Main Short Fibre Reinforced Cementitious Composites and Ceramics

# Short Fibre Reinforced Cementitious Composites and Ceramics

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Categories: Chemistry\\Materials
Year: 2019
Language: English
Pages: 139
ISBN 10: 3030008673
ISBN 13: 978-3030008673
Series: Advanced Structured Materials
File: EPUB, 54.22 MB

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© Springer Nature Switzerland AG 2019
Heiko Herrmann and Jürgen Schnell (eds.)Short Fibre Reinforced Cementitious Composites and CeramicsAdvanced Structured Materials95https://doi.org/10.1007/978-3-030-00868-0_4

Non-destructive Evaluation of the Contribution of Polymer-Fibre Orientation and Distribution Characteristics to Concrete Performance during Fire

Tyler Oesch1  , Ludwig Stelzner1   and Frank Weise1
(1)Bundesanstalt für Materialforschung und –prüfung, Federal Institute for Materials Research and Testing, 12205 Berlin, Germany

Tyler Oesch (Corresponding author)
Email: tyler.oesch@bam.de

Ludwig Stelzner
Email: ludwig.stelzner@bam.de

Frank Weise
Email: frank.weise@bam.de

Abstract
Although concrete itself is not a combustible material, concrete mixtures with high density, such has high-performance concretes (HPCs), are susceptible to significant damage during fires due to explosive spalling. Past research has shown that the inclusion of polymer fibres in high density concrete can significantly mitigate this fire damage. The exact mechanisms causing this increased spalling resistance are not yet fully understood, but it is thought that the fibres facilitate moisture transport during fire exposure, which in turn contributes to relief of internal stresses in the spalling-susceptible region. In this study, X-ray Computed Tomography (CT) was applied to observe the interaction between polymer fibres and cracking during thermal exposure. For this purpose, two concrete samples containing different polymer fibre types were subjected to incremental application of a defined thermal exposure. CT images were acquired before and after each thermal exposure and powerful image processing tools were used to segment the various material components. This enabled a detailed analysis of crack formation and propagation as well as the visualization and quantification of polymer fibre characteristics within the concrete. The results demonstrated that the orientation of both fibres and cracks in polymer-fibre reinforced concrete tend to be anisotropic. The results also indicated that crack geometry characteristics may be correlated with fibre orientation, with cracks tending to run parallel to fibre beds. Clear quantitative relationships were also observed between heating and increasing cracking levels, expressed in terms of both crack surface area and crack volume.
1 Introduction
1.1 Performance of Concrete During Fire
Although concrete itself is not a combustible material, concrete structural components are susceptible to explosive spalling during fire. The investigation and control of this phenomenon is very important since the spalling of individual components can have a significant effect on the overall fire resistance of structures. Structural fire resistance, in turn, has major implications both to the safety of first responders during fires as well as the costs associated with structural repair following a fire.
It has been demonstrated that this spalling behaviour is at least partially related to the presence of moisture within the concrete material [9, 28]. Spalling behaviour is also increased for high-strength concretes (HSCs), which generally possess a higher overall density and lower permeability [7, 27]. The increase in the popularity and use of these high-strength concretes in building construction heightens the urgency of developing better methods for predicting and mitigating the effects of this spalling behaviour [1].
Fibre-reinforced concretes have been used in building construction since at least the 1970s [30]. Fibres have generally been used in these concrete mixes to improve the ductility and durability of the material [13, 33]. Polymer fibres have also been shown, however, to significantly contribute to spall resistance within concrete components during fire [8, 9].
The exact mechanisms causing this increased spalling resistance are not yet fully understood, but it is thought that the fibres facilitate moisture transport during fire exposure, which in turn contributes to relief of internal stresses in the spalling-susceptible region [9, 25]. The formation of a fibre-induced micro-cracking network has been identified as one important aspect of this process [25]. At the present time, there is also no comprehensive understanding of how fibre properties, such as polymer type, diameter, length, shape, and density, affect overall spalling performance of concrete members during fire. Optimization of these parameters will need to be completed before polymer-fibre reinforced concretes are adopted into widespread use for fire protection.
1.2 X-Ray Computed Tomography
X-ray computed tomography (CT) has been used in non-destructive concrete research applications for more than 30 years [15, 19]. In this scanning method, a sample is placed on a rotating table between an X-ray source and an X-ray detector [4]. This causes an X-ray attenuation image of the sample to be projected upon the detector. By recording these projected images during the 360[image: $$^\circ$$] rotation of the sample, mathematically-based reconstruction algorithms can be used to produce a three dimensional representation of X-ray attenuation within the sample [3]. The X-ray attenuation, which is roughly correlated with density, of individual component materials within the sample can then be identified and objects made from these component materials can be individually separated and analysed.
1.3 Objectives and Significance
Previous research has shown that small cracks develop in the mortar that surrounds the fibres during curing (Fig. 1). One goal of this research was to investigate to what extent these curing cracks contribute to overall material permeability prior to and during heating.[image: ../images/450266_1_En_4_Chapter/450266_1_En_4_Fig1_HTML.png]
Fig. 1Scanning Electron Microscope (SEM) images of polymer fibres before (left) and after (right) heating to 300 [image: $$^\circ$$]C

Another goal of this research was to identify the presence of correlations between fibre and cracking orientation characteristics and to quantitatively define the strength of those correlations. Previous research has demonstrated that the fibre fields in FRCs tend to be highly anisotropic because of flow during the casting process [5, 6, 17, 18, 20–22, 26]. It is thought that this anisotropy could have a major effect on fire resistance and, if properly controlled, may serve as a means of significantly improving spalling resistance.
The third goal of this research was to quantitatively measure the crack growth during incremental heating through the use of X-ray computed tomography (CT). This CT-based data would be particularly well suited for the calibration and validation of computational models of the spalling phenomenon.
2 Materials and Sample Preparation
The investigated specimens were made of HSC and were reinforced with different amounts and types of polypropylene (PP) fibres (Table 1). The mixture HSC / PPa2 contained 2 kg/m[image: $$^3$$] conventional PP-fibres. In contrast, for HSC / PPb1 only 1 kg/m[image: $$^3$$] pre-treated PP-fibres was added. The PPb-fibres were pre-treated during the manufacturing process using electron irradiation. This leads to a decreased fibre-melt viscosity [24] and improves the fire performance of the concrete, despite the reduced amount of added PP-fibres.Table 1HSC mixture

[image: ../images/450266_1_En_4_Chapter/450266_1_En_4_Tab1_HTML.png]

Initially, cubes (100 [image: $$\times$$] 100 [image: $$\times$$] 100 mm[image: $$^3$$]) were cast for both mixtures. After demoulding on the next day, these cubes were stored under water for six days and subsequently in a climate chamber at 20 [image: $$^\circ$$]C and 65 % relative humidity for a minimum of 83 days. Subsequently, cylindrical specimens with diameters of 12 mm and lengths of 100 mm were extracted from the cubes. A single cylindrical sample from each of the two cubes was selected for heating and CT analysis. These two samples will henceforward be referred to as sample PPb1 and sample PPa2, in reference to their composition. Before the first CT-measurement was carried out, these cylinders were fixed firmly within a customized set of mobile clamps, which ensured consistent mounting positions during repetitive CT measurements.
3 Test Methods
After preparing and mounting the concrete cylinders, a CT-measurement was completed. Thereby, the initial structure of the concrete was analysed. Afterwards, the clamped concrete cylinders were heated using a special heating regime to reach specific maximum temperatures (see Thermal Loading). Subsequent to each heating/cooling phase, a further CT-measurement was carried out to investigate the crack formation in the fibre-reinforced HSC as a result of the thermal exposure.
During the test series, the specimens were heated to certain target temperatures (150, 160, 170, 180, 190, 200, 250, 300 [image: $$^\circ$$]C) using an electrical furnace (Fig. 2). During thermal testing, the heat was increased at a rate of 1 K/min until the respective target temperature was reached. The target temperature was then sustained for one hour, followed by cooling at a maximum rate of −0,5 K/min to room temperature prior to CT-scanning.[image: ../images/450266_1_En_4_Chapter/450266_1_En_4_Fig2_HTML.png]
Fig. 2Electrical furnace containing a typical clamped specimen

The used electrical furnace is controlled by a temperature controller. The oven temperature is determined on the basis of the temperature measurement of a thermocouple, which is fixed in the rear wall of the furnace. Figure 3 shows an example temperature curve measured with an additional installed thermocouple near the specimen in comparison with the target temperature curve. Thereby it can be seen that the temperature in the furnace is controlled very well during heating phase. During the cooling phase the actual cooling rate is slower than the prescribed one because of the nonlinearity of the natural cooling process.[image: ../images/450266_1_En_4_Chapter/450266_1_En_4_Fig3_HTML.png]
Fig. 3Example temperature curve for heating test at 200 [image: $$^\circ$$]C

