Crack Openings Determination of SFR Concrete B. PARMENTIER Belgian Building Research Institute (BBRI), Limelette, Belgium ;
[email protected] C. VAN GINDERACHTER Belgian Building Research Institute (BBRI), Limelette, Belgium
SUMMARY Cracking process is a common source of disaster for slabs on grade. Steel fibre reinforced concrete has been used since a long time to avoid large cracks for instance in long slabs. The advantages of SFRC for slabs on grade in terms of workability, working time and structural resistance are well known but no reference test and design methods exist. This is of importance to determine the effects of the drying shrinkage on the cracking behaviour. This lack of reference method was one problem the UE decided to try to solve by funding a European research programme to determine test and design methods for steel fibre reinforced concrete. Within the 10 European partners involved in this research the Belgian Building Research Institute (BBRI) was chosen to achieve a full-scale validation of a design procedure proposed by Stang & Olesen [3] for the control of shrinkage induced cracks. This paper deals with the potential utilization of the procedure mentioned above to calculate crack openings and crack inter-distances.
1
INTRODUCTION
The utilization of steel fibres into concrete is not new. One of the major markets for fibres is the industrial flooring. By incorporating this type of reinforcement into the cement bounded matrix the designer hopes for - a better control of the cracking process; - a reduced working time; - a better accessibility of the sub-grade to cast concrete; - potentially longer slab dimensions; - a reduced slab thickness This is of importance for the Serviceability Limit States (SLS) study of structures during the design procedure required by prEN 1992 (Eurocode 2). Despite the huge quantity of concrete used for slabs on grade no specific design methods for industrial concrete floors are explicitly described in Eurocode 2 or in Eurocode 7. Inside the consortium involved in a European BriteEURAM project funded to propose reference test and design methods for SFRC the Belgian Building Research Institute (BBRI) was chosen to achieve a fullscale validation of a design procedure proposed by Stang & Olesen for shrinkage induced cracks control.
2
TEST SET-UP
The goal of this part of the research is to check a theoretical model developed by Stang & Olesen [3] to calculate crack openings and crack inter-distances with the so-called “σ-w” approach for infinitely long slabs on grade submitted to restrained deformation (shrinkage). In order to achieve this task a full-scale study was elaborated to analyse the cracking behaviour of 3 slabs on grade associated with 3 different friction conditions with the sub-base. The supporting system is a scaffolding with three floors consisting of wooden formworks each supported by 4 timber beams. A picture of the system is given in Figure 1 while a section is given in Figure 2. Three slabs (25m x 1m x 0.12m) were tested with this system. The different characteristics of the slabs are given in Table 1.
The procedure aims to calculate the crack openings according to the stress-crack opening relationship in function of slab parameters (e.g. sub-base type). Figure 1: Picture of the whole system for restrained deformations. -1-
Each slab is made of concrete C25/30 cast with 25kg/m³ Dramix fibres RC65/60BN (incorporated in the truck mixer). The uni-axial tensile strength fctm is first supposed to be 0,5.fct,fl where fct,fl is the flexural tensile strength obtained with this type of concrete associated with this amount of fibres in 3 point bending tests. In this study the value of fctm was found to be 2.15 N/mm² and the Young Modulus E to be 30436 N/mm². These values will be checked after the cracks occur by testing concrete cores coming from the slabs with uni-axial tensile tests.
Slab 1 Slab 2 Slab 3
Slab 1
Compressive Resistance
Slump
[N/mm²]
[mm]
Sand
Age at notching [days]
29/05/01 17/12/01 20/12/01
162 3 3
Notch depth [mm] 120* 30 30
(*) Reduction of the section to the third of its original size.
Table 2: Sawing details of the slabs tested. Besides theses measurements internal strain measurements (embedded strain gages) and external strain measurements were also performed along the longitudinal dimension of the slab. At the ends of each slab different measuring points were also used on the depth of the slab in order to measure the differential shrinkage over the thickness.
It was first intended to not cut the slabs but after 162 days to wait cracks for slab 1 it was decided to cut the slab in the centre. So, the first slab was sawed to the third of its section while both other slabs were cut directly after 3 days of ageing just to obtain a reduced thickness of 9cm in place of 12cm. This is summarized in Table 2 were ef,28 is the free shrinkage at 28 days of the concrete used for the long slabs and kept in the test conditions. Sub-base
Date of casting
12 15 2 cm
εf,28
14
38.6
-
[µS] 5,5 100 Figure 2: Transversal section of the system.
-
Recycled 11538.9 aggregates 105 0/32 Limestone 41.3 85-95 Slab 3 aggregates 7/20 Table 1: Characteristics of the 3 slabs tested. Slab 2
-342 3
ANALYSIS OF THE CRACKING STATE OF THE SLABS
-408
The restrained shrinkage deformations of slabs 1, 2 and 3 are given in Figure 3, Figure 4 and Figure 5, respectively. SFRC Slab 1 Average over thickness
2600 2400 2200 2000 1800 1600
3 Days 7 Days 14 Days 20 Days 35 Days 56 Days 105 Days 229 Days
Shrinkage [µS]
1400 1200 1000 800 600 400 200 0 -200 -400 -600 0
2
4
6
8
10
12
14
16
18
20
22
24
Position [m]
Figure 3: Relative deformations along slab 1.
