Parmentier Et Al - The Flexural Behaviour of SFRC Flat Slabs (Final)

8/19/2019 Parmentier Et Al - The Flexural Behaviour of SFRC Flat Slabs (Final)

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FRC 2014 Joint ACI- fib International WorkshopFibre Reinforced Concrete: from Design to Structural Applications

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The flexural behaviour of SFRC flat slabs: the Limelette full-scale experiments for supporting design model codes

Benoit Parmentier 1, Petra Van Itterbeeck 1, Audrey Skowron 1

1 : Belgian Building Research Institute (BBRI), Limelette, Belgium.

Abstract

An experimental campaign on a full-scale SFRC flat slab with 70 kg/m³, without anytraditional reinforcement, was performed in 2011. These experiments were based on

uniformly distributed loading as well as concentrated loadings. The ultimate flexural load-

bearing capacity of the slab was checked according to the relationships given in the Model

Code 2010 recently published by fib (MC2010). The design was made on a full plastic

approach, using the characterization of the SFRC on small specimens. The tests confirmed the

ductile behaviour and the redundancy potential in SFRC flat slabs. The identification of the

worst yield lines pattern remains an important task for the designer, as it significantly

influences the results. The laboratory characterization showed discrepancies compared to

specimens directly sawn from the slab. The use of the in-situ properties in the design method,

nonetheless, seems to provide a good agreement with the results of the full-scale tests.

Keywords

Steel fibres, fibre reinforced concrete, flat slab, design, full-scale experiments.


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(a) (b)

Figure 1: (a) Slab geometry (dimensions in cm). Capital letters indicate (6x6m²) panels while

the notation “k#” refers to the column under the slab and the dashed line shows

the path of the pump during the pouring sequence.

(b) Loading frame for the ULS tests.

2.1

Fibre reinforced concrete propertiesAs sole reinforcement of the slab, hooked end steel fibres with a length of 60 mm and a

diameter of 1.0 mm are used. The characteristics of the steel fibres are summarized in

Table 1. The concrete composition (see Table 2) was adapted in such a manner that the

SFRC, with 70 kg/m³ of fibres (volume fraction V f = 0.89%), can be pumped. The coarse-to-

fine aggregate ratio is close to 50:50 in order to target a good workability with the fibres

(slump of 200 mm). This was confirmed on site by the slump measurements with the Abrams

cone. In the middle of the concrete discharging phase, the slump fluctuated between 200 mm

and 260 mm in function of the truck mixer.

Table 1: Nominal properties of the fibres

Fibre

Tensilestrength

[MPa]

Elasticitymodulus

[kPa]

Density

[kg/m³]

Length

[mm]

Diameter

[mm]

Aspect ratio

[/]

HE+ 1/60 1450 210 7850 60 1.0 60

The properties of the hardened concrete are presented in Table 3 for the two phases. For

the casting of the flat slab, the compressive resistance measured on 5 cubes of

150x150x150mm³ at 28 days was 43.7 MPa. The post-peak behaviour was characterized

according to EN 14651, using a three-point bending test on specimens taken from the last

truck mixer (phase 1) or specially delivered (phase 2). These specimens have a cross-sectionof 150x150mm² with a notch of 25 mm deep at mid-span (250 mm).

Steel frame

Jack

Loadcell


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Table 2: Concrete mix

Material Quantity

Cement [kg/m³] : 400Portland CEM I 52,5R HES 200

CEM V/A (V-S) 32,5N LH HSR 200

Coarse aggregate [kg/m³] : 840

Crushed limestone 4-8 400

Crushed limestone 6-14 440

Quartz sand 0/4 [kg/m³] 850

Water [l/m³] 215

High range water reducer [l/m³] 1.6

Steel fibres HE+ 1/60 [kg/m³] 70

Water/cement ratio (W/C) 0.54

The limit of proportionality f L, the peak flexural tensile strength f max, the residual flexural

tensile strengths f R,1, f R,2 , f R,3 and f R,4 for a crack mouth opening displacement (CMOD) of 0.5,

1.5, 2.5 and 3.5 mm, respectively, were measured for each series of specimens (see Table 3).

