 Open Access
Punching Behaviour of Reinforced Concrete Footings at Testing and According to Eurocode 2 and fib Model Code 2010
 Zoran Bonić^{1}Email author,
 Nebojša Davidović^{1},
 Todor Vacev^{1},
 Nikola Romić^{1},
 Elefterija Zlatanović^{1} and
 Jelena Savić^{1}
https://doi.org/10.1007/s4006901702138
© The Author(s) 2017
Received: 24 August 2016
Accepted: 17 July 2017
Published: 22 December 2017
Abstract
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.
Keywords
1 Introduction
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 mentioned.
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; Bonić et al. 2010; Brooms 2005; Fédération Internationale du Béton (fib) 2010; Hallgren and Bjerke 2002; Hallgren et al. 1998; Halvonik et al. 2016; Hegger et al. 2006, 2007, 2009; Husain et al. 2017; Kabir et al. 2016; Kee and Nam 2015; Kumer and Hoque 2015; Menetrey 2002; Muttoni and Schwartz 1991; Muttoni 2008; Muttoni and Fernández 2008, 2012; Olson (1989/2003); Pивкин 1967; Siburg and Hegger 2014; Siburg et al. 2014; Simões et al. 2016a, b; Talbot 1913; Timm 2003; 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.
Overview of previous experiments on column footings.
Author  Year  Type of support  Number of tested footings  Geometry of footing  

Shape  Dimension (mm)  Effective depth (mm)  
Simões et al. (2016)  2016  Surface  8  Square  1950 and 2120  497–516 
Kumer and Hoque (2015)  2015  Stabilized ground  1  Square  1524  212 
Siburg and Hegger (2014)  2014  Surface  13  Square  1200–2700  400–590 
Urban et al. (2013)  2013  Line  9  Octagonal  1948–2344  118–318 
2005–2009  Sand in the box/surface  22  Square  900–1800  150–470  
Timm (2003)  2003  Line  10  Square  760–1080  172–246 
Hallgren et al. (1998)  1998  Line/Surface  14  Square and circular  850–960  273–278 
Dieterle and Rostasy (1987)  1987  Surface  13  Square  1500–3000  320–800 
Kordina and Nölting (Hegger et al. 2009)  1981  Surface  11  Rectangular  1500–1800  193–343 
Dieterle and Steinle (1981)  1981  Surface  6  Square  1800–3000  700–740 
Rivkin (1967)  1967  Surface/clay and sand  3/6  Square  650 and 1000  95 
Richart (Hegger et al. 2009)  1948  Spring  149  Square and circular  610–3000  200–740 
Talbot (1913)  1913  Spring  20 (in punching)  Square  1520  250 
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 footingsoil 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
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 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 φ′ was adopted based on recommendations from the scientific literature (Bowles 2001). 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 φ′ = 36–40°. For these values of φ′ and for cohesion c′ = 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.
Achieved characteristics of test foundations.
Footing no.  Footing height h (mm)  Effective depth d (mm)  Concrete strength f_{cm} (MPa)  Rebar diameter (mm)  Reinforcement ratio ρ _{ t } (%)  Yield strength of reinforcement f_{ym} (MPa)  Soil modulus of compressibility M_{S} (MPa)  Ultimate load (kN) 

F1  200  175  30.37  8  0.40  570  54.0/61.2  1001/906^{a} 
F2  150  125  30.37  8  0.40  570  76.7  1050 
F3  125  100  16.83  8  0.40  570  48.0  430 
F4  175  150  16.83  8  0.40  570  39.5  656 
F5  150  125  15.28  8  0.40  570  46.0  451 
F6  150  125  7.92  8  0.40  570  37.5  440 
F7  150  125  15.83  8.5  0.27  477  60.2  527 
F8  150  125  15.83  8.5  0.48  477  66.5  645 
F9  150  125  15.83  8.5  0.91  477  57.0  720 
For the construction of the footings a threefraction 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 Table 2.
4 Testing Procedure
5 Comparison of the Test Results with the Eurocode 2
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 v _{ min }, and considering that C _{ Rd,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 c/d, gives the relationship a _{ cr }/d (according to the diagram in Fig. 10b). In most cases value a _{ cr } = a _{ EC2} is less than 2d, which means that the slope of the punching body of the footings is steeper than the slope of the slabs.
The smaller value from (1) and (5) governs the design.

