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

Shape Effect

Abstract

Influences of different geometrical shapes of annuli on measuring soil frictional stress were investigated:
1. The soil-annulus system was defined using the dimensionless Pi terms as: π₁ or π₁′=f(π₂, π₃, …, π₈) in which π₁=S/ρV², π₁′=F/ρV², π₂=h/b, π₃=b/d, π₄=λ/d, S is soil-shearing stress, F external frictional stress, ρ bulk density of soil, V frictional speed, h grouser height, b section width of annulus, d mean diameter of annulus, λ grouser span.
2. The component equations relating π₁ and each one of shape elements π_i(i=2, 3, 4) were expressed as: π_1h=f_h(π₂, π₃, π₄, …, π₈) =f_h=(π₂), similarly π_1b=f_b(π₃), π_1b′=f_b′(π₃), and π_1λ=f_λ (π₄) in which term π_i′s are the variables required to hold constant and constitute the establishing conditions of the component equations.
3. Each component equation was determined by the experiments. The test results showed that the influences of each one of shape elements on π₁ were unexpectedly large. Then, it was concluded that the stress concentration on the grousers would be the reason of arising the influence, considering the unusual soil deformation observed remarkably in the tests of certain shapes of annuli, such as the soil compaction in the direction of grouser movement and the flow of a part of the soil adjacent to grousers out from the annulus peripheral. And, in these cases, the term π₁′s obtained were relatively small. Then we concluded that the peak value with the change of shape element expressed relatively right value of the soil shear stress.
4. The new fact that the term π₁′ increases with the increase of the shape element π₃ was revealed theoretically, considering the influence of the frictional speed on the soil sheraing stress. The experimental value coincided well with the theoretical value.
5 A standard annulus which measures right soil-shearing stress was required to establish. Then, the annulus whose shape was determined by each shape element which measured peak π₁ value was recommended as the standard annulus.