Analysis on Influence of the Dispersion Degree of PVA Fibers on Pavement Performance of Cement-Stabilized Macadam

In order to study the effect of PVA fiber dispersion on the performance of cement-stabilized macadam as pavement base material, the dispersion factor Fvc is introduced (Fvc � 1 − Cvc, Cvc refers to dispersion coefficient of relative mass fraction proportion coefficient) as a factor to judge the dispersion degrees. Besides, the connections among Fvc and the compressive strength of the splitting strength of cement-stabilized macadam in various curing periods are analyzed. ,e research conclusions reveal that (1) when the mass ratio of PVA fibers to coal ash is higher than 1 : 50, resulting Fvc> 0.95, it means the PVA fibers can disperse evenly in the cement-stabilized macadam; (2) both the compressive strength and the cleavage strength of cement-stabilized macadam with PVA fibers are proportional to Fvc; moreover, both the compressive strength and the splitting strength of cement-stabilized macadam with PVA fibers are obviously stronger than those in the commonmacadam; and (3) under the same curing period and with the same Fvc value, both the compressive strength and the splitting strength in the first type of cement-stabilized macadam (volume content: 0.9 kg/m of PVA fibers) are stronger than those in the second type of cement-stabilized macadam (volume content: 0.6 kg/m of PVA fibers).


Introduction
Choosing graded gravel as aggregate, filling the gaps of the aggregate with some amount of cementing material and with enough mortar, the cement-stabilized macadam is employed widely in road base level, since it possesses in itself many merits such as relatively high strength, good antiseepage ability, fine frost resistance ability, and so on. However, its shortcomings such as low flexural strength as well as low crack resistance ability result in early cracks, which constrain its sparking merits, together with its application longevity [1,2].
Presently, the method [3][4][5][6] that adding fibers into cement-based materials to enhance its flexural strength as well as its crack resistance has been popular with many scholars from China, USA, and other developed nations. e fine toughness and relatively high modulus have enabled fibers to improve the properties of cement-based materials effectively during application. Khorami and Ganjian [7] discovered during research that when the mass of added agriculture waste fibers (such as bagasse, wheat, eucalyptus, and so on) is 4% of the cement mass, flexural behavior of the cementbased composite changes relatively obviously, not to mention that the properties of bagasse fibers are better than those of wheat and eucalyptus. Yang et al. [8][9][10][11] added polypropylene fiber into the cement-stabilized macadam, the result of which shows that the polypropylene fiber can improve its performance in contraction deformation and in flexural behavior. Yang et al. [12][13][14][15] and others added basalt fiber into the cement-stabilized macadam, the result of which shows that the basalt fiber can enhance the crack resistance and the fracture property of the macadam base. Xu et al. [16][17][18] added PVA fibers into the cement-stabilized macadam, the result of which shows that the PVA fibers bring higher load capacity and more flexible deformation properties, together with a hyperbolic contraction equation that presents precisely the drying shrinkages of super-high toughness cement base complex materials. According the research results [19], the compressive strength as well as the flexural behavior regarding concrete with silica fume and PVA fibers is stronger than that of common concrete; also, adding PVA fibers into the concrete can improve obviously the crack resistance of cement paste and concrete. Bengi et al. [20] studied brick wall painted with concrete to a conclusion that adding PVA fibers into solid, high-strength brick wall can increase around half of shear strength, the increased strength of which is 2.5 times higher than that found in common brick wall. Ghorbani's research [21,22] suggests that replacing some cement with rice husk ash (RHA) can increase the unconfined compressive strength of cement-based composites. Jamsawang et al. [23] has found that the surface of steel is more hydrophilic than other synthetic fiber types. And it is denser in the cemented sand and the substrate has no separation interface area, which provides the best overall bending performance. Ma's studies [24] have shown that the addition of basalt fiber cement soil can increase the plastic behavior of the sample. Nevertheless, all the above examples only covers the content of considering the effect of the amount of fibers mixed on the properties of complex materials, instead of studying farther the effect brought by fiber factors on complex materials properties.
Some Chinese scholars have studied the dispersion of fibers. Cao et al. [25] studied the dispersion of PVA fibers by means of fluorescence microscope, image processing technology, and statistics. Yang et al. [26] researched the influences on carbon fibers' (from carbon fiber cement coating, i.e., CFCC) dispersion resulted from lengths, amounts, mixing processes, dispersant and water-cement ratio and so on, with ways such as fresh pulp method and resistance measurement of hardening specimens. Cao et al. [27,28] studied dispersion of PVA fibers in cement-stabilized macadam, using image processing technology and statistics. Wang et al. [29] observed the fracture surface of carbon fiber concrete by means of scanning electron microscope, who also analyzed the distribution of factors from fracture surface with energy spectrum, as a dispersion study for carbon fiber distribution. Jie et al. [30] scanned the fracture surface with computerized tomography, and then classified the typical morphology of each component in the micrograph, and verified the distribution of the fiber with the grayscale recognition result of CT image. On the other hand, the above cases applied mainly image processing technology in scanning partial fracture surfaces of complex materials, with fiber (the diameter is very small) congealing with cement paste, thus resulting in a lack of credibility and perfection. As for resistance measurement of hardening specimens, this method can only work if the carbon fiber is conductive, thus not suitable for insulators such as PVA fibers.
PVA fibers possess strong strength and high modulus. Adding the PVA fibers into the cement-stabilized macadam can improve flexural strength as well as crack resistance, plus extending work longevity. Many scholars from China, USA, and other developed nations have achieved a lot in studying PVA fibers in cement-stabilized macadam, but the study on influence brought by the dispersion of PVA fibers requires further steps. In conclusion, this paper aims to study how the dispersion factor F vc (from PVC fibers) affects the compressive strength as well as splitting strength of cementstabilized macadam in various curing periods, and then find out the connection in them.

