Axial Impact Resistance of High-Strength Engineering Geopolymer Composites: Effect of Polyethylene Fiber Content and Strain Rate

: High-strength engineered geopolymer composite (EGC) materials exhibit excellent mechanical properties under quasistatic loading, thus showing great potential in military and civilian facilities subjected to impact or explosive loading. However, its dynamic mechanical response under high-speed loading is not fully understood. In this study, dynamic compressive test was performed on EGC with PE fiber contents of 0%, 0.5%, 1.0%, 1.5%, and 2.0% using the Split Hopkinson Pressure Bar (SHPB) test. The results indicated that EGC reinforced with 1.5% fiber exhibited optimal static and dynamic mechanical performance. In the strain rate range of 181 s − 1 to 201 s − 1 , when the fiber content increased from 1.0% to 1.5% and 2.0%, the dynamic compressive strength of the EGC increased by 24.3%, 28.8%, and 44.0%, respectively, compared to the matrix without fiber. Dynamic parameters of the EGC, including dynamic compressive strength, dynamic increase factor, and impact toughness, showed sensitivity to strain rates and increased with strain rate. A modified model, incorporating the fiber bridging effect, was proposed based on the CEB-FIP model, providing important guidance for practical engineering applications.


Introduction
In 2001, the terrorist incident of planes crashing into the Twin Towers in New York and the impact loading that was encountered during the service of the infrastructure (e.g., explosions, impacts, etc.) aroused great interest in building materials with excellent impact resistance.Traditional concrete has poor tensile properties and is brittle, which is often disastrous when subjected to impact loading.Fiber-reinforced concrete (FRC) has significantly improved tensile strength, fracture toughness, and fracture modes by adding discrete short fiber to the concrete [1][2][3].Engineered cementitious composites (ECCs) have garnered attention for their outstanding crack tolerance and superior tensile strength, with the behavior of multiple cracks expanding being widely studied [4][5][6][7].However, conventional ECCs tend to be high in cement, which has been the main cause of high CO 2 emissions in the construction sector, and its greenness is a concern [8,9].The use of geopolymer as a novel binding material is considered a significant breakthrough in the construction industry to reduce the carbon footprint.Geopolymer-utilized industrial byproducts, such as fly ash (FA), ground granulated blast furnace slag (GGBS), and metakaolin as precursors, react with alkaline activators (such as sodium hydroxide and sodium silicate solutions) to form a reaction [10,11].These activators dissolve the silicate and aluminate components in the precursors, thus initiating a polymerization reaction that ultimately produces an amorphous gel.Previous studies demonstrated that geopolymer concrete exhibited excellent early strength and durability, thus making it a promising material to replace traditional Portland cement concrete [12,13].The engineering geopolymer composite (EGC) is a low-carbon composite made of geopolymer gel, various aggregates, and short fiber [14][15][16][17][18].The EGC, similar to the ECC, also has excellent tensile properties, with tensile strengths of up to 10 MPa and tensile strains of up to 3-22%, which are accompanied by strain-hardening behaviors and multiseam spreading and have attracted a great deal of interest from researchers [17,[19][20][21].
In the developed EGC, FA or GGBS materials have been commonly used as precursors, while a blend of sodium hydroxide (SH) solution and sodium silicate (SS) solution acts as the alkali activator [22][23][24].FA is widely available globally and exhibits good processability.However, an FA-based EGC often requires high-temperature curing conditions to achieve the desired mechanical performance [25].GGBS, with a higher calcium content, could substitute for a portion of the FA, thereby accelerating the early reaction rate and enhancing early strength and making it suitable for actual engineering curing conditions [25,26].In previous studies on slag-fly ash-based EGCs, researchers have investigated the influence of variables such as the type of slag/fly ash ratio, the dosage of the alkali activator, the sand-tobinder ratio, the type of fiber, the fiber content, and the fiber length on both the workability and mechanical properties of the fresh paste [16,[26][27][28][29].For example, Lee et al. [30] and Choi et al. [22] achieved a mortar matrix with appropriate viscosity by adjusting the ratio of water to binder and the type of reducing activator.Suitable viscosity promotes the uniform dispersion of high aspect ratio fiber, thereby resulting in an EGC with a tensile strength of 13.06 MPa and a tensile strain of 7.5%.In terms of the fiber type, most of the studies used oiled polyvinyl alcohol (PVA) fiber and ultra-high molecular weight polyethylene fiber (UHMPE).PVA fiber has excellent fiber/matrix interfacial properties and has been one of the first fibers to be used in highly ductile composites (ECC/EGC), and PE fiber has also been used by a wide range of researchers as a result of its excellent tensile properties.The fiber content plays a pivotal role in determining the mechanical response of highly ductile composite materials (ECC/EGC).Ahmed and Ronnie et al. [31] explored the impact of fiber content (ranging from 0.5% to 2%) on the uniaxial tensile and three-point bending performance of EGCs.The results revealed that the optimal fiber volume fraction was 1%, at which the material exhibited excellent tensile strain and flexural hardening behavior.However, as the volume fraction of PE fiber increased, the compressive strength of the composite gradually decreased.Moreover, it was found that with higher PE volume fractions, the crack density in the EGC increases, thereby leading to a higher strain capacity [32].
For the dynamic mechanical properties of the EGC, it has been shown that regardless of precursor type and whether subjected to heat curing, the EGC's dynamic compressive strength exhibits significant strain rate sensitivity [17,[33][34][35].Furthermore, the fiber length, fiber volume fraction, and fiber distribution were closely associated with the EGC's performance under high-speed loading conditions [36,37].The dynamic compressive response of PVA-EGC at different fiber volume fractions (0%, 1%, 1.5%, and 2%) was studied, with the volume fraction of 1.5% identified as the optimal choice for considering both quasistatic and dynamic behavior, as per Wang et al. [36].Zhong et al. [38] conducted dynamic splitting tensile and dynamic compressive tests using recycled fiber instead of PVA fiber.Materials mixed with 0.25% recycled polymer and 1.75% PVA fiber demonstrated improved quasistatic performance and dynamic compressive response according to the results [38,39].Compared to the ECC, when the same PVA fiber was used, the EGC's ability to dissipate impact energy was 1.6 times that of the ECC.When the environmental temperature reached 100 • C, both the maximum impact load and duration of impact of the EGC were higher than the ECC.Therefore, the EGC was found to be more suitable for protective buildings in sub-high-temperature environments [40,41].Additionally, under both quasistatic and dynamic tensile loading, the PE-EGC exhibited superior mechanical performance compared to the PVA-EGC [17].However, to date, research on the mechanical response of PE-EGC under high strain rates has been limited.It is worth noting, particularly, the difference in wettability between PVA fiber and PE fiber, thus resulting in significant variations in the interface properties between the fiber and the matrix.PVA fiber has hydrophilic properties; hence, the free water in the specimens might have been reduced, thus potentially leading to a decrease in the dynamic compressive strength enhancement at high strain rates.The test results indicated that, at strain rates of 50 s −1 to 100 s −1 , the dynamic compressive strength of the PVA-EGC with a volume fraction of 0.5% of PVA fibers decreased instead of increasing compared to the matrix without fibers.This study systematically examined how varying the PE fiber content influenced the dynamic compressive behavior of the PE-EGC across different strain rates, thus utilizing the SHPB experimental setup and contributing to a deeper understanding of the reinforcing effects of PVA fiber and PE fiber, which are two commonly used fibers in EGCs.Additionally, the workability, quasistatic compressive, and quasistatic tensile properties were assessed.By integrating the empirical data, a modified CEB-FIP model, accounting for fiber content, was introduced, thus yielding favorable fitting outcomes.These findings were anticipated to enhance the comprehension of the PE-EGC's dynamic mechanical characteristics and have offered backing for its real-world utilization in high strain rate conditions.Figure 1 shows the flow chart of this study.
Buildings 2024, 14, x FOR PEER REVIEW 3 both quasistatic and dynamic tensile loading, the PE-EGC exhibited superior mech performance compared to the PVA-EGC [17].However, to date, research on the mechanical response of PE-EGC under high rates has been limited.It is worth noting, particularly, the difference in wettabili tween PVA fiber and PE fiber, thus resulting in significant variations in the interface erties between the fiber and the matrix.PVA fiber has hydrophilic properties; henc free water in the specimens might have been reduced, thus potentially leading to crease in the dynamic compressive strength enhancement at high strain rates.Th results indicated that, at strain rates of 50 s −1 to 100 s −1 , the dynamic compressive str of the PVA-EGC with a volume fraction of 0.5% of PVA fibers decreased instead creasing compared to the matrix without fibers.This study systematically examined varying the PE fiber content influenced the dynamic compressive behavior of the PE across different strain rates, thus utilizing the SHPB experimental setup and contrib to a deeper understanding of the reinforcing effects of PVA fiber and PE fiber, whic two commonly used fibers in EGCs.Additionally, the workability, quasistatic com sive, and quasistatic tensile properties were assessed.By integrating the empirical d modified CEB-FIP model, accounting for fiber content, was introduced, thus yieldi vorable fitting outcomes.These findings were anticipated to enhance the comprehe of the PE-EGC's dynamic mechanical characteristics and have offered backing for it world utilization in high strain rate conditions.Figure 1 shows the flow chart of this s

