Experimental–FEM Validation of ANN Models for One-Way HFRC Slabs

Panumas Saingam 1 Emailpanumas.sa@kmitl.ac.th

Burachat Chatveera 2 Emailcburacha@engr.tu.ac.th

Qudeer Hussain 3 Emailebbadat@hotmail.com

Gritsada Sua-iam 4 Emailgritsada.s@rmutp.ac.th

Preeda Chaimahawan 5✉ Emailpreeda.ch@up.ac.th

Chisanuphong Suthumma 6✉ Emailchisanuphong.s@ku.th

Afaq Ahmad 7,8✉ Emailafaq.ahmad@oslomet.no

1 Department of Civil Engineering, School of Engineering King Mongkut’s Institute of Technology Ladkrabang 10520 Bangkok Thailand

Department of Civil Engineering, Faculty of Engineering Thammasat University Rangsit campus), Pathum Thani 12121 Thailand

3 Department of Civil Engineering Kasem Bunding University Thailand

4 Department of Civil Engineering, Faculty of Engineering Rajamangala University of Technology Phra Nakhon 10800 Bangkok Thailand

5 School of Engineering University of Phayao Phayao Thailand

6 Department of Civil Engineering, Faculty of Engineering at Kamphaeng Saen Kasetsart University 73140 Nakhon Pathom Thailand

7 Department of Civil Engineering, Herff College of Engineering University of Memphis USA

8 Faculty of Technology, Art and Design OsloMet University Norway

Panumas Saingam¹, Burachat Chatveera², Qudeer Hussain³, Gritsada Sua-iam⁴, Preeda Chaimahawan⁵*, Chisanuphong Suthumma⁶*, Afaq Ahmad^7,8*

1. Department of Civil Engineering, School of Engineering, King Mongkut's Institute of Technology Ladkrabang, Bangkok 10520, Thailand., panumas.sa@kmitl.ac.th

2. Department of Civil Engineering, Faculty of Engineering, Thammasat University (Rangsit campus), Pathum Thani, 12121, Thailand, cburacha@engr.tu.ac.th

3. Department of Civil Engineering, Kasem Bunding University, Thailand: ebbadat@hotmail.com

4. Department of Civil Engineering, Faculty of Engineering, Rajamangala University of Technology Phra Nakhon, Bangkok, 10800, Thailand, gritsada.s@rmutp.ac.th

5. School of Engineering, University of Phayao, Phayao, Thailand, Email: preeda.ch@up.ac.th

6. Department of Civil Engineering, Faculty of Engineering at Kamphaeng Saen, Kasetsart University, Nakhon Pathom 73140, Thailand, chisanuphong.s@ku.th

7. Department of Civil Engineering, Herff College of Engineering, University of Memphis, USA.

8. Faculty of Technology, Art and Design, OsloMet University, Norway., afaq.ahmad@oslomet.no

* Correspondence: afaq.ahmad@oslomet.no, preeda.ch@up.ac.th, chisanuphong.s@ku.th,

ABSTRACT

Cement concrete is the most widely utilized construction material globally, recognized for its versatility, workability, and ability to create complex structural and non-structural components. Despite its extensive application, plain concrete exhibits inherent weaknesses, including low tensile strength, limited crack resistance, and brittleness caused by internal microcracking. These limitations highlight the need for enhancements in conventional cement concrete to satisfy the diverse structural and durability requirements of civil engineering. The incorporation of fibers in specific proportions has shown significant improvements in the mechanical properties of concrete. This study presents the validation of Artificial Neural Network (ANN) models, trained on 145 High-Performance Fiber-Reinforced Concrete (HFRC) samples, alongside the corresponding experimental results for one-way HFRC slabs and Finite Element Method (FEM) analyses on the behavior of 21 one-way slabs with varying volumetric proportions of steel and polypropylene fibers. One-way slabs underwent testing using a four-point bending method. Structural performance was evaluated based on strain, deflection, crack initiation, and ultimate failure load. Steel fibers were added in proportions ranging from 0.7% to 1.0% by volume, while polypropylene fibers were incorporated in increments of 0.1% to 0.9% at 0.2% intervals. Both Finite Element Analysis (FEA) and ANN predictions exhibited a strong correlation with experimental outcomes for the ultimate flexural load and mid-span deflection of the 21 reinforced concrete beams. FEA demonstrated remarkable quantitative precision, with minimal deviation from experimental results and a robust simulation of complex mechanical behaviors such as damage accumulation and ductility.

