(2003) found that the major principal stress and the octahedral stresses (both measured at 0.15 m depth) increased with increasing number of wheel passes, while the mean normal stress ([[sigma].sub.m]) remained almost the same.

Comparison of measured and simulated mean normal stress

Mean normal stress, cone index and rut depth were measured for eight repeated passes of the tractor for each combination of the experimental factors.

(3) Mean normal stress was higher at 0.15 m depth in dry soil and the stress attenuation with respect to depth was more pronounced for dry soil.

Averaged (eight repeated passes for each treatment) mean normal stress ([[sigma].sub.m]) with standard error bars at (a) 0.15, (b) 0.25 and (c) 0.35 m depths under the tractor rear wheel.

Measured and simulated mean normal stress ([[sigma].sub.m]) for front and rear tyre of the heavy rear axle treatment.

Variations in mean normal stress ([[sigma].sub.m]) as a function of rut depth for all the wheeling treatments.

Pappin [17] observed this problem and alternatively described the permanent strain with ratio of deviator stress amplitude to mean normal stress. Good performances of this model were reported without other verification found in the literatures.

where [q.sub.max] and [p.sub.max] are the maximum deviator stress and maximum mean normal stress and [p.sup.*] is a stress parameter defined by intersection of the failure line and the p-axis.