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Article

Study on the Compressive Stress–Strain Curve and Performance of Low-Slump Polypropylene Fiber Concrete after High Temperature

by
Bing Li
,
Wenbin Zheng
and
Yang Zhang
*
Department of Civil Engineering, Hainan University, Haikou 570228, China
*
Author to whom correspondence should be addressed.
Appl. Sci. 2023, 13(12), 7222; https://doi.org/10.3390/app13127222
Submission received: 22 April 2023 / Revised: 2 June 2023 / Accepted: 13 June 2023 / Published: 16 June 2023
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Abstract

:
This study aims to investigate the effect of high temperature on the mechanical properties of low-slump polypropylene fiber (PPF) concrete, and tests the tensile and compressive properties of 204 groups of low-slump PPF concrete with eight different dosages and four different lengths at normal temperature and after high temperature. The results of the compressive test showed that PPF can significantly improve the mechanical properties of concrete after high temperature when the fiber content is small, and the compressive strength of low collapse polypropylene fiber concrete after high temperature showed a tendency to rise and then fall at the same temperature with an increase of the fiber admixture. When the fiber content was 0.5 kg/m3, the compressive strengths of 3 mm, 9 mm, 15 mm and 19 mm reached their maxima, which were 9.65%, 11.33%, 7.90% and 2.87% higher than that of ordinary concrete, respectively. With an increase in fiber length, the effect of PPF on the compressive strength of concrete is not obvious. PPF at high admixture further increases the pore and air content in concrete, which decreases the compactness of the concrete, thus leading to a decrease in the compressive strength of the concrete. When the temperature was 800 °C and the fiber admixture was 5.0 kg/m3, the compressive strength of PPF concrete with different lengths reduced by 17.83%, 17.27%, 22.59% and 23.92%, respectively, compared to normal concrete. In addition, according to the results, the optimal combinations of strength at room temperature and after high temperature were 3 mm fiber length and 1.0 kg/m3 dosing and 9 mm fiber length and 0.5 kg/m3 dosing, respectively, which increased the compressive and tensile strengths by 17.15% and 25.72% at room temperature and by at least 6% and 20% after high temperature, compared to the concrete without fiber dosing. Moreover, the stress–strain constitutive equations of PPF concrete at normal temperature and after high temperature were established, which can be used for finite element simulation and related mechanical analysis of PPF after high temperature.