Materials
In this study, EGC was composed of FA, GGBS, alkali activator, quartz sand, ret water, and fiber.FA and GGBS, processed by Henan Hougang Co., Ltd., Zheng China, were used in accordance with the Chinese standard GB/T 18046-2017 [42], and chemical compositions are presented in Table 1.The particle size distributions of th cursors and quartz sand are shown in Figure 2. The activator solution was prepar mixing 10 M SH, processed by XiLONG SCIENTIFIC Co., Ltd., Guangzhou, China SS solution from Jiashan County Yourui Refractory Materials Co., Ltd., Jiaxing, C thus achieving a modulus of 2.3.Quartz sand was used as the fine aggregate, w average particle size of approximately 100 µm and a D50 of 126 µm.BaCl2 was use retarder to prolong the setting time of the fresh matrix.BaCl2 not only delaye

Materials
In this study, EGC was composed of FA, GGBS, alkali activator, quartz sand, retarder, water, and fiber.FA and GGBS, processed by Henan Hougang Co., Ltd., Zhengzhou, China, were used in accordance with the Chinese standard GB/T 18046-2017 [42], and their chemical compositions are presented in Table 1.The particle size distributions of the precursors and quartz sand are shown in Figure 2. The activator solution was prepared by mixing 10 M SH, processed by XiLONG SCIENTIFIC Co., Ltd., Guangzhou, China, with SS solution from Jiashan County Yourui Refractory Materials Co., Ltd., Jiaxing, China, thus achieving a modulus of 2.3.Quartz sand was used as the fine aggregate, with an average particle size of approximately 100 µm and a D50 of 126 µm.BaCl 2 was used as a retarder to prolong the setting time of the fresh matrix.BaCl 2 not only delayed the hydration of GGBS, thereby prolonging the setting time, but also enhanced workability [43].The physical parameters of the PE fiber are listed in Table 2. hydration of GGBS, thereby prolonging the setting time, but also enhanced workability [43].The physical parameters of the PE fiber are listed in Table 2.

Mix Proportions
To explore the influence of fiber volume fraction on EGC's quasistatic and dynamic behavior, five mixtures were employed.Based on previous research [32], a FA/GGBS ratio of 0.7:0.3 was adopted.As indicated earlier, including a certain proportion of slag can enhance the early strength of the mixture.These mixtures comprised a reference mixture (M) devoid of fiber and four additional mixtures with varying fiber volume fractions (based on concrete volume).Detailed mix proportions for all five mixtures, including the SS/SH ratio of 2.0 and the sand-to-binder ratio of 0.16, are presented in Table 3.

Mix Proportions
To explore the influence of fiber volume fraction on EGC's quasistatic and dynamic behavior, five mixtures were employed.Based on previous research [32], a FA/GGBS ratio of 0.7:0.3 was adopted.As indicated earlier, including a certain proportion of slag can enhance the early strength of the mixture.These mixtures comprised a reference mixture (M) devoid of fiber and four additional mixtures with varying fiber volume fractions (based on concrete volume).Detailed mix proportions for all five mixtures, including the SS/SH ratio of 2.0 and the sand-to-binder ratio of 0.16, are presented in Table 3.

Specimen Preparation
The mixing process is illustrated in Figure 3. Dry ingredients (FA, GGBS, sand, and retarder) were mixed for 2 min at the beginning of the mixing process.Following the dry mixing, the premixed and cooled activator solution was incorporated into the mixture.The combined materials were stirred for 3 min at 75 rpm to achieve a homogenous and flowable geopolymer matrix.PE fiber was then uniformly added and mixed for 3 min.This was followed by an additional 3 min of mixing to achieve a uniform and homogenous EGC.The freshly mixed EGC was promptly cast into molds and vibrated on a vibrating table for 2 min to eliminate entrapped air bubbles.To prevent the formation of shrinkage cracks and slow down moisture loss, all specimens were sealed with plastic film upon casting and remained indoors for 24 h.After demolding, the specimens underwent water curing for 27

Specimen Preparation
The mixing process is illustrated in Figure 3. Dry ingredients (FA, GGBS, sand, and retarder) were mixed for 2 min at the beginning of the mixing process.Following the dry mixing, the premixed and cooled activator solution was incorporated into the mixture.The combined materials were stirred for 3 min at 75 rpm to achieve a homogenous and flowable geopolymer matrix.PE fiber was then uniformly added and mixed for 3 min.This was followed by an additional 3 min of mixing to achieve a uniform and homogenous EGC.The freshly mixed EGC was promptly cast into molds and vibrated on a vibrating table for 2 min to eliminate entrapped air bubbles.To prevent the formation of shrinkage cracks and slow down moisture loss, all specimens were sealed with plastic film upon casting and remained indoors for 24 h.After demolding, the specimens underwent water curing for 27 days.

