Geoscience Reference
In-Depth Information
where a
max
=
peak horizontal ground surface acceleration; g
=
acceleration of gravity;
σ
v
σ
v
=
total vertical overburden stress;
=
effective vertical overburden stress;
r
d
=
stress reduction factor. The average value of r
d
is calculated as given by Youd
et al. (2001);
4113z
0
.
5
001753z
1
.
5
(
1
.
00
−
0
.
+
0
.
04052z
+
0
.
)
r
d
=
(4.2)
(
1
.
00
−
0
.
4177z
0
.
5
+
0
.
05729z
−
0
.
006205z
1
.
5
+
0
.
00121z
2
)
where z isthedepth below ground surface inmetres.
There have been various studies concerning the definition of stress reduction factor in
the literature (Idriss and Boulanger, 2003; Cetin et al., 2004). In most of these studies,
different formulations were proposed to calculate the variation of cyclic stress ratio that
would be induced by the design earthquake and almost all of them are only dependent
on thedepthinthe soilprofile. Intherecent formulation proposedby Cetin et al.(2004),
the effect of other factors such as peak acceleration on the ground surface, magnitude
of the design earthquake, and soil stiffness at the top 12m in addition to the depth from
thegroundsurfacewereconsideredasfactorscontrollingthevariationofstressreduction
factor or in more general terms variation of maximum shear stresseswithdepth.
The more comprehensive alternative is to calculate average shear stress with depth using
siteresponseanalyses.ThecomparisonofthevariationofCSRcalculatedusingthesim-
plified formulations proposed by Youd et al. (2001) and Cetin et al. (2004) and site
response analyses given in Figure 4.9 indicates significant differences among the three
approaches(AnsalandTonuk,2006).Thedifferencesarenotconsistentanddependvery
much on the properties of the soil stratification, shear wave velocity profiles, and peak
ground accelerations. The observed general trend indicates that the variation of CSR,
calculated by site response analysis is higher compared to CSR calculated using the
simplified stressreduction factor.
The CSR calculated by the procedure suggested by Youd et al. (2001) depends only on
depth of the element and ground water level and incapable to account for the changes
in the soil profile. Depending on the soil stratification and stiffness of the soil layers the
variation of CSR obtained by site response analysis could be considered more reliable.
Thusbasedontheresultsobtainedinthisstudy,theformulationsuggestedbyYoudetal.
(2001) in general yielded values onthe unsafe side.
The approach adopted to perform microzonation maps in terms of liquefaction suscep-
tibility was based on the method summarised by Youd et al. (2001) and Iwasaki et al.
(1982). The safety factors were calculated along the whole 20m depth of the borehole
for all liquefiable soil layers using the available SPT-N blow counts based on (a) CSR
using peak ground accelerations calculated from site response analysis and r
d
procedure
suggested by Youd et al. (2001) and (b) CSR calculated by site response analyses.
The liquefaction potential for each borehole was calculated according to the procedure
proposed by Iwasaki et al. (1982) using the variation of the safety factors with depth.
