Effect of mixture flowability on strength and fiber distribution of Ultra High-Performance Fiber Reinforced Concrete

. The uniformity of distribution and the orientation factor of steel fibers are crucial parameters that determine the strength and uniformity of properties of Ultra High-Performance Fiber Reinforced Concrete (UHPFRC). The paper considers the influence of flowability and the method of casting the concrete mixture on the strength and fracture energy in bending of UHPFRC. The flowability was determined by the spread diameter of the mixture from the H ä germann cone, which was 270, 300, and 350 mm. It was found that the compressive strength of UHPFRC increases from 142 to 155 MPa with an increase in the mixture spread diameter. The strength and fracture energy in bending of UHPFRC near the ends of the mold are on average 14.5 and 17.7% less than in the central part. A relationship has been established between the flexural strength of UHPFRC and the fracture energy as a function of the relative area of the fiber in the cross-section. The optimal flowability range of UHPFRC (270…290 mm) was established analytically and experimentally, in which there is no critical decrease in strength properties and the ability of the mixture to self-leveling is maintained. Negative effects were established when changing flowability, outside the specified range.


Introduction
Ultra High-Performance Fiber Reinforced Concrete (UHPFRC) is a relatively new structural building material with a minimum compressive strength of 130 MPa, high impact strength, and durability [1][2][3].In the fresh state, UHPFRC typically has a self-compacting consistency, allowing products to be produced without additional compaction or vibration.Using self-compacting mixture makes it possible to increase the fiber orientation coefficient due to the self-alignment of the fiber in the direction of the mixture flow.Increasing the fiber orientation coefficient in the direction parallel to the tensile load makes it possible to significantly improve the strength properties of UHPFRC.It was found in [4] that when the fiber orientation coefficient was changed from 0.45 to 0.8, the axial tensile strength increased from 5.5 to 11.3 MPa.In [5], the authors found that an increase in the orientation coefficient from 0.7 to 0.87 leads to an increase in tensile strength from 6.4 to 14.1 MPa for UHPFRC with 3% fiber, and for a composition with 1.5% an increase in the orientation coefficient from 0.71 to 0.89 led to an increase in strength from 4.9 to 8.9 MPa.
The fiber orientation coefficient in self-compacting mixtures depends on a large number of factors: the location of the forming element relative to the longitudinal axis of the mold [6], the type of the casting element [7], the ratio of the width of the formed product and the length of the fiber [8], and the length of the fiber itself [9].The rheological properties of the concrete mixture, such as yield stress and plastic viscosity, play a key role.In [10], the influence of the plastic viscosity of the suspending mortar on the strength and fracture toughness of UHPFRC was studied, which were increased by 55…75 and 70%, respectively, with an increase in plastic viscosity from 10 to 45 Pa•s.In [11], it was found that the value of plastic viscosity 53 Pa•s is optimal in terms of strength and fracture toughness.
However, the determination of the plastic viscosity of concrete is possible only in specially equipped laboratories, and the measured value may not be the same when using viscometers of various designs, which does not allow using this parameter to optimize and control the composition of UHPFRC directly in the manufacture of products.
The purpose of this work was to study the effect of the slump flow of the mixture from a standard cone on the strength of UHPFRC, as well as the distribution of steel fibers along the length of the molded product.Slump flow is one of the simplest and most affordable ways to indirectly determine the rheological properties of a concrete mix, and therefore it becomes necessary to determine the optimal value of this parameter.

Materials and mix composition
Portland cement CEM I 42.5 N with a specific surface area of 345 m 2 kg ⁄ and an activity of 47.5 MPa at the time of 28 days was used as a binder.Condensed silica fume (CSF) containing >85% amorphous silica was used as an active mineral additive.Limestone powder (LP) with a specific surface area of 280 m 2 kg ⁄ was used as a mineral filler.The content of CSF and LP was constant and amounted to 15 and 20% by weight of the cement, respectively.As a fine aggregate, quartz sand of fractions 0.1-0.4 and 0.4-0.8 was used in a ratio of 30:70 by volume, which corresponds to the maximum particle packing density.Brass coated corrugated steel fiber 15 mm long and 0.3 mm in diameter (l/d=50) was used in the amount of 1.5% of the mixture volume.A superplasticizer based on polycarboxylate ethers Sika ViscoCrete 24 HE was used.
Table 1 shows the composition of the studied concrete.The flowability of the UHPFRC was regulated by changing the content of the superplasticizer in the range of 1 ... 1.6% of the mass of cement.As a result, mixtures with a spread diameter of 270 ± 10, 305 ± 10, and 345 ± 10 mm were obtained, which were further designated as "270", "300", and "350", respectively.

