Random porosity fields and their influence on the stability of granular media

Abstract

SUMMARYIt is well established that the mechanical behavior of granular media is strongly influenced by the media's microstructure. In this work, the influence of the microstructure is studied by integrating advances in the areas of geostatistics and computational plasticity, by spatially varying the porosity on samples of sand. In particular, geostatistical tools are used to characterize and simulate random porosity fields that are then fed into a nonlinear finite element model. The underlying effective mechanical response of the granular medium is governed by a newly developed elastoplastic model for sands, which readily incorporates spatial variability in the porosity field at the meso-scale. The objective of this study is to assess the influence of heterogeneities in the porosity field on the stability of sand samples. One hundred and fifty isotropic and anisotropic samples of dense sand are failed under plane-strain compression tests using Monte Carlo techniques. Results from parametric studies indicate that the axial strength of a specimen is affected by both the degree and orientation of anisotropy in heterogeneous porosity values with anisotropy orientation having a dominant effect, especially when the bands of high porosity are aligned with the natural orientation of shear banding in the specimen.

Elastoplastic modelling of diffuse instability response of geomaterials

“…Computersimulated 3D images of regular packings of spherical and non-spherical particles [54] suggest that the void ratio distribution follows a Gaussian (normal) distribution. It is noted that other authors [55][56][57] advocate a truncated exponential distribution, but at this juncture, it is not clear how faithfully each type of distribution reproduces the void ratio distribution of actual granular materials. We herein use a Gaussian distribution in which the void ratio is made to spread about a mean value of 0.70 with a standard deviation of 0.025, which corresponds to a hypothetical medium sand as shown in Figure 8.…”

Deformation, fracture, and fragmentation in brittle geologic solids

“…6b. Planes of maximum weakness corresponding to an angle of principle anisotropy of ≈ 30 • from the vertical (loading) direction have been noted elsewhere in granular media and sedimentary rock (Goodman 1989;Andrade et al 2008).…”

Diffuse bifurcations engraving diverse shear bands in granular materials

“…Diffuse mode bifurcation, 3,64 pointwise local material bifurcation, 39,53,65 and their competing mechanism in failure in geomaterials 66 are still on-going research subjects. In previous works, 30,32,[67][68][69] occurrence of material bifurcations during transitional courses of deformations was investigated. In these studies, spatially varying material property § § In these figures and hereafter, we use the logarithmic axial compressive strain a ∶= −log(H∕H 0 ) (compression positive) and the logarithmic volumetric strain v ∶= log(V∕V 0 ) (expansion positive), where H and V denote, respectively, the current height and volume of the specimen after deformation, and H 0 and V 0 the initial ones before deformation.…”