1963
Earth Pressure from Strip Footings on an Anchored Sheet Pile Wall
Poussée des terres provenant de semelles filantes sur un mur de palplanches ancré
Denver H., Kellezi L.
GEO-Danish Geotechnical Institute, Lyngby, Denmark
ABSTRACT : A strip footing is frequently situated near a sheet pile wall. Assessment of the extra pressure on the wall generated by a
footing causes theoretical problems for the designer. The distribution of this pressure depends in fact on many parameters. Besides the
location and magnitude of the load a characterzation of the soil and the wall is neccesary for a rational design. Furthermore, the
movement of the wall has a significant impact on the pressure. In this paper an anchored wall is investigated where the movement in
failure is a rotation about the anchor point. The problem is solved by means of different analytical methods compared with solutions
by finite element modeling applied to a number of representative examples. These comprise different strengths for the cohesion-less
soil and different load scenarios. After a discussion of the results a simple calculation procedures is proposed.
RÉSUMÉ : Une semelle filante est souvent située à proximité d'un mur de palplanches. L'évaluation de la pression supplémentaire sur
la paroi générée par la semelle provoque des problèmes théoriques pour le concepteur. La répartition de cette pression dépend en fait
de nombreux paramètres. Outre l'emplacement et l'ampleur de la charge, une caractérisation du sol et du mur est nécessaire pour une
conception rationnelle. De plus, tout deplacement de la paroi a un impact significatif sur la pression. Dans cet article, une paroi ancrée
est étudiée lorsque le déplacement amenant à une défaillance consiste en une inclinaison autour du point d'ancrage. Le problème est
résolu par le biais de différentes méthodes d'analyse que l’on compare aux solutions de modélisation d’éléments finis, appliquées à de
nombreux exemples représentatifs. Celles-ci comprennent différentes forces pour un sol sans cohésion ainsi que différentes
configurations de charge. Une simple procédure de calcul est proposée après la discussion des résultats.
KEYWORDS: Sheet pile wall, continuous footing, earth pressure, finite element method, sand, stress distribution.
1
INTRODUCTION
Sheet pile wall design methods in Europe generally rely on
simplified earth pressure theories where the failure mechanism
of the soil is in fact not compatible with the wall deflections.
The Danish design method of sheet pile walls is based on
Brinch Hansen’s earth pressure theory, which assumes plastic
behaviour for the wall and the soil. The computer program
SPOOKS, which is a product from GEO-Danish Geotechnical
Institute, is successfully used for sheet pile wall design in
Denmark and abroad. The program calculates the required
driving depth, the maximum bending moment and the anchor
force for a user defined failure mode of the wall and the
adjacent soil. The wall may be either anchored or free and either
hinged or fixed in an anchor point. In the limit state a yield
hinge in the wall with an ultimate positive moment may develop
below the anchor level.
When excavating close to an existing building the effect of
the partial distributed loads, from for example strip foundations
(two dimensional (2D) conditions), or plate foundations (three
dimensional (3D) conditions), are usually implemented in the
sheet pile wall plastic design by means of the elasticity theory
and the principle of superposition, where the extra earth
pressure simply is added to the plastic solution. It is however
not correct in the plastic design to separately calculate the active
earth pressures from partial distributed loads without taking into
account the active pressure from the unit weight of the soil.
The objective of the present paper is to supplement an earlier
investigation for a free wall, Denver & Kellezi (2011), with
establishment of an empirical relationship to estimate the extra
earth pressure on an anchored sheet pile wall from a strip load
behind the wall. This relationship is compared with solutions
from finite elements (FE) results. The additional pressure is
found as the difference between the combined pressure from
self weight of the soil and the strip footing and the pressure
from only the self weight. In an attempt to assess the additional
pressure on the wall, different approaches are investigated:
Analytical calculations by the theory of plasticity on a
suitable rupture figure.
Empirical solutions inspired by Coulomb’s theory.
Numerical modelling by the FE method.
2
GENERAL
The earth pressure calculation on a wall is here illustrated by the
Danish method denoted as Earth Pressure Calculation. This
method has been proposed by J. B. Hansen (1953) and is
extensively used in Denmark. The pressure on the wall (
e
) is
calculated as a sum of three terms as given in equation (1).
e
=
γ’d
K
γ
+
qK
p
+ (
cK
c
)
(1)
These terms and the other parameters used in the calculation
are:
γ
’
the effective unit weight of the soil;
K
the earth pressure
coefficient (different for the three terms);
c
the cohesion of the
soil;
p
the surface load behind the wall, and
d
the depth along
the wall from the soil surface. The last term is enclosed in
parenthesis as this paper deals only with frictional soil.
In the Danish method the wall is considered composed of
several rigid parts interconnected by yield hinges. Each part is
assumed to rotate about a point and the earth pressure
coefficients are functions of the position of this point and the
direction of rotation (besides the friction angle of the soil,
φ
).
Examples of anchored walls with yield hinges are shown in
Figure 1, and examples of rupture figures used for calculation of
K
are shown in Figure 3. The result of each calculation is the
total force on the wall and the point of application. The normal
component of this force (
E
) is distributed along the wall. A part
of
E
is applied near the top as a Prandtl rupture zone.