1. Introduction

In recent years, various FRP materials have emerged, and new materials applied to concrete have made significant progress. Among these, PPF concrete is a new type of composite material that improves toughness and fire resistance by adding fibers. It is less brittle than ordinary concrete and widely used in various civil and commercial buildings due to its simplicity of construction and affordability [1,2,3]. The frequent occurrence of fire incidents in recent years has caused significant harm to property and the safety of lives, and fires are recognized as major dangerous disasters. Fires in buildings can damage the performance of building materials under high temperatures, which necessitates in-depth research on the mechanical behavior of concrete under such conditions. The use of high-strength concrete is a direct method of improving the bearing capacity and durability of buildings. However, relevant research has shown [4,5,6] that high-strength concrete is highly susceptible to peeling, due to its high-density gelatinous matrix and internal pore structure, making it more prone to cracking under fire. The addition of PPF polymer to concrete can reduce this cracking phenomenon [7,8,9] and improve the durability of the material. Several studies have investigated the mechanical properties of PPF concrete under the influence of temperature. Özbay and Türker et al. [10] found that the bending strength of PPF concrete after exposure to high temperature was significantly lower than that of ordinary concrete. Dharanipathi and Arumairaj [11] found that the addition of PPF improved the flexural strength and crack resistance of concrete. Ding et al. [12] investigated the relationship between temperature and pore pressure of self-compacting concrete with different diameters and doses of polypropylene fibers. They found that fine PPF fibers could effectively alleviate pore pressure, and the pore pressures of specimens with low-dose fine fibers were lower than those of specimens with high-dose coarse fibers. Petrus et al. [13] found that the compressive strength of PPF concrete at the same temperature was much higher than that of non-fiber-reinforced concrete. They also observed that PPF could promote adhesion between cement slurry and aggregate. Shirsath and Yaragal [14] found that PPF concrete could improve surface cracks of specimens, and the addition of steel fibers and polypropylene fibers could increase the splitting tensile strength of concrete within a certain temperature range (400–600 °C). Wu et al. [15] discovered that the cooling method had an impact on the residual compressive strength of self-compacting PPF concrete after being exposed to high temperatures, and naturally cooled specimens had higher residual compressive strength than water-cooled specimens. Jameran [16] pointed out that, with a fixed volume fraction of 1.5%, the ratio of steel fibers to polypropylene fibers was 3:1, and the residual compressive strength after 400 °C was the highest. Additionally, increasing PPF content could reduce the occurrence of concrete spalling. Bosnjak et al. [17] found that adding steel fibers and polypropylene fibers to concrete resulted in fracture energy at least two orders of magnitude higher than that of the control group. Smarzewski [18] demonstrated that the internal thermal damage to ultra-high-performance concrete reinforced with polypropylene fibers originates from the effects of micro-pore pressure, thermal decomposition of hydration products, thermal conductivity differences of various components, and the formation of micro-cracks within the concrete. Amin et al. [19] noted that lightweight concrete containing 0.4% volume fraction of polypropylene fibers had a residual compressive strength of 76% at 400 °C compared to that at room temperature. Krishna and Kaliyaperumal [20] found that adding 1% volume fraction of polypropylene fibers was more effective in preventing concrete spalling but had a minimal impact on the bonding characteristics of concrete. Roy et al. [21] discovered that adding polypropylene fibers can significantly reduce the loss of tensile strength in high-strength concrete, and the mass loss rate is proportional to the fiber content. Chen et al.’s research [22] showed that adding polypropylene and steel fibers can improve not only the bonding performance, but also the mechanical properties, of an ultra-high-performance concrete (UHPC) repaired cementitious composite system at high temperatures. It can also inhibit the high-temperature bursting and spalling of concrete. Meanwhile, Qin et al.’s results [23] demonstrated that adding a 0.2% volume fraction of polypropylene fibers to beam specimens of ultra-high-performance concrete cured at room temperature can effectively reduce the bursting of the beam surface under fire conditions. Zhang and Tan [24] suggested that the aspect ratio of polypropylene fibers is the critical factor that affects the spalling effect of UHPC concrete. Thinner and longer polypropylene fibers are better at preventing spalling. When the fiber content is below 3 kg/m3, UHPC can be prevented from peeling, and the critical value of the aspect ratio of peeling is not less than 300. Self-compacting concrete (SCC) is a current research hotspot. Ning et al.’s research [25] showed that a small amount of polypropylene fiber can effectively inhibit the explosive spalling of self-compacting concrete. Moosaei et al. [26] found that, compared with steel and glass fibers, polypropylene fibers can more effectively reduce the slump of concrete, and the mechanical properties of polypropylene fiber concrete with a volume fraction of 0.5% are optimal after being exposed to 800 °C. Xu et al. [27] found that when the mixing ratio of polypropylene and steel fibers is 1:0.2, the dynamic splitting performance and tensile toughness of concrete at high temperatures can be significantly improved. Kencanawati et al. [28] showed that when the amount of added polypropylene fiber does not exceed 2.5 kg/m3, the alkaline components in the concrete decrease with increase in temperature, and the degree of decrease increases with the increase in the amount of polypropylene fiber. Zheng [29] pointed out that when the addition of polypropylene fiber was 0.25% volume fraction, the impact strength of foamed concrete increased by 300% compared to a blank control group. To reduce the bursting and peeling of concrete shield tunnel segments under fire and to improve durability, Zhang et al. [30,31,32,33,34,35] investigated the fire performance of concrete shield tunnel segments with polypropylene fibers and their mixtures. Krishna et al. [36] observed that the hybrid mixture of polypropylene and micro-steel fibers exhibited good impact resistance at high temperatures. Meena and Ramana [37] stated that adding 0.5% PPF significantly improved various mechanical properties of concrete at high temperatures.
In summary, research on the effect of high temperature on PPF concrete mainly focuses on the following: the inhibitory effect of PPF on the bursting phenomenon of different types of concrete (including ultra-high performance concrete (UHPC), Self-compacting concrete (SCC), lightweight concrete, etc.); the performance of PPF applied in actual structural components (such as reinforced concrete beam-slab structures, concrete shield tunnel lining structures, etc.); the mixed mechanical properties of PPF with other fibers. No studies were found on the three-factor coupling effect of PPF length, PPF dosage, and temperature on multiple samples. This study conducted mechanical research on PPF concrete with eight dosages and four lengths after high temperature, to more fully understand the working mechanism of PPF in concrete and fill the gap in related research. Regarding research on stress–strain curves of PPF concrete, studies related to PPF concrete subjected to high temperatures mainly demonstrate the characteristic changes in compressive strength and modulus of elasticity of PPF concrete after exposure to high temperatures. However, experimental data show a large dispersion, and the conclusions of related studies differ significantly, indicating a need for further research [38,39,40,41]. On actual construction sites, the slump test is a simpler and more direct performance indicator that can quickly provide a general understanding of the concrete mix. Modern concrete buildings are typically constructed using concrete batching plants for batching, concrete mixers for mixing and transportation, and concrete pumps for pouring into the specified location. This also requires testing for the concrete’s slump. Studies have shown [42] that the degree of slump has a correlation with the mechanical properties of concrete. The determination of the slump degree is measured according to the relevant provisions of the specification GB/T50080-2002 Standard for Test Methods for the Properties of Ordinary Concrete Mixes [43]. According to the provisions of GB50164-92 “Concrete Quality Control Standard” [44], the slump degree grade is divided into four levels, and low-slump concrete refers to concrete with a slump degree range of 10–40 mm. In the actual practice of production, concrete segregation and segregation should be avoided as much as possible, and the working properties of low-slump concrete happen to meet the requirements. As the stability and integrity of low-slump concrete are better than normal concrete, higher strength can still be obtained with reduced cement dosage [45]. In environments such as pavement construction and bridge construction, low-slump concrete is used in large quantities due to its advantages [46]. Most of the concrete studied in the literature has a slump greater than 50 mm and is generally concentrated above 100 mm, resulting in few studies on low-slump concrete and almost a void in the study of low-slump PPF concrete. In actual manufacturing, transportation, and pumping of low-slump concrete, adequate vibration and the addition of fibers are needed to ensure that the low-slump concrete meets the commonly used acceptance standards for slump concrete. With increasing attention to fire hazards, the mechanical properties of low-slump PPF concrete after high temperature need to be urgently addressed, and the principal structural relationship of low-slump PPF concrete after high temperature has more value for practical engineering applications and theoretical analysis. S tests of low-slump polypropylene fiber (PPF) concrete at room temperature and after high temperature with different admixtures and lengths were conducted, and the physical and mechanical properties of PPF concrete were compared and analyzed, based on the test results. Finally, the principal structural relationship of low-slump PPF concrete after high temperature was conclusively identified, based on the test data.

2. Experimental Overview

2.1. Raw Materials and Mix Proportions

The cement used in the experiment was “Tianya” PC32.5 cement from Hainan, and the detailed parameters of the cement are shown in Table 1. The coarse aggregate was graded crushed stone with a maximum particle size of 40 mm and an apparent density of 2600 kg/m3. Fine aggregate was selected as medium sand with a fineness modulus of 3.0 and an apparent density of 2700 kg/m3. The polypropylene fiber used was a monofilament fiber with a diameter of 80 μm, and the cross-section of the PPF under the scanning electron microscope is shown in Figure 1. The mechanical properties of PPF are shown in Table 2. The mix proportion of the PPF concrete was consistent with that of ordinary concrete. The fiber content of the PPF concrete was divided into three levels with three different lengths and eight levels with four different lengths, according to the different properties of the test. The specific mix proportions and grouping details are shown in Table 3, and the fiber lengths used are illustrated in Figure 2. Due to the large number of variables, the description of variables in the following text often uses a combination of letter abbreviations and numbers, as detailed in Table 4.

2.2. Preparation and Curing of Test Blocks

Compared to producing dry and hard concrete, which requires special compression molding equipment, the production of low-slump concrete is not limited to using specific instruments. It only requires changing the order of raw material addition and extending the mixing time. The test specimens consisted of 60 sets of polypropylene fiber-reinforced concrete prisms and 144 sets of polypropylene fiber-reinforced concrete cubes, with three specimens in each group and dimensions of 100 mm × 100 mm × 300 mm and 150 mm × 150 mm × 150 mm, respectively. Figure 3 provides 3D drawings of the two sizes of PPF concrete. The lengths and dosages of the added fibers in accordance with the specific experiments are provided in Table 3. When adding fibers to concrete, it is necessary to prevent fiber agglomeration and uneven mixing. A small amount of PPF can be added to the concrete mixer multiple times. After sufficient mixing, the slump of some concrete was measured using a slump tester. The slump tester was a conical cylinder with a small mouth diameter of 100 mm, a large mouth diameter of 200 mm, and a height of 300 mm. The results showed that the average slump was between 10 mm and 40 mm, as shown in Table 3. After the test was completed, the mixture was remixed in the mixer, poured into the mold, fully compacted using a fine tamping rod or a vibrating table, the surface smoothed, and then left stand at room temperature in an environment with a temperature of 20 ± 3 °C and humidity of ≥90% for 24 h before demolding. After marking the surface of the specimens, they were placed in water for 28 days for curing, and then taken out and placed in a ventilated and dry place for 14 days for static curing.

