in which γf is the effective average shear strain
ef
induced in the soil at a certain depth by the design
earthquake ground shaking, Geff is the shear modulus at
this strain level, and Gmax is the maximum shear
modulus at a very low strain. This calculation is made
for three soil layers in the upper 20 feet (6.1 m) in Table
G-3. Then, using Figure G-11, γf is obtained for the
ef
respective values of effective overburden pressure.
From Figure G-12, the volumetric strains or percent
settlements are obtained for the effective shear strain in
each layer using an average (N1)60 value equal to 10
blows/0.3 m (10 blows/foot) in the upper 20 feet
(6.1 m). These volumetric strains are for magnitude 7.5
and should be reduced for the shorter duration of
shaking for magnitude 6.75 using Table G-4. Finally,
the correlations in Figure G-12 are based on
unidirectional shaking, and research by Pyke, et al.
(1975) indicates that the volumetric strains due to
multidirectional shaking are about twice those for
unidirectional shaking. Therefore, the volumetric
strains are doubled. The sum of the estimated
settlements in the upper 20 feet (6.1 m) is only 0.3
inches (0.7 cm), which is additive to the 9 inches (23
cm) of settlement due to liquefaction of the underlying
sands, leading to a total estimated settlement of about
92 inches (24 cm) beneath the building. (Note that the
settlement estimates for the sand above the water table
are sensitive to the level of acceleration. For example,
the calculated settlements in the upper 20 feet (6.1 m)
would increase from only 0.3 inches (0.7 cm) to
approximately 1.6 inches (4 cm) if the peak ground
acceleration increased from 0.25g to 0.50g, yet the
settlements associated with liquefaction 20 feet (6.1 m)
in depth would not change as long as liquefaction
occurs.)
(2) Consideration of the sand variability from
boring to boring as well as varying thicknesses of the
sand due to presence of clay lenses across the site would
lead to estimates of differential settlements between
footings. If these would lead to unacceptable structural
distress, then alternative mitigation measures (described
in paragraph F-5) would include: (1) densifying the
soils; (2) grouting the soils; (3) installing permeable
drainage columns; (4) installing a permanent dewatering
system to lower the ground water table to the base of the
liquefiable layer (note that the effects of this method in
causing consolidation of shallow clay lenses and deeper
clay strata would have to be evaluated); (5) using pile or
pier foundations to extend below the liquefiable layer;
and (6) stiffening the foundation system by tying
isolated footings together with well-reinforced grade
beams or mats.
G-16
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