Reduction of cracks in concrete slabs through the incorporation of polypropylene synthetic fiber

In the construction sector, concrete cracking is a very common problem, as it significantly reduces the lifespan and integrity of structures [1]. For this reason, research on this topic has increased in several countries, seeking quick and simple solutions.
In Colombia, research conducted by Dias, Calmon, and Vieira [2] focused on the plastic shrinkage of concrete, demonstrating that conventional concrete is very weak and practically lacks resistance to cracking. This problem significantly affects the appearance and structural strength of buildings, requiring additional processes, such as crack sealing, in $90\mathrm{\%}$$90\mathrm{\%}$90%90 \%$90\mathrm{\%}$ of cases for its resolution, resulting in relatively high additional costs.
Given this situation, the use of alternative materials that reduce or prevent the appearance of cracks is presented as a more sustainable and accessible strategy. Among them, synthetic polypropylene fiber has proven to be a promising option, improving the internal cohesion of concrete and controlling crack formation during the initial stages of setting and curing [3].
In Peru, research on concrete slab cracking has been very limited in the construction sector, or, where it exists, it has not generated sufficient general interest to warrant further study. This lack of scientific evidence stems from the widespread belief that concrete cracking is not a short-term problem and is therefore often ignored. However, when analyzed over the long term, it presents significant issues that require thorough investigation.
Numerous local, national, and international studies have promoted the use of unconventional natural and synthetic fibers to reduce concrete cracking. For example:
Chaisa and Maccarcco [4] they determined that the incorporation of 0.5 kg of fibers reduced settling by $69.95\mathrm{\%}$$69.95\mathrm{\%}$69.95%69.95 \%$69.95\mathrm{\%}$, considering that a higher fiber content would further reduce settling.
Prakash et al. [5] concluded that adding $0.5\mathrm{\%}$$0.5\mathrm{\%}$0.5%0.5 \%$0.5\mathrm{\%}$ polypropylene fibers to a concrete mix increased tensile strength by up to $24\mathrm{\%}$$24\mathrm{\%}$24%24 \%$24\mathrm{\%}$, suggesting that polypropylene fibers can be used to optimize the mechanical properties of concrete.
Similarly, Ghali et al. [6] found that compressive strength increased by $38.6\mathrm{\%}$$38.6\mathrm{\%}$38.6%38.6 \%$38.6\mathrm{\%}$ with the addition of polypropylene fiber. Qasim and Jassam [7] they determined that adding $40\mathrm{\%}$$40\mathrm{\%}$40%40 \%$40\mathrm{\%}$ polypropylene fiber increased compressive strength by $46.40\mathrm{\%}$$46.40\mathrm{\%}$46.40%46.40 \%$46.40\mathrm{\%}$ after 14 days.
Shan et al. [8] demonstrated that the incorporation of $1\mathrm{kg}/{\mathrm{m}}^3$$1\mathrm{kg}/{\mathrm{m}}^3$1kg//m^(3)1 \mathrm{~kg} / \mathrm{m}^{3}$1\mathrm{kg}/{\mathrm{m}}^3$ of polypropylene fiber improved compressive strength by $42.2\mathrm{\%}$$42.2\mathrm{\%}$42.2%42.2 \%$42.2\mathrm{\%}$ at 28 days, highlighting the importance of using polypropylene fibers in concrete mixtures.
Najaf and Abbasi [9] they reported that the addition of polypropylene macrostructural fibers increased compressive strength by $32\mathrm{\%}$$32\mathrm{\%}$32%32 \%$32\mathrm{\%}$ and flexural strength by $85\mathrm{\%}$$85\mathrm{\%}$85%85 \%$85\mathrm{\%}$, representing a significant improvement.
Maafi et al. [10] concluded that synthetic polypropylene fiber improved compressive strength by $23\mathrm{\%}$$23\mathrm{\%}$23%23 \%$23\mathrm{\%}$ and tensile strength by $21\mathrm{\%}$$21\mathrm{\%}$21%21 \%$21\mathrm{\%}$, emphasizing that the ideal amount of fiber is crucial for a significant improvement.
Zhao et al. [1] discovered that the addition of polypropylene and steel fibers resulted in increases of $29.1\mathrm{\%}$$29.1\mathrm{\%}$29.1%29.1 \%$29.1\mathrm{\%}$ in compressive strength and $53.4\mathrm{\%}$$53.4\mathrm{\%}$53.4%53.4 \%$53.4\mathrm{\%}$ in tensile strength, demonstrating the benefits of using both plastic and metallic fibers. Callamamani et al. [11] demonstrated that shorter synthetic fibers disperse more effectively compared to longer fibers, which tend to concentrate in one area of the concrete.
Christopher et al. [12] demonstrated that hybrid polyester and steel fibers improved compressive strength by $26\mathrm{\%}$$26\mathrm{\%}$26%26 \%$26\mathrm{\%}$, suggesting and recommending the combined use of different fibers in concrete.
Akbulut et al. [13] concluded that the use of synthetic fibers improves ductility, helps mitigate micro-cracks due to shrinkage, and improves performance under dynamic loads.

