2

2

We suggest that the resulting normal reaction of the soil N is axially symmetrical
for the area of contact -a [less than] x [less than] a. The hemispherical area of
contact is determined from the condition, that the pressure on the operating
surface P(x) must be limiting everywhere, including the edge of this
area [9], i.e.

P = A a², (1)

where A = 1/2υ [f₁ " (0) + f₂ " (0)] = the coefficient, depending on the shape
of the compressed body and the deformation properties of the soil,
which is determined by the expression:

υ = 2/πE₀ (1 + M²), (2)

where M = the coefficient of lateral expansion of the soil.

Substituting the value of A in equation [1] according to the compressing
force we will determine the hemisphere area of contact -a:

a = √(2PRυ), (3)

Where R = the radius of the roller.

From Fig. 1 it is clear, that the ratio of the depth of rut h to the width
of area of contact 2a is equal to the ratio of force of resistance to rolling
of the roller Pc to the compressing force P.

[Translator's Note: equation missing in the original.] (4)

Substituting the values of a and P in expression (4) we get the equation
determining the value of parameter υ characterizing the deformation properties
of the soil in the form:

υ = ((Bh²)/(4P²_cR)) (√(G² + Pc²_c)), (5)