calculate the cyclic stress ratio, as follows (Seed and
final critical (N1)60 values for the design earthquake of
Idriss, 1971; Seed et al., 1985):
′
linear portions of the curve in G-5, the final critical
τa
σ
a
= 0.65 max ⋅ o ⋅rd
CSR =
(N1)60 values are obtained as:
′
′
σo
g σo
′
( N1 ) 60critical (M 7.5,σo = 1tsf )
′
( N1 ) 60critical (M 6.75,σo ) =
where amax is the free field surface peak ground
K m ⋅Kσ
acceleration, which is equal to 0.25g for this example
′
problem, σo is to total vertical stress at depth z, σo is
(2) The critical (N1)60 curve is superimposed on
the effective vertical stress at depth z, and rd is a stress
the (N1)60 data in Figure G-9. Most of the data lie to the
reduction factor with values given by Figure G-7. The
left of the curve, indicating liquefaction is likely to
first five columns of Table G-2 show the calculation of
occur.
′
induced cyclic stress ratio, τ a / σo . Having this stress
ratio, Figure G-5 is used to obtain the corresponding
c.
Settlement
values of critical (N1)60 from the CRR curve for clean
sands (# 5 percent fines). This curve is approximated
The next step is to estimate the settlement of the soils
by the following equation:
below 20 feet (6.1 m) depth and also associated with the
compaction of the soils above 20 feet (6.1 m) depth.
a + cx + ex2 + gx3
The procedures presented in Tokimatsu and Seed (1987)
=
CRR7.5
for x < 30
are used. The Tokimatsu and Seed correlation for
1 + bx + dx 2 + fx3 + hx 4
volumetric strain (percent settlement) of saturated clean
sand for a magnitude 7.5 earthquake is shown in Figure
where:
G-10. The correlation is similar to that for liquefaction
a
=
0.048
shown in Figure G-5. For a magnitude 6.75 earthquake,
b
=
-0.1248
the curves in Figure G-10 are adjusted upward by the
c
=
-0.004721
factor Km equal to 1.13. The (N1)60 data below the
d
=
0.009578
water table average about 10 blows/0.3 m (10
e
=
0.0006136
blows/foot) (Figure G-9). The induced cyclic stress
f
=
-0.0003285
ratio below the water table is in the range of about 0.16
g
=
-0.00001673
to 0.19 (Table G-2). Comparing this stress ratio and a
h
=
0.000003714
value of (N1)60 equal to 10 blows/foot with curves in
(N1)60 cs
x
=
Figure G-10 (after adjusting them upward by a factor of
1.13) indicates a volumetric strain of about 2.5 percent.
However, for this site, the peak ground acceleration of
Thus, for a 30-foot (9.1 m) thickness of liquefied sand,
0.25g is caused by a magnitude 6.75 earthquake,
the estimated settlement is 0.025 x 30 feet (9.1 m) =
whereas the curve in Figure G-5 is for a magnitude 7.5
9 inches (23 cm).
earthquake. Therefore the curve needs to be adjusted to
a magnitude 6.75 condition using the factors in Table F-
(1) Estimates of settlements in the upper 20 feet
2 (Seed and Idriss, 1982; Seed et al., 1983, 1985). The
(6.1 m) of sands above the water table are made using
adjustment factor to the ordinate of the curve is 1.13.
the procedures described in Tokimatsu and Seed (1987).
This factor, denoted Km, is shown in Column VI of
The first step is to calculate the shear strain developed
Table G-2. A further adjustment of the curves has been
in the soils using the relationship:
recommended by Seed and Harder (1990) to account for
′
the possible reduction in values of τ a / σo causing
liquefaction if values of the effective overburden
Geff
0.65 ⋅amax ⋅σo ⋅rd
=
γff
e
′
pressure, σo , exceed 1 tsf (96 kPa). Their
g ⋅Gmax
Gmax
recommended adjustment factors, Kσ, are shown in
′
Figure G-8 and are a function of σo . Column VII in
Table G-2 shows the Kσ factors. Column VIII shows
′
and σo equal to 1 tsf (96 kPa). Column IX shows the
G-12
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