Flowability Test
Flowability tests were performed on all mixtures in accordance with ASTM-C1437-13 [44].The fresh EGC was cast into a conical mold in two layers, with each layer being thoroughly compacted with a tamping rod.After lifting the mold vertically, the fresh mixture was subjected to 25 jolts.The two diameters of the fresh mixture in the vertical direction were measured, and their average value was reported.

Quasistatic Test
To evaluate the tensile strain-hardening behavior of EGC, tensile tests were performed, as illustrated in Figure 4.The tensile specimens were dumbbell-shaped with dimensions of 330 mm × 60 mm × 13 mm.Each mixture was subjected to tensile test with six samples.Representative stress-strain curves were presented.Tensile tests were performed according to JSCE-2008 [45] using a displacement-controlled mode with a speed of 0.5 mm/min.Two linear variable displacement transducers (LVDTs) were employed on opposite sides of the specimen's center to measure tensile deformation during the test.mixture) were subjected to static compressive tests using a 5000 kN capacity universal test machine.The tests followed the ASTM C39/C39M-23 [46] and the elastic modulus according to ASTM C469/C469M-14 [47], thus employing a displacement controlled mode at 0.2 mm/min.To measure longitudinal strain during compressive testing, two strain gauges were affixed on opposite sides of the specimen's center.Additionally, two LVDTs were installed on both sides.Before the test, the specimens were leveled with high-strength gypsum.The experimental setup is shown in Figure 5.   Cylindrical specimens (φ50 mm × 100 mm) from each of the five mixtures (three per mixture) were subjected to static compressive tests using a 5000 kN capacity universal test machine.The tests followed the ASTM C39/C39M-23 [46] and the elastic modulus according to ASTM C469/C469M-14 [47], thus employing a displacement controlled mode at 0.2 mm/min.To measure longitudinal strain during compressive testing, two strain gauges were affixed on opposite sides of the specimen's center.Additionally, two LVDTs were installed on both sides.Before the test, the specimens were leveled with high-strength gypsum.The experimental setup is shown in Figure 5.The Split Hopkinson Pressure Bar (SHPB) test is widely employed experimental methodology for understanding the mechanical response of materials subjected to high strain rate loading conditions, as illustrated in Figure 6.The data analysis system processed the collected signals into waveforms used to calculate the stress and strain experi-

Axial Impact Test
The Split Hopkinson Pressure Bar (SHPB) test is widely employed experimental methodology for understanding the mechanical response of materials subjected to high strain rate loading conditions, as illustrated in Figure 6.The data analysis system processed the collected signals into waveforms used to calculate the stress and strain experienced by the cylindrical specimens (100 mm diameter and 50 mm height).Additionally, one-dimensional stress waves generated by the projectile impact on the incident rod are susceptible to environmental factors and the material properties of the SHPB rods.This susceptibility can introduce unstable oscillations in the data.Therefore, to meet the assumption of uniform stress distribution and reduce high-frequency stress waves while extending the rise time of the incident wave, copper disks measuring 20 mm in diameter and 2 mm in thickness were chosen as waveform shapers.

Axial Impact Test
The Split Hopkinson Pressure Bar (SHPB) test is widely employed experimen methodology for understanding the mechanical response of materials subjected to hi strain rate loading conditions, as illustrated in Figure 6.The data analysis system p cessed the collected signals into waveforms used to calculate the stress and strain expe enced by the cylindrical specimens (100 mm diameter and 50 mm height).Additional one-dimensional stress waves generated by the projectile impact on the incident rod susceptible to environmental factors and the material properties of the SHPB rods.T susceptibility can introduce unstable oscillations in the data.Therefore, to meet the sumption of uniform stress distribution and reduce high-frequency stress waves wh extending the rise time of the incident wave, copper disks measuring 20 mm in diame and 2 mm in thickness were chosen as waveform shapers.According to the principles of one-dimensional stress waves [49] and based on the assumption of stress uniformity, the average stress σ(t), strain ε(t), and strain rate ε(t) of the specimen can be determined by Equation (1).
where E b , A b and C b represent the elastic modulus (MPa), cross-sectional area (mm 2 ), and longitudinal wave velocity (m/s) of the bar, respectively.A 0 and l 0 represent the crosssectional area (mm 2 ) and thickness (mm) of the test specimen, respectively.Sample tests confirmed stress equilibrium, thus fulfilling the uniformity assumption (Figure 7).
where Eb, Ab and Cb represent the elastic modulus (MPa), cross-sectional area (mm 2 ), and longitudinal wave velocity (m/s) of the bar, respectively.A0 and l0 represent the crosssectional area (mm 2 ) and thickness (mm) of the test specimen, respectively.Sample tests confirmed stress equilibrium, thus fulfilling the uniformity assumption (Figure 7).

Flowability
The results of the flowability tests conducted on all mixtures are depicted in Figure 8, thereby illustrating a gradual decrease in the slump flow of the fresh geopolymer pastes as the PE fiber content increased.The slump flow of the mixtures was significantly impacted by the PE fiber content.When the PE fiber content was low, the distance between the fiber in the paste was relatively large, thus making it difficult for the fiber to overlap and aggregate.However, with an increase in the PE fiber content, the likelihood of fiber overlap and aggregation between the fiber increased, thereby leading to increased internal flow resistance caused by fiber bridging [50].Furthermore, related studies [51] have indicated that the mixing process promotes the formation of a water film around the PE fiber,

Flowability
The results of the flowability tests conducted on all mixtures are depicted in Figure 8, thereby illustrating a gradual decrease in the slump flow of the fresh geopolymer pastes as the PE fiber content increased.The slump flow of the mixtures was significantly impacted by the PE fiber content.When the PE fiber content was low, the distance between the fiber in the paste was relatively large, thus making it difficult for the fiber to overlap and aggregate.However, with an increase in the PE fiber content, the likelihood of fiber overlap and aggregation between the fiber increased, thereby leading to increased internal flow resistance caused by fiber bridging [50].Furthermore, related studies [51] have indicated that the mixing process promotes the formation of a water film around the PE fiber, thus reducing the available lubrication water and contributing to the observed decrease in the slump flow of the geopolymer paste.

Quasistatic Compressive Properties
Figure 9 illustrates the failure modes of the EGC with varying PE fiber content.It is evident from Figure 9 that the failure mode of the geopolymer matrix without fiber (Group M) significantly differed from that of the other groups.During the continuous compressive process at both ends of the specimen, the strain energy accumulated internally.When microcracks appeared, the internal energy was instantly released, thus leading to multiple block fractures in Group M specimens [52].Upon the addition of fiber, due to their bridging effect, the specimen did not fracture immediately upon reaching the ul-

Quasistatic Compressive Properties
Figure 9 illustrates the failure modes of the EGC with varying PE fiber content.It is evident from Figure 9 that the failure mode of the geopolymer matrix without fiber (Group M) significantly differed from that of the other groups.During the continuous compressive process at both ends of the specimen, the strain energy accumulated internally.When microcracks appeared, the internal energy was instantly released, thus leading to multiple block fractures in Group M specimens [52].Upon the addition of fiber, due to their bridging effect, the specimen did not fracture immediately upon reaching the ultimate compressive strength.Instead, it swiftly formed a longitudinally penetrating oblique crack.After loading, there was no observable spalling of fragments on the specimen surface, thereby maintaining its excellent integrity.While adding PE fiber enhanced the postfailure integrity of the specimens, it did not change their brittle fracture behavior.No significant changes in the failure mode of the specimens were observed with increasing fiber content.

