Resistance of Soils to Sinkage and Translation of Rigid Bodies A Study by Means of Dimensional Analysis 670172
Dimensional analysis is used to develop a general sinkage equation for probes of arbitrary shape, confirmed by a test in cohesionless sand giving a straight line over a range106 Existing equations for plate sinkage are special cases f the general one; but in contrast to the Reece equation the sinkage exponent will have approximately equal values or cohesive and frictional soil sent will have approximately equal values for cohesive and frictional soils.
The general equation promises to facilitate both testing (in that it allows the use of sharp probes) and the application of theory to realistic shapes. It is implicit in the existence of an aspect ratio exponent that resistance to translation cannot, in general, be derived by integration of the work done in sinkage.
A general equation for resistance is developed, and solved for the special cases of cylindrical and toroidal wheels in cohesionless and frictionless soils. The results are, in many cases, in agreement with published experimental data. The theory promises to facilitate both experiment and design, since it allows the scaling of resistance to wheels of different sizes and proportions.