Structural Response of Post-Tensioned Slabs Reinforced with Forta-Ferro and Conventional Shear Reinforcement under Impact Load

Abstract

Several researchers have studied how impact loads from impact hazards affect reinforced concrete (RC) slabs. There is relatively little research on impact loading effects on pre-stressed structures. The usage of fibers in structural elements intrigued researchers. In this paper, impact-loaded post-tensioned (PT) slabs with and without Forta-Ferro fibers were compared to post-tensioned slabs with plain concrete and conventional shear reinforcement. Forta-Ferro is a lightweight, low-cost fiber, and hence its effects on slab structural response under impact load deserve to be explored. Post-tensioned slabs’ impact resistance and energy absorption were tested using real-world situations of rapid and severe loads. Four identical 3.3 by 1.5 m concrete slabs were utilized in the experiment. The experiment involved dropping a 600 kg iron ball from 8 m onto each slab’s center of gravity. The slabs’ responses were investigated. The four slab configurations were tested for displacement, energy absorption, and cracking. Forta-Ferro fiber reinforcement is understudied, making this study significant. The study’s findings may help us comprehend fiber-reinforced concrete PT slabs’ impact resistance and structural performance. Engineers and designers of impact-prone buildings like slabs and bridges will benefit from the findings. The study also suggests adding Forta-Ferro fibers to post-tensioned slabs to improve durability and resilience against unanticipated impact hazards.

1. Introduction

Rock falls are natural hazards that can have detrimental effects on slabs and the structures they support. Structures in mountainous areas are particularly exposed to such accidental hazards. Understanding the potential risks, implementing mitigation measures, and conducting thorough geological assessments are essential steps to minimize the impact of rock falls on slabs and ensure the safety of people and property in areas prone to these hazards. When subjected to such accidents, slabs undergo dynamic behavior due to the impact load generated from free-falling massive rocks. Impact loading can cause complex behaviors in concrete elements such as compressive crushing, shear failure, tensile fracturing, and spalling, leading to severe structural damage [1,2]. This topic has garnered significant interest from researchers over recent years.

In recent decades, the use of fiber-reinforced concrete (FRC) has emerged as a viable approach for improving the performance of concrete elements under impact. Compared with conventional reinforced concrete, FRC elements exhibit superior resistance to localized damage and possess improved energy absorption capabilities under impact. Several investigations have shown that compared with conventional reinforced concrete, fiber-reinforced concrete elements showed superior resistance to localized damage, thus possessing improved energy absorption capabilities under impact [3,4]. The literature shows that fibers enhance concrete’s response under static and dynamic loading conditions. Wang et al.’s [5] study on steel-fiber-reinforced lightweight aggregate concrete found that adding steel fibers significantly improved its tensile strength, flexural toughness, and impact resistance. The addition of 1.0% to 1.5% steel fiber by volume improved the concrete’s toughness and energy absorption capacity, making it suitable for high durability under impact. Zhang et al.’s [6] study examined the fracture behavior of steel-fiber-reinforced concrete (SFRC) under various loading rates. They conducted three-point bending tests on notched beams. The results showed that peak load and fracture energy increased with higher loading rates, indicating enhanced fracture resistance and energy absorption capabilities. Cunha et al. [7] developed a model to simulate the tensile behavior of steel-fiber-reinforced self-compacting concrete. The study used a 3D smeared crack model for the concrete matrix and a Monte Carlo method for the random distribution of fibers. Experimental tensile tests validated the model, showing that the inclusion of steel fibers significantly enhances the concrete’s post-cracking tensile behavior, particularly in terms of toughness and energy absorption, making it more resistant to tensile cracking. Tokgoz et al.’s [8] study evaluated the structural behavior of steel fiber high-strength reinforced concrete and composite columns under eccentric loading conditions. The results showed that incorporating steel fibers significantly improved ductility, deformation capacity, and resistance to cracking and failure under load. Olivito et al.’s [9] study examined the mechanical behavior of steel-fiber-reinforced concrete, revealing that while compressive strength was slightly affected, tensile strength and post-cracking ductility significantly improved, indicating the fibers’ effectiveness in energy absorption and crack resistance. Atis and Karahan’s [10] study examined steel-fiber-reinforced fly ash concrete’s properties, focusing on strength, durability, and workability. They tested concrete mixtures with varying fly ash and steel fiber content. The results showed steel fibers improved tensile strength, drying shrinkage, and freeze–thaw resistance, while fly ash increased workability and freeze–thaw resistance. The study by Ding et al. [11] examined the impact of steel fibers and stirrups on self-consolidating concrete beams. The results showed that adding steel fibers significantly increased shear strength, transforming brittle failures into ductile flexural failures, and partially replacing stirrups.