Some of these properties will be used to calculate the loadbearing capacity of the slab with the

help of the analytical model from the MC2010.

Table 3: Mean properties of the hardened concrete at 28 days

(the coefficient of variation [%] is given in brackets)

Test standard(# specimens)

Slab casting

Phase 1

Control casting

Phase 2

Mean compressive resistance

f cm,cub [MPa]

EN 12390-3(5 specimens)

43.7 (2) 41.8 (1)

Limit of Proportionality f L [MPa]

EN 14651(9 specimens for phase 1 and 11specimens for phase 2)

5.1 (6) 4.5 (11)

Peak strength f max [MPa] 9.2 (19) 7.1 (22)

Residual strength at 0.5 mm CMOD - f R1,m [MPa] 8.6 (19) 6.4 (25)




Young’s modulus E cm [MPa] NBN B 15-203(3 specimens)

NA 33940 (2)

The average curves of the bending tests exhibit residual strengths of more than 60% of the

peak up to a mid-span deflection δ = 3 mm that corresponds to a CMOD of 3.5 mm (see

Figure 2). All the specimens exhibited a strain-hardening behaviour in bending, with an

increased loadbearing capacity beyond crack initiation in the concrete (after the limit of

proportionality (LOP), f L). By comparing the specimens taken during the execution of theslab and from the additional casting, we observe that the results differ in the mid-span


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deflection range [0.05..2] mm with a larger increase of the load for the samples taken from the

casting sequence of the flat slab. This can be explained by the higher number of fibres

counted across the broken section of the specimens taken from the slab pouring phase.

Finally, the coefficient of variation of the residual strengths of the different series ranged from18% up to 25%, which is quite common for this type of test characterised by a small cracked

section and no stress redistribution possibilities.

(a) (b)

Figure 2: a) The control specimens from the first casting phase exhibit larger residual forces

after the peak in three-point bending up to 2.0 mm (average curve for each series)

b) Test setup used for the tests

The control of the fibre dosage in the fresh concrete is achieved by taking samples of +/-

5.5 litres from the pump in the middle of each concrete discharging phase. The average fibre

dosage measured from the different truck mixers (one sample taken from each of the 7 truck

mixers in the middle of the delivery) is 63.8 kg/m³ with a minimum of 52.2 kg/m³ and a

maximum of 69.3 kg/m³. The observed individual values are lower than the target of 70

kg/m³, but the samples represent every time only one sample of 5.5 litres on a total volume of

10 m³ of concrete (truck capacity) which is rather limited. Later on, additional tests on 11

cylinder cores (Ø113 mm) drilled randomly from panels G-H-I showed an average dosage of

68.2 kg/m³ with a standard deviation of 7.4 kg/m³. The analysis of the distribution of the

fibres along the depth (on the same samples) did not reveal any heterogeneity. Hence, weassumed that fibres were distributed homogenously in (this part of) the slab. This should be

confirmed later by a detailed analysis on the full slab.

2.2 Uniformly distributed loads (SLS tests)

The slab is stripped 14 days after it was poured. At this stage, a first straight crack

appeared in the centre of the panels G-H-I along the E-W direction. The crack width was on

average around w = 0.3 mm. Another crack was also noticed in the centre of panels I-G to the

N-S direction. These cracks will be discussed later in §2.4.

0 0.5 1 1.5 2 2.5 3 3.5 40

5

10

15

20

25

30

35

40

Mid-span Deflection [mm]

L

o a d [ k N ]

1st casting (flat slab)

2nd casting (control)


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The first phase of the project deals with the evaluation of serviceability limit states

(deflections, cracks) of the slab under uniformly distributed loads (UDL). In order to evaluate

the deflection of the SFRC in this case, two flexible polyester water tanks of 6x6 m² are

installed on panels A and C (see Figure 3a). Thirty-six days after casting the slab, thesereservoirs are filled alternatively with water, at a rate of ±8000 litres per hour. The loading

principle consists of the filling of the water reservoirs alternatively in steps of 1 kN/m² (3.6

m³), while the deflections of the slab are measured by means of linear variable displacement

transducers (LVDT) distributed over the bottom of the slab.