The basic control perimeter is at the distance \( a_{EC2} = 2.0d \) from the column edge (column 7, Table 3—just as an illustration)Table 3
Punching forces of the footings registered by experiment and calculated according to Eurocode 2.
Footing label
V_{test} (kN)
(Belletti et al. 2015b)
b (mm)
(Belletti et al. 2015a)
d (mm)
(Bonić et al. 2010)
a/d
(Bonić 2011)
f_{cm} (MPa)
(Bowles 2001)
ρ _{ l } (%)
(Brooms 2005)
V_{R,aEC2=2d} (kN)
(Davidović et al. 2010)
V_{test}/V_{Rd,c}
(Dieterle and Steinle 1981)
V_{Rd} (a_{cr}/d) (kN)
(Dieterle and Rostásy 1987)
V_{test}/V_{Rd,c}
(Commentary 2008)
V_{Rd,c} (kN)
(EN 1992)
V_{test}/V_{Rd,c}
(Fédération Internationale du Béton (fib) 2010)
Bonic et al.
F1
1001/906
850
175
1.93
30.37
0.40
4890
–
776 (0.8)
1.29
786
–
F2
1050
850
125
2.7
30.37
0.40
530
1.98
396 (1.15)
2.65
400
2.63
F3
430
850
100
3.34
16.83
0.40
225
1.91
208 (1.45)
2.07
210
2.05
F4
656
850
150
2.25
16.83
0.40
956
0.69
468 (0.95)
1.40
476
1.38
F5
451
850
125
2.7
15.28
0.40
421
1.07
315 (1.15)
1.43
318
1.42
F6
440
850
125
2.7
7.92
0.40
339
1.30
254 (1.15)
1.73
256
1.72
F7
527
850
125
2.7
15.83
0.27
374
1.41
279 (1.15)
1.89
282
1.87
F8
645
850
125
2.7
15.83
0.48
453
1.42
339 (1.15)
1.90
342
1.89
F9
720
850
125
2.7
15.83
0.91
560
1.29
419 (1.15)
1.72
423
1.70
Hegger et al.
DF1
551
900
150
2.5
20.2
1.03
992
0.56
638 (1.0)
0.86
647.45
0.85
DF2
530
900
150
2.5
22
1.03
1020
0.52
656 (1.0)
0.81
666
0.80
DF4
1251
900
250
1.5
24.5
0.62
Negative
–
1403 (0.6)
0.89
1410
0.89
DF5
1130
900
250
1.45
17.6
0.73
Negative
–
1467 (0.6)
0.77
1475
0.77
DF6
2836
1200
395
1.27
19.0
0.87
Negative
–
3255 (0.5)
0.87
3282
0.86
DF7
2569
1400
395
1.52
20.9
0.87
Negative
–
3080 (0.6)
0.83
3090
0.83
DF8
1203
1200
250
2.00
22.5
0.88
6099
–
1532 (0.8)
0.79
1549
0.78
DF10
1638
1200
250
2.00
38.1
0.91
7351
–
1847 (0.8)
0.89
1867
0.88
Rivkin
21F
180
1000
95
4.2
16.6
0.25
158
1.14
157 (1.8)
1.15
158
1.14
Kumer Shill and Hoque
640
1524
212
3.12
13.8
0.56
880
0.73
747 (1.20)
0.86
753
0.85

