Improvement of fine-grained and cohesive soils 143
• The number of equivalent stress cycles N eq and the duration t d of the
design earthquake
• The liquefaction resistance of the soil expressed by the number of
stress cycles N 1  causing liquefaction
• The allowable pore water pressure ratio r g chosen for the design
With the calculated time factor T ad , the relative stone column spacing can
be determined from Figure 4.24 for various earthquake severities.
The selection of an adequate grading of the stone column material for
seismic applications requires special considerations. It is important that the
high permeability of the vibro stone column is maintained during the earthquake by a proper choice of the grading of the backfill material. Saito et al.
(1987) have presented a particle size selection standard for the use of gravel
in vertical drains as a countermeasure for sand liquefaction. The proposed
filter criterion, which was developed for dynamic loading conditions with
less restrictive lower limits for D 15  of the filter material when compared
with Terzaghi’s filter rule is given by Equation 4.46.
20
9
15
15
85
⋅
<
< ⋅
d
D
d
(4.46)
The notations D 15  and d 15  signify that 15% by weight of smaller grain diameters of the filter material and the natural soil, respectively, are passing the
sieve. Vrettos and Savidis (2004) describe an interesting case history of
the successful improvement of liquefiable silty sand by stone columns for
the foundation of an immersed road tunnel in Greece. The marine stone
column installation used gravel with a grain size distribution according to
the Saito criterion for highly permeable, choke-free drains. In total over
130,000 lin.m of stone columns with a diameter of 600 mm and a nominal
length of 15 m were executed from a barge to depths of up to 42 m applying the wet method. In Section 4.7.7, another example is described where
the high permeability of stone columns helped building the foundations of
a power plant in an earthquake-prone environment.
Ground improvement to mitigate the liquefaction potential of cohesionless soils by vibro replacement stone columns constructed using the dry
bottom feed method has become a standard foundation solution in the
United States. This method not only utilizes the compaction effect of the
depth vibrator, but also combines it with the enhanced drainage capacity of the stone columns placed within the less permeable sand material.
Stone backfill used in these instances generally consists of sufficiently hard,
durable, clean, crushed rock, free of vegetable matter and other deleterious
substances. The stone should have a sufficiently high durability index—
over 40 measured by the California Test 229 as specified by the State of
California, Department of Transportation. The gradation of the backfill
suitable for the bottom feed gravel system and designed for an SW sand
would be reflected by 100% passing the 50 mm sieve, 90%–100% passing
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