3.2 CT Scanning
During this research program, an acceleration voltage of 60 kV and current of 130 [image: $$\upmu$$]A were used for the X-ray source. The X-ray beam was also filtered using a 1 mm thick Aluminium plate immediately upon leaving the source in order to remove unwanted bandwidths from the X-ray beam and, in turn, make the resulting images more clear. The flat panel detector used for this scanning contained a 2048 [image: $$\times$$] 2048 pixel field. The resolution of the resulting CT images of the samples was 6.18 [image: $$\upmu$$]m.
4 Image Processing
4.1 Initial Processing Procedures
All image processing was completed using the program MATLAB [16]. The images were first corrected for beam hardening, which is a CT phenomenon causing the outer edges of the sample to appear brighter than its centre. During subsequent data analysis, it was found that the full sized sample image, which was 2048 [image: $$\times$$] 2048 [image: $$\times$$] 2048 voxels (a voxel is a 3D pixel), was much too large for the available image processing algorithms and computer system. Thus, a cubic sub-volume of 1200 [image: $$\times$$] 1200 [image: $$\times$$] 1200 voxels was digitally extracted from the centre of the original image and used for all subsequent analysis. Through the use of this sub-volume, all resulting computational demands and run times were reduced by a factor of approximately five times.
To enable the density and orientation analysis of the fibres and cracks, these materials first needed to be identified and separated within the images. Although individual component materials can generally be separated within CT images using grayscale segmentation methods that was not sufficient for these sample images. The reason for this complication was that the X-ray attenuation levels of the air pores, the cracks, and the polymer fibres were found to all be very similar and partially overlapping. Thus, more complex methods of fibre and crack detection needed to be developed.
4.2 Fibre Identification
Initially, template matching methods were used in an attempt to identify the polymer fibres, but with only limited success. One reason for the failure of this method may have been that the fibres had such a small size within the images (only approximately 2.5 voxels in diameter) that their shape was not sufficiently well-defined to consistently match the template characteristics. Another problem with this method was that the polymer fibres often exhibited significant bending within the material, which made it even more difficult to define and match a consistent fibre shape.
To overcome these limitations, a customized multi-step approach was developed for fibre identification that exhibited considerable versatility and accuracy. The individual steps of this analysis procedure will be outlined in the description below:
Step 1. The triangle segmentation method [34, 35] was used to identify a boundary between low attenuation elements within the sample, including air pores, cracks, and polymer fibres, and high attenuation elements, including aggregate and mortar, on the voxel intensity histogram (Fig. 4). Using this attenuation threshold, a sample image containing only air pores, cracks, and fibres could be created and used for further analysis (Fig. 5).[image: ../images/450266_1_En_4_Chapter/450266_1_En_4_Fig4_HTML.png]
Fig. 4Definition of low-high attenuation threshold on the voxel intensity histogram

[image: ../images/450266_1_En_4_Chapter/450266_1_En_4_Fig5_HTML.png]
Fig. 5Image of low-attenuation materials in sample PPb1 after step 1 (left) and step 2 (right)

Step 2. All objects within the low-attenuation image were individually analysed and those with a volume less than 16% of the standard individual fibre volume were removed from the image (Fig. 5). This was done in order to eliminate both noise and micro-pores from the image. The reason that some objects with less than 100% of the fibre volume were retained within the image was that, since the analysis was conducted upon a cubic sub-volume, many partial fibres existed along the image edge. It was desirable to retain these partial fibre segments for subsequent analysis steps as they were expected to contribute significantly to overall sample performance. The volume limitation of 16% was found through trial and error to produce a good balance between elimination of unwanted objects and retention of partial fibre segments.
Step 3. The objects within the image were contracted and then subsequently dilated by an amount equivalent to the fibre radius (rounded upward). This resulted in an image containing only objects larger in diameter than fibres. These macro-pores were subsequently removed from the image produced by step 2 in order to reduce the number of non-fibre objects (Fig. 6).[image: ../images/450266_1_En_4_Chapter/450266_1_En_4_Fig6_HTML.png]
Fig. 6Image of low-attenuation materials in sample PPb1 after step 2 (left) and after step 3 (right)

Through the removal of all objects with diameter larger than and volume smaller than that of the fibres in steps 2 and 3, it was originally thought that a clear, fibre-only image would result. It was soon found, however, that the samples contained may small micro-cracks of width similar to the fibre diameter even prior to the application of heat. Closer inspection revealed that these micro-cracks were almost exclusively present within the aggregate, rather than the mortar.
Step 4. Since the fibres, in contrast to the cracks, are only present within the mortar, and never within aggregates, it was possible to develop an algorithm for separating the fibres from the remaining cracks. In this algorithm, each object was dilated by an amount equivalent to the fibre radius (rounded upward) and the attenuation of this dilated region was analysed. If the attenuation of the dilated region around an individual object corresponded to that representative of mortar (Figs. 7 and 8), the object was considered a fibre and retained. All other objects were considered as micro-cracks within the aggregate and eliminated (Fig. 9).[image: ../images/450266_1_En_4_Chapter/450266_1_En_4_Fig7_HTML.png]
Fig. 7Attenuation image of the fibre-reinforced concrete material visually demonstrating the attenuation differences between aggregate and mortar

[image: ../images/450266_1_En_4_Chapter/450266_1_En_4_Fig8_HTML.png]
Fig. 8Definition of attenuation threshold boundaries for mortar material on the voxel intensity histogram

[image: ../images/450266_1_En_4_Chapter/450266_1_En_4_Fig9_HTML.png]
Fig. 9Image of low-attenuation materials in sample PPb1 after step 3 (left) and after step 4 (right)

The resulting fibre images for samples PPb1 and PPa2 can be compared in Fig. 10. Although these images still contain some non-fibre objects, the overall contribution of these objects to the measured fibre characteristics is assumed to be small. These non-fibre objects are thought to primarily consist of cracks or small voids that intersect with fibres as well as ring artefacts.[image: ../images/450266_1_En_4_Chapter/450266_1_En_4_Fig10_HTML.png]
Fig. 10Fibre images for samples PPb1 (left) and PPa2 (right)

As previously described, the sample PPa2 was fabricated to contain a fibre volume twice that of sample PPb1. The differences in fibre volume between the analysed sub-volumes of the two samples shown in Fig. 10, however, exhibit a much larger volume difference. The fibre volume percentage within each analysed sub-volume could be calculated by summing the number of voxels of fibre material and dividing that number by the total number of voxels in the image. Using this method a fibre-volume percentage of 0.202% was measured for the PPa2 sub-volume, which was very close to the 0.22% fibre-volume percentage used in the mix design.
For the PPb1 sub-volume, however, a fibre-volume percentage of only 0.044% was measured as opposed to the 0.11% fibre-volume percentage used in the mix design. There are many possible reasons for such a discrepancy. The most likely causes are inhomogeneity of fibre distribution within the sample and the presence of large aggregates or air-voids within the sub-volume selected for analysis. Both of these sources of error would be significantly reduced through the selection of larger sub-volumes for analysis. There is, thus, an impetus for further development of these image processing algorithms in order to reduce their computational requirements and enable the analysis of larger sub-volumes in future scanning and analysis efforts.
4.3 Fibre Analysis
Once the fibres had been identified and isolated within the images, they were then analysed for both density and orientation characteristics. The orientation analysis was completed using the Hessian-based method [6, 14]. In this method, the grayscale images resulting from CT are considered to be three-dimensional functions that are twice differentiable in all directions [10]. By calculating the Hessian matrix at a given voxel within a fibre, partial second derivatives can be computed:[image: \begin{aligned} H= & {} \left[ \begin{array}{ccc} \frac{\partial ^2 I}{\partial x^2} &{} \frac{\partial ^2 I}{\partial x \partial y} &{} \frac{\partial ^2 I}{\partial x \partial z}\\ \frac{\partial ^2 I}{\partial y \partial x} &{} \frac{\partial ^2 I}{\partial y^2} &{} \frac{\partial ^2 I}{\partial y \partial z}\\ \frac{\partial ^2 I}{\partial z \partial x} &{} \frac{\partial ^2 I}{\partial z \partial y} &{} \frac{\partial ^2 I}{\partial z^2} \end{array}\right] \end{aligned}]

(1)

with H = Hessian Matrix and I = Grayscale Sample Image Matrix.
At this point, the second derivative in the direction of the longitudinal axis of the fibre will be much less than those in the transverse directions. The orientation of fibres can, thus, be assessed by computing the eigenvalues and eigenvectors of the Hessian matrix at each voxel within a fibre (Fig. 11). The primary fibre orientation recorded at a single fibre voxel, therefore, is the eigenvector corresponding to the smallest eigenvalue [29].[image: ../images/450266_1_En_4_Chapter/450266_1_En_4_Fig11_HTML.png]
Fig. 11Eigenvectors of the Hessian matrix at two points within a fibre

For the fibre density analysis method, a small cell size was selected, comprising a cube with 120 voxel (742 [image: $$\upmu$$]m) long sides. The fibre image was broken up into an array of these cells, and the number of white (i.e., fibre) voxels in each was counted. By dividing the number of fibre voxels in each cell by the total number of cell voxels, estimates of local fibre density within the sample could be obtained.
The cell size used for the density analysis was selected such that the length of each cube side represented about a 10th of the overall length of a typical image array side. This meant that a sufficient number of cells (1000) would be available for analysis to enable meaningful statistical evaluation. This is because for a pseudo-random phenomenon, such as fibre density variation, a large number of samples need to be collected to observe meaningful trends within the statistical data. At the same time, however, there was a desire to avoid cell sizes that were too small because they might be too highly influenced by the presence of single fibres.
4.4 Cracking Analysis
The lack of a consistent size or shape for the crack geometry also made template matching techniques of limited use for crack identification. These characteristics made the use of a customized isolation approach similar to that used for the fibres unsuitable as well.
Past research has demonstrated, however, that many cracking characteristics can be measured through the observation of changes in void properties in images of progressively damaged samples [21, 23]. In this approach, all void characteristics, including volume, surface area, and orientation, within the initial, undamaged scan of a sample are assumed to be related to entrained and entrapped air. Thus, any change in these void characteristics, such as volume and surface area growth, seen in later scans of damaged samples can be assumed to be due to cracking and, thus, represented as crack characteristics.
It is important to note, however, that when analysing the orientation of cracks, a modified version of the approach used for fibre orientation analysis must be applied. Since cracks are planar objects, they cannot be characterized by a single, parallel vector in the way that fibres can. Rather, the cracks must be characterised by a vector which is perpendicular to the plane of the crack. Thus, in the Hessian characterization of crack orientation, the orientation angle represented by the eigenvector corresponding to the largest eigenvalue of the Hessian matrix must be used.
5 Results and Discussion
5.1 Results of Fibre Analysis
Various methods exist to depict and analyse orientation data in three dimensions. For the present analysis, coordinates have been converted from a Cartesian to a spherical system [32]:[image: \begin{aligned} r= & {} \sqrt{x^2 + y^2 + z^2} \ ,\end{aligned}]

