Micromechanical formulation of the mobilized stress ratio under principal stress rotation in granular materials

Homayoun Shaverdi,Mohd R Taha,Farzin Kalantary

doi:10.1051/epjconf/201714015025

Homayoun Shaverdi, Mohd R Taha + Show 1 more

Open Access

https://doi.org/10.1051/epjconf/201714015025

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Abstract

In this paper the mobilized stress ratio is investigated by using the static equilibrium at the micro scale level analysis. The mobilized stress ratio is obtained in the distribution of the contact normal, E (β ), and the inter-particle mobilized friction angle, ϕμ . The second invariant of the fabric tensor, α is used to account for fabric and its evolution. There is a difference between the theoretical rotation of principal stress axes that is obtained by the classical equations of the mechanics of materials and the experimental rotation of principal stress axes. The experimental rotation is related to the anisotropic parameter, α . The noncoincidence between the theoretical and experimental is related to the relative direction of the mobilized plane and the bedding plane. A comparison with experimental tests demonstrates the validity of this formulation.

Highlights

Experimental tests have shown that the gradual rotation of the principal stress axes during the progressive shearing of granular materials cause the gradual rotation of the preferred direction of the contact normal (Oda & Konishi, 1974, Oda, 1975, Arthur et al, 1977, Miura et al, 1986, Yang et al, 2016)
Equation, that required the distribution of the contact normals ( J1, J 2, J3 ) and the internal friction angle ( interparticle friction angle (IP) ), the developed equation can calculate the direction of the major principal stress by using the macro quantities directly
By the methods developed by Budhu (1985) and Ochiai (1975) to calculate the theoretical rotation of the principal stress axes (Eq(9)) we found that there is a difference between the real direction of the major principal stress and the theoretical of it

Summary

Introduction

Experimental tests have shown that the gradual rotation of the principal stress axes during the progressive shearing of granular materials cause the gradual rotation of the preferred direction of the contact normal (Oda & Konishi, 1974, Oda, 1975, Arthur et al, 1977, Miura et al, 1986, Yang et al, 2016). Roscoe et al, (1967) showed that the rotation of the principal stress axes happens during simple shear of sand. The contact normal tends to be coaxial with the principal stress direction during shear, while the principal strain increment tends to be coaxial but at a different rate. Fabric anisotropy has a major effect on the shear strength of granular materials in the presence of the rotation of the principal stress axes (Roscoe et al, 1970, Oda, 1972, Cai et al, 2013, Yang et al, 2016). Oda & Konishi (1974) by considering the static equilibrium at the micro scale analysis proposed the following equation:

Theoretical considerations

Mobilized stress ratio in simple shear test

Verification with the experimental tests

Conclusion