chapter 3 experimental study - upcommons.upc.edu

Experimental and Numerical Analysis of the Shear Failure in SFRC Experimental Study 42

_____________________________________________________________________________________

CHAPTER 3 EXPERIMENTAL STUDY

3.1. INTRODUCTION The experimental study that has been carried out in this thesis has two main objectives: 1. Characterise the concrete behaviour in mode II, it means the failure of SFRC

subjected to direct shear loading, and also the SFRC behaviour under direct shear loading combined with a compression of the shear plane.

2. Study if the set-up used to carry out the mixed-mode analysis is good enough to model the SFRC behaviour under mixed-mode conditions, since in that case this could be an easy test to characterise this behaviour.

To reach these objectives, push-off tests on prisms have been used to quantify the shear-stress displacement. With the aim of analysing if the set-up gives good results to study SFRC behaviour under mixed-mode conditions, different transversal compression have been applied to push-off specimens. The values that have been used to the transversal compression have been 0, 0.25·ft and 0.5·ft where ft is the tensile strength of the material. In all cases this transversal load has been maintained constant. Some specimens in which the compressive load has been let to grow freely according the shear crack growth have been tested as well. Three-point bending tests have been performed as well. With these tests SFRC behaviour in mode I has been characterised and data used in an inverse


_____________________________________________________________________________________

analysis from which parameters are obtained for modeling the push-off tests by means of a finite element software. To analyse the influence of the amount of fibres, two types of concrete were cast. One with 0.5% of fibres and another with 1% of fibres (regarding the total volume of the concrete). From each type of concrete, beams were also cast to characterise the mode I. As a reference, tests were also carried out on similar plain concrete specimens. The methodology for the push-off tests follows the work previously presented by [1]. For the three-point bending test the methodology used follows the work presented by [2]. 3.2. TESTING PROGRAMME As mentioned above two different types of tests were performed: three-point bending test and push-off tests. Beam tests have the aim of characterising the SFRC behaviour under flexural conditions and push-off tests have the aim of represent the concrete behaviour under shear direct loading. To be sure that tests were done following the methodologies specified in the previous section firstly some pilot tests were carried out. These tests were useful to calibrate the testing machines and to adjust the different set-ups used for each type of test. With the aim of analysing the influence of the amount of fibres in the SFRC behaviour, different concretes were cast changing the percentage of fibres. Plain concrete specimens were used as a reference in all tests and also in pilot tests. In Table 3.1, the number of tests done can be seen according to the type and the amount of fibres used.

Amount of Fibres Test Type 0.0% 0.5% 1.0%

Pilot Test 3 - 3 Beam Test Test - 3 3 Pilot Test 4 - - Push-off Test Test - 4 8

Table 3.1: Number of tests done according the type and

the amount of fibres. 3.3. MATERIALS USED Normal strength concrete has been used. Four different concretes have been cast to carry out all the experiments, the three-point bending tests and the push-off tests. The components of the mixture were the same but the percentage of fibres was changed as it has been indicated before. The fibres used in the


_____________________________________________________________________________________

concrete were Dramix ZP 30/50. The different concrete mixtures are shown in Table 3.2: Material Composition Composition Composition Composition

[kg/m³] [kg/m³] [kg/m³] [kg/m³] Amount of fibres (in vol.) 0.0% 1.0% 1.0% 0.5%

RAPID Cement 245 245 245 245 Fly ash 94.5 94.5 94.5 94.5 Microsilica 10.5 10.5 10.5 10.5 Water 137.9 138.9 140.0 141.3 Air agent SIKA15B 1.050 1.050 0.834 0.834 Plasticizer 2.94 3.28 4.27 3.80 0-4 SØ SAND KL.A Sand 753.6 753.1 753.7 753.3 4-8 SØ Gravel 454.4 453.3 451.3 451.0 8-16 SØ Gravel 594.4 568.4 568.3 581.3 zp30/50 Fibre 0.0 78.0 78.0 39.0

Table 3.2: Different compositions of the concretes that have been cast. With the same concrete that was used to cast the specimens, three cylinders of 190 mm height and 100 mm of diameter were made in order to calculate the compressive strength of each mixture. The testing machine to carry out the compressive tests is shown in Figure 3.1.

Figure 3.1: Testing Machine to carry out the compressive tests. The compressive strength has been calculated as the mean value of the three compressive strengths of the cylinders. The value of the characteristic strength


_____________________________________________________________________________________

has been calculated using the Spanish Code, EHE Instrucción de Hormigón Estructural (1998) as following

8' += ckcm ff (3.1) where fcm is the average compressive strength and f’ck is characteristic compressive strength of the concrete without taking into account the shape of the cylinder. To calculate fck a coefficient has to be applied to take in consideration the shape and of the specimen. In our case, the nearest coefficient shown in the Table 3.3 to our cylinder is 0.97 that corresponds to a cylinder of 200 mm height and a diameter of 100 mm.

Conversion Coefficient to Cylinder Specimen of 15 x 30 cm Type of specimen Dimensions (cm)

Variation Limit Mean Values 15 x 30 - 1.00 10 x 20 0.94 to 1.00 0.97 Cylinder 25 x 50 1.00 to 1.10 1.05

10 0.70 to 0.90 0.80 15 0.70 to 0.90 0.80 20 0.75 to 0.90 0.83

Cube

30 0.80 to 1.00 0.90 15 x 15 x 15 0.90 to 1.20 1.05 Prism 20 x 20 x 60 0.90 to 1.20 1.05

Table 3.3: Compressive Tests on different specimens at the same age (EHE Instrucción de

Hormigón Estructural (1998)).