(2)

[image: \begin{aligned} \theta= & {} \tan ^{-1}\left( \frac{y}{x}\right) \ ,\end{aligned}]

(3)

[image: \begin{aligned} \phi= & {} \cos ^{-1}\left( \frac{z}{r}\right) \ . \end{aligned}]

(4)

In this spherical coordinate system, orientations are characterized by angles [image: $$\theta$$] and [image: $$\phi$$] (Fig. 12). The angle [image: $$\theta$$] represents the azimuthal angle in the x-y plane from the x-axis (in this context the cylindrical axis of the sample is denoted as the z-axis), with [image: $$0< \theta < 360^\circ$$] (Eq. 3). The angle [image: $$\phi$$] represents the polar angle from the positive z-axis. Since the fibres are fully symmetric, a symmetry condition is likewise imposed on [image: $$\phi$$], with [image: $$0< \phi < 90^\circ$$] (Eq. 4).[image: ../images/450266_1_En_4_Chapter/450266_1_En_4_Fig12_HTML.png]
Fig. 12Spherical coordinate system

Figure 13 provides orthogonal projections of the fibre orientation data for samples PPb1 and PPa2. The depiction of three-dimensional data on a two-dimensional plane makes these projections unsuitable for evaluating isotropy along the [image: $$\phi$$]-axis but the projections can be used very effectively for evaluating isotropy along the [image: $$\theta$$]-axis. For sample PPb1, there appeared to be an anisotropic orientation of fibres along roughly the [image: $$\theta =30^\circ / 210^\circ$$] axis. A similar, although less clear anisotropy also appeared in the projection for sample PPa2. The darker colours of the PPa2 projection were caused by the higher fibre-volume content already discussed.[image: ../images/450266_1_En_4_Chapter/450266_1_En_4_Fig13_HTML.png]
Fig. 13Orthogonal projections of fibre orientation for samples PPb1 (left) and PPa2 (right). Projection radius: [image: $$0< \phi < 90^\circ$$]; projection circumference: [image: $$0< \theta < 360^\circ$$]

Fibre density results can be displayed in the form of histograms (Figs. 14 and 15). For clarity, the y-axis in these histograms has been depicted in logarithmic scale. This is necessary since the vast majority of cubic sub-volumes contain no fibres or only a few fibre voxels. These histograms confirm the higher fibre-volume content of sample PPa2.
5.2 Results of Cracking Analysis
The void data were also analysed using spherical coordinates and changes in void orientation characteristics, which correspond to crack orientation characteristics, can be depicted using orthogonal projections (Fig. 16).[image: ../images/450266_1_En_4_Chapter/450266_1_En_4_Fig14_HTML.png]
Fig. 14Histogram of fibre density for sample PPb1

[image: ../images/450266_1_En_4_Chapter/450266_1_En_4_Fig15_HTML.png]
Fig. 15Histogram of fibre density for sample PPa2

Recalling that the crack orientations were measured in terms of orientation normal to the cracking plane, it can be observed that for both PPb1 and PPa2, there appears to be an anisotropy along roughly the [image: $$\theta$$] = 130[image: $$^\circ$$]/310[image: $$^\circ$$] plane. This indicates that the primary orientation of the cracks is parallel to the primary fibre orientation. This is because the primary normal orientation of the cracks (depicted in Fig. 16) is roughly orthogonal to the primary fibre orientation (depicted in Fig. 13), which is typical for a plane running parallel to a line.[image: ../images/450266_1_En_4_Chapter/450266_1_En_4_Fig16_HTML.png]
Fig. 16Orthogonal projections of the normal orientation vectors measured for the cracks in samples PPb1 (left) and PPa2 (right) after 300 [image: $$^\circ$$]C heating. Projection radius: [image: $$0< \phi < 90^\circ$$]; projection circumference: [image: $$0< \theta < 360^\circ$$]

5.3 Comparison of Fibre and Cracking Characteristics
Comparison of fibre and cracking characteristics based purely on Figs. 13 and 16 is rather qualitative and difficult, however. In order to provide a more amenable means for direct comparison, histograms of fibre and crack-normal orientation were created and overlaid (Figs. 17 and 18).[image: ../images/450266_1_En_4_Chapter/450266_1_En_4_Fig17_HTML.png]
Fig. 17Relationship between fibre (red) and crack-normal (blue) [image: $$\theta$$]-orientation for sample PPb1

[image: ../images/450266_1_En_4_Chapter/450266_1_En_4_Fig18_HTML.png]
Fig. 18Relationship between fibre (red) and crack-normal (blue) [image: $$\theta$$]-orientation for sample PPa2

[image: ../images/450266_1_En_4_Chapter/450266_1_En_4_Fig19_HTML.png]
Fig. 19Relationship between fibre (red) and crack-normal (blue) [image: $$\phi$$]-orientation for sample PPb1

[image: ../images/450266_1_En_4_Chapter/450266_1_En_4_Fig20_HTML.png]
Fig. 20Relationship between fibre (red) and crack-normal (blue) [image: $$\phi$$]-orientation for sample PPa2

The relationship between the [image: $$\theta$$]-orientations of the fibres and the normal vectors to the cracking plane for PPb1 exhibit behaviour typical of cracks running along the primary fibre orientation direction, with very few fibres oriented along the directions normal to the cracking plane. This correlation is less clear for the PPa2 data. The reasons for this are unclear, but may be related to the higher volume of fibres contained within this sample. This increase in fibre volume may lead to more concerted behaviour of fibres through their combination in bundles as opposed to the less dense fibres in PPb1, which are more likely to interact with the concrete material individually. The presence of crack or ring artefacts within the fibre images could also contribute to this inconsistency.
Fibre-cracking histograms have also been created relative to the [image: $$\phi$$]-orientation (Figs. 19 and 20). Direct evaluation of these histograms is complicated by the fact that fibre density is not uniform along the [image: $$\phi$$]-axis due to exponential growth of volume in the unit sphere corresponding with linear increases in [image: $$\phi$$]-angle. Very similar trends in [image: $$\phi$$]-orientation are observable for the fibre and crack-normal data of both samples PPb1 and PPa2. These figures provide confirmation that an offset between the fibre and crack-normal orientation exists. Although not clearly orthogonal to one another, as would be expected for perfectly parallel cracks and fibres, this orientation offset does indicate that the cracks tend to orient themselves more strongly parallel to fibres than perpendicular to them.
A detailed analysis of fiber-crack interactions within localized regions of these samples can also be found in [31].
5.4 Correlation between Heating and Cracking Characteristics
Much clearer trends can be observed in the growth of cracking relative to temperature increase. Figures 21, 22, 23 and 24 depict the growth of cracking relative to applied heating for both samples PPb1 and PPa2. In these figures, two different measurements are used to evaluate cracking growth. Figures 21 and 22 are plotted relative to crack volume while Figs. 23 and 24 are plotted relative to crack surface area.[image: ../images/450266_1_En_4_Chapter/450266_1_En_4_Fig21_HTML.png]
Fig. 21Relationship between temperature and crack volume for sample PPb1

[image: ../images/450266_1_En_4_Chapter/450266_1_En_4_Fig22_HTML.png]
Fig. 22Relationship between temperature and crack volume for sample PPa2

[image: ../images/450266_1_En_4_Chapter/450266_1_En_4_Fig23_HTML.png]
Fig. 23Relationship between temperature and crack surface area for sample PPb1

[image: ../images/450266_1_En_4_Chapter/450266_1_En_4_Fig24_HTML.png]
Fig. 24Relationship between temperature and crack surface area for sample PPa2

In each of these figures, clear trends are visible between cracking and heating characteristics. These quantitative trends offer great promise for the calibration and validation of fire-damage models within finite element analysis codes for concrete. Basic fracture mechanics uses crack surface area as one parameter for calculating fracture energy [2]. This may make crack surface area the optimal damage parameter for use in numerical modelling.
Crack volumes have, however, also previously been shown to follow clear trends relative to work-of-load and stiffness reduction [11, 12]. The optimal numerical approach might be to develop a calibration and validation approach that combines the measurements of both of these cracking characteristics.
6 Conclusions
The results of this research effort have demonstrated that the orientation of both fibres and cracks in polymer-fibre reinforced concrete tend to be anisotropic. It is thought that this anisotropy is predominantly influenced by casting method, but can also be affected by the presence of large aggregates or voids within the sample. The results of the orientation analysis also indicated that crack geometry characteristics may be correlated with fibre orientation, with cracks tending to run parallel to fibre beds. This could have major implications for structural level performance since it would indicate that fire resistance may be related to casting method.
Clear quantitative relationships were also observed between heating and increasing cracking levels, expressed in terms of both crack surface area and crack volume. These relationships can serve as the basis for calibration and validation of finite element models used for simulating heat-related spalling behaviour.
7 Future Work
Future research is needed both to improve the accuracy and reliability of the analysis procedures used in this research and to develop new analysis procedures for evaluating phenomena of relevance to the spalling behaviour of concrete. One reason that only aggregated cracking and fibre characteristics could be measured in this research was the lack of accurate digital volume correlation (DVC) tools. The development and application of such tools would enable direct comparison, including subtraction, of individual image features among multiple images in a heating or loading series. This would not only make it easier to distinguish crack growth and fibre failure, but it would also enable more accurate measurements of crack-fibre property correlation. Up to the present time it has been very difficult to develop accurate DVC tools for concrete analysis because of the cracking discontinuities typical of concrete failure, which are generally more difficult for DVC methods to accommodate than the simple strains typical of plastically deforming materials.
New methods also need to be developed for assessing the cross-linking of fibre beds during heat-related cracking. Although this phenomenon has been observed using SEM, it has been difficult to develop a method that accurately quantifies the material behaviour. This is further complicated by the fact that many of the connecting cracks observed during SEM scanning appear to be below the resolution of most laboratory CT systems. It is believed that significant progress could be made in measuring this phenomenon through the skilled application of synchrotron-CT scanning in combination with DVC image processing tools.
Finally, further development of the image processing algorithms detailed in this paper is needed. These algorithms should be streamlined to enable orientation analysis of larger regions of interest within samples, which would minimize the magnitude of error introduced by individual material features, such as single stones or voids. Further research is also needed to improve the precision of the fibre-cracking orientation comparison and to statistically quantify the correlation level. Only through the accurate measurement of statistical correlation between fibre and cracking orientation can firm conclusions be drawn about the optimal casting procedures for the construction of fire-resistant building components.
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© Springer Nature Switzerland AG 2019
Heiko Herrmann and Jürgen Schnell (eds.)Short Fibre Reinforced Cementitious Composites and CeramicsAdvanced Structured Materials95https://doi.org/10.1007/978-3-030-00868-0_2