For the first three loading steps, the central deflection of the panels increases linearly. The

deflections are quite similar for panels A and C (see Figure 3b). After 3 kN/m² a first visible

crack appears at the bottom of panel A and in a similar way later on in panel C. The crack

opening in both panels was on average ±0.1 mm at this time. Because this value was small, it

was decided to continue the test up to 4 kN/m² for each panel. At this load level, the

maximum crack opening reaches respectively on average 0.4 mm and 0.5 mm for panel A andC and the central deflection is 9.4 mm and 7.2 mm. At this time it was decided to stop the test

and to keep this load level for one day. At the end of the next day, the panels were unloaded.

At this moment the central deflection had reached 15 mm for panel A and 13 mm for panel C

(increase of respectively 60% and 80%, see Figure 4) and the cracks at the bottom of the slab

opened up to on average 0.8-1.0 mm.

(a) (b)

Figure 3: (a) Uniformly distributed loads (UDL) on the slab. Note: dimensions in cm.

(b) Central deflection of panels A & C during loading/unloading with UDL.

2.3

Concentrated loads (ULS tests)

The second phase of the study focussed on the ultimate post-cracking behaviour of the

SFRC slab (ULS). To investigate this limit state, a concentrated load is applied to the centre

of different panels (centre, edge and corner panels) consecutively. The load is applied by

means of a jack with a capacity of 1000 kN and controlled by a hand pump. The jack wasinstalled in a reaction frame composed out of steel profiles HEA800 (as shown in Figure 1b).

0 200 400 600 800 1000 1200 1400 1600 18000

2

4

6

8

10

12

14

16

Time [hours]

C e n t r a l d e f l e c t i o n

[ m m ]

Panel A

Panel C

Loading stopped(4 kN/m²)

Unloading panel C

Unloading panel A


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The frame is anchored by using 2 dywidag bars (diameter 26 mm) drilled 30 cm deep in the

head of the columns through the thickness of the slab. This test setup does not allow the

investigating of potential punching shear problems due to the interaction between the reaction

frame and the slab at the connection with the columns. This failure mechanism was howevernot considered a problem for the SFRC used in this structure (Gossla, 2005;Michels, 2012).

The load is applied through a 30x30x5 cm³ steel plate. The force, continuously measured

by a load cell, is applied in steps of 50 kN and kept constant during 10 minutes to achieve

deflection stabilisation. This procedure allowed us to make some manual measurements of

crack openings and to make sure that the effective stable peak load is identified. In order to

check this, the increase of panel deflection was continuously monitored and when the increase

in panel deflection drops below 10% of the deflection increase at the beginning of the loading

plateau the test is continued.

The ULS tests are initiated five days after the SLS tests, at a concrete age of 42 days. The

first of these tests relates to a concentrated load applied in the centre of panel E. This test

would give the maximum load because of the large stress redistribution capacity of the slab in

this configuration. As foreseen, the central panel exhibits the maximum capacity for this

loading scheme with a maximum load of 328 kN (Figure 4). This load was considered as the

peak load because it was not possible to go beyond this value, and the deflections became

unstable. This first ULS test also illustrated well the remarkable plastic behaviour potential of

the material at peak load, with more than 40 mm of deflection increase before considering that

the ultimate capacity is reached. Based on the change in slope on Figure 4a and compared

with the linear elastic FEM-based prediction, we noticed a major crack initiation at a load of

±85 kN. We observed very similar deflections for the adjacent panels D and F while their

very low amplitude compared to those from the loaded panel E (see Figure 4a) demonstratethe effect of the full plastic hinge developed in the top of the slab along the columns k2-k14

and k3-k15. We also observe the development of a larger crack in N-S direction at the bottom

centreline of panel E in comparison with the crack extending along the W-E direction (see

Figure 4b). At the end of this first test the maximal crack opening reaches on average 8.5 mm

at the bottom of panel E. The full description of the crack pattern is presented in §2.4.

Afterwards, the load was applied in the centre of panel H and finally in the centre of panel

I in order to test an edge panel and a corner panel of the slab, respectively. The peak loads

and corresponding deflections of these experiments are presented in Table 4.

