Experimental Study on the Flexural Properties of Steel-Fibre-Reinforced Concrete Specimens with Different Heights

Abstract

Flexural strength is an important mechanical property of steel-fibre-reinforced concrete. By designing three-point bending tests of concrete with five specimen heights, three steel fibre types, and two steel fibre mixing methods, the effects of the specimen height, steel fibre mixing method, and steel fibre type on the peak load, effect of size, section characteristics, strain characteristics, and characteristics of the load–displacement curve of concrete specimens were studied. The results show that the peak load of the control group is basically linear with the height of the specimen. After adding three kinds of steel fibres, the peak load of the specimen is greater than that of the control group in the same case. The peak load of the specimen increases by adding three kinds of steel fibres, and the increase is closely related to the height of the specimen. The residual stage of the load–displacement curve of the milling steel fibre and the end hook steel fibre are relatively flat, while the residual stage of the load–displacement curve of the shear steel fibre is relatively large, and the residual load is also greater than the residual load of the shear steel fibre. The specimens in the control group show brittle failure characteristics. As the height of the specimens increases, the failed section of the specimens is smoother. The development of cracks in the steel fibre specimens is more tortuous than that of the control group, showing ductile failure characteristics. Some tensile failure zones are still present where the fibres are densely distributed, and the failure characteristics of the specimens are further explained and proven by the strain characteristics.

1. Introduction

Concrete materials are widely used in bridges, tunnels, housing construction, and other projects due to their wide range of sources and low prices. However, due to the poor ductility of concrete, brittle failure easily occurs when the deformation is too large. Therefore, it is of great practical significance to improve the ductility characteristics of concrete in tension, shear, and bending concrete members [1]. Fibres are widely used to improve the mechanical properties of concrete and form fibre-reinforced concrete (FRC) due to their high tensile strength, high tensile modulus, widely available sources, and low price [2]. At present, as material science develops, there is an increasing number of kinds of fibre materials such as plant fibre (cotton stalk fibre, straw fibre, sisal fibre, etc.), synthetic fibre (polypropylene fibre, polyvinyl alcohol fibre, polyethylene fibre, etc.), and inorganic fibre (glass fibre, steel fibre, carbon fibre, etc.) materials. However, different types of fibres have different morphologies, sizes, and material properties, which lead to differences in their mechanism of action and effects of improvement on concrete. It is necessary to further reveal the relevant differences.

Steel fibre has a low raw material cost, simple manufacturing process, and high production efficiency. Therefore, steel fibre is inexpensive and widely used to improve the mechanical properties of concrete. Scholars have carried out much research on this topic. Research has mainly focused on the steel fibre content [3], steel fibre type [4], steel fibre source [5], age [6], and aspect ratio of steel fibre [7] and has achieved fruitful research results. On this basis, Jang et al. [8] studied the effect of aggregate size on the flexural behaviour of high-strength steel-fibre-reinforced concrete (SFRC). Due to the different properties of the matrix, the effects of steel fibre improvement are different. Some scholars have studied steel fibres to improve alkali-activated slag (AAS) concrete [9], recycled concrete [10], lightweight aggregate concrete [11], self-compacting concrete [12], ultrahigh-performance concrete [13], foam concrete [14], alkali slag concrete [15], permeable concrete [16], and oil palm shell concrete [17]. For example, Mpalaskas et al. [18] tested the SFRC beam during the bending process and carried out acoustic emission monitoring (AE). It was found that the AE behaviour at low load level can well explain the amount of steel bars, thus indicating the final mechanical properties. Chalioris [19] studied the standard 150 mm cube made of FRC and pasted a small lead zirconate titanate (PZT) patch network on the surface of the sample. It was found that the mechanical impedance of FRC cracking was changed due to the repeated loading and various compressive stress levels, resulting in a corresponding change in the signal of each PZT.