Now the compressive strength can be calculated as

'ck

'ckck f.ff 970=α= (3.3)

Once we have the value of the characteristic compressive strength the value of the average strength fct,m can be calculated using the following expression

3 2300 ckm,ct f.f = (3.4)

where the values of fck and fct,m are expressed in N/mm2. On the other hand, with the value of the mean compressive strength the Young’s Modulus can be calculated as following (EHE Instrucción de Hormigón Estructural (1998):

3,8500 jcmj fE = (3.5)


_____________________________________________________________________________________

where Ej is the secant modulus, more suitable for deflection calculations (in our case cmod calculations). Sub index j indicates the value of E at a certain age. If the age is not 28 days, a coefficient must be applied. The values of the mean compression strength, mean tensile strength and the Young’s Modulus are shown in Table 3.4. Concrete Number Amount of Fibres Mean Compressive

Strength (N/mm2) Mean Tensile

Strength (N/mm2) Young’s Modulus

(N/mm2) Plain 1 0.0% 60.52 4.12 33372 SFRC 2 0.5% 60.18 4.11 33310 SFRC 3 1.0% 54.66 3.81 32258 SFRC 4 1.0% 58.36 4.01 32970

Table 3.4: Characteristics of different concrete cast.

The results of the table before could seem illogical, because an increase in the tensile strength of the concrete and in the Young Modulus could be expected as the percentage of fibres increases. However, some researchers have proposed that there is a decrease in the material strength as the percentage of fibres increases. This fact could explain the results obtained with the different mixtures that where cast (see Table 3.5):

Concrete Number Amount of Fibres % Air within the mixture

Plain 1 0.0% 7.0 SFRC 2 0.5% 7.8 SFRC 3 1.0% 10.0 SFRC 4 1.0% 9.0

Table 3.5: Percentage of air within the concrete mixture.

3.4. THREE-POINT BENDING TESTS 3.4.1. Test Description Next all the experimental procedures that they have been carried out in the flexural analysis are treated. Note that the procedure used in the performance of the three-point bending test is based on [2]. This test is used to evaluate some parameters of steel fibre reinforced concrete (SFRC) in terms of areas under load – deflection curve. These parameters can be obtained testing a notched beam under three-point loading. Since this thesis is not fully focussed on flexural behaviour but SFRC behaviour under shear tension, the mid – span deflection in the beams has not been measured and only measurements of the crack mouth opening displacement (CMOD) have been taken. The advantage of this test is a continuous measurement of the CMOD versus applied load as it is explained later. These measurements will be used as input data in an inverse analysis programme to get the parameters that control the stress-crack opening relationship in SFRC.


_____________________________________________________________________________________

Concrete beams of 150 x 150 mm cross-section with a length of 600 mm have been used. The span length of the beams is 500 mm, so the distance between supports and the edge of the beam is 50 mm. An illustration of the test and the set up to measure the CMOD versus Load is shown in Figure 3.2.

APPLIED LOAD

CMOD MEASURING DEVICE PLACED UNDER THE NOTCH

Figure 3.2: Illustration of the dimensions of the beams

and the set-up to measure the CMOD 3.4.2. Experimental Details 3.4.2.1. Manufacturing of the Specimens All specimens were cast in wood moulds of 600 mm length, 150 mm width and 150 mm height. Compaction of the specimens has been carried out through external manual vibration; in Figure 3.3, moulds and concrete just after cast in them are shown. The specimens have been demoulded 24 hours after they have been cast. Later on, the specimens have been cured in a tank in which the water was at a temperature of 35°C for fourteen days. After this the specimens were stored in other tank at room temperature, of 20°C. The two tanks were in a room in which the relative humidity is at least 95 %. Figures 3.4 and 3.5 show the two curing tanks.


_____________________________________________________________________________________

Figure 3.3: Moulds and concrete after vibration.

Figure 3.4: 35º C Tank with the specimens in it.

Figure 3.5: 20º C Tank with the specimens in it.


_____________________________________________________________________________________

The specimens have been notched using a vertical diamond impregnated saw. The procedure of the sawing has been as follows: beams have been turned 90° and have been sawn 25 mm (+/- 1 mm) depth at mid-span section. The width of the notch is 3.2 mm. The notches were done 15 days after the specimens were cast. Once they were made, specimens were put in the tank of 20°C. The specimens were in this tank at least for two weeks. Figure 3.6 shows the sawing procedure.

Figure 3.6: Sawing procedure of the beam.

3.4.2.2. Experimental Details To carry out the three-point bending tests, a machine capable of controlling the deflection was used, an INSTRON 5500 - R 6025 system (see Figure 3.7). The machine can load the beam with a constant rate of increase of the CMOD.

Figure 3.7: Test machine used to carry out the three-point

bending test measuring CMOD.


_____________________________________________________________________________________

Beams are supported on two rollers. Each of them has a length of 300 mm and its diameter is 30 mm. These rollers restrict the transversal displacement, while the longitudinal displacement and the rotation in the beam plane are permitted. To avoid the longitudinal movement of the beam as a rigid solid, one of the rollers has to be fixed. The necessary degrees of freedom that have to be provided for the rollers are shown in Figure 3.8.

Figure 3.8: Position of the load and supports of the beam specimen.

