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Seismic bearing capacity of strip footings near cohesive slopes using lower bound
limit analysis
Capacité portante séismique des fondations superficielles en bord des talus purement cohérents ;
une évaluation par défaut suivant la méthode du calcul à la rupture
Farzaneh O., Mofidi J.
School of Civil Engineering, University College of Engineering, University of Tehran, Tehran, Iran.
Askari F.
International Institute of Earthquake Engineering and Seismology, Tehran, Iran.
ABSTRACT: A finite element lower bound method together with linear programming technique are used to determine the seismic
bearing capacity of strip footings adjacent to purely cohesive slopes. The pseudo-static approach is utilized and the earthquake forces
consist of a horizontal load applied to the foundation and the inertia of the soil mass. It is assumed that the soil obeys the associated
flow rule and undrained behavior of soil under seismic condition can be modeled by Tresca yield criterion. The normalized seismic
bearing capacity of footing is considered as a function of dimensionless parameters which affect the stability of footing-on-slope
system. The effect of seismic coefficient,
k
h
, on bearing capacity of so-called system is investigated and design charts are presented
for a rational range of parameters.
RÉSUMÉ : L’approche par défaut de la théorie du calcul à la rupture, basée sur un modèle des éléments finis et la technique de la
programmation linéaire, a été utilisée pour évaluer la capacité portante sismique des semelles filantes en bord des talus. Le sol est
purement cohérent, obéissant au critère de plasticité de Tresca. Les sollicitations sismiques, étant par hypothèses pseudo-statiques,
sont les suivantes; une composante tangentielle s’ajoutant à la force normale de fondation et une composante horizontale de force
volumique appliquée au sol. La capacité portante normalisée , en fonction des paramètres du problème à été calculée et sa réduction
en fonction du coefficient séismique,
k
h
, a été présentée sous forme des diagrammes sans dimensions pour de larges gammes des
paramètres concernés .
KEYWORDS:Seismic bearing capacity, Strip footing, Slope, Lower bound, Linear programming.
1 INTRODUCTION
Some of engineering structures require to be built near a slope,
particularly in mountainous and hilly regions, so, stability of
these structures is one of the important problems of
geotechnical engineering. Bearing capacity of strip footings
near slopes has been investigated by numerous researchers but
most of these researches include the static condition and there
are only a few studies about stability of strip footings near
slopes under earthquake condition.
Available analytical limit state solutions for seismic bearing
capacity of strip footings near slopes include upper bound
method (Sawada et al. 1994, Askari and Farzaneh 2003), limit
equilibrium method (Sarma and Chen 1996, Sarma 1999,
Kumar and Kumar 2003, Choudhury and SubbaRao 2006) and
method of characteristics (Kumar and Rao 2003, Jahanandish
and Arvin 2008). Limit analysis methods (i.e. upper and lower
bounds) are direct approaches of classical plasticity theory for
calculation of collapse load in stability problems. Static and
kinematic approach of limit analysis lead to lower and upper
estimation of true collapse load respectively.
As lower bound solution gives a load which is below the
exact ultimate load, it is at safe side and therefore more
appealing. As there was no lower bound solution in the
literature, the current paper is presented to estimate seismic
bearing capacity of strip footings near cohesive slopes by lower
bound method. A brief theory and formulation of finite element
lower bound method is presented and more details can be found
in relevant references and won’t be covered here. It should be
mentioned that a MATLAB code has been provided by the
authors for determination of seismic bearing capacity of strip
footings near slopes.
2 PROBLEM DEFINITION
The problem of seismic bearing capacity of a strip footing
adjacent to a purely cohesive slope is shown in Figure 1.
Geometric parameters include the slope angle
, distance of
footing from the slope
a
, footing width
B
and height of the slope
H
. It is assumed that the soil obeys the associated flow rule and
Tresca yield criterion and has the undrained shear strength of
c
u
and unit weight of
.The base of the foundation is assumed
rough. The horizontal acceleration coefficient of earthquake (
k
h
)
is considered outward the slope which is more critical and the
vertical acceleration of earthquake is ignored in analyses.
Figure 1. Problem parameters
The approach of this paper is to consider the normalized
limit pressure as a function of dimensionless parameters
affecting the stability of the footing-on-slope system and can be
stated as:
) ,
,
, , (
h
u
k
c
B
H
B
aβf
p
(1)
