Deterministic and statistical size effect during shearing of granular layer within a micro‐polar hypoplasticity

Abstract

SUMMARYThe paper deals with numerical investigations of a deterministic and statistical size effect in granular bodies during quasi-static shearing of an infinite layer under plane strain conditions, free dilatancy and constant pressure. For a simulation of the mechanical behaviour of a cohesionless granular material during a monotonous deformation path, a micro-polar hypoplastic constitutive relation was used which takes into account particle rotations, curvatures, non-symmetric stresses, couple stresses and the mean grain diameter as a characteristic length. The proposed model captures the essential mechanical features of granular bodies in a wide range of densities and pressures with a single set of constants. In the paper, a deterministic and statistical size effect is analysed. The deterministic calculations were carried out with an uniform distribution of the initial void ratio for four different heights of the granular layer: 5, 50, 500 and 2000 mm. To investigate the statistical size effect, the Monte Carlo method was applied. The random distribution of the initial void ratio was assumed to be spatially correlated. Truncated Gaussian random fields were generated in a granular layer using an original conditional rejection method. The sufficient number of samples was determined by analysing the convergence of the outcomes. In order to reduce the number of realizations without losing the accuracy of the calculations, stratified and Latin hypercube methods were applied. A parametric analysis of these methods was also presented. Some general conclusions were formulated.

Non‐coaxiality and stress–dilatancy rule in granular materials: FE investigation within micro‐polar hypoplasticity

“…Moreover, the initial void ratio scattering in the specimen was also limited by the pressure-dependent void ratios e i (upper bound) and e d (lower bound) (Equations (A14) and (A15)). For details of the random field generation, the readers are referred to the papers by Tejchman and Górski [63,78]. In addition, one arbitrary random field withē 0 = 0.62 ( Figure 3 Figure 3.…”

“…The distribution of the max-min gaps was divided into 12 intervals with equal probabilities. From each interval only one realization was chosen and used as the input data to FEM calculations of a statistical size effect [63,78]. Next, two arbitrary random fields with the mean initial void ratiosē 0 = 0.62 ( Figure 3(a)) andē 0 = 0.58 were chosen from 12 random fields [78] for our FE analyses.…”

Finite element study of patterns of shear zones in granular bodies during plane strain compression

“…A further decrease of sample numbers can be obtained using Monte Carlo reduction methods. In the papers by Tejchman and Górski [57,58], two methods: a stratified and a Latin sampling method were considered. It should be pointed up that these methods were not used for the generation of two-dimensional random fields but for their classification.…”

Probabilistic Analysis Of A Space Truss By Means Of A Multidimensional Variable Description

“…However, nonlinear calculations for such a number of initial data are impossible due to lengthy computations. In order to determine the minimal sufficient number of field samples (estimating the results with a prescribed accuracy), convergence analysis of the outcomes was performed (Tejchman and Górski [27]). After each sample calculations, the improved expected values and standard deviations of the outcomes were estimated.…”

“…In the paper the stratified sampling method was applied (see Tejchman and Górski, [27]). The set of 55 random initial displacements were used.…”