Note that one contact has to be fixed to obtain two degrees of freedom. The beam is loaded through a steel piece of 90 mm length. The contact between this steel piece and the specimen is rounded to provide a line load in the mid-span section. To calibrate the machine at the loading speed specified by RILEM, a wooden beam has been used. 3.5. PUSH-OFF TESTS They have been many tests geometries that have been used with the aim of characterize the shear behaviour in SFRC. The main difficulty associated with the application of fracture mechanics theory in concrete is the effects of slow crack growth that can occur during testing. The importance of the slow crack growth varies with the relative stiffness of the test specimen and, in particular, with the strain energy stored in the test specimen prior to crack initiation. Before the crack is formed, the amount of strain energy stored in the test specimen due to Mode II shear can be very large. The specimens fail with unstable crack propagation with a considerable amount of noise, that is a typical brittle of fracture and hence slow crack growth is not considered to be a major factor with shear strength testing [7]. In this thesis, push-off tests on prisms have been used to quantify the shear stress-displacement behaviour of SFRC. As a reference, tests were also carried out on similar plain concrete specimens. The main objective of these tests is to analyse the relationship between the flexural response and the shear response in shear configuration. As it will be

SUPPORT

SUPPORT

L

LOADING DEVICE

F


_____________________________________________________________________________________

mentioned in next section, some changes have been introduced in the set-up defined by [1]. Table 3.6 shows the number of tests done in each type of the three different types of tests that were performed in order to obtain as much information as possible from the specimens. In some specimens, a lateral compressive pressure was introduced. This pressure can be considered as an active pressure, if a certain value of confinement is applied before the test has begun and the stress is maintained constant in the bolts, or a passive pressure, if the bolts are allowed to load freely as the specimen is dilating.

Amount of Fibres

Passive Conf. Active Conf. σt = 0.25·ft

Active Conf. σt = 0.50·ft

No Confinement

0.0% 4 0.5% 2 2 1.0% 2 2 2 2

Table 3.6: Number of experiments carried out in each type of test. Note that the value of ft

corresponds to the value of the tensile strength of the concrete used for the experiment (see Table 3.4)

3.5.1. Test Description The objective of this test is to characterize, at a material level, the failure of SFRC subjected to direct shear loading. With this test, load (or stress) – displacement of SFRC can be obtained. As the vertical displacement is measured, a relationship between the vertical and the horizontal displacement is easily obtained as well. As it has been mentioned before, two different kind of tests have been carried out: with and without lateral confinement of the specimen. Push-off tests without lateral confinement are based on the set-up defined in [7], while the tests that have been performed with a lateral confinement pressure, a new set-up has been design. Concrete prisms of 150 x 150 mm cross-section with a length of 260 mm have been used and the transversal cuts are 100 mm from the each side of the specimen. An illustration of the specimen is shown in Figure 3.8. As it can be seen from Figure 3.9, the two notches define a vertical shear plane that has a mean area of 90 cm2.


_____________________________________________________________________________________

Figure 3.9: Dimensions in cm of the specimens used.

The specimen width is 15 cm. 3.5.2. Experimental Details 3.5.2.1. Set-ups used 3.5.2.1.1. Set-up Without Lateral Confinement This set-up was developed by Barragán and Gettu (2001), [1] and it consists of measuring the vertical and the horizontal displacement of the specimen while it is being loaded. The loading bar was 25 mm width and 25 mm height. The measurements of the displacements are done by means of LVDTs placed horizontally and vertically on one of the faces of the specimen to measure the respective deformations. The vertical LVDT gives the load – line displacement, which can be taken as the slip after the crack is formed. The horizontal LVDT gives the dilatation of the crack or the crack opening. Figure 3.10 shows the set-up in which there is no confinement introduced.


_____________________________________________________________________________________

Figure 3.10: Set-up without lateral confinement. 3.5.2.1.2. Set-up With Lateral Confinement This set-up was designed with the aim of introducing a lateral confinement pressure just in the plane defined by the two notches, it means, in the shear plane. The measuring and the loading system are the same as in the case there is no confinement pressure. However, to introduce the lateral confinement, two steel bars are placed in each notched face of the specimen. The two bars are held together by means of two bolts, one of each side. Each bolt has strain gauges that permit the measurement of the strain in the bolts, while the specimen is being loaded, and consequently the load. As it will be mentioned in point 3.6.2. in some tests some problems occurred with the stress transmitted to shear plane that cause a flexural failure of the specimen instead of shear failure. To avoid this phenomenon, two steel pieces were placed in a hole made in the steel beam. These two pieces allow the bolts to rotate if the system is not perfectly aligned. As mentioned before, two different configurations were performed with lateral confinement: a first one with active compression of the specimen and a second one with a passive restraint. In the tests in which an active compression pressure has been introduced, the idea of the test is to maintain the tension in the bolts constant. With this aim,


_____________________________________________________________________________________

some springs discs have been placed in the bolts between the steel beam and the nuts to absorb the displacement of the bolts while the specimen is dilating due to the loading process. An illustration of the set-up with an active restraint is shown in Figure 3.11. In this figure, the spring discs and the washers to avoid a flexural failure can be seen.

Figure 3.11: Set-up with an active lateral confinement.

On the other hand, in tests in which a passive restraint has been introduced, no spring discs has been placed in order to obtain the tension increase in the bolts as the specimen is being loaded. If spring discs were placed, as in the previous case, there would not be stress increase in the bolts, since at the beginning of the test, there is no stress in the bolts. Figure 3.12 shows the set-up used in the tests in which a passive lateral confinement has been introduced.