Limited by the mixing process, steel fibres are generally randomly distributed in concrete, but some scholars have also expanded the study of the distribution of fibres, such as Wang et al. [20], who studied the evolution of damage to layered fibre-reinforced concrete. As progress has occurred, other steel fibres with excellent shapes and tensile strengths have been developed. For example, Menna et al. [21] studied the influence of high-performance double-hook-end steel fibres on the flexural properties of concrete. Yun et al. [22] considered the influence of normal-tensile-strength steel fibres (1200 MPa) and high-tensile-strength steel fibres (1500 MPa) in high-strength concrete. In the laboratory, some scholars have compared the effects of different loading methods on steel-fibre-reinforced concrete, such as static loading and impact loading methods [23], the three-point bending test (3PBT) and four-point bending test (4PBT) [24], and uniaxial and biaxial methods [25]. Some scholars have also studied the flexural performance of steel-fibre-reinforced concrete under cyclic loading [26], which has furthered research on loading methods. To promote the application of steel-fibre-reinforced concrete, the durability, fire resistance, and high-temperature performance of steel-fibre-reinforced concrete have been defined [27,28,29]. For example, Qiang et al. [27] carried out an experimental study of steel-fibre-reinforced concrete in acidic environments, and it was found that when the volume ratio of steel fibre is 1.5%, the corrosion resistance of steel-fibre-reinforced concrete is the best. Li et al. [28] carried out a flexural toughness test and inversion study of the thermal conductivity of steel-fibre-reinforced concrete members after fires, and it was verified that the incorporation of steel fibre into concrete helps to reduce its internal thermal stress difference and improve the crack resistance and fire resistance of the concrete. Li et al. [29] analysed the flexural behaviour of ultrahigh-performance hybrid-fibre-reinforced concrete under environmental and high-temperature conditions. The hybrid combination of polyethylene and steel fibre can effectively improve the proportional limit, fracture modulus, toughness, and toughness index of ultrahigh-performance concrete (UHPFRC).

Due to the complex structure of concrete, steel fibre is limited in its potential for adding improvement. Therefore, scholars have improved the flexural properties of concrete from different angles by mixing in other materials or fibres such as nanosilica and steel fibre mixtures [30], rubber powder and steel fibre mixtures [31], silicon powder (SF) and ground granulated blast furnace slag (GGBS) [32], alkali-activated slag-fly ash [33], and rice husk ash [34]. Fruitful research results have been achieved on steel fibre–polypropylene fibre mixing [35]; modified olefin fibre (MOF) and steel fibre mixing [36]; steel fibre and polyethylene fibre mixing [37]; NiTi shape-memory alloy, polypropylene, and steel fibre mixing [38]; natural fibre (coconut shell fibre) and circular straight steel fibre mixing [39]; steel fibre and glass fibre mixing [40]; and different types of steel fibre mixing [41]. In addition, due to the large probability of defects such as pores, cracks, and local defects in large-sized specimens, the flexural properties of concrete are different. Therefore, scholars have conducted much research on the effect of size on steel-fibre-reinforced concrete [42,43,44].

The above research shows a great deal of work on the flexural performance of fibre-reinforced concrete, which has great reference value for the research conducted in this paper. However, the flexural performance and strain characteristics of different steel-fibre-reinforced concretes under different specimen heights have not been studied. In this study, five kinds of concrete flexural specimens with different specimen heights and three kinds of steel fibre types were developed, and two kinds of fibres were added. The peak load, fracture characteristics, strain characteristics, and load–displacement curves of steel-fibre-reinforced concrete at different specimen heights were studied. The influence of the random distribution and layered distribution of steel fibres on the flexural characteristics was compared, and the variation in the number of steel fibres at different specimen heights was analysed with the aim of providing a reference for engineering design.

2. Three-Point Bending Test

2.1. Specimen Preparation

For this test, according to the C40 concrete standard, the specific mix proportion is shown in

Table 1. Mixing ratio of the specimen.

Name of the Material	Cement/kg	Sand/kg	Aggregate/kg	Water/kg
Numerical value	460	800	915	220

