Cranfield University

Ancillary Experiments
Benoit and Gottelund (2005) have continued the work from Earl and Alexandrou (2001)
and gave the following equation for the sinkage depth Z I at which Phase II is initiated:
Z
I
B � � c �
� �
� �1�
�
2 � � i �
Eq. 12
whereby B is equal to the diameter of the plate and at the same time equal to the maximum
extend of soil compression below the plate following the classical calculations of soil
compression below foundations based on Boussinesq (1885), � c is the critical density nec-
essary below the plate to initiate the formation of a cone, and � i is the initial density of the
soil. Whether the transition form and therefore the initiation of a cone development takes
place can be investigated, if the rut depth and the final density � f below the implement are
known and Eq. 12 is rearranged to:
2*
Z
B
I
� c � ( 1�
) *
If c � f
�
i
Eq. 13
� � Phase II will not be reached. An estimation of the situation for the experiments
in the soil bin laboratory I have values for � i = 1.38 Mg/m 3 , Z I = 0.1 m (assuming the rut
depth is the critical depth) and B = 0.7 m results in c
� = 1.78 Mg/m 3 . As c � f
Ph.D. Thesis Dirk Ansorge (2007)
172
� � is satis-
fied because � f is smaller than 1.6 Mg/m 3 no cone formation and thus no sideways
movement has taken place. Consequently the vector diagrams show a clear vertical soil
failure. This shows that the results from the soil bin agree with the theory developed for
plate sinkage tests.
A further justification of the vertical soil failure reported by this work, Ansorge (2005, a),
Trein (1995), and Seig (1985) can be derived from the passive earth pressure theory after
Rankine (1847) and Terzaghi (1943).
The earth pressure at rest theory is used to calculate the horizontal pressure component
� h in the soil which (below the tyre) pushes the soil horizontally against soil outside the