_____________________________________________________________________________________

Figure 3.12: Set-up with passive lateral confinement. 3.5.2.2. Manufacturing of Specimens All specimens were cast in wooden moulds of 600 mm length, 150 mm width and 150 mm height and were divided in two parts by a wooden piece of 80 mm width to obtain two specimens of 260 mm length. As the push-off specimens were made from the same mixture as the beam specimens, compaction and curing processes were carried out following the same procedures as in the case of the beams; they are described in detail in section 3.4.2.1 of this chapter. The specimens have been notched using a vertical diamond impregnated saw. The procedure of the sawing has been as follows: two notches were cut as shown in Figure 3.13, each of them of 75 mm length and 3.2 mm width. To ensure a distance of 60 mm between the two notches, cuts were made measuring the distance to cut from the same side of the specimen. The notches were cut 15 days after the specimens were cast. Once they were made, the specimens were put in the tank of 20°C. the specimens were in this tank for at least two more weeks. Figure 3.13 shows the sawing procedure.


_____________________________________________________________________________________

Figure 3.13: Sawing procedure of the push-off. 3.5.2.3. Experimental Details All tests were carried out using an Instron 8505 servo-hydraulic testing system under closed loop conditions. All tests were controlled by means of piston displacement, with a displacement rate of 0.001 mm/s following the procedure established in [1] The specimen was supported by a steel bar of 25 mm width placed at the bottom of it and for the loading bar, placed on the top, also of 25 mm width. The initial load of the test is less than 1 N that was enough to maintain the specimen in the right position to carry out the test The voltage signal from LVDTs and strain gages on the bolts were recorded connecting them to the data acquisition unit. 3.5.2.3.1. Set-up without Lateral Confinement Displacements were measured through two LVDTs. The horizontal one was placed 30 mm from each notch and the vertical one was placed measuring the displacement of the line defined by the roots of the two notches. The two LVDTs were suitably calibrated (see Annex – C) so displacements were obtained from the calibration function. It can be seen from Annex – C that these calibration functions are almost straight lines (note that the correlation factor of each function is almost 1.00). 3.5.2.3.2. Set-up With Lateral Confinement


_____________________________________________________________________________________

All considerations below are valid for both the set-up with passive restraint and for the set-up with active restraint. In this set-up, the measuring system of the horizontal dilation of the specimen has changed. However, the vertical displacement of the specimen is the same as in the case there was no confinement. To measure the horizontal displacement, two little holes of φ 8mm were made in one steel beam. Through each hole, the head of a LVDT was introduced. So in this set-up two measurements, each one from one face of the specimen, were done. The two little holes were made as near as it was possible from the specimen (10 mm from the faces of it) to avoid the influence of the deflection of the steel beam due to force in the bolt. Subsequently, the total horizontal deformation has been calculated as the average of the two horizontal measurements. The two horizontal LVDTs, the vertical LVDT and the two bolts were suitably calibrated (see Annex – C). The calibration of the LVDTs was made following the same procedure detailed in point before, while the calibration of the bolts was carried out introducing tension in steps and taking note of the voltage given by the data acquisition unit at those stresses. So displacements and stresses were obtained from the each calibration function. It can be seen from Annex – C these calibration functions are almost straight lines (note that the correlation factor of each function is almost 1.00). As it has been said in point 3.5, there were two different values of the transversal pressure, σt = 0.25·ft and σt = 0.50·ft. In the first test of 1% in volume of steel fibres with a lateral pressure of 0.50·ft, some problems occurred. As the compression was quite high, the specimen broke along the plane defined by the loading bar and the root of the upper notch instead of breaking in the plane defined by the roots of the two notches. To avoid that, two steel plates were placed between the upper notch and the upper side of the specimen and between the lower notch and the lower face of the specimen as it is shown in Figure 3.14.


_____________________________________________________________________________________

Figure 3.14: Specimen with two steel plates to force the specimen

to break in the shear plane. 3.6. RESULTS 3.6.1. Results of the Three-Point Bending Tests In Figures 2 and 3, typical tensile load CMOD response from three-point bending tests are shown. As can be seen, there is a big difference between SFRC and plain concrete behaviour when they are subjected to flexural load. Note that the two plots represent the same curves but changing the horizontal axis scale. There are some aspects that have to be discussed about the plots in terms of the curves and their characteristics according to the different zones of the curve described in Chapter 2 (point 2.2.2.1.). The first part of each curve corresponds to the pre-cracked concrete specimen. This part is controlled by the Young’s modulus E, and the tensile stress ft. E controls the initial slope and ft the end of the elastic phase, or first phase. As concrete behaves as a quasi-brittle material, the pre-cracking nonlinearity is not high (under tensile load). According to the theoretical model of the fibres and concrete response established in 2.3.2 the amount of fibres only affects the behaviour at larger deflections. This means that the elastic response of concrete is independent of the amount of fibres. So Young’s Modulus and tensile strength depend on the matrix mixture. From Figure 3.15, no important differences can be seen between plain and 1% SFRC or 0.5% SFRC in the


_____________________________________________________________________________________

elastic behaviour. However, 0.5% SFRC shows some difference in the initial slope that could be due to variability of concrete properties. As shown in Tables 3.5 and 3.4, the values of the tensile strength and the Young’s Modulus are similar for the different types of concrete.