Many methods are utilized to strengthen reinforced concrete (RC) elements to resist impact loads. Numerous research studies have employed fiber-reinforced polymers (FRP) [12,13,14]. Ref. [15] conducted a major study testing two-way reinforced concrete slabs enhanced with carbon-fiber-reinforced polymer (CFRP) sheets under impact stresses. The CFRP-reinforced samples exhibited a 10% higher impact load capability than regular samples, increasing to 25% for the static-loaded sample. However, CFRP sheets were ineffective in resisting punching shear failure, highlighting the limitation of CFRP in impact resistance. Similarly, Jahami [16] numerically compared CFRP-reinforced slabs to post-tensioned slabs, confirming that punching shear failure is crucial in impact loading and that CFRP is not appropriate for impact resistance.

Hao [17] examined how steel fibers in concrete affect the impact resistance of reinforced concrete beams. The study showed that spiral steel fibers absorb impact energy better and improve the structural performance of RC beams under impact loading. Hrynyk et al. [18] also examined impact-loaded steel-reinforced concrete slabs, indicating that steel fibers increased slab capacity, reduced crack widths and spacings, and mitigated impact damage. Saatci et al. [19] studied the effects of different shear reinforcements on impact-loaded RC slabs and found that steel fibers and shear studs significantly improve both static and impact behavior.

Researchers have compared the efficiency of fibers in enhancing punching shear resistance. Harajli et al. [20] compared steel and polypropylene fibers, finding that both types significantly increased punching shear capacity and exhibited ductile failures, dispersing more energy than conventional concrete. Al-Rousan [21] analyzed polypropylene-fiber-reinforced concrete two-way slab failures, showing that adding fibers and increasing slab thickness improved structural behavior and impact resistance.

Bhosale et al. investigated the fracture response of FRC with steel, synthetic, and hybrid fibers, finding that fibers improve fracture energy [22]. Gali et al.’s tests on self-compacting and normal concrete showed concrete type plays a significant role in FRC’s fracture response [23]. Ofuyatan et al. found coconut stems boost concrete slabs’ impact resistance [24]. Aghaee et al. noted increased fiber content enhances the number of blows to cause cracks and ultimate failure [25]. Wang et al. concluded steel fibers significantly enhance light weight concrete’s impact resistance [26].

Murali et al. noted a 14% increase in impacts to failure in layered fibrous concrete samples [27]. Wang et al. found natural flax fibers provide remarkable energy absorption and impact resistance, with less damage than plain samples [28]. Abirami et al. demonstrated FRC has significantly higher impact strength than non-fibrous concrete [29]. Mohammadi et al. found higher fiber percentages and lengths enhance impact resistance [30]. Al-Hadithi et al. suggested 1.5% fiber content improves absorbed energy and impact resistance [31]. Rao et al. reported slurry-infiltrated fibrous concrete slabs with reinforcement absorb significantly more energy than slabs without reinforcement [32]. Yahaghi et al. found a linear correlation between fiber volume fraction and impact resistance in oil palm shell fiber concrete [33]. Ramakrishna et al.’s study showed natural fibers increase impact resistance of fiber-reinforced cement mortar by 3 to 18 times compared to plain mortar slabs [34].

In recent years, extensive studies on the incorporation of Forta-Ferro fibers into concrete mixes have shown significant enhancements in mechanical characteristics and stability. A study conducted by Dashti et al. [35] demonstrated that the inclusion of Forta-Ferro fibers at a volume fraction of 0.4% can achieve a 15% increase in compressive strength and a substantial improvement in direct tensile strength. Consequently, this leads to a reduction in crack propagation and an enhancement in the overall ductility of concrete. The use of Forta-Ferro fibers in ultra-high-performance self-compacting concrete (UHPSCC) resulted in a 1% to 7% increase in compressive strength, a 20% to 30% increase in tensile strength, and a 16% to 26% increase in flexural strength. These improvements demonstrate the superior ability of Forta-Ferro fibers to enhance the toughness and resistance to cracking under stress of concrete [36]. Investigation of the compressive and flexural properties of Forta-Ferro-fiber-reinforced concrete revealed a significant enhancement in compressive strength, ranging from 10% to 20%. This indicates that these fibers have the potential to be used as a non-corrosive substitute for steel reinforcement in certain applications [37]. In addition, the incorporation of Forta-Ferro fibers into concrete that includes compressed nylon aggregates has been demonstrated to augment durability and mechanical characteristics, thus enhancing resistance to environmental deterioration and consequently improving the overall toughness and longevity of the material [38]. According to a study conducted by Alfoul et al. [39], the use of Forta-Ferro fibers in concrete has been shown to greatly improve its durability and lifespan by promoting more uniform distribution of stress. This, in turn, decreases the risk of catastrophic failure. Although Forta-Ferro fibers offer significant enhancements in compressive and tensile strengths, they may not completely substitute steel fibers in terms of flexural strength. A comparative analysis of Forta-Ferro and steel fibers revealed that Forta-Ferro fibers greatly improve compressive and tensile characteristics, but steel fibers still exhibit superior performance in flexural strength. This implies that a combination of both fibers may be used for applications that demand high flexural strength [40]. Furthermore, it has been suggested that the ideal volume fraction of 0.4% Forta-Ferro fibers should be used to achieve the highest possible compressive and tensile strength of concrete, without affecting its workability. This emphasizes a balanced strategy to enhance mechanical characteristics while ensuring that mixing and application remain easy [41].

