Mechanical Properties of Polypropylene Fiber Cement Mortar under Different Loading Speeds

: In this work, the relationships between the mechanical properties (i.e., compressive strength and ﬂexural strength) and loading speed of polypropylene ﬁber (PPF)-incorporated cement mortar at different ages (before 28 days) were studied. A total of 162 cubic samples for compressive strength tests and 162 cuboid samples for ﬂexural strength tests were casted and tested. Analytical relationships between the sample properties (i.e., sample age, PPF content, and loading speed) and compressive and ﬂexural strength were proposed based on the experimental data, respectively. Of the predicted compressive and ﬂexural strength results, 70.4% and 75.9% showed less than 15% relative error compared with the experimental results, respectively.

Fiber reinforcement of cement-based materials has shown a good improvement in mechanical properties [12]. Polypropylene fiber (PPF) is a cheap [13] and popular material in the construction industry. The polypropylene fiber market reached $122.7 billion in 2019 [14]. Many studies have been conducted to investigate the improvement of PPFincorporated cement-based materials' performance [15][16][17][18], especially the improvement in mechanical properties [19][20][21][22]. The addition of PPF can significantly reduce the drying shrinkage while improving the compressive strength and freeze-thaw resistance of concrete [23]. PPF has also been used in light-weight concrete to improve the compressive strength and the crack-resistance performance [15]. The incorporation of PPF in prepacked aggregate concrete also shows an improved resistance against elevated temperatures [24,25]. Medina et al. [26] reported that the water permeability and CO 2 diffusion are reduced due to the excellent cracking control of the PPF-incorporated concrete, which makes PPF-mixed concrete structures more resistant to CO 2 -induced durability deterioration (i.e., carbonation and corrosion), and results in more sustainable concrete structures.
The loading speed has a significant influence on the results of mechanical tests [27][28][29][30]. The first study of the loading speed influence on the mechanical properties of cement-based materials was performed by Abrams in 1917 [31]. Since then, a lot of research has been carried out to study the relationship between the loading speed and mechanical properties 2 of 17 of cement-based materials [27,28,32,33]. Kaplan [34] studied the influence of loading rate on the compressive strength of concrete and found that the moisture content is one of the important variables affecting the relationship between strength and loading speed. Fu et al. [35] found that both compressive strength and stiffness increase with increasing loading rate, and that wet concrete is relatively more sensitive to a change in loading rate than dry concrete. Bischoff and Perry [32] reviewed the relationship between compressive strength and loading speed, and found that the ultimate strength is affected most significantly by the loading rate, and a linear relationship was found between compressive strength and loading speed. Quantitative relationships between the loading speed and mechanical properties of PPF-incorporated cement mortar are still lacking, despite a lot of qualitative relationships having been obtained in the existing literature.
To fill the aforementioned knowledge gaps, a total of 162 cubic PPF-incorporated cement mortar samples for compressive strength tests and 162 cuboid PPF-incorporated cement mortar samples for flexural strength tests were casted and tested before 28 days of age in this work, and the relationships between mechanical properties (i.e., compressive and flexural strength) and loading speed of PPF-incorporated cement mortar at different ages were studied. Analytical relationships between the sample properties (i.e., sample age, PPF content, and loading speed) and compressive and flexural strength are proposed, respectively, based on the experimental data.

Raw Materials and Mixture Design
The mass ratio of the raw components for cement mortar was m cement /m water / m fine aggregate = 1.0:0.5:1.5. The cement used in this work was P.C. 32.5 Portland cement, which meets the Chinese standard GB 175-2007 [36]. The chemical composition and physical properties of the cement are presented in Table 1. Natural river sand with a fineness modulus of 2.49 was used in this work as fine aggregate, and the absorption of the fine aggregate was 2.28%. The gradation information of the fine aggregate is shown in Figure 1. Distilled water was used as mixing water. The polypropylene fiber (PPF) used in this work was produced by Tianyi Engineering Fiber Co., Ltd. (Changzhou, China), and a photograph of the fibers is shown in Figure 2, while the chemical and mechanical properties of the fiber are summarized in Table 2. Three cement mortar mixtures were prepared with the fiber volume fractions (V f ) of 0%, 0.5%, and 1.0%. No chemical mixture was used in this research.

