Geoscience Reference
In-Depth Information
Fig. 11.13. Comparison between numerical and analytical predictions ofthe bearing
capacity factor
ζ
for various combinations of soil crustcharacteristics (
C
u
,
H
/
B
), and
liquefiable soil density
(
D
r
)
identified as having a direct effect. In Figure 11.12, analytical predictions obtained for a
degradedfrictionanglearedistinguishedfromthoseobtainedforareducedeffectiveunit
weight.Thefirstthingtoobserveisthatthenumericalpredictionsareincloseagreement
withtheanalytical
-
U
relationshipsobtainedwiththemoreconservativeassumptionof
a degraded friction angle for the liquefied subsoil. Furthermore, it may be observed that
the numerical analyses predict reasonably well the relative effect of the afore mentioned
independent problem parameters
H
ζ
B
,
C
u
and
D
r
.
A key issue for the successful comparisons shown in Figures11.12 and 11.13 is the cor-
rectchoiceofan“equivalentuniform”valueoftheexcessporepressureratio
U
whichis
used to relate with the numerically predicted values of
/
. This is because, the analytical
solution assumes that
U
is uniform all over the liquefiable foundation soil, unlike the
numericalanalyseswhichshowclearlythatthepresenceofthefootingleadstoaconsid-
erably non-uniform distribution of
U
in the horizontal direction, as well as with depth.
Following a trial-and-error examination of various alternatives, it was finally found that
a best fit to the analytical predictions was obtained when
U
was computed as the mean
between the free field value
U
ff
and the average value below the footing
U
f oot
, com-
puted over an 1
ζ
.
2
B
×
1
.
2
B
area ofliquefiable soil,i.e. at the core of the failure wedge.
Among these two components,
U
ff
is easy to compute as in most cases of practical
interest the degradation of bearing capacity becomes a design issue only upon complete
liquefaction in the free field. Thus, it can be safely assumed that
U
ff
≈
00. The com-
putation of
U
f oot
is more tedious as it presumes that the 2-D distribution of
U
under the
footing,attheendofshaking,isknown.Fortheshakeofsimplicity,itwasfirstexamined
whether
U
f oot
could be related to the
U
value of a single “characteristic” point on the
axis of the footing. Among the various points which were considered (Figure 11.14), it
wasfinallyfoundthatthisrolecouldbeattributedtoapointatdepthbetween
z
c
=
1
.
0
.
60
B
and 0
.
80
B
below the crust.
The next step was to devise a simplified procedure for the computation of
U
at the char-
acteristicpoint,takingalsointoaccountthestressconcentrationcausedbythefoundation
