Figure 6: Comparison of FEM simulations of (a) settlement curve (b)
lateral displacement (c) excess pore water pressure for the ideal FEM
model vs. case(4a) + case(4b) (surcharge and PVD + vacuum and PVDs)
scenario
DiscussionAs it can be seen from all the simulations, the superposition law is not
valid in proposed cases. The algebraic summation of cases based on
different situations vs. FEM models is either decreasing or increasing.
The interaction between PVDs, surcharge and the vacuum or the coupling
effect can be easily seen on plotted curves.
The predicted surface settlement curves from FEM (verified and ideal)
models are compared with various scenarios. Figure 3(a) shows that in
the absence of PVDs in only the surcharge model (case 1(a)) the results
of the SUM case for settlement are underestimated after the 60th day. In
contrast, by the inclusion of PVDs, the results as shown in figure 4(a)
are overestimated after the 60th day. This is the time when the coupling
effect starts. From the figure 4(a) the decreasing effect of coupling
can be seen when the applied vacuum pressure is not constant and the
ultimate settlement is lesser than the summation of the described cases.
For the ideal constant 60 kpa vacuum case as shown in figure 5a the
resultant SUM case curve is underestimated similar to figure 3(a). In
the case with the inclusion of PVDs (6a) the results were overestimated
only 7 percent after the 75th day. Figure 6(a) and 4(a) show that for
discretizing complex models like combined surcharge and vacuum the
inclusion of PVDs with surcharge gives better predictions for both cases
with constant and variable applied vacuum pressure but for variable
vacuum the results would be underestimated by 40 percent in the final
settlement curve. By applying constant vacuum pressure the coupling
effect has been minimized in settlement curves. Models with the
inclusion of PVDs might be considered in the case of constant vacuum
pressure for preliminary prediction or empirical equations for surface
settlement (case 4(a) + case 4(b)). For variable vacuum pressure none of
the models could predict the settlement.
The predicted lateral displacement curves from FEM (verified and ideal)
models are compared with various scenarios. Figure 3(b) and 4(b) show
that for the field variable applied vacuum the resultant curve for
lateral displacement in the SUM case is overestimated while as shown in
figure 5b and 6b the resultant curve for lateral displacement in the SUM
case is underestimated for the ideal case. For the variable applied
vacuum in the field the predicted lateral displacement from the SUM case
is twice as compared to the FEM model at ground surface. It can be seen
that for this case the coupling effect reduced the lateral displacement
at the ground surface from 8cm to 4cm and reduced the lateral
displacement by about 30 percent in the very soft clay layer under the
surface. For cases with variable vacuum pressure considering the lateral
displacement from the case surcharge without PVDs (case 1(a)) might be
considered for empirical equation except for ground surface where 50
percent of the SUM cases (case 1(a) + case 1(b) or case 2(a) + case
2(b)) in both cases of surcharge with and without PVDs might be
considered for preliminary prediction or empirical equations related to
lateral displacement. In contrast, for the ideal constant 60 kpa case,
the SUM case is underestimated below the surface but agrees well on the
ground surface. For constant vacuum pressure, the coupling effect would
increase the lateral displacements for weak clay layers under the
surface but don’t affect the ground surface that might be attributed to
over-consolidation of the surface layer. Both models of the SUM cases
with the inclusion of PVDs and in absence of PVDs might (case 3(a) +
case 3(b) or case 4(a) + case 4(b)) might be considered in the case of
constant vacuum pressure for preliminary prediction or empirical
equations related to lateral displacement.
One of the main obstacles in any FEM modeling simulations or comprising
empirical or analytical solutions for combined vacuum and surcharge
preloading is excess pore pressure. In the previous sections some
aspects of this matter have been explained. Figure 3(c) shows that for
the field variable applied vacuum the resultant curve for excess pore
pressure in the SUM case is overestimated while as shown in figure 4(c)
the resultant curve for excess pore pressure till the day 95 is
underestimated while for the rest till 160th day it is overestimated.
Since the applied vacuum pressure was reduced to -20 kpa on the 120th
day none of the cases could predict the values of excess pore pressure.
Figure 3(c) and 4(c) show the complicated mechanism of coupling in the
dissipation of excess pore pressure. For the ideal case as shown in
figure 5(c) and 6(c), the SUM curve in some areas overestimates and in
some areas underestimates the FEM excess pore pressure because of the
coupling effect. The cases assuming PVDs inclusion along with surcharge
(case 2(a) and case 4(a)) agree best with both the ideal and verified
FEM curves and they can be used properly for an acceptable estimation of
excess pore pressure in systems with constant and variable vacuum
pressure. This agreement by the FEM model is exactly the mechanism that
was described in the first part of this literature. Although the vacuum
effect is the same as surcharge loading in accelerating the process of
consolidation, its acting mechanism is completely different and negative
excess pore pressure attributed to vacuum preloading is only a term for
describing the magnitude of applied suction through PVDs.
Figure 3(a) shows a draw-back in the settlement curve on the 75th day in
the case 1(b). This is the time when because of technical problems the
applied vacuum pressure has dropped in real-world projects and an
unloading condition occurred. In the absence of the surcharge preloading
the acquired settlement reduced from 60 cm to 40 cm. As (Chai, Carter et
al. 2006) reported this might be attributed to k0(no strain condition) where the vacuum pressure is no more larger thank0 condition to maintain the vertical
deformation. If even the potential inward forces of the vacuum
preloading are neglected, as it can be seen without any surcharge
preloading the occurrence of undesirable heave is expected after removal
or reduction in the vacuum preloading. This case clearly illuminates the
necessity of applying the combined system of the surcharge and vacuum
preloading to maintain the efficiency of the whole treatment process. At
least 30 percent of preliminary designed preload is recommended for the
surcharge preloading.
The false idea might exist that the vacuum preloading necessarily
induces surficial inward displacement. In fact as stated by (Chai, Ong
et al. 2013) outward, inward or inward near the ground and outward at
greater depth might occur.it can be seen that for all the cases in the
verified and ideal cases, outward displacement is dominant except for
the case that with PVDs and constant vacuum without surcharge preloading
(case 3(b)) that inward displacement near the ground and outward
displacement at greater depth dominates. As (Liu, Liang et al. 2019)
reported The ground settlement of the clayey soils during vacuum removal
is mainly attributed to fact that the Young’s modulus in the vertical
direction is higher than that in the horizontal direction because of the
soil anisotropy, and Lateral displacement is dominant for the ground
deformation during vacuum removal. As it can be seen in fig 3(b),
because of the variable applied vacuum pressure the lateral displacement
on ground surface is outward similar to the surcharge preloading. If the
magnitude and duration of the vacuum pressure don’t be high enough to
counter-effect the soil anisotropy and k0 state,
inward lateral displacement effect on ground surface should not be
expected. This case clearly shows the necessity of constant application
of a minimum quantity vacuum pressure that should be maintained the
whole time, even if a stepped vacuum pressure is determined in the
design procedure.ConclusionThe following conclusions are based on data, analyses, and
interpretation presented in this paper:
.