Punching Behaviour of Reinforced Concrete Footings at Testing and According to Eurocode 2 and fib Model Code 2010
International Journal of Concrete Structures and Materials
Punching Behaviour of Reinforced Concrete Footings at Testing and According to Eurocode 2 and fib Model Code 2010
Zoran Bonic´ 0
Neboj sˇa Davidovic´ 0
Todor Vacev 0
Nikola Romic´ 0
Elefterija Zlatanovic´ 0
Jelena Savic´ 0
0 Faculty of Civil Engineering and Architecture, University of Nisˇ , Aleksandra Medvedeva 14, Nisˇ , Serbia
Punching shear resistance of column footings and foundation slabs varies significantly in different standards. The reason for this is because standards define differently the position of the critical perimeter in which the punching shear resistance should be determined, and quantify the influences of the main parameters like effective depth, shear slenderness, compressive strength of concrete, longitudinal reinforcement ratio and tension yield stress of reinforcement in different ways. In order to quantify the level of safety in Eurocode 2 and in fib MC 2010, their design results are compared with the test results of the series of footings tested in completely realistic boundary conditions in terms of the subgrade soil. Besides the performed tests results, the analysis of the other investigations of the footing punching rested on the real soil is also included. Thus was obtained the answer to the question how individual characteristics of the footings and of the soil affect the punching bearing resistance and how accurately Eurocode 2 and fib MC 2010 predict the bearing capacity of the tested column footings. At the end, based on the test results and on the tests of others, and on and performed numerical analyses, a possible modification of Eurocode 2 in the field of reinforced concrete footing was proposed.
column footing; experiment; punching; reinforced concrete; Eurocode 2; fib MC 2010
Shallow foundations transmit structural loads to the
nearsurface soil. Column footings and foundation slabs are main
types of shallow foundations and structural members which
support columns. Control of punching of the columns
through those footings is mandatory part of the design of
reinforced concrete footings exposed to notable concentrated
forces through the columns. Complexity of the stress state in
the footing rested on deformable ground requires, along with
a detailed theoretical analysis, some experimental
investigations in order to draw correct conclusions and to confirm
the introduced theoretical postulates.
Behaviour of column footings and foundation slabs under
load depends in general case on the soil characteristics, type
and characteristics of the material of the footing and
intensity of the load. Typically, high concentrated loads in the
columns may lead to the abrupt failure of those footings—
punching the column through the footing.
Although foundations have essential influence on the
behaviour of the structure and to the soil, standards do not
pay enough attention to their analysis, and in some standards
the specific details of the foundation analysis are not even
2. Research Background
Concentrated load often causes high shear stresses in the
loading zone, which may lead to the nonductile, sudden
and brittle punching failure that was widely investigated at
different kinds of structures, and especially at punching of
flat slabs (Belletti et al. 2015a; Bonic´ et al. 2010; Brooms
2005; Fe´de´ration Internationale du Be´ton (fib) 2010;
Hallgren and Bjerke 2002; Hallgren et al. 1998; Halvonik
et al. 2016; Hegger et al. 2006, 2007, 2009;
Husain et al.
; Kabir et al. 2016;
Kee and Nam 2015
; Kumer and
Hoque 2015; Menetrey 2002; Muttoni and Schwartz 1991;
Muttoni 2008; Muttoni and Ferna´ndez 2008, 2012;
/2003); Pbdrby 1967; Siburg and Hegger 2014;
Siburg et al. 2014; Sim o˜es et al. 2016a, b;
Urban et al. 2013
; Vacev et al. 2015). There
are several models of punching of slabs and footings and
calculation methods but none of them was generally
accepted, so there exist significant differences regarding the
determination of the position of the critical control
perimeter in which the control of the of punching should be
conducted, as well as regarding the quantification of the
influences of the main parameters that affect the punching.
In the majority of standards and proposed design models a
unique control perimeter at certain distance from the
column faces is adopted. Thereat this distance may be
varied significantly depending on the standard and
proposed design model. Another way of determination of the
critical perimeter is represented in the Eurocode 2. Here the
position of the critical control perimeter is not constant, but
the checking of the punching shear resistance of the
concrete is conducted at several perimeters within the zone of
2d from the column edges, where d is effective depth of
the footing section. Thereat the control perimeter which
gives the lowest value of the punching resistance represents
the critical perimeter.
Complexity of behaviour of the soil and complexity of
the subsoil-structure interaction lead to the fact that in
majority of the standards is adopted the empirical method
of design of the punching shear resistance of reinforced
footings and reinforced foundation slabs. The fact that the
number of the tested footings is considerably lower than
the number of tested flat slabs lead to the situation that,
due to the similarity of the problem, for the design of the
punching shear resistance of reinforced concrete footings
and reinforced concrete foundation slabs take empirical
expressions obtained at the punching tests of reinforced
concrete flat slabs. Overview of the research of footings
done until now, according to the available literature data,
is presented in Table 1. Even when the punching tests are
conducted on footings, for the reason of simplification of
organization of the experiment, the soil was in most cases
simulated by hydraulic jacks, by steel springs, and by line
resting, which produces the same effect as uniform
reactive load of the soil. Punching investigation of the footing
rested on real soil was done in practice only by Hegger
et al. (2006, 2007, 2009)—in a sandbox, by Rivkin
—on sand and clay in situ, and by
and Hoque (2015)
on stabilized soil.
In the paper is treated the influence of the main parameters
to the punching shear resistance and punching behaviour of
the reinforced concrete footings and foundation slabs, like:
compressive strength of concrete, flexural reinforcement
ratio, shear slenderness of the footing, soil reactive pressure
distribution, stiffness of the footing-soil system, and
mechanism of footing punching.
The key result of the conducted parametric study will be
determination of the factors whose influence is dominant in
assessment of column footing punching.
