Influence of Wheel Load Shape on Vertical Stress Reaching
Subgrade through an Aggregate Layer
KAREN S. HENRY
INTRODUCTION
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
bearing-capacity soil with geotextiles for traffic in-
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-
STUDY OBJECTIVES
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 = 6B, 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
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