Effect of a Novel Vibration Mixing on the Fiber Distribution and Mechanical Properties of Ultra-High Performance Concrete

Abstract

A novel double-axis vibration mixing technology is presented to further enhance the performance of ultra-high performance concrete (UHPC). It improves the problem of inefficient zone in concrete mixing and enhances the homogeneity of concrete through the coupling of vibration and velocity fields during mixing. The X-CT scan results demonstrate that this novel technology improves the fiber distribution coefficient from 0.512 to 0.581. Moreover, the standard deviation of fiber orientation is reduced, the proportion of invalid fibers is decreased, and the pore space distribution is more uniform. The mechanical experimental results show that the new vibration mixing technology improves the mechanical properties of UHPC, and the percentage of early strength improvement is more significant; the impact compressive strength and the toughness of UHPC are also strengthened. The vibration mixing technology is expected to achieve the reduction of raw materials dosage with the same mechanical properties to reduce the cost and carbon emission.

1. Introduction

Ultra-high performance concrete (UHPC) is developed as a new concrete technology designs and produces based on the Modified Andreasen and Andersen (MMA) packing model [1] and maximum density theory [2], which means higher strength and a closed structure that can prevent the penetration of harmful substances such as chloride ions. It has high mechanical properties and its 28d compressive strength can usually reach more than several times that of ordinary concrete [3,4]. Meanwhile, UHPC has outstanding durability [5,6,7,8,9] and impact resistance [10,11] due to the high density and low porosity created by good grading. Therefore, UHPC is widely used in critical structures of large concrete projects, such as nuclear facilities, offshore structures [12] and bridges [13,14].

Fibers have been shown to bridge cracks and resist crack extension to reduce the brittleness of UHPC matrix [15,16,17], contributing to mechanical strength and toughness, even though UHPC is designed based on the maximum density of non-fibrous mortars.

The flexural and tensile properties of UHPC depend on the properties of the mortar, the fibers, and the fiber–mortar interface [4,18,19]. The type, length and volume of fibers, as well as fiber distribution and orientation, would result in significant changes in flexural properties. Increasing the fiber length or changing the shape of the fibers helps to improve the fiber-matrix contact and provides greater resistance to pullout under load compared to short and straight steel fibers [20]. In addition, as the proportion of fibers increases, the reinforcing effect of fibers on UHPC will be enhanced. However, the fiber itself is expensive, and increasing the amount of fiber will bring a significant increase in cost and carbon emission [20]; as the copper was coated on the surface of steel fibers to prevent the erosion and destruction of the fiber by chloride ions [7,21], increasing the amount of fiber will also cause potential heavy metal pollution problems. In addition, the excessive amount of fibers would inevitably produce an agglomeration effect, which has a marginal diminishing effect on the performance enhancement of UHPC, and significantly increases the plastic viscosity and yield stress of UHPC cementing system [22,23], which has negative effects on workability.

Therefore, improving the uniformity of steel fiber distribution and orientation to enhance the fiber utilization of UHPC has been an important topic in UHPC. Increasing the percentage of fibers or the amount of superplasticizer (SP) may have a positive effect on fiber distribution [24,25,26], but this also increases the cost of UHPC and has a negative impact on the environment. A laminar paving UHPC method was used to forcibly induce the orientation and distribution of steel fibers [27]. The fiber distribution and static properties were improved compared to the conventional molding method; however, this approach affects the homogeneity of the UHPC matrix and increases the work intensity during the construction phase, and is not advantageous to the release of interlayer cracks generated during the molding process. In any case, the improvement of rheological properties of UHPC mortar would have benefits for fiber distribution, which is recognized by many scholars [22,28,29,30].