[45]. The number of flexural specimens in each case was four. As shown in Figure 1, the length and width of the flexural specimens were 550 mm and 150 mm, respectively. The height was the changing variable, with values of 30 mm, 60 mm, 90 mm, 120 mm, and 150 mm. In the concrete, steel fibre was divided based on two kinds of mixing methods. The influence of different distribution forms of steel fibre on the flexural strength and failure characteristics was analysed. The height was divided into five equal parts, which increased the research scope of sample height and ensured the credibility of the research. Case A was as follows: Based on 50 kg of steel fibre per square, three different types of steel fibre were added. Case B was as follows: Five heights from low to high were set in turn to form evenly spaced arrangements of one to five layers of three types of fibres. Each layer had eighteen evenly arranged fibres, and the three kinds of steel fibres were the shear type, milling type, and end-hook type, as shown in Figure 2. When making the specimens, according to the ratio, the weight of each component material was weighed, a forced one-bed mixer was used to mix the material evenly, and then, the specimen was shovelled into the mould. The specimen of case A was directly vibrated and smoothed, while the specimen of case B needed to be layered, vibrated, and smoothed, and the concrete specimen was maintained in a standard curing room for 28 days. Taking A-M-30 and Y-30 as examples, the first letter, A, of A-M-30 indicates that the method of adding steel fibre is the same as that in case A; the second letter, M, indicates that the type of fibre is the milling type (the shear type and end-hook type are represented by the letters S and E, respectively); and the number in the third position, 30, indicates that the height of the specimen is 30 mm (the heights of the other specimens are the same). The letter in the first position, Y, of Y-30 represents the control group specimen without adding fibre, and the number in the second position, 30, is the same as in A-M-30.

2.2. Bending Test

As shown in Figure 3, the prepared specimens were placed on a concrete flexural testing machine, and the flexural strength of concrete specimens with different heights and different steel fibre types was tested by using the principle of a three-point bending test. The three-point bending test was carried out according to the “Fibre Concrete Test Method Standard” (CECS 13-2009) [46]. Before loading, the specimens were first marked with support and loading positions and then loaded until the specimen was destroyed, and the loading rate was 0.05 MPa/s. To test the deformation characteristics of the specimen before failure, strain gauges were installed on the middle and lower ends of the side of the specimen to monitor the deformation characteristics of the specimen during the loading process. During the loading process, the strain acquisition system was used to record the deformation characteristics. After the specimen was destroyed, the section characteristics and the number of fibres in the specimen were recorded by a camera.

3. Analysis of the Results

3.1. Peak Load

The peak load of the specimen was obtained by the flexural test. The peak loads of cases A and B are shown in Figure 4. As shown in Figure 4a, in case A, the peak load of all specimens increases with increasing specimen height. (To make the difference more specific, the curve is fitted by a quadratic term; the coefficient of determination R² is greater than 0.98.) The peak load of the control group basically changes linearly with the height of the specimen. After adding three kinds of steel fibres, the peak load of the specimen is greater than that of the control group at the same height. In addition, as the height of the specimen increases, the peak load growth rate of the steel-fibre-reinforced concrete specimen gradually increases, indicating that the higher the height of the specimen, the better the effect of fibre improvement on the peak load of the specimen, and the stronger the sensitivity of the specimen to the fibre. When the height of the specimen is small (30 mm), the effect of steel fibre on the peak load of the specimen is small, and the difference in the peak load of the specimen is small. When the heights of the specimen are 60 mm and 90 mm, the peak load capacities of the three fibre-reinforced specimens occur in the shear type, milling type, and end-hook type. When the specimen heights increase to 120 mm and 150 mm, the peak load capacities of the three fibre-reinforced specimens change, followed by those of the milling type, shear type, and end-hook type, indicating that in case A, the specimen height has an effect on the peak load of the three steel fibre types for improvement of the specimen.

As shown in Figure 4b, similar to case A, in case B, the peak loads of all specimens increase with increasing specimen height. After adding three kinds of steel fibres, the peak load of the specimen is greater than that of the control group at the same specimen height. In addition, when the specimen height changes from 30 mm to 90 mm, with increasing specimen height, the peak load growth rate of the steel-fibre-reinforced concrete specimen is greater than that of the control group. The difference in the peak load of the specimen gradually increases, indicating that the higher the specimen height, the better the effect of the peak load improvement of the fibre on the specimen, and the stronger the sensitivity of the specimen to the fibre. When the specimen height changes from 90 mm to 150 mm, the peak load growth rate of the steel-fibre-reinforced concrete specimen is basically the same as that of the control group, and the peak load difference in the specimen remains stable. When the height of the specimen is small (30 mm and 60 mm), the effect of steel fibre on the peak load of the specimen is small, and the difference in the peak load of the specimen is small. When the height of the specimen is 90 mm, the peak load capacities of the three kinds of fibre-reinforced specimens occur in the shear type, end-hook type, and milling type. When the heights of the specimen increase to 120 mm and 150 mm, the peak load capacities of the three fibre-reinforced specimens change, followed by those in the end-hook type, the shear type, and the milling type; this phenomenon is different from the phenomenon of case A, indicating that the fibre mixing method has an effect on the peak load of fibre-reinforced concrete.

In addition, when the height of the specimen is small (30 mm and 60 mm), the peak loads of the hook-type and shear-type steel-fibre-reinforced concrete specimens in case B are slightly larger than that of case A (when the heights of the specimen are 30 mm and 60 mm, the absolute value of the peak load difference in the corresponding case are between 0.12 kN and 1.13 kN), while the peak load of the milling steel-fibre-reinforced concrete specimen in case A is slightly larger than that in case B (the absolute value of the load difference is 0.08 kN when the height of the specimen is 30 mm, and the value is 0.32 kN when the height of the specimen is 60 mm) and when the heights of the specimen are 90 mm, 120 mm, and 150 mm. The peak load of the three kinds of steel-fibre-reinforced concrete specimens in case A is gradually greater than that in case B, and as the specimen height increases, the difference in the peak load of the steel-fibre-reinforced concrete specimens in case A is greater. When the specimen height is 90 mm, the absolute values of the difference in the peak load in the corresponding case are between 0.28 kN and 2.35 kN; when the heights of the specimen are 120 mm and 150 mm, the absolute values of the peak load difference in the corresponding case A are between 3.31 kN and 5.49 kN and between 5.56 kN and 8.67 kN.

The above analysis reveals that the peak load of the specimen shows an increasing trend when the three types of steel fibres are mixed with the method of case A and case B, and the range of increase is closely related to the height of the specimen. The peak load of the three kinds of fibres is closely related to the height of the specimen and the method of mixing.

3.2. Effect of Size

The flexural strength of the specimens in case A is calculated by using Equation (1), as shown in

Table 2. The flexural strength of specimens in cases A and B.

	Case A	Y	A-E	A-S	A-M	B-E	B-S	B-M
Specimen Height
30		3.33	3.80	4.44	4.08	4.64	4.83	3.81
60		3.25	3.54	4.10	3.87	4.49	4.60	3.60
90		3.04	3.33	3.85	3.55	3.69	3.86	3.27
120		2.39	3.13	3.55	3.43	2.84	2.79	2.60
150		2.26	2.99	3.21	3.34	2.73	2.70	2.50

. With increasing specimen height, the flexural strength of the concrete specimens in case A decreases, the flexural strength of the different types of steel-fibre-reinforced concrete specimens decreases differently, and the flexural strength is affected by the size.

$$\mathrm{f}=\frac{\mathrm{FL}}{{\mathrm{bh}}^2}$$

(1)

where F is peak load (N), L is distance between supports (L = 450 mm), b is specimen width (b = 150 mm), and h is specimen height (mm).

Based on the literature [44], the degree of the effect of size is introduced to quantitatively characterize the effect of size on the flexural strength of concrete. Taking the specimen with a height of 30 mm as a reference, the difference between the flexural strengths of different specimen heights and the flexural strength of the reference specimen is defined. The percentage of the flexural strength of the reference specimen is the degree of the effect of size, and the specific equation is Equation (2).

$${\gamma }_{60}=\frac{{\mathrm{f}}_{30}-{\mathrm{f}}_{60}}{{\mathrm{f}}_{30}}\times 100\%$$

(2)

In the equation, f₃₀ and f₆₀ are the flexural strengths of the specimens with heights of 30 mm and 60 mm, respectively, and the unit is MPa. The degree of the effect of size in the other case A can be obtained by the same method.

Figure 5 shows that as the specimen height increases, the effect of the size of the concrete specimen in each case increases, indicating that the larger the height of the concrete specimen, the greater the decrease in the flexural strength of the specimen, and the more significant the effect of size on the flexural strength. As shown in Figure 5a, the effect of the size of steel-fibre-reinforced concrete specimens in case A shows a trend of nonlinear change. Specifically, when the specimen heights are 60 mm–120 mm, the effect of size shows a quasilinear change, and when the specimen heights are 120 mm–150 mm, the growth rate slows. As shown in Figure 5b, the effect of the size of steel-fibre-reinforced concrete specimens in case B shows a trend of quasilinear change, i.e., basically maintaining the same rate of increase. The statistical size effect theory holds that the unit of nonuniform strength in the specimen is the root cause of the effect of size, and the probability of a unit of low strength is proportional to the effect of size. Therefore, as the specimen height increases, the effect of the size of the concrete specimen in each case increases. This is highly consistent with previous conclusions [45].

3.3. Characteristics of the Load–Displacement Curve

Figure 6 shows the characteristics of the load–displacement curve of the specimen. Figure 6 reveals that the load–displacement curve of the specimen can be divided into a slow growth stage (OA stage), a nearly linear growth stage (AB stage), a stage of sharp decrease (BC stage), and a residual stage (CD stage). In the OA stage, the load of the specimen gradually increases with increasing displacement, but the rate of increase is small, and the specimen has not yet produced obvious cracks. In this process, the external load is mainly borne by the cohesion of the matrix mortar. In the AB section, the load of the specimen increases rapidly with increasing displacement, and the two change approximately linearly and gradually increase to the peak load of the specimen. The specimen gradually produces obvious cracks that gradually penetrate the whole side of the specimen. In this process, the external load is mainly borne by the cohesion of the matrix mortar and the fibre anchoring force. In the BC section, the load of the specimen decreases rapidly with increasing displacement. In the CD section, the load of the specimen gradually tends toward stability with increasing displacement. The load in the stable state is the residual load. The crack of the specimen further expands, and the crack width gradually increases. The external load in this process is mainly borne by the fibre anchoring force.

Figure 7 and Figure 8 are the load–displacement curves of specimens with different heights in case A and case B, respectively. Figure 7 shows that after the steel fibre is added via the method of case A, the peak load and peak displacement (the displacement corresponding to the peak load) of the specimen increase as the specimen height increases, and the residual load of the steel fibre specimen also increases. However, different fibre addition methods and fibre types have an impact on the characteristics of the load–displacement curve of the specimen. As shown in Figure 7a, because there is no fibre in the control group, there is no fibre anchorage force, so when the matrix bonding force disappears, the load drops sharply; as a result, the curve does not exist in the CD section, the decrease in the BC section becomes more obvious, and the pattern of change in the OA section and AB section of the load–displacement curve at some specimen heights is very similar. As shown in Figure 7b–d, after adding three types of steel fibres in case A, the load–displacement curves of the specimens have a relatively complete slow growth stage (OA stage), nearly linear growth stage (AB stage), sharp decrease stage (BC stage), and residual stage (CD stage). Compared to the control group, the peak displacement of the specimens decreases after adding three types of steel fibres. When the shear-type steel fibre is added, the peak displacement of specimen A-S-150 is slightly larger than that of specimens A-M-150 and A-E-150. For the remaining specimens with different heights, a small peak displacement occurs based on the type of steel fibre.

The CD sections of the load–displacement curves of the three types of steel fibres in specimens with different heights show differences, indicating that with increasing specimen height, the fluctuation is greater. The CD sections of the load–displacement curves of the milling steel fibre and end-hook steel fibre are relatively flat, while the CD section of the load–displacement curve of the shear steel fibre shows relatively large values. In addition, the residual load values of the milling steel fibre and the end-hook steel fibre are also greater than the residual load of the shear steel fibre, while the difference in the residual load between the milling steel fibre and the end-hook steel fibre is small.

The analysis of Figure 8 shows that after adding steel fibre via the method of case B, the pattern is similar to the pattern of change of adding steel fibre via the method of case A. As the height of the specimen increases, the peak load and peak displacement of the specimen increase, and the residual load of the specimen after adding steel fibre also increases. However, different fibre addition methods and fibre types have an impact on the characteristics of the load–displacement curve of the specimen. As shown in Figure 8b–d, after adding three types of steel fibres in case B, the load–displacement curves of the specimens have a relatively complete slow growth stage (OA stage), nearly linear growth stage (AB stage), sharp decline stage (BC stage), and residual stage (CD stage). It is worth noting that the CD stage of B-M-150 has a slight rise, which is mainly due to the wavy surface of the milling fibre. Therefore, when the fibre is pulled out, there may be a climbing effect at its peak position, and the curve rises briefly. Compared to the control group, the peak displacement of the specimens decreases after adding three types of steel fibres. When the shear steel fibre is added, the peak load of specimen A-S-150 is slightly larger than those of specimens A-M-150 and A-E-150.

The method of adding fibre also affects the characteristics of the load–displacement curve of the specimen. The load of the CD section of case A first decreases sharply, and then, the rate of decline gradually slows, while the load of the CD section of case B first decreases sharply and then gradually stabilizes. The reason is mainly due to the random distribution of the fibre added in case A. The direction of the fibre is different, the direction of the anchoring force is also different, and the time to reach the ultimate bearing capacity is also different, so slow dissipation occurs. When the fibre is added in case B, the fibres are distributed in layers, and the fibre anchoring force basically appears and dissipates at the same time. When the matrix cohesion dissipates and is carried only by the fibre anchoring force, the case remains basically unchanged. When the fibres are pulled out, the bearing capacity is completely lost.

3.4. Strain Characteristics

Due to the large number of specimens in case A and the small difference in strain characteristics for the same type of specimen, only three specimens of case A of Y-90, A-M-90, and B-M-90 were selected for comparative analysis. The characteristic strain curves of the specimen are shown in Figure 9. Strain No. 1 refers to the strain gauge data from the middle end of the specimen, and strain No. 2 refers to the strain gauge data from the lower end of the specimen. As shown in Figure 9a, the strain curve of the specimen in the control group shows a basically stable trend and then a sharp increase. The specimen in the control group first deforms at the lower end of the specimen under the action of an external load, resulting in rapid expansion of the strain and failure of the strain gauge. With the continuous increase in the external load, the deformation generated at the lower end of the specimen rapidly expands to the middle end of the specimen in a short time, resulting in rapid expansion of the strain and failure of the strain gauge. As shown in Figure 9b, the strain curve of specimen A-M-90 is basically similar to that of the control specimen, but the difference is that the strain at the lower and middle ends of the specimen slowly increases and then increases sharply, resulting in the failure of the strain gauge. The main reason is that the steel fibre plays a bridging role, helps prevent the development of cracks, and reduces the rate of crack development so that the cracks develop slowly. The strain gauge can effectively monitor this process, while the control group specimens mainly rely on matrix adhesion. Once the matrix adhesion dissipates, the cracks develop rapidly, resulting in a sharp increase in strain and rapid failure of the strain gauge. As shown in Figure 9c, there is a large difference between the end and the lower end of the strain curve of specimen B-M-90. The strain at the lower end shows a basically stable trend at first and then a sharp increase, while the strain in the middle at the end shows a basically stable trend at first and then a slow increase. The growth rate is much lower than the rate of strain increase at the lower end. The main reason is that the steel fibre mixed in case B cannot play a role of crack resistance at its lower end, which leads to cracks and rapid failure of the strain gauge. However, when the crack develops upwards toward the concrete matrix with a steel fibre layer, the fibre can offer crack resistance, which limits the rate of crack development; thus, the strain in the middle at the end of the specimen increases slowly and then gradually increases to the upper limit of the monitored strain, resulting in the failure of the strain gauge.

4. Section Characteristics

4.1. Number of Cross-Section Fibres

Figure 10 shows the numbers of cross-section fibres (average values) of case A and case B. As shown in Figure 10a, the number of cross-section fibres in case A increases linearly with increasing specimen height. The slope of the linear relationship between the number of cross-section fibres and the specimen height in the milling type is smaller, followed by the shear type, while the end-hook type is the largest. As shown in Figure 10b, the number of cross-section fibres in case B also shows a linear increase with increasing specimen height, and the linear characteristics are stronger than those in case A. Among them, the slope of the linear relationship between the number of cross-section fibres of the three types of steel fibres and the height of the specimen is basically the same. The reason for the difference in the number of cross-section fibres between cases A and B is mainly the different fibre blending methods. The number of cross-section fibres in case A has great randomness, but the overall trend gradually increases with the height of the specimen. Figure 10a shows that the number of cross-section fibres in end-hook fibres is the largest, and the growth rate is the fastest, mainly because the single weight of the end-hook fibre is the smallest. Therefore, the number of end-hook fibres is the largest, and the growth rate is the fastest at the same volume blending rate. The single weight of the milling fibre is the largest. Therefore, the number of milling fibres is the smallest, and the growth rate is the slowest at the same volume blending rate. The single mass of the shear-type fibre is between the two masses, the number of shear-type fibres is between those of the two masses under the same volume blending rate, and the growth rate is also between those of the two masses.

4.2. Section Characteristics

As shown in

Table 3. Typical section characteristics.

Specimen Failure Diagram	Failure Characteristics	Annotation
	There are depressions in the upper or lower part of the failure section, and the other end of the failure line is close to the middle line.	FL: Failure line ML: Midline TFZ: Tensile failure zone SF: Steel fibre ET: Extract trace
	The failure line is approximately parallel to the midline and has different distances from the midline.
	The failure line is approximately coincident with the midline, and there is a tensile failure zone at the loading end.

, the typical section characteristics are summarized. The section characteristics of specimens in different cases are analysed in detail.

As shown in Figure 11, the steel fibre acts as a bridge during the crack propagation process of the specimen, connecting the two ends of the force and improving the stress distribution. During the loading process, the lower end of the specimen is mainly subjected to tension at both ends, and TFZ is formed.

Figure 12 shows the cross-sectional characteristics of the specimens under different conditions. As shown in Figure 12a–c, the concrete flexural specimen in the control group has no obvious deformation at the initial stage of loading. With increasing load, microcracks first appear in the mortar part of the loading section of the specimen. With a further increase in the load, the cracks develop rapidly, and the whole specimen is instantaneously broken into two pieces. The section is relatively flat, and the failure shows obvious brittle failure characteristics. However, when the height of the specimen is low, the failure is not strictly along the midline position. In addition, with the increase in the height of the specimen, the failed section of the specimen is flatter, the degree of fluctuation is smaller, and the failure is closer to the midline position. The main reason is that when the height of the specimen is small, the inhomogeneity of the concrete makes it impossible to destroy strictly along the midline position. As the height of the specimen increases, the inhomogeneity of the concrete gradually decreases.

During the loading process of concrete flexural specimens mixed with three kinds of steel fibres via two methods, the concrete matrix first cracks due to its low strength. After cracking, the tensile stress borne by the concrete on both sides of the microcrack is transferred to the steel fibre, and the steel fibre is gradually pulled out from the mortar matrix under tension. Due to the bridging effect of steel fibres, the development of cracks in concrete flexural specimens mixed with three kinds of steel fibres is more tortuous than that of specimens without steel fibres. The macroscopic cracks in concrete flexural specimens with lower specimen heights first appear in the tensile zone at the bottom of the specimen and slowly extend to the loading surface with increasing load, reaching the maximum bearing capacity. The specimen remains whole and can continue to bear a load, and the specimen shows certain ductile failure characteristics.

As shown in Figure 12d,e, after the milling steel fibre is added in case A, the failed section of the A-M-30 specimen fluctuates greatly, and the direction of the fluctuation is mainly affected by the distribution of the milling steel fibre. The milling steel fibre is distributed at different angles in the failed section. The milling steel fibre in the failed section has a significant effect on the flexural capacity of the specimen, and the milling steel fibre distributed in other parts has little or no effect on the flexural capacity of the specimen. Some of the milling steel fibre is pulled out, and its bridging effect causes the development of cracks in the concrete flexural specimen to be more tortuous than that of the specimen without steel fibre. There are still some tensile failure areas where the milling steel fibre is densely distributed, resulting in secondary cracks or debris shedding.

As shown in Figure 12f,g, the process of shear-type steel fibre failure is similar to that of milling-type steel fibres. Part of the shear steel fibre is pulled out, and its bridging effect causes crack development in the concrete flexural specimen to be more tortuous than that of the specimen without steel fibres. Some steel fibres parallel to the failed section are distributed in the failed section of the specimen. The effect of the improvement in such steel fibres on the flexural capacity of the specimen is much lower than that of steel fibres perpendicular to the failed section or at a certain angle with the failed section, and it almost does not play a bridging role. The influence on the fracture characteristics of the specimen is also very limited.

As shown in Figure 12h,i, the failed section of the specimen fluctuates greatly. Some of the end-hook steel fibre is pulled out, and its bridging effect causes crack development in the concrete flexural specimen to be more tortuous than that of the specimen without steel fibre. In the early stage of loading, the external load is borne by the bonding force and friction force between the fibre and the concrete matrix. In the later stage, the external load is borne by the anchoring force in the end-hook part of the matrix. Under the action of an external load, the end hooks of the end-hook steel fibre are straightened and gradually lose their bearing capacity.