Quasistatic Compressive Properties
Figure 9 illustrates the failure modes of the EGC with varying PE fiber content.It is evident from Figure 9 that the failure mode of the geopolymer matrix without fiber (Group M) significantly differed from that of the other groups.During the continuous compressive process at both ends of the specimen, the strain energy accumulated internally.When microcracks appeared, the internal energy was instantly released, thus leading to multiple block fractures in Group M specimens [52].Upon the addition of fiber, due to their bridging effect, the specimen did not fracture immediately upon reaching the ultimate compressive strength.Instead, it swiftly formed a longitudinally penetrating oblique crack.After loading, there was no observable spalling of fragments on the specimen surface, thereby maintaining its excellent integrity.While adding PE fiber enhanced the postfailure integrity of the specimens, it did not change their brittle fracture behavior.No significant changes in the failure mode of the specimens were observed with increasing fiber content.The stress-strain response of all the mixtures after quasistatic testing is shown in Figure 10.It can be observed from Figure 10 that all mixtures exhibited brittle failure.Due to the specimens' brittle failure, data from the descending portion of the curves were unavailable.In the initial loading stage of the specimens, the stress and strain changed proportionally, thus approaching a straight line indicating the predominant role of the geopolymer matrix at this stage.After reaching the ultimate axial compressive strength, the The stress-strain response of all the mixtures after quasistatic testing is shown in Figure 10.It can be observed from Figure 10 that all mixtures exhibited brittle failure.Due to the specimens' brittle failure, data from the descending portion of the curves were unavailable.In the initial loading stage of the specimens, the stress and strain changed proportionally, thus approaching a straight line indicating the predominant role of the geopolymer matrix at this stage.After reaching the ultimate axial compressive strength, the stress of the Group M specimens sharply dropped, thereby indicating the loss of loadbearing capacity.Upon the addition of PE fiber, the stress also sharply declined after reaching the peak value.As the fiber content increased further, the bridging effect of the fiber strengthened, thus resulting in some residual strength in the specimens.
As shown in Figure 11, the PE fiber content influenced the compressive strength and elastic modulus of the EGC subjected to static axial compressive loading.The static compressive strength of the reference mixture (Group M) was 109 MPa.The compressive strength of the specimens showed a significant decrease as the PE fiber content increased.Compared to the reference mixture, PE2.0 displayed a 22% decrease in compressive strength.Overall, the compressive strength of the EGC decreased as the fiber content increased, which is consistent with previous research [53].A similar decreasing trend was observed in the elastic modulus as in the compressive strength.Compared to the reference mixture, the elastic modulus of all the fiber-containing mixtures decreased by 15.0% to 28.5%.The decrease in both the compressive strength and elastic modulus was likely due to the impact of fiber on the mixture's flowability.This led to fiber overlap and aggregation, which reduced the density of the geopolymer matrix [8].Consequently, the overall compressive strength and elastic modulus of the geopolymer material decreased [54].Moreover, due to the hydrophobic nature of the PE fiber and its differing bonding properties with the matrix, it may not have effectively enhanced compressive strength.Therefore, a decrease in the compressive strength of the EGC relative to the M matrix was observed, thus ranging from 20.1% to 25.5%.
stress of the Group M specimens sharply dropped, thereby indicating the loss of loadbearing capacity.Upon the addition of PE fiber, the stress also sharply declined after reaching the peak value.As the fiber content increased further, the bridging effect of the fiber strengthened, thus resulting in some residual strength in the specimens.As shown in Figure 11, the PE fiber content influenced the compressive strength and elastic modulus of the EGC subjected to static axial compressive loading.The static compressive strength of the reference mixture (Group M) was 109 MPa.The compressive strength of the specimens showed a significant decrease as the PE fiber content increased.Compared to the reference mixture, PE2.0 displayed a 22% decrease in compressive strength.Overall, the compressive strength of the EGC decreased as the fiber content increased, which is consistent with previous research [53].A similar decreasing trend was observed in the elastic modulus as in the compressive strength.Compared to the reference mixture, the elastic modulus of all the fiber-containing mixtures decreased by 15.0% to 28.5%.The decrease in both the compressive strength and elastic modulus was likely due to the impact of fiber on the mixture's flowability.This led to fiber overlap and aggregation, which reduced the density of the geopolymer matrix [8].Consequently, the overall compressive strength and elastic modulus of the geopolymer material decreased [54].Moreover, due to the hydrophobic nature of the PE fiber and its differing bonding properties with the matrix, it may not have effectively enhanced compressive strength.

Quasistatic Tensile Properties
Figure 12b illustrates the typical tensile failure modes of the EGC with fiber contents ranging from 0.5% to 2.0%.The reference concrete displayed a failure mode characterized by single crack propagation, thus indicating brittle fracture characteristics.Thus, the discussion primarily centered on the failure modes observed in the EGC specimens containing fiber.Since not every crack traversed the entire specimen in its entirety, some of the cracks may be present in only a portion of the width of the specimen.Therefore, in this study, in order to have a more accurate count of the number of cracks in the specimen, the