Experimental Investigation on Bending Creep in Cracked UHPFRC

Daniene Casucci1, 2  , Catherina Thiele1   and Jürgen Schnell1
(1)Institute of Concrete Structures and Structural Engineering, Technische Universität Kaiserslautern, Kaiserslautern, Germany

(2)Hilti Corporation, Feldkircherstrasse 100, 9494 Schaan, Liechtenstein

Daniene Casucci (Corresponding author)
Email: daniele.casucci@bauing.uni-kl.de
Email: Daniele.Casucci@hilti.com

Catherina Thiele
Email: catherina.thiele@bauing.uni-kl.de

Jürgen Schnell
Email: juergen.schnell@bauing.uni-kl.de

Abstract
Investigations on ordinary fibre-reinforced concrete showed that the time-dependent deformations under tensile load in cracked concrete are larger than the deformations in uncracked concrete. The so-called tensile creep in the cracked cross section depends on some different factors like type of fibres, fibre content, load level, concrete mix, environmental condition, etc. Given the lack of sufficient data about tensile creep in ultra-high performance fibre-reinforced concrete (UHPFRC), a large experimental program financed by the DFG (Deutsche Forschungsgemeinschaft) was started at the University of Kaiserslautern.
1 Introduction
Depending on the fibre content, UHPFRC has often a strain-hardening behaviour. This means that in a tensile or in a bending test, after the formation of the first crack, it is possible to increase the applied load. The concrete full tensile capacity is reached with multiple fine cracks and the material is usually designed in cracked condition. The contribution of the fibres to the tensile strength is so high, that in some cases, it seems reasonable to avoid or reduce the amount of conventional reinforcement. Therefore it is necessary to investigate also the tensile long-term behaviour of the cracked UHPFRC.
The aim of this research project, which has been started at the University of Kaiserslautern, is to evaluate the long-term durability and reliability of this material, to estimate the deformations under sustained loads and to find out whether a load limitation has to be imposed in the future design codes. In this paper, besides the adopted test method, some results of the first year of measurements and observation are reported. An overall safe behaviour of steel fibres up to relatively high sustained loads (with respect to the tensile strength in static tests) could be observed.
While the literature concerning tensile creep in ordinary fibre-reinforced concrete has increased in the past years, such literature concerning UHPFRC is still very rare. A large part of the research concerning time-dependent strain in UHPFRC is oriented to the creep in uncracked cross sections and in early age behaviour. This is important to evaluate the internal stress during the hardening phase in restrained conditions for the possibility of cracking [3]. Recent studies concerning the tensile-creep behaviour of high and ultra-high performance concrete may be found in the literature [3, 6–9, 12, 13, 15]. This topic is difficult to investigate since the experiments are complex and the tensile-creep deformations have the same order of magnitude as the shrinkage [7]. The most important parameters of influence, beside the cuing condition [6], are the water-cement ratio [7], the content of silica [3, 6, 7, 15] the age of loading [3, 6, 7, 15] and of course the magnitude of the load [3, 6, 7, 12, 15]. Concerning the magnitude of the tensile creep, is very difficult to make a comparison of the literature, since the testing parameters varies a lot and results vary significantly. While according Rossi [13] tensile creep is smaller than the compressive, it is, according to Kordina of the same size or slightly larger [8]. In Garas [6] it was found that the tensile creep can be even larger than the compressive one. The non-linear behaviour between tensile stress and creep deformation, was found in tension for higher stress/strength ratio than for compression, i.e. of 60–70% [7, 8, 15]. Moreover, it seems that under tensile load the shrinkage has also a different behaviour. Reinhardt et al. [12] discovered that an increase of shrinkage for high performance concrete under tension corresponded with increasing compressive strength.
Concerning the tensile creep in cracked cross sections, an overview of the present literature can be found in [9] or [14]. The tensile creep may be caused by the fibre creep, by a time dependent fibre pullout and by the creep of the cementitious matrix. While polymeric fibres, depending on the material of the polymers, tend to be sensitive to the tensile fibre creep, steel fibres show a more stable behaviour since steel has much lower relaxation. Conventional hooked-end macro-steel fibres engages via a mechanical interlock with the concrete matrix, but show also an increase of the tensile deformation over the time in correspondence with cracks. Nieuwoudt [10] connects this increase to the compressive creep of concrete in the areas of high contact pressure of the fibre hook. Even if a failure is unlikely, the deformations and micro cracking of concrete enable the fibre hook to “slide” and this results in the macroscopic observed time-dependent deformations.
In comparison with the typical hooked-end fibres, UHPFRC steel fibres are usually smaller, with diameter between 0.1 and 0.3 mm, lengths between 6 and 20 mm [2] and are straight and smooth [4]. One of the first investigations of uniaxial tensile creep in UHPFRC specimens with smooth micro-steel fibres was made by Garas [6]. Besides the uncracked specimens used for the tensile creep experiments, he also investigated some pre-cracked specimens. Garas observed a quick stabilization of the tensile creep deformations and failure only for load level above 80% of the static resistance in the first minutes after the reloading in the sustained load test rig. Bărbos [1] found a positive influence of the fibres for the tensile creep of UHPFRC beams with conventional reinforcement. Also in this case, the displacements showed a quick stabilisation. He attributed the creep deformation to the formation of new cracks and not to the widening of the existing ones. Nishiwaki [11] investigated a UHPFRC with a cocktail of short and long hocked-end fibres and observed, beside the formation of new cracks, also a slight widening of the existing ones. No failure occurred and with a creep factor of ca. 0.3 after 28 days, the deformations were very small.
2 Experimental Investigation
Uniaxial and bending tensile sustained load tests with over 60 pre-cracked specimens were started. Some of the specimens were unloaded after a period of about 6 months and tested for the residual strength. Some others are still under load and will remain under observation for the next years. Several parameters have been investigated such as the influence of different load levels, age of loading, the specimen pre-damaging level, fibre volume and fibre length-diameter. Shrinkage, and compressive creep were measured in additional tests in order to identify the contribution of the tensile creep to the bending deformations. This paper will focus only on the results of the bending experiments.
2.1 Experimental Procedure
A standard for these kinds of tests is unfortunately still missing. However, in most of the literature reported in [9] or [14], the method is similar. A schematic representation of the testing procedure is given in Fig. 1. First the specimens are pre-loaded up to a certain load or deformation in a common testing machine (step 1), then are unloaded and installed in a creep test rig (step 2), where they remain under sustained load over a certain time. After that, the sustained load is removed and the specimens are tested up to failure for the determination of the residual strength (step 3). The sustained load is defined as a percentage of the load at the final point of the pre-loading phase.[image: ../images/450266_1_En_2_Chapter/450266_1_En_2_Fig1_HTML.png]
Fig. 1Schematization of the sustained load creep tests

2.2 Specimens and Test Rigs
The tests were performed in non-notched beams with a four-point bending setup. The four-point bending setup enables the observation of the average deformation of a larger area of the material compared to notched three-point bending. In the case of a strain-hardening material, it is more advantageous to observe distributed cracking over a large region of the sample than to observe only the small local area around a notch. The beams had a cross-section of 70 [image: $$\times$$] 70 mm, in accordance with the French guideline [4] for the adopted fibre length of 12.5 mm. The span was increased to a length of 940 mm and the central part with constant bending moment was 340 mm long. Besides enabling the observation of a large portion of the material, the larger length was also useful in reducing the required dead load. The vertical displacement was measured with two precision indicators, fixed on both sides in the mid-span of the beams. For the four-point bending tests, eight separate stacks containing three to four specimens each were constructed, as represented in Fig. 2.[image: ../images/450266_1_En_2_Chapter/450266_1_En_2_Fig2_HTML.png]
Fig. 2Sustained load bending tests rig

2.3 Concrete Mix
The adopted concrete mix is indicated in the Table 1. The steel fibres are manufactured by the company Krampeharex® and are straight brass alloy coated steel wires. Brass alloy coated fibres are the most common and guarantee a good connection with the concrete paste [10]. The water-cement ratio, under consideration of the water in the silica suspension, is 0.265 and the overall water-binder ratio is 0.23. A heat treatment for 48 h at 90 [image: $$^{\circ }$$]C was performed two days after casting of the specimens. The concrete had a compressive strength of 150–160 MPa if cured in laboratory conditions and 180–190 MPa after the heat treatment.Table 1Mix design of the investigated UHPFRC

Material
Content (kg/m[image: $$^{3}$$])