The use of shear reinforcement to resist punching failure is commonly tested in reinforced concrete slabs. The investigation by Shatarat et al. [42] focused on the punching shear behavior of flat slabs with various shear reinforcement configurations. They found that circular spiral stirrups provided the highest enhancement in punching shear capacity, improving it by 23% to 30%. Rectangular spiral stirrups and advanced rectangular spiral stirrups also showed significant improvements, with enhancements of up to 25% and 23%, respectively. Ordinarily closed rectangular stirrups increased punching shear capacity by 9% to 13%. These studies highlight the importance of shear reinforcement in preventing catastrophic punching shear failure, which can lead to the separation of the slab and column, causing a significant load transfer to adjacent elements not designed to endure such loads. Hassan et al. [43] developed a design equation for two-way slabs reinforced with FRP bars and stirrups, showing improved shear performance. In a previous study conducted by the authors of this paper with Jahami et al. [44], the impact behavior of rehabilitated post-tensioned slabs damaged by impact loading was examined. The study demonstrated that shear ties improved shear capacity and changed the crack pattern from shear to flexural.

Despite extensive research on reinforced concrete slabs, the performance of post-tensioned slabs under impact loads remains limited within the literature. Post-tensioned slabs have been widely used in recent years due to their advantages over reinforced concrete slabs, such as increased span capabilities, cost-effectiveness, improved durability, reduced maintenance, quicker construction schedules, enhanced performance against seismic and wind forces, and sustainability benefits through reduced environmental impact. Yet, the performance of PT slabs with fiber-reinforced concrete requires exploration.

This study focuses on the use of Forta-Ferro fibers, which are lightweight synthetic fibers, in post-tensioned slabs. The remarkable mechanical characteristics of Forta-Ferro fibers, including their high tensile strength, impact and shear resistance, flexural toughness, fatigue resistance, post-cracking residual strength, and durability, render them highly efficient in improving the performance of PT slabs subjected to impact loads. These specific characteristics guarantee that the slabs possess enhanced resistance to the forces exerted by impacts, thereby decreasing the probability of catastrophic failure and preserving their structural integrity in the long run.

This study aims to compare the impact response of PT slabs reinforced with 0.4% by volume Forta-Ferro to the response of conventional PT slabs, PT slabs with shear reinforcement in the form of ties, and PT slabs with a combination of both 0.4% by volume Forta-Ferro and shear ties. This paper is divided into several sections to present the research findings clearly. The Materials and Methods section details the experimental setup, the design of the four tested slabs, the support system, the impactor, and the physical properties of Forta-Ferro. The Results and Discussion section examines the experimental outcomes, focusing on displacement, damping factors, impact forces, and the observed crack patterns. This analysis highlights the effects of Forta-Ferro fibers and shear reinforcement on improving the slabs’ impact resistance. The study reveals promising results for the use of Forta-Ferro in areas prone to impact hazards, which are summarized in the Conclusion section, showing how Forta-Ferro enhances the structural integrity of post-tensioned slabs under impact loads.

2. Materials and Methods

In this section, the experimental setup, design of slabs, built support system, load generating impactor, Fort-Ferro fibers, and testing method are stated.

2.1. Experimental Setup

The experimental setup for this study was meticulously designed to investigate the behavior of post-tensioned concrete slabs reinforced with Forta-Ferro fibers under impact loads. Four identical simply supported concrete slabs, each measuring 3.3 × 1.5 × 0.18 m, were constructed, with one serving as the control without fiber reinforcement (PT-C), another incorporating 0.4% by volume of Forta-Ferro fibers into the concrete mix (PT-F), the third being reinforced with conventional shear reinforcement in the form of ties (PT-S), and the fourth casted with a combination of both conventional shear reinforcement and 0.4% Forta-Ferro fibers (PT-FS). The slabs were cast with a ready mix concrete of a compressive strength of 34 MPa at 28 days.

2.2. Design Calculations and Reinforcement

The slabs’ thickness and reinforcement computations were performed based on the ACI Building Code Requirements for Structural Concrete.