3. Experimental Investigation
For experimental testing program, conducted from 2009 to
2014, in situ specimens were provided along with subgrade
soil preparation in order to achieve required geotechnical
properties. Specimens were column footings with defined
dimensions and characteristics of concrete and
reinforcement. Figure 1 represents the scheme of the experimental
As one may see from Fig. 1, a steel frame for the
experimental purposes was made. Its role is reception of the
hydraulic jack reactive force. The frame is a steel space
structure consisted of a tin plate bottom and a space frame (a
pair of vertical rods, two pairs of struts and strong horizontal
crossbeam. The frame construction, as well as its dimensions
enable forming of failure surfaces in the soil under the
footing, in case of reaching sufficient value of force in the
column. In this experiment, a step further has been done in
respect to the earlier laboratory experiments documented in
literature, because the footing testing was conducted within
the completely realistic boundary conditions in terms of the
soil. Simultaneously, comparison and verification of the
a During the first test, the column stub failed at the load of 1001 kN. After a new column was constructed, the footing was punched at load of
earlier tests done in laboratories (taken from the literature),
with these in situ tests was provided.
For the adopted conditions of the footing and soil (data
given further in the paper) a soil bearing capacity analyses
were done according to Eurocode 7. Thereat, it was adopted
that the safety factors are equal to one. The internal friction
angle of the soil u0 was adopted based on recommendations
from the scientific literature
. As this angle is
increasing with the increase of the soil compaction, and
considering that the soil compaction increased during the
footing loading, the assessment of the ultimate bearing
capacity of the soil was performed for different values in the
range u0 = 36–40 . For these values of u0 and for cohesion
c0 = 0, the ultimate axial forces in the column were in the
range of 215.8–429.0 kN. Since the achieved punching
forces during the experiment were significantly higher (even
1050 kN), and soil failure under the footing was not
registered, one may conclude that Eurocode 7 gives conservative
results for the footings encompassed by this experiment.
All tested footings failed by punching of the column
through the foundation body, and measured forces are given
in Table 2.
The experiment was performed by digging a pit with
layout dimensions 4 9 5 m, and depth of 3 m, in which the
prepared steel frame was lowered to the bottom (Figs. 2, 3).
The excavated material was replaced with river aggregate of
controlled density and size distribution (Fig. 4). Thus
prepared mixture was embedded into the 30 cm thick layers,
and the compaction of each layer was done by vibrating
plate. After the compaction of each layer, evaluation of
compaction was done by circular plate load test and by
dynamic test with light falling weight device (Fig. 5). The
measured mean values of the modulus of compressibility in
the layers were in the range of 43.3–66.7 MPa. Also,
compaction of the top layer of subgrade soil was controlled
before testing of each footing, and these values were in the
range of 37.5–76.7 MPa (Table 2), and they correspond to
normal compaction of subgrade soil.
Footing was loaded by hydraulic jack with axis-symmetric
vertical force until the occurring of punching of the footing
(Figs. 6, 7). The adopted dimensions of the specimens—
precast column footings were 85 9 85 cm in layout (Fig. 8).
The selected footing dimensions correspond in layout to the
experiments of Hallgren and Hegger
(Hallgren and Bjerke
2002; Hallgren et al. 1998; Hegger et al. 2006, 2007; 2009)
(for the purpose of result comparison). The footing depths
were 12.5–20.0 cm and the diameters of the applied steel
reinforcing bars were Ø8 and Ø8.5 mm. The reinforcement
ratio of the footings was ranging from 0.27 to 0.91%. The
properties of the used steel were determined on three
samples. The obtained mean values were as follows: tensile
strength ftm = 536–653 MPa and yield fym = 477 and
For the construction of the footings a three-fraction
concrete with maximum aggregate size of 16 mm and standard
Portland cement were used. Concrete compressive strength
was obtained at the time of testing using three cube
specimens with dimension of 15 cm and one standard cylinder
specimen, and all averaged values were converted to a
standard cylinder. Mean values for all specimens are given in
4. Testing Procedure
The specimens (precast footings) were placed on the soil
surface and loaded by vertical centric force applied by a
hydraulic jack positioned between the crossbeam and the
footing column stub (Figs. 6, 7). Load increments were set at
approximately 50 kN. The load was kept constant at every
step until the subgrade soil consolidation finished for the
applied load, which was registered by observing the process
of vertical displacements at the points on the footing corners
and on the column stub. During the experiment, the
following parameters were measured every second: strains in
the reinforcement and in the concrete of the footings, vertical
displacements of the points on the footing corners and on the
column stub, intensity of the applied force during loading,
and value of the contact pressures in the subgrade soil.
Applied force was measured by dynamometer HBM RTN—
C3 (Fig. 7), and vertical displacements of the corner and
column stub were measured by using linear variable
differential transformer (LVDT) gauges (Fig. 7). During the
testing, the contact soil pressure was measured by soil pressure
cells Ace Instruments with diameter of 100 mm and capacity
of 3.0 MPa (Fig. 9).
5. Comparison of the Test Results with the Eurocode 2
For the purpose of mutual comparison of the results from
the performed experimental investigations with the results of
the punching analysis given by the up-to-date standards, the
Eurocode 2 (2008) was used. In this standard the punching
shear resistance should be checked at the column periphery
and within the basic control perimeter at a distance of
aEC2 ¼ 2:0d from the column face, where d is the effective
depth. This document does not prescribe explicitly the
control perimeter that should be adopted as governing for the
footings (distance aEC2 in the expression (1)), but
recommends checking of different perimeters at distance smaller
then 2.0d from the column face. The lowest value of the
resistance found in this way governs the design (Fig. 10).
