Study of the Similitude on soil-Machine System (II)

Abstract

For studying the similitude technique of the soilmachine system, the long rectangular blades which the ratio of two side lengths of 1:3 were tested on dry sand and mud in a soil bin. It became evident fron the tests that there were not substantial differences between the actions of cutting or bulldozing by the blades and the results of former test of the horizontal penetration of the cones. And we found that
1) The relation R=A₁H^k1 were obtained between the side length of the blade H and draft R and the mean values of k₁ were 2.21 on sand and 2.12 on mud. The draft force was not affected by the density or hardness of sand in the range of this test conditions and it increased with the cutting depth on sand, but, on the contrary, the depth did not affect on mud and the moisture contents, that is, the hardness had direct effects.
2) The relation of the depth and the draft on sand was represented by R′=A₂z′^k2 and the mean value of k₂ was 1.13.
3) The differences of the actions of the blades to soil due to change of the cutting angle α and β, did not affect to the draft force on mud except the case of the angle α on sand.
4) In addition to draft force R, side length of blade H, the specific weight of soil γ, the penetrating resistance p, the shear resistance τ, and the depth of blade z were included as the variables for the similitude studies of this system by the dimensional analysis, And Pi terms of these variables were ∏₁=R/pz², ∏₂=γz/p, ∏₃=H/z, ∏₄=α, ∏₅=β and the functional relationship of these Pi terms may be expressed as ∏1=f(∏₂, ∏₃, ∏₄, ∏₅)
The both systems including the penetrating resistance p and the shearing resistance τ were considered as the another system and separated individually as p-system and τ-system to find which is the better variable for this system on similitude study.
5) There were the following relations between ∏₁ and the other ∏ terms.
∏₁=A₆∏₂^k6, ∏₁=A₇∏₃^k7, ∏₁=A₈∏₄^k8
And further, it may be found that these individual formulas were able to combine to the product of each Pi terms as
∏₁=A∏₂^k6, ∏₃^k7, ∏₄^k8, ∏₅^k9
Then, if the design conditions were satisfied, the similarity of this system would be valid and the values of ∏₁ would be able to predict from the model tests.
6) But, there are a problem that the control of the soil strengths is very difficult and the design conditions are not satisfied easily, then, the distorted model must be used.
7) When the both model and prototype were tested on the same soil conditions and same depth, we had simpler relation between the distortion factor and prediction factor than on test under the same condition of ∏₃, that is, z/z_m=n_H.
On the test under the same soil and same dapth, ∏₃ was distorted and distortion factor of this term β₂ and the prediction factor δ₂ on ∏₁ terms may be represented as
δ₂=-β₂^-k7=n_H^k7
where n_H was the scale length, k⁷ was the exponent shown in the above. Then, the draft force of protototype R was calculated from
R=n_H^k7R_m
R_m: Draft force on model blade