Raw Materials.
e marking number of the composite Portland cement employed in the experiment is p.c32.5, manufactured by Zhongshan Cor., Ltd in Xuzhou city, Jiangsu province, China. e testing result meets regulation and requirements, and the indexes are shown in Table 1 below. e aggregate (specifications: 0-5 mm, 5-10 mm, 10-15 mm, 15-25 mm, and 25-30 mm) in the experiment is limestone coming from stone material factory in Chaoyang River, Chongqing city, China. e testing results show that the aggregates meet all mechanical performance requirements. Table 2 shows the physical parameters of the PVA fiber taken in the test, and its appearance is shown in Figure 1. e composite proportions in the experiment comply with requirements in Code for Aggregate Test of Highway Engineering JTG E42-2005. For data concerning the proportions, refer to Table 3.

Testing Methods.
In this experiment, PVA fibers were treated by dry mixing and dispersing with the mass ratio of PVA fibers to coal ash of 1 : 0, 1 : 25, 1 : 50, and 1 : 75. e treatment equipment used a pure slurry mixer. Quantitative PVA fibers and coal ash were added into the mixing pot. e mixing rate was built-in low-speed mixing, and the mixing time was set to 3 minutes. After one minute of each stirring, the PVA fibers and coal ash in the mixing pot were manually turned over to ensure that the PVA fibers could be fully mixed with coal ash. e above blended PVA fibers were labeled as ①, ②, ③, and ④ PVA fibers in turn, and the coal ash used was first-class fly ash with a fineness of 320 meshes and a density of about 2.4 g/cm 3 . According to the requirements of Test Methods of Materials Stabilized with Inorganic Binders for Highway Engineering (JTG E51-2009), the optimum moisture content and maximum dry density of cement-stabilized macadam material were determined by compaction test. e test results showed that the optimum moisture content of the cement-stabilized macadam material was 4.8% and the maximum dry density was 2.301 g/cm 3 when the cement content was 4%. e mixing test of ① PVA fibers and cement-stabilized macadam was carried out. Four cement-stabilized macadam samples were selected for each mixing according to gradation design and compaction test results. e length of PVA fiber was 12 mm, and the volume content was 0.6 kg/m 3 and 0.9 kg/m 3 . After mixing test, one sample of cementstabilized macadam was taken to mark and place, and two samples were taken separately after repeating the above test. Finally, three labeled samples with volume doping of 0.6 kg/ m 3 and three labeled samples with volume doping of 0.9 kg/ m 3 were obtained. After repeating the above experiments, 18 labeled samples with volume fraction of 0.6 kg/m 3 and 0.9 kg/m 3 of PVA fibers ②, ③, and ④ were obtained. Finally, 18 samples of PVA fibers and coarse aggregates with particle size of 9.5 mm were separated from the samples by water washing method. e separated PVA fibers and coarse aggregates were dried at 150°C in the laboratory oven and weighed at last. e cement-stabilized macadam samples (samples that with PVA fibers and that without) were moulded into cylinders, as per Test Methods of Materials Stabilized with Inorganic Binders for Highway Engineering (JTG E51-2009). In experiments that study compressive strength and splitting strength, there were four kinds of PVA fibers employed (PVA fibers ①,②,③, and ④), with volume content of 0.6 kg/m 3 and 0.9 kg/m 3 . e curing temperature was for 20°C ± 2°C, with relative humidity no lower than 95%. Setting curing period was 7 days, 28 days, and 90 days. Figure 2 was about moulded cement-stabilized macadam sample. As for the 25 specimens dried on the left, they had been used for compressive strength tests.
We conducted compressive strength test and splitting strength test to cement-stabilized macadam samples with electro-hydraulic bending and compression testing machine and universal testing machine. In the tests, the running velocity was kept at 1 mm/min, and the test processes are shown in Figures 3 and 4. ere were six parallel samples, and the test result came from the average value of the six result values. We deleted the test values whose variation coefficient C v was larger than or equal to 15%, and replaced them with new test results using new samples.