Methods
The flowability of UHPFRC was determined using the Hägermann cone.The prepared fresh concrete mixture was placed in a cone in one step, after which the cone rose, allowing the mixture to spread under its weight.After the mixture stopped spreading, the diameter of the spread was measured in two mutually perpendicular directions.The spread value was determined as the arithmetic mean of two measurements.For each composition, the test was repeated 2 times, the average value was taken as the final result.
To determine the effect of the flowability of the mixture on the distribution of steel fibers, a sample of 400x100x40 mm in size was made from each composition.The mixture was fed into the mold using a chute located at an angle of 45 degrees to the horizon (Figure 1).During molding, there was no additional compaction or vibration.Cubes of size 50×50×50 mm were also made from this mixture without using vibration to determine the compressive strength.After 24 hours, the samples were removed from the molds and subjected to steam treatment at a temperature of 80℃ for 48 hours and then stored for another 48 hours in a laboratory room at a temperature of 20±3℃.
To determine the flexural strength and fracture energy, 6 prism specimens 40 × 47.5 × 130 mm in size were sawn from each plate.The samples were divided into 3 groups of 2 specimens depending on the distance from the casting point (Figure 2).
where: F -maximum flexural load, N; l -distance between supports, mm; b, h -width and heigh of specimen, mm.The fracture energy of an individual sample was determined by the equation: where W -the work required to deform the specimen, defined as the area under the load-deflection curve, N • mm.
The work W was determined by integrating the load-deflection diagram up to a deflection value of 6 mm: When determining the compressive strength, the samples were loaded at a rate of 2 MPa/s.The average value was determined from the two highest test results.
The average flexural strength and fracture energy in each section was determined as the arithmetic average of the results of two tests.
After the bending test, the relative fiber content in the cross-section was determined.The sample was cut at a distance of 5-10 mm from the main crack, after which a photo of the cross-section was taken.With the help of specially developed software, the contours of the fibers were identified in the image, and the area of the obtained objects was calculated (Figure 3).The relative area of the fibers was determined by the equation: Where A f,m -measured area of steel fibers in cross-section, pixels; A total -total area of cross-section, pixels.The average relative fiber content in each section was determined as the arithmetic mean of the values of the two samples.compressive strength increases and amounts to 142.1, 145.0, and 155.5 MPa with a flow diameter of 270, 300, and 350 mm, respectively.This effect is due to a smaller volume of entrapped air in a mixture with higher flowability, which is confirmed by the results of determining the average density.According to data from the literature [12,13], the relationship between the volume of entrapped air and the spread diameter of the mixture, determined by the Hägermann cone, was obtained.A graphical display of data is shown in Figure 5.The experimental data were approximated by the following equation: Where SF -slump flow of fresh concrete mixture determined on the Hägermann cone, mm.
According to the equation obtained, it is possible to estimate the content of entrapped air in the mixture, which will be 3.7, 2.8 and 1.5% for compositions with a spread diameter of 270, 300 and 350 mm, respectively.
Equation ( 5) can also be used to determine the minimum allowable flowability of a self-compacting UHPFRC that does not result in a critical reduction in compressive strength.
To analyze the influence of the volume of entrapped air on the relative decrease in the strength of concrete, the classical Feret equation was used [14,15]: where V b , V w , V air -volume of binder (cement and silica fume), water and entrapped air per cubic meter of concrete, l; K -complex value depending on cement activity, aggregate used and age of concrete, MPa.By dividing the strength of concrete with some content of entrapped air R air by the control concrete strength R ref , the relative reduction in compressive strength can be determined.It has been assumed that the minimum possible entrapped air content for commonly used UHPFRCs is 1%.The strength of concrete with 1% entrained air was taken as R ref .Using Equation 6 to find R air and R ref , we get: For the concrete composition studied in this work, the volume of the binder (cement and silica fume) and water is 351 and 252 liters, respectively.Substituting these values into equation 8, and assuming that the allowable reduction in strength is 10% ( R air R ref = 0,9), we obtain that the volumetric content of entrapped air should be no more than 4.3%.From equation 6, we obtain that the spread diameter of the mixture with such a volume of entrapped air is 250 mm.Important to note that this limit is not constant and depends on the composition of the mixture due to the nonlinearity of the law of concrete strength -at large values of ( ) a small change in the amount of entrapped air leads to a greater decrease in strength.However, it is easy to redefine the new boundary if the composition of the concrete is known.