Sample Preparation
The cubic cement mortar samples used for the compressive strength tests were cast with the dimensions of 70.7 × 70.7 × 70.7 mm, while the cuboid samples for the flexural strength tests were cast with the dimensions of 40 × 40 × 160 mm. After mixing, all samples were placed under room temperature condition at ±23 • C. After 12 h, the samples were de-molded and immersed in water at 23 ± 1 • C. In this work, three fiber volume fractions of cement mortar were designed to study the influence of the fiber content on mechanical properties, and for each mixture, three different loading speeds were used to study the influence of loading speed on mechanical tests; three duplicates were used for the compressive and flexural strength tests of each mixture at the designated age. Thus, for each mixture, 162 cubic and cuboid samples were cast, respectively.

Sample Preparation
The cubic cement mortar samples used for the compressive strength tests were cast with the dimensions of 70.7 × 70.7 × 70.7 mm, while the cuboid samples for the flexural strength tests were cast with the dimensions of 40 × 40 × 160 mm. After mixing, all samples were placed under room temperature condition at ±23 °C. After 12 h, the samples were de-molded and immersed in water at 23 ± 1 °C. In this work, three fiber volume fractions of cement mortar were designed to study the influence of the fiber content on mechanical properties, and for each mixture, three different loading speeds were used to study the influence of loading speed on mechanical tests; three duplicates were used for the compressive and flexural strength tests of each mixture at the designated age. Thus, for each

Sample Preparation
The cubic cement mortar samples used for the compressive strength tests were cast with the dimensions of 70.7 × 70.7 × 70.7 mm, while the cuboid samples for the flexural strength tests were cast with the dimensions of 40 × 40 × 160 mm. After mixing, all samples were placed under room temperature condition at ±23 °C. After 12 h, the samples were de-molded and immersed in water at 23 ± 1 °C. In this work, three fiber volume fractions of cement mortar were designed to study the influence of the fiber content on mechanical properties, and for each mixture, three different loading speeds were used to study the influence of loading speed on mechanical tests; three duplicates were used for the compressive and flexural strength tests of each mixture at the designated age. Thus, for each

Test Setup
The compressive and flexural strength tests were carried by a YAW-2000D pressure testing machine produced by China Jinan Tianchen Testing Machine Manufacturing Co., Ltd. The test setup is presented in Figure 3. The three-point (i.e., center-point) loading flexural test was carried out with a span of 100 mm. In this work, three loading speeds (i.e., Sustainability 2021, 13, 3697 4 of 17 0.3, 0.6, and 1.0 kN/s) were applied to study the influence on the mechanical test results. The average value of the test results of three duplicates was reported.

Test Setup
The compressive and flexural strength tests were carried by a YAW-2000D pressure testing machine produced by China Jinan Tianchen Testing Machine Manufacturing Co., Ltd. The test setup is presented in Figure 3. The three-point (i.e., center-point) loading flexural test was carried out with a span of 100 mm. In this work, three loading speeds (i.e., 0.3, 0.6, and 1.0 kN/s) were applied to study the influence on the mechanical test results. The average value of the test results of three duplicates was reported.

Compressive Strength and Flexural Strength Test Results
The  Table 3, and it can be seen that in the very early age, the absolute compressive and flexural strength values did not change under different loading speeds or with different PPF contents. This might be due to the weakness of cement mortar at a very early age (0.5 days). As the curing continued, the incorporation of PPF cement mortar's mechanical properties (i.e., compressive and flexural strength) showed enhancement. The increasing of the loading speed also showed improvement in the mechanical performance of the cement mortar at a later age.

Compressive Strength and Flexural Strength Test Results
The  Table 3, and it can be seen that in the very early age, the absolute compressive and flexural strength values did not change under different loading speeds or with different PPF contents. This might be due to the weakness of cement mortar at a very early age (0.5 days). As the curing continued, the incorporation of PPF cement mortar's mechanical properties (i.e., compressive and flexural strength) showed enhancement. The increasing of the loading speed also showed improvement in the mechanical performance of the cement mortar at a later age.
Ltd. The test setup is presented in Figure 3. The three-point (i.e., center-point) flexural test was carried out with a span of 100 mm. In this work, three loading (i.e., 0.3, 0.6, and 1.0 kN/s) were applied to study the influence on the mechan results. The average value of the test results of three duplicates was reported.

