Static Sandpiles Research Articles

Analysis of tangential contact boundary value problems using potential functions.

This paper presents an analysis technique of high-order contact potential problems and its application to an elastic settlement analysis of a shallow foundation system subjected to a combined traction boundary condition. Closed-form solutions of potential functions are derived for an elastic half-space subjected to bilinear tangential traction boundary conditions over rectangular surface regions. Using the principle of superposition, the present solutions provide a means to form an approximate and continuous solution of elastic contact problems with higher-order tangential boundary conditions. As an application example, an elastic settlement analysis of a rigid footing founded on a dense granular soil is performed under a tangential traction boundary condition prescribed in an analogy with the stress equilibrium states of static sandpiles. A generalized solution approach to combined normal and tangential traction boundary value problems is discussed in the context of foundation engineering.

Analytic solutions for the stress field in static sandpiles

In the present paper we propose a new class of analytical solutions for the equilibrium problem of a prismatic sand pile under gravity, capturing the effects of the history of the sand pile formation on the stress distribution. The material is modeled as a continuum composed by a cohesionless granular material ruled by Coulomb friction, that is a material governed by the Mohr–Coulomb yield condition. The closure of the balance equations is obtained by considering a special restriction on stress, namely a special form of the stress tensor relative to a special curvilinear, locally non-orthogonal, reference system.This assumption generates a class of closed-form equilibrium solutions, depending on three parameters. By tuning the value of the parameters a family of equilibrium solutions is obtained, reproducing closely some published experimental data, and corresponding to different construction histories, namely, for example, the deposition from a line source and by uniform raining. The repertoire of equilibrated stress fields that we obtain in two special cases contains an approximation of the Incipient Failure Everywhere (IFE) solution and a closed-form description of the arching phenomenon.

Constitutive relations in dense granular flows

We use simulations to investigate constitutive relations in dry granular flow. Our system is comprised of polydisperse sets of spherical grains falling down a vertical chute under the influence of gravity. Three phases or states of granular matter are observed: a free-fall dilute granular gas region at the top of the chute, a granular fluid in the middle and then a glassy region at the bottom. We examine a complete closed set of constitutive relations capable of describing the local stresses, heat flow, and dissipation in the different regions. While the pressure can be reasonably described by hard sphere gas models, the transport coefficients cannot. Transport coefficients such as viscosity and heat conductivity increase with decreasing temperature in the fluid and glassy phases. The glass exhibits signs of a finite yield stress and we show that the static sand pile is a limit of our glassy state.

