Anisotropic stress state and small strain stiffness in granular materials: RC experiments and DEM simulations
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Anisotropic stress state and small strain stiffness in granular materials: RC experiments and DEM simulations Meisam Goudarzy . Vanessa Magnanimo
. Diethard Ko¨nig . Tom Schanz
Received: 21 May 2018 / Accepted: 16 August 2020 / Published online: 7 October 2020 Ó The Author(s) 2020
Abstract The paper combines experimental and numerical analyses to study the relation between small strain stiffness and micro-structure of an idealized granular material under isotropic and anisotropic stress conditions. Results from the resonant column device on glass ballotini show that the relation between the maximum shear modulus and anisotropic stress components strongly depends on the applied stress path. Discrete element simulations (DEM) are performed to investigate the material behaviour along isotropic compression, triaxial compression and constant K0 deformation. The DEM analysis reveals that each stress path is associated with a characteristic evolution of the coordination number, i.e., the average
number of contacts per particle. In turn, the maximum shear modulus is found to be a direct function of the coordination number. In order to include the microstructure interpretation in the analytical description, a modified version of Hardin’s relation is proposed as a function of coordination number, void ratio and mean pressure. Keywords Resonant column Maximum shear modulus Discrete element simulations Coordination number
1 Introduction and state of the art M. Goudarzy D. Ko¨nig T. Schanz Chair of Soil Mechanics, Foundation Engineering and Environmental Geotechnics, Ruhr-Universita¨t Bochum, Bochum, Germany e-mail: [email protected] D. Ko¨nig e-mail: [email protected] V. Magnanimo (&) Multi Scale Mechanics (MSM), Faculty of Engineering Technology, Mesa?, University of Twente, P.O. Box 217, Enschede 7500AE, The Netherlands e-mail: [email protected] V. Magnanimo Construction Management & Engineering (CME), Faculty of Engineering Technology, University of Twente, P.O. Box 217, Enschede 7500AE, The Netherlands
A realistic representation of elasticity, exhibited by soils at very small strains, is essential for a proper description of many geomechanical problems. They include geotechnical applications for which the soil displacements are requested to be small, like in the regions around foundations and excavations in urban areas (for more examples and applications see [3]) or the development of elastic–plastic constitutive models, where the elastic regime needs a proper description, e.g. [7, 23]. Several authors have carried on experimental studies about the influence of material characteristics (e.g. void ratio and grain size distribution) and initial conditions on the small strain properties of geo-materials, e.g. [6, 21, 22, 31, 44, 47, 52].
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Meccanica (2020) 55:1869–1883
The majority of those studies are restricted to isotropic stress conditions. However, the stiffness of geomaterials is affected by the state of stress in the soil. Som
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