2043
Active earth thrust on walls supporting granular soils: effect of wall movement
Pression active des terres sur des murs soutenant des sols granulaires: l’effet du mouvement du
mur
Loukidis D.
University of Cyprus, Cyprus
Salgado R.
Purdue University, USA
ABSTRACT: The methods currently used in the design practice of retaining walls supporting granular soils (sand, gravel, silt, and
their mixtures) assume that the soil friction angle and, consequently, the active earth pressure coefficient
K
A
are independent of wall
movement. However, the mobilized friction angle inside the retained soil in reality first reaches a peak value and then decreases
towards to the critical state value as shear strain increases with wall movement. This study aims to investigate the development and
evolution of the active earth pressure by modeling the soil mechanical behavior in a realistic way in a series of finite element analyses.
Based on the numerical results, an equation is proposed for the estimation of
K
A
as a function of the initial relative density and the
wall crest displacement.
RÉSUMÉ : Les méthodes actuellement utilisées dans la pratique de la conception des murs de soutènement supportant des sols
granulaires (sable, gravier, limon et leurs mélanges) supposent que l'angle de frottement du sol et, par conséquent, le coefficient de
pression active des terres
K
A
sont indépendantes du mouvement du mur. Toutefois, l'angle de frottement mobilisé à l'intérieur du sol
retenu atteint en réalité d'abord une valeur de pic, puis diminue vers la valeur d'état critique à mesure que la déformation en
cisaillement augmente avec le mouvement du mur. Cette étude vise à étudier le développement et l'évolution de la pression active des
terres par la modélisation du comportement mécanique des sols de manière réaliste dans une série d'analyses par éléments finis.
Sur la
base des résultats numériques
, une équation est proposée pour l'estimation de
K
A
en fonction de la densité relative initiale et le
déplacement en crête du mur.
KEYWORDS: retaining wall, active earth pressure, sands, finite element analysis.
1
INTRODUCTION
The active earth pressure is expressed as the product of the
vertical effective stress σ
v
in the retained soil mass or backfill
and the active earth pressure coefficient
K
A
. The earliest and
simplest methods for the calculation of the active earth pressure
for purely frictional soils are those based on the Coulomb and
Rankine theories. For a retained soil with horizontal free surface
and a vertical wall backface, Coulomb’s solution yields
2
A
2
cos
sin
sin
cos 1
cos
K
(1)
The Coulomb solution can be proven to be equivalent to a
rigorous limit analysis upper bound solution. It is also in good
agreement with other upper bound solutions (Chen 1975,
Soubra and Macuh 2002), as well as the lower bound solution
by Lancellotta (2002), with the differences not exceeding 7%.
Furthermore, these methods, which are currently used in
design practice, assume that
and, consequently, the active
earth pressure coefficient
K
A
are constant, i.e. their values do
not change as the wall moves. However, the value of the
mobilized friction angle in reality depends on a number of
factors, such as the current mean effective stress, and, most
importantly, the shear strain. Granular soils, unless in a very
loose state, are strain-softening materials, meaning that the
mobilized friction angle first reaches a peak value
p
and then
decreases towards to the critical state value
c
. Hence, the active
state developing inside the mass of the supported soil is a
function of the wall movement.
The goal of this study is to investigate the development and
evolution of the active earth pressure as the wall moves away
from the retained soil using finite element (FE) analysis. The
study focuses on retaining wall that are free to translate and
rotate, such as gravity walls, cantilever walls and self-supported
(cantilevered) sheet pile, secant pile or slurry walls. The
mechanical behavior of the soil is captured realistically using a
two-surface constitutive model based on critical state soil
mechanics.
2
FINITE ELEMENT METHODOLOGY
The FE analyses were performed using the code SNAC (Abbo
and Sloan 2000). A typical finite element mesh is shown in Fig.
1. The mesh consists of 8-noded, plane-strain quadrilateral
elements and includes the wall, the supported soil and the
foundation soil. The free surface of the supported soil is
horizontal and without surcharge. The wall has a rectangular
cross-section with width
B
and height
H
, and is modeled as a
linear elastic material with very large Young’s modulus so that
it can be considered rigid. The retaining wall is also embedded a
small distance
D
into the foundation soil. The analyses start
with the supported soil at rest (
K
0
state). No interface elements
are placed between the soil and the wall. As a consequence,
slippage between the wall and retained soil occurs due to the
formation inside the soil mass of a shear band parallel to the
wall backface. This roughness condition is realistic for walls
made out of concrete; however, this may not be the case for
sheet pile walls.
