Cranfield University

Experimental Methods
Depth, mm
0
100
200
300
400
500
600
700
Displacement, mm
0 50 100 150 200
Figure 9: Soil displacement vs. depth after a pass of an 800/10.5/2.5b: □
800/10.5/2.5; - - 5% and - 30% increase in density; and▲ LSD
When Eq. 1 is differentiated with respect to depth, the displacement change, i.e. the aver-
age increase in soil density is derived:
�d(
z)
� � �d
�(
z)
� s
�z
Eq. 2
Thus │s│ is a direct measure of the relative increase in soil density caused by vertical soil
movement and will be used to compare the treatments.
The method to determine density increase by measuring soil displacement with the draw-
string transducer is much more accurate than the gravimetrical method as shown by detect-
ing significant differences between individual treatments. The maximum error in measur-
ing the depth of a layer is +/- 0.5 mm which would result in less than 1% error in soil den-
sity increase in the worst case; i.e. if all points over the 500 mm depth range line up in such
a way that the top has a larger displacement of + 0.5 mm than in reality and the bottom has
0.5 mm less than in reality. This is unlikely due to the large amount of measurements and
handling errors do not exist with the drawstring method.
The curvature of the soil displacement graph raised the question whether a linear function
was appropriate. Fitting different regression functions to the soil displacement data justi-
fied the linear regression function approach described earlier for a depth range from 0 –
500 mm depth. Each full regression model function included both a non linear and a linear
Ph.D. Thesis Dirk Ansorge (2007)
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