According to the Eurocode 2 the punching shear resistance
of the concrete, vRd at distance aEC2\2:0d from the
periphery of the loaded area is calculated as:
vRd ¼ CRd;c k ð100 ql fck Þ
where aEC2 is the distance from the periphery of the loaded
area to the control perimeter considered, determined
iteratively, CRd;c ¼ 0:18=cC the empirical factor with cC being
tqheffiffiffiffimffiaterial resistance factor for concrete (1.5), k ¼ 1 þ
2d00 2:0 (d in mm) the size effect factor of effective
depth, fck the characteristic cylinder compressive concrete
strength, ql the flexural reinforcement ratio, vmin ¼ 0:035
k3=2 fc1k=2 the minimal punching shear capacity, d the
effective depth of a slab (footing).
Eurocode 2 allows reduction of the punching force for the
part of the reactive pressures under the punching body, so for
a concentrated load the net applied shear force that causes
the punching of the column through the foundation,VEd;red ;
is given by the expression valid for uniformly distributed
stresses in the subgrade soil:
VEd;red ¼ VEd
where VEd is the column load, rn the effective soil pressure
(without the influence of the self-weight of the footing)
within the control perimeter considered, A0 the area within
the control perimeter considered.
Based on that, after transformations, column load VEd is:
VEd ¼ VEd;red A
A0 ¼ 1 AA0
where A is the area within the base of the footing.
Eurocode 2 defines the shape of the control perimeter
(Fig. 10a). Position of the most unfavourable control
perimeter (denoted as a = acr) within the basic control
perimeter has to be always determined by iterative
procedure. After the perimeter ucr (acr) and its surface area A0 are
determined, the net applied shear capacity can be calculated
c/d, gives the relationship acr/d (according to the diagram in
Fig. 10b). In most cases value acr = aEC2 is less than 2d,
which means that the slope of the punching body of the
footings is steeper than the slope of the slabs.
Also, Eurocode 2 limits maximum punching shear
resistance of the footing vRd;max (at the column periphery with
perimeter u0) is limited to:
vRd;max ¼ 0:4 m fcd
vRd;max ¼ 16
where v ¼ 0:6 1 2f5ck0 is the factor accounting for the
strength reduction of concrete compression struts in cracked
concrete due to lateral tension stresses, fcd ¼ acc fck =cC the
design concrete compressive strength with acc = 1.0 being a
coefficient taking account for long-term effects.
The smaller value from (1) and (5) governs the design.
Hegger et al. (2006)
, this equation
significantly overestimates the maximum punching shear capacity
for higher concrete classes. To overcome this problem, a new
equation for the assessment of vRd;max at the column
periphery of the loaded area with a length of u0 (instead
Eq. (5)) is proposed by Hegger
(Halvonik et al. 2016)
where vRd;c ¼ CRd;c k ð100 ql fck Þ1=3. Certainly, the
applied shear force can be reduced only by the effective soil
pressure within the column perimeter u0.
In order to indicate the significance of the control
perimeter when using the expression (1), a comparative
calculation of punching of the tested footings was carried out
according to the expression (1), for the cases when:
The basic control perimeter is at the distance aEC2 ¼
2:0d from the column edge (column 7, Table 3—just as
The critical control perimeter is equalled to critical
control perimeter aEC2 ¼ acr which gives minimal
punching force (column 9, Table 3)
The critical control perimeter is at the distance obtained
using the diagram from Fig. 10b), (column 11, Table 3).
In these calculations, for the purpose of comparison with
the test results, all material and strength reduction factors
incorporated in the Eurocode 2 equations were taken as
unity. Based on that, the obtained results are given in
Table 3. Besides that, specified calculation was also
VRd ¼ vRd ucr d
Additionally, in the comments to the Eurocode 2, in the
European Concrete Platform—ECP (2008), there are
instructions for determination of the position of the critical
perimeter and recommendations for using of a special
diagram obtained using Eq. (1), but without the minimal value
vmin, and considering that CRd,c = 0.12. These directions for
the ratio of the footing length to the column length l/c and
for the ratio of the column length to the effective slab depth
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performed for the remained footings rested on real ground,
and tested until punching (from Table 2).
Using the expression (4), for the control perimeters that
are distant from the column face (i.e., where aEC2 2:0d),
one gets high values for area within the control perimeter A0,
and consequently high values for the punching capacity of
the footing, VEd, according Eq. (3), (Bonic et al., column 7,
footing F1 and Hegger et al., column 7, footings DF8 and
DF10). Also, if one would adopt for the control perimeter
the distance of 2.0d from the column edge, then the basis of
the punching body could be greater than the footing base, in
case of footings with smaller dimensions in layout and
relatively high values for d, Considering that the column force
is subtracted by the part of the reaction encompassed by
control perimeter, the governing force for the control of
punching would be very low. Moreover, there may be cases
in which the control perimeter is obtained out of the footing
layout, which would lead to a situation that the governing
punching force is negative (Hegger et al., column 7, footings
DF4–DF7). Because of that, the assessment of the column
footing punching in the basic perimeter at distance aEC2
2:0d regarding the column face (Table 3, columns 7 and 8),
is given just as an illustration, and it should not be applied in
Recommendations based on the ECP (2008), (Fig. 10b,
columns 11 and 12 in Table 3) give almost the same results
as the calculation in the columns 9 and 10, (which was quite
as expected, because the diagram used to determine the
position of the control section for the calculation of columns
11 and 12 was based on Eq. (1)). For the purpose of finding
the minimal punching force using of these diagrams instead
of punching control in several perimeters can be
One may conclude from columns 4 and 9 that for shear
slenderness ratios, e.g., a=d 2:5 one gets control
perimeters at the distance acr d from the column edge, which
corresponds to the slope of the punching body of 45 . For
the values of the ratio a/d B 2.5 from the column 4, one gets
ratios acr/d B 1 from the column 9, while for higher values
of the ratio a/d one gets ratios acr/d [ 1. This corresponds to
the conclusions in the other experimental investigations of
footings (done with surface type supports and in laboratory
(Hegger et al. 2006, 2007, 2009; Siburg and
Hegger 2014; Sim o˜es et al. 2016)
where it was concluded
that the slope angle of the punching body towards the
horizontal plane decreases with increased slenderness of the
footing, which corresponds to the results of the experiment,
and may be seen in Fig. 11. From Fig. 11 one may clearly
notice that this angle changes with the increase of the
effective depth of the footings, so for the footing F3 this
angle amounts to around 35 , and for the footings with the
greater effective depth, F2 and F1, the angle is
approximately 45 .