2.3. Experimental Apparatus and Equipment

The temperature heating device is depicted in Figure 4. It consisted of an RX3 model box-type resistance furnace that could operate at up to 380 V and with an output of nearly 24 kW. The furnace temperature could rise at a rate close to 20 °C/min and could reach a maximum temperature of 1280 °C. The furnace’s interior dimensions were 500 mm × 400 mm × 400 mm. Prism specimens were tested at 25 °C, 200 °C, 300 °C, 400 °C, 600 °C, and 800 °C, while cube specimens were tested at 25 °C, 600 °C, and 800 °C. The mechanical test employed a computerized data acquisition and control hydraulic servo universal testing machine with a 30 t capacity, as shown in Figure 5. Before conducting the uniaxial compression test, transverse and longitudinal strain gauges were attached to the center of the four sides of the prism specimen’s long edge. The test should be performed at an air temperature of 28 ± 3 °C and a humidity of 78 ± 5%. Before the strength test, the central axis of the concrete test piece should be aligned with the compressive central axis of the press, and the upper surface of the concrete test block should be parallel to the upper pressing plane of the press to prevent eccentric damage. The compressive test’s loading rate was set at 0.5 MPa/s, and the splitting tensile test was set to 0.05 MPa/s, in accordance with the relevant provisions of the Standard for Test Methods of Properties of Plain Concrete Mixes (GB/T 50080-2002) [43] and the Standard for Test Methods of Mechanical Properties of Plain Concrete (GB/T 50081-2002) [47], with reference to the methods used in Zhao’s test [48]. Splitting tensile test device diagram see Figure 6. To obtain more precise test results and the control test error, a force sensor was included between the test block and the indenter plane of the test machine in the uniaxial compressive test, as shown in Figure 7.

3. Test Results and Analysis

3.1. Axial Compression Test Results and Analysis

3.1.1. Peak Strain

The relationship curve between peak strain and temperature of PPF concrete after high temperature exposure is shown in Figure 8. The symbols in the figure represent the length and dosage of PPF fibers. See Table 4 for descriptions of the symbols. The peak strain of the PL0C0 ordinary concrete group at room temperature was 1.761 × 10−3, while the peak strain of the PL9C1.5 fiber reinforced concrete group at room temperature was 11.14% lower than that of the PL0C0 group. The peak strains of the other groups with different dosages and lengths were slightly higher. The group with the highest peak strain was PL3C1.5, which was 15.16% higher than that of the plain concrete group. It can be seen that under a certain amount of PPF fiber dosage and at a certain length, randomly distributed PPF fibers could achieve a certain toughening effect. When the temperature was between 200 °C and 300 °C, the peak strain slowly increased with the increase in temperature, and the peak strain of the PL0C0 concrete group was higher than that of the fiber reinforced concrete group. Among them, the peak strain of the PL9C1.5-T200 group was 20.8% lower than that of the PL0C0-T200 group, while the peak strains of the PL9C1.5-T300 and PL9C1.0-T300 groups were 19.05% and 25.58% lower than that of the PL0C0-T300 group, respectively. It was observed that the peak strain did not change much between 25 °C and 300 °C, which is because, as the temperature increases, the evaporation of free water in the cement paste accelerates the hydration of the cement paste, increases the density of the C-S-H gel structure, and causes the cement paste to shrink and produce high-strength siloxane [49,50]. The removal of free water is similar to steam curing, which accelerates the hydration of the cement, and repairs the damage inside the concrete. The reason for the lower peak strain of PPF concrete, than that of ordinary concrete, is analyzed as follows. PPF fibers melt at around 170 °C and vaporize at around 370 °C. The connecting holes formed by the melting of PPF may be transformed into micro-cracks, increasing the crack propagation path. As the temperature increases, the porosity inside the PPF concrete increases rapidly, and the crack propagation gradually transitions from micro-cracks to macro-cracks [51,52]. Therefore, when the temperature was below 400 °C, the peak strain of PPF concrete was smaller than that of ordinary concrete. When the temperature reached 400 °C, a significant increase in peak strain was observed. The peak strain of the PL3C1.0-T400 group was 11.11% higher than that of the group without fibers, while the peak strains of the other fiber-reinforced concrete groups were lower than that of the group without fibers. After the temperature exceeded 400 °C, the peak strain increased rapidly with increasing temperature. The growth rate of peak strain in the fiber-reinforced concrete group was greater than that in the group without fibers, and different combinations of fiber lengths and contents showed different growth trends. Overall, the longer the fiber length and the lower the content, the greater the peak strain of the concrete after high temperature. Compared with the group without fibers (PL0C0), the peak strain of the PL15C0.5 group after 400 °C increased the most, with an increase of 36.89% at 600 °C, while the peak strain of the PL3C1.5 group decreased by 9.58%. An increase in porosity, the connectivity of micro-cracks, and the local aggregation of high-density fibers can lead to a decrease in the internal cohesion of concrete, inadequate stress transfer paths, and a decrease in toughness [18]. Within the condition of ensuring that the fibers do not break, the anchorage length of the fibers affects the bonding force between the concrete matrix. Short polypropylene fibers and high polypropylene fiber content can lead to the above situation.