The moment capacity of each slab was calculated based on the following formulae:

$$M_n=A_{ps}{f}_{ps}\left(d_p-{\displaystyle \frac{a}{2}}\right)+A_s{f}_y\left(d-{\displaystyle \frac{a}{2}}\right)$$

(1)

$$f_{ps}=f_{pu}\left[1-{\displaystyle \frac{{\gamma }_p}{{\beta }_1}}\left({\rho }_p{\displaystyle \frac{f_{pu}}{{f^{\prime }}_c}}+{\displaystyle \frac{d\omega }{d_p}}\right)\right]$$

(2)

where “$f_{ps}$” is the stress in the pre-stressed reinforcement at nominal strength, “$f_{pu}$” is the specified tensile strength of pre-stressing tendons, “$d_p$” is the distance from the extreme compression fiber to the centroid of the pre-stressed reinforcement but not less than 80% of the overall slab’s thickness, “${\gamma }_p$” is a factor based on the criteria (fpy ¼ 0.80 fpu for high strength pre-stressing bars, 0.85 for stress-relieved strands, and 0.90 for low-relaxation strands), “ω” is the reinforcement index.

Based on the above calculations, the reinforcement of the slabs was selected. Each slab had 2 tendons, 7 wire strands each, with a cross-sectional area 99 mm² spaced 0.5 m, as well as lower and upper mesh reinforcement with a diameter of 8 mm with center-to-center distance 0.2 m in both directions (Figure 1 and Figure 2). The tendons were stressed using a hydraulic jack to reach a stress of 1480 MPa.

2.3. Slabs’ Supports and Impactor

The supporting system consisted of IPE 400 steel sections placed on the short edges of the slabs, which were in turn supported on rectangular strip footings (Figure 3). The slabs were anchored to the IPE sections to avoid uplifting at the level of the support. The critical phase of the experiment involved subjecting the four slabs to a dynamic impact load, achieved by releasing the impactor from a height of 8 m to hit both slabs at their center of gravity. The impactor was a spherical iron ball with a mass of 600 kg. A crane was used to hold the impactor (Figure 4). The positioning of the impactor was facilitated by employing a total station topographic instrument prior to its release.

2.4. Testing System

The slabs were mounted by accelerometer sensors at fixed locations on each slab (Figure 5). The position of accelerometers was selected to allow recording the maximum response of the slabs but away from the impacted area because the expected damages in the impact area would generate non-realistic readings. The accelerometers were connected by wires to a data acquisition system to record the response of the slabs during impact. Each accelerometer sensor can record up to 500 g of load with sensitivity of 10 mV/g, a frequency range between 10,000 Hz and 15,000 Hz, and a resonance frequency greater than 50 Hz [20]. The data acquisition system used in this experiment was composed of National Instrument CompactDAQ (cDAQ-9178 with eight channels) and a measurement card (NI 9234) (Figure 6).

The system allowed the precise measurement of acceleration due to impact. The slabs’ displacements were computed from the collected acceleration results by applying double integration with respect to time. The following equations were used to perform the calculations:

$$\mathrm{V}\left(\mathrm{t}\right)=\int \mathrm{a}\left(\mathrm{t}\right)\mathrm{d}\mathrm{t}$$

$$\mathrm{D}\left(\mathrm{t}\right)=\int \mathrm{V}\left(\mathrm{t}\right)\mathrm{d}\mathrm{t}$$

where “a” is the acceleration, “V” is the velocity, and “D” is the slab displacement. The above double integration was calculated using Labview© code. This code was developed to acquire the accelerometer data and then it was integrated using a pre-defined block. The Labview block can double integrate the data to directly obtain the displacement, as shown in Figure 7.

The obtained values of displacements were incorporated into the calculation of the impact force and the damping factor. During testing, some accelerometers failed and could not record the response.

Table 1. Accelerometer locations and results.

Sensor Slab	ACC1 (1650 mm)	ACC2 (1195 mm)	ACC3 (650 mm)	ACC4 (1150 mm)
PT-C
PT-F
PT-S
PT-FS

shows the locations of the four accelerometers used measured from the edge of the slab and summarizes the results obtained. To compare the results, ACC2 was considered as readings from the four slabs could be collected. The damages and cracks generated due to impact were traced and compared as well.

2.5. Forta-Ferro Properties

Forta-Ferro (Figure 8) is a macro synthetic fiber composed of 100% virgin copolymer/polypropylene, which is color-blended and known for its ease of application and finishing. The material comprises of intertwined bundle monofilament and fibrillated fibers, resulting in a concrete reinforcement with high performance characteristics. The macro synthetic fiber exhibits exceptional long-term durability, contributes to structural improvements, and effectively mitigates temperature-induced and shrinkage-related cracking. The Forta-Ferro material has characteristics of being non-corrosive, nonmagnetic, and possessing complete resistance to acid and alkali substances. The physical properties of Forta-Ferro are listed in

Table 2. Physical properties of Forta-Ferro.