Vibration mixing technology has been proven to have a positive effect on the static mechanical properties of fiber-free concrete [31]. The mixing motion of conventional mixers consists of circular, axial and radial movements. These three mixing methods do not allow the “binder agglomerates” to disperse sufficiently. However, for a better mixing process, material displacement must be accomplished by well-coordinated convective and diffusive motions. In the mid-19th century, researchers enhanced the amplitude of vibration in the mixing process by adding vibration equipment to the mixer [32,33]. After continuous research and improvement, self-falling mixers with vibratory mixing capabilities were used to improve the homogeneity of Portland cement cementitious materials. Vibration mixing technology allows the cementitious material and the water film attached to its surface to be continuously detached and destroyed by vibration and impact, and the new cementitious material surface tends to be clean and quickly wetted by water, providing more space for hydration reactions. However, unlike the tiny size of the gelling material, the agglomeration effect of steel fibers often comes from the fiber-to-fiber tooth cooperation. It is not known whether the vibratory mixing technique can disrupt the agglomeration effect of steel fibers and improve the uniformity of steel fiber distribution in the UHPC matrix. Therefore, this study will aim to test whether the novel vibration mixing technique can improve the uniformity of fiber distribution in the UHPC matrix as well as the static and dynamic mechanical properties.

2. Materials

2.1. Raw Materials

The cementitious material used in the test is $P_{II}$ 52.5 Portland cement, which meets GB175–2007 and ASTM C150, producted by Dalian Onoda Cement Co., Ltd, the micro-silica fume and fly ash used in this test are produced by Elkem International Trading (Shanghai) Co., Ltd and Shenzhen DaoTe Technology Co., Ltd separately.

The Portland cement, fly ash and silica fume are the main raw materials of UHPC and the particle size of all three is concentrated from 5 to 100 μm, which would guarantee the maximum density and minimum porosity of products, and the chemical composition of main raw materials is shown in the

Table 1. Chemical composition of raw materials.

Materials	Cement	Fly Ash	Silica Fume
CaO	63.6%	17.60%	0.2%
SiO2	19.7%	65.65%	95.4%
Al2O3	4.5%	6.91%	0.3%
Fe2O3	3.0%	0.06%	0.8%
SO3	2.9%	-	0.2%
MgO	1.3%	0.08%	-
K2O	0.7%	0.04%	-
Na2O	0.1%	0.35%	-
TiO2	0.3%	0.15%	-
P2O5	-	0.02%	-

. The aggregates used in this research are river sands, produced in Jiangsu Province. And the particle size of the sands is within 1.25 mm to ensure there is no coarse aggregate. A kind of short straight steel fibers with an ultimate tensile strength of 2900 MPa was used, which has a diameter of $0.2\pm 0.02$ mm, a length of 12∼13 mm and a modulus of elasticity of more than 210 GPa. The SP was provided by Sobute New Materials Co., Ltd., Nanjing, China, and its solid content was 40%.

2.2. Specimen Preparation

The preparation principle of UHPC is the MAA theory and the maximum density theory [34,35], where Portland cement, river sand, silica fume, fly ash, SP and fibers are mixed together in tightly packed and maximum density theory. Based on the previous research results [31], the specific mixing mass ratio is: binder: sand: water: SP: fibers = 1240:992:200:14:195, where binder equals to the sum of the Portland cement, silica fume and Fly ash, which means that B/S = 1240/992 = 1.25, and W/B = 200/1240 = 0.16.

The same proportion of raw materials of UHPC will be mixed by DT60ZBW twin-shaft vibratory mixer [31,36]. The power for the machine is selected appropriately, where 3 kw is used in vibration input power and the mixing input power is 5.5 kw. The mixer used in this can also be regarded as those traditional double-blade forced ones as long as the vibration function is turned off. Two groups of specimens are prepared as normal group (N-UHPC) and vibration mixing group (VM-UHPC), where both groups are mixed and formed in DT60ZBW double-blade mixer. However, N-UHPC only holds double-blade forced mixing, but VM-UHPC would hold three mins of double horizontal shaft vibration mixing after four mins normal mixing, as shown in the Figure 1. All specimens would be shaken on the shaking table for 120 s to eliminate the large air bubbles generated during the molding process. To keep moisture, the plastic sheet would be used to cover the specimens and all specimens would be place them under the temperature of $(20\pm 2)$ °C for 24 h until being demolded. After demolding, all specimens would be placed in the standard maintenance room ($(20\pm 2)$ °C, RH 95%) for 28 days and then tested, except part specimens for the specific age mechanical properties tests.

