Influences of Scales and Different Geometrical Shapes of Annuli on Measuring Soil Frictional Stress (I)

Scale effect

Abstract

The method and the conclusions of this investigation were as follows:
1. The soil-annulus system was defined as: |π_J=f_J(π₂, π₃, …, π₈)(j=1, 9, 10)…|π_J′, π₈′| in which π₁=S/ρV², π₁′=F/ρV², π₂=h/b, π₃=b/d, π₄=λ/d, π₅=ρVd/μ, π₆=d/D, π₇=σ/ρV², π₈=c/ρV², π₈′=a/ρV², π₉=z/λ, and π₁₀=J/λ and the nomenculature |π_J′, π₈′| means both π_J′ and π₂′ are exchangeable with π₁ and π₂. And S is soil-shearing stress, F external frictional stress, c cohesion, a adhesion, ρ bulk density of soil, μ coefficient of viscosity of soil, D diameter of soil particle, d mean diameter of annulus, b section width of annulus, h grouser height, λ grouser span, σ normal stress, V frictional speed, Z annulus sinkage, and J horizontal displacement.
2. Under the condition of in situ test, we found that the system was a distorted model in which π₅ and π₆ were distorted by length scale. Therefore, some scale effect was inevitable when the π₅ or π₆ was valid.
3. Then, prediction equations were expressed as: π_JP=δ_J·π_Jm…|π_JP′, δ_J′, π_jm′| in which p expresses prototype, m model, and δ_J prediction factor.
The behaviours of δ_J, were investigated by experiment, utilizing scaled annuli and High-Speed Annular Shear Device KS-2. The device is designed to be able to control shear speed and normal stress, and to which annuli of different sizes are able to be attached.
4. In the soil-shear test at maximum shear failure, no scale effect was observed for the different types of soils from dry sand to soft clay and for the length scale change from unit to about 1.7.
5. The soil shear strain as expressed by π₁₀ at maximum shear failure increased with the increase of the scale. This was most remarkable in dry sand, followed by sandy loam and soft clay in order.
The reason was considered that the system distortion reached maximum for dry sand, because dry sand is a plastic body, whereas strain is a quantity valid for elastic body.
6. In soil-steel (annulus) external friction test, the frictional stress increased remarkably in proportion to the annulus size for dry sand, while the trend became weak for sandy loam, and no scale effect was observed for soft clay.
7. When the system distortion was interpreted as soil particle size becomes smaller relatively, i. e. frictional plane becomes smooth with the increase of annulus size, the test results were coincided qualitatively with existing test result and friction theory which claim that external frictional stress increases with the increase of the smoothness of the frictional plane.