Property	Value
Specific gravity	0.91
Density	910 kg/m3
Tensile strength	620 MPa
Length	54 mm

. Forta-Ferro is typically used at ratios of 0.2%, 0.27%, 0.33%, 0.4%, 0.5%, and 1% by volume of concrete. In this study, 0.4% by volume of Forta-Ferro fibers were used, which was chosen to be the average value of these recommended dosages. Prior casting the post-tensioned slabs and preparing them for the experiment, a concrete mix sample was prepared, and cylindrical samples were collected. Samples were divided into two groups. The first group was without fibers, while to the second group, 0.4% by volume of fibers were added. At 28 days, the splitting tensile test and compressive strength test were performed according to the ASTM C496/C496M and C39/C39M, respectively. The stress–strain curves were plotted (Figure 9 and Figure 10). The results showed that the presence of fibers increased the ductility and tensile strength of concrete. Figure 11 is a bar chart representation for the change in compressive and tensile strength of the concrete mix upon addition of fibers. The results showed that the tensile strength increased by around 17.5%, while the compressive strength increase was around 8%. This clearly highlights the important role of Forta-Ferro in enhancing the tensile capability of concrete, which in turn shall enhance the impact resistance of the slab under impact.

3. Results and Discussion

Figure 12 depicts the state of four post-tensioned slabs after an impact. The tension zones (bottom faces) of the PT-C, PT-F, PT-S, and PT-FS slabs are shown in Figure 12a–d, respectively. The PT-C slab had extensive cracking and spalling, whereas the PT-F slab revealed minor cracks, suggesting the presence of fiber effect. The PT-S slab exhibited visible fractures while maintaining an acceptable degree of structural integrity because of shear reinforcement. On the other hand, the PT-FS slab demonstrated controlled cracking, which can be attributed to the combined influence of fibers and shear reinforcement. Figure 12e–g illustrate the compression zones, namely, the top faces, of the identical slabs. The PT-C slab exhibited surface cracks, whereas the PT-F slab had comparable but of lesser severity cracks. In compression, the PT-S slab exhibited controlled fracture propagation, while the PT-FS slab demonstrated minimum cracking, suggesting superior performance.

In this section, the experimental outcomes are presented and discussed. From the testing methodology described above, the acceleration values were collected, from which the displacement values were deduced. Other parameters including damping factor, impact force, and crack patterns were investigated as well in this section, which are discussed below.

3.1. Displacements

The displacement at each accelerometer was computed as mentioned above using the double integration for the acceleration curves (Figure 13).

Table 3. Maximum displacement and impact force.

Slab	Impact Load (kg)	Maximum Displacement (mm)	Impact Force (kN)	Shear Strength (kN)	Impact Force/Maximum Displacement (kN/mm)
PT-C	600	130	622	605	4.72
PT-F	600	82	580	605	7.07
PT-S	600	57	831	1690	14.49
PT-FS	600	40	1179	1690	29.04

summarizes the maximum displacement values for ACC2.

The four slabs have the same moment capacity and thus shall exhibit the same displacement under impact load. For slab PT-C, the maximum recorded displacement was 130 mm. For slabs PT-S, PT-F, and PT-FS, the maximum displacements were 57 mm, 82 mm, and 40 mm, respectively. PT-C showed higher displacement than PT-F, PT-S, and PT-FS. Examining the damage in the slabs (Figure 12), PT-C collapsed, which led to the cease of response and acceleration recording, while the other slabs remained capable of absorbing the forces generated due to impact. PT-F, PT-S, and PT-FS exhibited the ability to effectively absorb and disperse energy. In addition, the latter exhibited moderate failure, in contrast to PT-C, which experienced complete structural failure. Forta-Ferro fibers are known to provide post-crack residual strength to the concrete, reducing the extent of cracking and enhancing the overall structural integrity. The Forta-Ferro fibers enhanced the residual strength, enabling slabs PT-F, PT-S, and PT-FS to continue supporting the loads, while slab PT-C lost its load-carrying capacity and failed. This justifies the reduced displacement as well recorded in PT-F, PT-S, and PT-FS, while PT-C experienced more sudden and brittle failure, which led to higher displacement. The findings are similar to what have been concluded in other studies such as in the study by Wang and Chouw [29], which deduced that non-fibrous concrete samples suffered more damage compared to fibrous concrete. Similarly, Harajli [21] highlighted that conventional concrete, without fiber reinforcement, tends to fail in a more brittle manner under impact loading.