Granular materials: constitutive equations and strain localization

Strain localization into shear bands is commonly observed in natural soil masses, as well as in human-built embankments, footings, retaining walls and other geotechnical structures. Numerical predictions for the process of shear band formation are critically dependent on the constitutive equations employed. In this paper, the plane strain “double-shearing” constitutive model (e.g., Spencer, A.J.M., 1964. A theory of the kinematics of ideal soils under plane strain conditions. Journal of the Mechanics and Physics of Solids 12, 337–351; Spencer, A.J.M., 1982, Deformation of ideal granular materials. In: Hopkins, H.G., Sewell, M.J. (Eds.), Mechanics of Solids. Pergamon Press, Oxford and New York, pp. 607–652; Mehrabadi, M.M., Cowin, S.C., 1978. Initial planar deformation of dilatant granular materials. Journal of the Mechanics and Physics of Solids 26, 269–284; Nemat-Nasser, S., Mehrabadi, M.M., Iwakuma, T. 1981. On certain macroscopic and microscopic aspects of plastic flow of ductile materials. In: Nemat-Nasser, S. (Ed.), Three-dimensional Constitutive Relations and Ductile Fracture. North-Holland, Amsterdam, pp. 157–172; Anand, L., 1983. Plane deformations of ideal granular materials. Journal of the Mechanics and Physics of Solids 31, 105–122) is generalized to three dimensions including the effects of elastic deformation and pre-peak behavior. The constitutive model is implemented in a finite element program and is used to predict the formation of shear bands in plane strain compression, and plane strain cylindrical cavity expansion. The predictions from the model are shown to be in good quantitative agreement with the recent experiments of Han, C., Drescher, A., (1993. Shear bands in biaxial tests on dry coarse sand. Soils and Foundations 33, 118–132) and Alsiny, H., Vardoulakis, I., Drescher, A., (1992. Deformation localization in cavity inflation experiments on dry sand. Geotechnique 42, 395–410) on a dry sand. The constitutive model is also used to predict the stress state in a static sand pile — a topic which has occupied the attention of many investigators in recent years. In our simulations we model an initially loose sand mass as a cohesionless material with a mobilized internal friction coefficient which evolves from an initial value of zero to a saturation value. The formation of a sand pile is numerically modeled as a two-step process: (i) In the first step a conical sand mass is placed between a flat rigid surface and an axi-symmetric conical mold. Interaction between the sand mass and the rigid base plate is modeled using an interface friction coefficient which has the same value as the saturation value of the internal friction coefficient. The sand mass (which is confined between the base plate and the conical mold) is subjected to gravity loading, and the system is allowed to equilibrate. (ii) In the second step the conical mold is quickly lifted and the sand mass allowed to reach a new equilibrate, but slightly slumped configuration. In the process of slight slumping, there is non-homogeneous plastic deformation of the sand pile. This non-homogeneous plastic deformation, coupled with the evolving internal friction coefficient, naturally gives rise to a static stress state which exhibits the interesting feature that the vertical stress distribution at the base of the sand pile does not have a maximum under the apex of the cone, but shows a local dip there.

Soil Densification Due to Static Sand Pile Installation for Liquefaction Remediation

ABSTRACT Among various soil densification techniques, the sand compaction pile (SCP) has been one of the most frequently used methods to improve loose deposits of sandy soils encountered in Holocene or reclaimed lands. In this method, columns of densely compacted sand are created in the ground by imparting vibration to the sand at the bottom of a pipe which is lifted stepwise while supplying sand from the ground surface. Because of noise and vibration produced during its installation, the SCP is losing its popularity and an alternative technique employing a static driving force is being exploited to install columns of dense sand. To study the degree of soil densification due to such static sand pile installation, multiple series of large-scale hollow cylindrical torsional shear tests were conducted in the laboratory on clean fine sand, simulating stress changes conceived to be occurring in a soil element in the vicinity of the pile being penetrated. To determine the stress changes in the field during the pile penetration, analysis was conducted based on the classical theory of elasticity. The sequence of stress changes thus established was applied to saturated sand specimens prepared in a torsional hollow cylindrical shear test apparatus. This process allows complex stress paths to be reproduced in the specimens, including the rotation of a principal stress direction. In the course of the tests, shear stresses were applied first undrained on loose and medium dense fine sands and induced pore water pressure was dissipated by opening the valve of the drainage system, thereby monitoring the volume decrease of saturated samples. Particular attention was drawn to the influence of the amount of shear strains imposed undrained on the soil specimens on the subsequent drained volume changes. It was found that a volume change of 5 ~ 10% was observed in the test samples, which is considered sufficiently great to bring about substantial densification in the sand. The experimental results of the tests were shown to provide a basis for the assessment of soil densification due to static sand pile penetration. On this basis, a diagram was provided to facilitate the evaluation of the degree of soil densification. In addition, case studies were carried out by taking advantage of soil improvement projects which have recently been implemented at three sites in Japan. These are considered to provide field verification on the effectiveness of soil densification due to static sand pile installation. Finally the degree of in-situ densification as evidenced by increased SPT N-value was interpreted in the framework of the conception established through the laboratory tests.

Incipient failure in sandpile models

Elastoplastic and constitutive equation theories are two approaches based on very different assumptions for creating a continuum theory for the stress distributions in a static sandpile. Both models produce the same surprising prediction that in a two-dimensional granular pile constructed at its angle of repose, the outside wedge will be on the verge of failure. We show how these predictions can be tested experimentally.