To cope with the requirements of different experiments on the physical size of the specimens, according to GBT 50081-2019 and GBT 31387-2015, $40\times 40\times 160$ mm UHPC quadratic prism specimens were prepared for industry CT scanning for fiber distribution and orientation calculation; $100\times 100\times 100$ mm UHPC cube specimens were prepared for compressive strength and splitting tensile strength testing; $100\times 100\times 400$ mm UHPC quadratic prism specimens were prepared for flexural strength testing; and $⌀73.6\times 200$ mm cylindrical specimens would be used for impact loading tests, and the cylindrical specimens after curing were cut into small specimens with a height of 50 mm, as shown in the Figure 2. To reduce the negative influence of the mold on the inhomogeneity of fiber distribution and cutting accuracy, only the middle three specimens (2, 3 and 4) were selected and polished before tests.

3. Testing Methods

3.1. Fiber Distribution

The distribution of steel fibers in $40\times 40\times$ 160 mm specimens with different mixing process was obtained by X-ray CT measurement. The scanning accuracy of the CT is 1:1500, in other words, during the scanning process, the CT images can capture constantly every 26.7 μm as one pixel along with the length of the specimen. The main methods to characterize fiber distribution are CT 3D image analysis method and cross-sectional image analysis method. In this paper, the cross-sectional image method is used to analyze the fiber distribution at the section of specimens. The image analysis process of fiber distribution is given in Figure 3.

Initially, the cross-sections were randomly selected in the direction perpendicular to the length. Since the length of the steel fibers used in this study are 12∼13 mm, the vertical distance between adjacent cross-sections of the same specimen should longer than 13 mm to avoid repeated counting of same one steel fiber. Then, RGB images of the cut surfaces of specimens were scanned and photographed by an industrial CT scanner, and the RGB images were converted into binary images by a reasonable threshold algorithm. Only two shades of gray, black and white, exist in the obtained binary images, with black corresponding to the matrix and white corresponding to the steel fibers. A total of 25 cross-sectional images of N-UHPC group and 24 cross-sectional images of VM-UHPC were acquired in this study.

Each binary image will be segmented into 4 × 4 cells, and the number of fibers within each cell was counted based on a computer vision algorithm; when one fiber passes through more than one cell, the ratio of the area of that fiber in that cell to its total area in the 2D image would be considered as the proportion of that fiber in that cell. Fiber distribution number (${\alpha }_f$) would be used to assess fiber distribution in the same section. The closer the ${\alpha }_f$ value is to 1, the more uniformly the fibers are dispersed in the matrix; conversely, the closer it is to 0, the less well the fibers are dispersed.

$${\alpha }_f=exp[-\frac{1}{x_0}·\frac{\sqrt{{\sum }_{i=1}^n{(x_i-x_0)}^2}}{n}]$$

(1)

where,

• n is the number of cross-sectionally evenly divided cells, equal to 16;
• $x_i$ represents the number of fibers in the ith cell; and
• $x_0$ is the average number of fibers in each cell.

3.2. Fiber Orientation

The fiber dispersion effect is mainly related to the fiber body characteristics, fiber doping, matrix characteristics, casting method and specimen size. The angle between the fiber and the micro-crack often determines the ability of the fiber to prevent further crack extension [37,38], especially for short straight steel fibers. When a UHPC beam structure is subjected to load, cracks in the tension zone tend to be approximately perpendicular to the height direction of the concrete. This is an extremely simplified theory, because cracks will always develop along the weak surface and the direction of crack development is related to the state of stress. In practice, however, the more steel fibers perpendicular to the cross-section, the stronger the flexural and tensile properties of UHPC beam structures tend to be. The fiber orientation becomes worse due to the increased fiber agglomeration phenomenon, with the increase of fiber doping, the fiber utilization efficiency may be reduced instead. Therefore, if the proportion of steel fibers is too large, it will not only cause the instability of UHPC structure due to the distribution of fibers, but also increase the cost. When the ratio of steel fibers to UHPC matrix is determined, improving the direction of steel fiber distribution is beneficial to the tensile strength [39,40].