The critical control perimeter is equalled to critical control perimeter \( a_{EC2} = a_{cr} \) 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 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 \( a_{EC2} \approx 2.0d \)), one gets high values for area within the control perimeter A _{0}, and consequently high values for the punching capacity of the footing, V _{ Ed }, 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 \( a_{EC2} \approx 2.0d \) regarding the column face (Table 3, columns 7 and 8), is given just as an illustration, and it should not be applied in practical use.
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 recommended.
On the diagram in Fig. 13 are drawn the ratios a _{ cr }/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 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 906 kN.
6 Comparison of the Test Results with the fib MC 2010
The angle of rotation of the slab ψ 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 ψ. As LoA increases, so the calculated slab rotations generally decrease, leading to higher punching shear capacities.
6.1 LoA I
6.2 LoA II
Bending moment inside the column strip can be estimated with m _{ sd } = V _{ Ed }/8. The value for r _{ s } 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.
6.3 LoA III
m _{ sd } 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 ψ can be calculated on the basis of a nonlinear analysis of the structure and with full account of cracking, tensionstiffening effects, yielding of the reinforcement and any other nonlinear 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.
Punching forces of the footings registered by experiment and calculated according to fib MC 2010.
Footing label  V_{test} (kN) (Belletti et al. 2015b)  b_{c} (mm) (Belletti et al. 2015a)  b (mm) (Bonić et al. 2010)  d (mm) (Bonić 2011)  a/d (Bowles 2001)  f_{cm} (MPa) (Brooms 2005)  ρ _{ l } (%) (Davidović et al. 2010)  f _{ y } (MPa) (Dieterle and Steinle 1981)  V_{R}_{Lo1} (kN) (Dieterle and Rostásy 1987)  V_{test}/V_{R}_{Lo1} (Commentary 2008)  V_{RLo2} (kN) (EN 1992)  V_{test}/V_{R}_{Lo2} (Fédération Internationale du Béton (fib) 2010) 

Bonic et al.  
F1  1001/906  260  850  175  1.93  30.37  0.40  570  589  –  757  – 
F2  1050  175  850  125  2.7  30.37  0.40  570  246  4.28  323  3.25 
F3  430  175  850  100  3.34  16.83  0.40  570  133  3.23  188  2.29 
F4  656  175  850  150  2.25  16.83  0.40  570  240  2.73  390  1.68 
F5  451  175  850  125  2.7  15.28  0.40  570  174  2.59  273  1.65 
F6  440  175  850  125  2.7  7.92  0.40  570  125  3.51  219  2.01 
F7  527  175  850  125  2.7  15.83  0.27  477  194  2.72  200  2.64 
F8  645  175  850  125  2.7  15.83  0.48  477  194  3.33  280  2.30 
F9  720  175  850  125  2.7  15.83  0.91  477  194  3.72  343  2.10 
Hegger et al.  
DF1  551  150  900  150  2.5  20.2  1.03  552  229  2.41  479  1.15 
DF2  530  150  900  150  2.5  22  1.03  552  239  2.22  496  1.07 
DF4  1251  150  900  250  1.5  24.5  0.62  552  593  2.11  1174  1.07 
DF5  1130  175  900  250  1.45  17.6  0.73  515  577  1.96  1140  0.99 
DF6  2836  200  1200  395  1.27  19.0  0.87  552  1089  2.60  2712  1.05 
DF7  2569  200  1400  395  1.52  20.9  0.87  552  965  2.66  2644  0.97 
DF8  1203  200  1200  250  2.00  22.5  0.88  552  521  2.31  1263  0.95 
DF10  1638  200  1200  250  2.00  38.1  0.91  552  678  2.41  1581  1.04 
Rivkin  
21F  180  200  1000  95  4.2  16.6  0.25  304  166  1.09  73  2.47 
Kumer Shill and Hoque  
640  200  1524  212  3.12  13.8  0.56  414  307  2.08  623  1.03 
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 V_{test}/V_{R}_{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 Eurocode 2.
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 (F2f_{cm} = 30.37 MPa, F6f_{cm} = 7.92 MPa, and F8f_{cm} = 15.83 MPa), while the rest characteristics remained the same. The second series consisted of three footings with different reinforcement ratio (F7ρ _{ l } = 0.27%, F8ρ _{ l } = 0.48%, and F9ρ _{ l } = 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; Simões et al. 2016). One may also notice that footings with lower concrete 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.
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 (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 Hallgren 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.
7.2 Influence of the of the Effective Depth and Shear Slenderness of the Footing
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 stiff behaviour.
7.3 Settlement of the Footings and the Mechanism of Their Punching
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 development (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 Steel
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 ε ≅ 2.7‰ − 2700 microstrains, and for the footing F9 is ε ≅ 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 Pressures
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 (1989/2003), Cummings (1936) summarizes previous experimental research of vertical normal stresses in sand, which was earlier published by SteinerKick (1879), Strohschneider (1909), Goldbeck (1917), Enger (1920, 1929), Kögler and Schedig (1927, 1929), and Faber (1933). All mentioned researchers registered concentration of contact pressures on the sand ground under applied concentrated force.
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/m^{2}, while in the soil pressure cell 2 were under 800 kN/m^{2}. 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 (f _{ ck } = 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 axissymmetric 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 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 V_{test}/V_{EC2}. Reason for the ratios V_{test}/V_{EC2} > 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 FootingSoil System
For the footings from Table 1, which were rested on the soil, and with parameters necessary for the calculation of k _{ s } cited in the literature, the following values of the stiffness footingsoil system were calculated. The obtained values are presented in Table 5.
Although the sample of the examined footings was small, one may see from Fig. 22 that for values of k _{ s } 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 present. These conclusions primarily relate to foundation slabs and footings of higher shear slenderness.
8 Proposed Method of Calculation
Values of k _{ s } for the examined footings.
Author  Footing  k _{s} 

