calculate the cyclic stress ratio, as follows (Seed and

final critical (*N*1)60 values for the design earthquake of

Idriss, 1971; Seed et al., 1985):

′

linear portions of the curve in G-5, the final critical

= 0.65 max ⋅ o ⋅*r*d

(*N*1)60 values are obtained as:

′

′

′

( *N*1 ) 60*critical *(*M *7.5,*σ*o = 1*tsf *)

′

( *N*1 ) 60*critical *(*M *6.75,*σ*o ) =

where amax is the free field surface peak ground

acceleration, which is equal to 0.25g for this example

′

problem, *σ*o is to total vertical stress at depth z, *σ*o is

(2) The critical (*N*1)60 curve is superimposed on

the effective vertical stress at depth z, and *r*d is a stress

the (*N*1)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 / *σ*o . Having this stress

ratio, Figure G-5 is used to obtain the corresponding

values of critical (*N*1)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.

The procedures presented in Tokimatsu and Seed (1987)

=

for x < 30

are used. The Tokimatsu and Seed correlation for

1 + *bx *+ *dx * 2 + *fx*3 + *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 *K*m equal to 1.13. The (*N*1)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 (*N*1)60 equal to 10 blows/foot with curves in

(*N*1)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 *K*m, 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 / *σ*o causing

liquefaction if values of the effective overburden

*G*eff

0.65 ⋅*a*max ⋅*σ*o ⋅*r*d

=

′

pressure, *σ*o , exceed 1 tsf (96 kPa). Their

*G*max

recommended adjustment factors, Kσ, are shown in

′

Figure G-8 and are a function of *σ*o . Column VII in

Table G-2 shows the *K*σ factors. Column VIII shows

′

and *σ*o equal to 1 tsf (96 kPa). Column IX shows the

G-12

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