Review Methods for PVA Fibers' Dispersion in Cement-Stabilized Macadam.
Choose the dispersion factor (which is F vc ) of PVA fibers to review their dispersion. Here, F vc � 1 − C vc , C vc refers to dispersion coefficient of relative mass fraction proportion coefficient.
e "relative mass fraction proportion coefficient" [27] refers to ratio of the actual mass of PVA fiber to the corresponding theory mass value in the NO. I sample. e ratio of the actual mass of coarse aggregate to the corresponding theory mass is named as C P/gi (see formula (1)). e relative coarse aggregate mass fraction proportion coefficient is named as mass fraction proportion coefficient thereinafter (see formula (3)): where m pi and m gi are actual mass of PVA fibers (unit: g) and coarse aggregate (diameter: 9.5 mm; unit: kg) in the NO. I    Advances in Civil Engineering sample, respectively; m p and m g are theory mass of PVA fibers (unit: g) and coarse aggregate (diameter: 9.5 mm; unit: kg) in every sample, respectively; C P/gi is the average value of mass fraction proportion coefficient in every sample; and C vc is the dispersion coefficient of mass fraction proportion coefficient.

Data Analysis regarding the Dispersion of PVA Fibers in
Cement-Stabilized Macadam. e data are collected in Table 4.
Take the ratio of coal ash mass to PVA fibers mass as the abscissa, and the F vc as the ordinate; see Figure 5 for their connection.
According to the conclusions from Figure 5 [31], when the coal ash is not added, the value F vc is far larger than 0.5, which means the value F vc is far smaller than 0.95, with the C vp between the actual PVA fibers mass and the corresponding theory mass larger than 0.1. us, it is concluded that the PVC fibers cannot disperse evenly in the cementstabilized macadam in the above case. However, when the mass ratio of PVA fibers to coal ash is of 1 : 50, then the F vc is equal to 0.5, the F vc is equal to 0.95, the C vp is equal to 0.1. Hence, it is concluded that the PVA fibers can disperse evenly exactly in the case. On the basis of the above two cases, it is concluded that when the ratio of PVA fiber mass to the coal ash mass is 1 : 25, the PVA fibers cannot disperse evenly. If the very ratio is 1 : 75, the conclusion is that the PVA fibers can disperse evenly. ereinafter, we set the F vc of 0.95 as a critical point, where the PVC fibers can disperse evenly exactly. When the value of F vc is below 0.95, the PVC fibers cannot disperse evenly, and vice versa. In addition, it is considered that there are no PVC fibers when the value of F vc is of 0.75, so as to facilitate analysis.

Data Analysis on PVA Fibers Enhancing Mechanical
Properties  Table 6. e relationship between F vc and compressive strength is shown in Figures 6 and 7.
According to the above Figure 6 (with fiber content as 0.6 kg/m 3 , curing periods as 7 days, 28 days, and 90 days) and Figure 7, F vc is positively related to the compressive strength.
e situation when the curing period is of 90 days and the fiber content is of 0.6 kg/m 3 is the only case studied here. e compressive strength value of the cement-stabilized macadam with evenly dispersed PVA fibers is around 4.8% higher than it in macadam where PVA fibers cannot disperse evenly, and is about 16.1% higher than it is in common cement-stabilized macadam. On the other hand, when the fiber content is of 0.9 kg/m 3 , the compressive strength value of the cement-stabilized macadam with evenly dispersed PVA fibers is around 6.2% higher than it is in macadam where PVA fibers cannot disperse evenly, and is about 17.8% higher than it is in common cement-stabilized macadam.
When the abscissa value F vc is of 0.95 (a critical point), the PVA fibers can disperse evenly exactly in cement-stabilized macadam. It is concluded that when the value of F vc is larger than 0.95, the PVA fivers have dispersed evenly; in the area between 0.75 and 0.95, the PVA fivers unite groups by groups, and the lower the value of F vc , the more groups it can    Advances in Civil Engineering The ratio of coal ash mass to PVA fibers mass   Advances in Civil Engineering nd, resulting in less dispersion. According to Figures 6 and 7, the compressive strength of cement-stabilized macadam added with PVA bers is stronger than that of common cement-stabilized macadam, because the base will crack under outside force. According to Material Sheet Interface [32], for cement-stabilized macadam added in bers, as shown in Figure 8, base cracks happen in several surfaces, together with interface debonding, ber pull-out, the fracture of base as well as bers. If the crack penetrates the surface, then the material is damaged. In the process of damage, more energy is absorbed due to the existence of bers. us, the macadam with bers possesses higher compressive strength.
As mentioned in the last paragraph, when the value of F vc is below 0.95, there are many group-gathered PVA bers distributed randomly in the macadam; so, the macadam fails to diverse and disperse the stress. e area with ber groups becomes the point to cause or even start the crack. As the crack extends around, the macadam sample is damaged. When the value of F vc is above 0.95, according to Material Sheet Surface, the interface of composites contains threedimensional interfacial phases in the transition zone between two phases with only a few microns. e interfacial phase is very thin but has very complex structure. e chemical composition, thermal properties, and mechanical properties of the interfacial phase change gradiently. e interface microstructure together with its properties resulted from heat stress, interracial crystallization e ect, and interface chemical e ect during transition period will a ect the macroscopic properties, enhancing properties of the complex materials. As a consequence, the more the PVA bers disperse, the more the three-dimensional interface phrase will be, and the strength of the macadam will be higher.
We employ the software MATLAB to t the F vc (PVC ber contents are of 0.6 kg/m 3 and 0.9 kg/m 3 , with curing period of 90 days) with the compressive strength, and we get linear functions as follows: y 3.718x + 3.047,   We use MATLAB to draw the two functions of the t in the same picture, as shown in Figure 9. In Figure 9, when the curing period is of 90 days and the same F vc value is chosen, the compressive strength of cement-stabilized macadam with PVA ber of 0.9 kg/m 3 is stronger than that of cementstabilized macadam with PVA ber of 0.6 kg/m 3 . us, the content of PVA bers can a ect the compressive strength in the macadam, and in due scope they are positively related.

Splitting Experiment.
e test results are listed in Table 7, and the corresponding connection between F vc and splitting strength is in Table 8. See Figures 10 and 11 for the connection between F vc and splitting strength.
e connection trends between splitting strength and dispersion factor F vc are illustrated in Figure 10 ( ber content: 0.6 kg/m 3 ; curing periods of seven days, 28 days, and 90 days), and Figure 11 ( ber content: 0.9 kg/m 3 ; curing periods of seven days, 28 days, and 90 days). According to the two gures, F vc is positively related to the splitting strength. e situation when the curing period is of 90 days and the ber content is of 0.6 kg/m 3 is the only case study here. e splitting strength value of the cement-stabilized macadam with evenly dispersed PVA bers is around 5.6% higher than it in macadam where PVA bers cannot disperse evenly, and is about 22.6% higher than it in common cement-stabilized macadam. On the other hand, when the ber content is of 0.9 kg/m 3 , the splitting strength value of the cement-stabilized macadam with evenly dispersed PVA bers is around 5.4% higher than it in macadam where PVA bers cannot disperse evenly, and is about 25.8% higher than it in common cement-stabilized macadam.
When the abscissa value F vc is of 0.95 (a critical point), the PVA bers can disperse evenly exactly in cement-stabilized macadam. e cement-stabilized macadam withbers possesses higher splitting strength than that without bers. Because the failure of cement-stabilized macadam without bers is brittle failure, it is known from concrete fracture mechanics [33] that the fracture failure of brittle materials is the result of crack propagation that already exists. In another word, fracture degrees depend on the value stress force that widens the existing cracks. When the work created by outside force (i.e. strain energy) is more than the surface work that creates new surfaces during cracking, the existing cracks will extend automatically to fracture. Since PVA bers enhance toughness, the splitting strength of cement-stabilized macadam with PVA bers depends not only on the hydration intensity but also on the acting force between the bers and the cement. e force between the PVA bers and the cement includes the bite force between the ber and the cement and the bonding between the ber and the cement hydration product. As a result, the cleavage damage is a comprehensive result, and the splitting strength of cement-stabilized macadam with bers will be obviously higher than that of cement-stabilized macadam without bers.
For cement-stabilized macadam with bers, when the value of F vc is larger than 0.95 (in this condition, the PVA bers have dispersed evenly), the cleavage damages cause the cracks inside the macadam to expand, together with the total system energy to decrease. e decreased energy is used for creating new free surfaces. e critical condition for cracks to expand is that the expanding force (i.e. strain energy release rate) is equal to the extension resistance (the extension resistance refers to the resistance created when the cracks are expanding to make free surfaces). e polymerhydration product three-dimensional net structure (created from reaction between PVA bers and cement hydration product) enhances the extension resistance.
ere are mainly three basic types of crack gap expansion under various loads according to fracture mechanics ( Figure 12).
When the cement-stabilized macadam is damaged by splitting, the crack propagation type belongs to the type III outer shear type, and the stress eld strength factor is as follows:

Advances in Civil Engineering
where KI refers to intensity factor that re ects the intensity of crack stress eld and Y refers to geometric shape factor, which is related to crack types and geometric shapes of samples. e crack will be a key to KI when the cement-stabilized macadam and the stress remain the same to one another. When the value of F vc is larger than 0.95, the PVA bers disperse evenly. Group gatherings will occur to PVA bers if the value of F vc decreases; so, more holes will appear in the cement-stabilized macadam, increasing the value of c. As a consequence, under same stress, the higher the dispersion degree of PVA bers, the smaller the gaps as well as KI will be. According to fracture principles, brittle fracture happens when KI > KIc (the second parameter refers to fracture toughness).
us, the larger the value of F vc , the smaller the value of KI will be, resulting higher splitting strength, and vice versa.
We employ the software MATLAB to t the F vc (PVC ber contents are of 0.6 kg/m 3 and 0.9 kg/m 3 , with curing period of 90 days) with the splitting strength, and we get linear functions as follows:    Advances in Civil Engineering y 0.4992x + 0.2738, y 0.5739x + 0.228, e above two liner functions were drawn in the same drawing by MATLAB, as is shown in Figure 13. In Figure 13, when curing period is of 90 days, the splitting strength of cement-stabilized macadam with PVA ber of 0.9 kg/m 3 is stronger than that of cement-stabilized macadam with PVA ber of 0.6 kg/m 3 . us, the content of PVA bers can a ect the splitting strength in the macadam, and in due scope they are positively related. Splitting strength has been one of the main indicators in road structure design, and the actual road surfaces are of aged period. In this case, the larger the value of F vc is (i.e. the higher the dispersion degree is), the better it will be.

Conclusions
(1) e content of coal ash a ects F vc greatly. F vc is positively related to the content ratios of coal ash.
When the mass ratio of PVA bers to coal ash is larger than 1 : 50, then F vc is larger than 0.95. In this case, the PVA bers can disperse evenly in the cement-stabilized macadam. (2) Adding PVA bers can improve the compressive strength of cement-stabilized macadam. When the ber content is of 0.6 kg/m 3 and 0.9 kg/m 3 , the compressive strength value of the cement-stabilized macadam with evenly dispersed PVA bers is around 4.8% and 6.2% higher, respectively, than it is in macadam where PVA bers cannot disperse evenly. On the other hand, the compressive strength value of the cement-stabilized macadam with PVA bers is around 16.1% and 17.8% higher than it is in common cement-stabilized macadam (where PVA bers do not exist). Moreover, under the same curing period, the compressive strength of the cementstabilized macadam with 0.9 kg/m 3 of PVA ber content is stronger than that in cement-stabilized macadam with 0.6 kg/m 3 of PVA ber content. fiber content is of 0.6 kg/m 3 and 0.9 kg/m 3 , the splitting strength value of the cement-stabilized macadam with evenly dispersed PVA fibers is around 5.4% and 5.6% higher, respectively, than it is in macadam where PVA fibers cannot disperse evenly. On the other hand, the splitting strength value of the cement-stabilized macadam with PVA fibers is around 22.6% and 25.8% higher than it is in common cement-stabilized macadam (where PVA fibers do not exist). Moreover, under the same curing period and with the same F vc , the splitting strength of the cementstabilized macadam with 0.9 kg/m 3 of PVA fiber content is stronger than that in cement-stabilized macadam with 0.6 kg/m 3 of PVA fiber content.

Data Availability
e float data used to support the findings of this study are included in the article. All the data of this experiment are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.