Granular materials: constitutive equations and strain localization

Strain localization into sheaf bands is commonly observed in natural soil m asses, as well as in human-built embankments, footings, retaining walls and other geotechnical structures. Numerical predictions for the process of sh ear band formation are critically dependent on the constitutive equations e mployed. In this paper, the plane strain "double-shearing" constitutive mod el (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 Soli ds 12, 337-351; Spencer, A.J.M., 1982, Deformation of ideal granular materi als. 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 p lastic flow of ductile materials. In: Nemat-Nasser, S. (Ed.), Three-dimensi onal Constitutive Relations and Ductile Fracture. North-Holland, Amsterdam, pp. 157-172; Anand, L., 1983. Plane deformations of ideal granular materia ls. Journal of the Mechanics and Physics of Solids 31, 105-122) is generali zed to three dimensions including the effects of elastic deformation and pr e-peak behavior. The constitutive model is implemented in a finite element program and is used to predict the formation of sheer bands in plane strain compression, and plane strain cylindrical cavity expansion. The prediction s from the model are shown to be in good quantitative agreement with the re cent experiments of Han, C., Drescher, A., (1993. Shear bands in biaxial te sts on dry coarse sand. Soils and Foundations 33, 118-132) and Alsiny, I-I. , 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 w hich evolves from an initial value of zero to a saturation value. The forma tion of a sand pile is numerically modeled as a two-step process: (i) In th e first step a conical sand mass is placed between a Aat rigid surface and an axi-symmetric conical mold. Interaction between the sand mass and the ri gid base plate is modeled using an interface friction coefficient which has the same value as the saturation value of the internal friction coefficien t. 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 equilib rate. (ii) In the second step the conical mold is quickly lifted and the sa nd mass allowed to reach a new equilibrate, but slightly slumped configurat ion. In the process of slight slumping, there is non-homogeneous plastic de formation of the sand pile. This nonhomogeneous plastic deformation, couple d with the evolving internal friction coefficient, naturally gives rise to a static stress state which exhibits the interesting feature that the verti cal stress distribution at the base of the sand pile does not have a maximu m under the apex of the cone, but shows a local dip there. (C) 2000 Elsevie r Science Ltd. All rights reserved.