NLFEA of the Behavior of Polypropylene-Fiber-Reinforced Concrete Slabs with Square Opening

Abstract

The bending behavior of one-war reinforced concrete (RC) slabs with polypropylene fibers (PF) was examined in this study under the effect of different opening ratios using the nonlinear finite element analysis (NLFEA) method. The investigated parameters include the effect of different square opening ratios between 0 and 24% and PF volume percentages between 0 and 1% with 0.1% increments. The objectives of this study were fulfilled using 88 NLFEA models with different combinations of the studied parameters, including 11 control slabs without openings. The slab’s behavior was studied focusing on different structural performance characteristics, such as ductility, using energy-based and deflection-based approaches, stiffness (initial and yielding), cracking, and ultimate load strength. In addition, other structural performance parameters were considered, such as the crack opening, failure modes, and strain values, which were recorded for all specimens during the loading history. Moreover, the load-carrying capacity of the slabs was compared, looking at the NLFEA method’s results and the theoretical prediction results based on the sectional analysis method. However, it was observed that the inclusion of PFs of different percentages has a superior effect on the behavior of RC slabs with small openings (less than 2% opening ratio) compared to the acceptable improvements obtained for sabs with larger opening sizes. Consequently, PF could be utilized as a replacement for conventional steel rebars for RC slabs with small openings. In addition, increasing the PF percentage increases the resulting crack-opening value at failure due to the provided stabilization effect, in addition to increasing the system’s ability to sustain loads.

1. Introduction

Creating an opening within reinforced concrete (RC) structures is essential in some cases, such as slabs, where it is required for installation purposes involving different sizes (e.g., heating and conditioning pipe ducting, electric escalators, and elevators). However, large openings contain weak points due to the absence of reinforcement rebars at their locations, which threaten the slab’s stability and structural performance. In contrast, slabs with small-size openings could maintain their behavior and internal stability [1,2]. In addition, the position of the opening plays a major role in determining the resulting strength and ductility reduction with respect to the maximum positive and negative moment regions [3,4,5,6,7]. It is recommended that RC slabs are designed based on the strip method, despite the lack of existing literature on this topic and the need for further investigations, as inadequate calculations and precise instruction can cause the strip method to underestimate the RC slab’s load capacity [8]. Moreover, there is still some unclearness regarding how to determine the opening size that will not affect the slab’s allowable load-carrying capacity [9].

The structural performance characteristics are all susceptible to being affected by the presence of an opening, including the ultimate load capacity, stiffness, and energy dissipation. Therefore, an efficient reinforcement method is especially needed to mitigate the effects of the opening, including the effects of its size and position. Discontinuous steel fibers were previously utilized and proved to be an efficient and promising technique for improving the tensile capacity and toughness of the original RC structures [10,11,12,13], followed by the inclusion of fiber-reinforced concrete (FRC) material in the strengthening and retrofitting fields [14,15,16,17]. However, the cyclic behavior of strengthened slabs, including the cracking performance and ultimate strength, was significantly improved by the addition of synthetic fibers [18]. The cyclic behavior of one-way RC slabs reinforced with glass-fiber-reinforced polymers was experimentally investigated by Hassanli et al. [19] following the addition of synthetic fiber. It was found that the fibers reduced the width and deflection of cracks and enhanced energy absorption, with no observed enhancement in the slab’s ductility.

Several researchers demonstrated that discontinuous steel fibers might be the only efficient method for maintaining the integrity and stability of RC slabs with high redundancy [20], due to their ability to replace steel reinforcements [21]. Therefore, the utilization of combined steel such as discontinuous fibers and rebars emerges as an innovative hybrid technique for upgrading the structural capacity of the RC members [22,23,24]. Based on this, hybrid reinforcements have gained much appreciation due to their efficiency in improving the structural design quality of RC slabs (strength and serviceability) [25], and their ability to reduce the costs and shorten the time of the process, in addition to the partial replacement of steel [26,27,28]. However, this technique might increase the probability of punching shear due to their high slenderness and relative stiffness values [29].

