3521
Seismic Design of Restrained Rigid Walls
Conception Sismique de Murs Rigide de Soutien
Yi F.
Chief Engineer, CHJ Consultants, CA, USA
ABSTRACT: In current practice, the increment of seismically induced earth pressure on a rigid, non-yielding wall is generally taken
as the product of seismic coefficient (
!
) and the soil mass behind the wall,
∆
!
=
!
∙
!
, as developed by Wood (1973) and
modified by Whitman (1991). Wood’s study and most of the research thenceforth were based on the assumption that the wall and the
retained soil are connected to a rigid base. This assumption neglects the fact that comparing to the mass mobilized by an earthquake,
the size of the wall and its retained soil are relatively small. In other words, even though the wall is connected to a relatively rigid
base, the base exhibits certain movement during an earthquake. In addition, there is much disagreement in current practice related to
the value of
!
used with respect to the relationship to peak ground acceleration (PGA). In this study, a series of elasto-plastic
pseudostatic finite element analyses were performed to assess the appropriateness of the Wood (1973) equation for determining the
seismically induced lateral earth pressures on the stem of the restrained wall, and relationships were established between
!
and PGA
based on the momentum conservation law. The results indicate that the increment of seismic earth pressure acting on non-yielding
wall is a function of
!
and the supporting condition. They also indicate that a value of
!
of 25% of PGA seems reasonable and
somewhat conservative for the design of normal structures.
RÉSUMÉ: L’augmentation de pression des terres induite par un séisme sur un mur rigide et résistant à une rupture est généralement
calculée comme le produit du coefficient sismique (
!
) et de la masse de sol retenu derrière le mur,
∆
!
=
!
∙
!
, comme
développé par Wood (1973) et modifié par Whitman (1991). L’étude de Wood et la plupart de ses recherches ont été basées sur
l’hypothèse que le mur et le sol qu’il retient sont connectés à une base rigide. Cette hypothèse néglige le fait qu’en comparaison de la
masse mobilisée par un tremblement de terre, la taille du mur et du sol qu’il retient sont relativement petites. En d’autres termes,
même si le mur reste connecté à une base relativement rigide, la base subit certains déplacements durant un tremblement de terre. Des
désaccords existent sur la valeur de
!
par rapport à l’accélération maximale du sol (PGA). Dans cette étude, une série d’analyses aux
éléments finis élasto-plastiques pseudostatiques a été réalisée pour évaluer la validité de l’équation de Wood (1973) pour déterminer
les pressions sismiques latérales induites sur le pied du mur de soutènement et la relation entre
!
et PGA a été examinée en se basant
sur la loi de conservation des moments. Les résultats indiquent que l’augmentation de pression terrestre sismique agissant sur le mur
est une fonction de
!
et de la condition de support. Il est également établi qu’une valeur de
!
de 25% du PGA semble raisonnable
et également conservative pour la conception de structures normales.
KEYWORDS: earth pressure, restrained, seismic, non-yielding wall, pseudostatic seismic coefficient, peak ground acceleration
1
INTRODUCTION
Since the late 1920s, seismic earth pressure acting on retaining
walls has been widely studied by researchers. Okabe (1926)
pioneered the research by introducing pseudostatic force into
Coulomb earth pressure theory. Mononobe and Matsuo (1929)
finalized Okabe’s theory and established the well-known
Mononobe-Okabe (M-O) method, which continues to be widely
used in current practice despite many criticisms and its
limitations. Similar research and simplifications have been
conducted since then (Seed and Whitman, 1970). The M-O
method is based on an important assumption that the wall
structure displaces a sufficient amount to develop a fully plastic
stress state in the soil near the wall, and thus is generally
applied for cantilever walls. However, some wall structures,
such as massive gravity walls founded on rock or basement
walls or bridge abutments restrained on the top and bottom, do
not move sufficiently to mobilize the shear strength of the soil
and thus the M-O method cannot be directly applied. Motivated
by the lack of well-defined design procedures and design data
for evaluating seismic earth pressures on such wall structures,
Wood (1973) analyzed the response of a homogeneous linear
elastic soil trapped between two rigid walls connected to a rigid
base and obtained an equation for seismic earth pressure as
∆
!
=
!
∙
!
. Whitman (1991) suggested the value of
F
approximately equal to unity. While a great deal of additional
research has been performed since the 1970s (Veletsos and
Younan, 1994; Wu and Finn, 1999; Ostadan, 2004; Maleki and
Mahjoubi, 2010), Wood’s equation is still recommended by
various authorities (FEMA, 2003; FHWA, 2009) in current
practice.
Wood’s study and most of the research thenceforth (Ostadan,
1998, 2004; Maleki & Mahjoubi, 2010) were based on the
assumption that the wall and the retained soil are connected to a
rigid base. This assumption neglected the fact that, compared to
the mass mobilized by an earthquake, the size of the wall and its
retained soil are relatively small. In other words, even if the
wall is connected to a relatively rigid base, the base exhibits
certain movement during an earthquake event, and the wall will
also move together with the supporting base, even it is “locally”
restrained. This will certainly result in changes in earth
pressures on the back of the wall.
Another important issue in the seismic earth pressure
equations is the lack of clarity of the pseudostatic seismic
coefficient (
!
). Conflicts are even exhibited in the
specifications. For example, ASSHTO (2010) suggests
!
equal
to the half of PGA while the NCHRP report (Anderson et al.,