Results in Table 3 confirm the assumption given in
Halvonik et al. (2016)
that position o the critical control
perimeter, that is, the ratio acr/d does not depend of the other
parameters, which affect the punching shear resistance of
column footings, like the compressive strength of concrete
and flexural reinforcement ratio, but only from the shear
slenderness of the footing—a/d. Because of that, the
following theoretical analysis of the dependence of the ratio
acr/d on the shear slenderness of the footing (a/d) is
conducted (Fig. 12).
For the various control perimeters, that is, for different
values of a and ratio a/d the following theoretical analysis
was done, according to
Halvonik et al. (2016)
: the reduced
punching shear force VEd,red (a) of various control perimeters
was calculated, and as a governing value was adopted the
minimum value of VEd,red (a). In assessment of the VEd, red
(a) the upward force within assumed control perimeter at
distance ‘‘a’’ due to the reactive soil pressure was subtracted.
A uniformly distributed soil pressure under the footings was
assumed. Thus was obtained the dependence of the ratio acr/
d on the ratio a/d, which is presented in the diagram in
Fig. 13. The calculation is conducted for common depths of
pad foundations and foundation slabs, that is, for
d = 100–800 mm.
On the diagram in Fig. 13 are drawn the ratios acr/d and a/
d for 50 experimentally investigated footings, according to
Halvonik et al. (2016)
, which were not rested on real soil.
The same ratios are entered for the footings which were
rested on real soil in experiments, too.
From the diagram one may conclude that the theoretically
calculated values show good agreement with the
Fig. 12 Relation between acr/d and shear slenderness a/
d and comparison with experimental results.
experimental results, which confirms the correctness of the
calculation of the position of the critical control perimeter in
the standard EC2.
In further analyses the punching force of the footing F1
was not taken into account, because in this footing stub
failure occurred at force value of 1001 kN. After making a
new column, the footing was punched at force value of
6. Comparison of the Test Results with the fib MC 2010
International Organization fib has introduced a new
document (Model Code 2010) with new model for the
assessment of punching shear resistance of flat slabs and
foundations. This physical model is based on the Critical
shear crack theory (CSCT) and it has been calibrated by
large number of experiments on isolated flat slab elements,
but also can be used for column footings and foundation
slabs. The first model based on Critical shear crack theory
has been developed and later refined by Muttoni and
(Muttoni and Schwartz 1991; Muttoni 2008;
Muttoni and Ferna´ndez 2008, 2012)
, and later it was subject of
numerous studies and analyses
(Belletti et al. 2015a;
Halvonik et al. 2016; Siburg et al. 2014; Simo˜ es et al. 2016)
This model determines the design punching shear force, VEd,
and design punching shear resistance, VRd,c without
punching shear reinforcement by expression:
f ck b0d
VRd;c ¼ kw cC
where fck is the characteristic cylinder compressive concrete
strength, d the effective depth of footing, cC the material
safety factor for concrete (1.5), b0 the critical perimeter
length is determined as b0 = keb1,red where factor ke
considers a non-rotationally symmetric shear force
distribution, set to ke = 0.9 for inner columns and b1,red is
perimeter length at distance 0.5d from the column face. As
well as the Eurocode 2, the fib MC 2010 also allows for
reduction of the punching force for the part of the effective
reactive pressures inside the critical perimeter b0, e.g.
DVEd = A0.5d rgd. kw is the parameter which depends on
the rotations of the slab around the support region outside
the critical shear crack w (in radians), and calculated as
with factor kdg (effect of the maximum aggregate grain size
dg) defined as kdg = 32/(16 ? dg) C 0.75.
The angle of rotation of the slab w can be obtained
experimentally or using some of the proposed theoretical
expressions according to MC 2010. Application of a specific
theoretical expression depends on the complexity of the
concrete design case, so one may tell four levels of
approximation: LoA I–LoA IV, with increasing of the
exactness of determination of the rotation w. As LoA
increases, so the calculated slab rotations generally decrease,
leading to higher punching shear capacities.
6.1 LoA I
Level of Approximation I is suitable for predesign or
initial sizing of structural elements, where a conservative
calculation method is acceptable (Fe´de´ration Internationale
du Be´ton (fib) 2010). According to
Siburg et al. (2014)
I approach can achieve a reliable estimate of the punching
shear resistance by assuming complete utilisation of the
flexural reinforcement over the column (mSd = mRd). Large
crack widths and large slab rotations are presumed. For LoA
I rotation of the slab is defined as:
w ¼ 1:5 rs d fydEs
where Es is the Young’s modulus of the flexural
reinforcement, fyd the design value of tension yield stress of
reinforcement, rs the distance between the column axis and
position where the radial bending moment is equal to zero
and can be estimated as 0.22L (L = max. span of slab). For
footings, the position where the radial bending moment
becomes zero can be assumed to be at the edge of the footing
if the flexural stiffness of the footing can be regarded as
(Siburg et al. 2014)
6.2 LoA II
In slabs where significant bending moment redistributions
are considered for design of the bending reinforcement, the
slab rotation can be calculated as:
w ¼ 1:5 rs d fydEs
where msd is the average bending moment per unit length in
the support strip of the column, mRd the design average
flexural strength per unit length in the support strip.