3.1.2. Peak Stress

The relationship between peak stress and temperature of PPF concrete after high temperature is shown in Figure 9. At room temperature, the peak stress of ordinary concrete PL0C0 was the lowest, which was 30 MPa. When the temperature was below 300 °C, the peak stress always decreased with increase of temperature, and the addition of PPF of any dosage and length was beneficial to improve the peak stress of concrete. The most significant improvement s observed in the PL3C1.0 and PL3C1.5 groups, with an average increase of peak stress by 19.53% and 19.60%, respectively, compared to the peak stress of the group without fiber-reinforced concrete. The reason for this is that when the temperature is below 170 °C, the addition of PPF and the cement paste in concrete form a complex three-dimensional network structure, which enhances the bridging and anchoring effects between the components of the concrete, thereby buffering and absorbing energy generated by external forces, to a certain extent. When the temperature is between 170 °C and 300 °C, the PPF melts, causing an increase in the porosity of concrete, which increases the paths for water vapor to escape along, thereby reducing the pore pressure and lowering the extension of micro-cracks caused by high steam pressure [53]. This indicates that the addition of fibers has a promoting effect on stress at lower temperatures. When the temperature was higher than 300 °C, the peak stress of most PPF concrete groups decreased more rapidly with increase in temperature, and the peak stress of fiber-reinforced concrete gradually became lower than that of ordinary concrete. The reason for this phenomenon is that the increase in residual porosity volume significantly reduces the strength of the concrete. After the temperature exceeds 300 °C, the holes left by completely melted and vaporized PPF increase the paths of micro-crack extensions, leading to an increase in residual pore volume. At the same time, after 500 °C, the chemical composition of concrete decomposes, leading to an increase in pore volume. The data results showed that, when the PPF content was 0.5 kg·m−3 and the length was 9 mm, the peak stress after 300 °C was, on average, 6.49% higher than that of ordinary concrete.

3.1.3. Elastic Modulus

Due to the influence of temperature on the elastic modulus of concrete after exposure to high temperatures, there is no obvious elastic phase. Therefore, the secant modulus of elasticity Ec,T is calculated as 40% of the slope of the line connecting the origin of the stress–strain curve to the peak stress point. The relationship between the elastic modulus and temperature is shown in Figure 10. At room temperature, the elastic modulus of PPF concrete was higher than that of ordinary concrete PL0C0, and the increase in elastic modulus was particularly significant, with the largest increase observed in PL3C1.5 and PL15C1.5, which had increased ratios of 21.65% and 17.42%, respectively. The addition of PPF could effectively suppress the cracking of concrete, and there was a positive correlation between the increase in PPF content and length and the elastic modulus. With an increase in temperature, the elastic modulus of PPF concrete with different contents and lengths decreased. However, there was no significant correlation between the content and length of fibers and the change in the elastic modulus. The presence of fibers at temperatures between 200 °C and 300 °C reduce the elastic modulus of concrete, as high temperatures, above 170 °C, cause the PPF to melt, increasing the internal porosity and weakening the cross-section of the concrete. The average loss of elastic modulus at 300 °C was 44.97%. The critical temperature at which the elastic modulus decreased most significantly was 400 °C, where it decreased by 70% compared to that at room temperature [54]. The elastic modulus of fiber-reinforced concrete at 400 °C was higher than that of ordinary concrete, with the highest increase in strength reaching 64.84%. When the temperature rose to 600–800 °C, the influence of fiber content and length on the elastic modulus could be ignored, as, at high temperatures, the development of concrete cracks is dominated by macroscopic cracks, and the role of the internal micro-structure disappears. At higher temperatures, the deterioration of the concrete material itself makes the elastic modulus maintain a relatively stable value, of only 1% to 3% of that at room temperature.

3.1.4. Poisson’s Ratio

The Poisson’s ratio νc,T of PPF concrete is defined as the ratio of transverse strain to longitudinal strain. The curve of the Poisson’s ratio νc,T with respect to temperature T is shown in Figure 11. At room temperature, the bridging effect of fibers slows down the propagation of cracks, and increases the deformation capacity of concrete, and, therefore, the Poisson’s ratio of PPF concrete is higher than that of ordinary concrete. The Poisson’s ratio of the ordinary concrete group was 0.206, and the highest Poisson’s ratio was in the PL3C0.5 group, which was 11.31% higher than that of ordinary concrete. At 200 °C, the Poisson’s ratio of all groups showed a decreasing trend, and the decrease in Poisson’s ratio in fiber concrete was less than in ordinary concrete. This is because the continuous evaporation of free water in PPF concrete promotes reaction between water and cement particles, fills the micro-cracks inside, strengthens the aggregation between concrete components, and reduces the transverse strain. When the temperature was below 300 °C, the fluctuation range of the Poisson’s ratio of PPF concrete and ordinary concrete was within 12.73%. After the temperature reached 400 °C, the Poisson’s ratio increased rapidly with temperature, and the dispersion of the Poisson’s ratio of different PPF contents and lengths increased with temperature. The reason for this is that higher temperatures have a greater impact on the Poisson’s ratio, and different types of PPF have different degrees of weakening effect on the concrete section. In addition, PPF melts and gasifies at high temperatures, releasing some of the internal thermal stress, which makes the change in Poisson’s ratio more complex as the temperature increases, although, overall, it tends to increase. From the graph it can be observed that, after the high temperature of 400 °C was reached, relatively stable maximum and minimum Poisson’s Ratio appeared in the PL15C1.0 and PL15C0.5 groups, respectively, which were 5.7% higher and 7.37% lower than the Poisson’s ratio of ordinary concrete, respectively.