The morphological features of steel fibers in CT scan images can represent the orientation of steel fibers in three-dimensional space, as shown in Figure 4. The section of the steel fiber in the scanned image is an ellipse, and $Cos\theta =D/L_{max}$ exists between its long axis and the pinch angle. When $L_{max}=D$, at this time $Cos\theta =1$, $\theta =0^{\circ }$ indicating that the steel fibers are distributed exactly along the height direction. Additionally, the distance between each section is greater than the length of the steel fibers, avoiding the same steel fiber being double counted.

The angle of orientation of a single steel fiber is from 0 to 90 degrees, and the angle of orientation of each effective fiber for each cross-section in different mixing methods will be counted, and then the effect of vibration mixing technology on the angle of orientation of steel fibers has been verified.

3.3. Pore Structure

Compared to ordinary concrete, UHPC has ultra-high mechanical properties, excellent durability and outstanding toughness due to its highly dense structure [41,42]. The density of the pores differs from the sample matrix and presents different grayscale values when X-rays penetrate different media [43]. Therefore, the obtained CT images can be used to characterize both the structure and distribution of the pores.

In this research, the X-CT scan images of different mixing groups were also used to determine the effect of the vibration mixing technique on the density and pore distribution of the UHPC matrix. And a computer vision algorithm was used to analysis the size of the pore structure, the location distribution, and the position relationship with the steel fibers in different cross-sections.

3.4. Static Mechanical Tests

With the guidance of the GB/T31387-2015 and GB/T50081-2019, at least three samples were measured for one group of tests at each curing age. The average data were used as the mechanical strength of each group of UHPC, including compression strength, flexural strength and splitting tensile strength. Meanwhile, the standard deviations of each series were recorded and shown as the error bars.

3.5. Impact Resistance Test

Split-Hopkinson pressure bars (SHPB) were used to test the ability of UHPC prepared in different ways to resist impact loading. The diameter of cylindrical press bar is 75 mm, Young’s modulus $E=200$ GPa, density $\rho =7850$ kg/m³, length $L=5.5$ m, and Poisson’s ratio equal to 0.28. The bumpers are accelerated using gas guns, the air pressure of the gas gun is adjusted to 0.6 MPa every time before the incident bar is released. Both sides of specimens are polished to a degree of non-parallelism of less than 0.01 mm to minimize the effect of non-parallelism on the dynamic mechanical properties obtained [44,45]. The polished samples were placed between the incident and transmission bars. Additionally, vaseline was applied to the ends of the bars and specimens to reduce the frictional effect at the specimen-bar interface.

To derive the experimental stress–strain response and strain rate, the measured strain gauge signals were processed. Stress and strain of the measured signals were calculated using incident, transmitted and reflected pulses according to the conditions of one-dimensional wave propagation. The extracted signals were subsequently filtered by using 5 pts Savitzky–Golay filter to reduce the oscillations caused by the dispersion of the transmitted waves.

The calculations were carried out by the following equations.

$$\epsilon =\frac{2C}{l_0}\int {\epsilon }_R$$

(2)

$$\sigma =E·\frac{A}{A_0}·{\epsilon }_T$$

(3)

where,

• ${\epsilon }_R$ and ${\epsilon }_T$ represent the reflected and transmitted impulse;
• A and $A_0$ denote the cross-sectional area of the bars and specimens;
• $l_0$ represents the length of specimens (50 mm); and
• $C=\sqrt{E/\rho }$ [46].