Quasistatic Tensile Properties
Figure 12b illustrates the typical tensile failure modes of the EGC with fiber contents ranging from 0.5% to 2.0%.The reference concrete displayed a failure mode characterized by single crack propagation, thus indicating brittle fracture characteristics.Thus, the dis-cussion primarily centered on the failure modes observed in the EGC specimens containing fiber.Since not every crack traversed the entire specimen in its entirety, some of the cracks may be present in only a portion of the width of the specimen.Therefore, in this study, in order to have a more accurate count of the number of cracks in the specimen, the number of cracks that crossed the four equidistant lines in the transverse direction of the specimen were counted and averaged to obtain the number of cracks in each specimen, as shown in Figure 12a.In addition, in order to avoid the interference of the displacement gauge fixture on the crack observation, this study reported the number and width of cracks in the 60 mm observation section in the middle of the specimen.Finally, the average number of cracks for three specimens of each mixture was reported.The crack widths were calculated based on the number of cracks, as well as the deformation of the scale length, at which time it was assumed that the matrix deformation was negligible [22].From Figure 12b and Table 4, it can be observed that the number of cracks in the specimens gradually increased, which is consistent with the trend of fiber content variation.PE 2.0 exhibited the greatest tensile strain capacity among all the mixtures and also had the greatest number of cracks.The average crack number increased by 314.0% and 96.6% when the fiber content increased from 0.5% to 1.0% and 1.5%, respectively, but it only increased by 12.9% when the fiber content increased from 1.5% to 2.0%.From this, it can be inferred that the ability of further increasing the fiber content from 1.5% to induce cracks decreases significantly.There was a gradual decrease in the average crack width as the fiber content increased from 0.5% to 1.0% and 1.5%.Compared to PE1.5, the average crack width in PE2.0 increased by 4.1 µm, but it only increased by 2.7%.Overall, as the fiber content increased, the number of fibers at both ends of the crack increased, and so did the fiber bridging capacity [53].The stress-strain curves for all mixtures are depicted in Figure 13.All EGC samples, except for the reference mixture M, exhibited strain-hardening behavior under tensile loading.In contrast to its compressive behavior, the tensile properties of the EGC, including tensile strength and ultimate strain, gradually improved with increasing fiber content.PE1.0 exhibited a tensile strength of 2.90 MPa and an ultimate strain of 4.26%.A significant strain-hardening stage was observed during which cracks continuously initiated and propagated, thus leading to noticeable fluctuations in the stress-strain curve.When the fiber content increased to 1.5%, the tensile strength of PE1.5 reached 5.63 MPa, with an  The stress-strain curves for all mixtures are depicted in Figure 13.All EGC samples, except for the reference mixture M, exhibited strain-hardening behavior under tensile loading.In contrast to its compressive behavior, the tensile properties of the EGC, including tensile strength and ultimate strain, gradually improved with increasing fiber content.PE1.0 exhibited a tensile strength of 2.90 MPa and an ultimate strain of 4.26%.A significant strainhardening stage was observed during which cracks continuously initiated and propagated, thus leading to noticeable fluctuations in the stress-strain curve.When the fiber content increased to 1.5%, the tensile strength of PE1.5 reached 5.63 MPa, with an ultimate strain of 4.70%.This represents an increase of 94.1% and 10.3%, respectively, compared to PE1.0.Additionally, the tensile strength and ultimate strain of PE2.0 were 10.1% and 16.0% higher, respectively, than those of PE1.5.As the number of cracks increased, the stress-strain curve also exhibited more fluctuations.As the fiber volume fraction increased, the fiber reinforcement index (V f L f /d f ) of PE0.5, PE1.0, PE1.5, and PE2.0 increased from 2.50 to 5.00, 7.50, and 10.0, respectively, thus significantly enhancing the tensile performance of the EGC.Due to the inherent hydrophobicity of the PE fiber, the interface adhesion between the fiber and the matrix was mainly achieved through friction.As the fiber content increased, this mechanism facilitated an increase in the number of fiber bridging cracks, thereby ultimately resulting in the enhancement of the tensile strength of the EGC [53].14 depicts the failure modes of the specimens under impact loading at varying strain rates.The observed trend indicates an intensification of fragmentation with increasing strain rate.This was characterized by a rise in the number of smaller fragments with reduced volume, alongside a significant increase in both the number and width of cracks.The reference specimens, without fiber, exhibited a pulverized failure mode under various strain rates.The inclusion of the PE fiber demonstrably restrained the lateral deformation experienced by the specimens, thereby inducing a notable alteration in their failure mode.Observation of the fracture surfaces revealed numerous fibers bridging various small fragments.Figure 14 reveals a continuous improvement in the integrity of the EGC specimens at all strain rates with increasing fiber volume.This enhancement was attributed to the bridging effect of the fiber.Similar phenomena have been observed in studies on concrete reinforced with steel fibers and organic fibers [48,55].At a strain rate of approximately 120 s −1 , increasing the volume fraction of the PE fiber resulted in a decrease in both the number of fragments and crack widths.This phenomenon was attributed to the enhanced bridging effect of the fiber, which hindered crack propagation and facilitated energy dissipation.However, exceeding a strain rate of 155 s −1 compromised the integrity of the EGC specimens.

Stress-Strain Relationship
Figure 15 depicts the stress-strain curves for the matrix and the EGC at different strain rates.Determining a constant strain rate has been a major challenge in SHPB experiments, so choosing an accurate strain rate measurement method is critical.For this experiment, the strain rate was chosen based on the slope of the main linear portion identified in the straintime curve during the uniform deformation phase of specimen loading.Figure 15 depicts all the groups exhibiting a pronounced linear relationship in their stress-strain curves before the peak stress.This indicates a clear elastic stage, with stress directly proportional to strain.Subsequently, the curve enters a nonlinear strengthening stage, during which cracks initiate and propagate, and fiber bridges to restrain crack propagation [38,56].A notable difference was observed between the descending portions of the dynamic and static stress-strain curves.The descending segment of the static curve was characterized by a pronounced decline, whereas the descending segment of the dynamic curve exhibited gradual and relatively flat behavior.During this stage, cracks rapidly developed, thus leading to the formation of large cracks and eventual fracture.Throughout the process from crack initiation to specimen failure, most fibers experienced processes such as debonding, pull-out, or fracture from the matrix, thus consuming a considerable amount of energy [57].With increasing strain rates, an increase in the strain rate resulted in a steeper slope for the linear portion of the curve.

Stress-Strain Relationship
Figure 15 depicts the stress-strain curves for the matrix and the EGC at different strain rates.Determining a constant strain rate has been a major challenge in SHPB experiments, so choosing an accurate strain rate measurement method is critical.For this experiment, the strain rate was chosen based on the slope of the main linear portion identified in the strain-time curve during the uniform deformation phase of specimen loading.Fig- ure 15 depicts all the groups exhibiting a pronounced linear relationship in their stressstrain curves before the peak stress.This indicates a clear elastic stage, with stress directly proportional to strain.Subsequently, the curve enters a nonlinear strengthening stage, during which cracks initiate and propagate, and fiber bridges to restrain crack propagation [38,56].A notable difference was observed between the descending portions of the dynamic and static stress-strain curves.The descending segment of the static curve was characterized by a pronounced decline, whereas the descending segment of the dynamic curve exhibited gradual and relatively flat behavior.During this stage, cracks rapidly developed, thus leading to the formation of large cracks and eventual fracture.Throughout the process from crack initiation to specimen failure, most fibers experienced processes such as debonding, pull-out, or fracture from the matrix, thus consuming a considerable amount of energy [57].With increasing strain rates, an increase in the strain rate resulted in a steeper slope for the linear portion of the curve.

