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 (*N*1)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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