4. Results and Analysis

4.1. Fiber Distribution

To illustrate and calculate the distribution of steel fibers in UHPC matrix under the conditions of different mixing methods, fiber distribution coefficients, as shown in Equation (1), was designed and used to characterize the distribution of steel fibers in UHPC matrix. The fiber content in each cross-section could be obtained and counted by computer quantification based on the X-CT image data. The images of fiber distribution corresponding to several typical fiber distribution coefficients are shown in Figure 5. For every 0.05 increase in the fiber distribution coefficient (from left to right in the figure), it can be clearly seen that the agglomeration of fiber distribution slows down, and when the fiber distribution coefficient is greater than 0.60, it can be considered that the fibers are basically distributed in all parts of the cross-section. The steel fibers will be clustered at the bottom of the samples, due to the rate of hydration and the effect of gravity. When the distribution coefficient is less than 0.5, this clustering is quite obvious. This can result in significant fiber waste, as damage to the concrete often occurs in the weakest areas [47].

Figure 6 counts the numbers and cumulative frequency of the fiber distribution coefficients for 25 X-CT scan images of normal mixing groups and 24 X-CT scan images of vibration mixing groups. The distribution coefficients that differ from the representative values within ±0.1 will be grouped together. The mean value of the fiber distribution coefficient for fiber-reinforced concrete with normal mixing is 0.512 and the standard deviation is 0.0422; the corresponding mean value for the vibration mixing group is 0.581 and the standard deviation is 0.0416. The fiber distribution coefficient of the vibrating mixing group is higher than that of N-UHPC group, and the standard deviations of the two are quite close. This indicates that the vibration mixing technology can enhance the uniformity of steel fiber distribution and mitigate the negative effects caused by the clustering effect. From the cumulative frequency curves of fiber distribution coefficients, it can be seen that although the fiber distribution coefficients of different mixing methods belong to different intervals, the fiber distribution coefficients conform to the characteristics of uniform distribution within a certain range, and the slope and $R^2$ of the two fitted curves are close to each other, indicating that the vibration mixing technology can improve the uniformity of fiber distribution of UHPC entirely.

4.2. Fiber Orientation

It can be seen from the Figure 5 that the fibers close to the mold surface tend to line up more along the mixing flow direction or specimen height direction than those far from the formwork surface, which is caused by the wall effect [48,49].

In this research, based on the relationship between steel fiber orientation and cross-sectional shape (Figure 4), 4152 steel fibers were extracted from 25 CT scans of plain stirred steel UHPC, and 3439 steel fibers from 24 CT scans of vibratory stirred UHPC; the statistical plots of steel fiber orientation are shown in Figure 7a,b, respectively.

As can be seen from the Figure 4, the distribution of steel fibers in the UHPC matrix basically conforms to the statistical law of Gaussian distribution, and the probability distribution of fiber orientation in the vibratory mixing group has a slight tendency to shift to the left, compared with the normal mixing group. This is due to the fact that the vibration mixing technology increases the effective viscosity of the UHPC matrix and weakens the agglomeration phenomenon of steel fibers, which makes the steel fibers more inclined to be arranged along the height direction of the mix.

After the fiber inclination angle exceeds 60°, the fiber pull-out process causes severe damage to the matrix and does not help to improve the tensile strength of the material [50,51]. In this study, steel fibers with an angle of more than 60° with the height direction were defined as invalid fibers, and the percentage of invalid fibers was calculated to compare and analysis the effects of the vibratory mixing technology. Overall, 613 invalid fibers existed in the normal mixing group, accounting for 14.8% of the total fibers; and 423 invalid fibers existed in the vibratory mixing group, accounting for 12.3% of the total fibers.

Compared to the difference in fiber distribution coefficients, the vibration mixing technique did not have a significant effect on the orientation of the fibers. However, as can be seen from the Figure 7, the vibration mixing technique still makes the distribution of steel fibers more uniform. The $R^2$ of the fitting curve VM-UHPC groups is bigger than that of N-UHPC groups, and the standard deviation of the fitted Gaussian distribution of VM-UHPC is also less than that of N-UHPC groups, indicating that the vibration mixing technique can slightly enhance the overall fiber orientation, as evidenced by the percentage of invalid fibers.