Laskhmi et al. [14] demonstrated that as the polypropylene fiber content increases, shrinkage initially decreases but then tends to stabilize or even increase if the dosage is too high. The optimum percentage is around $1.0-1.5\mathrm{kg}/{\mathrm{m}}^3$$1.0-1.5\mathrm{kg}/{\mathrm{m}}^3$1.0-1.5kg//m^(3)1.0-1.5 \mathrm{~kg} / \mathrm{m}^{3}$1.0-1.5\mathrm{kg}/{\mathrm{m}}^3$. Dosages above $1.5\mathrm{kg}/{\mathrm{m}}^3$$1.5\mathrm{kg}/{\mathrm{m}}^3$1.5kg//m^(3)1.5 \mathrm{~kg} / \mathrm{m}^{3}$1.5\mathrm{kg}/{\mathrm{m}}^3$ reduce the cohesion of the mixture and increase porosity, inducing cracking.
In contrast, Kistan et al. [15] obtained different results from previous studies, indicating that the incorporation of plastic fibers as a substitute for fine aggregate led to a $16.9\mathrm{\%}$$16.9\mathrm{\%}$16.9%16.9 \%$16.9\mathrm{\%}$ reduction in compressive strength and a $17.6\mathrm{\%}$$17.6\mathrm{\%}$17.6%17.6 \%$17.6\mathrm{\%}$ reduction in flexural strength.
Similarly, Mohammed and Kasim [16] they concluded that the increase in waste polyethylene fibers reduced compressive strength by $15.74\mathrm{\%}$$15.74\mathrm{\%}$15.74%15.74 \%$15.74\mathrm{\%}$, negatively affecting workability and performance.
In Peru, the use of concrete is highly standardized in all types of construction, as it is an efficient building material. Therefore, ignoring the problem of cracking represents negligence on the part of researchers that must be addressed as soon as possible [17].
At the national level, there is no standardized test that directly assesses the presence of cracks in slabs.
This situation highlights a research gap: the lack of standardized tests to evaluate concrete's behavior in response to cracking and the absence of technical criteria to optimize the dosage of synthetic fibers according to local material and climatic conditions. In this regard, ASTM C1579 is a valuable reference, providing an experimental method for analyzing plastic shrinkage cracking in physical models that simulate concrete slabs. Although it is a US standard, its adaptation to the Peruvian context allows for obtaining representative results without compromising the test's technical validity.
Therefore, this research aims to analyze the effect of incorporating polypropylene synthetic fiber on reducing the number, width, and length of cracks in physical models of concrete slabs with ${\mathrm{f}}^{\prime }\mathrm{c}=210\mathrm{kg}/{\mathrm{cm}}^2$${\mathrm{f}}^{\prime }\mathrm{c}=210\mathrm{kg}/{\mathrm{cm}}^2$f^(')c=210kg//cm^(2)\mathrm{f}^{\prime} \mathrm{c}=210 \mathrm{~kg} / \mathrm{cm}^{2}${\mathrm{f}}^{\prime }\mathrm{c}=210\mathrm{kg}/{\mathrm{cm}}^2$. Tests were conducted with different dosages of polypropylene fiber in the mix: MP ( $0\mathrm{g}/{\mathrm{m}}^3$$0\mathrm{g}/{\mathrm{m}}^3$0g//m^(3)0 \mathrm{~g} / \mathrm{m}^{3}$0\mathrm{g}/{\mathrm{m}}^3$ ), DM-01 ( $500\mathrm{g}/{\mathrm{m}}^3$$500\mathrm{g}/{\mathrm{m}}^3$500g//m^(3)500 \mathrm{~g} / \mathrm{m}^{3}$500\mathrm{g}/{\mathrm{m}}^3$ ), DM-02 ( $1000\mathrm{g}/{\mathrm{m}}^3$$1000\mathrm{g}/{\mathrm{m}}^3$1000g//m^(3)1000 \mathrm{~g} / \mathrm{m}^{3}$1000\mathrm{g}/{\mathrm{m}}^3$ ), and DM-03 ( $2000\mathrm{g}/{\mathrm{m}}^3$$2000\mathrm{g}/{\mathrm{m}}^3$2000g//m^(3)2000 \mathrm{~g} / \mathrm{m}^{3}$2000\mathrm{g}/{\mathrm{m}}^3$ ). These were evaluated at $7,14,21,28$$7,14,21,28$7,14,21,287,14,21,28$7,14,21,28$, and 35 days to determine the impact of the fiber on crack formation.
The aim of this research is to identify the optimal dosage of polypropylene synthetic fiber that provides the greatest benefits to concrete in terms of cracking and formation. By discovering its ability to reduce cracking, not only can the lifespan of structures be increased, but long-term maintenance and repair costs can also be reduced-topics of interest for future scientific studies.

Based on Tang's approach [18], this research was classified as applied, as it seeks to improve the plasticity of conventional concrete by incorporating polypropylene synthetic fiber at dosages of 500,1000 , and $2000\mathrm{g}/{\mathrm{m}}^3$$2000\mathrm{g}/{\mathrm{m}}^3$2000g//m^(3)2000 \mathrm{~g} / \mathrm{m}^{3}$2000\mathrm{g}/{\mathrm{m}}^3$, with fiber lengths of 2 to 2.5 cm , to determine the optimum dosage. The approach is quantitative, as it uses concrete design parameters established by the ACI-318 standard, incorporates an unconventional additivepolypropylene synthetic fiber-and obtains data through the ASTM C1579 standard formula .
This research aims to analyze the behavior and progression of the number, width, and length of cracks appearing in physical models of slabs, as determined and proposed by ASTM C1579, which simulates crack formation in concrete. To this end, four mix designs were developed: MP $\left(0\mathrm{g}/{\mathrm{m}}^3\right)$$\left(0\mathrm{g}/{\mathrm{m}}^3\right)$(0(g)//m^(3))\left(0 \mathrm{~g} / \mathrm{m}^{3}\right)$\left(0\mathrm{g}/{\mathrm{m}}^3\right)$, DM-01 $\left(500\mathrm{g}/{\mathrm{m}}^3\right)$$\left(500\mathrm{g}/{\mathrm{m}}^3\right)$(500(g)//m^(3))\left(500 \mathrm{~g} / \mathrm{m}^{3}\right)$\left(500\mathrm{g}/{\mathrm{m}}^3\right)$, DM-02 $\left(1000\mathrm{g}/{\mathrm{m}}^3\right)$$\left(1000\mathrm{g}/{\mathrm{m}}^3\right)$(1000(g)//m^(3))\left(1000 \mathrm{~g} / \mathrm{m}^{3}\right)$\left(1000\mathrm{g}/{\mathrm{m}}^3\right)$, and DM-03 (2000 $\mathrm{g}/{\mathrm{m}}^3$$\mathrm{g}/{\mathrm{m}}^3$g//m^(3)\mathrm{g} / \mathrm{m}^{3}$\mathrm{g}/{\mathrm{m}}^3$ ). Three of these mix designs incorporated polypropylene synthetic fiber to compare them with the control concrete (MP) and determine the optimal mix design that provides the greatest structural benefits.