Exact calculation of force networks in granular piles

We present calculations of forces for two-dimensional static sand pile models. Using a symbolic calculation software we obtain exact results for several different orientations of the lattice and for different types of supporting surfaces. The model is simple, supposing spherical, identical, rigid particles on a regular triangular lattice, without friction and with unilateral springlike contacts. Special attention is given to the stress tensor and pressure on the base of the pile. We show that orientation of the lattice and the characteristics of the supporting surface have a strong influence on the physical properties of the pile. Our results agree well with numerical simulations done on similar systems and show, in some specific cases, a dip, i.e., a depression under the apex of the pile. We also estimate that the algorithm we have developed can be easily adapted to other configurations and models of granulates and can be used in other physical cases where piecewise linear systems are encountered.

Stress in Static Sand Piles: Role of the Deformation in the Case of Silos and Oedometers

Nous presentons une realisation experimentale de mouvement sans force consistant a appliquer successivement a une goutte de mercure macroscopique deux potentiels localement asymetriques et periodiques, decales dans l'espace. Chaque potentiel est cree par un systeme d'electrodes et la force appliquee a la goutte est d'origine electrocapillaire. Nous etudions la vitesse macroscopique de la goutte en fonction des temps d'adressage de chaque potentiel et mettons en evidence differents regimes de vitesse. Un ajustement des differents temps permet a certaines gouttes de se deplacer a vitesse finie alors que d'autres, ayant des vitesses locales differentes dans chaque potentiel, ont une vitesse macroscopique nulle. Ce systeme joue donc le role d'un filtre. Nous etudions egalement le cas ou les systemes d'electrodes sont adresses de facon stochastique.

Stress in Static Sand Piles: Role of the Deformation in the Case of Silos and Oedometers

En depit de certaines approches, les deformations jouent un role important dans la determination des contraintes dans les milieux granulaires. Nous reexaminons la theorie de Janssen des silos, qui postule la proportionnalite (σ v = k siloσh ) entre contraintes verticale (σ v ) et horizontale (σh), en introduisant les deformations pour determiner k silo . Apres un examen des differentes theories possibles, nous proposons une nouvelle methode de calcul de k silo , qui tient compte de la relation fondamentale de Rowe reliant la dilatance a l'etat de contrainte. Nous comparons cette nouvelle valeur a la loi dite de Jaky (k jaky = 1 - sinφ, ou φ est l'angle de frottement solide) qui est un des meilleurs fits experimentaux.

Comment on “Stress Propagation and Arching in Static Sandpiles” by J.P. Wittmer $\mathit{et~al.}$ About the Scaling Hypothesis of the Stress Field in a Conic Sandpile

This paper is a short comment about the paper propagation and arching in static sandpiles by Wittmer, Cates and Claudin iii. It concern8 the validity of the radial stress field (RSF) scaling assumption used to calculate the stress distribution in a conic granular material and its agreement with different experimental data.

Stress propagation and Arching in Static Sandpiles

We present a new approach to the modelling of stress propagation in static granular media, focussing on the conical sandpile constructed from a point source. We view the medium as consisting of cohesionless hard particles held up by static frictional forces; these are subject to microscopic indeterminacy which corresponds macroscopically to the fact that the equations of stress continuity are incomplete -- no strain variable can be defined. We propose that in general the continuity equations should be closed by means of a constitutive relation (or relations) between different components of the (mesoscopically averaged) stress tensor. The primary constitutive relation relates radial and vertical shear and normal stresses (in two dimensions, this is all one needs). We argue that the constitutive relation(s) should be local, and should encode the construction history of the pile: this history determines the organization of the grains at a mesoscopic scale, and thereby the local relationship between stresses. To the accuracy of published experiments, the pattern of stresses beneath a pile shows a scaling between piles of different heights (RSF scaling) which severely limits the form the constitutive relation can take ...