According to Mitchell and Cook [29], the utilization of steel fibers is an effective method for upgrading the flexural capacity of RC slabs. Their results revealed that installing discontinuous fibers within RC members with a more than 1.3% volume fraction significantly improves the slab’s behavior [30], with the efficiency of the steel fibers being reduced upon the increase in the slab’s depth due to the 3D fibers’ orientation. Moreover, the performance of slabs with different thicknesses and span lengths was examined by Michels et al. [30] based on the ultimate limit state (ULS) [31], where new design instructions were provided. In sum, the behavior of structural members was investigated in the literature under the effect of existing openings. The role of carbon-fiber-reinforced polymer (CFRP) strengthening in upgrading the structural behavior was investigated using numerical techniques such as ABAQUS 17 software [32]. Additionally, the behavior of plain and reinforced slabs was studied by Pujadas et al. [33], where slabs were reinforced with 9 kg/m³ plastic polyolefin fibers. It was revealed that major improvements were recorded in ductility, stress redistribution capacity, and post-cracking propagation. The flexural performance of one-way slabs strengthened when the PF of different percentages was studied (0, 0.3, 0.6, and 0.9) % with square and circular openings by Al-Rousan [34].

However, a square opening with four different ratios was examined (0, 2.0, 4.5, and 8.0%) with three circular openings of 1.57, 3.53, and 6.28% ratios. It was concluded that square openings have a larger negative effect on the slab’s behavior compared to circular openings, with stresses concentrated at the square opening’s edges leading to cracking at these locations. Detailed behavior slabs with square openings were adopted in this study, with different PF percentages varying between 0 and 1%, with 0.1% increments and wider opening ratios between 0 and 24.5%. The NLFEA models were validated using experimental data from the literature to determine their accuracy, precision, and reliability. Generally, previous research has shown that the strengthening of one-way slabs with polypropylene fiber requires further investigation. Therefore, this study aims to investigate the actual behavior of RC slabs with different opening sizes and PF strengthening percentages. The obtained results were used to construct actual and reliable guidelines on the stress distribution behavior and ultimate capacities of the simulated slabs. In sum, this research mainly focuses on exploring an efficient and simple reinforcement method with an acceptable cost as a possible alternative to conventional reinforcing methods. The flowchart used to fulfill the research objectives is illustrated in Figure 1.

2. Experimental Work Review

Simply supported one-way RC slabs of (1.10 × 0.50 × 0.07) m³ dimensions for the length, width, and height, respectively, were constructed and tested by Al-Rousan [34], with the test conducted as illustrated in Figure 2. The investigated parameters included in the experiment are illustrated in Figure 3, where (f) stands for PF volume fraction, for which four percentages were used (0, 0.3, 0.6, and 0.9%). The other parameters are the opening existence (with or without), the length of the square opening side (100, 150, and 200 mm), and the circular opening diameters (100, 150, and 200 mm). In addition, four 10 mm diameter reinforcement rebars were used, with 460 MPa and 660 MPa yield and ultimate strengths, respectively, distributed in the longitudinal and transverse directions of the structural member. However, the openings and steel bars were cut before the concrete casting into the wooden formworks in which the steel mesh was installed. Finally, the PF fibers had a 165 MPa tensile strength value with 0.91 specific gravity. The utilized synthetic fibers were circular with 30–40 μm size and biaxial orientations, resulting in increased toughness, increased stiffness, enhanced clarity, improved oil and grease resistance, and enhanced barrier properties to water vapor and oxygen.

3. Numerical Modeling Methodology

The first step in the modeling procedure was to validate the NLFEA models using experimental work from the literature. The test conducted by Al-Rousan [34] was utilized in this study for the validation stage, which is to be further extended to investigate the effect of other parameters, including the PF strengthening ratios and opening sizes, using ANSYS 15 commercial software [35]. The adopted tolerance values were equal to 5.0% for the displacement and 0.5% for the loading capacity, using the Newton–Raphson method to solve the structural system as an iterative procedure in which the convergence is checked at the end of every loading substep.