Dynamic Strength and Dynamic Increase Factor
The dynamic compressive strength of all the mixtures across different strain rates is presented in Figure 16.An increase in the strain rate was accompanied by a gradual increase in the dynamic compressive strength of the specimens, thus suggesting a degree of linearity in their response.This observation highlights the sensitivity of the specimens to strain rate.Two main factors may contribute to this phenomenon: First, in dynamic compressive tests, the short loading time of the specimens prevented microcracks from maturing into macrocracks.To dissipate the transferred energy, a large number of microcracks needed to form within a short period, which consumed more energy.A direct correlation was observed between the increase in the strain rate and the corresponding rise in the number of cracks, thus leading to the enhancement of the dynamic ultimate compressive strength.Secondly, during high-speed impact processes, the inertia effect of the peripheral parts of the specimens inhibited the lateral deformation of the central part, thus resulting in the specimens being in a confined state.Higher strain rates enhanced the inhibitory effect, thus resulting in increased dynamic ultimate compressive strength.
turing into macrocracks.To dissipate the transferred energy, a large number of microcracks needed to form within a short period, which consumed more energy.A direct correlation was observed between the increase in the strain rate and the corresponding rise in the number of cracks, thus leading to the enhancement of the dynamic ultimate compressive strength.Secondly, during high-speed impact processes, the inertia effect of the peripheral parts of the specimens inhibited the lateral deformation of the central part, thus resulting in the specimens being in a confined state.Higher strain rates enhanced the inhibitory effect, thus resulting in increased dynamic ultimate compressive strength.
The influence of the PE fiber content and strain rate on the dynamic compressive strength was evident.Specimens without fiber exhibited a moderate strength increase (18.1%) from 94.8 MPa to 112 MPa, as the strain rate rose from 73.0 s −1 to 160 s −1 .However, the presence of PE fiber significantly enhanced this trend.At fiber volume fractions of 0.5% and 2%, the strength increased by 28.1% and 79.4%, respectively, with increasing strain rate.This indicates a stronger reinforcing effect with higher fiber content.It is worth noting that at low strain rates, the fiber-free specimens displayed slightly higher strength.However, this trend reversed at higher strain rates, with fiber-reinforced specimens exceeding or matching those without fibers.However, when the content of PE fibers was higher, the fibers tended to agglomerate more easily, thereby leading to uneven distribution within the specimens and an increase in internal defects [58].Therefore, overall, the dynamic ultimate compressive strength of the specimens with 2% fiber content, represented by PE2.0, was slightly lower than that of the specimens with 1.5% fiber content, represented by PE1.5.

Dynamic Increase Factor
The dynamic increase factor (DIF) has been widely used to assess the strain rate sensitivity of dynamic compressive strength.Multiple studies have reported a log-linear relationship between the dynamic compressive strength of concrete-like materials and the The influence of the PE fiber content and strain rate on the dynamic compressive strength was evident.Specimens without fiber exhibited a moderate strength increase (18.1%) from 94.8 MPa to 112 MPa, as the strain rate rose from 73.0 s −1 to 160 s −1 .However, the presence of PE fiber significantly enhanced this trend.At fiber volume fractions of 0.5% and 2%, the strength increased by 28.1% and 79.4%, respectively, with increasing strain rate.This indicates a stronger reinforcing effect with higher fiber content.It is worth noting that at low strain rates, the fiber-free specimens displayed slightly higher strength.However, this trend reversed at higher strain rates, with fiber-reinforced specimens exceeding or matching those without fibers.However, when the content of PE fibers was higher, the fibers tended to agglomerate more easily, thereby leading to uneven distribution within the specimens and an increase in internal defects [58].Therefore, overall, the dynamic ultimate compressive strength of the specimens with 2% fiber content, represented by PE2.0, was slightly lower than that of the specimens with 1.5% fiber content, represented by PE1.5.

Dynamic Increase Factor
The dynamic increase factor (DIF) has been widely used to assess the strain rate sensitivity of dynamic compressive strength.Multiple studies have reported a log-linear relationship between the dynamic compressive strength of concrete-like materials and the strain rate using a base 10 logarithm.In this investigation, Equation (2) was utilized to describe the relationship observed between the EGC and the strain rate.The findings are presented visually in Figure 15.
where represents the strain rate.Table 5 presents the results of parameters a and b for different groups.As shown in Figure 17, the DIF of the specimens exhibited a strain rate-dependent increase.Worthy of note was the significant increase in the strain rate sensitivity of the geopolymer concrete observed upon the addition of fiber, irrespective of the fiber content.In comparison to the reference mixture, the slope of the DIF for PE0.5 increased from 0.232 to 0.570, while for PE1.0, the slope increased to 1.16, thus emphasizing once again the important role of fiber in strain rate sensitivity.When explaining the reasons for the strain rate sensitivity, the lateral inertial effect was widely considered as a factor [59][60][61].The addition of PE fiber provided additional resistance to concrete crack propagation, thus increasing the strain rate sensitivity.Similar phenomena have also been observed in geopolymer concrete reinforced with PVA fiber, where the presence of PVA fiber increased the DIF by more than 3.56 times compared to ordinary geopolymer concrete [33,38,55].
Buildings 2024, 14, x FOR PEER REVIEW 17 of 25 strain rate using a base 10 logarithm.In this investigation, Equation ( 2) was utilized to describe the relationship observed between the EGC and the strain rate.The findings are presented visually in Figure 15.
where represents the strain rate.Table 5 presents the results of parameters a and b for different groups.As shown in Figure 17, the DIF of the specimens exhibited a strain rate-dependent increase.Worthy of note was the significant increase in the strain rate sensitivity of the geopolymer concrete observed upon the addition of fiber, irrespective of the fiber content.In comparison to the reference mixture, the slope of the DIF for PE0.5 increased from 0.232 to 0.570, while for PE1.0, the slope increased to 1.16, thus emphasizing once again the important role of fiber in strain rate sensitivity.When explaining the reasons for the strain rate sensitivity, the lateral inertial effect was widely considered as a significant factor [59][60][61].The addition of PE fiber provided additional resistance to concrete crack propagation, thus increasing the strain rate sensitivity.Similar phenomena have also been observed in geopolymer concrete reinforced with PVA fiber, where the presence of PVA fiber increased the DIF by more than 3.56 times compared to ordinary geopolymer concrete [33,38,55].3.4.5.Dynamic Toughness Dynamic toughness, the ability of a material to absorb energy, is quantified by the area under the stress-strain curve and reflects its resistance to impact.The impact 3.4.5.Dynamic Toughness Dynamic toughness, the ability of a material to absorb energy, is quantified by the area under the stress-strain curve and reflects its resistance to impact.The impact toughness of a material can be calculated by using Equation (3), which computes the area enclosed by the stress-strain curve.
Figure 18 illustrates the impact of the PE fiber volume fraction on the dynamic impact toughness under various strain rates.An overall increase in the specimens' impact toughness to impact was observed with an increasing strain rate.Figure 16 shows that the impact toughness of the specimens generally increased with the increase in the strain rate.For example, when the strain rate was increased from 74 s −1 to 158 s −1 and 201 s −1 , the impact toughness of PE1.5 increased by 40.0% and 54.6%, respectively.This observation indicated the strain rate sensitivity of both the reference concrete and the EGC.Across all strain rates, specimens containing PE fiber exhibited higher dynamic impact toughness compared to the reference concrete.It was further observed that the impact toughness of PE0.5 displayed a close resemblance to that of the reference concrete, while the impact toughness of PE1.0 demonstrated a similar level of toughness to PE1.5.This was attributed to the bridging of cracks by the PE fiber during crack propagation, thus leading to debonding, sliding, or pull-out behavior, as well as increasing the energy absorption capacity and enhancing the specimen's impact toughness.Moreover, considering the diameter of the PE fiber, even with only a 1% volume fraction, there was still enough fiber present in the concrete to form a grid [62].Hence, there was little difference in the impact toughness between PE1.0 and PE1.5.At low strain rates (<90 s −1 ), the specimens with PE fiber ranging from 0.5% to 1.5% in volume exhibited similar dynamic impact toughness values.The application of higher strain rates resulted in more extensive damage to the specimens, which was characterized by an increased number and size of cracks, elevated peak strain values, and a marked improvement in the energy absorption capacity exhibited by the fiber [63].Therefore, under highly damaged conditions, the fiber with higher volume fractions could absorb more energy, with PE2.0 exhibiting the maximum impact toughness.Additionally, PE2.0 demonstrated the highest compressive strength exhibited under high strain rate loading conditions, which also contributed to its maximum impact toughness.
toughness of a material can be calculated by using Equation (3), which computes the area enclosed by the stress-strain curve.
Figure 18 illustrates the impact of the PE fiber volume fraction on the dynamic impact toughness under various strain rates.An overall increase in the specimens' impact toughness to impact was observed with an increasing strain rate.Figure 16 shows that the impact toughness of the specimens generally increased with the increase in the strain rate.For example, when the strain rate was increased from 74 s −1 to 158 s −1 and 201 s −1 , the impact toughness of PE1.5 increased by 40.0% and 54.6%, respectively.This observation indicated the strain rate sensitivity of both the reference concrete and the EGC.Across all strain rates, specimens containing PE fiber exhibited higher dynamic impact toughness compared to the reference concrete.It was further observed that the impact toughness of PE0.5 displayed a close resemblance to that of the reference concrete, while the impact toughness of PE1.0 demonstrated a similar level of toughness to PE1.5.This was attributed to the bridging of cracks by the PE fiber during crack propagation, thus leading to debonding, sliding, or pull-out behavior, as well as increasing the energy absorption capacity and enhancing the specimen's impact toughness.Moreover, considering the diameter of the PE fiber, even with only a 1% volume fraction, there was still enough fiber present in the concrete to form a grid [62].Hence, there was little difference in the impact toughness between PE1.0 and PE1.5.At low strain rates (<90 s −1 ), the specimens with PE fiber ranging from 0.5% to 1.5% in volume exhibited similar dynamic impact toughness values.The application of higher strain rates resulted in more extensive damage to the specimens, which was characterized by an increased number and size of cracks, elevated peak strain values, and a marked improvement in the energy absorption capacity exhibited by the fiber [63].Therefore, under highly damaged conditions, the fiber with higher volume fractions could absorb more energy, with PE2.0 exhibiting the maximum impact toughness.Additionally, PE2.0 demonstrated the highest compressive strength exhibited under high strain rate loading conditions, which also contributed to its maximum impact toughness.