3.2. Damping Factor

Another factor was studied, which is the damping factor of the slabs. The damping coefficient represents the ability of a material to dissipate energy during dynamic loading. To compute its value, the first two peak accelerations ${\mathrm{a}}_1\mathrm{a}\mathrm{n}\mathrm{d}{\mathrm{a}}_2$ were recorded, and the following equations were used for the calculations:

$$\mathsf{\delta }=\mathrm{l}\mathrm{n}\left({\displaystyle \frac{{\mathrm{a}}_1}{{\mathrm{a}}_2}}\right)={\displaystyle \frac{2\mathsf{\pi }}{\sqrt{1-{\mathsf{\xi }}^2}}}$$

(3)

where $\mathsf{\xi }$ is the damping ratio. To find the damping ratio, the above equation can be rearranged as

$$\mathsf{\xi }=\sqrt{{\displaystyle \frac{{\mathsf{\delta }}^2}{4{\mathsf{\pi }}^2+{\mathsf{\delta }}^2}}}$$

(4)

The peak accelerations were collected from the response curves (Figure 14).

The bar chart in Figure 15 shows the values of the first two peak accelerations recorded to calculate the damping ratio.

The obtained damping ratios were as follows: 0.328 for PT-FS, 0.262 for PT-F, 0.226 for PT-S, and 0.216 for PT-C. PT-FS, which combines fiber reinforcement and shear ties, demonstrated the highest damping ratio, demonstrating its greater ability to dissipate energy. This indicates that the combination of fibers and shear reinforcement improves the damping performance by enhancing both the tensile strength and shear capacity of the concrete matrix.

PT-F, which is fiber reinforced, had a notable damping ratio, highlighting the efficacy of fibers in augmenting energy dissipation by bridging cracks and strengthening the resilience of the concrete. PT-S, when equipped with shear ties, exhibited a moderate damping ratio, which indicates that its main purpose is to enhance shear strength rather than dissipate energy. The control slab, PT-C, exhibited the lowest damping ratio, which signifies the natural damping characteristics of post-tensioned concrete without any supplementary reinforcements.

The obtained values emphasize the crucial significance of integrated reinforcing in enhancing the impact resistance and vibration control of concrete slabs. The greater damping performance of PT-FS makes it ideal for structures that experience impact loads. This is owing to its increased tensile strength and ability to manage cracks with fibers, as well as its enhanced shear capacity from shear ties. The substantial influence of fibers on enhancing the structural performance of concrete slabs under dynamic loading is emphasized by the high damping ratio of PT-F. The control slab PT-C functions as a reference point, highlighting the natural capacity of post-tensioned slabs to dampen vibrations. However, the limited performance of PT-S suggests that shear reinforcement alone should be complemented with additional forms of reinforcement to enhance energy dissipation. Although the combination of shear reinforcement and fibers in slabs is not yet commonly investigated, the enhancement in the energy dissipation obtained in PT-S and PT-F align with the studies conducted by Hao [18], which showed that steel fibers absorb impact energy better and improve structural performance under impact, and by Harajli [21] and Al-Rousan [22], who both found that adding fibers, in addition to shear reinforcement, significantly increased structural behavior under impact loads. This suggests the necessity of combining shear reinforcement with fibers for optimal performance, as examined for PT-FS in the results obtained.

3.3. Impact Force

The impact history revealed a significant peak in force magnitude at the instant of collision of the load with the slab, followed by smaller values caused by the load bouncing afterwards. The initial impact had a significantly greater magnitude in comparison to the later impacts. The initial load value had a higher magnitude than the values recorded after the collision, which had a lower magnitude for a relatively long duration for the slabs to go back to the static position. The maximum displacement was computed based on the approach discussed earlier. The values obtained were subsequently utilized to compute the average impact force. The equation used to calculate the average impact force is presented below. The impact force values for each slab are presented in Table 3, along with the ratio of the impact force to the maximum displacement.

$$F_{\mathrm{avg}}\cdot {\mathrm{y}}_{\max }-{\displaystyle \frac{{\mathrm{F}}_{\mathrm{avg}}^2}{2\mathrm{K}}}=\mathrm{m}\mathrm{g}\mathrm{h}=\mathrm{I}\mathrm{m}\mathrm{p}\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{E}\mathrm{n}\mathrm{e}\mathrm{r}\mathrm{g}\mathrm{y}$$

(5)

where “m” is the mass of the impactor = 600 kg; “g” is the acceleration due to gravity; “h” is the height from which the impactor was left to fall freely = 8 m; ${\mathrm{F}}_{\mathrm{avg}}$ is the average impact force; and K is the shear stiffness defined as K = GA/L (where A is the critical perimeter multiplied by the thickness, and L is the distance between the support and the impact point and G is the shear modulus).