Cement CEM 52.5 N
728

Water
80

Sand DM 0.125 / 0.5
816

Quartz flour
510

Microsilica suspension
226

Super plasticizer
29.7

Steel fibre (2% or 4%)
164 / 328

2.4 Test Program
A “reference” combination of 12 beams was tested extensively with scheduled sustained loads 40, 60, 80 and 90% of the residual strength in the pre-loading tests (series 1). The bending creep in non-cracked concrete was measured with two beams loaded at 40 and 60% of the residual strength in the pre-loading tests (series 2). Unfortunately, with loads higher than 60% of the residual strength in the pre-loading tests, cracks would appear making difficult the evaluation of the results.
The influence of fibre slenderness was investigated in four beams containing fibres with 0.400 mm diameter. These fibres have the same length of 12.5 mm as the fibres used in the other experiments, but had a length-diameter ratio of 31.3 instead of 71.4 of the 0.175 mm diameter fibres (series 3).
For investigating the effect of the fibre content, four tests with 4% fibre volume and sustained load levels of 40 and 80% were performed (series 4).
The heat treatment minimizes the effects of creep and shrinkage. However, a test series on specimens without heat treatment was also performed. A total of four specimens were cured in laboratory conditions, with humidity of about 50% and other three were cured in water and sealed with wet cloth (series 5 and 6). This measure was intended to avoid any kind of drying shrinkage.
Additionally, three specimens were also tested at ages of 2 and other three at the ages of 13 days. Two of these specimens were pre-loaded and one not. Also in this case the load was only 50% of the residual strength, not to induce cracks in the uncracked specimens (series 7).
Six dog-bone shaped specimens and six beams were tested for each different concrete mix according to the French guideline [2]. With these tests, a deformation level for the pre-loading phase was defined. This deformation was a vertical displacement of 1.5 mm for the beams with 0.40 mm diameter fibres and of 4 mm for the beams with 0.175 mm fibres. These values were chosen so that the UHPFRC would have a well-developed crack pattern during the experiments and so that at the same time the residual strength would still be considerable, larger than 70% of the maximum load.
Since the specimens were piled, more specimens received the same external load. Therefore the actual load in test differed from the scheduled indicated in Table 2.
The test program for the sustained load tests on beams is summarized in Table 2. Here the fibre length, diameter, fibre content and the load level are given. A total of 33 bending creep tests were performed.Table 2Sustained load test program

Series
Investigated parameter
Fibre length; Diameter; content
Number of tests

1.
12.5; 0.175; 2%
40 / 60 / 80 /90
5 / 3 / 2 / 2

2.
Bending creep in uncracked concrete
12.5; 0.175; 2%
(Ca. 40 / 60) without pre loading
1 / 1

3.
Length / diameter ratio
12.5; 0.40; 2%
40 / 80
2 / 2

4.
Fibre content
12.5; 0.175; 4%
60
2

5.
Without heat treatment
12.5; 0.175; 2%
40 / 80
3 / 1

6.
Water curing and sealing
12.5; 0.175; 2%
2 / 1

7.
Concrete age in cracked and non-cracked concrete
12.5; 0.175; 2%
4 / 2

Total
33

2.5 Compressive Creep and Shrinkage
To estimate the contribution of the compressive creep to the deformation of the beam specimens, 27 cylinders with a diameter of 104 mm were tested for a period between two weeks and four months. The tests were performed with three load levels of 0.25, 0.45 and 0.65 f[image: $$_{\mathrm {c}}$$] with a concrete age of 2, 13 and 28 days. For each combination, a sealed specimen, an unsealed specimen and a heat-treated specimen were tested.
3 Test Results
In this section, some representative results of the creep tests will be shown in order to draw the first conclusion of this experimental test program. The following Table 3 illustrate the naming adopted in the following paragraphs for the single specimens.Table 3Naming of the specimens

No.
Significance

1.
Specimen number
PK01, PK02, [image: $${\ldots }$$]

2.
Curing
Wb.: heat treatment curing W.: water curing k. B.: curing in laboratory condition

3.
n. Vb.: without pre load Wb.:
2T: age at load beginning of two days
13T: age at load beginning of thirteen days
sealed: sealed specimen
0.4Ø: fibre diameter of 0.4 mm instead of 0.175 mm
4%: fibre content of 4% instead of 2%

4.
L = XX%: load level

3.1 Bending Tests
Figure 3 shows the creep deformations of all the specimens of test series 1. Despite the large scatter, a slight correlation between the load level and the bending creep deformation could be observed. One of the specimens (PK05Wb. in Fig. 3) collapsed after 23 days with a load of 79% of the residual strength at the end of the pre-loading phase. During the pre-loading, this specimen exhibited a dramatic decrease in resistance after having reached the maximum load. An examination of the cross section after the collapse showed a particularly unfavourable fibre-orientation characteristics. Fibres were indeed laying almost parallel to the crack plane without offering an effective crack bridging (Fig. 4). Other specimens contained within the same stack as specimen PK05Wb (for instance PK07Wb.) were also affected by this collapse.
Figure 5 shows a comparison between cracked and non-cracked specimens. In this diagram, only specimens that can be directly compared for charge and load levels are shown. The pre-cracked UHPFRC showed always larger creep deflection than the uncracked ones.
Figure 6 shows the results of the specimens with age of 2 and 13 days. These results indicate that increasing deformation is present within samples of lesser age as compared to samples of greater age. A clear difference between the deformation levels of pre-cracked and non-cracked samples was again visible within this dataset, however the difference between non-cracked and pre-cracked concrete remains of the same proportion. This suggest that deformations in cracked concrete are mainly due to the creep of the compression area.[image: ../images/450266_1_En_2_Chapter/450266_1_En_2_Fig3_HTML.png]
Fig. 3Creep deflection for specimens in test series 1 of Table 2

[image: ../images/450266_1_En_2_Chapter/450266_1_En_2_Fig4_HTML.png]
Fig. 4Cross section of the collapsed specimen PK05Wb

[image: ../images/450266_1_En_2_Chapter/450266_1_En_2_Fig5_HTML.png]
Fig. 5Creep deflection for cracked and non-cracked specimens (series 2 of Table 2)

[image: ../images/450266_1_En_2_Chapter/450266_1_En_2_Fig6_HTML.png]
Fig. 6Creep deflection for specimens of series 2 of Table 2 (these specimens were cured in laboratory conditions)

The sealing of the specimens seems not to have a pronounced influence on the beams as shown in Fig. 7 for two different load level of about 40 and 60%. Specimens with 0.4 mm fibre diameter showed slightly smaller creep deflections than those with 0.175 mm (Fig. 8).
In general, a stabilization of the displacements occurred within the first 30 days. Some of the specimens were unloaded after 147 days and residual strength tests were performed. Although the largest displacements occurred within the first month, a continuous increase could be stated for the whole observation period.[image: ../images/450266_1_En_2_Chapter/450266_1_En_2_Fig7_HTML.png]
Fig. 7Creep deflection for specimens of series 6 in Table 2

[image: ../images/450266_1_En_2_Chapter/450266_1_En_2_Fig8_HTML.png]
Fig. 8Creep deflection for specimens with 0.4 mm fibre diameter (series 3 in Table 2)

3.2 Residual Strength Tests
Fig. 9Residual strength tests on heat-threated beams (naming of the specimens defined in Figs. 3, 5 and 6)

3.3 Compressive Creep and Shrinkage
Figure 10 reports the basic creep coefficient [image: $${\varphi }_{\mathrm {b}}$$](t,t[image: $$_{0}$$]) for some of sealed specimens. The [image: $${\varphi }_{\mathrm {b}}$$](t,t[image: $$_{0}$$]) is defined according the following equation:[image: \begin{aligned} \varepsilon _{\mathrm {cc}}(t,t_{0})= & {} \sigma (t_{0}){[\varphi _{\mathrm {b}}(t,t_{0})]}/E_{\mathrm {c}} \end{aligned}]

(1)

whereby [image: $${\varepsilon }_{\mathrm {cc}}$$](t,t[image: $$_{0}$$]) is the strain, [image: $${\sigma }$$](t[image: $$_{0}$$]) is the compressive stress, E[image: $$_{\mathrm {c }}$$] elasticity modulus of concrete, and t[image: $$_{0 }$$] the age of the concrete at the beginning of the loading. The results were extrapolated with the equation of the experimental method of EN 1992-1-2 [5]. The dashed lines in Fig. 10 indicates this approximation. In Fig. 10 one can observe that the basic creep reduces significantly as the age of the sample at the time of loading increases from 2 to 28 days. The results indicate that the stress-deformation non-linearity limit rises with the age of the concrete for values below 0.65 f[image: $$_{\mathrm {c}}$$]. This can be observed in Fig. 10 from the slight difference between the specimen loaded with 0.25 and 0.45 f[image: $$_{\mathrm {c}}$$] and the larger difference between these lower loads and that of 0.65 f[image: $$_{\mathrm {c}}$$]. Figure 11 shows the test rig for the compressive creep and the basic and drying shrink age.[image: ../images/450266_1_En_2_Chapter/450266_1_En_2_Fig10_HTML.png]
Fig. 10Compressive creep, at the age of 2, 8 and 28 days. The dashed lines indicate the progression according to the experimental method of EN 1992-1-2

[image: ../images/450266_1_En_2_Chapter/450266_1_En_2_Fig11_HTML.png]
Fig. 11Compressive creep test rig (left and centre) and deformation diagram (right) of the Shrinkage in sealed specimens (blue) and non-sealed specimens (yellow). The dashed lines indicate the profile according the EN 1992-1-2

4 Conclusions
For an investigation of the creep behaviour of concrete, a few months are not usually enough to gain an exhaustive knowledge of the material. However, it seems that UHPFRC exhibits a stabilization of the time dependent deformation in a relatively short time, even in cracked condition. That means that the working principle of the fibres seems not to be subject to degradation over the time. The only collapsed specimen was a one with an unfavourable fibre orientation and a high sustained load of 79% of the residual strength after pre-loading. This indicates that the fibre orientation has also a relevance for the creep deformation and ultimate resistance. This parameter, although difficult to investigate, should somehow be taken into account. One possible way is correlating it to the post crack behaviour of the specimens.
The effect of the load level was found to be low. At this time, no further conclusions about the effects of loading can be drawn given the scatter within the data of the cracked specimens.
The sustained load had almost no impact on the residual strengths. More important seems to be the post-cracking behaviour and how fast the load displacement curve drops at the unloading point. In the bending tests, no influence of sealing was observed. Tests of samples containing higher fibre content and different fibre diameters did not exhibit any significantly different load performance than the standard reference samples.
Acknowledgements
This research was possible thanks to the Deutsche Forschungsgemeinschaft (DFG), which financed and implemented a new research-training group (RTG) named “Stochastic Models for Innovations in the Engineering Sciences” at the University of Kaiserslautern.