Bonic et al.  F2  0.22 
F3  0.17  
F4  0.57  
F5  0.30  
F6  0.30  
F7  0.23  
F8  0.21  
F9  0.24  
Hegger et al.^{a}  DF1  0.56 
DF2  0.32  
DF4  0.70  
DF5  0.83 
Punching forces according to Eurocode 2 model and according to the proposed solution.
Label  V_{test} (kN) (Belletti et al. 2015b)  d (cm) (Belletti et al. 2015a)  V_{Rd,c}ECP (kN) (Bonić et al. 2010)  V_{test}/V_{Rd,c} (Bonić 2011)  V_{Rd,cprop}. (kN) (Bowles 2001)  V_{test}/V_{Rd,cprop.} (Brooms 2005) 

Bonic et al.  
F2  1050  12.5  400  2.63  482  2.18 
F3  430  10  210  2.05  257  1.67 
F4  656  15  476  1.83  475  1.38 
F5  451  12.5  318  1.42  342  1.32 
F6  440  12.5  256  1.72  247  1.78 
F7  527  12.5  270  1.95  316  1.67 
F8  645  12.5  328  1.97  364  1.77 
F9  720  12.5  405  1.78  427  1.69 
Hegger et al.  
DF1  551  15  647  0.85  571  0.96 
DF2  530  15  666  0.80  596  0.89 
DF4  1251  25  1410  0.89  1181  1.06 
DF5  1130  25  1475  0.77  1153  0.98 
DF6  2836  39.5  3282  0.86  2255  1.26 
DF7  2569  39.5  3090  0.83  2157  1.19 
DF8  1203  25  1549  0.78  1242  0.98 
DF10  1638  25  1867  0.88  1629  1.0 
Rivkin  
21F  180  9.5  158  1.14  206  0.87 
Kumer Shill and Hoque  
640  21.2  747  0.85  594  1.08 
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 engineering practice.
9 Conclusions

Recommendations based on ECP (Dieterle and Rostásy 1987) 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 punching resistance.

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 effective depths.

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 \( V_{test} /V_{EC2} . \) Concentration of contact pressure is primarily the consequence of the stiffnesses coefficient k _{ s }. It primarily relates to foundation slabs and to footings of higher shear slenderness.

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 practice.
Declarations
Acknowledgements
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.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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