Civil Engineering Reference
In-Depth Information
(
)
−
(
)
N
160
1
+
0 004
.
FC
29 53
.
ln
M
⎡
⎤
w
⎢
⎢
⎢
⎢
⎥
⎥
⎥
⎥
(
)
+
()
−
370
.
ln
σ
′
P
0
05
FC
+
16 85
+
2 7
Φ
−
1
P
()
=
va
L
CRR
P
exp
−
.
[1.7]
eq
L
13 32
.
⎣
⎦
CRR
eq
(
P
L
)/
CSR
eq
,
can be evaluated for a selected value of
P
L
, and a liquefaction hazard
curve based on
F
S
(
P
L
) can be developed. The above assessment can be
extended to multiple soil layers near ground surface and thus the thickness
of liquefi ed soil layers can be evaluated, which is useful for pile-foundation
stability analysis. By repeating the above analysis for individual earth-
quakes included in a synthetic catalogue, liquefaction hazard potential at a
site over a certain period can be assessed. Similarly, a liquefaction hazard
curve based on the factor of safety shown in Equation [1.7] can be devel-
oped (see Goda
et al.
, 2011, for other applications). The probabilistic
assessment of
P
L
is an important step towards performance-based geotech-
nical earthquake engineering; such information can be utilised to make
decisions on ground improvement to mitigate the liquefaction-related risk
of structures.
To illustrate an application of PLHA, consider a sand soil layer (with
FC
Therefore, a conventional factor of safety,
F
S
(
P
L
)
=
=
20%) that is 5 m below ground surface. The water table is 2 m below
ground surface. The total vertical stress
σ
v
and vertical effective stress
σ
′
v
are 100 and 70 kPa, respectively. The
in-situ
SPT blow count is
N
=
5 and
V
S12
6.3. This is a typical soil
layer encountered in the Vancouver area of B.C. (City of Richmond). The
site is subjected to an earthquake scenario of
M
w
=
125 m/s; with the correction factors,
N
1,60
=
=
7.04 and
r
jb
=
44.9 km
200 m/s, PGA is calculated
as 0.223
g
(note: this PGA value is greater than that shown in Fig. 1.4
because of the larger site amplifi cation); subsequently,
r
d
(i.e. 16th event in Fig. 1.4). Assuming that
V
S30
=
=
0.746 and
CSR
eq
=
0.994
(from Equation [1.5]). The evaluation procedure is shown in Fig. 1.7a,
noting that the seismic demand due to this event falls outside of the 95%
confi dence line.
To further demonstrate PLHA, a liquefaction hazard curve based on the
factor of safety with
P
L
0.154 (from Equation [1.6]). Finally, for the considered scenario,
P
L
=
0.5 is developed by considering the same sample
soil and seismic activities. In the assessment, PSHA is conducted to con-
struct a synthetic earthquake and ground motion catalogue for soft soil
conditions (
V
S30
=
200 m/s), and for each event, the factor of safety (as in
Equation [1.7]) is calculated. Based on the long list of the factor of safety
values over one million years, samples of the annual maximum factor of
safety are identifi ed and then plotted in Fig. 1.7b as a liquefaction hazard
curve. The curve provides useful information on the non-exceedance of a
specifi c value of the factor of safety. For instance, one may be interested in
=
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