Concrete material was modeled using the smeared cracking approach, using the SOLID65 element, which can capture the cracking and crushing behaviors. This is a three-dimensional element defined by eight nodes. Each node has three degrees of freedom with the presence of translations in the three nodal directions, x, y, and z, for each node. The concrete compressive strength is affected by the addition of PF fibers, where compressive strength values of 38.9, 40.8, 42.4, and 44.3 MPa were recorded for mixtures of PF percentages equal to 0.0, 0.3, 0.6, and 0.9, respectively, with 2.92, 3.13, 3.34, and 3.42 MPa, and 16,626, 17,934, 19,024, and 20,481 MPa values for the splitting tensile strength and the modulus of elasticity, respectively, as reported in the experimental work by Al-Rousan [34]. The concrete material was also defined using the Poisson’s ratio and the shear transfer coefficient, where the 0.2 and 0.8 values were selected based on the previous knowledge in this field and the other research in the literature, respectively. Generally, the role of fibers is mainly expressed by the crack-bridging ability, which is directly reflected by the crack-propagation process and reduces the crack spacing and width. The utilized stress–strain curves of the concrete material for the simulation process with different PF percentages (0.0, 0.3, 0.6, and 0.9%) were experimentally obtained by Al-Rousan [34], as illustrated in Figure 4a, with the tensile behavior of the concrete material modeled as linear elastic, with strength values ranging between 2.89 and 3.51 MPa.

The current work illustrates the ability of the PFs to improve their flexural and tensile capacities based on the number of utilized PFs and their orientation per unit area, which was computed using the probability method [36]. Steel reinforcement was modeled using the LINK 180 element, with equal compression and tension properties at each node of the ends of the link element. This includes two nodes, and each node has three degrees of freedom. This element can predict large deflections, large strain, rotation, stress stiffening, creep, and plasticity. Steel has a 200 GPa modulus of elasticity, 0.3 Poisson’s ratio, and 460 MPa yield strength, as per the experimental results. In addition, steel plates were simulated using the SOLID 45 element, with plasticity, stress, strain, and swelling prediction capabilities and no cracking or crushing abilities, with a 0.3 Poisson’s ratio and 200 GPa modulus of elasticity. This element is suitable for modeling dimensional solid structures defined by eight nodes. Translations are present in the three nodal directions, x, y, and z, for each node.

The steel stress–strain curve used for the simulation process was experimentally obtained by Al-Rousan [36], as shown in Figure 4b. The bond at the concrete–steel interface was assumed to be a perfect bond; therefore, no bond-slip model was included in the simulated model. The total applied load was divided into multiple load steps or load increments. Newton–Raphson equilibrium iterations provide convergence at the end of each load increment within a tolerance limit equal to 0.001 and a load increment of 0.22 kN. When large numbers of cracks appear throughout the concrete, the loads are applied gradually, with smaller load increments.

The mesh size of the simulated models was selected after a convergence study including three mesh sizes of 15, 25, and 40 mm, where the load–deflection curves, convergences, and computational costs were compared. Detailed results are illustrated in Figure 5 for the differences between the tested and simulated values, along with the computational time to system failure, provided in minutes. A mesh size of 25 mm was adopted, which provides the best accuracy and solution convergence with less than 5% error. In addition, the meshing of the models is illustrated in Figure 6 for the RC slabs with or without openings, where the geometry and the reinforcement detailing are presented, as introduced in the ANSYS software [35], to address the objectives of the study. In addition, the load–deflection curves of the experimental and the finite element analysis results were compared, as shown in Figure 7, with the ultimate load–deflection values illustrated in

Table 1. NLFEA RC slab details and ultimate load capacity in kN.

PF Volume Fraction	Opening Ratio
	0.0%	0.5%	2.0%	4.5%	8%	12.5%	18.0%	24.5%
0.0%	40.68 [40.60]	39.00	36.20 [34.40]	26.44 [24.10]	19.16 [17.20]	14.70	12.41	11.00
0.1%	41.91	39.74	37.58	27.65	20.09	15.14	12.89	11.54
0.2%	43.03	40.94	38.84	28.79	20.96	15.55	13.32	12.03
0.3%	44.06 [44.30]	42.03	39.99 [37.90]	29.86 [27.20]	21.75 [19.70]	15.92	13.72	12.49
0.4%	44.99	43.00	41.02	30.86	22.48	16.26	14.07	12.91
0.5%	45.81	43.87	41.93	31.78	23.14	16.56	14.38	13.29
0.6%	46.54 [46.30]	44.63	42.72 [39.9]	32.63 [29.30]	23.73 [21.10]	16.82	14.65	13.62
0.7%	47.17	45.28	43.39	33.41	24.25	17.04	14.88	13.92
0.8%	47.69	45.82	43.95	34.11	24.70	17.23	15.07	14.18
0.9%	48.12 [48.20]	46.25	44.38 [42.30]	34.75 [31.30]	25.08 [22.50]	17.39	15.22	14.40
1.0%	48.45	46.57	44.70	35.31	25.40	17.51	15.33	14.58

[40.60] is the experimental ultimate load capacity.

for all specimens, where the experimental results of some specimens are presented in brackets. The differences were minor and the NLFEA models could be extended to further investigate the effect of other sensitive parameters.

