Geoscience Reference
In-Depth Information
F
undrained
=
ρ
a
g
B
s
u
a
g
g
tan
,
F
drained
=
(10.2)
φ
where:
F
undrained
and
F
drained
arethe dimensionless parameters for undrained and drained load-
ingrespectively:
a
g
is thehorizontal acceleration inthesoil beneath thefoundation
φ
isthe angle ofshearing resistance of the soil
ρ
isthe density of the soil
g
is thegravitational acceleration
Several bearing strength surfaces appear in the literature dating from about the time
of the paper by Butterfield and Gottardi (1994), Gottardi and Butterfield (2003). Bear-
ing strength surface expressions for conventional bearing capacity equations are given
by Pender (2006). Eurocode 8, Part 5 (CEN, 2003) has a bearing strength surface which
allowsfortheeffectofearthquakeaccelerationinthesoilbeneathastripfoundation.The
surface specified in EC8 is
f
8
V
F
,
H
,
M
,
H
c
T
M
c
M
1
e F
c
T
β
1
f F
c
M
χ
−
−
=
+
−
1
=
0
(10.3)
V
a
1
V
b
V
c
1
V
d
m F
k
k
m F
k
k
−
−
−
−
where: the numerical values for the eight parameters in this equation,
a
-
d
,
c
T
,
c
M
,β
and
, are specified in Annexe F of EC8, Part 5. There are two sets of parameters, one
for undrained conditions and the other for drained behaviour of the soil. Note that Equa-
tion(10.3) employs a slightly different notation from that used inEC8, Part 5.
χ
The background to the derivation of this surface is given by Salenc¸on and Pecker
(1994a, b) and Pecker (1997). Design examples using this equation are given in Chap-
ter10 of Fardis et al.(2005).
Figures10.1and10.2showthesurfacesfortheshorttermundrainedloadingofsaturat
ed
clay and drained loading of cohesionless soil. Both surfaces are limited to positive
V
values simply because there must always be a
co
mpressive load on the foundation. The
diagrams have positive and negative values f
or
H
as the earthquake is a back and fourth
motion. Similarly, the foundation moment
M
can be positive and negative during the
earthquake. Thus the surfaces in Figures 10.1 and 10.2 present the upper halves only of
the complete surfaces. In Equation (10.3) this is handled by using only the magnitude of
the normalised horizontal shear and moment.
TheEC8expressionsaredevelopedforastripfoundation.Thedocumentdoesnotinclude
shapefactorsthatwouldallowthecapacitytobeincreasedtohandlerectangularfounda-
tions, although Paulocci and Pecker (1997) have given expressions for these.
