Geoscience Reference
In-Depth Information
Mass
element
Beam
elements
Rigid
elements
Solid (plane strain)
elements
Mass
element
Gap
elements
Infinite elements
Fig. 9.11. Two-dimensional finiteelement discretisationand the types
ofelements applied
without P-
δ
effects
without P-
δ
effects
rocking on a rigid
soil
rocking without up lift
Nb
Nb
Nb χ
rocking without uplift
rocking on a rigid soil
uplift
initiation
uplift
initiation
q
c
Rotation,
q
Rotation,
q
(a)
(b)
Fig. 9.12. Characteristic moment-rotation pushover curves of a shallow foundation
(a)without and (b) withP-
δ
effects
The ultimate capacity of the soil-foundation system under combined of vertical load N,
shear force Q, and moment M is best expressed in terms of the interaction surface in
M-N-Q space. Several references can be cited for numerous examples on such a rep-
resentation (e.g. Butterfield and Ticof, 1977; Pecker, 1998; Houlsby, 2003). For slender
structuresthatareofinteresthere,mostsignificantistheultimatediagraminM-Nspace.
Anexampleofsuchadiagram,indimensionlessform,isgiveninFigure9.13.Itisbased
on an idealised elastoplastic Winkler model with the limiting pressures p
u
, being equal
to
(
π +
2
)
S
u
, where S
u
is the undrained shear strength of the “
ϕ =
0” soil. The figure