Keywords:

One-way slabs

Hybrid fibers

Ductility

Flexural strength

Crack patterns

ABAQUS, ANN

1. INTRODUCTION

Cement concrete is the most prevalent construction material globally due to its versatility, workability, and ability to form complex shapes for structural and non-structural members. However, despite its widespread use, plain concrete exhibits inherent limitations, including its weakness in tension, low resistance to cracking, and brittleness resulting from internal microcracking. These limitations challenge the long-term durability and performance of concrete structures, necessitating advancements in concrete technology to meet the diverse structural and durability demands in civil engineering. Plain concrete exhibits limitations in qualities such as flexibility (or tensile) strength, behavior after cracking, resistance to fatigue, and susceptibility to brittle failure [1, 2]. The inherent brittleness of concrete, particularly as its strength increases, poses a significant challenge to its application as a construction material. This increased strength often results in reduced elasticity, representing a critical limitation. However, incorporating short fibers effectively balances strength and ductility in concrete [3]. The initiation of microcracks, which contribute to the material’s inherent mechanical weaknesses, can be mitigated by including various types of fibers [4].

The inherent brittleness of plain concrete is primarily due to its low tensile strength and its propensity to crack under loading. Traditional methods of enhancing concrete properties, such as increasing the cement content, often yield diminishing returns or raise environmental concerns due to the high carbon footprint associated with cement production. Therefore, alternative methods, such as incorporating fibers, have gained significant attention in recent years to improve concrete’s mechanical and durability properties. Fiber-reinforced concrete (FRC) is an advanced form of concrete that incorporates fibers into the mix to enhance its performance. These fibers, which can be made of steel, polypropylene, glass, or synthetic materials, help bridge cracks, enhance crack resistance, and improve the overall toughness of the material. [5]. Hybrid fibers have emerged as a significant innovation in materials science, particularly for enhancing the mechanical properties of construction materials like concrete and composites. The integration of hybrid fibers, which often combine various types (such as steel, polypropylene, or glass), optimizes the bridging mechanism that alleviates crack propagation under stress. This bridging mechanism is vital, as it not only helps arrest crack growth but also improves key mechanical properties. One area of improvement is flexural strength. The presence of hybrid fibers significantly increases the material's resistance to bending forces. This capability is crucial in structural applications where components are subjected to fluctuating loads. Alongside flexural strength, hybrid fibers also enhance splitting tensile strength, enabling the material to withstand tensile stresses that can lead to separation or failure.

Lastly, the economic implications of incorporating hybrid fibers into construction materials warrant further study. While there is potential for enhanced durability and reduced maintenance costs, a cost-benefit analysis comparing traditional materials with hybrid fiber-reinforced options would help engineers and construction professionals make informed decisions about material selection. In conclusion, hybrid fibers represent a promising avenue for bolstering material performance. However, addressing these research gaps through focused studies can lead to broader applications and advancements in smart material solutions for construction and beyond.[6, 7].

