Geoscience Reference
In-Depth Information
discrete springs for the rotational and vertical stiffness of the footing, as is catered for
in the majority of software packages for the analysis of structures. The attraction of the
bed of springs is simply that it allows modelling of the progressive uplift of the shallow
foundation under moment loading. The quest to achieve a correct ratio of vertical to
rotationalstiffnessistoensurethatanyprogressiveupliftfromtheedgesofthefootingis
modelled realistically.
4.2. NONLINEAR SOILSTRESS-STRAIN BEHAVIOUR
What we have touched upon only briefly so far is the fact that the reaction pressure
beneath our footing is limited by the ultimate bearing pressure of the soil beneath. We
arethenpresentedwiththepossibilitythattheelasticcalculationsdiscussedabovemight
be totally misleading and that nonlinear soil behaviour will eliminate the peaks in the
pressure distribution at the edges of the foundation. If this was the case then the linear
pressure distribution of the bed of springs might be found to be a more realistic pressure
distributionnotonlybecauseofcomputationalconveniencebutalsobecauseitrepresents
more adequately the actual behaviour of the soil-structure interaction. Presented below
are some results along these lines, but at this stage for strip foundations rather than the
square footings discussedabove.
The basis of this work is an implementation in FLAC (
F
ast
L
agrangian
A
nalysis of
C
ontinua, Itasca, 2005) of a simplified nonlinear stress-strain model for soil (Pender,
1999). The average bearing pressure-settlement curve calculated for a rigid strip foun-
dation subject to gradually increasing vertical load on a saturated clay (undrained shear
strength of 50kPa) produced by this model is shown in Figure 10.12a. The numerical
result approaches thetheoretical ultimate bearing pressure
(
q
u
=
5
.
14
s
u
=
257kPa
)
.
1
250
a
b
0.8
200
0.6
150
0.4
100
0.2
50
0
0
0
0.01
0.02
0.03
0.04
0.05
0
0.01
0.02
0.03
0.04
0.05
Settlement / foundation width
Settlement / foundation width
Fig. 10.12. (a) Average bearing pressure-settlement curve for a rigidstrip
foundation on a nonlinear soil.(b) Decreasing ratio of rotational to vertical stiffness
as bearing failureis approached