4. Results and Discussion

In this study, a total of 88 specimens were simulated. The effect of different opening ratios between 0 and 24.5% was investigated using various PF percentages, from 0 to 1%, with a 0.1% increase. In the following section, the results are compared in terms of the failure modes, load–deflection behavior, ultimate load and deflection values, compressive and tensile strains, energy consumption, ductility, and stiffness values. The results are illustrated in

Table 2. NLFEA stiffness calculations.

Slab	Cracking			Yielding			Ultimate
	Load, kN	Deflection, mm	Stiffness, kN/mm	Load, kN	Deflection, mm	Stiffness, kN/mm	Load, kN	Deflection, mm	Stiffness, kN/mm
SPF0.0OP0.0	10	1.34	7.46	40.00	11.39	3.51	40.68	23.19	1.75
SPF0.0OP0.5	9.61	1.34	7.17	38.42	11.39	3.37	39	24.19	1.61
SPF0.0OP2.0	8.92	1.34	6.66	35.71	11.39	3.14	36.2	25.39	1.43
SPF0.0OP4.5	6.51	1.34	4.86	26.05	11.39	2.29	26.44	27.59	0.96
SPF0.0OP8.0	4.72	1.34	3.52	18.88	11.39	1.66	19.16	29.79	0.64
SPF0.0OP12.5	3.62	1.34	2.7	14.48	11.39	1.27	14.7	31.99	0.46
SPF0.0OP18.0	3.06	1.34	2.28	12.23	11.39	1.07	12.41	33.19	0.37
SPF0.0OP24.5	2.71	1.34	2.02	10.84	11.39	0.95	11.00	35.39	0.31
SPF0.1OP0.0	10.32	1.34	7.70	41.28	11.39	3.62	41.91	24.19	1.73
SPF0.2OP0.0	10.6	1.34	7.91	42.20	11.39	3.71	43.03	25.39	1.69
SPF0.3OP0.0	10.85	1.34	8.10	43.41	11.39	3.81	44.06	26.59	1.66
SPF0.4OP0.0	11.08	1.34	8.27	44.33	11.39	3.89	44.99	27.79	1.62
SPF0.5OP0.0	11.28	1.34	8.42	45.13	11.39	3.96	45.81	28.99	1.58
SPF0.6OP0.0	11.46	1.34	8.55	45.85	11.39	4.03	46.54	30.19	1.54
SPF0.7OP0.0	11.62	1.34	8.67	46.47	11.39	4.08	47.17	31.39	1.50
SPF0.8OP0.0	11.75	1.34	8.77	46.99	11.39	4.13	47.69	32.59	1.46
SPF0.9OP0.0	11.85	1.34	8.84	47.41	11.39	4.16	48.12	33.79	1.42
SPF1.0OP0.0	11.93	1.34	8.90	47.73	11.39	4.19	48.45	34.99	1.38

and

Table 3. NLFEA energy and ductility calculation.

Slab	Energy Absorption, kN.mm				Ductility
	Elastic	Yielding	Ultimate	Total	Displacement	Energy
SPF0.0OP0.0	7.38	253.84	478.6	739.82	2.04	1.89
SPF0.0OP0.5	7.08	243.83	498.74	749.65	2.12	2.05
SPF0.0OP2.0	6.57	226.33	506.37	739.27	2.23	2.24
SPF0.0OP4.5	4.80	165.41	428.01	598.22	2.42	2.59
SPF0.0OP8.0	3.48	119.79	352.32	475.59	2.62	2.94
SPF0.0OP12.5	2.67	91.91	302.65	397.23	2.81	3.29
SPF0.0OP18.0	2.25	77.59	270.39	350.23	2.91	3.48
SPF0.0OP24.5	2.00	68.77	232.08	302.85	3.11	3.37
SPF0.1OP0.0	7.61	261.96	535.81	805.38	2.12	2.05
SPF0.2OP0.0	7.82	269.07	601.99	878.88	2.23	2.24
SPF0.3OP0.0	8.00	275.47	669.19	952.66	2.33	2.43
SPF0.4OP0.0	8.14	281.4	737.3	1026.84	2.44	2.62
SPF0.5OP0.0	8.32	286.41	805.71	1100.44	2.55	2.81
SPF0.6OP0.0	8.45	290.98	874.4	1173.83	2.65	3.01
SPF0.7OP0.0	8.56	294.91	960.78	1264.25	2.76	3.26
SPF0.8OP0.0	8.66	298.16	1010.46	1317.28	2.86	3.39
SPF0.9OP0.0	8.74	300.85	1077.32	1386.91	2.97	3.58
SPF1.0OP0.0	8.80	302.92	1142.84	1454.56	3.07	3.77

