KAREN S. HENRY

dure. A comparison of the maximum vertical stress

The U.S. Army design procedure to stabilize low-

beneath circular and rectangular loads as a function of

depth indicated that the differences were insufficient

volves placing aggregate on geotextiles (U.S. Army

to warrant a change in the design procedure for rect-

and U.S. Air Force 1995). It is based on the assump-

angular load geometries that have length/width ratios

tion that the applied surface load (the wheel load) is in

of 3 or less, and, furthermore, that assuming that the

the shape of a circle (e.g., Henry 1999). The vertical

load is circular is conservative.

stress that reaches the subgrade from the applied wheel

The details of the analysis are presented fully in

load is then estimated on the basis of the assumption

this report. The techniques may be used to examine

that the aggregate is an elastic, homogeneous, isotro-

other load geometries, including those of tracked ve-

pic half-space and, therefore, that the stress distribu-

hicles.

tion can be estimated by using the Boussinesq method

(e.g., Newmark 1942). The stress distribution deter-

mined by the Boussinesq approach is assumed to be

accurate for the prediction of stresses distributed

through compacted crushed rock and through asphalt

The goal of this study was to determine whether

(e.g., Barenberg et al. 1975, Yoder and Witzcak 1975).

the shape of the wheel load at the ground surface sig-

However, it is not clear that a circular area accurately

nificantly influences the maximum vertical stress at

predicts stress for non-circular wheel load shapes. For

depth (i.e., that reaches the subgrade) given that the

example, a common configuration of dual wheels on a

aggregate layer behaves as a linearly elastic material.

single axle has been modeled as a rectangular area (e.g.,

If a significant difference were to be found between

Giroud and Noiray 1981). To quantify the extent to

the vertical stresses at depth applied by uniformly

which the shape of the applied load influences the stress

loaded circles versus rectangles, then appropriate

that reaches the subgrade through the aggregate layer,

changes would be made in design guidance developed

I analyzed the influence of the shape of the wheel load

for vehicles that apply loads that are more accurately

on the maximum vertical stress at depth predicted by

modeled as rectangles than circles.

the Boussinesq method.

I used the Boussinesq equations to estimate maxi-

Since it is the maximum vertical stress (i.e., the

mum vertical stresses for uniformly loaded circles

stress beneath the center of the loaded area) that is used

(Newmark 1942) and rectangles (Newmark 1935). I

in the design procedure, I examined the influence of

assumed unit loads and areas, and considered a large

the shape of the applied load on the maximum vertical

range in length-to-width ratios for rectangular wheel

stress predicted by the Boussinesq approach. If sig-

loads so that the range of wheel load shapes applied

nificant differences in the maximum vertical stresses

by military vehicles was well represented. The longest

below uniformly loaded rectangles and circles were

rectangle that I studied, at *L *= 6*B*, where *L *is the con-

found, then the wheel load shape (i.e., rectangle or

tact length and *B *is the contact width, is too extreme to

circle) should be accounted for in the design proce-

model wheeled vehicles. The range of normalized