Flexural strength and fracture energy
Figure 6 shows graphs of the strength and fracture energy of samples depending on the distance from the mixture casting point.It can be seen from the graphs in Figure 6 that the strength and fracture energy of samples made from a concrete mixture of the same flowability is not the same and depends on the distance that the mixture has overcome during the casting process.The highest values of strength and fracture energy are achieved in the central part of the mold, regardless of the flowability of the mixture.Closer to the ends of the mold, the values decrease symmetrically.On average, near the ends of the mold, the value of strength and fracture energy is less by 14.5 and 17.7%, respectively.Similar results were obtained in [16] on smaller samples.In [17], as a result of numerical simulation, a decrease in the coefficient of the orientation of fibers near the ends of the mold was established.This effect is explained by the fact that, immediately after mixing, the fiber is randomly oriented, and this randomness is preserved in the first part of the form.With the further flow of the mixture, "stabilization" and orientation of the fibers parallel to the direction of the mixture flow occurs.Upon reaching the end of the mold, the fiber is again oriented randomly due to collision with the walls of the mold.Further analysis of the results is given for samples cut from section 2.
As can be seen from Figure 7-a, the mixture with a flowability of 270 mm has the highest flexural strength and is 25 MPa.With an increase in flowability to 300 and 350 mm, the flexural strength decreases to 23 and 18 MPa, respectively.
The fracture energy of mixtures with flowability of 270, 300, and 350 mm was 17.8, 16, and 14 N mm ⁄ , respectively.As with flexural strength, there is a tendency for the fracture energy to decrease with increasing mixture flowability.The exception is a mixture with a spread diameter of 300 mm.This is explained by the fact that with an increase in flowability, the tendency to segregation of steel fibers under the action of gravity increases, which leads to an uneven distribution of the fibers over the sample cross-section, as well as to the appearance of direct contact between the fibers.Figure 7 shows photographs of the cross-section of samples made from mixtures with different flowability, from which it can be seen that in a mixture with a spread diameter of 350 mm, there is significant segregation of the fibers.

Relative fiber area
The graph in Figure 8-a shows the relationship between the relative fiber area and the distance from the mixture casting point.The general nature of the curves is similar to the graphs in Figure 6, which confirms the assumption of a chaotic distribution of fibers at the ends of the mold and more aligned in the center.Figure 8-b shows the relationship between the flexural strength and fracture energy of UHPFRC and the relative fiber area in the section.It can be seen from the graph that there is a good correlation between the two parameters.

Practical recommendations
Based on the test results obtained, practical recommendations were formulated for choosing the optimal workability of self-compacting UHPFRC, in which, on the one hand, the ability of the mixture to self-leveling is preserved, and on the other hand, there is no critical decrease in the main physical and mechanical characteristics of the material.Figure 9 shows a graph of flexural strength and fracture energy versus flowability (according to the results of the tests), which is divided into 5 zones depending on the change in material properties associated with a change in flowability.

Fig. 9. Practical recommendations for choosing flowability of UHPFRC
Zone 1 (SF<250 mm): corresponds to a reduction in compressive strength of more than 10% due to the increased volume of entrapped air, the mixture has insufficient flowability for self-leveling.Zone 2 (SF=250…270 mm): the reduction in compressive strength is within acceptable limits, however, but the mixture still has insufficient flowability for self-leveling.Zone 3 (SF=270…290): the optimal range of UHPFRC flowability, in which the strength either does not decrease or is within acceptable limits and the mixture exhibits the ability to self-level.Zone 4 (SF=290…340): flexural strength is reduced more than 10%, the beginning of fiber segregation.Zone 5 (SF>340): fracture energy is reduced by more than 10%, accompanied by significant fiber segregation.

Conclusions
Based on the results obtained in this work, the following conclusions can be drawn:  The compressive strength and density of UHPFRC increases with increasing flowability (from 142.1 to 155.5 MPa and from 2.48 to 2.54 g cm ⁄ ) due to the decreased content of entrapped air in the mixture (from 3.7 to 1.5%);  The flexural strength and fracture energy of UHPFRC varies along the length of the mold.The highest values are achieved in the central part of the mold; closer to the ends, the flexural strength and fracture energy are on average 14.5% and 17.7% lower.This is due to the better distribution of the fiber in the central part of the mold due to the orientation of the fiber during the casting of the mixture;  The flexural strength decreases with increasing flowability above 270 mm, the fracture energy decreases with increasing flowability above 300 mm.This is due to a significant segregation of the fiber along the height of the crosssection;  The values of strength and fracture energy correlate with the experimentally determined relative fiber area.The relationship is linear;  It has been analytically and experimentally substantiated that flowability in the range of 270…290 mm is optimal for self-compacting UHPFRC.In this range, there is no decrease in the strength, the mixture is self-levelling, and the steel fiber is distributed evenly over the cross-section of the samples.Changing the flowability of the mixture less than 270 mm or more than 290 mm leads to a decrease of mechanical properties and uniformity of fiber distribution.
This work was financially supported by the Ministry of Science and Higher Education of Russian Federation (grant # 075-15-2021-686).Tests were carried out using research equipment of The Head Regional Shared Research Facilities of the Moscow State University of Civil Engineering

Fig. 1 .
Fig. 1.The equipment used in this work: a) Hägermann cone for flowability test; b) casting device.

Fig. 2 .
Fig. 2. Specimens for determination of flexural strength and fracture energy: a) schematic illustration (dimensions in mm); b) finished specimens.The prism samples were tested for bending at a loading rate of 0.4 mm/min with the registration of the "load-deflection" diagram.The distance between the supports was 100 mm.According to the resulting diagram, the maximum force acting on the sample during the test was determined, and then the ultimate flexural strength of the sample was calculated using the equation:

Fig. 3 .
Fig. 3. Determination of relative fiber area: a) reference image; b) image with captured steel fibers.

Fig. 8 .
Fig. 8. Relationship between relative fiber area and flow distance (a) and correlation between flexural strength/fracture energy and relative fiber area (b).