Figure 3.15: Load-CMOD responses for plain concrete, 0.50% and 1.00% SFRC. The second part of the curve is between the cracking load and the peak load. If the load is increased, micro-cracks form at the mortar/aggregate interfaces leading to the pre-peak non-linearity. With a further increment in stress, more micro-cracks are progressively formed at interfaces between the mortar and aggregate of smaller size. The peak load is reached when micro-cracks randomly distributed throughout the material become a dominant macro-crack, localized in a narrow zone. It seems obvious that the development of micro-cracks depends on the percentage of fibres in concrete. So here appears the first important difference between plain and SFRC. For much higher percentages of fibres, higher is the peak-load. In other words, fibres in concrete causes an increase in the peak-load, and more importantly, an extraordinary increase of the peak-CMOD (CMOD corresponding to peak-load). So fibre reinforced concrete is much more ductile than plain concrete (the brittleness of concrete is improved if a certain percentage of fibre are added). This fact can be observed in Figure 3.16:

0

5000

10000

15000

20000

25000

30000

35000

0.00 0.25 0.50 0.75 1.00

CMOD (mm)

Load

(N)

0.00% Fibres 0.50 % Fibres 1.00 % Fibres


_____________________________________________________________________________________

06000

1200018000240003000036000

0.00% 0.50% 1.00%

Percentage of Fibres

Load

(N)

0.000.100.200.300.400.500.60

CM

OD

(mm

)

Peak Load Peak CMOD

Figure 3.16: Values of Peak Load and Peak CMOD versus the

percentage of fibres.

From the above figure it seems that there is a linear relationship between the peak load and the percentage of fibres. The correlation factor of the peak load versus the percentage of fibres is R2 = 0.9956 and the equation of the line is:

y = 7744.8 · x + 7150.6 where y = Peak Load and x = % of Fibres. However, as mentioned before, the major influence of fibres is the sharp increase of the Peak CMOD with a small quantity of fibres. Although a big increase in Peak CMOD is produced from 0.5% to 1%, the most important difference is produced from plain concrete to 0.5% SFRC. This indicates the importance of fibres in concrete ductility. Lastly the post-peak softening of the curve is treated. Plain concrete, immediately after the peak-load is reached, fractures progressively. The major mechanism responsible of this type of failure is the so-called bridging mechanism which breaks the continuity of the dominant macro-crack so that the smaller discontinuous segments can no longer grow unstably. The bridging is provided by the interlocking of aggregates, by the strain hardening capacity of unbroken ligaments between macro-crack segment and by voids which attract and trap macro-cracks. In SFRC additional significant bridging is provided by fibre reinforcement [13]. This behaviour can be observed in Figure 3.17. As shown, the SFRC curves (either 0.5% or 1%) exhibit far more gradual post-peak tension softening than plain concrete. This behaviour is analogous to peak-load versus percentage of fibres behaviour commented before. Small percentages of fibres induce an extraordinary different behaviour in terms of ductility. However, once a certain amount of fibres is added to concrete, there is no significant change in the shape of the curve.


_____________________________________________________________________________________

Figure 3.17: Load-CMOD responses for plain concrete, 0.50% and 1.00% SFRC.

If we observe the results of the ultimate load versus the percentage of fibres we can see an increase of the ultimate load as the quantity of fibres increases. This increase function can be modelled as a straight line If it is so, R2 = 0.9705 and the equation is

y = 5691.1 · x + 5114.8 where y = Ultimate Load and x = % of Fibres. Figure 3.18 shows the relationship between the Ultimate Load versus de percentage of fibres. The relationship between the Ultimate cmod and the amount of fibres is shown as well.

0

3000

6000

9000

12000

15000

0.00% 0.50% 1.00%


Load

(N)

5.10

5.20

5.30

5.40

5.50

5.60

CM

OD

(mm

)

Peak Load Ultimate CMOD

Figure 3.18: Values of Ultimate Load and Ultimate CMOD versus the

percentage of fibres. Lastly it would be appropriate to compare the values of Fracture Energy, GF, for each concrete, to evaluate changes in concrete behaviour due to the addition of

0

5000

10000

15000

20000

25000

30000

35000

0.00 1.00 2.00 3.00 4.00 5.00 6.00

CMOD (mm)

Load

(N)

0.00% Fibres 0.50 % Fibres 1.00 % Fibres


_____________________________________________________________________________________

fibres. In SFRC the tests cannot be performed until zero load, so GF cannot be calculated by integrating the load-displacement curve. That is the reason why vertical displacement had not been measured, and why CMOD was measured. The comparisons will be done in chapter 4 when the results of the inverse analysis programme are discussed. 3.6.2. Results of the Push-off Tests The processing of the results obtained from the push-off tests, must be done in terms of σ(ω,δ) and τ(ω,δ), where ω is the vertical displacement and δ is the horizontal displacement, to investigate the combined behaviour of tensile and shear stresses in concrete. In Figures 3.19, 3.20 and 3.21 typical shear stress vs. vertical and horizontal displacement responses for plain and SFRC are shown. Figure 3.19, shows a typical stress-displacements in the case of plain concrete. As it can be seen, the response is practically linear up to failure, which is strongly brittle resulting in unstable control of the test. This fact generates that the post peak response in this kind of concretes cannot be obtained. Figures 3.20 and 3.21 show two typical stress-displacements regarding to SFRC, one for 0.50 % in volume of fibres and the other one for 1.00 % of fibres. Both 0.5% and 1% SFRC, exhibit a softening a gradual post-peak tension softening due to dowel-action and pull-out of fibres.

Figure 3.19: Typical shear stress-displacements response in plain concrete.

0.0

1.5

3.0

4.5

6.0

7.5

0 0.05 0.1 0.15 0.2 0.25 0.3

Displacement (mm)

Stre

ss (M

Pa)

Vert. Displa. (mm) Hor. Displa. (mm)


_____________________________________________________________________________________

Figure 3.20: Typical shear stress-displacements in 0.5% SFRC.