4.3. Pore Structure and Distribution

In the UHPC, the pore solution has the lowest density and X-ray absorption, therefore, it has the smallest gray value in the 3D image; on the other hand, the steel fiber has the highest density and its gray value is the largest.

Taking N-UHPC#01 and VM-UHPC#01 as examples, Figure 8 depicts the spatial distribution and location of the UHPC pore solution. In Figure 8b,d, the closer the color is to yellow, the higher the confidence level of the presence of voids here. The size and spatial location of the pores are different for each cross-section. Additionally, the large pore structures (red boxes) are significant hazards to the stability of the structure.

The distribution of steel fibers and the distribution of air bubbles show opposite trends in the scanned view of the normal mixing UHPC specimens. Under the influence of gravity and cement paste, steel fibers tend to agglomerate on the bottom surface of UHPC specimens, while large pore structures are more often found on the top surface (forming surface) of UHPC specimens. This can lead to differences in the structural and mechanical strength of the concrete on both sides; after all, concrete damage is more likely to develop along the direction of the weakest layer. However, with the additional vibration provided by the vibration mixing technique, the distribution of pores is more homogeneous, as shown in Figure 8d. Some pores are surrounded by steel fibers on the inside, and the large pore structure on the top surface is significantly reduced.

The ratio of the area of suspected pores (the area except purple) to the cross-sectional area (1600 mm²) for all X-CT scanned images of both mixing methods is less than 8.0%, and the average porosity of the vibratory mixing group was 4.2%, which was slightly lower than the average value of 5.0% for the normal mixing group, indicating that the vibration mixing technique might have a positive effect on reducing the porosity of UHPC. However, the micro-cracks and microporous structures generated by factors such as water evaporation were not included in the analysis data due to the scanning accuracy of X-CT images.

4.4. Mechanical Test Results

The slump of fresh UHPC with both normal mixing and vibration mixing was 290 mm. Similar to UHPC without fiber [31], vibration mixing had little effect on the workability of UHPC. The main reason may be that this test used a polycarboxylic acid SP with a solid content of 40%, which made the fresh UHPC have better workability.

According to the test standard for compressive strength of concrete cubic specimens, UHPC specimens of different ages and different mixing methods will be tested for compressive strength at the required ages, and the compressive strength results are illustrated in Figure 9a and

Table 2. Compressive strength of UHPC specimens under different mixing methods.

Age	N-UHPC	VM-UHPC	Enhancement Rate
(d)	(MPa)	(MPa)	(%)
3	81.4	94.4	16.0
7	86.2	105.4	22.2
14	100.7	113.0	12.2
28	110.4	119.4	8.1

. The compressive strength of VM-UHPC is higher than that by traditional mixing at each age, moreover, the standard deviation of the samples made by vibratory mixing is smaller than that by traditional mixing at each age. Therefore, vibration mixing technology has a positive and significant effect on enhancing the compressive strength and maintaining its stability of UHPC. On the other hand, vibration mixing technology is more effective in improving the early strength of UHPC than the later strength. It enhanced more than 16.0% of compressive strength of UHPC with the same raw materials and ratio, the number of enhancement percentage increases and peaks at 22.2% the seventh day and then decrease to 8.1% at the 28th day. Additionally, this is consistent with the fiber distribution data observed and calculated from the CT scan.

The flexural strength of UHPC by different mixing methods is illustrated in

Table 3. Flexural strength of UHPC specimens under different mixing methods.

