Table 4. Maximum vertical stress at various depths below
applied wheel load of 115 kN and contact pressure of 414
kPa according to Newmark (1942) and trapezoidal stress dis-
tribution used by Giroud and Noiray (1981).*
Stress
Stress
Depth
according to
according
below
trapezoidal
to Boussinesq
Ratio of the
applied
stress
(Newmark)
trapezoidal
stress, z
distribution
method
stress to the
(m)
(kPa/psi)
(kPa/psi)
Boussinesq stress
0.1
275.4/39.9
400.1/58.0
0.69
0.2
198.1/28.7
342.1/49.6
0.58
0.3
151.0/21.9
265.7/38.5
0.57
0.4
120.4/17.5
210.0/30.5
0.60
0.5
99.7/14.5
151.1/21.9
0.66
0.6
85.2/12.4
116.2/16.9
0.73
0.7
74.8/10.8
91.2/13.2
0.82
0.8
67.3/9.8
73.0/10.6
0.92
0.9
61.9/9.0
59.6/8.6
1.04
1.0
57.9/8.4
49.4/7.2
1.17
*The Boussinesq method used to generate results in this report did not add
the pressure due to the weight of the overburden (= γ z) whereas the trapezoi-
dal method used did. The calculations were carried out in this manner to be
consistent with how the original researchers presented them. If the weight of
the overburden were added to the stresses estimated by the Boussinesq
method, the differences in stresses at depths of up to 1 m would be even
greater than those listed in Table 5.
from 30 to 40 kPa (CBR of about 1.5) (e.g., Fannin
through a granular layer to the subgrade follows
and Sigurdsson 1996; Fig. 15). The ratio of the trap-
the same pattern as that given by the Boussinesq
ezoidal stress below a rectangle to the Boussinesq
theory. Yoder and Witzak (1975) also refer to the
stress below a circular plate for these loading con-
use of a Boussinesq distribution of stresses below
ditions ranges from 0.61 for a 0.25-m- (10-in.-) thick
traffic loading for the purposes of pavement de-
aggregate to 0.78 for the 0.5-m- (20-in.-) thick ag-
sign. Indeed, mobility models also incorporate
gregate (Giroud and Noiray 1981, Newmark 1942).
Boussinesq stress distributions.* Although trap-
Thus, until further investigation, use of the guid-
ezoidal stress distribution below rectangular-
ance in TM5-818-8, which incorporates the
shaped loads is commonly used in shallow foun-
Boussinesq stress distribution through the aggre-
dation design (e.g., Perloff 1975), Giroud and
gate, is recommended.
Noiray (1981) did not cite other work that uses
trapezoidal stress distribution to estimate traffic
The aggregate quality significantly influences
the stress distribution through it (Herner 1955),
loading stresses through aggregate.
and this should not be discounted as a potential
The significant difference in estimation of
factor in the observed unconservative design for
stresses at the surface used by the two methods
static loading by the Giroud and Noiray method
warrants further investigation. There is limited
described above. For example, when a 45-kN (10-
evidence suggesting that the Giroud and Noiray
kip) load was applied by an airplane tire at 690
(1981) method is unconservative for static load-
kPa (100 psi), the vertical stress reaching the
ing conditions in both reinforced and unreinforced
subgrade through a 0.6-m- (24-in.-) thick layer of
test sections when the aggregate layers are 0.25 to
sand was about twice that of the stress reaching
0.50 m thick and the subgrade strength ranges
the subgrade through a layer of crushed limestone
(Herner 1955). McMahon and Yoder (1960) dem-
onstrated that, for compacted, crushed limestone
*Personal communication, G.L. Blaisdell, Research Civil
base rock layers ranging in thickness from 0.1 to
Engineer, US Army Cold Regions Research and Engi-
0.3 m (4 to 12 in.) and loaded with circular plates,
neering Laboratory, Hanover, N.H., 1997.
16
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