Figure 3.21: Typical shear stress-displacements in 1% SFRC. However, 0.5% and 1% SFRC behave in a very different way as it can be seen from Figure 3.22 and 3.23, in which a comparison between the three different types of concrete shear stress vs. vertical and horizontal respectively are shown.

Figure 3.22: Comparison between plain, 0.5% and 1% SFRC

stress-vertical displacement.

0.0

1.5

3.0

4.5

0 1 2 3 4 5 6 7

Displacement (mm)

Stre

ss (M

Pa)


0.0

1.5

3.0

4.5

6.0

7.5

9.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Displacement (mm)

Stre

ss (M

Pa)


0.0

1 .5

3 .0

4 .5

6 .0

7 .5

9 .0

0 .00 1 .00 2 .00 3 .00

V ertica l D isp lacem en t (m m )

Stre

ss (M

Pa)

1% F ib res 0 .5% F ib res 0% F ib res


_____________________________________________________________________________________

Figure 3.23: Comparison between plain, 0.5% and 1% SFRC

stress-horizontal displacement. It would seem logical that maximum shear stress increased with the percentage of fibres. However, there is a big decrease of peak shear stress in 0.5% SFRC. Moreover, this concrete exhibits a completely different behaviour as 1% SFRC in terms of displacements. The residual horizontal displacement is much larger than the vertical one, while both 1% SFRC and plain concrete it is the other way round. The first point could be explained taking into account that in plain concrete, the nature of the material makes the test unstable and it is possible that the testing machine registers values of stress larger than they really are. This effect is shown in Figure 3.24:

Figure 3.24: Maximum shear stress and vertical displacement

vs. percentage of fibres. The second point that could be explained is the following: the amount of fibres allows the crack to dilate but the percentage of fibres is not high enough to restrict the horizontal displacement as in the case of 1% SFRC. This fact can be seen the two different types of fracture in Figure 3.25.

0 .0

1 .5

3 .0

4 .5

6 .0

7 .5

9 .0

0 .0 0 0 .2 5 0 .5 0 0 .7 5 1 .0 0 1 .2 5 1 .5 0

H o r iz o n ta l D is p la c e m e n t (m m )

Stre

ss (M

Pa)

1 % F ib re s 0 .5 % F ib re s 0 % F ib re s

3.00

4.00

5.00

6.00

7.00

8.00

9.00

0.00% 0.50% 1.00%


Stre

ss (M

Pa)

0.000

0.100

0.200

0.300

0.400

0.500

0.600

Dis

plac

emen

t (m

m)

tmax Vert. Displa.


_____________________________________________________________________________________

Figure 3.25: (a) 0.5% (left), (b) 1% SFRC (right) failures. As it can be seen comparing Figure 3.26 (a) and (b) the crack is much more dilated in 0.5% than in 1% SFRC, while the vertical displacement is smaller in the first case than in the second one. So if the amount of fibres is not high enough, we can interpret this test to be that of a controlled test on plain concrete. Another way to analyse the high dilation in 0.5% SFRC test specimen can be seen in Figure 3.26 in which the increase of the relative difference between maximum shear stress and residual shear stress and the small decrease between 0.50% and 1.00% SRFC are clear .

Figure 3.26: Relative and absolute differences between maximum and residual shear stress vs.

the percentage of fibres. The shear failure can be explained in detail using Figure 3.27 in which vertical vs. horizontal displacement are plotted. The first part (until point A) is controlled by the concrete matrix. Until point A is reached, there are almost no horizontal displacements. Point A corresponds the first crack load and it is at this point in which the horizontal displacement begins to grow.

0.0020.0040.0060.0080.00

100.00

0.00% 0.50% 1.00%


Dec

reas

e (%

)

0.001.302.603.905.206.50

Stre

ss (M

Pa)

Relative diference between Peak Shear Stress and Ultimate Shear StressAbsolut diference between Peak Shear Stress and Ultimate Shear Stress


_____________________________________________________________________________________

0.00.51.01.52.02.53.0

0.00 1.00 2.00 3.00 4.00

Horizontal Displacement (mm)

Vert

ical

Dis

plac

emen

t (m

m)

1% Fibres 0.5% Fibres 0% Fibres

Figure 3.27: Vertical vs. Horizontal displacements.

This increase in the crack width activates the fibre contribution and completely cracks the matrix. Hereafter, the fracture can be considered as a shear process in which the load is transferred by the fibres [1]. This fact explains the brittle rupture of plain concrete in point A. Another significant conclusion that can be done from Figure 3.27, is the significantly different behaviour in terms of horizontal displacements. In 0.5% SFRC once point A has been reached, for a certain horizontal displacement increment, the vertical displacement is much smaller than for the case of 1% SFRC. This can be seen as another way of explaining larger dilation in 0.5% SFRC that we have discussed above. Up to here, only tests without lateral confinement have been treated. Now the tests with active and lateral restraint are going to be treated according to different parameters. This analysis is performed in two ways:

• Comparing the same concrete (same amount of fibres) with different

tests. • Comparing the same tests with different percentage of fibres in concrete.

Analysis of 1.0% SFRC test results To begin with this analysis, shear stress vs. vertical and horizontal displacements plots must be respectively observed in Figures 3.28 and 3.29.

A

B

B


_____________________________________________________________________________________

0 .0

2 .0

4 .0

6 .0

8 .0

10 .0

12 .0

0 .00 0 .50 1 .00 1 .50 2 .00 2 .50 3 .00

V ertica l D isp lacem en t (m m )

Stre

ss (M

Pa)

N o R es tra in t 0 .50 ·ft P ass ive R es tra in t 0 .25 ·ft

Figure 3.28: Shear stress-vertical displacement in 1.00% SFRC in No Restraint, Passive Restraint and Active Restraint (σc = 0.25·ft and σc = 0.50·ft).

