Geoscience Reference
In-Depth Information
3.3. CHARACTERISTIC RESULTS
3.3.1. Static nonlinear (“pushover”) analysis
Figure 9.10 sketches the problem considered here: a B
=
2b
=
6m wide foundation on
moderately soft soil layer, supporting a 2h
=
12m high bridge pier (an effective aspect
ratio 2h
/
b
=
4).
Two different models of soil-foundation interaction are implemented to determine the
static response to progressively increasing lateral(inertial like) loading:
•
an elastoplasticWinkler model and
•
a finite-element inelastic model
Details of the models are described in Apostolou (2007), while an extensive calibration
of these methods against centrifuge experiments have been presented in the 4th ICEGE
Conference (Apostolou et al., 2007). The finite element mesh and some of its character-
istics areshown in Figure 9.11.
A typical “pushover” moment-rotation relationship of the foundation under constant
vertical load is sketched in Figure 9.12(a,b). In both figures uplifting of the founda-
tion signals the end of the linear M-
range, and in both there is a limited moment
capacity, associated with a bearing capacity failure mechanism. The difference between
the two figures stems from the consideration of P-
θ
δ
effects in Figure 9.12(b), as the
additional moment, Nh
θ
, of the structure weight becomes significant at large values of
rotation.
The elastic rotation is obtained through the rotational stiffness of the foundation in full
contact with the soil. Analytical closed form expressions for a variety of foundation
shapes, and idealised soilprofiles has been presented byGazetas (1991).
F
I
2h
N
G(z)=G
2b
H
s
Rigid
bedrock
Seismic
excitation
Fig. 9.10. Slender structure-foundation-soil system studied