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Nishiwaki, T., Kwon, S., Otaki, H., Igarashi, G., Shaikh, F.U., Fantilli A.P.: Experimental study on time-dependent behavior of cracked UHP-FRCC under sustained loads. In: Serna, P., Llano-Torre, A. (eds.) Creep Behaviour in Cracked Sections of Fibre-reinforced Concrete. Proceedings of the International RILEM Workshop FRC-CREEP (2016)

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© Springer Nature Switzerland AG 2019
Heiko Herrmann and Jürgen Schnell (eds.)Short Fibre Reinforced Cementitious Composites and CeramicsAdvanced Structured Materials95https://doi.org/10.1007/978-3-030-00868-0_1

Study of Crack Patterns of Fiber-Reinforced Concrete (FRC) Specimens Subjected to Static and Fatigue Testings Using CT-Scan Technology

Miguel A. Vicente1  , Gonzalo Ruiz2  , Dorys C. González1  , Jesús Mínguez1  , Manuel Tarifa2   and Xiaoxing Zhang2
(1)Department of Civil Engineering, University of Burgos, Burgos, Spain

(2)Department of Applied Mechanics, University of Castilla – La Mancha, Ciudad Real, Spain

Miguel A. Vicente (Corresponding author)
Email: mvicente@ubu.es

Gonzalo Ruiz
Email: Gonzalo.Ruiz@uclm.es

Dorys C. González
Email: dgonzalez@ubu.es

Jesús Mínguez
Email: jminguez@ubu.es

Manuel Tarifa
Email: ManuelAgustin.Tarifa@uclm.es

Xiaoxing Zhang
Email: zhangxiaoxinhrb@gmail.com

Abstract
This paper demonstrates the widely accepted hypothesis that the compressive testing is a particular case of a cyclic test where failure occurs during the first cycle. To perform this, a test on 32 fiber-reinforced high-performance concrete specimens have been carried out. Sixteen of them have been tested under low-cycle fatigue compressive loading up to failure. Eight of them have been tested under monotonic compressive loading, until failure too. And the last eight specimens have remained intact. All of them have been scanned using a Computed Tomography (CT) Scan in order to define the pattern of their damage, which includes voids and cracks. The results show that the average damage maps of monotonic and fatigue series are statistically identical, which confirms the hypothesis previously described. In addition, both series are different to the intact series, which means that not a random damage distribution occurs when specimens collapse.
1 Introduction
During the last years, the progressive increase of the strength of concrete is leading to slender structures, where cyclic loads have a more relevant influence. Thus, fatigue phenomena in concrete are of increasing interest and the development of accurate predictive models has a great scientific interest.
A significant amount of fatigue models for concrete have been developed until now. They establish a relationship between the maximum and the minimum stress ratio of the cyclic load with the number of cycles up to failure (usually called as “fatigue life”) [1, 4, 7, 11, 12, 15, 18, 19].
Most fatigue models consider the hypothesis of convergence to the “initial distribution”, which means that the static testing is a particular case of cyclic testing where the fatigue life is equal to 1. This hypothesis is supported by the fact that the crack patterns obtained in both cases are equal.
The aim of the research conducted by the authors is to check if this hypothesis is true or false. To perform this, the Computed Tomography (CT) technology is used, in combination with a homemade post-processing software, in order to define the crack pattern within the specimens.
Computed tomography is a nondestructive technique, based on absorbing X-rays, that permits the visualization of the internal microstructure of material up to micro-range resolution.
The field of application is very wide. This is a well-known technology in medicine, because of its enormous advantages, but it is also very useful in other fields. For example, this technology is also very common in veterinarian, or paleontology. In materials engineering, this technology is starting to be widely used to analyse the internal microstructure of a wide variety of materials: metals, rocks, composites, etc.
This technology is also very useful for the study of concrete microstructure. Most of the macroscopic responses of concrete elements can be explained through the understanding of the microstructure. For example, the freeze-thaw behavior of concrete strongly depends on pore sizes and pore distribution. Moreover, in case of fiber-reinforced concrete, the use of CT-Scan can provide useful information related to the fiber distribution and orientation, which strongly influences its macroscopic response [5, 9, 10, 14, 16].
In recent years, many research have been conducted in order to study the internal microstructure of concrete using this technology [2, 3, 5, 6, 8–10, 13, 14, 17].
The research shown in this paper uses the CT-Scan or detect internal “damage” of concrete, which includes pores and cracks. This technology is able to define the density of each specimen voxel by assigning a shade of a grey. Light shades of grey correspond to high density and dark shades of grey correspond to low density. A more detailed explanation of the CT-Scan technology can be found in [17].
2 Experimental Procedure
Next, the experimental procedure and the scanning procedure are described.
2.1 Materials Characterization
In this case, fiber reinforced high performance concrete cubic specimens were performed. Their shape was cubic with 40 mm in edge-length, cut from prism of 150 [image: $$\times$$] 150 [image: $$\times$$] 700 mm.
The concrete compressive strength [image: $$f_{\mathrm {c}}$$] was 101 MPa, with a standard deviation of 3 MPa.
A total of three series of concrete cubes were performed, named “intact”, “monotonic” and “cyclic”. The intact and the monotonic series were composed by 8 specimens each. The cyclic series was composed by 16 specimens. A total of 32 specimens were performed.
Specimens belonging to monotonic series were subjected to a monotonic compressive load up to failure. Specimens belonging to cyclic series were subjected to a low-cycle cyclic load up to failure. Finally, specimens belonging to intact series were not tested.
2.2 Fatigue Tests
Specimens belonging to cyclic series were subjected to low-cycle cyclic load up to failure. The tests were carried out at a loading frequency of 10 Hz under sinusoidal stress cycles, varying between [image: $$0.36\,\cdot$$] f[image: $$_{\mathrm {c}}$$] and [image: $$0.82\,\cdot$$] f[image: $$_{\mathrm {c}}$$]. Table 1 shows the fatigue life of all the specimens.
The tests were carried out using a hydraulic jack with a load capacity of [image: $${\pm }$$]250 kN.Table 1Specimens tested under cyclic load (cyclic series)

Cycles for [image: $${\sigma }_{\mathrm {max}} = 0.82 \cdot$$] f[image: $$_{\mathrm {c}}$$]; [image: $$\sigma _{\mathrm {min}} = 0.36 \cdot$$] f[image: $$_{\mathrm {c}}$$]

Specimen
Cycles
Specimen
Cycles
Specimen
Cycles
Specimen
Cycles

1f
1066
5f
1115686[image: $${^\mathrm{a}}$$]
9f
19186
13f
2700

2f
3128
6f
25
10f
90
14f
88

3f
214
7f
111
11f
144
15f
152076

4f
29189
8f
460
12f
3305
16f
1

[image: $${^\mathrm{a}}$$]Run-out

The results show a wide scatter in the service life of the test specimens. This is very common in concrete and it is due to the inherent scatter of the material, which particularly conducts to a wide scatter in terms of service life.[image: ../images/450266_1_En_1_Chapter/450266_1_En_1_Fig1_HTML.png]
Fig. 1CT-Scan: Y.CT COMPACT with a YXlon tube of 225 kV/30mA at University of Burgos (Spain)

2.3 Scanning of the Specimens
Once the specimens belonging to the monotonic and the cyclic series had been tested, they were scanned using a CT-Scan. In addition, the specimens belonging to the intact series were also scanned.
The CT-Scan used was a Y.CT COMPACT device of the University of Burgos (Spain). It is equipped with a YXlon tube of 225 kV/30mA (Fig. 1). The CT-Scan has a post-processing software which provides 2D slices of 1024 [image: $$\times$$] 1024 pixels. Thus, for a section of 40 [image: $$\times$$] 40 mm[image: $$^{2}$$], the resolution of the scanner is 55 [image: $$\times$$] 55 [image: $${\upmu }$$]m[image: $$^{2}$$]. The vertical distance between slices is 100 [image: $${\upmu }$$]m. The amount of slices per specimen is 401. The voxel has a volume of 55 [image: $$\times$$] 55 [image: $$\times$$] 100 [image: $${\upmu }$$]m[image: $$^{3}$$].
Each voxel is identified by its center of gravity (coordinates X, Y and Z) and a grey color belonging to a grey scale, from black to white depending on the voxel density. A total amount of 256 grey colors are identified in the grey scale.
Light grey corresponds to high density and dark grey corresponds to low density. Figure 2 shows a slice of a specimen. The total number of voxel is approximately [image: $$4.2\cdot 10^{8}$$].[image: ../images/450266_1_En_1_Chapter/450266_1_En_1_Fig2_HTML.png]
Fig. 2CT-Scan slide

The post-processing methodology is as follows.
First, once all the voxels had been identified, the ones belonging to damage were extracted. These “damaged” voxels (or empty voxels) are the ones with a density (i.e. a grey color) below a threshold. The result is a 3D image containing only the empty voxels, i.e. the voxels belonging to pores or cracks (Fig. 3).[image: ../images/450266_1_En_1_Chapter/450266_1_En_1_Fig3_HTML.png]
Fig. 3Example of empty voxels distribution

The average number of empty voxels per specimen in every series is shown in Table 2. In case of intact series, empty voxels belongs only to voids, meanwhile in case of monotonic and cyclic series, empty voxels belongs to voids and cracks.Table 2Empty voxels per specimen in every series