The efficiency of fiber-reinforced concrete largely depends on the type, content, and distribution of the fibers within the concrete matrix. Several experimental studies have explored the optimal combinations of steel and polypropylene fibers to achieve the best mechanical properties for specific applications. It has been observed that a unique interaction exists between steel and polypropylene fibers, where the addition of one type of fiber can enhance the effectiveness of the other. For one-way slabs, the optimal performance in terms of load capacity and flexibility was achieved with a combination of 0.7% steel fibers and 0.9% polypropylene fibers. This specific blend maximized the structural efficiency under unidirectional loading conditions. Conversely, for slabs, the ideal fiber combination consisted of 0.9% steel fibers and 0.1% polypropylene fibers, which effectively enhanced both the load-bearing capacity and resistance to cracking under multidirectional loading. These results highlight the synergistic interaction between steel and polypropylene fibers, demonstrating that the precise proportions of these materials should be tailored to the specific slab type and expected loading scenarios to achieve optimal performance outcomes [8–15]. The observed synergy between steel and polypropylene fibers suggests an optimal balance between the two materials that varies with slab configuration and applied loading conditions. The performance improvements of fiber-reinforced slabs can be attributed to the complementary mechanisms provided by each fiber type. While steel fibers improve the slab’s strength and toughness, polypropylene fibers control crack formation and improve the post-cracking behavior, resulting in a more resilient and durable concrete structure [8–15].

Steel fibers have been proven to effectively enhance the flexibility and crack resistance of concrete. Additionally, shrinkage cracks can be mitigated by incorporating steel and glass fibers at a volumetric ratio of 0.1% [16]. However, using a combination of various fibers has proven to be more effective in improving a range of mechanical properties and the impact and blast resistance of concrete under both normal and elevated temperatures [17–19]. Hybrid fiber-cementitious composites enhance the mechanical properties and durability of concrete structures under various loading conditions:

Cyclic Loading: These composites distribute stress evenly, increasing resistance to cracking and fatigue.

ii.

Seismic Loading: They improve ductility and energy absorption, allowing structures to withstand lateral forces during earthquakes.

iii.

Static Loading: By boosting tensile strength, they enhance the load-bearing capacity of concrete.

iv.

Impact Loading: The added fibers increase toughness, helping concrete absorb energy from sudden impacts without significant damage.

These composites also show promise for retrofitting masonry and concrete structures, enhancing load capacity, extending service life, and preserving original aesthetics. Their versatility makes them valuable in both new construction and structural rehabilitation.[20–22].

Concrete behavior is ruled considerably by its compressive strength, but tensile strength also plays a significant role in determining the appearance and durability of concrete. Fibers are added to enhance flexural and tensile strengths, the crack-arresting system, and the fundamental matrix's post-cracking ductile behavior. To control the plastic and drying shrinkage cracking, a volumetric proportion of 0.1% of the polypropylene and glass fibers was found adequate [23] Polypropylene has a unique chemical structure and is chemically inert, preventing chemicals from attacking the fibers. Polypropylene fiber-reinforced concrete enhances abrasion resistance in concrete floors by controlling bleeding during the plastic state. This enhanced concrete will, in turn, help reduce the thickness of members and, hence, reduce the structure’s weight, making handling and shipping the concrete even easier [24].

In ordinary concrete, where compaction is achieved with mechanical vibrators, the incorporation of fibers is a reliable and widely used approach to mitigate cracking caused by paste contraction, particularly with thin artificial fibers at a volumetric content of less than 0.5% [25]. Experimental research on fiber-reinforced concrete has demonstrated that increasing the fiber volume significantly enhances its mechanical properties, including compressive, tensile, and bending strengths. These improvements are attributed to the fibers' ability to reinforce the concrete matrix and resist crack propagation under various stress conditions. However, this enhancement comes at the cost of reduced workability, as the increased fiber content hinders the smooth flow and compaction of the concrete mix. Consequently, achieving an optimal balance between mechanical performance and workability requires careful consideration of the fiber volume in the mix design [26].