Dynamic Compressive Strength Prediction
In the past, several typical DIF prediction formulas have been developed concerning the relationship between the DIF and strain rate.These formulas can be broadly categorized into two types: those based on power law variations and those adopting logarithmic functions.A review of typical DIF prediction formulas has been provided here.Among these, the CEB-FIP model, developed by the Comité Euro-International du Béton, has received particular attention due to its widespread adoption [64].The expression is provided below: Khan et al. [33] conducted extensive experimental research on fiber-reinforced geopolymer concrete and proposed an empirical formula using a logarithmic function: where α = 1 5+9 f c,imp / f cm0 , f c,imp is the impact compressive strength, and A comparison of the empirical formulas' predictions with the experimental data is shown in Figure 19.The results indicate that these empirical formulas poorly matched the experimental data and failed to adequately describe the dynamic DIF response of the EGC.The applicability range of the empirical formula proposed by Grote et al. [65] deviated from the strain rate range of the experimental results, despite the absence of coarse aggregates in the mixtures used in this study and the inclusion of fiber components.On the other hand, the logarithmic function-based DIF prediction model proposed by Khan et al. [33] provided a better prediction of the experimental results at a strain rate of around 200 s −1 in this study but still tended to overestimate the DIF overall.In the CEB-FIP model, 80 MPa was selected as the input parameter for static compressive strength.The CEB-FIP model underestimated the transition strain rate, but its overall trend matched the experimental results.Additionally, composite materials with organic fiber seemed to have higher transition strain rates, which is consistent with previous research findings [38,61].The significant influence of the fiber content on the EGC's DIF necessitated the development of a modified model.This model aims to accurately represent EGC's dynamic response across varying strain rates, thereby providing a reliable foundation for engineering applications and numerical simulations.Drawing upon the experimental data, the strain rates were restricted to a range between 69 s −1 and 201 s −1 .Subsequently, a modified model, derived from the CEB-FIP model, was proposed to precisely predict the dynamic response of the EGC under dynamic loading.This model is expressed by Equation ( 7).Drawing upon the experimental data, the strain rates were restricted to a range between 69 s −1 and 201 s −1 .Subsequently, a modified model, derived from the CEB-FIP model, was proposed to precisely predict the dynamic response of the EGC under dynamic loading.This model is expressed by Equation (7).
ε represents the loading strain rate, .ε c = 0.00003 s −1 , and m and n are the parameters of considered account for the fiber content.The matching results between the modified model and the experimental data in this study are presented in Figure 20, with the outcomes of parameters m and n summarized in Table 6.As shown in Figure 20, the modified model exhibits good agreement with the experimental data.This highlights the effectiveness of the proposed modification in accurately capturing the dynamic response of the EGC across varying fiber contents.Furthermore, in order to validate the effectiveness of the proposed modified model, a comparison was conducted with previously obtained dynamic test results on PVA-EGC.The comparison results, as shown in Figure 21, demonstrate a good agreement [38].However, it should be noted that this study did not precisely determine the transition strain rate of the EGC.In order to achieve a more comprehensive understanding of the dynamic behavior of the EGC, it is hoped that future studies will further explore and provide precise information regarding the transition strain rate of EGC.This deeper comprehension of the material's mechanical properties under various strain rates will contribute to the development of more robust references for practical engineering applications.[38].

Conclusions
This study investigated the influence of fiber content on various aspects of the EGC, including workability, quasistatic mechanical properties, and dynamic compressive performance.The following significant conclusions have been drawn from the experimental results: (1) The incorporation of PE fiber significantly enhanced the tensile properties of the EGC through fiber bridging, thus leading to significant strain-hardening behavior and improved compressive damage modes.However, with the increase in fiber content, the workability of the EGC decreased, thus leading to an increase in porosity and a decrease in compressive strength.(2) The EGC exhibited good impact resistance under high-rate impact loading, which was further enhanced with increasing fiber content.Under equivalent strain rates, the EGC maintained its integrity, while the reference concrete fractured into powder.(3) Compared to the reference concrete, the EGC showed higher strain rate sensitivity, with PE1.5 exhibiting the highest sensitivity.Increasing the strain rate led to a gradual improvement in the EGC's dynamic compressive performance, as evidenced by rising peak stress, dynamic increase factor, and impact toughness.Considering the workability, quasistatic mechanical properties, and dynamic compressive performance of the EGC, a 1.5% fiber volume content is optimal.