for the stiffness calculations, energy, and ductility, respectively. The notation used to describe the simulated slabs is illustrated by the following example (SPF0.0OP0.0), where the first script (S) represents a slab structural member, and the second (PF), along with the following number, represents the percentage of added PF. Finally, the third manuscript (OP) and the following number is the opening ratio percentage. Due to the similarities in the specimens’ behavior, only the results for 18 specimens were introduced, while the 88 specimens illustrate the load-carrying capacity of one-way slabs.

4.1. Failure Modes

The failure modes of the one-way slabs were examined in the NLFEA models for slabs with and without openings, as illustrated in Figure 8, where slabs with different opening ratios are presented. However, the cracking propagation in a one-way slab without an opening is initiated by the appearance of a crab at the slab’s bottom tensile face, parallel to the loading points, with the propagation of more flexural cracks in the vertical direction at higher loading levels. TCrack propagation continues until the steel bars yield at the tensile face, and final failure occurs upon the crushing of the concrete material within the compression zone of the maximum bending moment. In addition, increasing the utilized PF percentages increases the induced flexural cracking, as shown in Figure 8.

The crack propagation of one-way slabs with an opening starts with the propagation of the flexural cracks at the opening corners and extends toward the slab’s edges, which are further propagated longitudinally at the side surface of the opening. However, the width of the induced cracks is notably increased when the steel reinforcement yields within the opening region and ends up crushing the concrete at the slab’s compression face. Generally, cracks begin at the edges of the opening, at the bottom face directly below the two loading points. Later, they gather extensively, close to the opening corners, and spread diagonally in the longitudinal direction.

The behavior of the crack openings was plotted against the applied loading, and is illustrated in Figure 9 for one-way RC slabs with different PF percentages. The crack opening was calculated using two reference nodes of 150 mm finite distance, whose positions were fixed to the left and right of the opening, between the transducers, before loading. The crack opening was measured by comparing the relative distance at the end of the simulation and the original 150 mm distance. Figure 9 illustrates the role of PF in stabilizing and controlling the crack growth, especially at high deflection values. However, it was found that increasing the PF percentage increases the resulting crack-opening value at failure due to the stabilization effect, in addition to increasing the system’s ability to sustain loads. It could be stated that PF’s ability to stabilize the propagated cracks is improved by 5, 13, and 16% for PF percentages of 0.3, 0.6, and 0.9%, respectively.

4.2. The Load vs. Deflection Behavior

The simulated RC slabs without an opening show a linear behavior before they reach the first flexural cracking load, followed by a rapid increase until the occurrence of steel yielding. After that, the curve is flattened until specimen failure occurs. However, the value of the load and deflection where the curve is flattened was affected by the size of the opening. The obtained load–deflection curves were classified based on the studied parameters in this work: the PF ratio and the opening size (Figure 10 and Table 1). An inspection of Table 1 results reveals that increasing the PF volume fraction increased the ultimate load capacity, whereas the capacity was reduced when the opening size was increased. The two factors had similar effects on the ultimate deflection value, where increasing the PF ratio increases the deflection value compared to the reduction corresponding to the increase in the opening size. This is could be due to the reduction in the quantity of the concrete and the reinforcement steel, resulting in a reduction in the RC slab’s stiffness and capacity.

The NLFEA models were extended for an in-depth investigation of the behavior of the one-way RC slabs with different opening sizes and PF percentages. However, the PF percentages varied between 0.0% and 1.0%, while the ratio of the opening size was between 0.0% and 24.5%, as shown in Table 1 and Figure 11. The values of the ultimate load capacity were plotted under the effect of different PF percentages and opening sizes, as illustrated in Figure 11. However, it could be stated that increasing the percentage increases the ultimate load capacity, while a reduction is observed upon increases in the opening size ratio.