Bending moment inside the column strip can be estimated
with msd = VEd/8. The value for rs can be adopted as the one
for level I of approximation.
The rotation of a flat slab has to be calculated along two
principal directions of the slab. The maximum rotation is
governing for punching shear capacity. This equation also
applies for slabs where the flexural reinforcement is increased
in columns in order to increase their punching shear capacity.
w ¼ 1:2 rs d fydEs
rs is calculated for the flat slab using a linear elastic
msd is calculated from a linear elastic (uncracked) model,
as the average value of bending moment in the support strip.
6.4 LoA IV
The rotation w can be calculated on the basis of a
nonlinear analysis of the structure and with full account of
cracking, tension-stiffening effects, yielding of the
reinforcement and any other non-linear actions relevant to
provide an accurate assessment of the structure. This method is
very complex and limited to special cases.
In Table 5 is given calculation of shear capacity according
to fib MC 2010 model for the same footings that were
calculated according to Eurocode 2 in Table 3, that is, for the
footing rested on real ground, and tested until punching
(from Table 1).
Calculation is conducted for the first two levels of
approximation, that is, for LoA I and LoA II (columns 9 and
11 respectively). Like in Table 3, in these calculations, all
material and strength reduction factors incorporated in the fib
MC 2010 equations were taken as unity for the purpose of
comparison with the test results (column 1).
Comparison of results obtained according to LoA I and
LoA II and obtained by testing is given in the columns 10
and 12 respectively. Data from these columns indicate that
approximation LoA II gives results which are much closer to
the test results than approximation LoA I. This was expected
because approximation LoA I is intended for predesign or
initial sizing of structural elements.
From the columns 12 (Tables 3, 4) one may notice that,
generally speaking, results obtained by fib MC 2010 model
are better compared with the Eurocode 2, because almost all
values of the ratio Vtest/VR-Lo2 for fib MC 2010 model are
more conservative, i.e., greater than 1.0.
One may also conclude that, according to the quality of
prediction of the punching shear resistance, obtained results
can be divided into two groups. Into the first group fall the
footings with effective depths d lower than 150 mm
(footings from the series Bonic et al. and Rivkin) for which fib
MC 2010 model gives notably more conservative results
regarding the Eurocode 2, because it significantly
underestimates the punching shear resistance of the tested footings.
Into the second group fall the footings with effective depths
d higher than 150 mm (footings from the series Hegger et al.
and Kumer, Shill, and Hoque) for which fib MC 2010 gives
better results compared to the Eurocode 2, i.e., values of the
ratio Vtest/VR-Lo2 are greater than 1.0 or very close to 1.0.
Considering that the effective depths of the practical column
footings and foundation slabs are greater than 150 mm, one
may conclude that fib MC 2010 model gives results more
applicable in practice. This also indicates that Eurocode 2
gives more space for the improvement of the calculation
procedure, so further work will be primarily related to the
7. Influence of the Footing Characteristics on Its Punching Capacity
For the analysis of the influence of individual
characteristics of the footing on its punching capacity, deflection of
the footing as a function of applied load was considered.
Thereat, the deflection of the footing represents difference
between recorded settlement of the column stub and settling
of the footing corner.
7.1 Influence of the Concrete Compressive
Strength and Reinforcement Ratio
Influence of the concrete compressive strength and
reinforcement ratio is elaborated on two series of the tested
footings. Thereat every series consisted of footings with
same remained characteristics, besides the analysed one. The
first series consisted of three footings with different concrete
compressive strength (F2-fcm = 30.37 MPa,
F6fcm = 7.92 MPa, and F8-fcm = 15.83 MPa), while the rest
characteristics remained the same. The second series
consisted of three footings with different reinforcement ratio
(F7-ql = 0.27%, F8-ql = 0.48%, and F9-ql = 0.91%),
while other characteristics remained the same. Qualitative
influence of the considered characteristics of the footings on
their behaviour under load is given in Fig. 13.
From Fig. 13a can be seen that influence of the concrete
compressive strength on the registered punching capacity of
the footing significant (registered punching forces of the
footings were F2—1050 kN, F6—440 kN, and F8—
645 kN). This is expected, and it is in concordance with
previous laboratory testing of footings
(Hegger et al.
2006, 2007, 2009; Siburg and Hegger 2014; Simo˜ es et al.
. One may also notice that footings with lower concrete
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compressive strength manifest significantly more ductile
behaviour. Higher bending values were registered in the
starting phases of loading At the footing F8 than at the
footing F6, which may be result of different compactness of
the soil of these footings.
From Fig. 13b can be observed that influence of the
reinforcement ratio on the registered punching capacity of
the footing is not high (registered punching forces of the
footings were F7—527 kN, F8—645 kN, and F9—720 kN)
which is in concordance with previous investigations
(Hallgren et al. 1998; Menetrey 2002)
. Regarding the
ductility, tested footings show relatively similar behaviour.
In order to determine quantitative influence of the concrete
compressive strength and reinforcement ratio on the
punching capacity of the footings, the influence of different
dimensions of the footings is eliminated and the normalised
punching shear resistance vn in the control perimeter is
For all footings rested on real soil, according to Table 1,
value vn is calculated, whereat the notation is kept from
previous expressions, and values for A0 and u are taken from
the calculation in the column 9, Table 3. Dependences
obtained vn(fck) and vn(ql) are presented as diagrams in
Fig. 14a, b.
