Strona 2_redak - Instytut Agrofizyki im. Bohdana Dobrzańskiego ...

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and therefore the angle of inclination of the normal directions to the slip plane is
described by the equations presented in figure 3.6c.
Figure 3.7 presents the stress condition realized in the direct shear apparatus.
Point P in the Mohr graph illustrates the values of normal stress σ and maximum
tangential (shear) stress τ measured in a horizontal shear plane. Point P is not
identical with point T – the point of tangency of the Coulomb-Mohr yield criterion
of strength with the Mohr circle [150]. Therefore, the plane in which the Coulomb-
Mohr yield criterion is fulfilled does not coincide with the horizontally enforced
shear plane, but is inclined to it at the angle δ/2. The angle of long granule axis
preferred inclination γ 2 was referred not to the plane in which the Coulomb-Mohr
yield criterion is fulfilled, but to the horizontal shear plane.
a) b)
failure surface
slip surface
horizontal surface P
T
c)
Fig. 3.7. Sample of granular material in direct shear test: a) diagram of Mohr for state of stress in the
sample, b) orientation of preferred direction of long axis of grains against theoretical slip plane γ 2 ,
c) image of deformation of the sample
The results of the measurements are presented in figure 3.8 as graphs of the
relation of the angle of internal friction φ to the angle of slip plane inclination to the
direction of grain long axes or to the normal direction of the normals at contact points.
The closest agreement of the relations φ(γ 1 ) and φ(γ 2 ) was obtained in the case of
rapeseed. In both the tests performed on rapeseed the maximum of the angle of internal
friction, φ = 29 o , occurred at similar values of the angles γ 1 ≈ γ 2 ≈ 35 o . Considering the
fact that the plane of the higher main stress σ 1 is inclined to the slip plane at an angle
α = π/4+φ/2 it is easy to note the agreement of the obtained maximum of the angle of
internal friction with the results obtained by Oda [126-128]. The author found that in
the course of non-dilatational hardening of granular material the normal directions to
the points of contact concentrate around the direction of the major principal stress, and
that the direction gradually rotates with increasing tangential (shear) stress. The main