-2-
SFRC Slab 2 Up Position 2600
1 3 Days 10 Days 17 Days 28 Days 42 Days 63 Days ABS 63 Days
2200 2000 1800 Relative Shrinkage [µS]
1600
0.8
0.6
Absolute Shrinkage [mm]
2400
1400 1200 1000
0.4
800 600 0.2
400 200 0
0
-200 -400 -600
-0.2 0
2
4
6
8
10
12
14
16
18
20
22
24
Position [m]
Figure 4: Relative deformations along slab 2. SFRC Slab 3 Up Position
2400
7 Days
2200
14 Days
2000
28 Days
1800
42 Days
1600
61 Days
1400
ABS 61 Days
1
0.8
0.6
1200 1000
0.4
800 600 0.2
400
Absolute Shrinkage [mm]
Shrinkage [µS]
2600
200 0
0
-200 -400 -600
-0.2 0
2
4
6
8
10
12
14
16
18
20
22
24
Position [m]
Figure 5 : Relative deformations along slab 3.
-3-
Different observations can be made: - the average (restrained) shrinkage (over the thickness) along the slabs depends on the position. This shrinkage is uniform in the central part of the slab and increases on the last 2.5m at each extremity; - at 61 days the average shrinkage reaches ±400µS (300µS) at the extremities and ±200µS in the central part of the slab cast on sand (on gravel); - the cracking behaviour is observed by analysing the distribution of sudden positive deformation peaks. These observations were correlated with visual inspection and measurements will be discussed further. Only one crack has been observed for slabs 1 and 2 (in the centre) while slab 3 presents multiple cracks along its length. The evolution of the cracks as function of time is given in Figure 6 for the 3 slabs. It can be said that only one crack occurs for slabs 1 and 2 at the place of sawing while 5 cracks are observed for slab 3 along the length. The maximal crack opening reach 0.57mm and 0.41mm for slabs 1 and 2, respectively while it ranges from 0.25mm to 0.90mm for slab 3 (crack openings of 0.1mm are observed but do not represent cracks over the whole slab thickness). The distance between the cracks for this last slab ranges between 3m and 5m. The age of first cracking is about 40 days for slabs 2 and 3 while it is 219 days for slab 1.
4
THEORETICAL CONSIDERATIONS ON THE PROPOSED MODEL Before comparison between full-scale tests and the proposed model can be made some considerations can be presented. With the assumption of a particular stress-crack opening relationship and according to the input parameters the model gives two results for an infinitely long slab on grade: sinh(λ.l) = E.h l = τ .w 0
σ (w) ft
= 1−
2
w.ξ 1 + − 1 2.τ 0
forξ > 0
(1) for ξ = 0
E ft
w 2τ 0 ξ .w + for ξ ≥ 0 2 Eh E.h.2
and thus for: the simple-drop relationship Ö
(2)
σ w = γ . ft
2 2. τ 0 . 1 + ξ .h . ft .(1 − γ )2 − 1 E τ 0 w ξ .h = 2 h E ft 2 . .(1 − γ ) τ 0 E
for ξ ≠ 0 for ξ = 0
(3)
Cracks of SFRC Slabs
1
Absolute Shrinkage [mm]
0.8
Slab 1 - 11.9m Slab 2 - 11.9m
0.6
Slab 3 - 6.7m Slab 3 - 11.9m
0.4
Slab 3 - 14.3m Slab 3 - 17.9m
0.2
Slab 3 - 21.1m
0
-0.2 0
50
100
150
200
250
Age [Days]
Figure 6: Cracks of the 3 slabs in function of the time (legend : distances from left side of the slab).
-4-
Remarks
the bi-linear relationship
f − α .w (4a) σw = t 1 σ 2 − α 2 .w (4b) for
- it should be noted that the cracks should be observed between l and 2l. Moreover this distance is independent of the assumption made on the stress-crack opening relationship (simple-drop or bi-linear);
Ö
- theoretical solutions for the bi-linear relationship can be found for w1 simultaneously;
0 < w ≤ w1 = ( f t − σ 2 ) /(α1 − α 2 ) w1 < w ≤ σ 2 / α 2
w=
4.τ 0 .E 4.h.α12 − E.ξ
(
)
(5)
for w ≤ w1
E.ξ E.τ 0 2 2 w2 . α 22 − + w. 2.α 2 . f t − 2.σ 2 .α 2 − + σ 2 − 2.σ 2 . f t + f t = 0 4.h h
(
)
- in order to determine the toughness class the use of verification chart is needed [5]. The σ-w relationship for 3 point bending test can be reproduced with the theory of the crack band analysis. The Load-CMOD (or deflection) curve can be used to check the characteristics of the concrete used (in accordance with a specific dosage of fibres and specific type of fibres) and the assumption of the stress crack opening relationship.
