2084
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
were located at the same vertical level (they are not to allow
room for the extruding hydraulic circuits), the anchor would be
characterized by four (vertical) symmetry planes. Although this
is not exactly true, it has been here assumed for computational
convenience that the different socket elevations only slightly
violate such symmetries: accordingly, only a quarter of the
whole geometry has been considered and discretized.
The FEM mesh employed is shown in Figure 3. The
discretization – performed by adopting quadratic tetrahedral
elements - is finer around the sockets and the tie rod, i.e. where
the solution is expected to exhibit the largest gradients. The
external soil boundaries have been placed sufficiently far from
the anchor, so as to not affect the global pull-out response.
Since the main purpose of this preliminary study was the
highlighting of SSI mechanisms, for the sake of simplicity no
sophisticated material models have been considered. In
particular, the soil mechanical behaviour has been modelled by
means of a simple Mohr-Coulomb perfectly-plastic constitutive
relationship with non-associated flow rule (i.e. with different
friction and dilatancy angles), while a von Mises perfectly-
plastic associated model has been adopted for the anchor
structural members. A linear variation along the depth has been
introduced for the soil Young modulus, to account for the
stiffening induced by the increase in normal confinement.
Moreover, as is commonly done in SSI analyses, a widthless
perfectly-plastic interface layer has been interposed between the
anchor and the surrounding soil to allow both shear and tension
detachments.
Figure 3. FEM model.
Apparently, the length of the tie rod, i.e., the socket
extrusion depth, greatly influences the pull-out capacity of the
anchor: as deeper anchors are considered, larger discrete models
should be defined, implying an increase in computational costs.
Conversely, in order to investigate how the strength
contribution coming from the steel sockets is affected by the
initial stress state, an approximate approach has been here
adopted for the first preliminary analyses. In particular, to
simulate a real higher embedment, the same model in Figure 3
has been used for different physical depths, by using an
equivalent ``embedment surcharge''
emb
on the top of the
reduced model (obviously, this assumption neglects the
frictional pull-out resistance provided by the missing upper
soil).
q
2.2
Main inferences from FEM analyses
In what follows, the main observations derived from the
analysis of the preliminary FEM results (with embedment
surcharge) are qualitatively summarized.
All the pull-out tests have been performed by imposing a
prescribed upward displacement
at the top of the tie rod,
recording the corresponding reaction forces to quantify the
global resistance provided by the neighboring soil. While the
total pull-out force readily results from the top reaction forces,
two distinct contributions can be recognized and estimated on
the basis of the FEM outputs. In particular, the global capacity
has been split into a first frictional component mobilized along
the tie rod, and a second contribution directly carried by the
steel sockets.
Figure
4. Total displacement contour plot at the onset of failure.
As an example, Figure 4 illustrates the contour plot of the
total displacement (absolute value) at the onset of the collapse.
The global failure mechanism takes place in the form of a soil
wedge surrounding the anchor and moving upward as the
anchor itself is pulled-out. Such a failure mechanism is further
illustrated in terms of the plastic shear strain in Figure 5: the
shear strain concentrations take place along the tie rod and close
to the sockets, so that the formation of a failure wedge is
apparent.
Figure
5. Plastic shear strain contour plot at the onset of failure.
Figure 6 shows, for four different
emb
values, the pull-out
curves (force vs. displacement) estimated for the whole
anchorage, i.e. four times the force computed for the quarter
anchor (this would rigorously hold if the steel sockets were at
the same elevation). In all the cases considered, the mechanical
response of the anchorage is overall ductile and the limit pull-
out load (horizontal plateau) is achieved after quite large
displacements. Besides the expected increase in the bearing
capacity at larger
emb
, it is also worth noting that, owing to the
aforementioned spatial variation of the soil Young modulus, the
limit load is achieved at about the same displacement level
q
q
.
Figure 6. Pull-out responses at increasing embedment surcharge.
Both the above frictional and socket strength contributions
have been separately evaluated for all the FEM analyses
performed. The obtained values – not reported here for the sake
of brevity – show that the lateral frictional forces and the
contribution provided by the steel sockets are quantitatively
comparable. Such large lateral forces could not be explained by
assuming a standard
0
k
distribution for the confining stress (
0
stands for the at rest earth pressure coefficient) all around the tie
rod. In contrast, the numerical simulation shows a significant
increase in confining stresses as the anchor is pulled-out, up to
values much larger than the at rest ones. Figure 7 illustrates the
final contour plot of the radial stress, in which the severe
perturbation of the initial (linear) at rest distribution is evident.
k
