Cranfield University

Appendix
Rel. Density
3
2,5
2
1,5
1
0,5
0
y = -0,2432Ln(x) + 2,6726
R 2 =0,8698
y =-0,123Ln(x) +2,4221
R 2 =1
10 100 1000
Pressure (kPa)
Figure 7: Virgin compression line for sandy loam soils ■ from O’Sullivan et al.
(1998) and ♦ from the soil bin studies based on the average density increases
from Ansorge and Godwin (2007)
To validate the heuristically chosen � = 5 the 900/10.5/1.9 experiment was evaluated for a
smaller � of 4, representing a denser soil. P for � = 4 was calculated using the dependencies
of � 2 and � 3 on � 1 from Table 6. The slope (-0.2432) of the resulting VCL is identical to
the slope for � =5. The intercept of 2.6929 is larger than the one which was derived from � =5
(2.6726). The overall effect of changing � is evaluated in Figure 9 whereby the prediction of
the 900/10.5/1.9 for � = 4 is compared to both the measured data and the predictions for
� =5. The smaller � results in a larger deviation of the rut depth at the surface and only a
close agreement between measured and predicted data below 400 mm compared to the
measured soil displacement. The smaller rut depth for � = 4 is followed by a larger decrease
in soil displacement within the top 250 mm resulting in a smaller soil displacement over the
entire depth of the soil profile. Transferring the observations from Figure 9 for the
900/10.5/1.9 back to the other treatments, shown in Figure 8, results in a general reduction in
predicted soil displacement which consequently reduces the overall close agreement shown
Figure 10. Therefore the selection of � =5 is justified as this shows overall a closer
agreement.
Fitting linear regression functions through the top 500 mm of the measured and predicted data
of Figure 8 estimating the average increase in soil density as described by Ansorge and
Godwin (2007a) and plotting the measured against predicted average density increase results
in close agreement as shown in Figure 10 to within +/- 2 % errors. The data is spread
uniformly around the line of slope 1 and does not exhibit a general offset confirming the
Ph.D. Thesis Dirk Ansorge (2007)
207