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where
(%) is the ground surface inclination and N SPT is the average SPT blow count
within the liquefiable soil layer.
θ
Observethat,althoughtheyrefertothree(atleastseemingly)differentengineeringprob-
lems,Eqs.11.12,11.13and11.14h av eanapparentsimilarity,especiallyifonerecognizes
that the terms
N 0 . 88
a cr ] λ and
appearing in Eqs.11.13 and 11.14 are directly
orindirectlyrelatedtothe(degraded)factorofsafetyagainstanearthquake-inducedfail-
ure, i.e. theterm
[
a max /
[ θ/
SPT ]
2 . 50 ofEq.11.12.
[
1
/
FS deg ]
6. Performance-based design issues
The findings of the two previous sections can be combined with a value of the allow-
able seismic settlement
ρ all and be used for the preliminary analytical evaluation of the
liquefaction performance of strip foundations. For the readers' convenience, Table 11.2
summarizes the equations and the sequence of computations needed for that purpose.
Note that the dependence of excess pore pressures under the footing on the final set-
tlements (e.g. Eq.11.11) makes the solution algorithm non-linear. However, this should
cause minor concern as 3 to 4 iterations are usually sufficient for convergence and the
associated computations aresimple.
In addition, Figures11.22 and 11.23 present charts for quick computations of seismic
settlements
ρ dyn ,normalizedagainstthewidthofthefooting B ,intermsofthefollowing
non-dimensional problem parameters:
B ,
- the thickness of the clay crust H
- the average bearing pressure q
B ,
- the undrained shear strengthof the clay crust C u H ,and
- the intensity of seismicmotion and the extent of liquefaction expressed as
/
a max T 2 Z liq ·
N
ρ o
B =
0
.
016
·
(11.15)
B
The friction angle of the sand
is also a problem parameter. Nevertheless, for the antic-
ipated range of values for liquefiable sands (e.g.
ϕ
38 o ) its effect is relatively
minor, and consequently the charts were drawn for an average value
32 o
ϕ o
=
35 o .Notein
additionthat,duetopracticaldrawingdifficulties,onlytwodistinctvaluesoftheseismic
intensity parameter are considered in the charts,
ϕ o
=
01 and 0.06. For common
strip foundations, the lower value corresponds to weak seismic motions and the larger to
strong ones. For instance, when B
ρ o /
B
=
0
.
=
3
.
0m,
-
ρ o /
B
=
0
.
01 may represent a seismic motion with a max
=
0
.
10g, T
=
0
.
30s,
3 cycles and Z liq =
N
=
5m, while
ρ o /
=
.
=
.
=
.
-
B
0
06 may represent a seismic motion with a max
0
30g, T
0
40s,
N
=
7 cycles and Z liq =
5m.
 
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