830
Proceedings of the 18
th
International Conference on Soil Mechanics and Geotechnical Engineering, Paris 2013
undrained loading are smaller when the soil is compacted well.
This advantage has led to the adoption of total stress analyses in
the United States. Total stress analyses have been developed
through the work of Lowe and Karafiath (1960), Duncan et al.
(1990), and the U. S. Army Corps of Engineers (2003).
These methods relate the undrained strength of the soil
determined from consolidated-undrained laboratory tests to the
effective stresses in the embankment before drawdown. As
developed by Lowe and Karafiath (1960), Duncan et al. (1990),
and the U. S. Army Corps of Engineers (2003), the undrained
strength was related to the stresses along the trial failure
surface, which were determined by limit equilibrium analyses.
Limit equilibrium analyses were used because the finite element
method was largely unavailable when the method was
developed.
Today, with finite element capabilities more
routinely available, it seems more logical to use finite element
analyses to evaluate the stress state prior to drawdown, as
described here. The principal steps in the total stress method
described here are:
•
Evaluate the consolidation stresses in the embankment using
finite element analyses, modeling steady seepage conditions
with the water level high;
•
Use these stresses, with the results of consolidated-
undrained triaxial tests, to determine undrained strengths
throughout the embankment; and
•
Determine the factor of safety after drawdown by the finite
element strength reduction method.
2 PROPOSED METHOD OF ANALYSIS
The geometry of the embankment being analyzed is represented
by a finite element model.
The model should include
appropriate boundary conditions, mesh density, element type,
etc.
The long-term effective consolidation stresses control the
undrained strength during drawdown.
The consolidation
stresses within the embankment are determined using a finite
element model that includes steady state seepage and long-term
boundary loads, such as the reservoir water. At this stage, all of
the soils are modeled using linear elastic stress-strain properties.
Determination of the appropriate undrained shear strength
for RDD is the most important and the most complex step in the
analysis. The undrained strength, s
u
, of a compacted soil can be
related to the major effective consolidation stress,
’
1c
, and
other factors, such as the minor principal consolidation stress,
anisotropic strength and deformation characteristics,
compaction prestress effects, and the degree of principal stress
rotation from consolidation to failure. If strengths are being
determined using samples taken from an existing earth
embankment, the additional factors of disturbance and
recompression will also influence the measured strengths.
Isotropically consolidated undrained,
ICU,
triaxial
compression tests on specimens compacted to the same relative
compaction as the soil in the field are relatively easy to perform,
but they do not replicate all of the factors mentioned earlier,
such as stress rotation, anisotropy, and compaction prestress,
which also influence the undrained strength. In the proposed
method, the effects of these factors are included by applying an
empirical adjustment factor, R, to the strengths measured in
ICU tests, i.e. the adjusted strength is expressed as
100
u ADJ
u ICU
s
R
s
(1)
where:
s
u-ADJ
= undrained strength adjusted for the influence of the
factors noted above; and
s
u-ICU
= undrained strength measured in ICU laboratory tests.
The value of the empirical factor R must be determined by
back analysis of RDD failures. Based on the two available,
well-documented case histories, the value of R was found to be
70. Additional well-documented case histories of RDD failure
would make it possible to refine this value. Some of the
laboratory tests from the cases analyzed here were performed on
samples taken from the embankments.
The value of R
determined for these cases may include effects of disturbance
and recompression, which would not be reflected in tests on
samples compacted in the laboratory.
The adjusted undrained strength is used in the analysis of
stability after drawdown.
The model geometry from the
consolidation stress analysis is used along with modified
constitutive and strength properties to calculate the factor of
safety by the strength reduction method.
For the stability analysis, undrained strengths are assigned to
those portions of the model where negligible drainage will
occur during drawdown.
Drained strength parameters are
assigned to the portions of the zones where drainage will occur.
These include zones of materials with high permeability and
areas near the surface of the slope where the drainage path is
short. The depth of this drained zone along the slope surface
can be estimated using one-dimensional consolidation theory.
This paper follows the recommendations of Griffiths and
Lane (1999) and uses non-convergence as the failure criterion in
the strength reduction analysis.
3 EXAMPLES
The proposed method is compared to the limit equilibrium
method, using the RDD failures at Pilarcitos Dam and Walter
Bouldin Dam as benchmark cases.
3.1
Pilarcitos Dam
Pilarcitos Dam is a 23.8 m high homogenous earth dam built
from compacted sandy clay with a total unit weight of 21.2
kN/m
3
. The lower 17.7 m of the upstream slope is inclined at
2.5H:1V, and the upper 6.1 m is inclined at 3H:1V. The long-
term water level was 1.8 m below the crest.
A rapid drawdown slide occurred in 1969 after the reservoir
level was lowered 10.7 m over the course of 43 days. This case
has been considered by a number of researchers, including
Wahler and Associates (1970) and Duncan et al. (1990).
Laboratory strength tests were performed on samples from
the embankment by Wahler and Associates (1970). A drained
zone 0.46 m thick (measured perpendicular to the slope face)
was used for the drawdown analysis. This depth corresponds to
90% dissipation of excess pore pressure in 43 days, based on an
assumed coefficient of consolidation of 46 cm
2
/day.
The Pilarcitos Dam finite element model was created using
the software Phase
2
v.8.011. A rigid foundation was assumed
and the nodes along the base of the embankment were fixed.
The consolidation stress analysis assumed linear elastic stress
strain behavior with E = 10.8 MPa for both the consolidation
stress and drawdown analyses. Poisson’s ratio
,
, was assumed
to be 0.42 for the drained portion of the embankment, and 0.49
for the undrained portion. The drained zones in the drawdown
analysis used a drained friction angle of 45° based on the
Wahler and Associates (1970) tests. The stresses prior to
drawdown were calculated in three-stages, using effective stress
analyses. Gravity loads within the embankment were applied in
the first stage. The boundary loads of the water in the reservoir
were applied in the second stage. In the third stage, pore
pressures corresponding to steady state seepage were assigned
to the nodes in the embankment.
The ICU triaxial compression test data obtained by Wahler
and Associates (1970) was used to express undrained strength
as a function of
’
1c
as shown in Figure 1. The ICU strength
(solid) line was fitted to these points and also to match the
