2938
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
improvement took place (2006), cement prices were
significantly higher because of global demand, and the
estimated cost for the DSM option was estimated to be $150
million (2011 US dollars).
2 PREFABRICATED VERTICAL DRAINS FEASIBILITY
STUDY
Installation of prefabricated vertical drains (PVDs) is a cost-
effective foundation improvement technique at sites where a
surcharge load will be applied (e.g., an MSE berm). In general,
PVDs are installed in soft soils to improve the drainage
characteristics hence accelerating the dissipation of excess pore
pressures generated during stage construction of embankments.
The time it takes for pore pressures to dissipate depends upon
the permeability of the dredge and the spacing between PVDs
and it can be estimated using well known radial flow equations
(e.g., Barron, 1948).
Initially, the use of PVDs to improve the foundation
strength appeared unfeasible due to the massive weight of the
proposed 21-m high MSE berm which was required to gain the
needed airspace. Typically, the maximum height of an MSE
berm on soft soils is dictated by the undrained shear strength of
the underlying soft material. At the CIL site, the maximum
height that could have been built using standard design
techniques would have been on the order of 7.5-m (i.e., about
13.5 m shorter than required to achieve the target airspace of 17
million cubic meters).
Standard design techniques assume that when PVDs are
installed in soft soils: (i) the excess pore pressures generated
between PVDs during loading is uniform; and (ii) only
undrained shear strength is mobilized during loading. The
maximum excess pore pressures (
U
max
) generated after
placement of a soil lift (i.e., 3 m for the CIL project) is
estimated assuming that the soil lift is placed at once and it
generates excess pore pressures (i.e., the pressure of the water
stored within the dredge) approximately equal to the weight of
the soil lift. Although it is recognized that excess pore pressures
at the PVD location is nil and increases with radial distance
from the PVD (Figure 2), it is typically assumed that excess
pore pressures between PVDs are uniform and equal to
U
max
.
Figure 2. Pore Pressure Model
Because piezometers are located to monitor the maximum
pore pressure, the radial variation is usually neglected.
However, this conservative assumption made for computation
and monitoring expedience not only neglects the fact that the
excess pore pressures is not uniform but also does not take into
consideration how PVDs change the dredge response to loading.
In theory, drained parameters could be used to represent the
shear strength of soft soils with PVDs if the applied loads (i.e.,
construction of the MSE berm) are imposed slowly enough to
allow all excess pore pressures to dissipate as loading takes
place. In practice, this could not be implemented because the
rate of loading would need to be too slow to be feasible.
3 VIRTUAL SAND PILES: HYBRID DRAINED-
UNDRAINED MODEL
The centerpiece of innovation for the design and construction of
this massive MSE berm was the improvement of the weak
dredge/alluvium foundation material using the concept of
‘virtual sand piles’, also described as the Hybrid Drained-
Undrained (HDU) model (Espinoza et al., 2011).
The virtual sand pile concept is illustrated Figure 2. As
shown in this figure, the closer the dredge is to the PVD the
smaller the generated excess pore pressure and the faster that
are dissipated. Hence, depending upon the speed of
construction, it can be assumed that there are two distinct zones
with different shear strength characteristics during loading: a
drained zone, near the PVDs, and an undrained zone further
from the PVDs. This concept constitutes a significant departure
from standard design of soft cohesive soils with PVDs and it is
the central element of the design. The development of the novel
HDU design methodology for PVD design, to analyze the
strength characteristics of the soft foundation soils during
construction made the use of PVDs feasible for the CIL Project.
Subsequently, a more realistic model was developed to
consider that: (i) the soils located closer to PVDs dissipate
excess pore pressures generated during construction to more
quickly than the soils located farther away from PVDs (Figure
2); and (ii) the rate of construction influences the maximum
excess pore pressure that could be generated (i.e., pore pressures
dissipate as the soil lift is placed). To simplify the model
development, the rate of berm placement construction was
assumed constant and equal to
R
c
. For each lift of soil, it was
assumed that excess pore pressures starts to dissipate soon after
it was placed (see Figure 3). Assuming an exponential decay
function, the resulting excess pore pressure equation as a
function of time is:
p
t
c
t t
e R tu
for
1 )(
(1)
where:
t
p
is the time that takes to place the fill and
is a
parameter that is related to Barron’s Equations (1948)
developed for sand drains:
2
2
i
v
n
r
c
F
(2)
2
2
2
2
4
1 3 ) ln(
1
n
n n
n
n F
n
(3)
e
i
r
r n
(4)
and
c
v
is the coefficient of consolidation;
r
i
is the radius of
influence of the PVDs; and
r
e
is the equivalent radius of the
PVD. The maximum pore pressure takes place at
t
=
t
p
. It
follows that after fill placement, it is assumed that excess pore
pressure dissipates according to the same decay function, then:
p
t t
t
c
t t
e e R tu
p
p
for
1 )(
)
(
(5)
4 SELECTING THE DIAMETER OF THE VIRTUAL
SAND PILE
Equations (1) through (5) were used to select the appropriate
PVD spacing along with the corresponding rate of construction
such that the soils near the PVDs would generate significantly
smaller pore pressures that would allow to model the dredge
around the PVD as a virtual sand pile. This meant that these
soils could be considered to have a drained response during
loading. The modified procedure consists of selecting the
magnitude of excess pore pressure that would have negligible
effect on MSE berm stability and then back-calculate the
