Page 326 - Numerical Analysis and Modelling in Geomechanics

F.BASILE 307
have been taken as 0.0 and 0.99 for the axial response of the shaft and the base,
respectively, and 0.9 for the lateral response.
For the axial response, the profile of soil modulus has been derived from the
correlation E =400C u for the linear analyses and from E =1500C u for the
s
s
nonlinear analysis. For the lateral response, the profile of soil modulus has been
assumed to increase linearly with depth from a value of zero at the top of the
London Clay (conservatively) at a rate of 4.14 MPa/m for the linear analyses and
6.15 MPa/m for the non-linear analysis. The soil Poisson’s ratio has been taken as
0.5.
The applied vertical loads (V) result from the combined effect of live and dead
loads, whereas the horizontal loads (H) and moments (M) are generated by the
high-speed trains braking and accelerating. For the load case presented herein,
the loads acting on the cap have been estimated as V=14,200 kN, H=470 kN and
M =3200 kNm.
This problem has been analysed using the computer programs MPILE,
DEFPIG and PGROUPN (both the linear and non-linear versions). Table 10.7
summarises the main results obtained from the analyses. In the linear range, there
is a reasonably good agreement between the group deformations and axial load
distribution predicted by the different codes. However, it is important to note the
significant differences between the predictions of the pile head lateral loads and
bending moments. As discussed previously, due to the interaction between the
axial and lateral responses of the piles, higher loads are expected to occur for the
piles in the leading row than for the piles in the trailing row of the group. While
this load-deformation coupling effect is modelled by the PGROUPN analysis,
MPILE and DEFPIG disregard the interaction between the axial and lateral
responses and therefore predict the same lateral loads and bending moments for
both the leading and trailing rows of the group. This results in a significant
underestimate of the maximum values of lateral load and bending moment and
hence may lead to an unsafe design of the piles.
If the effects of soil non-linearity are accounted for by means of the
PGROUPN analysis, two main features of behaviour are observed:

1 A prediction of lower (and more realistic) group deformations.
2 A decrease of predicted loads on the most heavily loaded row of piles (i.e.
the leading row) and hence a more uniform load distribution between the
piles.

It should be emphasised that in this case, due to the low load level, the
differences between the linear and non-linear PGROUPN results are mainly a
consequence of the higher value of soil modulus adopted in the non-linear analysis
(i.e. an initial value), rather than the effect of soil non-linearity.
This observation confirms the view already expressed by other authors
(Randolph, 1994; Mandolini and Viggiani, 1997): at low load levels (and hence