4. Test Results and Analysis of Compressive Strength

The relationship between PPF admixture and compressive strength of concrete at room temperature is shown in Figure 12. The number at the end indicates the average compressive strength that could be achieved by a specimen. It can be seen that the PPF admixture significantly increased the compressive strength of concrete. The compressive strength decreased as the PPF fibers became longer for the same PPF content, while an increase in PPF content for the same PPF fiber length led to an initial increase and then a decrease in the compressive strength. The peak point of increase occurred at the lower PPF content, which was in agreement with the findings of Ferreira et al. [55]. The appropriate amount of PPF fiber length and admixture can increase the compressive strength of concrete because the bridging effect of PPF is greater than the negative effect of porosity. A small amount of admixture and short length of PPF fibers can fill the internal pores of concrete. However, an increase in fiber length and admixture leads to a decrease in the apparent density and an increase in porosity, which results in a decrease in strength. Additionally, too long fibers may form tangles inside, which decreases the uniformity of distribution, also increases porosity. The compressive strengths of PPF concrete with PPF fiber lengths of 3 mm and 9 mm were highest at a PPF admixture of 1 kg/m3, which increased by 17.15% and 14.85%, respectively, compared to ordinary concrete. The compressive strength of PPF concrete with PPF fiber lengths of 15 mm and 19 mm reached a maximum at a PPF admixture of 0.5 kg/m3, which increased by 11.25% and 11.2%, respectively. With an increase in PPF admixture, the compressive strength of 19 mm long PPF concrete was initially lower than that of ordinary concrete, while the compressive strength of 15 mm long PPF concrete was only 1.37% higher than that of ordinary concrete. When the PPF admixture amount reached 5 kg/m3, the compressive strength of PPF concrete with 9 mm length was 2.67% lower than that of ordinary concrete, while the compressive strength of PPF concrete with 3 mm length was 6.52% higher than that of ordinary concrete. This indicates that the effect of polypropylene fiber admixture on the mechanical properties of concrete after high temperature is more significant compared to the fiber length, due to the greater porosity brought about by the large admixture, compared to that brought about by the length [56].
The effect of PPF admixture on the compressive strength of concrete at high temperatures is illustrated in Figure 13. After being exposed to temperatures of 600 °C and 800 °C, relatively few cracks were observed on the surface of PPF concrete specimens. This is largely due to the fact that PPF, after melting and vaporizing at high temperatures, creates many holes inside the concrete, increasing its internal connectivity. As a result, water vapor and heat can escape more easily, reducing vapor pressure and providing more free space. This also acts as a thermal shock absorber, reducing the damage to the micro-structure of the concrete [57]. In contrast, the strengths of plain concrete after being exposed to maximum temperatures of 600 °C and 800 °C were only 68% (28 MPa), 35% (14.3 MPa), and 22% (9.1 MPa) of that at room temperature. The compressive strength of PPF concrete showed a trend of increasing and then decreasing with increase of the fiber admixture, except for the compressive strength of concrete with a fiber length of 9 mm, which reached its maximum with the same admixture. The law of compressive strength follows a decreasing trend with the increase of length. This is likely because the pores of PPF after high-temperature melting and vaporization cause an increase in porosity, which reduces the area of the concrete matrix subjected to load. Moreover, the PPF pores increase the path of micro-crack expansion, causing the strength of concrete after high temperature to be much lower than that of concrete at normal temperature. Increasing fiber length leads to higher porosity and larger capillaries, which weaken the effective load-bearing cross-sectional area of concrete. Similarly, increasing the number of fibers also leads to higher porosity, which weakens the effective load-bearing area, while providing more paths for micro-cracks to develop. As shown in Figure 13a, the maximum compressive strength was achieved for 3 mm, 9 mm, 15 mm, and 19 mm when the fiber admixtures were 0.5 kg/m3, which is 4.21%, 6.29%, 0.86%, and 0.32% higher than that of normal concrete, respectively. The compressive strength reduced by 17.64%, 15.43%, 24%, and 27.04% at a 5.0 kg/m3 fiber admixture. Figure 13b shows that the residual strength of PPF concrete after 800 °C was consistent with that after 600 °C. The effect of PPF type showed less dispersion in strength, and the trend of the curve was closer, indicating that the effect of PPF type on the compressive strength of concrete kept decreasing at higher temperatures. The macro-cracks which developed from micro-cracks and the calcification damage of the material are the main causes of the decrease in strength. When the fiber content is small, PPF can significantly improve the mechanical properties of concrete after high temperature. The compressive strength of low collapse polypropylene fiber concrete after high temperature showed a trend of rising and then falling at the same temperature with increase in fiber admixture. When the fiber admixture was 0.5 kg/m3, the compressive strengths of 3 mm, 9 mm, 15 mm and 19 mm reached their maxima of 9.65%, 11.33%, 7.90% and 2.87%, representing improvement over ordinary concrete, The effect of PPF on the compressive strength of concrete due to increase in fiber length was not obvious. According to the literature [58], the residual strength of ordinary PPF-free concrete is highest when exposed to high temperatures. However, the conclusion from literature [53] that the variation of PPF type has an insignificant impact on the fluctuation of residual compressive strength, differs significantly from the conclusion of the low collapse degree PPF concrete tests in this paper. In addition, the literature [59,60] has shown that the compressive strength of ordinary PPF concrete with a PPF admixture of 3.6 kg/m3 is higher than that of PPF concrete. The conclusion that the compressive strength of concrete is higher than that of PPF concrete slightly differs from the results of this paper, which indicate that different collapse degrees have inconsistent effects on the performance of PPF concrete. Therefore, the study of low collapse degree in this paper is practically and realistically significant. In the present experimental study, the residual compressive strength of PPF concrete significantly decreased when the admixture amount exceeded 0.5 kg/m3, regardless of fiber length, and the rate of strength decrease significantly accelerated as the fiber length increased. The maximum residual compressive strength was achieved with a dosing rate of 0.5 kg/m3 and a fiber length of 9 mm, which differs greatly from the study of PPF concrete with conventional collapse at room temperature. The research in this paper shows that PPF can significantly improve the mechanical properties of concrete after high temperature when the fiber content is small under high temperature conditions, and the effect of high dosing of PPF on the mechanical properties of concrete after high temperature is more significant. This is consistent with the change of compressive strength at room temperature.

5. Tensile Splitting Test Results and Analysis

The splitting tensile strength results for plain concrete and PPF concrete at room temperature are shown in Figure 14, and the numbers in the bars represent the maximum splitting tensile strengths that the specimens could reach. It can be seen from the graph that the curve trend of tensile strength at lower temperatures was consistent with compressive strength. As the PPF content increased, the tensile strength initially increased, followed by a decrease. The tensile strength of plain concrete at room temperature was 3.11 MPa, and the peak tensile strengths of PPF, with lengths of 15 mm and 19 mm, were is achieved at a smaller dosage (0.5 kg·m−3). The peak tensile strength of 3 mm and 9 mm PPF concrete occurred at a higher dosage (1.0 kg·m−3), due to the shorter fiber length. Moreover, the curve shows that shorter fiber length resulted in a more significant improvement in tensile strength. The peak tensile strengths of PPF concrete at room temperature were PL3C1.0, PL9C1.0, PL15C0.5, and PL19C0.5, respectively. Compared to the compressive strength of ordinary concrete, they increased by 25.72%, 18.33%, 5.14%, and 0.64%, respectively.
The mechanism underlying the above phenomena needs clarification. The compactness of the internal structure of concrete, the tightness of the connection between various components inside the concrete, the number of defects, and the number of micro-cracks are all key factors affecting tensile strength. The three-dimensional mesh structure formed by PPF [61]. and the concrete colloid. can bridge the internal cracks of the concrete, effectively weaken the stress concentration at the crack tip, redistribute the stress, and change the crack direction, delaying the rate of micro-crack development [62,63,64] and effectively improving the splitting tensile strength of PPF concrete. The effect of fiber content on porosity is negligible. As dosage increases, the internal porosity increases, and the increase in fiber length also leads to a slight increase in porosity, providing more paths for crack propagation. Therefore, with an increase in fiber dosage, the compressive strength first increases and then decreases. However, the decrease in compressive strength is smaller than the effect of dosage. Short PPF is recommended for actual engineering applications under the same conditions.
The splitting tensile strength test results for polypropylene fiber (PPF) reinforced concrete after exposure to high temperatures are shown in Figure 15. The tensile strengths of PPF concrete at 600 °C and 800 °C were approximately 1/66-1/60 and 1/70-1/90, respectively, of the residual compressive strength of ordinary concrete at room temperature. The curves for 3 mm and 9 mm length PPF concrete after high-temperature exposure show an initial increase followed by a decrease in tensile strength with increasing fiber dosage, which reached a maximum at a dosage of 0.5 kg·m−3. The fiber content had the largest effect on the 9 mm length specimens, with an increase in strength of 0.54 MPa and 0.42 MPa at 600 °C and 800 °C, respectively. For the 15 mm and 19 mm length specimens, the splitting tensile strength decreased with increasing fiber dosage, indicating that longer lengths had a more negative effect on tensile strength. The overall decrease in splitting tensile strength from 600 °C to 800 °C was approximately 20%, indicating further deterioration of the internal structure of the concrete and increased porosity, due to the decrease in the bonding ability of the C-S-H gel. The significant decrease in splitting tensile strength under high-temperature conditions can be attributed to the coarsening effect of temperature on the pore distribution [65,66,67], which may cause pores resulting from melting and vaporization.