Compressive Strength and Flexural Strength Test Results
The  Table 3, and it can be seen that in the very early absolute compressive and flexural strength values did not change under different speeds or with different PPF contents. This might be due to the weakness of cem tar at a very early age (0.5 days). As the curing continued, the incorporation of PPF mortar's mechanical properties (i.e., compressive and flexural strength) showed e ment. The increasing of the loading speed also showed improvement in the me performance of the cement mortar at a later age.

The Influence of Loading Speed on the Mechanical Tests Results
The compressive and flexural strength increases or decreases of 0.6 kN/s and 1.0 kN/ in terms of 0.3 kN/s are concluded in Table 4. A higher loading speed usually accompa nied higher compressive and flexural strength results. Kaplan [34] studied the influenc of loading rate on the compressive strength of concrete. The moisture content was found to be one of the important variables affecting the relationship between strength and load ing speed. When compression loads are applied to a sample, the micropore networ within the matrix tends to close, and then the pore solution is compressed. This process i usually accompanied by a pressure gradient in liquid phase. At a higher loading speed the pressure gradient may give rise to hydrostatic pressure in the pores. This, in turn delays the onset of excessive cracking within the solid phase and thereby gives rise to a increase in the compressive and flexural strength, since the flexural strength sample als has a compression section. Fu et al. [35] also found that the moisture content of concret is an important factor influencing the strength under different loading speeds.

The Influence of Loading Speed on the Mechanical Tests Results
The compressive and flexural strength increases or decreases of 0.6 kN/s and 1.0 kN/s in terms of 0.3 kN/s are concluded in Table 4. A higher loading speed usually accompanied higher compressive and flexural strength results. Kaplan [34] studied the influence of loading rate on the compressive strength of concrete. The moisture content was found to be one of the important variables affecting the relationship between strength and loading speed. When compression loads are applied to a sample, the micropore network within the matrix tends to close, and then the pore solution is compressed. This process is usually accompanied by a pressure gradient in liquid phase. At a higher loading speed, the pressure gradient may give rise to hydrostatic pressure in the pores. This, in turn, delays the onset of excessive cracking within the solid phase and thereby gives rise to an increase in the compressive and flexural strength, since the flexural strength sample also has a compression section. Fu et al. [35] also found that the moisture content of concrete is an important factor influencing the strength under different loading speeds.

The Influence of PPF Content on the Mechanical Test Results
The compressive and flexural strength increases or decreases of PPF mortar in terms of plain mortar are concluded in Table 5. It can be seen from Table 5 that the compressive strength of the PPF mortar was higher than the plain mortar of the same age and loading speed. The improvement in compressive strength came principally from the fibers interacting with the advancing cracks [37]. When withstanding an increasing compression load, fibrous mortar samples might develop lateral tension, thus initiating microcracks, and then these microcracks could advance into macrocracks. As the advancing microcracks approached a fiber, debonding at the fiber-matrix interface began due to the tensile stresses perpendicular to the expected path of the advancing crack. When the advancing microcracks finally reached the fiber-matrix interface, the tip of the crack encountered a process of blunting because of the already presented debonding cracks. The blunting process reduced the crack-tip stress concentration, thus blocking the forward propagation of the crack and even diverting the path of the crack. The blunting, blocking, and even diverting of the crack allowed the fibrous mortar samples to withstand additional compressive load, thus upgrading its compressive strength over the plain mortar samples.

Analytical Model for the Compressive Strength Prediction of PPF Mortar under Different Loading Speeds
There are several available mathematical models that can be used to predict the compressive strength development of cementitious materials with age, as concluded in Table 6.
The prediction models presented in Table 6 are based on the plain cementitious materials without the addition of PPF. The error between the prediction models and the compressive strength test results of plain cement mortar under a 0.3 kN/s loading speed in this work is shown in Figure 6.
Note: In the models, (f c ) t denotes the compressive strength under different ages, (f c ) 28 denotes the compressive strength at 28 days of age, and t represents the sample age (days). [39] ( ) ( ) 28 [40] ( ) ( ) The prediction models presented in Table 6 are based on the plain cementitious materials without the addition of PPF. The error between the prediction models and the compressive strength test results of plain cement mortar under a 0.3 kN/s loading speed in this work is shown in Figure 6. It can be seen from Figure 6 that the ACI 209 model provided the best prediction results for plain cement mortar compressive strength. Thus, in this work, the proposed prediction model for PPF mortar under different loading speeds was based on the ACI 209 model. A series of very good linear relationships between the fiber content and compressive strength under a 0.3 kN/s loading speed can be observed in Figure 7, with all fitting parameters (R 2 ) being higher than 0.97. For the linear relationship between the fiber content and compressive strength, the basic relationship can be summarized as:

CEB-FIP
where (fc)%PPF denotes the compressive strength of different contents of PPF fiber, x denotes the PPF fiber content, k1 denotes the fitting parameter in terms of the fiber content's influence on compressive strength, and (fc)0%PPF denotes the compressive strength of plain cement mortar. It can be seen from Figure 6 that the ACI 209 model provided the best prediction results for plain cement mortar compressive strength. Thus, in this work, the proposed prediction model for PPF mortar under different loading speeds was based on the ACI 209 model. A series of very good linear relationships between the fiber content and compressive strength under a 0.3 kN/s loading speed can be observed in Figure 7, with all fitting parameters (R 2 ) being higher than 0.97. For the linear relationship between the fiber content and compressive strength, the basic relationship can be summarized as: where (f c ) %PPF denotes the compressive strength of different contents of PPF fiber, x denotes the PPF fiber content, k 1 denotes the fitting parameter in terms of the fiber content's influence on compressive strength, and (f c ) 0 %PPF denotes the compressive strength of plain cement mortar.  In this work, the compressive strength of plain cement mortar under different ages was predicted using the ACI 209 model. The relationship between the fiber content's fitting parameter k and the sample age is presented in Figure 8. Thus, the time-dependent model for the PPF cement mortar compressive strength prediction model can be expressed as:  (2) where (fc)t,%PPF denotes the compressive strength (MPa) of cement mortar at age t (days) with x (%) content of PPF fiber, (fc)28,%PPF denotes the compressive strength (MPa) of cement mortar at age 28 (days) with 0 (%) content of PPF fiber.   In this work, the compressive strength of plain cement mortar under different ages was predicted using the ACI 209 model. The relationship between the fiber content's fitting parameter k and the sample age is presented in Figure 8. Thus, the time-dependent model for the PPF cement mortar compressive strength prediction model can be expressed as: where (f c ) t,%PPF denotes the compressive strength (MPa) of cement mortar at age t (days) with x (%) content of PPF fiber, (f c ) 28 %PPF denotes the compressive strength (MPa) of cement mortar at age 28 (days) with 0 (%) content of PPF fiber.  In this work, the compressive strength of plain cement mortar under different ages was predicted using the ACI 209 model. The relationship between the fiber content's fitting parameter k and the sample age is presented in Figure 8. Thus, the time-dependent model for the PPF cement mortar compressive strength prediction model can be expressed as:  (2) where (fc)t,%PPF denotes the compressive strength (MPa) of cement mortar at age t (days) with x (%) content of PPF fiber, (fc)28,%PPF denotes the compressive strength (MPa) of cement mortar at age 28 (days) with 0 (%) content of PPF fiber.   The relationship between the loading speed and compressive strength of plain cement mortar is summarized in Figure 9. A series of linear relationships could be obtained, with all linear fitting parameters (R 2 ) being higher than 0.91. Similar to the influence of fiber content, the time-dependent relationship of loading speed in terms of the compressive strength's linear fitting parameter "k 2 " and sample age are presented in Figure 10. The relationship between the loading speed and compressive strength of plain cement mortar is summarized in Figure 9. A series of linear relationships could be obtained, with all linear fitting parameters (R 2 ) being higher than 0.91. Similar to the influence of fiber content, the time-dependent relationship of loading speed in terms of the compressive strength's linear fitting parameter "k2" and sample age are presented in Figure 10.      The relationship between the loading speed and compressive strength of plain cement mortar is summarized in Figure 9. A series of linear relationships could be obtained, with all linear fitting parameters (R 2 ) being higher than 0.91. Similar to the influence of fiber content, the time-dependent relationship of loading speed in terms of the compressive strength's linear fitting parameter "k2" and sample age are presented in Figure 10.      Figure 11, and the prediction errors are shown in Figure 12. It can be seen that the predicted compressive strength for all of the mixtures was close to the experimental data, which indicates that Equation (3) can be used to predict the compressive strength of PPF cement mortar under different loading speeds for various sample ages. A total of 44.4% of the predicted data showed less than 10% error compared with the experimental data; this value improved to 70.4% when the error acceptance increased to 15%. Only 13.0% of the predicted data showed an error higher than 20%.  Figure 11, and the prediction errors are shown in Figure 12. It can be seen that the predicted compressive strength for all of the mixtures was close to the experimental data, which indicates that Equation (3) can be used to predict the compressive strength of PPF cement mortar under different loading speeds for various sample ages. A total of 44.4% of the predicted data showed less than 10% error compared with the experimental data; this value improved to 70.4% when the error acceptance increased to 15%. Only 13.0% of the predicted data showed an error higher than 20%.   The predicted compressive strength in terms of experimental compressive strength is summarized in Figure 11, and the prediction errors are shown in Figure 12. It can be seen that the predicted compressive strength for all of the mixtures was close to the experimental data, which indicates that Equation (3) can be used to predict the compressive strength of PPF cement mortar under different loading speeds for various sample ages. A total of 44.4% of the predicted data showed less than 10% error compared with the experimental data; this value improved to 70.4% when the error acceptance increased to 15%. Only 13.0% of the predicted data showed an error higher than 20%.

