829
Rapid Drawdown Analysis using Strength Reduction
Analyse
d’
abaissement rapide utilisant la force de réduction
VandenBerge D.R., Duncan J.M., Brandon T.L.
Virginia Tech, Blacksburg, VA, USA
ABSTRACT: The undrained shear strength during rapid drawdown is controlled by the properties of the embankment fill material and
the consolidation stresses prior to drawdown. Current design methods use limit equilibrium analyses to evaluate both the
consolidation stresses and the stability of the slope after drawdown. The method described in this paper uses the finite element
method to calculate the consolidation stresses throughout the slope during steady state seepage before drawdown. Undrained shear
strengths are calculated for all nodes in the model based on the major principal effective consolidation stresses and the results of ICU
triaxial tests. The undrained strength of each element in the model is determined by interpolation from the strengths at the
surrounding nodes. Using these strengths and an elastic-plastic constitutive model, the stability of the slope is evaluated by the
strength reduction method. Back analysis of rapid drawdown failures suggests that undrained strengths from ICU tests should be
reduced by 30% for the rapid drawdown condition.
RÉSUMÉ : La résistance du sol non drainé pendant l´abaissement rapide est contrôlée par les propriétés des matériaux de remplissage
du remblai et des contraintes de consolidation avant l´abaissement. Les méthodes de design actuels l´analyse d´équilibre limité pour
évaluer aussi bien la consolidation des contraintes que la stabilité des pentes après l´abaissement. La méthode décrite dans cet article
utilise la méthode des éléments finis pour calculer les contraintes de consolidation tout au long de la pente pendant
l´infiltration en état permanent avant l´abaissement. Les résistances du sol non drainé sont calculées pour tous les nodules du modèle
en fonction des majeur principal consolidation stress et des résultats d´essais triaxiales ICU. La résistance du sol non drainé pour
chaque élément du modèle est déterminée par l´interpolation des résistances aux nodules environnants. En utilisant ces résistances et
un modèle constitutif élastique-plastique, la stabilité de la pente est évaluée par la méthode de la réduction des résistances. La rétro-
analyse des défaillances des abaissements rapides semble indiquer que les résistances non drainés d´essais ICU devrait diminuer d´un
30% pour conditions d´abaissement rapide.
KEYWORDS: rapid drawdown, finite element, strength reduction, total stress analysis, earth dams, slope stability
1 INTRODUCTION
Rapid drawdown (RDD) has long been recognized as one of the
critical design conditions for the upstream or riverside slope of
dams and levees. The rapid drawdown condition occurs when
the water level adjacent to a slope or embankment is lowered
quickly after a long period of being elevated either at the normal
operating level for a dam or in the case of levees, during a
prolonged flood. Rapid removal of the supporting water load
from the upstream face of the embankment, combined with
changes in pore pressure, results in an undrained unloading
condition in which total stresses decrease, but shear stresses
within the embankment increase. Both effective stress and total
stress methods have been developed to analyze stability during
rapid drawdown and are discussed in the following sections.
1.1 Effective stress methods
The principal difficulty with effective stress methods is that the
pore pressures during the drawdown must be known, and
drawdown is an undrained loading condition. Estimating pore
pressures during undrained loading is a difficult and uncertain
undertaking.
Bishop (1954) proposed the
B
method to estimate pore
pressures at the end of drawdown. The
B
method assumes that
the changes in pore pressure during drawdown are equal to the
changes in major principal stress. Li and Griffiths (1988)
approximated the pore pressures at the end of drawdown by
means of transient seepage analyses. Lane and Griffiths (2000)
used assumptions similar to the
B
method along with finite
element strength reduction analysis.
These effective stress methods result in pore pressures at the
end of drawdown that do not reflect the tendency of the soil to
dilate or compress. Thus they result in the same pore pressures
at the end of drawdown for poorly compacted and well-
compacted soils. In reality, the pore pressures at the end of
drawdown for poorly compacted soils are much higher than for
well-compacted soils, because well-compacted soils tend to
dilate under the increased shear stresses during drawdown.
Thus neither the
B
method nor the transient seepage analysis
method, which do not reflect the quality of compaction of the
fill, can provide a useful evaluation of stability during
drawdown, and should not be used for this purpose.
Berilgen (2007) computed pore pressures during drawdown
using an elastic-plastic constitutive model that included the
effects of shear dilation. This procedure would be expected to
result in more realistic estimates of pore pressure at the end of
drawdown, but unfortunately requires analyses using complex
constitutive relationships.
1.2 Total stress methods
Total stress methods do not require pore pressures at the end of
drawdown to be estimated. The effect of these pore pressures is
instead accounted for in the undrained strengths of the
compacted soil. Well-compacted soil is stronger than poorly
compacted soil, reflecting the fact that the pore pressures due to