Age	N-UHPC	VM-UHPC	Enhancement Rate
(d)	(MPa)	(MPa)	(%)
3	11.2	14.5	29.5
7	12.0	14.8	23.1
28	13.6	16.9	24.6

and Figure 9b. Among the three typical mechanical properties, the improvement of flexural strength of UHPC by the vibration mixing technology is the most significant. The flexural strength of UHPC specimens produced by the vibration mixing are always higher than that of the N-UHPC during the whole process of hydration reaction, despite the differences of flexural strength of two methods decreased slightly. In the early stage of curing, at the third day, the flexural strength of the N-UHPC is 11.2 MPa, while the number of VM-UHPC group is 14.5 MPa, which increases 29.5% of that of the former. Since the hydration reaction is gradually completed (the 28 day), the flexural strength of the N-UHPC increased to 13.6 MPa, while the figure of VM-UHPC increased to 16.9 MPa, which shows there is still 24.6% enhancement effect by the vibration technology. Although the standard deviation of the samples in the vibration mixing group increased slightly compared to the conventional mixing group, the flexural strengths of each sample in the vibration mixing group are still significantly higher than that of the conventional mixing group. In conclusion, the data of flexural strength test illustrate that vibration mixing technology can improve the flexural strength of UHPC during the whole hydration process.

The calculated splitting tensile strength data of different groups of UHPC at specific ages are shown in the

Table 4. Splitting tensile strength of UHPC specimens under different mixing methods.

Age	N-UHPC	VM-UHPC	Enhancement Rate
(d)	(MPa)	(MPa)	(%)
3	8.15	10.05	23.6
7	9.07	10.32	13.8
28	10.39	11.61	11.8

and Figure 9c. Concrete being a brittle material, steel fibers play a key role in enhancing the tensile strength of concrete. The difference in splitting tensile strength at early ages prepared by the two methods was significant, reaching 23.6%. This difference decreases with increasing age, which indicates that the trends of all three mechanical strengths are similar. At the age of day 28, the splitting compressive strength of the UHPC made by the vibration technology reached 11.61 MPa, while the figure of N-UHPC was 10.39 MPa, and the difference between the two was reduced to 1.22 MPa (11.8%).

4.5. Impact Test Results

Figure 10 illustrate the incident, reflected and transmitted waves of two groups of UHPC by strain gauge stations. The sum of the incident wave ${\sigma }_i$ and the reflected wave ${\sigma }_r$ should be equal to the transmission wave ${\sigma }_t$ to achieve stress balance, according to the one-dimensional stress wave theory [45].

The average stress–strain curves of two kinds of specimens at almost same strain rates are obtained and presented in Figure 11. Dynamic compressive strength ($f_d$) is determined as the peak stress of the stress–strain curve [45]. It is indicated in Figure 11 that although they have similar stress–strain rates, the dynamic compressive strength of UHPC prepared by vibration mixing technology is higher than that of the N-UHPC group under the condition of no lateral restraint, and the strain at failure is also higher than that of the latter. All UHPC specimens were not crushed after the SHPB test due to the bonding effect of the steel fibers to the matrix, only a few concrete fell off from the surface of destruction surface, indicating that the steel fibers greatly improved the impact resistance of the concrete material and contributed to a certain deformation capacity of the brittle concrete. Moreover, the energy absorption capacity of UHPC, commonly referred to as toughness, used to reflect the impact resistance of the specimen, defined as the area under the stress-strain curve [45,52,53]. The deformation capacity of UHPC is enhanced due to the more uniform fiber distribution by the vibratory mixing technology, which also means the axial strain and dynamic compressive strength were improved, and UHPC specimens can absorb more destruction energy with the enhancements of the vibration mixing technology.

4.6. Mechanisms

Vibration mixing has been proven to have a positive effect on the mechanical properties of UHPC [31]. The vibration action maximizes the UHPC slurry movement action through the conversion from electrical energy to mechanical energy and finally to concrete internal energy. The internal friction coefficient of the mixture decreases after vibration [32,54,55], and a more dispersed cement concrete system facilitates the generation of C-S-H, which has been proven to be a major hydration product and source of strength for Portland cement [56,57]. The vibration energy is maximized on the mix, and the mix close to the mixing shaft is strongly vibrated for easy mixing and homogeneity, overcoming the shortcomings of the inefficient zone that exists with traditional mixing methods [58,59]. The vibration mixing technology neither needs no change in the quality of raw materials or their proportions, nor does it add an excessive amount of construction work. Instead, by adding uninterrupted vibration to the mixing process, the propagation of the vibration wave gradually decays, creating a discontinuous energy gradient centered on the vibration axis, which is the opposite and complementary to the velocity gradient with increasing radius Figure 12. This novel technology is fully able to combine the advantages of traditional compulsory mixing and the empowering effect of vibration.