6. Analysis of Variance (ANOVA)

To further investigate the strength effects of temperature, polypropylene fiber (PPF) length, and PPF content, a three-factor analysis of variance was performed, and the results are shown in Table 5. The three-factor analysis of variance was used to study the effects of PPF content, PPF length, and temperature on the strength. From Table 5, it can be seen that PPF content, PPF length, and temperature were significant (F = 47.924, p = 0.000 < 0.05; F = 73.448, p = 0.000 < 0.05; F = 24410.222, p = 0.000 < 0.05), indicating that the main effects existed and that PPF content, PPF length, and temperature had a differential effect on strength. Based on the size of the F-value, it can be determined that the order of the influencing factors was temperature > PPF length > PPF content. Under conditions where PPF content, PPF length, and temperature were significant, the significance of the two-way interaction between them was explored. The results showed that the interaction of PPF content × PPF length, PPF content × temperature, and PPF length × temperature (F = 3.229, p = 0.040 < 0.05; F = 12.614, p = 0.000 < 0.05; F = 7.021, p = 0.002 < 0.05) were all significant, and the significance ranking was PPF content × temperature > PPF length × temperature > PPF content × PPF length. It can be seen that the significance of the interaction related to temperature was the most obvious, and the interaction of PPF content × temperature was the most significant. The comprehensive ranking shows that temperature > PPF length > PPF content > PPF content × temperature > PPF length × temperature > PPF content × PPF length. Figure 16, Figure 17 and Figure 18 show the mean square histograms under each influence parameter, and the values at the top of the histograms represent the mean values of compressive strength, from which it can be seen that the strength variation was not particularly obvious under the influence of PPF admixture and PPF length.

7. Stress–Strain Behavior of Low Slump PPF Concrete after High Temperature Exposure

7.1. Stress–Strain Curves of Polypropylene Fibers with Different Dosages and Lengths after High Temperature Exposure

This section only studies the stress–strain curves of low-dosage (dosage less than, or equal to, 1.5 kg/m3) PPF concrete. This is because the research on peak compressive strength and peak strain in this paper shows that the negative effect of PPF on concrete is significant with high dosage, and the study of stress–strain curves of high-dosage PPF concrete is not realistic and does not meet actual production needs. The stress–strain curve of PPF concrete with temperature changes is shown in Figure 19. Compared to ordinary concrete, the stress–strain curve for PPF concrete is sharper. With increasing temperature, the most noticeable effect is the decrease in peak stress. The curve progresses forward, and the peak strain increases as the peak stress decreases. At high temperatures, the curve takes on a hump-like shape. The stress–strain curve for PPF concrete at different dosing levels and lengths at the same temperature can be compared to the stress–strain curve for PPF concrete at the same dosing level, which tends to flatten out more as the length is extended. The increase in the area enclosed by the curve indicates that its ability to absorb external energy also increased. The stress–strain curve for PPF concrete at the same length also tended to flatten out with increased dosing levels, and the area enclosed by the curve and strain tended to become larger. In summary, increasing fiber content and length enhances the instantaneous impact of concrete energy to a certain extent, improving ductility. According to the literature [68], 300–400 °C is a turning point where the trend of change accelerates due to increased internal hydration, complete evaporation of free water, and gradual decomposition of crystalline water. Between 25 °C and 300 °C, the temperature effect produced less temperature stress, resulting in fewer internal micro-cracks. After 400 °C, the curve tended to flatten out. After 600 °C, the peak stress dropped to about 35% of that at room temperature, and the curve tended to flatten out overall. After 800 °C, the peak point shifted down to almost the limit, and the peak stress was only a few MPa.... The curve characteristics of PPF concrete were basically similar to those of ordinary concrete. Overall, the presence of PPF increased the area enclosed by the curve in relation to the horizontal axis and significantly enhanced the energy absorption rate compared to normal concrete. After high temperature exposure at 800 °C, the PL9C0.5 group had the highest peak residual stresses of 12.7 MPa and 4.8 MPa, respectively, while the rest of the PPF concrete specimens, with different dosing levels and lengths, had significantly lower peak stresses.

7.2. Compressive Stress–Strain Curve Equation

The mathematical expressions for the concrete stress–strain curve have been studied and proposed by many scholars and national regulations [69,70,71]. The curve is generally divided into two parts, including the ascending part and the descending part. The mathematical function expressions generally include a polynomial, a rational fraction, power function, exponential function, and combination of trigonometric functions. As mentioned earlier, the presence of fibers can improve the elastic modulus and compressive strength of concrete to some extent. Therefore, in this paper, the ascending part of the curve was fitted using a polynomial function, and the descending part was fitted using a rational fraction function. The basic equation for fitting the stress–strain curve was based on the curve proposed by Zhenhai Guo [69], and the mathematical expression is shown in Equation (1):
α x + 3 − 2 α x 2 + α − 2 x 3 ( 0 ≤ x ≤ 1 ) x β ( x − 1 ) 2 + x x ≥ 1
where y = σ/σc(T), x = ε/εc(T), σc(T) represents the peak stress at temperature T, and εc(T) represents the peak strain at temperature T. Value α represents the ratio of the initial tangent modulus of the curve to the secant modulus at the peak point, and its value range is 1 < α < 5/3. β is related to the area of the curve and the strain axis envelope of the descending segment, and its value range is β > 0.