Series
Intact
Monotonic
Cyclic

Number of Specimens
8
8
16

Voxels
Mean
73,254
1,472,215
1,089,281

Std. Dev.
26,134
238,492
438,796

% Voxels
Mean
0.02%
0.35%
0.26%

Std. Dev.
0.01%
0.06%
0.10%

It should be noted that the number of empty voxels belonging to the intact series are significantly smaller than the ones belonging to monotonic and cyclic series. That is because empty voxels in intact series belong to pores only, meanwhile empty voxels in monotonic and cyclic series includes pores and cracks.
In order to compare the empty voxel distributions (crack patterns) from the different series, a novel numerical procedure, designed by the authors, have been developed, named “Circumferential test”. Next, this procedure is explained.
2.4 Circumferential Test
The circumferential test is the procedure for analyzing the raw data from the CT-scan in order to disclose the extent of damage generated in the mechanical tests.
Next, the steps for analyzing the data are exposed:
First, the coordinates x[image: $$_{\mathrm {i}}$$], y[image: $$_{\mathrm {i}}$$] and z[image: $$_{\mathrm {i}}$$] of each individual voxel are normalized according to the following expression: [image: \begin{aligned} x_{rel,i}= \frac{2\cdot x_{i}}{x_{max}} \end{aligned}]

(1a)

[image: \begin{aligned} y_{rel,i}=\frac{2\cdot y_{i}}{y_{max}} \end{aligned}]

(1b)

[image: \begin{aligned} z_{rel,i}=\frac{z_{i}}{z_{max}} \end{aligned}]

(1c)

where x[image: $$_{\mathrm {max}}$$], y[image: $$_{\mathrm {max}}$$] and z[image: $$_{\mathrm {max}}$$] are the real dimensions of each individual specimen.
Next, each voxel is identified by a pair of coordinates, the normalized distance of the voxel to the center of gravity of the cross-section where the voxel is placed d[image: $$_{\mathrm {i}}$$] and the height of the voxel h[image: $$_{\mathrm {i}}$$], according to the following expressions (Fig. 4):[image: \begin{aligned} d_{i}= & {} \sqrt{\left( x_{rel,i}-x_{G,rel,i}\right) ^{2}+\left( y_{rel,i}-y_{G,rel,i}\right) ^{2}} \end{aligned}]

(2)

[image: \begin{aligned} h_{i}= & {} z_{rel,i} \end{aligned}]

(3)

where x[image: $$_{\mathrm {G,rel,i}}$$] and y[image: $$_{\mathrm {G,rel,i}}$$] are the normalized coordinates of the center of gravity of the considered section. Coordinate d[image: $$_{\mathrm {i}}$$] varies from 0 to [image: $$\sqrt{2}$$] while h[image: $$_{\mathrm {i}}$$] varies from 0 to 1.
Coordinates d and h are divided into twenty subdivisions each, so that the voxels are clustered for all the combinations of d and h coordinates. Thus, the whole cube volume is divided into 400 sub-volumes. For each, the relative frequency of occurrence of empty voxels is calculated, according to the following expression:[image: \begin{aligned} \text {Relative frequency,}\quad i= & {} \frac{N_{i}}{N_{t}} \end{aligned}]

(4)

where N[image: $$_{\mathrm {i}}$$] is the number of empty voxels belonging to each individual sub-volume and N[image: $$_{\mathrm {t}}$$] is the total number of empty voxel of the specimen.[image: ../images/450266_1_En_1_Chapter/450266_1_En_1_Fig4_HTML.png]
Fig. 4Voxel coordinates

In addition, a random damage distribution was simulated inside a theoretical 40 mm edge-length using a Monte Carlo model with 10[image: $$^{6}$$] points. This theoretical distribution was used to compare it with the real distribution in order to decide if empty voxels in real specimens are randomly distributed or not.
3 Results and Discussion
Next, the results of CT-Scan are shown. First, the results are shown by means of 3D histograms of each specimen. In addition, the histogram of the random distribution is shown. Second, the results are compressed and shown by means of 2D histograms in the d direction first and in the h directions next, in order to be analyzed appropriately.
3.1 3D Histograms
Using all the information explained above, a 3D histogram can be drawn, where x-axis is the parameter h, y-axis is the parameter d and z-axis is the relative frequency. Figures 5, 6, 7 and 8 show all the 3D histograms.[image: ../images/450266_1_En_1_Chapter/450266_1_En_1_Fig5_HTML.png]
Fig. 5Theoretical 3D histogram

Note than random histogram shows a triangular shape along d parameter, with a maximum at d [image: $$=$$] 1, since such sub-volume corresponds to the longest ring inside the cube.[image: ../images/450266_1_En_1_Chapter/450266_1_En_1_Fig6_HTML.png]
Fig. 63D histogram of the intact seriesspecimens

Histograms belonging to intact series specimens show high peaks. These ones represent the presence of large pores with a great amount of empty voxels.[image: ../images/450266_1_En_1_Chapter/450266_1_En_1_Fig7_HTML.png]
Fig. 73D histogram of the monotonic series specimens

[image: ../images/450266_1_En_1_Chapter/450266_1_En_1_Fig8_HTML.png]
Fig. 83D histogram of the cyclic series specimens

In case of monotonic and cyclic series specimens, less peaks are observed. That is because of the presence of cracks, which show more distributed empty pores along the specimen. In consequence, the presence of pores is mitigated.
3.2 2D Histograms Along the H Direction
In order to easily analyze the results, the 3D histograms were aggregated along the h direction, obtaining 2D histograms which represent the relative frequency of occurrence of empty voxels along the d coordinate, i.e., transverse to the load direction. Figures 9, 10 and 11 show the 2D histograms of the different series. Each histogram show the individual data of the specimens (drawn as bar diagrams) and also the average histogram. Additionally, the histogram belonging to the random distribution is shown, in order to be able to compare real and theoretical distributions.[image: ../images/450266_1_En_1_Chapter/450266_1_En_1_Fig9_HTML.png]
Fig. 92D histogram of the intact series specimens

[image: ../images/450266_1_En_1_Chapter/450266_1_En_1_Fig10_HTML.png]
Fig. 102D histogram of the monotonic series specimens

[image: ../images/450266_1_En_1_Chapter/450266_1_En_1_Fig11_HTML.png]
Fig. 112D histogram of the cyclic series specimens

Figures 11, 12 and 13 show the comparison between the theoretical distribution and the real distributions of intact, monotonic and cyclic series. Additionally, the 90% confidence interval is defined by the upper and the lower limits.[image: ../images/450266_1_En_1_Chapter/450266_1_En_1_Fig12_HTML.png]
Fig. 12Comparison between theoretical and intact series

[image: ../images/450266_1_En_1_Chapter/450266_1_En_1_Fig13_HTML.png]
Fig. 13Comparison between theoretical and monotonic series

[image: ../images/450266_1_En_1_Chapter/450266_1_En_1_Fig14_HTML.png]
Fig. 14Comparison between theoretical and cyclic series

Figure 12 shows that theoretical histogram is, in general, inside the confidence interval. This means that, from a statistical point of view, it can be assumed that both distributions are equal, i.e., intact series follow a random distribution. Empty voxel, i.e., pores, are randomly distributed inside the specimens along the d direction.
On the contrary, Figs. 13 and 14 show that theoretical histogram is partially outside the confidence interval. This means that, from a statistical point of view, it can be assumed that both monotonic and cyclic series do not follow a random distribution along the d direction. In consequence, it can be affirmed that cracks are not randomly distributed inside the specimens.
In case of monotonic and cyclic series, the behavior is quite similar. Between d [image: $$=$$] 0 and d [image: $$=$$] 0.8 approximately, real damage is below theoretical damage. On the contrary, between d [image: $$=$$] 0.8 and d [image: $$=$$] [image: $$\sqrt{2}$$], real damage is above theoretical damage. This means that cracks appear mostly on the edge of the specimens.
Figure 15 show the comparison between the real distributions of monotonic and cyclic series. Additionally, the 90% confidence interval is defined by the upper and the lower limits.[image: ../images/450266_1_En_1_Chapter/450266_1_En_1_Fig15_HTML.png]
Fig. 15Comparison between monotonic and cyclic series

Figure 15 shows that the average monotonic histogram is inside the confidence interval of cyclic series and viceversa. This means that, from a statistical point of view, it can be assumed that both distributions are equal, i.e., the crack pattern of both monotonic and cyclic series are equal along the d direction.
3.3 2D Histograms Along the D Direction
Similarly to the previous case, the 3D histograms were aggregated along the d direction, obtaining 2D histograms which represent the relative frequency of occurrence of empty voxels along the h coordinate, i.e., parallel to the load direction. Figures 16, 17 and 18 show the 2D histograms of the different series. As occurs in the previous case, each histogram show the individual data of the specimens (drawn as bar diagrams) and also the average histogram. Additionally, the histogram belonging to the random distribution is shown, in order to be able to compare real and theoretical distributions.[image: ../images/450266_1_En_1_Chapter/450266_1_En_1_Fig16_HTML.png]
Fig. 162D histogram of the intact series specimens

[image: ../images/450266_1_En_1_Chapter/450266_1_En_1_Fig17_HTML.png]
Fig. 172D histogram of the monotonic series specimens

[image: ../images/450266_1_En_1_Chapter/450266_1_En_1_Fig18_HTML.png]
Fig. 182D histogram of the cyclic series specimens

Figures 19, 20 and 21 show the comparison between the theoretical distribution and the real distributions of intact, monotonic and cyclic series. Additionally, the 90% confidence interval is defined by the upper and the lower limits.[image: ../images/450266_1_En_1_Chapter/450266_1_En_1_Fig19_HTML.png]
Fig. 19Comparison between theoretical and intact series

[image: ../images/450266_1_En_1_Chapter/450266_1_En_1_Fig20_HTML.png]
Fig. 20Comparison between theoretical and monotonic series

[image: ../images/450266_1_En_1_Chapter/450266_1_En_1_Fig21_HTML.png]
Fig. 21Comparison between theoretical and cyclic series