Moreover, the vibration mixing technology also improves the distribution of steel fibers in UHPC. The space occupied by free water not involved in the reaction and the pores and micro-cracks inside the sample are considered as the weak space of concrete. The vibration mixing technique effectively attenuates the sinking effect and agglomeration effect of steel fibers, allowing more steel fibers to be distributed in the area where there are relatively fewer steel fibers. When the steel fibers pass through the weak space of concrete, it can improve the mechanical properties of the weak space and its surrounding concrete. On the one hand, it has been shown that the micro-morphology of the fiber surface can induce the hydration of silicate cement. On the other hand, in the process of hydration of Portland cement, at the early age (especially before the 7th day), although there is more than the strength of ordinary concrete, but the hydration product has not been fully formed, it still has not formed a complete and dense skeletal structure. At that time, the uniformly distributed steel fibers would become one of the most important skeletal structures of UHPC.

However, after the generation of hydration products gradually increases, the positive effect of hydration products on mechanical properties would become more and more significant and gradually greater than the effect of steel fiber distribution on them, which leads to the mechanical properties of UHPC prepared by vibration mixing are always greater than those of N-UHPC at all ages, but the differences between the two groups are gradually decreasing with time.

5. Conclusions

The performance enhancement and mechanism of UHPC by vibration mixing technology were studied and discussed. The effects of the vibration mixing technique on the uniformity of fiber distribution at the microscopic level and the static mechanical properties, dynamic compressive strength and toughness at the macroscopic level were investigated and analyzed.

• The vibration mixing technology has a positive effect on enhancing the uniformity of the distribution of steel fibers in UHPC. The cross-sections of different samples were scanned by X-CT and the number of fiber distributions at different locations in the same cross-section was counted using a computer. The fiber distribution coefficient and the percentage of fibers in the favorable direction (within 60°) of tensile strength were calculated and analysis to evaluate the effect of vibratory agitation technique on the enhancement of fiber distribution in UHPC. The results of scanning and calculations show that the vibration mixing technique could enhance the uniformity of fiber distribution in the UHPC matrix and reduce the agglomeration effect of steel fibers. The average fiber distribution coefficient was improved from 0.512 to 0.581 with same uniformity in different sections. Furthermore, the vibration mixing technology has a positive effect on the improvement of fiber orientation, and the effective fiber percentage of tensile strength is increased from 85.2% to 87.7%, which indicates that the vibration mixing technology may have a positive effect on the improvement of tensile properties of UHPC especially in some beam or plate structures.
• Vibratory mixing technology can improve the static properties of UHPC. The static test results show that the vibratory mixing technique can improve the static strength of UHPC at various ages, including compressive strength, tensile strength and flexural strength. In the early age stage, the improvement of static mechanical properties by a more uniform distribution of steel fibers is more obvious because the hydration of concrete is not yet complete. The enhancement of the mechanical properties of UHPC by the vibratory mixing technique is more effective in the early stage of hydration. At the age of 28 days, the static mechanical properties of the vibratory mixing group were still better than those of N-UHPC.
• The results of SHPB based impact tests show that the vibratory mixing technique helps to improve the mechanical strength, impact resistance and toughness of UHPC.
• The vibration mixing method proposed in this research can be used to produce higher quality UHPC or reduce the usage of possible high energy-consuming raw materials, cement for instance, to obtain UHPC with the same performance as traditional mixing methods in the future. The vibration mixing technology would provide a reference for future design and manufacturing of UHPC to mitigate the emission of pollutants, $C{O}_2$ especially, from cement production and transportation.