Analytical Model for Flexural Strength Prediction of PPF Mortar under Different Loading Speeds
Non-linear relationships between the cement mortar's flexural strength and its independent variables (i.e., sample age, fiber content, and loading speed) can be performed by the Vipulanandan correlation model [41,42] as follows: where Y stands for the flexural strength of cement mortar; A, B, and C represent the model parameters; X denotes the independent variables (i.e., sample age, fiber content, and loading speed).
In this work, for plain cement mortar without PPF admixture and under a 0.3 kN/s loading speed, the flexural strength in terms of sample age can be written as: where (f f ) t stands for the flexural strength of plain mortar under 0.3 kN/s at different ages, and (f f ) 28 represents the flexural strength of plain mortar under 0.3 kN/s at 28 days of age. The fitting results between the sample age and flexural strength of plain mortar are shown in Figure 13. The fitting parameter (R 2 ) was as high as 0.9464.

Analytical Model for Flexural Strength Prediction of PPF Mortar under Different Loading Speeds
Non-linear relationships between the cement mortar's flexural strength and its independent variables (i.e., sample age, fiber content, and loading speed) can be performed by the Vipulanandan correlation model [41,42] as follows: ( ) where Y stands for the flexural strength of cement mortar; A, B, and C represent the model parameters; X denotes the independent variables (i.e., sample age, fiber content, and loading speed).
In this work, for plain cement mortar without PPF admixture and under a 0.3 kN/s loading speed, the flexural strength in terms of sample age can be written as: where ( Figure 14, with all fitting parameters (R 2 ) being higher than 0.98. For the linear relationship between the fiber content and compressive strength, the basic relationship can be summarized as: where (ff)%PPF denotes the flexural strength of different contents of PPF fiber, x denotes the PPF fiber content, k3 denotes the fitting parameter in terms of the PPF content's influence on flexural strength, and (ff)0%PPF denotes the flexural strength of plain cement mortar. A series of linear relationships between the fiber content and flexural strength under a 0.3 kN/s loading speed can be observed in Figure 14, with all fitting parameters (R 2 ) being higher than 0.98. For the linear relationship between the fiber content and compressive strength, the basic relationship can be summarized as: where (   In this work, the flexural strength of plain cement mortar of different ages can be described by the fitting relationship in Figure 13. The relationship between the fiber content's fitting parameter k3 and sample age is presented in Figure 15. Thus, the time-dependent model for the PPF cement mortar compressive strength prediction model can be expressed as: tt f x f tt =+ ++ (7) where (ff)t,%PPF denotes the flexural strength (MPa) of cement mortar at age t (days) with x (%) content of PPF fiber, and (ff)28,%PPF denotes the flexural strength (MPa) of cement mortar at age 28 (day) with 0 (%) content of PPF fiber. Figure 15. The relationship between the fiber content's fitting parameter "k3" and sample age. In this work, the flexural strength of plain cement mortar of different ages can be described by the fitting relationship in Figure 13. The relationship between the fiber content's fitting parameter k 3 and sample age is presented in Figure 15. Thus, the timedependent model for the PPF cement mortar compressive strength prediction model can be expressed as: x + t 2.50 + 1.18t f f 28,0%PPF (7) where (f f ) t,%PPF denotes the flexural strength (MPa) of cement mortar at age t (days) with x (%) content of PPF fiber, and (f c ) 28 %PPF denotes the flexural strength (MPa) of cement mortar at age 28 (day) with 0 (%) content of PPF fiber.  