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IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 2
Three-dimensional analysis of two-pile caps
not submitted to flexure. The principal design guidelines are pro-
vided by an array of codes such as the Canadian National Code
(CSA Standard A23.3-94), the Australian National Code (AS3600-
1994), the New Zealand National Code (NZS3101: Part2: 1995)
and the FIB Model Code 1990. Despite that, each code has its own
materials and loading safety factors and different design method-
ologies. In particular the NBR-6118: 2007 [11] only mentions the
preference for tridimensional strut and tie models in spite of linear
and non-tridimensional models.
1.1 Justification
Researches have been evolving to a consensus that the struts
and tie model is assumed to be the most accurate method to
represent the structural behavior of pile caps. Notwithstanding,
there still remains a dissent in the literature, for example, in the
subject of the configuration of compressive struts and distribution
of stresses inside the specimen. Delalibera [1] affirms that “there
is a lack of knowledge on the geometrical shape of compressive
stresses that forms the struts in pile caps submitted to axial and
eccentric loads” and “numerical analysis of rigid pile caps have
demonstrated that the distribution of stress in the struts on the
surface of piles is not uniform, demanding an adaptation to the
chosen hypothesis”.
Therefore, this paper has the main objective to verify the behav-
ior of reinforced concrete pile caps with two piles by comparing,
on one side, Delalibera’s [1] experimental results and, on the
other side, non-linear numerical analysis results. Experimental
and numerical results comparison has the merit to expose dis-
crepancies and convergences between them, and, hence, vali-
dates the finite elements method software analysis. Moreover,
numerical analysis contributes to the corroboration of the pile
caps theoretical fundaments.
The crack pattern is analyzed in this paper, including initial crack
formation in Stadium II and its propagation within the structure,
besides stress and strain distribution in pile caps and steel bars. In
addition, the load carrying capacity and pile caps collapse by con-
crete splitting and compressive struts crushing in the nodal zones
is verified.
2. Analysis Method
A numerical analysis of five pile caps with two piles is developed,
as described on Table 1. For that, the finite element software AT-
ENA 3D [2], from Cervenka Consulting, was used. The pile caps
perpendicular tension stresses within the structure) with the forma-
tion of several cracks before the collapse. In relation to anchorage,
Blévot & Frémy [3] proved that the reinforcing bar slipping of ridged
steel bars without hooks only occurs after the strut crushes.
Mautoni [4] noted that most pile caps were subjected to a fragile
collapse by struts splitting in nodal zones. Before the structural
collapse the cracks ran parallel to the struts. This fact was also
noted in experimental tests conducted by Clarke [5] and Sabnis &
Gogate [6].
Studying the strut and tie model, Adebar et. al. [7] proved that the
collapse of pile caps is due to the concrete splitting with the expan-
sion of compressive stresses (concrete crushing and increase of
cracks) and the subsequent yielding of ties rebars.
Delalibera & Giongo [8] demonstrated the formation of cracks par-
allel to the struts in pile cap models. The authors verify that pile
caps collapse by concrete splitting and crushing in the superior
nodal zone (C-C-C), on the interface between the column and the
pile cap, and in inferior nodal zones (C-C-T), on the interface be-
tween the piles and the pile cap. Moreover, the authors support
that in the design of pile caps the column’s forces are equally di-
vided in two halves at the cross-section between the column and
the pile cap. Reinforcing bars adherence analysis conducted by
Delalibera [1] demonstrated that there is no tie steel bar slipping
due to struts compressive stresses favorable contribution. This re-
duces tensile stress values and significantly diminishes reinforcing
bar strains in inferior nodal zones.
According to Souza et. al. [9] it is important to mention that there is
not yet a general procedure accepted to pile caps design. Despite
the existence of several design procedures, there is still a large
difference among them. Most of national codes recommend deep
beams, bending beams or truss models for the design pile caps.
Notwithstanding, Souza et. al. [9] demonstrated that many pile
caps designed to flexural collapse presented a fragile rupture by
shear. The authors also attested that pile caps are submitted to a
complex tridimensional non-linear strain distribution nominated as
D-region. In general, D-regions are developed due to static order
(caused by load actions) and geometric disturbances (caused by
abrupt geometric changes). Particularly in the case of pile caps,
all the structure behaves as a D-region due to the concentration of
stresses both in the superior and inferior sections caused by the
intersection between the column and the pile cap, and between the
pile and the pile cap.
It is worth mentioning that in the last decades, according to Su &
Chandler [10], struts and tie models have been one of the most
popular and rational methods of structural analysis of structures
Table 2 – Concrete properties
Pile caps
Piles and columns
Poisson’s ratio (
n
)
0,2
0,2
Specific Fracture Energy (G )
F
2
79 J/m
2
116 J/m
Tension Stiffening Factor (c )
ts
0,40
0,40
Modulus of Elasticity (E )
c
30.320 MPa
41.060 MPa
Characteristic Compressive Strength (f
ck
)
40 MPa
73 MPa
Ultimate Concrete Tensile Strength (f
tk
)
3,2 MPa
4,6 MPa