The control slab, PT-C, exhibited the highest maximum displacement of 130 mm and an impact force of 622 kN intensity. The incorporation of fibers in PT-F reduced the maximum displacement to 82 mm, and the impact force calculated was 580 kN. Shear reinforcement ties in PT-S further improved performance, reducing displacement to 57 mm and significantly increasing the impact force to 831 kN. The combined reinforcement in PT-FS demonstrated the best performance, with the lowest maximum displacement of 40 mm and the highest impact force of 1179 kN. The calculated impact force of PT-F was almost close to the impact force generated in PT-C. Yet, PT-S and PT-FS showed 25% and 48% increase in magnitude compared to PT-C, respectively. The ratio of force to maximum displacement was computed and the results showed 34%, 68%, and 84% for PT-F, PTS, and PT-FS enhancement, respectively, compared to PT-C. The results indicate that PT-C, lacking any additional reinforcement, has the least resistance to impact, manifesting in major deformation under impact load. PT-F showed an enhancement in the slab’s ability to absorb impact energy. The incorporation of Forta-Ferro fibers made the concrete more tough thus more resilient to impact load. Dashti and Nematzadeh (2020a) demonstrated that the inclusion of Forta-Ferro fibers increases tensile strength and controls crack propagation, thus improving toughness and resilience under dynamic loads. Similarly, PT-S due to the presence of ties had larger load bearing capacity and demonstrated high stiffness after collision. This correlates with Hassan et al. [37], who noted that shear reinforcement is critical in improving impact performance, particularly in mitigating crack formation and providing additional load-bearing capacity. Yet, the combined reinforcement in PT-FS demonstrated the best performance with a superior force-to-displacement ratio. The interaction between fibers and shear reinforcement indicated a significant improvement in structural performance, providing both toughness and stiffness essential for impact resistance.

3.4. Shear Strength and Crack Pattern

The cracks and failure of the slabs after impact were carefully examined. All cracks on the bottom face of the two slabs were traced to deduce the mode of failure (

Table 4. Tension and compression damage patterns.

Slab	Bottom Face (Tension)	Top Face (Compression)
PT-C
PT-F
PT-S
PT-FS

).

In addition, the shear strength, “${\mathrm{V}}_{\mathrm{c}}”,$ was computed for the slabs based on the ACI equations.

$${\mathsf{\vartheta }}_{\mathrm{c}}=\left(0.29\mathsf{\lambda }\sqrt{{{\mathrm{f}}^{\prime }}_{\mathrm{c}}}+0.3{\mathrm{f}}_{\mathrm{p}\mathrm{c}}\right)+{\mathsf{\vartheta }}_{\mathrm{p}}$$

(6)

$${\mathsf{\vartheta }}_{\mathrm{c},\mathrm{d}\mathrm{y}\mathrm{n}}={\displaystyle \frac{\sqrt{{{\mathrm{f}}^{\prime }}_{\mathrm{c},\mathrm{d}\mathrm{y}\mathrm{n}}}}{\sqrt{{{\mathrm{f}}^{\prime }}_{\mathrm{c}}}}}\ast {\mathsf{\vartheta }}_{\mathrm{c}\mathrm{o}\mathrm{n}}$$

(7)

$${\mathrm{V}}_{\mathrm{c}}={\mathsf{\vartheta }}_{\mathrm{c}}{\mathrm{b}}_0\mathrm{d}$$

(8)

where “${\mathrm{b}}_0$” is the perimeter of the critical section; “${\mathrm{f}}_{\mathrm{p}\mathrm{c}}$” is the average prestressing stress value in the two directions; and “${\mathsf{\vartheta }}_{\mathrm{P}}$” is the vertical component of all effective pre-stress stresses crossing the critical section.

The value of dynamic shear strength, ${\mathrm{V}}_{\mathrm{c},\mathrm{d}\mathrm{y}\mathrm{n}}$, was then calculated. On the one hand, the shear strength for slabs PT-C and PT-F prior to impact was 605 kN. On the other hand, PT-S and PT-FS had the same shear strength, which differed from the two slabs mentioned earlier due to the presence of shear reinforcement, which was found to be 1690 kN. After impact, the value of impact force determined was compared to the shear strength computed using the above equations. As shown in Table 3, the impact forces of slabs PT-C, PT-F, PT-S, and PT-FS were 622, 580, 831, and 1179 kN, respectively. Comparing the shear strength to the impact forces, it was found that PT-C had an impact force larger than the shear strength of the slab, while the other slabs had impact forces less than the shear strength of the slabs.

The crack profiles of the four specimens were compared. It should be noted that the control slab PT-C suffered extensive damage and almost total failure. The punching cone was vivid in this slab. In addition, there was a large area of spalled concrete and bending in the reinforcement at the bottom face of the slab, indicating flexural failure. The other slabs showed minimal damage when compared to PT-C and showed a wider spread of cracks. Both PT-F and PT-S showed an enhanced behavior. Yet, PT-F showed wider spread in thin cracks than PT-S, which showed less spread of cracks with larger crack widths. PT-FS showed minimal crack widths and remained intact with the greatest energy dissipation. Thus, incorporating fibers and shear reinforcement shifted the mode of failure from pure punching to a combination of shear and flexural failure, which enhances the overall structural performance. It can be concluded that the Forta-Ferro fibers could enhance the tensile strength of concrete, which led to smaller crack widths and less crack propagation in the tested slabs. This is similar to the findings of Dashti et al. [35], which stated that the inclusion of Forta-Ferro fibers at a volume fraction of 0.4% can substantial enhancement in direct tensile strength, leading to a reduction in crack propagation and an improvement in the overall ductility of concrete.