(a) (b)Figure 4: Deflection (a) and crack openings (b) versus load during the ULS 1 test

0 20 40 60 80 1000

50

100

150

200

250

300

350

Central deflection [mm]

L o a d

[ k N ]

Panel E (loaded)

Panel D

Panel F

Panel E (FEM lin elast.)

0 2 4 6 8 100

50

100

150

200

250

300

350

Crack opening at mid-span [mm]

L o a d

[ k N ]

Panel E : W-E crack

Panel E : N-S crack


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Table 4: ULS tests on the flat slab – Experimental results

Test ULS 1 - Pcentral panel (E) ULS 2 - Pedge panel (H) ULS 3 - Pcorner panel (I)

Peak load [kN] 328 143 54Deflection at peak load [mm] 27 51 19

2.4

Crack pattern

As mentioned before, the slab was already cracked in some parts due to its self-weight just

after the formwork was removed (see Figure 5a). Two long cracks appeared at the bottom of

the slab (w ≅ 0.3 mm) and at the top of the slab above edge and inner columns ( w ≅ 0.06).The particular cement type (CEM V/A) used as part of the concrete mix could be the reason

of the reduced flexural strength at early age but this was not confirmed so far. However,

because the largest cracks were far from the fields tested under UDL and the cracks at top ofthe slab were limited in both length and crack opening, it was estimated that their influence on

the deflections behaviour was rather limited. For the ULS test, it is also our opinion that the

reduced time between the removal of the formwork and the ULS tests (28 days) did not

induce any major detrimental effect (corrosion, carbonation, etc.) on the flexural capacity of

the slab (in any way not exceeded) caused by the presence of these cracks.

At the end of the UDL tests, a long crack appeared along the W-E direction at mid-span of

panels A-B-C together with circular cracks around columns k1 and k4 (see Figure 5b). The

first ULS experiment in panel E was characterised by a large crack at mid-span over the

bottom side along the N-S direction (Figure 5c). This crack initiated in the centre of the panel

and proceeded to the free edges of the slab while the load increased up to the peak loading.Another orthogonal crack appeared and was followed by radial cracks starting from the centre

of the panel. At peak load, the slab also presented radial cracks above the head of the internal

columns and a large circular one connecting them. This last crack was repeated with a larger

radius at some locations. The same cracking pattern was observed for the two other ULS tests

with the difference that the large circular crack flowing from column to column was not fully

completed.

(a) (b) (c)

Figure 5: Cracking pattern induced by the self-weight (a), by the UDL tests (b) and by the

ULS 1 test (c). Note: dotted lines indicate cracks at the top of the slab.


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3 Check of ultimate resisting moment of the slab

A first insight about the deflection and stress distribution in the slab was obtained with a

FEM-based commercial software. Then, the analytical model described in the MC2010 wasused to estimate the ultimate flexural capacity of the SFRC slab. In the following, we only

focus on the first ULS test to check the design relationships.

3.1

Calculation of the ultimate flexural capacity of the slab

The fib Model Code 2010 (MC2010), which was recently published, allows the designer to

calculate the ultimate capacity of any SFRC structure. In a particular case, we use the rigid-

plastic (RP) model approach to estimate the ultimate flexural capacity of the slab.

The RP model takes static equivalence into account as shown in Figure 6, i.e. f Ftu resultsfrom the assumption that the whole compression is concentrated in the top fibre of the section.

Figure 6: Simplified rigid plastic model adopted to compute the ultimate tensile strength in

uniaxial tension f Ftu by means of the residual nominal bending strength f R3

Hence, the equation for f Ftu and wu=CMOD3 is obtained, from the rotational equilibrium at

ULS, when a stress block in tension along the section is taken into account:

33 RFtu f f = (1)

For slab elements without conventional reinforcement with prevalent bending actions, the

resisting moment m R

can be estimated by considering a rigid plastic relationship:

6

².

