Sample size effects on the critical state shear strength of granular materials with varied gradation and the role of column-like local structures

Assessing the shear strength of coarse granular soils is challenging because testing devices in the laboratory often limit the maximum particle size (d_max). Although engineering standards define representative elementary volumes (REVs) using the aspect ratio α = X/d_max, where X is the characteristic sample size, they often disagree on the minimum α, as the effects of sample scale on shear strength are still not well understood. This paper presents a discrete-element study on the combined effect of specimen size and grading on the critical state shear strength of granular materials. The study covers a wide range of aspect ratios and demonstrates that the macroscopic response is stable for α ≥ 15 – which is significantly higher than the standard requirement of α ≥ 10 for simple shear tests. The granular microstructure is also strongly affected by α and the formation of column-like structures of grains carrying strong contact forces, reaching sample size independent conditions only for α ≥ 20. Such column-like structures are shown to be primarily composed of the largest classes of grains, supporting the fact that grading has no effect on the critical state shear strength and d_max correctly serves to scale a granular sample to the size of the testing device.