Comparison of Continuum Stresses in Granular Material Computed by Volume Average Approach and Boundary Average Approach Under Static and Quasi-Static Conditions

Abstract

Averaging approaches have been widely used to estimate continuum stress in granular materials to facilitate the assimilation of granular materials’ behavior into a continuum mechanics framework. At present, selection criteria for the appropriate averaging approach are still poorly understood. This paper compares the stresses computed by two popular averaging approaches, i.e., volume average approach (VAA) and boundary average approach (BAA) in order to investigate relative errors between the two approaches under various conditions. The comparisons between VAA and BAA under a static condition were first carried out based on the rigid particle analytical framework proposed by Rothenburg, L. [1980] “Micromechanics of idealized granular systems,” Ph.D. thesis, Carleton University, Ottawa, followed by discrete element modelling (DEM) simulations using PFC3D under a quasi-static condition. The results of theoretical comparison suggested that the relative error in the computed stresses by VAA with an omission of overlap could be grossly estimated by the ratio of overlap to length of contact branch, while the relative error in the computed stresses by VAA with an omission of external contacts could be grossly estimated by the ratio of maximum particle diameter to specimen size. At the ratio of maximum particle diameter to specimen size of 5, which is usually taken as the minimum recommended ratio to minimize boundary effect, the relative error caused by omitting the external contacts was as high as 20%. Numerical comparisons suggested that the relative errors of the two approaches under a quasi-static condition were significantly influenced by the strain energy ratio defined in this study. The VAA was recommended as a preferred computation method over the BAA when the strain energy ratio was considerably lower than unity.