Polypropylene has played a vital role in improving construction quality by reducing deflection and, consequently, providing greater structural stability. Polypropylene fibers have been shown to reduce concrete spalling. Surface cracks typically form when the internal vapor pressure within the concrete exceeds the surface pressure [27]. Cracks frequently form within the first hour after concrete is poured into molds, even before it has gained sufficient strength. These early-stage cracks are critical entry points for harmful substances, such as water, chlorides, and other chemicals, that can infiltrate the concrete matrix. Over time, this infiltration can lead to severe issues, such as spalling of the concrete surface or corrosion of the embedded reinforcement. Such degradation not only undermines the durability of the concrete but also compromises its structural integrity, significantly affecting its long-term performance and safety [28–31].

The compressive strength of the concrete is slightly affected by the increase in polypropylene and glass fibers [32]. The most optimal results were obtained with volume ratios of 1.5 kg/m³ and 2 kg/m³. Mixing polypropylene fibers has slowed down the degradation, resulting from reduced permeability, and reducing the shrinkage and expansion of concrete. This approach contributes to maintaining the structure in a more serviceable condition [33]. The size and quantity of steel fibers significantly influence the mechanical properties of hybrid fiber-reinforced concrete (HFRC). Research indicates that even a small addition of steel fibers can lead to a noticeable increase in concrete compressive strength, as the fibers effectively distribute and mitigate internal stresses. However, the impact on tensile strength is comparatively modest, as the fibers primarily contribute to crack bridging and resistance rather than directly increasing the tensile capacity[34]. This highlights the importance of optimizing fiber size and content to achieve desired performance improvements in HFRC [35]. The highest compressive strength was achieved with a mix of 75% steel fibers and 25% polypropylene fibers by weight, due to the high modulus of elasticity of steel and the low modulus of elasticity of polypropylene fibers. It was also suggested that increasing the fiber content enhances concrete's tensile strength. Using a specific fiber blend resulted in a notable improvement in split tensile strength [36]. Polypropylene fibers at a 0.1% volume fraction were less effective for on-grade slabs, whereas a 0.5% volume fraction of polypropylene fibers provided significantly better resistance to impact loading [37].

The type, content, and distribution of fibers within the concrete matrix significantly influence the performance of fiber-reinforced concrete. Experimental investigations have extensively examined the optimal steel and polypropylene fiber blends to maximize mechanical properties for various applications[38]. A notable synergy exists between these two fiber types, where the presence of one enhances the performance of the other. Steel fibers provide strength and stiffness, improving load-bearing capacity, while polypropylene fibers contribute to crack resistance and energy absorption. This unique interaction enables tailored combinations to meet specific structural demands, demonstrating the importance of balancing fiber characteristics for superior concrete performance. [39–41]. The investigation of the effects of SF and PF suggests an optimal balance between these materials that varies with slab configuration and applied loading conditions. The performance improvements of fiber-reinforced slabs can be attributed to the complementary mechanisms provided by each fiber type. While steel fibers improve the slab’s strength and toughness, polypropylene fibers control crack formation and improve the post-cracking behavior, resulting in a more resilient and durable concrete structure [42–44].

To address these challenges in the construction industry, structural engineers must evaluate the performance and response of RC structures under extreme loading environments [45–51]. This assessment involves assessing the load-carrying capacity of RC structures, particularly their brittle behavior and the failure mechanisms that prevent catastrophic failure. Engineers use nonlinear analysis procedures to study the brittle behavior of RC structures, which involve complex calculations. However, this nonlinear finite element analysis (NLFEA) software package, such as ABAQUS [52] and ADINA [53], is commonly used for research purposes. The packages used in the industry for the analysis of such behaviour (i.e., SAP 2000 and ETABS) [54] are generally effective in predicting flexural failure modes; they often struggle with accurately forecasting shear (brittle) failure modes [55]. Since shear failures are typically brittle and catastrophic, occurring with little to no warning, it is crucial for structural analysis tools to predict such failure modes accurately. Accurate predictions are essential for developing cost-effective and safe design solutions that ensure the structural integrity and resilience of RC frame structures. Inaccurate estimates can result in unsafe designs by overestimating structural capacity and ductility [56–62].