Regression analysis from Fig. 14a shows that punching
capacity is proportional to the concrete compressive strength
by exponent of 0.50. This corresponds to the conclusions of
(Hallgren et al. 1998)
, who states that punching
capacity at slabs with lower shear slenderness, like, for
example, footings, is proportional to the concrete
compressive strength by the exponent of 0.76, while in the tests with
thinner slabs, Braestrup and Gardner, according to
et al. (1998)
, showed that this influence is lower and that it
amounts from 1/3 to 1/2. This corresponds to some other
standards, for example SIA 262, which take into account this
influence by exponent of 1/2. Regression analysis from
Fig. 14b shows that punching capacity is proportional to the
reinforcement ratio by exponent of 0.23, which also
correspond to the earlier investigations of
Hallgren et al. (1998)
Based on this, one may state that Eurocode 2, which in the
expression (1) takes the influence of both parameter with
exponent 1/3, underestimates the influence of the concrete
compressive strength, while at the same time it overestimates
the influence of the reinforcement ratio.
Finally, in Fig. 15 is presented the influence of these two
parameters on the ratio Vtest=VEC2 for the footings rested on
real soil. From the figures one may conclude that Eurocode 2
reflects the influence of these parameters for their usual
practical values, in a satisfactorily way, regarding
conservativeness of the relation Vtest=VEC2:
7.2 Influence of the of the Effective Depth and Shear Slenderness of the Footing
Influence of the shear slenderness of the footing is
considered on a series of three footings with different shear
slenderness (F3—a/d = 3.34, F4—a/d = 2.25, F5—a/
Fig. 15 Comparison of the results of the punching tests and punching capacity according to Eurocode 2 regarding: a concrete
compressive strength (fck); b reinforcement ratio (ql).
Fig. 17 Comparison of the results of the punching tests and punching capacity according to Eurocode 2 regarding: a effective
depth (d); b shear slenderness of the footing (a/d).
d = 2.7—according to the column 4 in Table 3), while the
other characteristics were almost the same. Qualitative
influence of this parameter on behaviour of the cited footings
under load is presented in Fig. 16.
From Fig. 16 one may see that shear slenderness does not
affect significantly on punching capacity, but it affects very
much on ductile behaviour of the footing. So the footing F3
shows prominently ductile, and the footing F4 prominently
Having in mind thatqEffiuffiffirffiffiocode 2 model limits the size
effect factor k (k ¼ 1 þ 2d00 2:0), it can be concluded that
this standard relates before all to slabs and footings whose
effective depth is d 200 mm: However, the data given
through the diagram in Fig. 17 reveal different results.
Namely, from Fig. 17a and b one may conclude that
Eurocode 2 model does not reflect in a satisfactorily way the
influence of the footing depth d and shear slenderness a/d in
the range of compact footings (higher section depth, i.e.,
lower shear slenderness), regarding conservativeness of the
7.3 Settlement of the Footings and the
Mechanism of Their Punching
During the experimental examination, settlements of the
column and footing corner were measured, completely
according to Figs. 6 and 7. As expected, the settlements of
the points on the footing corners and on the column stub
were approximately uniform at the initial phase of loading,
and then the settlements under the column stub grew faster
(Davidovic´ et al. 2010)
. Typical measured settlements for
these two points are given in Fig. 18, for the footings F6 and
For the footing F6 maximal settlement was recorded at the
punching force of 440 kN, on the column stub, and it
amounted 10.0 mm, and settlement of the footing corner was
4.0 mm. In the footing F9 maximal settlement of the footing
was recorded at the punching force of 720 kN, on the
column stub, and amounted 24.0 mm, and settlement of the
footing corner was 5.0 mm. According to Fig. 18, settlement
of the footing can be divided into four phases. In the first
phase, settlements of the column and of the footing corner
grow approximately equally. In this phase the footing acts as
a stiff one, there are almost no cracks and no deflection of
the footing. Further on, in the second phase (from
approximately 150 kN for footings F6 and F9), one may notice
stagnation of the settlement of the footing corner, while the
settlement of the column stub continues to grow faster with
the increase of the applied force, which leads to the
deflection of the footing. The footing deflection and crack
(Vacev et al. 2015)
continues until the load value
reaches 300 kN in footing F6, and approximately 600 kN in
footing F9. In the third phase the settlement of the footing
corner rests, while the settlement of the column progresses
more intensely as the load level increases. This phase
continues until the load value reaches 400 kN in footing F6 and
700 kN in footing F9. At those load levels the fourth phase
starts, and also the last stage of punching, when the
settlement of the column grows very fast, the cracks and
crushings are spread through the whole footing volume, and the
final punching occurs
(Vacev et al. 2015)
7.4 Strains in Concrete and in Reinforcement
During the testing of footings the strains in concrete and in
reinforcing steel were measured, completely according to
Figs. 6 and 7. Strain distribution in concrete and
reinforcement of footings was according to expectations: maximum
compressive strains occur on the top side of the footings in
the zone next to the column, and maximum tensile strains
occur on the bottom side of the footings in the zone beneath
the column. Typical measured strains in concrete and
reinforcement steel is given for the footings F6 and F9 in
Figs. 19 and 20.
From Fig. 19 one may notice that expectedly maximal
deformations in reinforcement are reached immediately near
the column, or in the column axis. Reinforcement
deformations reached the yield point, or values near the yield
point (reinforcement yield point for the footing F6 is
e % 2.7% - 2700 microstrains, and for the footing F9 is
e % 2.25% - 2250 microstrains). One may observe that
reaching of the high values in the reinforcement practically
means punching of the footing.
Maximal contractions in the concrete are expectedly
recorded in the strain gages immediately near the column.
From Fig. 20 one may notice that in the concrete of both
footings first appear compressive deformations which later
decrease and turn into tension.
