response of the mixture may be dependent on volumetric packing of the clay matrix which can be described through the use of clay specific volume and clay volumetric strain which treat the sand as inert space filler. At the other extreme, when the sand particles become sufficiently close to interact, a granular specific volume characterises the potential for interaction between individual sand grains.

The role of models in civil engineering

We do a disservice in engineering education if we fail to convey an appreciation of the limits of applicability of the models that permeate our teaching. A proper understanding of the potential for constitutive modelling of soils can provide engineers with an ability to select an appropriate level of complexity of modelling for the intended application. A hierarchical development of models can aid this selection of appropriate complexity. A classification of models is described and examples of hierarchical development are given. The need for development of models to be integrated with experimental studies is emphasised.