As shown in Figure 12j,k, after the milling steel fibre is added in case B, the failed section of the B-M-60 specimen fluctuates greatly, the direction of the fluctuation is mainly affected by the steel fibre, and the parallel distribution of the steel fibre has a great influence on the flexural capacity of the specimen. Part of the steel fibre is pulled out, and its bridging effect causes crack development in the concrete flexural specimen to be more tortuous than that of the specimen without steel fibre. There are still some signs of fibres being pulled out where the fibre distribution is dense. In addition, the arrangement of fibres is basically arranged in rows, which is mainly consistent with the expected design. The mixed steel fibres play a bridging role under the external load, resulting in the opposite orientation of fibres to that of the lower end of the specimen (the location of the initial crack).

As shown in Figure 12l,m, it is easier to observe the shear fibre and the milling fibre in case B than the end-hook fibre, and the layered distribution and traces of pulling out in the cross-section are relatively obvious. The layered distribution of steel fibres can effectively control the propagation of cracks. The strong combination of steel fibre and concrete and its high tensile strength can resist tensile stress concentration when concrete cracks, slow crack propagation, and limit the widths of cracks.

As shown in Figure 12n,o, after the end-hook steel fibre is added in case B, the phenomenon that the end hooks of the end-hook steel fibre are straightened is more obvious than when the end-hook steel fibre is added in case A. The end-hook steel fibre is anchored to the concrete matrix through the end hooks, which can effectively increase the tensile capacity of the lower end of the flexural-failed section of the concrete. The end hooks can be better combined with the concrete when the concrete is cracked, and part of the tension is transferred to the steel fibre, thereby delaying and inhibiting the expansion of the crack. The combination of the end hooks and the concrete increases the friction between the fibre and the concrete, which hinders the propagation of the crack and limits the expansion and width of the crack.

5. Conclusions

In this paper, through a flexural test of steel-fibre-reinforced concrete in different specimen heights, the influence of the steel fibre type and mixing method on the peak load, section fibre number, characteristics of the load–displacement curve, section characteristics, and strain characteristics of the specimen was analysed. The following conclusions were obtained:

(1)

The addition of three types of steel fibres enhances the peak load of concrete specimens in both case A and case B. In case A, the peak load increases proportionally with the specimen height, exhibiting a linear relationship in the control group. The peak load of specimens with added steel fibres surpasses that of the control group at equivalent specimen heights. The impact of concrete specimen size on flexural strength becomes more pronounced as the specimen height increases in both cases, highlighting the close correlation between peak load and specimen height as well as the method of fibre addition;

(2)

In case A, the quantity of cross-sectional fibres exhibits a linear increase with the rise in specimen height. Notably, the milling type demonstrates the smallest slope in the linear relationship between the number of cross-sectional fibres and specimen height, followed by the shear type, while the end-hook type exhibits the largest slope. Similarly, in case B, the number of cross-sectional fibres also experiences a linear growth with increasing specimen height, and this linear characteristic is more pronounced than in case A. Furthermore, the three types of steel fibres share a consistent slope in the linear relationship between the number of cross-sectional fibres and specimen height;

(3)

The load–displacement curve of the specimen can be divided into a slow growth stage (OA stage), a nearly linear growth stage (AB stage), a sharp drop stage (BC stage), and a residual stage (CD stage). The load–displacement curves of the three types of steel fibres at different specimen heights show differences in the CD stage of the load–displacement curve, which basically shows that as the height of the specimen increases, the fluctuation increases. In addition, the load on the CD section in case A first decreases sharply and then gradually slows, while the load on the CD section in case B first decreases sharply and then gradually stabilizes;

(4)

The control group exhibits distinct brittle failure characteristics, characterized by a flatter failed section and reduced fluctuation as the specimen height increases. In contrast, the specimens with three types of steel fibres in both methodological cases demonstrate a more tortuous development of cracks compared to those without steel fibres. In flexural concrete specimens with lower heights, macroscopic cracks initially emerge in the tensile zone at the bottom, gradually extending to the loading surface with increasing load. Tensile failure areas, densely populated with fibres, may still experience secondary cracks or debris shedding.