Both the reinforcement and concrete deformations
development can be divided into four phases, as is the case for the
footing settlement. In the first phase deformations grow in
both materials. After that, the second phase starts (from
approximately 150 to 200 kN in footings F6 and F9) in
which reinforcement deformations start to grow faster with
load increase, and along with that compressive concrete
deformations begin to stagnate, and after that to turn into
tension. In the third phase (from approximately 250 kN in
footing F6 and 600 kN in footing F9) reinforcement
deformations grow even faster and approach the yield point, while
concrete deformations decrease and turn to compression. In
the fourth phase (from 400 kN in footing F6 and 700 kN in
footing F9) footing punching occurs. Reinforcement
deformations are high and may be far above the yield point, while
concrete deformations decrease and may turn again into
pressure (see Fig. 20). Footings F6 and F9 have the same
height but they differ considerably regarding their concrete
compressive strength and reinforcement (Table 2), which
causes more ductile behaviour of the footing F6, which may
be noticed from Fig. 19.
7.5 Mechanism of Footing Punching
From Figs. 18, 19, and 20 one may notice that the
mechanism of footing punching is developing in four phases
like the settlement of the footing and developing of the
deformations in reinforcement and concrete and that those
phases are practically coincident on the mentioned figures.
In the first phase the footing acts as a stiff body,
settlements of the column stub and footing corner grow
approximately equally and there is no significant bending of the
footing. In the second phase of loading, due to the
considerable reinforcement deformations achieved, much faster
settlements occur under the column compared with the soil
under the footing corner (footing bending) and along with
that decrease of the compressive deformations on the upper
part of the footing near the column. In the third phase high
reinforcement deformations occur, and they are near or at he
yield point causing further decrease of the compressive
deformations, and then emerging of tensile concrete
deformations. Then the column begins to ‘‘dive’’ into the
footing, producing a crack at the joint of the column and the
footing. Fourth and the last stage of punching is
characterized by even faster increase of the reinforcement tension
strains—practically its yielding, and with decrease of the
strains in the footing concrete next to the column. At the end
of this stage the reinforcement strains and the settlement of
the column rise very fast in the column zone, and punching
cracks reach the column, thus encompassing completely the
punching body, and finally it leads to its separation from the
body of the footing.
7.6 Influence of the Distribution of the Soil
The punching capacity of the footing is, among other
things, conditioned by of distribution of the soil pressures
under the footing. Number of previous investigations
register occurrence of the concentration of contact pressures
under the centre of gravity of the loaded surface (in case of
soil without cohesion). Thus, by citations of
Olson and Lai
/2003), Cummings (1936) summarizes previous
experimental research of vertical normal stresses in sand,
which was earlier published by Steiner-Kick (1879),
Strohschneider (1909), Goldbeck (1917), Enger (1920,
1929), Ko¨gler and Schedig (1927, 1929), and Faber (1933).
All mentioned researchers registered concentration of
contact pressures on the sand ground under applied concentrated
For the expected convex distribution of the soil pressures,
the soil reaction within the control perimeter is greater than
for the uniform distribution, which gives as a consequence
footings with higher capacity. Those were the reasons why,
during the experiment for different stiffnesses of the
footingground system, the redistribution of the contact pressures
was tracked depending of the increase of the load level. In
Fig. 21 are given recorded contact pressures for the footings
F6 and F9, as they are typical footings.
In the case of the footing F9 can be observed that the
pressures in the beginning grow approximately uniformly as
the load rises, and after that pressure concentration under the
column occurs (soil pressure cell 1), and then the pressure
concentration gradually spreads to the soil pressure cell 2.
So, at the moment of punching of the footing the pressures
under the column (soil pressure cell 1) were 1200 kN/m2,
while in the soil pressure cell 2 were under 800 kN/m2. The
reason for such behaviour one should look in the fact that
with the load increase a gradual decrease of the footing
stiffness occurs, before all because of the cracking of the
concrete cover, and then because of the shear crack
propagation towards the footing column and increase of the plastic
deformations in the reinforcement and in the concrete. It
means that with gradual separation of the punching body
from the footing, the load is more and more transferred onto
the soil through the base of this body. This is even more
observable in the case of the footing F6, where due to the
very low compressive concrete strength (fck = 7.92 MPa),
the cracking of the concrete and forming of the punching
body occurs earlier. During the loading process and after the
punching failure the ground pressure under the punching
cone body was almost uniform.
As quoted earlier, for the assessment of the punching
capacity, Eurocode 2 suggests reduction of the punching
force for the amount of the reactive pressure of the soil
within the control perimeter, whereat a uniform distribution
of the contact pressures is assumed. However, as one may
see from Fig. 21, distribution of the contact pressure for
footings subjected to loading under axis-symmetric
conditions in most cases is not uniform and depends on the
stiffness of the footing and on the load intensity.
One may say that the basic reason for considerably higher
values of the punching forces during experimental
examination regarding the Eurocode 2 lies just in the fact that at all
the footings concentrations of the contact pressures were
recorded in the area under the column, that is, under the
punching body. This is one of the basic differences
compared to the previous investigations of Hegger
(Hegger et al.
2006, 2007, 2009)
. Concentration of the contact pressures
under the footings examined here is significantly higher, and
that is primarily due to the smaller footing depth, and
consequently to their lower stiffness. Different stiffness of tested
footings, compared to the previously tested footings can be
seen from Table 5. Thus with the increase of the force in the
Fig. 22 Comparison of results of the punching tests and
stiffness coefficient ks.
column, a redistribution of the contact pressure and its
concentration under the footing centre occurs, so at the
failure load of the footing maximal contact pressure is far
higher than the average pressure under the footing.
Significant concentration of the contact pressures under
the punching body that occurred with the increase of the
applied load was the reason for higher punching forces
achieved in our investigations regarding the previous
experiments. Consequently we obtained greater ratios of
Vtest/VEC2. Reason for the ratios Vtest/VEC2 [ 1 at slender
footings, according to Belletti et al. (2015b), also could be
the compressive membrane action effect.