0 .0

2 .0

4 .0

6 .0

8 .0

10 .0

12 .0

0 .00 0 .25 0 .50 0 .75 1 .00 1 .25 1 .50

H o rizo n ta l D isp lacem en t (m m )

Stre

ss (M

Pa)

N o R es tra in t 0 .50 ·ft P ass ive R es tra in t 0 .25 ·ft

Figure 3.29: Shear stress-horizontal displacement in 1.00% SFRC in No Restraint, Passive Restraint and Active Restraint (σc = 0.25·ft and σc = 0.50·ft).

The first point that must be discussed is that the elastic phase of any test result is not affected by the restraint pressure, and we consider that the decrease in the 0.25·ft elastic slope is due to concrete non-uniformity. As it has been explained before, this fact occurs because at those stages of the test, the fracture is controlled mainly by the matrix (see the almost negligible horizontal displacements in Figure 3.29). If we follow the shape of each curve from the beginning of the test to the end, we see that the inelastic pre-crack zone is wider as the transversal load grows. This means that to break completely the matrix, a higher shear stress is necessary when the lateral pressure increases. This leads to an increase in the peak shear stress (excepting the case in which the lateral confinement is 0.25·ft). If this case is not taken into account, (see paragraph before) we see an increase in this stress of 27% from No Restraint test to Passive Restraint and of 30% from Passive Restraint to Active Restraint (σc = 0.50·ft) – the increase between σc = 0.25·ft and σc = 0.50·ft is 41.6%. See Figure 3.31.


_____________________________________________________________________________________

6.00

7.00

8.00

9.00

10.00

11.00

12.00

No Restraint Passive Restraint Sigma C. = 0.25·ft Sigma C. = 0.50·ft

Compressive Restaint (MPa)

Max

She

ar S

tres

s (M

Pa)

Figure 3.31: Peak shear stress vs. type of test. When the peak stress is reached, the post-peak phase begins. It can be seen from Figures 3.28 and 3.29 that post-peak branch of tests takes higher values of the shear stress as the lateral restraint is increased. That is to say that for a certain level of both the vertical and horizontal displacements, the shear stresses that can be transferred by the fibres are higher as the compressive stresses in concrete increase. This leads to improvements in the ductility of concrete through the application of a higher transversal load. It can be seen as well that the end of the test varies when the lateral pressure increase. This fact can be seen in Figure 3.31. In this figure, residual shear stress and the correspondent horizontal displacement are plotted. The effect of fibres and the boundary conditions are clearly visible in the increase of the residual shear stress. However, the results of the horizontal displacements are not as expected.

Figure 3.31: Ultimate horizontal displacement and residual

shear stress vs. type of test. All these features can be globally observed in Figure 3.32, in which the higher ductility of the specimens that are more compressed is clearly visible. For a certain increase in the vertical displacement, the horizontal displacement produced is much smaller as the lateral pressure is increased.

0.000.200.400.600.801.001.201.401.601.802.00

No Restra in t Pass iveRestra in t

S igm a C . =0.25·ft

S igm a C . =0.50·ft

C om pressive Resta in t (M Pa)

Hor

izon

tal D

ispl

acem

ent

(mm

)

0.000.501.001.502.002.503.003.504.004.505.00

Stre

ss (M

Pa)

U ltim ate H orizon ta l D isp lacem ent R esidual Shear S tress


_____________________________________________________________________________________

0 .0

1 .0

2 .0

3 .0

4 .0

0 .0 0 0 .2 5 0 .5 0 0 .7 5 1 .0 0 1 .2 5 1 .5 0

H o riz o n ta l D is p la c e m e n t (m m )

Vert

ical

Dis

plac

emen

t (m

m)

N o R e s tra in t 0 .5 0 ·ft P a s s ive R e s tra in t 0 .2 5 ·ft

Figure 3.32: Vertical vs. Horizontal displacements. Analysis of 0.5% SFRC test results Most of this analysis will be done according to the results plotted in Figures 3.33 and 3.34. Beginning with the latter, it is interesting that larger horizontal deformations are permitted by the fibres in the no restraint test. That deflection does not permit the measurement of the vertical displacement because the horizontals LVDTs fell when the horizontal deflection reached the limit of 7 mm. Once the specimen is restrained and the horizontal strain is restricted, the vertical displacements are measured correctly.

Figure 3.33: Shear stress-vertical displacement in 0.50% SFRC in No Restraint, and Active Restraint (σc = 0.25·ft).

0 .0

1 .0

2 .0

3 .0

4 .0

5 .0

6 .0

7 .0

8 .0

9 .0

0 .0 0 .5 1 .0 1 .5 2 .0 2 .5 3 .0 3 .5

V e rtic a l D is p la c e m e n t (m m )

Stre

ss (M

Pa)

N o R e s tra in t 0 .2 5 ·f t


_____________________________________________________________________________________

Figure 3.34: Shear stress-horizontal displacement in 0.50% SFRC in No Restraint, and Active

Restraint (σc = 0.25·ft). Following the same reasoning as in 1.0% SFRC tests, there is a big increase in maximum shear stress and in the residual shear stress. The increase in the ductility of the concrete it is more than 450% and the increase in the maximum shear stress is over 85% (see Figures 3.35 and 3.36).

Figure 3.35: Peak shear stress and the correspondent vertical displacement in 0.50% SFRC in

No Restraint, and Active Restraint (σc = 0.25·ft).