4.3. Concrete and Steel Strain Behavior

The distribution of the developed strains throughout the specimen’s depth is plotted in Figure 12, under different loading levels, for an RC slab with 0.9% PF and 0.0% opening ratios. Flexural cracks emerged when the concrete and steel strains were below 200 $\mathsf{\mu }\mathsf{\epsilon }$, with the concrete strain increasing up to 600 $\mathsf{\mu }\mathsf{\epsilon }$, which is 34% of the concrete ultimate strain capacity $\left({\mathsf{\epsilon }}_{cu}\right)$ between the cracking and yielding region, compared to 1000 $\mathsf{\mu }\mathsf{\epsilon }$ for steel, which is equal to 44% of the steel-yielding strain $\left({\epsilon }_y\right)$. However, when the steel reinforcement yielded, the concrete’s strain equalled 1000 $\mathsf{\mu }\mathsf{\epsilon }$ (34% of ${\epsilon }_{cu}$), while the steel’s strain was 2300 $\mathsf{\mu }\mathsf{\epsilon }$ (100% of ${\epsilon }_y$). Between the steel’s yielding and failure, the concrete strain was 1400 $\mathsf{\mu }\mathsf{\epsilon }$ (54% of ${\epsilon }_{cu}$), and the strain of steel was 2900 $\mathsf{\mu }\mathsf{\epsilon }$ (126% of ${\epsilon }_y$). Upon the failure of steel, the concrete strain was 2600 $\mathsf{\mu }\mathsf{\epsilon }$ (100% of ${\epsilon }_{cu}$), while the steel strain was 5200 $\mathsf{\mu }\mathsf{\epsilon }$ (226% of ${\epsilon }_y$). In addition, increasing the PF percentage or the opening size ratio resulted in a simultaneous increase in the concrete compressive strain and the steel tensile strain, by different percentages. Moreover, the slab with an opening had larger steel strain values, caused by the additional opening that was created as a result of the increased distance between the slab’s fiber at the compression side and the neutral axis of the flexural member.

4.4. Yielding Stiffness

The behavior of the RC slab’s stiffness is illustrated in Figure 13, as the values were normalized with respect to the control specimen (PF = 0, and OP = 0), where the effect of the PF percentage and opening ratio were examined. The initial stiffness $\left(K_E\right)$ was obtained by dividing the cracking load by the corresponding cracking deflection value, while the yielding stiffness $\left(K_Y\right)$ was calculated by dividing the yielding load by the corresponding yield deflection. The yielding stiffness was determined through the slope of the load–deflection curve, as well as the post-cracking up to the point of yielding, with a moment of inertia equal to the cracked moment of inertia, as illustrated in Figure 13. It was found that increasing the PF percentage improves both the initial and yielding stiffness capacities, with a 23% difference due to the flexural crack’s propagation.

The initial and yielding stiffnesses were reduced for RC slabs with openings compared to those without an opening due to the reduction in the concrete and steel reinforcement amounts. However, increasing the PF percentage also increases the slab stiffness, including the initial and yielding values, as shown in Figure 13. As a result, the PF volume fraction of 0.6% and the opening ratio of 6.28% were considered the best-fit ratios, as per the initial and yielding stiffness. In addition, there was a slight increase in PF stiffness (0.6–0.9%) and a considerable enhancement in the stiffness of PF (from 0.3% to 0.6%), while the difference between the opening ratio ranged from 6.28% to 8%. Finally, the opening ratio negatively affected the initial stiffness [37], as the stiffness was reduced by 11% when the opening ratio was 0.5%, to 83% when the opening ratio was 24.5%.