7.3. Fitting Results

The parameters α and β are the shape parameters of the curve. Parameter α was calculated from the ratio of the cutline modulus to the tangent modulus after high temperature in the above section, and the value of β was obtained from the falling section of the measured stress–strain curve by curve fitting. Nonlinear curve fitting was achieved by the fitting function in OriginPro software developed by OriginLab. The fitted α and β values were obtained by the custom function, and the fitted R2 values were both close to 1, indicating that the curve proposed by Zhenhai Guo [69] could simulate the stress–strain curve of low slump PPF concrete with different lengths and admixtures very well. To make the equations more concise, the α and β values derived from fitting at different temperatures were used for secondary fitting to obtain the α, β, and temperature-dependent parametric equations. The R2 of the secondary fitting was close to 1, and the product of the R2 values of the two fits was also close to 1. The fitting process cannot be listed in detail, due to the space limitation of the article. The doping amounts and lengths of different PPF parameter values were fitted after high temperature, and the specific expressions are shown in Equation (2), which utilized temperature T value values between 25 °C and 800 °C. All gradually decreased with increasing temperature, while showing a trend of first increasing and then decreasing, indicating that the ability to absorb energy first weakened and was then slightly enhanced. The model also considers the change pattern of the upper and lower sections after high temperature, which can be used for the whole process of PPF finite element simulation of concrete structure after high temperature. Table A1 shows the correlation coefficients of the values of parameters α and β with PPF admixture and length, and also see Appendix A. The table shows that the correlation coefficients of α and β values were three each, and the fitted correlation coefficients R2 were close to 1.0.
α = x T − 25 800 2 + y T − 25 800 + z β = u T − 25 800 2 + v T − 25 800 + w

8. Conclusions

In general, the addition of PPF enhanced the Poisson’s ratio, peak strain, peak stress, and elastic modulus of concrete at room temperature. In comparison to regular low-slump concrete, the most considerable enhancement in Poisson’s ratio was observed in the PL3C0.5 group, whereas the most substantial improvements in peak strain, peak stress, and elastic modulus were seen in the PL3C1.5 group, with enhancements of 11.13%, 15.6%, 19.6%, and 21.65%, respectively.
The changes in several parameters of Poisson’s ratio, peak strain, peak stress, and modulus of elasticity after high temperature are related to the amount and length of PPF admixture and depend on the change in porosity, release of vapor pressure, and the degree of material deterioration. The PL15C0.5 group had the maximum peak strain after 600–800 °C, with an increase of 36.66% in the average peak strain compared to the fiber-free concrete group, while the minimum was found in the PL3C0.5 group with a 7.17% decrease in average peak strain, compared to the fiber-free concrete group. This indicates that longer PPF has a toughening effect on concrete at low admixture levels, and the peak strains of PPF concrete all increased to varying degrees after high temperatures. The largest increase in peak stress after 600 °C was in the PL9C0.5 group, which was 6.70% higher than the fiber-free concrete group, and the largest decrease was in the PL9C1.5 group, which was 29.41% lower. Overall, the presence of PPF reduces the peak stress of concrete, and the weakening effect brought about by the increase in content is more obvious than the weakening effect produced by the increase in length. A significant weakening of the modulus of elasticity occurred at 400 °C. In contrast, the addition of fibers was able to increase the modulus of elasticity of the concrete, to some extent, with the degree of reduction and increase depending on the change in porosity due to PPF. The Poisson’s ratio increased by 5.8% and decreased by 8.68%, respectively, compared to the fiber-free concrete.
The compressive strength and splitting tensile strength of PPF concrete at room temperature were significantly influenced by both the lengths of fibers and the amounts of admixture. The strength exhibited a decreasing trend with increasing PPF length. At an admixture amount of 5.0 kg/m3, the fiber specimens with a length of 19 mm showed the most significant drop, with a compressive strength drop of 8.2% compared to normal concrete, while the effect of admixture on strength demonstrated an initial increase followed by a decrease with higher admixture levels. The maximum compressive strength and splitting tensile strength were achieved at 48.5 MPa and 3.9 MPa, respectively, with a PPF fiber length of 3 mm and an admixture amount of 1.0 kg/m3. This resulted in a strength increase of 17.15% and 25.72% compared to concrete without PPF.
The change in compressive and splitting tensile strengths of PPF concrete under high temperature follows the same pattern as that at room temperature. Under high temperature conditions, PPF with smaller content can significantly improve the mechanical properties of concrete after high temperature. The compressive strength of low collapse polypropylene fiber concrete after high temperature shows a trend of rising and then falling at the same temperature with increase in the fiber admixture. When the temperature wass 800 °C and the fiber admixture was 0.5 kg/m3, the compressive strengths of 3 mm, 9 mm, 15 mm and 19 mm reached their maxima of 9.65%, 11.33%, 7.90% and 2.87% over ordinary concrete. The effect of PPF on the compressive strength of concrete was not obvious with the increase of fiber length, and the rate of strength reduction in PPF concrete with a large admixture was much higher than that caused by the length of PPF. The maximum compressive and tensile strengths were achieved with a PPF admixture of 0.5 kg/m3 and a length of 9 mm, resulting in a 6.29% increase in compressive strength and a 28.57% increase in tensile strength at 600 °C, and an 11.33% increase in compressive strength and a 20% increase in tensile strength at 800 °C, compared to normal concrete.
Based on Zhenhai Guo’s stress–strain model for concrete, we developed full-curve principal structural equations for the stress–strain of PPF concrete at both room temperature and high temperature. Our results show that the stress–strain curve model proposed by Zhenhai Per can be used to fit the stress–strain curve of low-slump PPF concrete after exposure to high temperatures. The fitting method takes into account the effects of temperature, PPF admixture, and PPF length on the two important curve parameters α and β. Finally, the normalized fitting produces equations and tables that relate α and β to temperature, PPF content, and PPF length, which can be used to obtain accurate stress–strain curves for PPF concrete at specific temperatures, PPF contents, and lengths.

Author Contributions

Project administration, supervision and writing—review & editing, B.L.; Formal analysis, investigation and writing—original draft, W.Z.; funding acquisition and resources, Y.Z. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by National Nature Science Foundation of China grant number 51768017.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data used to support the findings of this study are included within the article.

Conflicts of Interest

The authors declare no conflict of interest.