Around the globe, the Nonlinear finite element analysis (NLFEA) [12, 13] is an appreciated supplement to experimental studies, providing a detailed understanding of the behavior of RC members under various loading scenarios. Researchers can precisely simulate complex structural responses by utilizing sophisticated NLFEA tools [52, 53]. These tools incorporate advanced 3D finite element meshes to model structural geometry in detail, nonlinear material laws to capture the realistic behavior of concrete and reinforcement under stress, and failure criteria to predict crack propagation, yielding, and ultimate failure modes [63–66]. Furthermore, iterative techniques are employed to address the complexities of nonlinear behavior, ensuring convergence and stability in the evaluation. This method provides a powerful means of evaluating RC member performance, offering insights that are often challenging to obtain through experimental testing alone. [67–70].

This study focuses on the structural performance of hybrid fiber-reinforced concrete (HFRC) one-way subjected to flexural loading. The research highlights the limitations of plain cement concrete, including its low tensile strength, susceptibility to cracking, and brittleness. These issues can compromise the durability and longevity of concrete structures, necessitating enhancements in material properties. To address these challenges, the study incorporates both steel and polypropylene fibers, which are widely recognized for enhancing concrete's mechanical properties. 21 one-way slabs. The experimental setup included four-point bending tests for the slabs and three-point bending tests for selected samples. The variables examined included different volumetric proportions of steel fibers (ranging from 0.7% to 1.0%) and polypropylene fibers (from 0.1% to 0.9% in 0.2% increments).

2. TESTING PROGRAM

2.1 Materials

In this study, readily available industrial materials are used to investigate the effect of hybrid fiber on the load-carrying capacity of one-way. The Ordinary Portland Cement (OPC) of ASTM Type-I, 43 Grade [71] has been used. The physical properties of the OPC are presented in Table 1. Coarse aggregate, passing through a 25 mm sieve and retained on a 4.75 mm sieve, as per the ASTM. The fine aggregate, passing through a 9.5 mm sieve and retained on a 150 µm sieve, was obtained from Laurancepur and used as fine aggregate in the concrete mix [72]. The properties of both fine and coarse aggregates, determined through laboratory testing, are provided in Table 2.

Table 1

Physical Properties of Cement
No.	Description	Details
1	Consistency (C)	28.75%
2	Initial-Setting-Time (IST)	58 min & 31 min
3	Final-Setting-Time (FST)	210 min & 45 min
4	Soundness (S)	No expansion
5	Fineness (F)	3190 cm²/g
6	Specific Gravity (SG)	3.03
7	Compressive Strength (CS)	41 MPa

Table 2

Properties of Fine-Aggregate Sand Coarse-Aggregate Sand Used in Testing
No.	Description	Coarse-Aggregates	Fine-Aggregates
1	Water Absorption	0.82%	1.21%
2	Fineness Modulus	-	2.4
3	Specific Gravity (SG)	2.71	2.67

The hybrid fibers utilized in this study comprised steel and polypropylene, with their physical properties detailed in Table 3. The steel fiber, identified as Dramix® 3D, is a hooked-end, cold-drawn wire fiber classified as Type-I under ASTM A-820 [73]. These fibers are produced in glued or bundled forms to facilitate uniform distribution within the concrete matrix. Although predominantly employed in the mining sector, this fiber type has also been widely adopted in tunneling and underground construction projects. The polypropylene fibers used in this study are Chemrite PF fibers, high-quality, pure polypropylene fibers (PF) designed to reduce plastic and dry cracking while enhancing the surface properties and durability of mortar and concrete. The properties of both fibers are provided in Table 3.

