Numéro
J. Phys. I France
Volume 7, Numéro 12, December 1997
Page(s) 1501 - 1512
DOI https://doi.org/10.1051/jp1:1997210
DOI: 10.1051/jp1:1997210
J. Phys. I France 7 (1997) 1501-1512

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

P. Evesque

Laboratoire MSSM URA 850 CNRS, École Centrale de Paris, 92295 Châtenay-Malabry Cedex, France



(Received 6 May 1997, revised 28 July 1997, accepted 8 September 1997)

Abstract
Despite a few recent approaches, which may be viewed as continuation or rediscovery of ancient works, strain plays an improtant role in the mechanics of granular materials. We give an example of the importance of strain in the peculiar case of the Janssen theory of silos. A new method is proposed for calculating the constant $k_{\rm silo}$ which relates horizontal to vertical stresses ( $\sigma_{\rm v}=k_{\rm silo}\sigma_{\rm h}$). This approach uses Rowe's law of dilatancy and the typical stress-strain behaviours of soil under monotonous and cyclic loading. This $k_{\rm silo}$ is compared with the experimental best fit which is known as the Jaky constant, i.e. $k_{\rm Jaky} = 1 -{\rm sin}\varphi$, where $\varphi$ is the friction angle. It is found that $k_{\rm silo}$ lies quite near the experimental one $k_{\rm Jaky} = 1 -{\rm sin}\varphi$.

Résumé
En dépit de certaines approches, les déformations jouent un rôle important dans la détermination des contraintes dans les milieux granulaires. Nous réexaminons la théorie de Janssen des silos, qui postule la proportionnalité ( $\sigma_{\rm v}=k_{\rm silo}\sigma_{\rm h}$) entre contraintes verticale ( $\sigma_{\rm v}$) et horizontale ( $\sigma_{\rm h}$), en introduisant les déformations pour déterminer $k_{\rm silo}$. Après un examen des différentes théories possibles, nous proposons une nouvelle méthode de calcul de $k_{\rm silo}$, qui tient compte de la relation fondamentale de Rowe reliant la dilatance à l'état de contrainte. Nous comparons cette nouvelle valeur à la loi dite de Jaky ( $k_{\rm Jaky} = 1 -{\rm sin}\varphi$, où $\varphi$ est l'angle de frottement solide) qui est un des meilleurs fits expérimentaux.



© Les Editions de Physique 1997

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