Cranfield University

Appendix
The VCL parameters created with the plate sinkage tests predict the 900/10.5/1.9 tyre closer
to its real data than the best estimation using the triaxial data for the VCL parameters whereby
axial and radial load is applied at the same time as described in Appendix 1.5.2. Still the best
estimation is gained with tyre data itself. This result justifies moreover the approach taken
with the estimation of the VCL parameters only from contact pressure and rut depth when
knowing the DBD profile with depth of the soil.
11.1.7 Sinkage Prediction from Real and Small Scale Plate Sinkage Data
Plate sinkage data of the soil bin was available and utilized to predict plate sinkage
parameters k and n, which were in turn used with the approach from Bekker (1960) to predict
rut depth.
11.1.7.1 Theory of Bekker – Sinkage Equations for Tyres
The general plate sinkage equation according to Bekker (1960) is as follows:
p � k * z
n
Eq. 2
whereby p is the pressure in kPa, z is the sinkage depth in m and n (dimensionless) and k in
kPa are empirical factors describing soil behaviour. k and n are empirically gained when
plotting pressure of a plate [kPa] on the y – axis against sinkage [m] on the x-axis in double
logarithmic scale. K is the intercept at 1 m sinkage and n is the slope of the linear function on
log-log scale. The plate geometry influences k and for higher accuracy k can be derived from:
( / � ) k b k k � c �
Eq. 3
K c and k� are empirical factors describing soil behaviour in relation to the shortest length of
the contact area or the diameter of the plate b in m. c K and k� are gained by plotting k for
different plate sizes on the Y-axis and the corresponding 1/b on the x-Axis. Both axis are on
linear scale. When a linear regression line is fitted, � k is the intercept at 1/b=0 and kc is the
slope of the line which could be negative. Eq. 3 is substituted into Eq. 2 and solved for z:
Ph.D. Thesis Dirk Ansorge (2007)
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