In their study, Saatci and Arsan [19] discovered that the addition of shear studs and steel fibers to reinforced slabs resulted in a notable enhancement in both static and impact performance. The inclusion of steel fibers increased the level of ductility and altered the failure mode from shear punching to flexural bending. The results of this investigation are consistent with the findings that PT-S and PT-FS slabs, which were reinforced using shear reinforcement, exhibited significantly greater impact resistance and lower displacements compared to the control slab, PT-C.

In the previous study conducted by the authors [37], the effect of shear reinforcement on the behavior of rehabilitated post-tensioned slabs was investigated. It was found that the use of shear reinforcement enhanced the punching shear capacity and altered the crack pattern from shear to flexure. The current investigation supports this conclusion, since PT-S and PT-FS slabs exhibited enhanced shear strength and more desirable crack patterns in comparison to PT-C.

4. Conclusions

This paper compares the response of four post-tensioned (PT) slabs under impact loads: PT-C control slab, PT-F with 0.4% by concrete volume of Forta-Ferro fibers, PT-S with tie shear reinforcement, and PT-FS having a combination of Forta-Ferro and ties. The aim was to see the efficiency of using 0.4% Forta-Ferro, which is the average recommended dose in post-tensioned slabs, as well as to see how they contribute to the structural response of slabs under impact loads. Four PT slabs were designed to have identical moment capacity.

From this study, the following observations were recorded:

• PT-C exhibited the largest displacement, while PT-FS had the least recorded displacement. PT-S showed higher displacement than PT-F.
• The highest damping ratio obtained was for PT-FS, followed by PT-F, PT-S, and PT-C.
• The ultimate impact force calculated was for PT-FS.
• PT-C underwent total failure with a punching cone formation and large spalling of concrete. PT-S and PT-F showed relatively acceptable damage. PT-FS had minimum damage with the formation of thin flexural cracks, indicating a change in the structural response from punching to flexural.

From the above observations and upon analyzing the results, the following conclusions were drawn:

• Forta-Ferro fibers in the concrete slab contributed to enhanced ductility, controlled cracking, post-crack residual strength, and energy absorption. These factors collectively allow the fiber-reinforced slab to exhibit lower displacement and remain resilient, even when subjected to impact loads, compared to the slab without fibers. Slabs prone to impact hazards shall have high ductility and shall be more resilient to avoid catastrophic irreparable failures.
• Shear reinforcement enhanced the slab ductility yet was unable to control the cracking.
• The combination of Forta-Ferro and shear reinforcement resulted in the ultimate performance and resilience on PT slabs. PT-FS exhibited the best results with the lowest displacement, highest impact force, and greatest force-to-displacement ratio, indicating significant enhancement in toughness and stiffness for optimal impact resistance.
• The damping ratios of the four post-tensioned slabs (PT-FS, PT-F, PT-S, PT-C) when subjected to impact load provided valuable information about how different reinforcement techniques affect the structural performance of the slabs. The lower damping factor in the slab with fibers, combined with its ability to withstand the impact without collapsing, suggests that the Forta-Ferro fibers play a crucial role in improving the resilience and post-failure behavior of the concrete. The fibers contribute to controlled cracking, energy absorption, and maintaining structural integrity, all of which collectively lead to a more robust and durable structural response.
• The control slab PT-C experienced extensive damage and almost total failure due to an impact force exceeding its shear strength, with pronounced punching failure. Incorporating fibers and shear reinforcement in the other slabs significantly improved their behavior, shifting the failure mode from pure punching to a combination of shear and flexural failure in PT-F and PT-S and pure flexural in PT-FS, thereby enhancing overall structural performance and energy dissipation.
• The use of 0.4% of Forta-Ferro fibers is convenient to enhance the dynamic structural behavior of post-tensioned slabs.

The results obtained provide promising indications about the use of Forta-Ferro in areas prone to hazards such as rock-falls. The results showed the resilience provided to slabs when Forta-Ferro fibers were added in terms of controlled deflection and cracks, higher impact resistance, and higher damping ratios than the slabs with ordinary reinforcement and those without additional shear reinforcement.. For further studies, it is recommended to compare the behavior of post-tensioned slabs with fibers to post-tensioned slabs reinforced with conventional shear reinforcement. It is also worth investigating how the variation of the percentage of fibers used will affect the structural performance of slabs under dynamic loadings.