Environmental Engineering Reference
In-Depth Information
1.0
Measurements
eoretical normal
eoretical log-normal
0.8
Maximum 5% critical
deviation value
0.6
Normal
0.26
0.32
0.4
Log-normal
0.22
0.32
0.2
0.0
0
500
1000
1500
2000
Pile capacity (kN)
Figure 14.1
Observed and theoretical distributions of within-site pile capacity.
particular cumulative percentage near the tail. Therefore, the assumed distribution will lead
to results on the conservative side.
From the definition, the within-site variability is inherent in a particular geological set-
ting and a geotechnical construction procedure at a specific site. The within-site variability
represents the minimum variability for a construction procedure at a site, which cannot be
reduced using load tests.
14.3 uPDatIng PIle CaPaCItY WIth ProoF loaD teStS
14.3.1 Proof load tests that pass
For proof load tests that are not carried out to failure, the pile capacity values are not known
although they are greater than the maximum test loads. Define the variate,
x
, as the ratio
of the measured pile capacity to the predicted pile capacity (called the “bearing capacity
ratio” hereafter). At a particular site,
x
can be assumed to follow a log-normal distribution
(Whitman 1984; Barker et al. 1991) with the mean and standard deviation of
x
being μ and
σ and those of ln(
x
) being η and ξ, where σ or ξ describes the within-site variability of the
pile capacity. Suppose the specified maximum test load corresponds to a value of
x
=
x
T
. For
example, if the maximum test load is twice the design load and an FOS of 2.0 is used, then
the value of
x
T
is 1.0. Using the log-normal probability density function (PDF), the probabil-
ity that the test pile does not fail at the maximum test load (i.e.,
x
>
x
T
) is
∞
∫
‡
2
Ž
1
2
1
2
ln()
x
−
η
‰
‰
‰
‰
px
(
≥
x
)
=
exp
−
d
x
(14.1)
T
ξ
πξ
x
x
T
Noting that
y
= (ln(
x
) − η)/ξ,
Equation 14.1
becomes
∞
∫
1
2
1
2
ln()
x
−
η
ln()
x
T
−
η
=−
=
T
px
(
≥
x
)
=
exp
−
y
2
d
y
1
Φ
ΦΦ−
(14.2)
T
ξ
ξ
π
ln()
x
−
η
T
ξ
Search WWH ::
Custom Search