7.7 Influence of the Stiffness of the Footing-Soil
Distribution of the contact pressures under the footing may
be also observed as a function of stiffness of the system
consisted of the footing and the soil under it, which is
expressed through the coefficient of stiffness ks:
where Ec is the modulus of elasticity of the concrete of the
footing (according to fib MC 2010), Es the modulus of
elasticity of the soil under the footing, Ifooting the moment of
inertia of the cross section of the footing, L, B the length,
width of the footing.
For the footings from Table 1, which were rested on the
soil, and with parameters necessary for the calculation of ks
cited in the literature, the following values of the stiffness
footing-soil system were calculated. The obtained values are
presented in Table 5.
For the calculated values ks from Table 5, and values of
the ratio Vtest/VRd,c from the column 12 of Table 3, a
diagram of dependence of those values was made for the quoted
footings, and it is presented in Fig. 22.
Although the sample of the examined footings was small,
one may see from Fig. 22 that for values of ks lower
than & 0.5, the footings behave as flexible structural
elements under which a concentration of contact pressures
occurs, and because of that, an increase of the punching
capacity regarding the predictions that gives Eurocode 2 is
ks ¼ Es L3 B
Table 5 Values of ks for the examined footings.
Author Footing ks
Bonic et al. F2 0.22
Hegger et al.a DF1 0.56
a For the remained footings examined by Hegger ks was not calculated because there were no data about the modulus of elasticity of the soil
under the footing Es.
Table 6 Punching forces according to Eurocode 2 model and according to the proposed solution.
Vtest (kN) d (cm) VRd,c-ECP (kN) Vtest/VRd,c VRd,c-prop. (kN)
(Belletti et al. (Belletti et al.
(Bonic´ et al. 2010)
Fig. 23 Comparison of results of punching tests according to the proposed method of assessment regarding: a footing depth d;
b shear slenderness a/d.
present. These conclusions primarily relate to foundation
slabs and footings of higher shear slenderness.
8. Proposed Method of Calculation
Bearing in mind the quoted differences in results given by
the expression (1) comparing to the experimentally obtained
results, a modification of the punching capacity expression is
vRd;c ¼ CRd;c k ðfck Þ
where k ¼ 2d00; CRd;c ¼ 0:18=cc and the rest of notation
and method of calculation is the same as in expression (1).
Thereat for the governing control perimeter (aEC2 in
expression (14)), one should take the section according to
the diagram given by ECP (2008), that is, by Fig. 10b).
According to the expression (14), the calculation procedure
for the footings from Table 3 was repeated, and the obtained
results, as well as the results given by the current Eurocode 2
model are presented in Table 6. Thus, columns 11 and 12
from Table 3 are now columns 3 and 4 in Table 6.
Comparing the results from the current Eurocode 2 model and the
proposed method (columns 4 and 6 from Table 5) one may
see that the proposed solution gives results which are closer
to the experimental ones.
Based on the results from Table 5, the diagrams Vtest/VRd,
as a dependence of the effective depth d and of the shear
slenderness a/d were obtained, see Fig. 23. One may
observe that the diagrams obtained by expression (14) better
reflect the influence of the footing depth and shear
slenderness compared to the current Eurocode 2, whose results are
presented in Fig. 17a, b.
The proposed calculation procedure is aimed to the
harmonization of the quantification of the influence of the
applied concrete compressive strength and reinforcement
ratio in the expression for the punching capacity given in
Eurocode 2 with the results of experimental investigations of
footings conducted in this research, as well as with the
results of previous investigations.
Like the Eurocode 2, the proposed procedure assumes
uniformly distributed stresses in the subgrade soil.
Considering the registered unevenness of the contact
pressures under the footing (Fig. 21) it is necessary to investigate
the possibility of including of this phenomenon into the
calculation procedure for footing punching.
Also, for the complete acceptation of the proposed
calculation procedure is certainly necessary to conduct
additional experimental investigations so that it could be
confirmed on greater number of samples. Besides that, more
experimental data would provide more reliable data for the
realized statistical analyses and conclusions drawn. Also, it
is necessary that the examined footings have higher effective
depth in order to better reflect the footings in daily
Experimental investigations conducted on footings rested
on real ground, performed numerical calculations, as well as
results of other researchers, set the ground for the following
Recommendations based on ECP
(Dieterle and Rosta´sy
give almost the same results as the calculation that
determines the minimal punching force within the area
bounded by basic control perimeter, so using of those
diagrams may be recommended instead of control in
several perimeters in calculations of column footings
Results of the calculations of punching on tested footings
indicate that fib MC2010 model gives results that are
very close to the experimental ones. This code gives
more conservative results regarding the Eurocode 2,
which above all relates to the footings with higher
The performed regressive analysis for the footings rested
on real soil shows that punching capacity of the footings
is more influenced by the compressive concrete strength
than by the reinforcement ratio, although Eurocode 2
takes them into account equally.
There was recorded a significant concentration of the
contact pressures under the punching body of the footing
with the increase of the applied load. This was the reason
for higher punching forces achieved regarding the
previous experiments and greater ratios Vtest =VEC2:
Concentration of contact pressure is primarily the
consequence of the stiffnesses coefficient ks. It primarily
relates to foundation slabs and to footings of higher shear
For the final acceptation of the proposed calculation
procedure is certainly necessary to conduct additional
experimental investigations so that it could be confirmed
on greater number of samples. Besides that, more
experimental data would provide more reliable data for
the realized statistical analyses and conclusions drawn.
Future testing of footings with higher effective depth
would certainly supplement the results of this research
and contribute to its application in daily engineering
This study was funded by Ministry of Science and
Technological Research of Republic of Serbia (Grant No.
TR 36028 and TR 36016). The authors thank to Prof.
Hegger and his team from RWTH AACHEN UNIVERSITY
on the database of tested footings.
Compliance with ethical standards
Conflict of interest
The authors declare that they have no conflict of interest.
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