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

0 1 2 3 4 5 6 7

Horizontal D isplacem ent (m m )

Stre

ss (M

Pa)

N o R estra int 0.25·ft

0.00

2.00

4.00

6.00

8.00

10.00

No Restraint Sigma C. = 0.25·ft


Stre

ss (M

Pa)

0.00

0.10

0.20

0.30

0.40

0.50

Dis

plac

emen

t (m

m)

Peak Shear stress Peak Vert. Displa.


_____________________________________________________________________________________

Figure 3.36: Residual shear stress and the correspondent horizontal displacement in 0.50%

SFRC in No Restraint, and Active Restraint (σc = 0.25·ft). Analysis of 1.0% SFRC Passive Restraint Test The scope of this analysis is to evaluate the coupled behaviour between shear and tensile stress. This is the only test where this analysis can be done because in the rest of them, compressive stresses have been maintained constant. To analyse this behaviour, Figure 3.37 and 3.38 are shown; note that in both figures, the compressive stress are expressed in MPa x10 to make the plot clearer. In Figure 3.37 shear and compressive stresses in concrete vs. the vertical displacement is plotted. The shear stress curve is of the usual shape in which an elastic regime, pre-peak phase and a post-peak behaviour is clearly visible. The most important aspect of the figure is the correspondence between shear and compressive stresses. In the elastic phase the compressive stress almost does not increase while the first crack is formed, the compressive stress begins to grow. The curvature from the end of the elastic phase until peak shear tress is negative; once the peak shear stress is reached, there is a changing in the curvature of the compressive stress. This fact implies that until the peak stress, the vertical displacement produced for a certain increment in the shear stress is less than the displacement produced after the maximum shear stress. This is due to fact that the pre-peak shear stress is governed by the concrete with the fibres while the post-peak behaviour only depends on the fibres.

0.00

2.00

4.00

6.00

8.00

No Restraint Sigma C. = 0.25·ft


Ulti

mat

e H

oriz

onta

l D

ispl

acem

ent (

mm

)

0.00

1.00

2.00

3.00

4.00

Res

idua

l She

ar S

tres

s (M

Pa)

Ultimate Horizontal Displacement Residual Shear Stress


_____________________________________________________________________________________

Figure 3.38: Shear and compressive stresses vs. vertical displacement

in a 1.00% SFRC passive restraint test. In Figure 3.39 the stresses are plotted vs. the horizontal displacement. The line described by the compressive stress is due to the linear-elastic regime produced in the bolts transmitted to concrete as an imposed displacement.

Figure 3.39: Shear and compressive stresses vs. horizontal displacement

in a 1.0% SFRC passive restraint test. Results in terms of a Mohr-Coulomb Failure Criterion An important interpretation of the tests carried out is the representation of the results in a Mohr-Coulomb Failure Criterion. This analysis only can be done with those tests in which a lateral pressure has been introduced, -is needed measurements of compressive stresses in concrete. We can express the criteria as following:

( ) C+= φστ tan (3.6)

where φ is the friction angle and C is the cohesion.

0.00

2.00

4.00

6.00

8.00

10.00

12.00

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50

Vertical Displacem ent (m m)

Stre

ss (M

Pa)

Shear Stress (MPa) Tensile Stress (MPa)*10

0.00

0.10

0.20

0.30

0.40

0.50

0.00 0.20 0.40 0.60 0.80 1.00 1.20

Horizontal Displacement (mm)

Stre

ss (M

Pa)


_____________________________________________________________________________________

A linear regression has been done with the 1% SFRC results (see Figures 3.40). in order to optimize the values of the friction angle and the cohesion. Figure 3.40 takes into account all results shown in Table 3.7 for σ and τ from all tests carried out:

Shear Stress (MPa) Normal Stress (MPa) passive1 7.594 0.283 passive2 8.769 0.197 0.25 ft1 7.947 0.832 0.25 ft2 8.158 0.810 0.50.ft 11.402 1.616

Table 3.7: Shear and normal failure stresses in 1.00% SFRC tests.

As it can be seen from Figure 3.49 even though the correlation seems not to fit very well (i.e., the correlation factor R² = 0.6139), we can check the results calculating the value of the tensile stress obtained as the intersection between the Mohr-Coulomb Criterion and the normal stress axis – the concrete fails without the existence of a shear stress.

Figure 3.49: Mohr-Coulomb Criterion of 1.0% SFRC tests.

The value of the tensile strength obtained is ft = 4.41 MPa. This value is a little bit higher (12%) than the mean tensile strength obtained following the Spanish Codes (see Table 3.4). This means that we have a relatively good measurement of the cohesion in SFRC. However, to be sure that the fitting of the Mohr criterion is good enough, it would be necessary to compare the value of the friction angle. Nevertheless, we have not found any work in which friction angle in SFRC is studied. We have only found some values in plain concrete of the friction angle [9], where the friction angle goes from tanφ ∈ [0.7 , 1.0]. Starting from the assumption that the friction angle should be greater in SFRC than in plain concrete, we can only say that results seems reasonable, even thought we do not have any other results to compare.

y = 1.6527x + 7.2933R2 = 0.6139

-16.0

-12.0

-8.0

-4.0

0.0

4.0

8.0

12.0

16.0

-5.0 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0

Compressive Stress (MPa)

Shea

r Str

ess

(MPa

)

Shear stress Mohr Coloumb (+) Mohr-Coloumb (-) Lineal (Shear stress)

chapter 3 experimental study - upcommons.upc.edu

Documents