116
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
Table 4. Correlations for Sand (Column A = Number in Table x
Row B)
Column A = number in table x row B
B
E
0
E
R
p
*
L
q
c
f
s
N
A
(kPa)
(kPa)
(kPa)
(kPa)
(kPa)
(bpf)
E
0
(kPa)
1
0.125
8
1.15
57.5
383
E
R
(kPa)
8
1
64
6.25
312.5
2174
p
*
L
(kPa)
0.125
0.0156
1
0.11
5.5
47.9
q
c
(kPa)
0.87
0.16
9
1
50
436
f
s
(kPa)
0.0174
0.0032
0.182
0.02
1
9.58
N
(bpf)
0.0026
0.00046
0.021
0.0021
0.104
1
Table 5. Correlations for Clay (Column A = Number in Table x
Row B)
Column A = number in table x row B
B
E
0
E
R
p
*
L
q
c
f
s
s
u
N
A
(kPa)
(kPa)
(kPa)
(kPa)
(kPa) (kPa) (bpf)
E
0
(kPa)
1
0.278
14
2.5
56
100
667
E
R
(kPa)
3.6
1
50
13
260
300
2000
p
*
L
(kPa)
0.071
0.02
1
0.2
4
7.5
50
q
c
(kPa)
0.40
0.077
5
1
20
27
180
f
s
(kPa)
0.079
0.003
8
0.25
0.05
1
1.6
10.7
s
u
(kPa)
0.010
0.003
3
0.133
0.037
0.62
5
1
6.7
N
(bpf)
0.001
5
0.000
5
0.02
0.005
6
0.09
1
0.14
1
8 SHALLOW FOUNDATIONS
8.1 Ultimate bearing capacity
The general bearing capacity equation for a strip footing is:
1 '
2
u
c
p c N BN DN
q
(39)
Where p
u
is the ultimate bearing pressure, c’ the effective stress
cohesion intercept, γ the effective unit weight of the soil, N
c
, N
γ
,
and N
q
bearing capacity factors depending on the friction angle
φ’. The assumptions made to develop this equation include that
the unit weight and the friction angle of the soil are constant.
Therefore the strength profile of the soil is linearly increasing
with depth. For strength profiles which do not increase linearly
with depth, this equation does not work and can severely
overestimate the value of p
u
. However equations of the
following form always take into account the proper soil
strength:
u
p k s D
(40)
Where k is a bearing capacity factor, s is a strength parameter
for the soil, γ is the unit weight of the soil, and D is the depth of
embedment. The parameter s can be the PMT limit pressure p
L
,
the CPT point resistance q
c
, or the SPT blow count N. Table 6
gives the values of k for various soils and various tests in the
case of a horizontal square foundation on horizontal flat ground
under axial vertical load.
Table 6. Bearing capacity factors k for in situ tests
Strength parameter
Clay
Sand
PMT p
L
(kPa)
1.25
1.7
CPT q
c
(kPa)
0.3
0.2
SPT N(bpf)*
60
75
* Ultimate bearing capacity p
u
in kPa.
8.2 Load settlement curve method for footings on sand
The typical approach in the design of shallow foundations is to
calculate the ultimate bearing capacity p
u
, reduce that pressure
to a safe pressure p
safe
by applying a combined load and
resistance factor, use that safe pressure to calculate the
corresponding settlement, compare that settlement to the
allowable settlement, and adjust the footing size until both the
ultimate limit state and the serviceability limit state are satisfied.
In other words the design of shallow foundations defines two
points on the load settlement curve: one for the ultimate load
and one for the service load. It would be more convenient if the
entire load settlement curve could be generated. Then the
engineer could decide where, on that curve, the foundation
should operate. This was the incentive to develop the load
settlement curve method (Briaud, 2007).
Five very large spread footings on sand up to 3m x 3m in
size were loaded up to 12 MN at the Texas A&M University
National Geotechnical Experimentation Site (Fig. 15a).
Inclinometer casings were installed at the edge of the footings
as part of the instrumentation. They were read at various loads
during the test and indicated that the soil was deforming in a
barrel like shape (Fig. 15b). This is the reason why the
pressuremeter curve was thought to be a good candidate to
generate the load settlement curve for the footing. Note that,
during these tests, the inclinometers never showed the type of
wedge failure assumed in the general bearing capacity equation.
It is reasonned that the footings were not pushed to sufficient
penetration to generate this type of failure mechanism.
The transformation required a correspondence principle
between a point on the pressuremeter curve and a point on the
footing load settlement curve (Fig. 16). This correspondence
was established on the basis of two equations: the first one
would satisfy average strain compatibility between the two
loading processes and the second one would transform the PMT
pressure into the footing pressure for corresponding average
strains. These equations are:
0.24
o
s
R
B
R
(41)
/
,
f
L B e
d p
p f f f f
p
(42)
Where s if the footing settlement, B the footing width, ∆R/R
o
the relative increase in cavity radius in the PMT test, p
f
the
average pressure under the footing for a settlement s, f
L/B
, f
e
, f
δ
,
f
β,d
the correction factors to take into account the shape of the
footing, the eccentricity of the load, the inclination of the load,
and the proximity of a slope respectively, Γ a function of s/B,
and p
p
the pressuremeter pressure corresponding to ∆R/R
o
. The
Γ function was originally obtained from the large scale footing
load tests on sand at Texas A&M University (Jeanjean, 1995,
Briaud, 2007) and then supplemented with other load tests. This
led to the data shown on Fig. 17. Using all the curves (Fig. 17a),
a mean and a design Γ function were obtained (Fig. 17b). The
design Γ function curve is the mean Γ function curve minus one
standard deviation.
The f correction factors have been determined through a
series of numerical simulations previously calibrated against the
large scale loading tests (Hossain, 1996, Briaud, 2007). Their
expressions are as follows