Table 3

Physical properties of fibers
No.	Description	Micro PF	Macro Hooked SF
1	Length (mm)	14	38
2	Diameter	22 µm	0.5 mm
3	Aspect Ratio	636	76
4	Thermal conductivity	-	Low
5	Specific Gravity	0.91	7.85
6	Tensile strength (MPa)	400	1100
7	Elongation at Failure	15%	3.50%
8	Melting point	1700°C	2530°C
9	Young’s Modulus (kN/mm2)	0.45	20

Incorporating different types of fibers tends to reduce the workability of the concrete mixture [74]. To counteract this, a poly naphthalene-based admixture, Chemrite-NN, was employed as a water-reducing agent at a dosage of 0.6%–2% by weight of cement in compliance with ASTM C494 [75]. This superplasticizer was used to improve the workability of freshly prepared fiber-reinforced concrete (FRC). Superplasticizers offer several advantages, including enhanced workability and placement, faster setting times, and a reduced risk of segregation. Error! Not a valid bookmark self-reference. The various properties of the superplasticizer used in this study are presented.

Table 4

Properties of admixture (Chemrite-NN) used in concrete mixes
No.	Description	Details
1	pH value of NN	App. 8
2	Toxicity	Non-toxic
3	The density of chemicals. at 25°C	App. 1.18 kg/lit
4	Chloride content of NN	Nil (EN 934-2)
5	Transportation	Non-hazardous

2.2 Fabrication of Samples

A total of 20 hybrid fiber-reinforced concrete (HFRC) specimens and one plain cement concrete (PCC) specimen were prepared, with a focus on one-way specimens. The one-way slabs measured 1016 mm × 457 mm × 100 mm. The HFRC specimens were designed using a hybridization technique that combines steel fibers (SF) and polypropylene fibers (PF) in varying volumetric proportions. Expressly, four SF volumetric fractions—0.7%, 0.8%, 0.9%, and 1%—and five PF volumetric fractions—0.1%, 0.3%, 0.5%, 0.7%, and 0.9%—were incorporated. This systematic variation aimed to assess the influence of fiber combinations on the mechanical performance of the slabs under different loading conditions. These slabs are divided into four groups for the discussion, as described in Table 5. Group 1 has five samples with different PF % (0.1%, 0.3%, 0.5%, 0.7%, and 0.9%) but the same SF 0.7%. Similarly, Group 2 has five samples with different PF% (0.1%, 0.3%, 0.5%, 0.7%, and 0.9%), but the same SF of 0.8%. The same applies to Group 3 (SF 0.9%) and to Group 4 (SF 1.0%). The fiber ratios were chosen to minimize cracking and shrinkage during the early stages of curing [76].

Table 5

Sample Details for one-way with Fiber Distribution
No	Sample label	Group	Percentage of SF	Percentage of PF	Mix ratio
1	S-M1		0%	0%	0.0 & 0.0
2	S-M2	Group1	0.7%	0.1%	0.7 & 0.1
3	S-M3		0.7%	0.3%	0.7 & 0.3
4	S-M4		0.7%	0.5%	0.7 & 0.5
5	S-M5		0.7%	0.7%	0.7 & 0.7
6	S-M6		0.7%	0.9%	0.7 & 0.9
7	S-M7	Group2	0.8%	0.1%	0.8 & 0.1
8	S-M8		0.8%	0.3%	0.8 & 0.3
9	S-M9		0.8%	0.5%	0.8 & 0.5
10	S-M10		0.8%	0.7%	0.8 & 0.7
11	S-M11		0.8%	0.9%	0.8 & 0.9
12	S-M12	Group3	0.9%	0.1%	0.9 & 0.1
13	S-M13		0.9%	0.3%	0.9 & 0.3
14	S-M14		0.9%	0.5%	0.9 & 0.5
15	S-M15		0.9%	0.7%	0.9 & 0.7
16	S-M16		0.9%	0.9%	0.9 & 0.9
17	S-M17	Group4	1.0%	0.1%	1.0 & 0.1
18	S-M18		1.0%	0.3%	1.0 & 0.3
19	S-M19		1.0%	0.5%	1.0 & 0.5
20	S-M20		1.0%	0.7%	1.0 & 0.7
21	S-M21		1.0%	0.9%	1.0 & 0.9

The concrete mix design used for all specimens was consistent, with a mix ratio (MR) of 1:1.4:2.8 (cement (C): fine aggregates (FA): coarse aggregates (CA)), and a water-to-cement (w/c) ratio of 0.48. The only variation across the mixes was the volumetric ratios of hybrid fibers. For the one-way slabs, reinforcement consisted of seven 10-mm-diameter steel bars with a yield strength of 420 MPa, placed longitudinally, and three bars of the same specifications, positioned transversely, all spaced equally. The plan and cross-sectional views of the slab specimens are illustrated in Fig. 1 and Error! Reference source not found..