Appendix A

Table
Table A1. Coefficient between parameter values α, β and temperature T.
Table A1. Coefficient between parameter values α, β and temperature T.
CoefficientPL0C0PL3C0.5PL3C1.0PL3C1.5PL9C0.5PL9C1.0PL9C1.5PL15C0.5PL15C1.0PL15C1.5
αx0.0340.7140.061.388−0.19−0.25−0.100.0640.251−0.47
y−1.46−2.04−1.15−2.42−0.11−1.09−1.04−1.36−1.16−40.25
z1.721.701.511.851.591.551.491.61.571.47
βu−20−27.94−0.90−11.88−7.025.425.26−13.5−8.0615.47
v26.9139.536.299.479.46−4.91−4.7612.3414.82−16.9
w5.757.28.176.035.9512.912.59.726.5013

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Figure 1. The section of PPF. (a) shows the distribution of polypropylene fibres in concrete within the concrete under SEM at a magnification of 500× and (b) shows the cross-sectional morphology of the polypropylene fibres under SEM at a magnification of 1500×.
Figure 1. The section of PPF. (a) shows the distribution of polypropylene fibres in concrete within the concrete under SEM at a magnification of 500× and (b) shows the cross-sectional morphology of the polypropylene fibres under SEM at a magnification of 1500×.
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Figure 2. Display diagram of different fiber lengths.
Figure 2. Display diagram of different fiber lengths.
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Figure 3. Three dimensional drawing of sample size.
Figure 3. Three dimensional drawing of sample size.
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Figure 4. RX3 model box-type resistance furnace.
Figure 4. RX3 model box-type resistance furnace.
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Figure 5. Floor plan of the universal testing machine.
Figure 5. Floor plan of the universal testing machine.
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Figure 6. Splitting tensile test device diagram.
Figure 6. Splitting tensile test device diagram.
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Figure 7. Uniaxial compressive test device diagram.
Figure 7. Uniaxial compressive test device diagram.
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Figure 8. Relationship between peak strain and temperature.
Figure 8. Relationship between peak strain and temperature.
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Figure 9. The relationship between peak strain and temperature.
Figure 9. The relationship between peak strain and temperature.
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Figure 10. The relation between elastic modulus and temperature.
Figure 10. The relation between elastic modulus and temperature.
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Figure 11. The relation between Poisson’s ratio and temperature.
Figure 11. The relation between Poisson’s ratio and temperature.
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Figure 12. Compressive strength of PPF concrete at ambient temperature.
Figure 12. Compressive strength of PPF concrete at ambient temperature.
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Figure 13. Compressive strength of PPF concrete after elevated temperatures.
Figure 13. Compressive strength of PPF concrete after elevated temperatures.
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Figure 14. Split tensile strength of PPF concrete at ambient temperature.
Figure 14. Split tensile strength of PPF concrete at ambient temperature.
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Figure 15. Split tensile strength of PPF concrete after elevated temperatures.
Figure 15. Split tensile strength of PPF concrete after elevated temperatures.
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Figure 16. PPF Dosage & PPF Length.
Figure 16. PPF Dosage & PPF Length.
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Figure 17. PPF Length & Temperature.
Figure 17. PPF Length & Temperature.
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Figure 18. PPF Dosage & Temperature.
Figure 18. PPF Dosage & Temperature.
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Figure 19. The full stress–strain curve of PPF concrete specimens at different temperatures.
Figure 19. The full stress–strain curve of PPF concrete specimens at different temperatures.
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Table
Table 1. Cement Specifications.
Table 1. Cement Specifications.
Coagulation Time (min)Compressive Strength (MPa)Flexural Strength
(MPa)		Stability of ConcreteSpecific Surface Product (m2·kg−1)
early
condensate		end
condensate		3 d28 d3 d28 dqualified350
14027223.553.14.38.7
Table
Table 2. Physical and mechanical properties of PPF.
Table 2. Physical and mechanical properties of PPF.
Length (mm)Diameter (μm)Density (g·cm−3)Tensile Strength (MPa)Elastic Modulus (GPa)Melting Point (°C)
3, 9, 15, 19800.912102.2165
Table
Table 3. Concrete Mix Ratio and PPF parameter.
Table 3. Concrete Mix Ratio and PPF parameter.
Test CategoryWater
(kg/m3)		Cement
(kg/m3)		Sand
(kg/m3)		Stone
(kg/m3)		PPF Content
(kg/m3)		PPF Length
(mm)		Test Block Size (mm)
Uniaxial Compression Test18539460112200/0.5/1/1.53/9/15100 × 100 × 300
Compressive strength test18539460112200/0.5/1/1.5/
2/2.5/3/4/5		3/9/15/19150 × 150 × 150
splitting tensile test18539460112200/0.5/1/1.53/9/15/19150 × 150 × 150
Table
Table 4. Variable Symbol Description.
Table 4. Variable Symbol Description.
Variable SymbolVariable Description
PL0C0Blank control group without fibers
PL3C0.5PPF concrete with a length of 3 mm and a dosage of 0.5 kg/m3. The other lengths and dosage of PPF concrete are represented in the same way.
PL3C0.5-T200After experiencing a peak temperature of 200 °C, PPF concrete with a length of 3 mm and a dosage of 0.5 kg/m3 was used. The representation method for PPF concrete at other temperatures was the same.
εc,TPeak strain
fc,TPeak stress
Ec,TElastic modulus
νc,TPoisson’s ratio
Table
Table 5. Three-factor ANOVA results.
Table 5. Three-factor ANOVA results.
Source of DifferenceSquare SumdfMean SquareFp
Intercept31,684131,684246,266.4270.000 **
PPF Dosage12.33226.16647.9240.000 **
PPF Length28.34939.4573.4480.000 **
Temperature6281.11223140.55624,410.2220.000 **
PPF Dosage × PPF Length2.49360.4153.2290.040 *
PPF Dosage × Temperature6.49241.62312.6140.000 **
PPF Length × Temperature5.41960.9037.0210.002 **
Residual1.544120.129
Note: In p-values, “*” indicates a more significant effect of this factor on intensity and “**” indicate a highly significant effect of this factor on intensity.
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Li, B.; Zheng, W.; Zhang, Y. Study on the Compressive Stress–Strain Curve and Performance of Low-Slump Polypropylene Fiber Concrete after High Temperature. Appl. Sci. 2023, 13, 7222. https://doi.org/10.3390/app13127222

AMA Style

Li B, Zheng W, Zhang Y. Study on the Compressive Stress–Strain Curve and Performance of Low-Slump Polypropylene Fiber Concrete after High Temperature. Applied Sciences. 2023; 13(12):7222. https://doi.org/10.3390/app13127222

Chicago/Turabian Style

Li, Bing, Wenbin Zheng, and Yang Zhang. 2023. "Study on the Compressive Stress–Strain Curve and Performance of Low-Slump Polypropylene Fiber Concrete after High Temperature" Applied Sciences 13, no. 12: 7222. https://doi.org/10.3390/app13127222

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