Densification and Hysteresis of Sand under Cyclic Shear

by Vincente Cuellar, Ingeniero de Caminos; Madrid, Spain; formerly, Grad. Research Asst., Northwestern Univ., Evanston, Ill.,
Marshall L. Silver, (A.M.ASCE), Assoc. Prof. of Materials Engrg.; Univ. of Illinois at Chicago Circle, Chicago, Ill.,
Raymond J. Krizek, (M.ASCE), Prof. of Civ. Engrg.; Northwestern Univ., Evanston, Ill.,
Zdeněk P. Bažant, (M.ASCE), Prof. of Civ. Engrg.; Northwestern Univ., Evanston, Ill.,

Serial Information: Journal of the Geotechnical Engineering Division, 1977, Vol. 103, Issue 5, Pg. 399-416

Document Type: Journal Paper


The accumulation of inelastic strain due to the irreversible rearrangement of grain configurations associated with deviatoric strains is characterized by a nondecreasing material variable, termed the rearrangement measure; this variable, in turn, forms the basis of an intrinsic time scale and other related variables termed the densification measure and distortion measure. The shear modulus is identified to be a function of the mean normal stress and the second invariant of the strain deviator. In contrast with empirical methods, the material behavior is described herein by a constitutive law that satisfies all invariance requirements of continuum mechanics; thus, this law should, in principle, be generally applicable, including the cases of nonsinusoidal loadings with varying amplitudes, general multiaxial stress states, and nonproportional stress component histories. In addition, the law automatically exhibits hysteretic damping and is fully continuous, i.e., it contains no inequalities, such as those used in plasticity to distinguish unloading.

Subject Headings: Strain | Hysteresis | Sandy soils | Shear modulus | Inelasticity | Grain (material) | Distortion (structural) | Shear stress

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