These physical models will be manufactured with a material that prevents water absorption.
To determine the optimal dosage, a formula proposed in ASTM C1579, known as the "Crack Reduction Index," will be used. This index is directly proportional to the fiber-reinforced concrete and inversely proportional to the control concrete. Comparative graphs of the Crack Reduction Index versus Fiber Dosage were developed for each aspect of the cracks (number, length, and width), showing the dosage that yielded the greatest possible benefit for the concrete.

According to Navidi [19] a sample is a subgroup of the population, since it is rarely possible to accurately measure the entire population. Therefore, this subset seeks to faithfully represent the total population under study. For this research, 20 specimens were prepared to represent the population of concrete slabs.
The sample size for the physical models was calculated using formula (2), adopting a $90\mathrm{\%}$$90\mathrm{\%}$90%90 \%$90\mathrm{\%}$ confidence level ( $Z=1.645$$Z=1.645$Z=1.645Z=1.645$Z=1.645$ ), a probability of success $\mathrm{p}=0.95$$\mathrm{p}=0.95$p=0.95\mathrm{p}=0.95$\mathrm{p}=0.95$, considering 12 favorable precedents out of 13 consulted studies, and a margin of error $\mathrm{e}=0.08(8\mathrm{\%})$$\mathrm{e}=0.08(8\mathrm{\%})$e=0.08(8%)\mathrm{e}=0.08(8 \%)$\mathrm{e}=0.08(8\mathrm{\%})$. Substituting the values into the formula yields $\mathrm{n}\approx 20.08$$\mathrm{n}\approx 20.08$n~~20.08\mathrm{n} \approx 20.08$\mathrm{n}\approx 20.08$. However, given the experimental conditions and the minimal practical difference , a sample size of $\mathrm{n}=20$$\mathrm{n}=20$n=20\mathrm{n}=20$\mathrm{n}=20$ is also considered acceptable, which implies an effective margin of error of $\approx 8.02\mathrm{\%}$$\approx 8.02\mathrm{\%}$~~8.02%\approx 8.02 \%$\approx 8.02\mathrm{\%}$. It should be noted that the reviewed precedents mostly correspond to compression and tensile strength tests, etc., and not to specific cracking tests. Therefore, the choice of $\mathrm{p}=0.95$$\mathrm{p}=0.95$p=0.95\mathrm{p}=0.95$\mathrm{p}=0.95$ is based on previous evidence on general material improvements and is recognized as a conservative approach in the absence of specific local experimental studies on cracking.

The properties of polypropylene synthetic fiber were characterized to better understand its behavior in concrete. This characterization allows for the identification of its physical and mechanical properties, such as tensile strength, density, melting point, water absorption, and coefficient of friction, which influence the material's ability to control the appearance and propagation of cracks.

Table 1: Breakdown of the number of samples for each dosage of polypropylene synthetic fiber proposed in the research.

The materials used in this research were selected based on the researcher's needs, with the aim of optimizing the study's execution. The purpose of this research was to replicate and utilize materials commonly available in the local market for construction in this sector.
The physical molds were manufactured using phenolic wood boards, following the specifications detailed in Figure 1. This material was selected for its ability to prevent water absorption, which is essential to ensure the quality of the formwork in the slab molds.

For the preparation of the concrete, coarse and fine aggregates from the Yocará quarry were used, which were processed and selected. This type of material is one of the most commonly used in housing construction in the city of Juliaca, where the research was conducted.
The key material in this study is polypropylene synthetic fiber, a necessary component due to its accessibility to the population and its viability in the building construction process. This fiber was acquired from local plastic supply stores in Juliaca, providing the raw material for its unconventional application in the concrete used in this research.

The dosage used in this study was $210\mathrm{kg}/{\mathrm{cm}}^2$$210\mathrm{kg}/{\mathrm{cm}}^2$210kg//cm^(2)210 \mathrm{~kg} / \mathrm{cm}^{2}$210\mathrm{kg}/{\mathrm{cm}}^2$, developed by the researchers themselves, who were also responsible for the article. This ensured the integrity and reliability of the results obtained during its execution. The design and testing were supported by the Laboratory of the Peruvian Union University, which guaranteed the results of all the tests necessary for the proper execution of this research.
The materials required for the mix design were crushed stone and coarse sand, for which laboratory tests were conducted to determine the physical properties necessary for the concrete mix design. The tests performed on both the coarse and fine aggregates, in accordance with ASTM standards for mix design, were: particle size analysis (ASTM C-136), moisture content (ASTM D-2216), specific gravity and absorption (ASTM C-128), and unit weight (ASTM C-29). The results of these tests are presented in the following data table:

The cement used in the mix was RUMI Type IP, one of the most common cements used in residential slab construction due to its low cost and good performance in cold climates. It has a density of $2.8\mathrm{g}/{\mathrm{cm}}^3$$2.8\mathrm{g}/{\mathrm{cm}}^3$2.8g//cm^(3)2.8 \mathrm{~g} / \mathrm{cm}^{3}$2.8\mathrm{g}/{\mathrm{cm}}^3$, according to the supplier's technical data sheet.
The mix design of $210\mathrm{kg}/{\mathrm{cm}}^2$$210\mathrm{kg}/{\mathrm{cm}}^2$210kg//cm^(2)210 \mathrm{~kg} / \mathrm{cm}^{2}$210\mathrm{kg}/{\mathrm{cm}}^2$ was developed following the guidelines of the American standard ACI 211.1, which explicitly outlines the steps for proper concrete mix design. The resulting mix design required for this research was as follows:

During the preparation of the concrete, the slump test was performed in accordance with ASTM C143 to verify the workability of the designed concrete.