4.5. Ductility Index (Displacement-Based Approach)

The displacement ductility index $\left({\mu }_{∆}\right)$ is defined as the displacement ratio at the failure and yielding stages. The effect of the PF volume fraction and the opening size ratio were evaluated regarding the displacement ductility behavior by normalizing the specimen’s ductility index $\left({\mu }_{∆}\right)$ according to the displacement ductility capacity of the control specimen $\left({{\mu }_{∆}}^{*}\right)$ (PF = 0%, and OP = 0%), as illustrated in Figure 14. It was found that increasing the PF volume fraction improves the displacement ductility, while increasing the ratio of the opening size has an inverse effect. In addition, the PF volume fraction percentage of 0.6% and the opening ratio of 6.28% were found to be the best values, as long as the displacement ductility index was stable, based on the flattened section of the curves presented in Figure 14. The behavior shown in Figure 14 can be explained by the fact that adding the PF material to the concrete mixture will enhance its ultimate deflection values, especially when a higher percentage is utilized. Furthermore, creating an opening in a slab reduced its load-carrying capacity but increased its deflection capabilities because of the lower loading rates. As a result of the previously mentioned observation, the displacement ductility index has different behaviors under different PF percentages and opening ratios. The behavior is proportional to the PF percentage and inversely proportional to the opening ratio.

4.6. Ductility Index (Energy-Based Approach)

The energy absorption measurements were all calculated, including the yielding $\left({EA}_Y\right)$, ultimate $\left({EA}_U\right)$, and total $\left(EA\right)$, and used to evaluate the ductility of the simulated slabs using the energy-based approach. However, the values were obtained by computing the constrained area under the load–deflection curve up to the ultimate point and the yielding point. The effect of the PF volume fraction and the opening size ratio were evaluated according to the displacement ductility behavior by normalizing the specimen’s ductility index $\left({\mu }_{EA}\right)$ according to the displacement ductility capacity of the control specimen $\left({{\mu }_{EA}}^{*}\right)$ (PF = 0%, and OP = 0%), as illustrated in Figure 15. An inspection of Figure 14 reveals that increasing the PF percentage or the opening size ratio has a positive effect on the EA capacity at all stages. The ultimate EA improvement percentages were between 3% and 22% at different PF percentages, as per Figure 15. In the same context, the opening ratio considerably enhanced the displacement ductility index by percentages from 5% to 39% for the RC slabs with an opening ratio of from 0.5% to 24.5%, respectively. Figure 15 shows that the EA ductility index was enhanced by 16%, 18%, and 22% for PF volume fractions of 0.3%, 0.6%, and 0.9%, respectively. The percentages of 6.28% and 0.6% were the best values for the opening ratio and the PF volume fraction, respectively, as per the EA ductility index.

4.7. Strength Capacity Comparison

The ultimate load capacity was theoretically calculated for all of the simulated specimens using the sectional analysis method, for which the equivalent stress block was adopted. The ratio between the NLFEA and the calculated results was computed and plotted against the different PF percentages, as shown in Figure 16, where it could be concluded that the capacity of the PF-reinforced slabs could be predicted using a margin of safety ranging from 14 to 34%. It is clear from the figure that the NLFEA prediction is affected by the PF volume percentage, which consequently affects the safety factor compared to the theoretical prediction. Figure 16 reveals that increasing the PF percentage will reduce the safety margin between over- and under-estimation.

5. Conclusions

The following conclusions can be drawn from this study:

• The slab’s performance is improved proportionally by different percentages depending on the added PF volume fraction, including the slab’s overall structural characteristics, such as the ultimate and cracking load capacities, stiffness, and internal cracking stability.
• The slab’s opening ratio has an inversely proportional relationship with the slab’s behavior related to the stress concentration at the corners of the square openings and their associated cracking intensity.
• PF’s ability to stabilize the propagated cracks is improved by 5, 13, and 16% for PF percentages of 0.3, 0.6, and 0.9%, respectively.
• Increasing the PF percentage or the opening size ratio resulted in a simultaneous increase in the concrete compressive strain and the steel tensile strain by different percentages. Moreover, a slab with an opening experienced larger steel strain values caused by the opening that was created as a result of the increased distance between the slab’s fiber at the compression side and the neutral axis of the flexural member.
• The slab’s load capacity could be predicted using the sectional analysis method with a 14–34% margin of safety resulting from the inclusion of the PF reinforcements.
• Based on the innovative NLFEA models, new guidelines were proposed to address the ultimate load-carrying capacity of the one-way RC slabs in terms of the PF percentage and the square opening ratio.

6. Recommendations

It is recommended that polypropylene fibers are used either to strengthen the structural behavior of one-way RC slabs or replace the conventionally used steel reinforcement, as they showed high efficiency in improving the overall structural performance. It is also recommended to examine the slab’s behavior after an opening is created by evaluating the load, serviceability, and durability of the affected structural members.