Conclusions
This study investigated the influence of fiber content on various aspects of the EGC, including workability, quasistatic mechanical properties, and dynamic compressive performance.The following significant conclusions have been drawn from the experimental results: (1) The incorporation of PE fiber significantly enhanced the tensile properties of the EGC through fiber bridging, thus leading to significant strain-hardening behavior and improved compressive damage modes.However, with the increase in fiber content, the workability of the EGC decreased, thus leading to an increase in porosity and a decrease in compressive strength.(2) The EGC exhibited good impact resistance under high-rate impact loading, which was further enhanced with increasing fiber content.Under equivalent strain rates, the EGC maintained its integrity, while the reference concrete fractured into powder.(3) Compared to the reference concrete, the EGC showed higher strain rate sensitivity, with PE1.5 exhibiting the highest sensitivity.Increasing the strain rate led to a gradual improvement in the EGC's dynamic compressive performance, as evidenced by rising peak stress, dynamic increase factor, and impact toughness.Considering the workability, quasistatic mechanical properties, and dynamic compressive performance of the EGC, a 1.5% fiber volume content is optimal.(4) Considering the bridging effect of fiber, a modified model based on CEB-FIP was proposed and achieved a good fit, thus providing references for practical engineering applications and numerical models.
Compared to previous studies on the dynamic mechanical properties of PVA-EGC [36], this study found that PE fiber significantly increased the dynamic compressive strength of the EGC under dynamic loading.This indicates that PE fiber is more suitable for resisting various dynamic loading in EGC compared to PVA fiber.However, it was worth noting that although a modified model based on the CEB-FIP model was proposed in this study, the direct relationship between fiber content and parameters in the modified model has not been established.Further research is needed to provide a more comprehensive theoretical basis for engineering design.

Figure 2 .
Figure 2. Particle size distributions of the components.

Figure 2 .
Figure 2. Particle size distributions of the components.

Figure 4 .
Figure 4. Test setup of direct tensile test: (a) Tensile test specimen size.(b) Tensile test specimen size.

Figure 4 .
Figure 4. Test setup of direct tensile test: (a) Tensile test specimen size.(b) Tensile test specimen size.
Buildings 2024, 14, x FOR PEER REVIEW 9 of 25 thus reducing the available lubrication water and contributing to the observed decrease in the slump flow of the geopolymer paste.

Figure 8 .
Figure 8.Effect of fiber length on flowability.

Figure 8 .
Figure 8.Effect of fiber length on flowability.

Figure 8 .
Figure 8.Effect of fiber length on flowability.

Figure 9 .
Figure 9. Quasistatic representative compressive failure modes of all mixtures.

Figure 9 .
Figure 9. Quasistatic representative compressive failure modes of all mixtures.

Figure 11 .
Figure 11.Quasistatic compressive strength of cylinder for all mixtures.

Figure 11 .
Figure 11.Quasistatic compressive strength of cylinder for all mixtures.

25 Figure 12 .
Figure 12.Schematic diagram of statistical method of crack number and typical tensile failure modes of EGC: (a) statistical method; (b) typical tensile failure modes.

Figure 12 .
Figure 12.Schematic diagram of statistical method of crack number and typical tensile failure modes of EGC: (a) statistical method; (b) typical tensile failure modes.

Buildings 2024 , 25 Figure 13 .
Figure 13.Quasistatic uniaxial tensile stress-strain curves of all mixtures.3.4.Dynamic Compressive Properties of EGC 3.4.1.Failure Mode Figure 14 depicts the failure modes of the specimens under impact loading at varying strain rates.The observed trend indicates an intensification of fragmentation with increas-

Figure
Figure14depicts the failure modes of the specimens under impact loading at varying strain rates.The observed trend indicates an intensification of fragmentation with increasing strain rate.This was characterized by a rise in the number of smaller fragments with reduced volume, alongside a significant increase in both the number and width of cracks.The reference specimens, without fiber, exhibited a pulverized failure mode under various strain rates.The inclusion of the PE fiber demonstrably restrained the lateral deformation experienced by the specimens, thereby inducing a notable alteration in their failure mode.Observation of the fracture surfaces revealed numerous fibers bridging various small fragments.Figure14reveals a continuous improvement in the integrity of the EGC specimens at all strain rates with increasing fiber volume.This enhancement was attributed to the bridging effect of the fiber.Similar phenomena have been observed in studies on concrete reinforced with steel fibers and organic fibers[48,55].At a strain rate of approximately 120 s −1 , increasing the volume fraction of the PE fiber resulted in a decrease in both the number of fragments and crack widths.This phenomenon was attributed to the enhanced bridging effect of the fiber, which hindered crack propagation and facilitated energy dissipation.However, exceeding a strain rate of 155 s −1 compromised the integrity of the EGC specimens.

Figure 16 .
Figure 16.Dynamic compressive strength strain of all mixture versus strain rate.

Figure 16 .
Figure 16.Dynamic compressive strength strain of all mixture versus strain rate.

Figure 17 .
Figure 17.Summary of fitted logarithm curves for all mixtures.

Figure 17 .
Figure 17.Summary of fitted logarithm curves for all mixtures.

Figure 18 .
Figure 18.The impact toughness of geopolymer mixtures under different strain rate.

3 )Figure 18 .
Figure 18.The impact toughness of geopolymer mixtures under different strain rate.

Buildings 2024 , 25 Figure 19 .
Figure 19.Comparison of DIF between the test results and existing models.

Figure 19 .
Figure 19.Comparison of DIF between the test results and existing models.

Figure 20 .
Figure 20.Verification of the proposed DIF model: (a) Modified model results of the DIF at diff strain rate show good agreement with test results; (b) calculation versus experimental values.

Figure 20 .
Figure 20.Verification of the proposed DIF model: (a) Modified model results of the DIF at different strain rate show good agreement with test results; (b) calculation versus experimental values.

Figure 20 .
Figure 20.Verification of the proposed DIF model: (a) Modified model results of the DIF at different strain rate show good agreement with test results; (b) calculation versus experimental values.

Figure 21 .
Figure21.Modified model results of the DIF showed good agreement with test results[38].

Table 1 .
Chemical composition of FA and GGBS.

Table 1 .
Chemical composition of FA and GGBS.

Table 2 .
Physical and mechanical properties of PE fiber.

Table 2 .
Physical and mechanical properties of PE fiber.
Where V f , L f , and d f represent fiber volume, length, and diameter, respectively.
days.Where Vf, Lf, and df represent fiber volume, length, and diameter, respectively.

Table 4 .
Average crack number and average crack width of EGC.
Data in parentheses are standard deviations.

Table 4 .
Average crack number and average crack width of EGC.
Data in parentheses are standard deviations.

Table 5 .
Values of parameters a and b in different EGC specimens.

Table 5 .
Values of parameters a and b in different EGC specimens.

Table 6 .
Parameters of DIF fitting equation.
[38]fied model results of the DIF showed good agreement with test results[38].