Using the developed mix design, a total of 8 specimens were prepared to evaluate the compressive strength of the hardened concrete. These specimens were cured at 7 and 28 days, submerged in water tanks. Under identical environmental conditions for each specimen evaluated , as part of the tests necessary for quality control of the construction materials used. The following table shows the results obtained from the tests carried out in the Concrete Laboratory of the Peruvian Union University:

Based on the concrete mix design, this was established as the Control Concrete (CP), which served as the basis of the research, to which synthetic polypropylene fiber was incorporated to obtain the following dosages:

In Peru, there is no specific standard or guideline that details or explains the measurement of drying shrinkage cracks in concrete. Standards NTP 399.022, NTP 399.013, NTP 399.011, and NTP 399.015 provide general guidelines for evaluating cracks in concrete, without specifying a direct and simple method.

For this reason, the present research is based on the American standard ASTM C1579. This standard was used with the objective of proposing the use of physical models (see figure 1), which seek to accurately represent real slabs for applied research purposes.
Simultaneously with the verification of a suitable mix design, 20 samples of the physical slab models were molded: 5 control concrete slabs (MP), 5 MP-01 slabs, 5 DM-02 slabs and 5 DM-03 slabs.

After molding, the samples underwent a continuous curing process under identical environmental conditions, as the objective was to simulate the actual curing of concrete slabs in construction. Therefore, simply immersing them in water was not representative of the real-world conditions anticipated in the research. Consequently, it was determined that the best way to cure the physical slab models was to water their surfaces daily, supplemented by a cover that would help retain moisture for an extended period, thus ensuring that the samples remained in constant contact with moisture for proper concrete curing.

Data on the number, width, and length of cracks were collected as the curing process progressed. Days $7,14,21,28$$7,14,21,28$7,14,21,287,14,21,28$7,14,21,28$, and 35 after pouring were determined to be the most suitable for obtaining sample data, allowing for organized recordkeeping with assessments every 7 days after pouring on these five designated dates.
During January and February 2025, the city of Juliaca (Puno) experienced typical rainy season weather conditions. During the curing and testing of the concrete samples, the average temperature hovered around ${11.5}^{\circ }\mathrm{C}.{}^{\circ }\mathrm{C}$${11.5}^{\circ }\mathrm{C}.{}^{\circ }\mathrm{C}$11.5^(@)C.^(@)C11.5^{\circ} \mathrm{C} .{ }^{\circ} \mathrm{C}${11.5}^{\circ }\mathrm{C}.{}^{\circ }\mathrm{C}$, with
minimum values of $4^{\circ }\mathrm{C}$$4^{\circ }\mathrm{C}$4^(@)C4^{\circ} \mathrm{C}$4^{\circ }\mathrm{C}$ and maximums of ${18}^{\circ }\mathrm{C}$${18}^{\circ }\mathrm{C}$18^(@)C18^{\circ} \mathrm{C}${18}^{\circ }\mathrm{C}$, while the average relative humidity remained at $72\mathrm{\%}$$72\mathrm{\%}$72%72 \%$72\mathrm{\%}$, with a range of $6580\mathrm{\%}\mathrm{\%}$$6580\mathrm{\%}\mathrm{\%}$6580%%6580 \% \%$6580\mathrm{\%}\mathrm{\%}$, which were obtained using external climate measurement equipment.
The application of ASTM C1579 is based on the design of the physical slab forms, which induce cracking in the concrete due to the presence of three raised sections in their structure, creating areas of reduced width where cracks tend to form. Although the original test established by the standard is performed over a short period of 3 to 4 hours-corresponding to the setting time-in this study, the procedure was adapted for an extended evaluation of 35 days, encompassing the complete curing and post-curing process. These modifications do not affect the comparative validity of the results, since at the time of measurement the cracks are fully developed and stabilized within the concrete's structural system, allowing for reliable visual evaluation.

During each week following sample molding, data were collected to support the results of this research, evaluating the frequency, width, and/or length of cracks that appeared in the samples during the curing period. Considering the behavior and nature of the cracks, a random pattern was observed in their appearance, with no predictable trend in their number or location.
A handheld crack gauge was used to accurately, practically, and efficiently measure the width and length of the cracks.

Crack measurement in concrete slabs was performed using a manual crack gauge. The surface of the physical slab models was cleaned beforehand. Each visible crack was identified and marked, and its width was determined by placing the crack gauge's millimeter scale over the crack and recording the value. This measurement was repeated at different points to obtain an average. The length of each crack was measured with the same instrument, adding together sections in the case of irregular cracks. The total number of cracks was counted within the measurement area of the various molds created for each mix design.
Many of the cracks initially analyzed appeared insignificant, but over time they developed considerably, becoming detrimental to the concrete slabs. Many of the cracks assessed at the final date were due to the merging of smaller cracks that connected linearly to form a crack of considerable size for the slabs. While some cracks maintained their width and length throughout the assessment period, others developed further, increasing in size and becoming visible without the need for a crack gauge.
The following tables present the results of the visual evaluation, which numerically show the process of appearance and growth of cracks, divided according to the doses used in the research and described previously.

Twenty physical molds were prepared and experimentally evaluated by visual inspection and manual measurements using a crack width gauge, with the aim of recording and analyzing the crack formation and development process.

Through data collection, a consistent pattern was identified in the width of cracks in concrete slabs. Therefore, based on the researchers' assessment, it was deemed appropriate to establish a method for classifying the severity of cracks present in the slabs. Using the observed crack width as a reference, the following classification table was developed to provide a theoretical and visual understanding of the risk range and significance of cracks in concrete slabs.

The data for this research were collected on five different dates after the pour to observe the growth, width, and length of the cracks. Therefore, the data from each date will be analyzed independently to identify when the greatest benefits for the concrete slabs were observed.

In this research, four statistical tests were used to analyze and express the relationships and significance of the data collected from the samples. These statistical tests help to understand the levels of significance in each sample analyzed, facilitating a consistent technical analysis.
The SPSS software version 30.0.0 (Statistical Package for the Social Sciences) was used to perform all statistical tests on the quantitative data obtained during the research.
The statistical tests used were the following:

Descriptive statistical analysis of data allows us to determine the number of data points, the maximum, the minimum, the mean, and the standard deviation, which are necessary to understand the nature of the quantitative data collected on different dates.

This analysis is fundamental to obtaining an overall perspective of the data and establishing a solid foundation that facilitates the exploration of the relationships between the sample designs proposed for this research [20].
Descriptive statistical analysis allowed for the identification of the maximum and minimum crack width and lengths. The minimum width recorded in the samples was 1 mm , while the maximum reached 4 mm , values present in all analyzed samples. Similarly, the minimum crack length was 4 mm and the maximum reached 450 mm , considering the five measurement dates.
This behavior indicates that the cracks have grown irregularly over time, without a predictable pattern.
Furthermore, taking the control concrete (MP) as an example, it was observed that the average width of the cracks evolved as follows:

These values suggest a progressive increase in crack width over time.
On the other hand, the average length of the cracks in the control concrete (MP) showed the following variation:

Initially, relatively large cracks were recorded, reflected in high average length values. However, over time, smaller cracks began to appear, altering the average lengths. This behavior suggests that while cracks continue to appear, their distribution changes over time.
This example indicates, as in the other sample designs, that the average widths and lengths do not follow a progressive growth pattern, but rather adapt to the appearance of new cracks present in the samples throughout the measurement period.

The Shapiro-Wilk statistical test allows you to evaluate a data set by interpreting: " $\mathrm{p}\mathrm{\_}$$\mathrm{p}\mathrm{\_}$p_\mathrm{p} \_$\mathrm{p}\mathrm{\_}$value $>0.05$$>0.05$> 0.05>0.05$>0.05$ ", which accepts the null hypothesis and indicates a normal distribution of the data, and " $\mathrm{p}\mathrm{\_}$$\mathrm{p}\mathrm{\_}$p_\mathrm{p} \_$\mathrm{p}\mathrm{\_}$value $<0.05$$<0.05$< 0.05<0.05$<0.05$ ", which rejects the null hypothesis and indicates that the data does not follow a normal distribution [20].
The following are the results of the Shapiro-Wilk statistical test for the sample designs analyzed on the different measurement dates, analyzing each date independently of the others.

Applying the Shapiro-Wilk statistical test, it was identified that the crack width and length variables in the different sample designs (MP, DM-01, DM-02, and DM-03) and at different concrete ages ( $7,14,21,28$$7,14,21,28$7,14,21,287,14,21,28$7,14,21,28$, and 35 days) mostly showed a p -value $<0.05$$<0.05$< 0.05<0.05$<0.05$, indicating that they did not follow a normal distribution. However, the crack length did follow a normal distribution in DM-01 ( p -value $=0.076$$=0.076$=0.076=0.076$=0.076$ ), DM-02 ( p -value $=0.348$$=0.348$=0.348=0.348$=0.348$ ), and DM-03 ( p -value $=0.417$$=0.417$=0.417=0.417$=0.417$ ) at 7 days; in DM-02 ( p -value $=0.072$$=0.072$=0.072=0.072$=0.072$ ) at 21 days; and in DM-02 ( p -value $=0.068$$=0.068$=0.068=0.068$=0.068$ ) and DM-03 ( p -value $=0.058$$=0.058$=0.058=0.058$=0.058$ ) at 28 days. In DM$02(\mathrm{p}=0.057)$$02(\mathrm{p}=0.057)$02(p=0.057)02(\mathrm{p}=0.057)$02(\mathrm{p}=0.057)$ and DM-03 ( $\mathrm{p}=0.058$$\mathrm{p}=0.058$p=0.058\mathrm{p}=0.058$\mathrm{p}=0.058$ ) at 35 days, a significant decrease was observed. Since parametric tests, such as ANOVA, require this assumption to be met, and most of the data did not satisfy it, nonparametric tests were used. To compare the four sample designs at each concrete age, the Kruskal-Wallis test was applied, and in cases where significant differences were found, the Mann-Whitney U test was used for pairwise comparisons. This approach ensures appropriate and reliable statistical analysis for interpreting the effect of polypropylene synthetic fiber on concrete cracking.

Since the normality test indicated that not all the data followed a normal distribution, analysis of variance (ANOVA) was not appropriate for this research. Instead, the Kruskal-Wallis test was chosen, as it is more flexible and suitable when the assumption of normality is not met in at least one of the analyzed groups.

The Kruskal-Wallis test results showed that at 7 days there were no significant differences in crack width or length among the different sample designs. However, over time, differences in crack width began to appear, becoming significant at 14 days ( $\mathrm{p}=0.023$$\mathrm{p}=0.023$p=0.023\mathrm{p}=0.023$\mathrm{p}=0.023$ ), 21 days ( $\mathrm{p}=0.031$$\mathrm{p}=0.031$p=0.031\mathrm{p}=0.031$\mathrm{p}=0.031$ ), 28 days ( $\mathrm{p}=0.003$$\mathrm{p}=0.003$p=0.003\mathrm{p}=0.003$\mathrm{p}=0.003$ ), and 35 days ( $\mathrm{p}=0.004$$\mathrm{p}=0.004$p=0.004\mathrm{p}=0.004$\mathrm{p}=0.004$ ). This suggests that
the effect of sample design on crack width becomes more pronounced over time, differentiating one sample design from another.
On the other hand, although the crack lengths did not show significant differences according to the Kruskal-Wallis test, the Mann-Whitney U test was applied to verify whether there was at least a small difference between each sample design (DM-01, DM-02, and DM-03) and the control concrete (MP). To identify this difference, the significance value ( p -value) of the test was analyzed, where a p -value $<0.05$$<0.05$< 0.05<0.05$<0.05$ indicates a statistically significant difference between the compared groups, while values close to 0.05 could suggest trends or small differences that might be relevant to the research.

After determining, using the Kruskal-Wallis statistical test, that there was a significant difference between at least two of the sample designs, the Mann-Whitney U test was applied. This is a non-parametric test used to compare each sample design (DM-01, DM-02, and DM-03) with the standard sample (SP). The objective is to identify which sample design shows significant differences compared to the standard sample.

The Mann-Whitney U test results show that, overall, there are no statistically significant differences in crack width and length between the standard concrete (MP) and the sample designs (DM-01, DM-02, and DM-03) on most of the days analyzed, as the p -values are greater than 0.05 . However, the crack width in DM-02 on days 28 ( p -value $=0.073$$=0.073$=0.073=0.073$=0.073$ ) and $35(\mathrm{p}$$35(\mathrm{p}$35(p35(\mathrm{p}$35(\mathrm{p}$-value $=0.073)$$=0.073)$=0.073)=0.073)$=0.073)$ shows a trend toward statistical significance, suggesting a possible reduction in crack width with the addition of fibers. Similarly, in DM-03, the width showed significant differences on days 21 ( p -value $=0.048$$=0.048$=0.048=0.048$=0.048$ ), 28 $(\mathrm{p}$$(\mathrm{p}$(p(\mathrm{p}$(\mathrm{p}$-value $=0.021)$$=0.021)$=0.021)=0.021)$=0.021)$, and $35(\mathrm{p}$$35(\mathrm{p}$35(p35(\mathrm{p}$35(\mathrm{p}$-value $=0.021)$$=0.021)$=0.021)=0.021)$=0.021)$, indicating that the addition of fibers in this design could have a significant effect on reducing crack width. Regarding crack length, no significant differences were found on any of the days evaluated, suggesting that the polypropylene synthetic fiber may have a greater influence on reducing crack width than on crack length. However, although the statistical test did not show a significant difference, this does not imply that
there was no reduction in crack length and width. Therefore, a technical analysis of the data will be performed to corroborate the statistical results and determine an exact percentage reduction, thus complementing the statistical tests for a better understanding of crack reduction in concrete slabs.

Based on the statistical analysis of data collected during the construction phase, the aim is to determine the optimal dosage of polypropylene synthetic fiber in concrete slabs. To this end, a technical analysis of the information obtained at each curing stage will be performed to understand the cracking process. However, since the Mann-Whitney U test showed a significant difference between the Standard Sample (SS) and the Sample Designs (DM-01, DM-02, and DM03) at 28 and 35 days, it was decided to identify the optimal dosage using the data corresponding to 28 days. This is because, at this stage, the concrete completes its curing process and reaches its maximum strength, which is more beneficial for the research.

Cracks develop during the concrete curing phase, allowing them to be identified through visual observation of their growth. Their appearance is related to the expansion and contraction processes of the material, manifesting primarily in areas where the concrete is thinner. Data collection at the five curing stages allowed for a progressive analysis of crack formation and propagation, as detailed in the following three graphs (Time vs. Width, Length, and Cracks), considering the maximum value for width and length, and the total frequency for the number of cracks.

The three graphs illustrate the process of crack appearance and propagation during the curing period, allowing for an understanding of crack formation behavior in the simulated concrete slabs. Figures 8 and 9 show the maximum data values corresponding to MP, DM-01, DM-02, and DM-03; therefore, the width and length values shown in the graphs are determined by the maximum crack data and their respective dimensions on the measurement dates. Figure 10, on the other hand, shows the relationship between the number of cracks and the curing time, clearly demonstrating the pattern of crack appearance and evolution in the physical models of the concrete slabs.
The development of these graphs aims to identify the percentage differences in the growth and/or appearance of width, length, and cracks in the physical models of concrete slabs.
Figures 8 and 9 present the graphs showing the relationship between the average width and length of the cracks and the curing time for the different sample designs, considering days $7,14,21,28$$7,14,21,28$7,14,21,287,14,21,28$7,14,21,28$ and 35 . Based on these data, a table was created showing the percentage variations in width and length between each of the measurement dates.

The table indicates that, between days 21 and 28 , the physical models show the last significant crack formation in terms of width, with a variation ranging from a minimum of $4.88\mathrm{\%}$$4.88\mathrm{\%}$4.88%4.88 \%$4.88\mathrm{\%}$ in DM-02 to a maximum of $13.77\mathrm{\%}$$13.77\mathrm{\%}$13.77%13.77 \%$13.77\mathrm{\%}$ in MP. In contrast, between days 28 and 35 , corresponding to the period after curing, the width variations do not exceed $3\mathrm{\%}$$3\mathrm{\%}$3%3 \%$3\mathrm{\%}$, which does not represent a relevant increase.
When analyzing crack lengths in the physical models, it is observed that between days $7-14$$7-14$7-147-14$7-14$ and 14-21, the percentage variations are negative. However, this does not imply that the crack length is decreasing. In fact, it reflects the appearance of new, shorter cracks, which significantly alters the average for each sample. This behavior reveals an erratic and random crack formation pattern that does not follow a defined trend or respond to the implemented control measures.
However, between days 21 and 28, the formation of new cracks begins to cease, focusing solely on the spontaneous growth of existing cracks. During the period from 28 to 35 days, this growth decreases even further, reaching a maximum of only $3.75\mathrm{\%}$$3.75\mathrm{\%}$3.75%3.75 \%$3.75\mathrm{\%}$ in MP, which represents a relatively small increase compared to the samples evaluated.
This analysis helps to directly understand the process of crack formation and propagation in physical models. It also identifies that, around day 28, the cracks stop growing progressively and begin to stabilize, maintaining the same dimensions or, at most, showing a growth rate of less than $4\mathrm{\%}$$4\mathrm{\%}$4%4 \%$4\mathrm{\%}$, which implies a tendency toward stabilization in crack formation and propagation.

Figure 9 presents a histogram showing the number of cracks recorded on each measurement day. The values reflect the number of cracks observed in the physical molds for each sample design, allowing visualization of how crack presence varies over time and identification of the point at which they begin to stabilize or cease altogether.
The objective of this research is to determine the optimal incorporation of polypropylene synthetic fiber. Therefore, the graphs in Figures 7, 8, and 9 initially show, visually, which sample designs meet this research requirement.
Considering that MP is the baseline of the study, represented by the red line in each graph, the following interpretations can be made.

The American standard ASTM C 1579 presents formula (1), which provides a way to identify crack reduction in partially or totally controlled samples, using as dependent data the width, length and/or average number of cracks of MP and each sample design (DM-01, DM-02 and DM-03) to calculate crack reduction in percentage terms.
By applying formula (1) relating each sample design (DM-01, DM-02 and DM-03) to MP for each measurement date, the corresponding percentages were determined and used to develop the graphs showing the crack reduction.

Figure 31 illustrates a graph showing the crack reduction ratio (CRR) in width versus its respective percentage reduction for each sample design compared to the control sample (DM-01 vs. MP, DM-02 vs. MP, and DM-03 vs. MP). Each line corresponds to a specific post-casting data collection date, which explains why each comparison shows a different behavior. However, all follow a similar reduction trend within their own comparison for each analyzed date.
As mentioned previously, analyzing the data for 28 days (red line) shows that comparisons between DM-01 and MP, and between DM-02 and MP, reveal reductions in crack width of $11.32\mathrm{\%}$$11.32\mathrm{\%}$11.32%11.32 \%$11.32\mathrm{\%}$ and $18.41\mathrm{\%}$$18.41\mathrm{\%}$18.41%18.41 \%$18.41\mathrm{\%}$, respectively. However, the comparison between DM-03 and MP does not show a decrease, but rather an increase of $28.75\mathrm{\%}$$28.75\mathrm{\%}$28.75%28.75 \%$28.75\mathrm{\%}$ in crack width. This increase represents a clear disadvantage that must be considered when incorporating this mix design into concrete.
Considering only the width variable, it is understood that design DM-03 does not contribute to reducing crack width in concrete, so its incorporation does not provide any significant benefit. In contrast, designs DM-01 and DM-02 do reduce crack width, with DM-02 standing out for achieving the greatest reduction, with a CRR of $18.41\mathrm{\%}$$18.41\mathrm{\%}$18.41%18.41 \%$18.41\mathrm{\%}$.
Figure 32 shows the crack reduction ratio (CRR) in length and its respective percentage reduction. Evaluating the data obtained at 28 days, it is observed that only design DM-02 achieves a reduction in crack length, with $11.46\mathrm{\%}$$11.46\mathrm{\%}$11.46%11.46 \%$11.46\mathrm{\%}$, the highest value among the designs analyzed. In contrast, designs DM-01 and DM-03 not only fail to reduce crack length, but
actually cause an increase of $10.92\mathrm{\%}$$10.92\mathrm{\%}$10.92%10.92 \%$10.92\mathrm{\%}$ and $3.88\mathrm{\%}$$3.88\mathrm{\%}$3.88%3.88 \%$3.88\mathrm{\%}$, respectively, which is an important aspect to consider when applying them to concrete slabs.

Focusing solely on crack length, it is concluded that sample designs DM-01 and DM-03 do not contribute to reducing it in the physical models; on the contrary, they cause a considerable increase. In contrast, design DM-02 represents a favorable alternative for incorporating polypropylene synthetic fiber, achieving an $11.46\mathrm{\%}$$11.46\mathrm{\%}$11.46%11.46 \%$11.46\mathrm{\%}$ reduction in crack length.

Finally, Figure 33 shows the Crack Reduction Ratio (CRR) for the number of cracks and its corresponding percentage reduction. Analysis of the data processed at 28 days shows that all sample designs-DM-01, DM-02, and DM-03exhibit a reduction in the number of cracks, with respective reduction percentages of $37.84\mathrm{\%},32.43\mathrm{\%}$$37.84\mathrm{\%},32.43\mathrm{\%}$37.84%,32.43%37.84 \%, 32.43 \%$37.84\mathrm{\%},32.43\mathrm{\%}$, and $43.24\mathrm{\%}$$43.24\mathrm{\%}$43.24%43.24 \%$43.24\mathrm{\%}$.
When considering only the number of cracks, it is observed that all dosages (DM-01, DM-02, and DM-03) achieve a reduction in the total number of cracks in the physical models, indicating that any of them is viable for use in concrete. Ordering their effectiveness in crack reduction from highest to lowest, DM-03 shows the greatest reduction, followed by DM-01, and finally DM-02.
The addition of DM-02 ( $1000\mathrm{g}/{\mathrm{m}}^3$$1000\mathrm{g}/{\mathrm{m}}^3$1000g//m^(3)1000 \mathrm{~g} / \mathrm{m}^{3}$1000\mathrm{g}/{\mathrm{m}}^3$ ) of polypropylene synthetic fiber to concrete slabs represents an approximate increase of $\mathrm{S}/.40$$\mathrm{S}/.40$S//.40\mathrm{S} / .40$\mathrm{S}/.40$ per cubic meter, equivalent to a $12-16\mathrm{\%}$$12-16\mathrm{\%}$12-16%12-16 \%$12-16\mathrm{\%}$ increase over the base cost of conventional concrete ( $\mathrm{S}/$$\mathrm{S}/$S//\mathrm{S} /$\mathrm{S}/$.
$250-330/{\mathrm{m}}^3$$250-330/{\mathrm{m}}^3$250-330//m^(3)250-330 / \mathrm{m}^{3}$250-330/{\mathrm{m}}^3$ ) (depending on the urban area where the construction takes place). Despite the initial additional cost, this secondary reinforcement significantly reduces the formation of plastic shrinkage cracks and improves surface durability, decreasing the need for early repairs or maintenance. Therefore, for local construction companies, the implementation of fiber-reinforced concrete can be economically advantageous in the medium term, extending the service life of slabs and pavements and reducing rehabilitation costs associated with cracking.

The graph shows the development of cracks in the concrete after 28 days of evaluation for four sample designs: MP (control concrete without fibers) and DM-01, DM-02, and DM-03, which incorporate different amounts of polypropylene fiber $(500,1000$$\left(500,1000\right.$(500,1000:}\left(500,1000\right.$(500,1000$, and $2000\mathrm{g}/{\mathrm{m}}^3$$2000\mathrm{g}/{\mathrm{m}}^3$2000g//m^(3)2000 \mathrm{~g} / \mathrm{m}^{3}$2000\mathrm{g}/{\mathrm{m}}^3$, respectively). The crack width remains practically constant at around $3-4\mathrm{mm}$$3-4\mathrm{mm}$3-4mm3-4 \mathrm{~mm}$3-4\mathrm{mm}$ in all designs. However, both the length and number of cracks decrease significantly with increasing fiber content: the control concrete (MP) exhibits the greatest crack length ( 443 mm ) and the highest number of cracks ( 37 ), while DM-02 and DM-03 show notable reductions, reaching $188-220\mathrm{mm}$$188-220\mathrm{mm}$188-220mm188-220 \mathrm{~mm}$188-220\mathrm{mm}$ in length and $21-25$$21-25$21-2521-25$21-25$ cracks, demonstrating that the addition of polypropylene fiber helps limit the appearance and propagation of cracks in the concrete.

Understanding the behavior of polypropylene synthetic fibers in concrete during the first hours of setting is a practical way to explain the mechanisms of evaporation reduction and, consequently, the risk of shrinkage cracking. Based on previous results, the presence and formation of cracks during the first hours of setting were evaluated in the Control Sample (MS) and in Design Sample 02 (DS-02), since the latter provided the greatest benefits to the concrete at the end of the 28-day curing period.
The evaporation rate test explains the concrete's ability to retain water during setting, evaluating the rate at which moisture is lost from the surface to the environment. This behavior is crucial because, during the first few hours, concrete is in a plastic state and is highly vulnerable to shrinkage and the formation of surface cracks.
The water evaporation rate test establishes a minimum limit for controlling water loss in concrete, which is $1.0\mathrm{kg}/{\mathrm{m}}^2\cdot \mathrm{h}$$1.0\mathrm{kg}/{\mathrm{m}}^2\cdot \mathrm{h}$1.0kg//m^(2)*h1.0 \mathrm{~kg} / \mathrm{m}^{2} \cdot \mathrm{~h}$1.0\mathrm{kg}/{\mathrm{m}}^2\cdot \mathrm{h}$ during the first hour of evaluation, according to ASTM C1579. This reference value allows us to determine if the concrete mix is losing moisture at a rate that could compromise its performance during initial setting. Furthermore, the standard specifies progressive control values: at 2 hours, the rate should exceed $2.0\mathrm{kg}/{\mathrm{m}}^2\cdot \mathrm{h}$$2.0\mathrm{kg}/{\mathrm{m}}^2\cdot \mathrm{h}$2.0kg//m^(2)*h2.0 \mathrm{~kg} / \mathrm{m}^{2} \cdot \mathrm{~h}$2.0\mathrm{kg}/{\mathrm{m}}^2\cdot \mathrm{h}$; at 3 hours, $3.0\mathrm{kg}/{\mathrm{m}}^2\cdot \mathrm{h}$$3.0\mathrm{kg}/{\mathrm{m}}^2\cdot \mathrm{h}$3.0kg//m^(2)*h3.0 \mathrm{~kg} / \mathrm{m}^{2} \cdot \mathrm{~h}$3.0\mathrm{kg}/{\mathrm{m}}^2\cdot \mathrm{h}$; and at 4 hours, $4.0\mathrm{kg}/{\mathrm{m}}^2\cdot \mathrm{h}$$4.0\mathrm{kg}/{\mathrm{m}}^2\cdot \mathrm{h}$4.0kg//m^(2)*h4.0 \mathrm{~kg} / \mathrm{m}^{2} \cdot \mathrm{~h}$4.0\mathrm{kg}/{\mathrm{m}}^2\cdot \mathrm{h}$. Meeting these limits ensures that the concrete retains the minimum amount of water necessary for cement hydration and reduces the risk of shrinkage cracking. Table 18 presents the average results of the two tests for the Control Sample (CS) and Design Sample 02 (DS-02).
The fiber-reinforced mix (DM-02) exhibited an average cumulative evaporation rate of $5.05\mathrm{kg}/{\mathrm{m}}^2\cdot \mathrm{ha}$$5.05\mathrm{kg}/{\mathrm{m}}^2\cdot \mathrm{ha}$5.05kg//m^(2)*ha5.05 \mathrm{~kg} / \mathrm{m}^{2} \cdot \mathrm{ha}$5.05\mathrm{kg}/{\mathrm{m}}^2\cdot \mathrm{ha}$ at 4 hours, compared to $6.32\mathrm{kg}/{\mathrm{m}}^2\cdot \mathrm{h}$$6.32\mathrm{kg}/{\mathrm{m}}^2\cdot \mathrm{h}$6.32kg//m^(2)*h6.32 \mathrm{~kg} / \mathrm{m}^{2} \cdot \mathrm{~h}$6.32\mathrm{kg}/{\mathrm{m}}^2\cdot \mathrm{h}$ for the control concrete (MP). This represents a $20.09\mathrm{\%}$$20.09\mathrm{\%}$20.09%20.09 \%$20.09\mathrm{\%}$ reduction in moisture loss for the mixes with polypropylene fibers. This result is consistent with the function of polypropylene fibers in disrupting capillary channels and distributing free water more evenly, thereby reducing its rapid migration to the surface and, consequently, the risk of shrinkage cracking during the initial hours of setting.
Analyzing cracking during the first few hours of setting helps to understand the initial benefits of crack reduction in concrete, since the material is still in a plastic state and highly susceptible to surface water loss. Evaluating the behavior of concrete at this critical stage allows for assessing the effectiveness of control measures, such as the incorporation of synthetic polypropylene fibers, which distribute internal stresses, reduce the evaporation rate, and limit the propagation of microcracks.

The tables show the data collected during the first four hours of curing, a period in which fresh concrete is most susceptible to surface cracking due to rapid water loss through evaporation. This stage is critical because the concrete has not yet developed sufficient internal strength, which favors the appearance and propagation of shrinkage cracks. The information obtained allowed for the creation of comparative graphs that represent the evolution of the concrete's behavior during this interval, facilitating the identification of trends in crack formation and growth over time. Thus, the results not only demonstrate the magnitude of the problem under normal conditions but also highlight the beneficial effect of incorporating polypropylene synthetic fibers as a strategy to control and reduce early cracking.