1631
Pseudo static analysis considering strength softening in saturated clays during
earthquakes
L’analyse pseudo statique considérant la force de ramollissement dans l’argile saturée lors des
tremblements de terre
Tsai C.-C.
National Chung Hsing University, Taiwan
Mejia L.H., Meymand P.
URS Corporation, 1333 Broadway, Suite 800, Oakland, California 94612, USA
ABSTRACT: Cyclic softening and strength loss of saturated clays during earthquakes is often an important consideration in
engineering problems such as slope stability, dam and levee safety, and foundation bearing capacity. This paper proposes/updates a
simplified procedure for evaluating cyclic softening (amount of strength loss) that may be expected in saturated clays during
earthquakes and implements it in pseudo-static analysis. The procedure has two main steps: (1) estimation of an equivalent cyclic
shear strain amplitude and associated number of cycles induced in the soil mass by an earthquake; and (2) estimation of softening and
strength loss in the soil mass. The proposed procedure provides reasonable, first-order estimates of cyclic softening consistent with
the other developed procedures. In addition, the results of applying the estimated strength softening in pseudo-static analysis are
compared with case histories identified as involving cyclic softening of clays.
RÉSUMÉ : Le ramollissement cyclique et la perte de résistance de l’argile saturée lors des tremblements de terre est souvent un
facteur important dans les problèmes d'ingénierie tels que la stabilité des pentes, les barrages et digues de sécurité, et la capacité
portante des fondations. Cet article propose /met à jour une procédure simplifiée pour l'évaluation du ramollissement cyclique
(montant de la perte de résistance) auquel on peut s'attendre dans l’argile saturée lors de tremblements de terre et le met en œuvre a
travers l'analyse pseudo statique. La procédure comporte deux étapes principales: (1). l’estimation d'une amplitude de déformation
cyclique de cisaillement équivalent et le nombre de cycles associé induits dans la masse du sol par un tremblement de terre; et (2)
l'estimation de ramollissement et la perte de force dans la masse du sol. La procédure proposée prévoit de façon raisonnable, des
estimations cycliques de ramollissement de premier ordre, compatible avec d'autres procédures. Par ailleurs, les résultats de
l'application de la force de ramollissement estimée dans l'analyse pseudo statique se comparent bien avec des cas identifiés dans le
passé et impliquant le ramollissement cyclique des argiles.
KEYWORDS: Cyclic loading, strength softening, clay, strain approach
1 INTRODUCTION
Cyclic softening of clays is commonly understood as the
reduction in soil stiffness and strength due to repeated cyclic
loading, as shown in Figure 1. Experiments by Idriss et al.
(1978) showed that the initial stiffness and the ordinates of the
backbone curve of soft clay are reduced after several cycles.
Matasovic and Vucetic (1995) discussed the coupling of cyclic
pore-water pressure generation and softening of clay and the use
of a threshold strain concept.
Recent case histories have revealed evidence of cyclic
softening of clays during earthquakes. The 1999 Chi-Chi,
Taiwan Earthquake caused extensive ground failure and
structural damage in Wufeng, Taiwan. Some of the most
interesting cases of damage involved ground failure in areas
underlain by low plasticity clayey soils (Chu et al. 2008).
During the 1999 Kocaeli earthquake, in situ deformation
measurements at the Carrefour Shopping Center showed
significant vertical strains in ML/CL and CH strata. Martin et
al. (2004) concluded that the ML/CL layer had exhibited
“liquefaction type behavior” while “a definitive explanation for
significant earthquake-induced settlements in a high-plasticity
clay stratum (CH) in Lot C has not yet been found.”
Recently, Boulanger and Idriss (2007) developed a
procedure for evaluating the potential for cyclic softening in
clay-like fine-grained soils during earthquakes. Their procedure
uses a stress-based approach similar to that used in semi-
empirical liquefaction procedures. Mejia et al. (2009) applied a
procedure similar to the Boulanger and Idriss procedure to
estimate post-cyclic strengths of clay-like fine-grained soils and
applied it to dam safety evaluation. Tsai and Mejia (2011)
utilized cyclic strain to evaluate cyclic softening of clayey soils,
which is different from the previous stress-based approach. This
paper updates the Tsai and Mejia procedure by adopting the
most recent study, especially for estimating equivalent number
of cycles in the strain-based approach. The revised procedure is
first compared with another more complex analysis procedure
by analyzing the same design case. Then it is applied to case
histories involving strength loss, and is found to provide
reasonable estimates of behavior consistent with the field
observations.
max
max
G
max
c
G
max
CYCLIC LOOP AT CYCLE
N
CYCLIC LOOP AT CYCLE
N=
1
INITIAL LOADING BACKBONE CURVE AT CYCLE
N=1
DEGRADED BACKBONE
CURVE AT CYCLE
N
Figure 1. Illustration of cyclic softening of clays.
2 CYCLIC SOFTENING MODELS FOR CLAY
Matasovic and Vucetic (1995) proposed a modified hyperbolic
model to describe the stress (
)-strain (
) behavior (with coupled
