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.