Civil Engineering Reference
In-Depth Information
x
=
x
4
x
=
x
3
x
=
x
2
u
p
u
m
x
=
x
1
m
p
m
y
u
Y
m
k
p
k
Y
k
x
=
0
b/60
3b/80
y
FIGURE 4.9
Typical family of p-y curves for the proposed criteria.
sands. API RP2A (2007) recommends that the p-y curve be calculated using the
information from that study.
The ultimate lateral bearing capacity for sand has been found to vary from a
value at shallow depths determined by
Equation (4.21)
to a value at deep depths
determined by
Equation (4.23)
. At a given depth, the equation giving the small-
est value of p
u
should be used as the ultimate bearing capacity.
p
us
= ð
C
1
H
+
C
2
D
Þγ
H
(4.23)
p
ud
=
C
3
D
γ
H
(4.24)
where p
u
= ultimate resistance (force/unit length) (in kN/m) (s = shallow,
d = deep);
= effective soil weight (in KN/m
3
); H = depth (in m);
=angle
of internal friction of sand (in degrees); C
1
, C
2
, C
3
= coefficients determined
from
Table 4.15
as a function of
γ
ϕ′
ϕ′
; and D = average pile diameter from surface
to depth (in m).
The relationship between lateral soil resistance and deflection (p-y curve) for
sand is nonlinear. If there is no definitive information available, the curve may
be approximated at any specific depth H, according to API RP2A, by the fol-
lowing equations:
kH
Ap
u
y
P
=
Ap
u
tanh
(4.25)
where A is a factor to account for the cyclic or static loading condition, evalu-
ated by A = 0.9 for cyclic loading and by A
≥
0.9 for static loading, so that:
= ½
3
:
−
:
8
ð
H/D
Þ
A
0
0
(4.26)
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