In this work, the flexural strength of plain cement mortar of different ages can be described by the fitting relationship in Figure 13. The relationship between the fiber content's fitting parameter k3 and sample age is presented in Figure 15. Thus, the time-dependent model for the PPF cement mortar compressive strength prediction model can be expressed as: tt f x f tt =+ ++ (7) where (ff)t,%PPF denotes the flexural strength (MPa) of cement mortar at age t (days) with x (%) content of PPF fiber, and (ff)28,%PPF denotes the flexural strength (MPa) of cement mortar at age 28 (day) with 0 (%) content of PPF fiber. Figure 15. The relationship between the fiber content's fitting parameter "k3" and sample age. The relationship between the loading speed and flexural strength of plain cement mortar is summarized in Figure 16, in which a series of linear relationships were obtained, with all linear fitting parameters (R 2 ) being higher than 0.94. Similar to the influence of fiber content, the time-dependent relationship of the loading speed's linear fitting parameter "k 4 " and sample age is presented in Figure 17. The relationship between the loading speed and flexural strength of plain cement mortar is summarized in Figure 16, in which a series of linear relationships were obtained, with all linear fitting parameters (R 2 ) being higher than 0.94. Similar to the influence of fiber content, the time-dependent relationship of the loading speed's linear fitting parameter "k4" and sample age is presented in Figure 17.      The relationship between the loading speed and flexural strength of plain cement mortar is summarized in Figure 16, in which a series of linear relationships were obtained, with all linear fitting parameters (R 2 ) being higher than 0.94. Similar to the influence of fiber content, the time-dependent relationship of the loading speed's linear fitting parameter "k4" and sample age is presented in Figure 17.
where (f f ) t,%PPF,kN/s denotes the flexural strength (MPa) of cement mortar at age t (days) with x (%) content of PPF fiber and a test loading speed of y (kN/s), and (f c ) 28,%PPF,0.3kN/s denotes the flexural strength (MPa) of cement mortar at age 28 (days) with 0 (%) content of PPF fiber under a test loading speed of 0.3 (kN/s). The predicted flexural strength in terms of experimental compressive strength is summarized in Figure 18, and the prediction errors are shown in Figure 19. It can be seen that the predicted flexural strength for all mixtures was close to the experimental data, which indicates that Equation (8) can be used to predict the flexural strength of PPF cement mortar under different loading speeds and various sample ages. Of the prediction results, 55.6% showed less than 10% error compared with the experimental data, 75.9% had a relative error less than 15%, and 16.7% had a relative error higher than 20%. The predicted flexural strength in terms of experimental compressive strength is summarized in Figure 18, and the prediction errors are shown in Figure 19. It can be seen that the predicted flexural strength for all mixtures was close to the experimental data, which indicates that Equation (8) can be used to predict the flexural strength of PPF cement mortar under different loading speeds and various sample ages. Of the prediction results, 55.6% showed less than 10% error compared with the experimental data, 75.9% had a relative error less than 15%, and 16.7% had a relative error higher than 20%.    Figure 18, and the prediction errors are shown in Figure 19. It can be see that the predicted flexural strength for all mixtures was close to the experimental dat which indicates that Equation (8) can be used to predict the flexural strength of PPF c ment mortar under different loading speeds and various sample ages. Of the predictio results, 55.6% showed less than 10% error compared with the experimental data, 75.9 had a relative error less than 15%, and 16.7% had a relative error higher than 20%.

Conclusions
In this work, the effect of polypropylene fiber content and loading speed on the compressive and flexural strength of cement mortar at different ages was studied. Analytical equations for compressive and flexural strength development prediction for cement mortar with different polypropylene fiber contents under different loading speeds were proposed. The main conclusions can be drawn as follows: