Extensive data of the strength and dilatancy of 17 sands in axisymmetric or plane strain at different densities and confining pressures are collated. The critical state angle of shearing resistance of soil which is shearing at constant volume is principally a function of mineralogy and can readily be determined experimentally within a margin of about 1°, being roughly 33° for quartz and 40° for feldspar. The extra angle of shearing of ‘dense’ soil is correlated to its rate of dilation and thence to its relative density and mean effective stress, combined in a new relative dilatancy index. The data of o′max – o′crit in triaxial or plane strain are separately fitted within a typical margin of about 2°, though the streneth of certain sands is underpredicted in the 1000–10000 kN/m2 range owing to the continued dilation of their crush-resistant grains. The practical consequences of these new correlations are assessed, with regard to both laboratory and field testing procedures. L'auteur analyse de nombreuses d...

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The strength and dilatancy of sands

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

Within a granular material stress is transmitted by forces exerted at points of mutual contact between particles. When the particles are close together and deformation of the assembly is slow, contacts are sustained for long times, and these forces consist of normal reactions and the associated tangential forces due to friction. When the particles are widely spaced and deformation is rapid, on the other hand, contacts are brief and may be regarded as collisions, during which momentum is transferred. While constitutive relations are available which model both these situations, in many cases the average contact times lie between the two extremes. The purpose of the present work is to propose constitutive relations and boundary conditions for this intermediate case and to solve the corresponding equations of motion for plane shear of a cohesionless granular material between infinite horizontal plates. It is shown that, in general, not all the material between the plates participates in shearing, and the solutions for the shearing material are coupled to a yield condition for the non-shearing material to give a complete solution of the problem.

Frictional–collisional constitutive relations for granular materials, with application to plane shearing

The dilatancy and strength of an assembly of individual particles in contact when subjected to a deviatoric stress system is found to depend on the angle of friction $\phi\_\mu$ between the particle surfaces, on the geometrical angle of packing, $\alpha$, and on the degree of energy loss during remoulding. The Mohr-Coulomb criterion of failure which is strictly applicable to a continuum is shown not to have general application to a discontinuous assembly of particles. A theoretical and experimental study of ideal assemblies of rods and uniform spheres establishes expressions for the relation between the rate of dilatancy and the maximum stress ratio for any ideal packing. The solution is extended to the case of a random assembly of irregular particles by investigating the conditions under which the mass dilates such that the rate of internal work absorbed in frictional heat is a minimum. Experiments on random masses of steel, glass, and quartz in which all the physical properties are measured independently show that the minimum energy criterion is closely obeyed by highly dilatant dense over-consolidated and reloaded assemblies throughout deformation to failure. An additional rate of energy has to be supplied to account for losses due to rearranging of loose packings, when the value of $\phi$ to satisfy the theory increases to $\phi\_f$ by an amount dependent on the degree of remoulding. The external stresses applied to an assembly are to be integrated over the $\alpha$-plane defined with reference to figure 14(a) as a plane of repetition of pattern over which the particles interlock, and the resulting forces are to be in equilibrium for sliding on particle interfaces at (45-$\frac{1}{2}\phi_f$) to the direction of the major principal stress. For the special case of no volume change these two planes are identical and the solution agrees then with that based on the Mohr-Coulomb theory. The well-known slip plane in drained discontinuous assemblies is proved to be the result of failure and nothing whatsoever to do with the peak strength. The findings are discussed in the light of previous contributions to the subject.

The stress-dilatancy relation for static equilibrium of an assembly of particles in contact

The size and shape of soil particles reflect the formation history of the grains. In turn, the macroscale behavior of the soil mass results from particle level interactions which are affected by particle shape. Sphericity, roundness, and smoothness characterize different scales associated with particle shape. New experimental data and results from published studies are gathered into two databases to explore the effects of particle shape on packing density and on the small-to-large strain mechanical properties of sandy soils. In agreement with previous studies, these data confirm that increased angularity or eccentricity produces an increase in emax and emin. Furthermore, the data show that increasing particle irregularity causes a decrease in stiffness yet heightened sensitivity to the state of stress; an increase in compressibility under zero-lateral strain loading; an increase in the critical state friction angle cs; and an increase in the intercept of the critical state line there is a weak effect on the slope . Therefore, particle shape emerges as a significant soil index property that needs to be properly characterized and documented, particularly in clean sands and gravels. The systematic assessment of particle shape will lead to a better understanding of sand behavior.

Particle Shape Effects on Packing Density, Stiffness, and Strength: Natural and Crushed Sands

Synopsis Hvorslev's equation for the shear strength of clay is shown to define a surface in a space of three variables σ′, e and τ. The progressive yielding of a sample defines a loading path in this space, and the paths taken by samples in differing tests can be correlated if a boundary energy correction is applied. The final portions of all paths then lie in a unique surface, and the paths end at a unique critical voids ratio line. At the critical voids ratio state unlimited deformation can take place while σ′, e and τ remain constant. The two concepts of the existence of such a surface and such a critical voids ratio line are verified by an analysis of results of triaxial tests on a clay. Similar tests on silt and sand also confirm the concepts, although some inaccuracy is inherent in these tests. Finally results of tests on granular media in a simple shear apparatus are presented which confirm closely the applicability of both concepts to the yielding of granular media. On montre que l'equation de Hvo...

On The Yielding of Soils

The Paper is concerned with the use of a self-boring pressuremeter to obtain in situ measurements of the properties of sands. A brief description of the instrument and of its method of operation is given. A review of the interpretation of pressuremeter tests in sand is presented and a new interpretation is described in which allowance is made for the volume change that occurs in sand when it is sheared. It is assumed that the stress–dilatancy theory is valid, and that sand fails with a constant ratio of principal stresses. The analysis allows a value for the angle of internal friction φ′ and a value for the angle of dilatation ν to be determined. Experimental results of tests in sand at the Wash and in the hydraulic fill at the Kernick dam are presented; the resulting values of φ′ are compared with those deduced from cone penetration tests and triaxial tests. Values of shear modulus G and in situ horizontal stress σ′h are also measured and reported. L‘etude a pour l'objet l'utilisation du pressiometre aut...

Pressuremeter tests in sands

A series of tests is reported in which a self-boring pressuremeter has been expanded in a large sample of sand, approximately 1 m high by 1 m in diameter, contained in a triaxial test chamber. The pressuremeter has been either cast into the sample during sample preparation, or drilled into the prepared sample. The method of Hughes et al. (1977) is used to obtain values of the angle of internal friction o′ and the angle of dilation ν and these values are compared with those obtained for the same sand in the simple shear apparatus. The theoretical limit pressure for the expansion of a cylindrical cavity in a finite body of sand is calculated, and the difference between the observed and calculated values of limit pressure is attributed to end effects. The effects of disturbance during drilling are examined by comparing a ‘drilled in’ test with ‘cast in’ tests. L'Article se rapporte a une serie d'essais dans lesquels un pressiometre auto-foreur a ete dilate dans un grand ehantillon de sable d'environ 1 m de h...

Laboratory studies of the pressuremeter test in sand

An extension of the analysis of undrained pressuremeter tests, which allows the complete undrained shear stress-shear strain curve to be derived directly from the observed relation between the applied pressure and the radial expansion of the membrane of the pressuremeter, is presented. It takes account of volume change, thus facilitating pressuremeter tests in permeable soils such as sands, silts and silty clays. The likely consequences of applying the new analysis are assessed. /TRRL/

C. P. Wroth

Papers

On The Yielding of Soils

Pressuremeter tests in sands

Laboratory studies of the pressuremeter test in sand

Analysis of the pressuremeter test allowing for volume change

British experience with the self-boring pressuremeter