2

². 3,

t f t f m RFtu

lab R == (2)

where t is the thickness of the slab. By introducing the average properties of the concrete

(worst results from phase 2, see Table 3) and the thickness of the slab into Eq. (2), we can

calculate the flexural resisting moment m R = m R,lab = 42.7 kNm/m. This is what we basically

can calculate from the laboratory characterization without any safety factor. But we need to

take two specific SFRC properties into account in the real structure compared to the

characterisation in the laboratory: the fibre orientation and the redistribution capacity of the

full-scale structure. For this project, a reduction coefficient K =0.9 is used to mainly express

the size effect on the post-peak performances (RILEM TC 162-TDF, 2003). Moreover,redistribution factor K Rd = 1.3 was used (Di Prisco et al., 2014).


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3.2 Comparison with experimental results and discussion

We used the yield line theory to estimate the load producing the ultimate flexural strength

of the slab. The yield line theory is a kinematic plastic method which is an upper boundsolution for the design problem (Johansen, 1962). Therefore, it is crucial to identify the worst

case in terms of cracking pattern i.e. the situation providing the lowest ultimate loadbearing

capacity. For this project, we use the work method to compute the ultimate load. The method

is based on the assumption that at failure, the external energy expended by the moving load

(W e) must be equal to the internal energy dissipated by rotations around the yield lines (W i).

This method is particularly suited for the design of flat slabs (Kennedy and Goodchild, 2003).

We first need to identify the actual yield lines pattern which causes the ultimate “failure”

of the slab at the end of the ULS 1 test. Two patterns were assumed to be relevant regarding

to the cracking pattern observed after the test. The first one (see Figure 7a) starts with a long

crack surrounding the internal columns (ultimate negative moment m’) associated with radial

cracks at the bottom of the slab (ultimate positive moment m). The second one (see Figure

7b) is more global with straight negative yield lines in the centre of the panels and positive

yield lines along the column axes crossing the full slab on its length (i.e. 3 panel lengths are

activated by the concentrated load and the self-weight). For the ULS tests, the loads included

in the analysis are the peak concentrated load Pu = 328 kN and the self-weight q = 5 kN/m².

For the circular yield line pattern, the radius of the crack is R=4,24 m. Moreover, if the fibres

are uniformly distributed along the depth of the slab, we can assume that m=m’=m R. Based

on a slab geometry survey, we also reassess the thickness of the slab to be 210 mm. This

depth was used in further calculations. Other yield line patterns have also been considered:

(1) circular pattern with more radial cracks at bottom, (2) local fan pattern around the internal

column, etc. but were not in agreement with the real cracking pattern observed or generatedlarger ultimate capacity.

Circular & radial yield lines pattern Global folded plate failure mechanism

(a) (b)

Figure 7: Yield line patterns used for the calculation of the ultimate capacity of the slab

SEC. B-B’

B B’

SEC. A-A’

A

A’

SEC. A-A’


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δπ+δ=

34

R q 4PW

2

ue

δ+δ=

22

LL3q 2PW xyue (3) & (4)

θ+θπ= pni R 2m4

R 2'm4W pnyi R 2mL3'mW θπ+θ= (5) & (6)

If we assume δ = θ . R and θ n = θ p = θ ,

( )3

qR m28P

2

R u

π−π+=

If we assume δ = θ . L x /2 and θ n = θ p = θ ,

2

qL3m24P

2

R u −= (7) & (8)

==→ R FS,R mm 29.6 kNm/m ==→ R FS,R mm 25.5 kNm/m

If we compare this value with m R,lab = 42.7 kNm/m (even without any redistributionfactor), we can conclude that there is a large discrepancy between the laboratory

characterization and the full-scale tests. In order to confirm this, prisms were sawn in the slab

from the same direction (N-S), specifically in panel I. Due to logistic problems, this was the

only panel where specimens could be sawn from. These prisms exhibited dimensions

equivalent to the requirements of the EN 14651 except the height which was 210 mm. Based

on the analysis of 9 small beams with a notch depth of 36 mm, we found an average residual

strength f R3,m = 3.5 MPa (COV = 21%) meaning a reduction of almost 50% compared to the

initial lab characterization. This result stresses the heterogeneous distribution of the fibres in

the slab or specific orientation of the fibres in the prisms poured from phase 2. However, if

this residual strength is used to compute the m R,lab and then multiplied by the orientation

factor (0.9) and a redistribution factor (1.3), we find m R,lab = 30.1 kNm/m which is very closeto what we found from the full-scale test analysis.