Figures 19, 20 and 21 shows that theoretical histogram is, in general, inside the confidence interval for all series. This means that, from a statistical point of view, it can be assumed that all the distributions are equal, i.e., intact, monotonic and cyclic series follow a random distribution. Empty voxel, i.e., pores, are randomly distributed inside the specimens along the height of the specimens.
Figure 22 shows the comparison between the real distributions of monotonic and cyclic series. Additionally, the 90% confidence interval is defined by the upper and the lower limits.[image: ../images/450266_1_En_1_Chapter/450266_1_En_1_Fig22_HTML.png]
Fig. 22Comparison between monotonic and cyclic series

In concordance with the information shown in Figs. 20, 21 and 22 shows that the average monotonic histogram is inside the confidence interval of cyclic series and viceversa. This means that, from a statistical point of view, it can be assumed that both distributions are equal, i.e., the crack pattern of both monotonic and cyclic series are equal along the h direction.
Considering the information provided by Figs. 14 and 21 it can be affirmed that monotonic and cyclic distributions are equal, which demonstrate the hypothesis shown at the beginning of this paper.
4 Summary and Conclusions
The CT-Scan combined with a specific post-processing software is a useful tool to measure the internal damage of concrete specimens. In case of intact specimens, damage refers to pores, while in case of tested specimens, damage refers to pores and cracks.
In this paper, the Circumferential Test is shown. This is a specific protocol, developed by the authors, to measure the damage distribution. Using the data provided by the CT-Scan it is possible to check if damage follows a random distribution or not. In addition, a theoretical random distribution was simulated, using a Monte Carlo model. This simulation was used as the random distribution reference.
Results provided by CT-Scan and later analyzed with the Circumferential Test show that damage (i.e. pores) inside the intact series specimens follow a random distribution, while damage (i.e. pores and cracks) inside the monotonic and cyclic series specimens do not follow a random distribution.
In addition, results show that both monotonic and cyclic follow the same damage distribution. This conclusion demonstrate the hypothesis of convergence to the “initial distribution”, which means that the static testing is a particular case of cyclic testing where the fatigue life is equal to 1.
Acknowledgements
The authors are grateful for the financial support from the Ministerio de Economía y Competitividad BIA2015-686678-C2-R, Spain, Junta de Comunidades de Castilla – La Mancha, Spain, Fondo Europeo de Desarrollo Regional, gran PEII-2014-016-P and INCRECYT Program.

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© Springer Nature Switzerland AG 2019
Heiko Herrmann and Jürgen Schnell (eds.)Short Fibre Reinforced Cementitious Composites and CeramicsAdvanced Structured Materials95https://doi.org/10.1007/978-3-030-00868-0_6

Short Composite Fibres for Concrete Disperse Reinforcement

Arturs Lukasenoks1  , Andrejs Krasnikovs1  , Arturs Macanovskis1  , Olga Kononova1   and Videvuds Lapsa2
(1)Concrete Mechanics laboratory, Institute of Mechanics, Riga Technical University, Riga, Latvia

(2)Faculty of Civil Engineering, Institute of Building Production, Riga Technical University, Riga, Latvia

Arturs Lukasenoks (Corresponding author)
Email: Arturs.Lukasenoks@rtu.lv

Andrejs Krasnikovs
Email: Andrejs.Krasnikovs@rtu.lv

Arturs Macanovskis
Email: Arturs.Macanovskis@rtu.lv

Olga Kononova
Email: Olga.Kononova@rtu.lv

Videvuds Lapsa
Email: Videvuds.Lapsa@rtu.lv

Abstract
Short composite fibres are a relatively new product for concrete disperse reinforcement. In this experimental research, 14 different composite fibres were developed and single fibre pull-out micromechanics was investigated. Three main groups of composite fibre were—composite glass fibres (GF), composite carbon fibres (CF) and hybrid fibres (HF). Composite fibre manufacturing consisted of glass, carbon or combined fibre filament preparation, impregnation with epoxy resin, epoxy curing, quality control and cutting in short discrete macro- fibres. All three composite fibre groups were manufactured with straight, uneven and undulated geometries. Fibre surface finish was smooth and rough. Uneven fibre geometry was achieved by not aligning all fibre filaments in fibre tow. Undulated geometry was a result of interlaced fibres. The rough fibre outer surface finish was achieved by adding an extra layer of epoxy resin containing fine quartz grains. All macro-fibres were cut in 50 mm length. Single fibre pull-out samples with a pre-defined crack between two concrete parts were prepared to investigate fibre pull-out behaviour. Fibre pull-out laws were obtained and analysed. Composite fibre improvement geometry and surface with roughening outer surface made a huge impact on fibre pull-out resistance.
1 Introduction
Development of composite fibres is very important due to many problems related to polymer, glass and carbon fibre usage in concrete for disperse reinforcement. There is a necessity to use large volume fractions 2–2.5% of polymer fibre to achieve a tangible increase in load bearing performance of low strength concretes [1]. Large amounts of fibres significantly worsen concrete consistency, a new approach for concrete design with target consistency is necessary. Fibres with higher strength and elasticity modulus are necessary for higher strength concretes. Due to fibre small diameter glass, basalt or carbon fibres have significant problems with introducing in concrete. When fibres are introduced into the concrete mix, fibre rolls and clews are formed—problems with fibre homogeneity in the concrete occurs. Each fibre roll or clew with air voids is another defect in the concrete which reduces strength. Difficulties with fibre introduction become more pronounced with fibre volume fraction increase. Mentioned fibres can be introduced in concrete mixes produced in high-speed mixers, unfortunately, high mixing energy and shear forces brakes and mills fibres in shorter parts [2]. Small fibres can work bridging only small crack openings.
Glass, basalt and carbon fibres are used more widely due to advanced manufacturing technologies and reduced cost. Several attempts to introduce glass, basalt and carbon fibres in the construction industry were found—long carbon fibres and commercial product Minibar [3, 4]. Basalt Minibar fibres are recommended to use in high volume fractions (1.5–3%) to achieve tangible results. Long carbon fibre composite fibres were used for increasing concrete plate’s impact load resistance [4, 5].
In the present investigation, short composite macro-fibres were manufactured as unidirectional carbon and glass composite rods. Rods were cut in discrete fibres with L/d ratio from 18.1 to 56.1. A varying number of filaments in macro-fibre (changing filament volume fraction V[image: $$_{\mathrm {f}}$$] in composite fibre) as well as using different material filaments in one macro-fibre it is possible to obtain reinforcing fibres with different strengths and elastic properties. Composite fibres can be developed for very specific use; composite fibres with a smooth surface for high strength concretes to increase ductility, fibres with a rough surface or uneven geometry results in good anchorage for low and average strength concrete reinforcement [6]. Higher fibre anchorage in concrete can be also achieved by making fibre outer surface rough [7].
2 Materials and Methods
Overview of Experimental program for composite fibres and different concrete matrices is shown in Table 1.Table 1Concrete mixture proportions

Fibre type
Fibre denomination
Concrete matrix
Depth, angle configuration

M1
M2
M3

Composite glass fibres
GF1
-
-
x
25 mm depth, 0-degree angle to pull-out force

GF2
x
x
x

GF3
-
-
x

GF4
-
-
x

GF5
-
-
x

Composite carbon fibres
CF1
x
x
x

CF1-A
x
x
x

CF1-B
x
x
x

CF2
x
x
x

CF2-A
x
x
x

CF2-B
x
x
x

CF3
-
x
x

Hybrid fibres
GC1
-
-
x

CG1
-
-
x

3 Concrete Materials and Mix Design
Portland cement Aalborg White CEM I 52.5 R is used as binder in experimental mixes, naturally fractioned and washed quartz sand 0–1 mm as main aggregate. Quartz powder and silica fume was used as micro filler. Poly-carboxylate based high range water reducing admixture was used to control mix workability. Tree types of concrete mixtures were designed (mixture proportions are presented in Table 2). First type concrete mixture is high strength concrete (M1) with cement content 800 kg/m[image: $$^{3}$$]), with silica fume, water to cement w/c ratio 0.25. The second type concrete mixture is normal strength concrete (M2) with cement content 550 kg/m[image: $$^{3}$$], having silica fume and with w/c ratio equal to 0.55. The third type concrete mixture was low strength (M3) with cement content 400 kg/m[image: $$^{3}$$], without silica fume, and having water to cement ratio w/c equal to 0.7. The amount of micro-filler was adjusted in order to achieve paste content 550 l [image: $${\pm }$$] 7% in all cases.
All three concrete types were designed to achieve target compressive strength and have good workability and stability in fresh stage. Workability was defined to have slump flow classes measured in accordance with EN 12350-8: 580 mm.Table 2Concrete mixture proportions

Material
Density, t/m[image: $$^{3}$$]
M1
M2
M3

Cement CEM I 52,5 R (Aalborg White)
Water
3,13
1
800
200
550
300
400
300

Sand 0–1 mm (SaulkalneS)
2,65
1100
1200
1400

Microsilica (Elkem 920D)
2,22
133,3
50
0

Quartz powder 0–120 mk (Anyksciai)
2,65
66,5
250
250

HRWR (Sika D400)
1,07
25
6,5
3

w/c ratio

0,25

0,55

0,75

paste volume, l

605,5

611,4

516

Table 3Fibre properties

Fibre type
Fibre denomination
Fibre geometry, surface
Diameter, mm
L/d ratio
Reinforcement ratio
Specific weight, kg/m[image: $$^{3}$$]

Composite glass fibres
GF1
Uneven, smooth
2,18
22,9
0,534
1195

GF2
Straight, smooth
1,52
32,9
0,751
1746

GF3
Straight, rough
2,04
24,5
0,482
1507

GF4
Undulated, smooth
1,88
26,6
0,657
1310

GF5
Undulated, smooth
1,85
27,0
0,696
1270

Composite carbon fibres
CF1
Straight, smooth
1,77
28,3
0,578
1129

CF1-A
Straight, smooth
1,30
38,6
0,635
1291

CF1