(6)
for w > w1 with: 9 9
w: l:
λ2 = 9 9
τ0
crack opening [m] distance between the cracks [m]
ξ
E.h
4.1
is the initial cohesion of the interface slab/sub-base [kPa] ξ is the friction parameter of the interface slab/sub-base [Mpa/m] E is the Young modulus [Mpa] h is the thickness of the slab [m] ft is the uni-axial tensile strength [Mpa] γ is the toughness class w2, w1, α1, α2 are parameters describing the bi-linear stress-crack opening relationship
9 9 9 9 9 9
The two possible assumptions describing the toughness of SFRC are illustrated in Figure 7 for the concrete used in this study.
Characterization of the ground restraint
One of the most difficult task when dealing with the model is the determination of the parameters characterizing the interaction between the sub-base and the slab when moving occurs. Some authors use a linear relation between the movement of the slab and the horizontal force needed to cause this movement. This relation can be written as:
τ ( x) = τ 0 + ξ . u ( x)
Note that some authors simplify this relation by omitting the parameter “τ0” which represents the initial cohesion in the sub-base. Finally, some reference papers (ACI Committee 325 propose an alternative way by approaching the reality by a curve under the form: τ = k2.uα
(8)
Where τ is the shear stress, u is the displacement of the slab and k2 and α are constants depending on the subbase material and the vertical load which acts on the slab.
2.5 Simple-Drop Gamma=0.35 Bi-linear SFRC
2
(7)
Bi-linear PC
[MPa]
1.5
1
0.5
0 0
0.2
0.4
0.6
0.8
1
w [mm ]
In the reference paper of Stang & Olesen equation (7) is used. This model will be used to analyse the effect of the variation of the friction parameters. The analysis was carried out for SFRC slab on grade with the parameters of the slabs used in the framework of this study. The friction parameters were obtained from friction test results by Pettersson [2], Parmentier [1] or Stang & Olesen Error! Reference source not found..
Figure 7: Stress-crack opening relationship models according to Table 3.
-5-
4.2
Stang & Olesen parameters and the CSTC parameters. The results for the crack interdistance (min between 23.7m and 47.4m) are not very close to the observed values (average of 4m).
Comparison PC/SFRC with the model
Table 4 gives the results obtained according to the input parameters of Table 3 (characteristics of the slab on sand) and the assumption of simple-drop stress-crack opening (S-CO) relationship. τ0 [kPa]
2.7
ξ [Mpa/m]
2.8
E [MPa] h [m] ft [MPa]
30 436 Mpa 0.12 2.15 SFRC
PC
0 0.35 (wW1 SFRC C25/30 ; 25 kg/m³ h=12 cm ; ft=2.15 Mpa ; E=30436 MPa 2 xi=1 [Mpa/m] xi=1 [Mpa/m] xi=10 [Mpa/m] xi=10 [Mpa/m] xi=20 [Mpa/m] xi=20 [Mpa/m] xi=50 [Mpa/m] xi=50 [Mpa/m] xi=100 [Mpa/m] xi=100 [Mpa/m] xi=500 [Mpa/m] xi=500 [Mpa/m] xi=1000 [Mpa/m] xi=1000 [Mpa/m] lim w1
1.6 1.4 w [mm]
The toughness class of 0.35 is calculated by using verification chart based on 3 point bending test achieved in CSTC on RILEM beams of C25/30 with 25kg/m³ of fibres (same as for the 3 long slabs).
1.8
1.2 1 0.8 0.6 0.4 0.2
Results S-C
Concrete type
0
w
L
[mm]
[m]
SFRC
1.91
47
PC
3.53
61
relationship Simple drop
0
Table 4: Theoretical results. 5
5
10
15
20
25
30
τ0 [kPa]
Figure 8: Sensibility analysis of the ground restrain parameters according to the bi-linear S-CO relationship and wW1 SFRC C25/30 ; 25 kg/m³ h=20 cm ; ft=2.15 Mpa ; E=30436 MPa 2
The results are given at page 8.
xi=1 [Mpa/m] xi=1 [Mpa/m] xi=10 [Mpa/m] xi=10 [Mpa/m] xi=20 [Mpa/m] xi=20 [Mpa/m] xi=50 [Mpa/m] xi=50 [Mpa/m] xi=100 [Mpa/m] xi=100 [Mpa/m] xi=500 [Mpa/m] xi=500 [Mpa/m] xi=1000 [Mpa/m] xi=1000 [Mpa/m] lim w1
1.6 1.4 w [mm]
By comparing the theoretical solutions and the observed values it appears that : - The values calculated with the bi-linear relationship are lower than with the simple-drop relationship - The comparison between real cracks and theoretical values with bi-linear relationship are in good agreement for sand as sub-base (slab 1) with Pettersson parameters while the other parameters give overestimation of the crack opening and crack spacing. - For recycled aggregates (slab 2) the results are also overestimated for the crack opening as well as for the crack spacing. - For graded gravel (slab 3) the results for the crack opening are quite good for the Pettersson parameters and slightly overestimated with the
1.8
1.2 1 0.8 0.6 0.4 0.2 0 0
5
10
15
20
25
30
τ0 [kPa]
Figure 9: Sensibility analysis of the ground restrain parameters according to the bi-linear S-CO relationship and w