4 Summary and Conclusions

Full-scale tests on an SFRC flat slab (with 70 kg/m³) without conventional reinforcement

were performed in order to analyse the potential of SFRC in this field of applications. The

study presented in this paper aimed at supporting the design relationships given in the fib

Model Code 2010 and in particular the calculation of the ultimate bending capacity from a

full plastic approach. Moreover, the tests allowed us to confirm the ductile behaviour and theredundancy potential in flat slabs. The project was achieved without any conventional rebars

in order to only focus on the steel fibres contribution. In real situations, anti-progressive

collapse rebars would be used from columns to columns to provide a robust structure. The

shear, punching and other design situations were out of the scope of this analysis. The

failures observed on the full-scale experiment were clearly associated with bending.

At the serviceability limit states, the slab presented cracks up to 0.5 mm, for an alternate

uniformly distributed loading condition, up to 4 kN/m². Until now, the model of the MC2010

however does not provide an analytical solution to calculate the crack opening for elements

reinforced by fibres only. This appeared to be a problem only if the slab is cracked under

service conditions. While the short-term maximum deflection observed at q = 2 kN/m²reached 1.2 mm without major cracks, we can however argue that the slab would be cracked


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at long term because of the creep (assuming a final creep factor of around 2.5 generates a

long-term maximum deflection beyond the value of 2.0 mm which was the deflection

observed at cracking). It means that long-term deflections should be calculated according to a

nonlinear model unless the concrete quality is better than the one used within this study.

For the ultimate limit state of the central panel, the use of the yield line theory combining

with the observed crack pattern allows to calculate the resisting moment of the full-scale

application. This result was firstly not in agreement with the ultimate bending capacity

computed from the characterization bending tests achieved in the laboratory on small prisms.

Flexural resistances obtained from samples directly sawn from the slab revealed however

lower post-peak properties. The use of these characteristics within the design guidelines from

the MC2010, together with a redistribution factor of 1.3, seemed to give a much better

agreement with the full-scale results.

Finally, research is still ongoing on companion specimens (round slabs with a diameter of

1700 mm and small round slabs with a diameter of 800 mm) to evaluate if the casting processof the slab had so much influence in comparison to the casting of the small prisms in their

moulds.

5 References

BCA (2001), Flat slabs for efficient concrete construction, British Cement Association, UK.

Destrée X. (2004), Structural application of steel fibre as only reinforcing in free suspended

elevated slabs: conditions - design - examples. Proceedings of the 6th RILEM

Symposium on Fibre-Reinforced Concretes (FRC) - BEFIB 2004, di Prisco M., Felicetti

R., Plizzari G. (Eds), Varenna, Italy, pp. 1073-1082.

Di Prisco M., Martinelli P. and Dozio D. (2014), The structural redistribution coefficient

K Rd : a numerical approach for its evaluation. Submitted manuscript for Cement &

Concrete Composites.

(2013), fib Model Code for Concrete Structures 2010, fédération internationale du Béton ( fib),

Lausanne, Switzerland.

Gossla U. (2005), Development of SFRC free suspended elevated flat slabs, Internal report,

Aachen University of Applied Sciences, Germany.

Johansen K. W. (1962), Yield-line theory. Cement and Concrete Association, London, UK.

Kennedy G. and Goodchild C. (2003), Practical yield line design. British CementAssociation, United Kingdom.

Michels J. (2009), Bearing capacity of steel fibre reinforced concrete. Ph.D. thesis, University

of Luxembourg, Luxembourg.

Michels J., Waldmann D., Maas S. and Zürbes A. (2012), Steel fibers as only reinforcement

for flat slab construction - Experimental investigation and design. Construction and

Building Materials, Vol. 26, No. 1, pp. 145-155.

RILEM TC 162-TDF (2003), Test and design methods for steel fibre reinforced concrete -

Recommendations for the σ-ε design method. Materials and Structures, Vol. 36,

No. 262, pp. 560-567.

Parmentier Et Al - The Flexural Behaviour of SFRC Flat Slabs (Final)

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