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1. Introduction
Pile caps are an important structural element which transmits forc-
es of the superstructure to the infrastructure. According to Fusco
[3], pile cap’s structural behavior must be sufficiently rigid to allow
that its deformations do not affect the superstructure stresses nei-
ther the onsite foundation.
In the last decades, great advances in this area were achieved
with the development of the struts and ties model to describe pile
cap’s structural behavior. Since 1980’s, finite element software’s
evolution and structural monitoring allowed a deeper knowledge of
pile caps inner stresses and, hence, allowed the development of
less conservative and more realistic design models. Nowadays, it
is possible to analyze pile caps’ behavior in detail, observing stress
flow in the struts and ties, crack pattern, plastic strains, among
other relevant aspects.
Studies in this field have proved that the struts and ties model is the
best representation of the structural behavior of pile caps. The struts
and ties theory is the result of Blévot e Frémy’s [4] pioneer work,
which framework was the observation that most of the pile caps ruin
were due to a brittle collapse as a result of concrete splitting.
Adebar et al. [5] and Miguel [1] researches proved pile caps col-
lapse due to concrete splitting as a result of compressive stresses
expansion (cracking increase with concrete collapse) followed by
ties yielding.
Delalibera [6], through a statistical analysis of variance, deter-
mined four main variables that influence in the pile cap’s struts
stress flow and load bearing capacity, which are the column and
piles cross-section dimensions, external vertical load eccentricity
and pile caps height. In addition, through experimental and numeri-
cal models, [6] proved that the pile caps structural behavior is influ-
enced by column and piles cross-section dimensions, struts angle,
pile caps height and existence or not of splitting reinforcement.
In reference to pile caps design, most design codes recommend
deep beams, bending or truss models. In spite of that, pile caps are
volume structures that present discontinuity zones due to the non-
dissipation of local disturbances and, therefore, Bernoulli’s hypoth-
esis is not applied. In this particular case, Saint Venant principle is
applied. In pile caps, tensions are not uniform due to stresses con-
centration in the superior and inferior nodal zones which generates
a discontinuity zone (D-region) in all the element
s
. According to
Fusco [3], struts and ties model should be adopted to the elemen-
tary treatment of stresses distribution in the regularization zones
of structures subjected to Saint Venant principle. Thus, bending
theory and linear models do not correctly represent the behavior
of pile caps.
Su and Chandler [7] noted the lack of an established design mod-
el. The authors affirmed that, in the last decades, struts and tie
s
model has been one of the most popular and rational methods of
structural analysis not submitted to bending. And the main design
directives were given by national codes such as the Canadian [8],
Australian [9] and Neo Zeland [10] Standards and the CEB-FIP. In
the CEB-FIP:1973 [11] the procedures for the design of pile caps
are described and in the
fib-
Model:2010 [12] design procedures
are prescribed for structures or elements with discontinuities using
struts and tie models.
Despite that, each of the design code has its own safety factors and
different design methodologies. Brazilian ABNT NBR 6118:2007
[13] only mentions its preference to tridimensional struts and ties
models in relation of linear and non-tridimensional ones. The refer-
ences largely adopted in Brazil, according to Ramos [14] are the
strut and tie model and the CEB-FIP code.
Clarke [15] observed that ties bars anchorage is positively influ-
enced by struts confining action, which would dispense the use
of hooks. Studies conducted by Rausch et al. [16], Miguel [1] and
Delalibera [6] demonstrated that ties stresses are not constant, oc-
curring a significant reduction in the inferior nodal zones. More-
over, at the border of the ties the strains are close to zero. Buttignol
[17] has shown, through numerical analysis in pile caps with two
and three piles, that the ties stresses are not constant through the
bars and, at their borders, stresses were very low, dispensing the
use of hooks.
In addition, adherence is not a determinant factor to pile cap’s ul-
timate strength capacity, since ties bars slipping occur after pile
cap’s collapse. Clarke’s [15] experimental results have shown that
ties bars without hooks slipped only after the crushing of the struts.
Finally, splitting reinforcement can contribute to the increase of pile
cap’s ultimate strength capacity and to the control of cracking. Butt-
ignol [17] analyzed numerical models with splitting reinforcement
(steel bars disposed perpendicular to the struts in order to combat
tensile stresses and to resist concrete splitting) as proposed by
[6], demonstrating an increase in pile cap’s resistance, which pre-
sented high strains in the struts cross-section as a result of tensile
stresses action within this region.
1.1 Justification
Despite the advances on pile cap’s research in the last decades,
an analysis about the influence of the concrete compressive char-
acteristic strength in the structural behavior of pile caps is still
needed. There are few references about this matter which are con-
centrated in beams analysis.
According to Delalibera [6], an increase in pile cap’s stiffness in-
creases the element strength capacity. And the collapse of rigid
pile caps occurs by concrete splitting followed by struts crushing.
Therefore, it is preferable to increase pile cap’s height (stiffness
increment) than to increase concrete compressive strength.
Through numerical modeling of three-pile caps using the finite ele-
ment software ATENA 3D, this paper demonstrates that the varia-
tion on the concrete compressive strength (f
ck
) is not followed by
a significant gain in pile cap’s resistance. Moreover, high tensile
stresses were observed within the struts and in the nodal zones.
These results highlight the fact that in the case of a necessary
increase in the ultimate strength capacity of pile caps, a simple
increase in the concrete compressive strength will not result in a
consistent benefit. To obtain an increase in the load bearing capac-
ity, it will be necessary to adopt one of the hypotheses brought by
[6] and cited before.
To sum up, this paper has the merit of bringing to light a fundamen-
tal property of pile cap’s behavior, which must be taken in account
by designers and constructors.
2. Analysis method
The analysis was developed with numerical modeling of three-
pile caps with complementary reinforcement passing through
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IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 1
T. E.T. BUTTIGNOL | L.C. ALMEIDA