Fig. 1

(a) Plan view of (a) one-way slab, and (b) experimental arrangement under four loading conditions

To evaluate the performance of the one-way slabs, three deflection gauges were positioned at the bottom to measure deflections at 1/3rd, 2/3rd, and the midpoint of the slab. Strain gauges were also installed on the tension side to record the maximum strain values. The load was applied incrementally in 5 kN steps using a load cell, with measurements taken of the applied load and vertical deflections at the first visible crack and at the point of slab crushing. This setup ensured precise measurements of the slabs’ behavior under increasing loads, providing valuable data on their structural response and ultimate failure mechanisms, as illustrated in Fig. 1. A straightforward testing method was developed for evaluating one-way slabs under flexural loading. The testing setup involved placing the slab specimens on the experimental frame, which is supported as end conditions for a one-way slab under four-point loading, as illustrated in Fig. 2.

Fig. 2

Four-point flexural testing of a one-way slab under four loading conditions

The study’s primary objectives were to identify the slabs’ first-cracking and ultimate-failure loads. Deflection in the slabs was measured using a Linear Variable Differential Transformer (LVDT) positioned at the center of the slab, the location expected to experience maximum deflection. To monitor strain responses, three strain gauges were strategically placed on the bottom fiber of the slabs. These gauges were connected to a Vishay strain indicator and a portable P3 recorder, supporting up to four strain gauge circuit inputs. The P3 recorder was interfaced with a computer program, enabling real-time data acquisition and analysis. This setup comprehensively assessed the slabs' structural behavior by combining precise deflection measurements with detailed strain monitoring. Deflection and strain data were systematically recorded throughout the testing process. Based on the collected data, comprehensive structural and flexural analyses were conducted. The results of the flexural tests for the slabs are detailed in Tables 5 & 6.

3. FINITE ELEMENT ANALYSIS OF RC STRUCTURAL CONFIGURATIONS

ABAQUS[52] recognized for its advanced finite element analysis (FEA) capabilities and accuracy in modelling materials such as concrete and steel [52, 53]was employed to develop finite element models that capture the behavior of RC frames with high precision. In this modelling approach, concrete was simulated using 3D solid stress elements, while the reinforcing bars were represented by wire elements capable of full 3D deformation. Reliable simulation results were ensured by applying suitable boundary conditions and load setups that enabled the gradual and uniform application of loads. The model underwent calibration and refinement to incorporate key parameters, including the concrete's shape factor, viscosity coefficient, dilation angle, mesh type, and element size. This refined model then supported an extensive parametric study, which explored the influence of these variables on the behavior of RC frame, thereby improving the accuracy and generalizability of the numerical analyses.

3.1 Compressive uniaxial stress-strain relationship for concrete

Figure 3 illustrates the simplified upper-bound tensile stress-displacement relationship utilized in this study. For the CPD model, there are key parameters that must be defined, including (i) the viscosity parameter, which helps smooth out the material response in Abaqus/Standard, and (ii) the dilation angle, 𝜓, representing the angle of inclination of the failure surface relative to the hydrostatic axis. The dilation angle controls the plastic flow and overall material behavior under loading [52].

Fig. 3

Stress-strain curve of concrete used in the model [52]

The different concrete material properties used in ABAQUS Standard, defining materials and step modules, are given in Table 6. The elasticity modulus (E_c) of concrete was calculated using the ACI code given byEq: 1

Table 6

Different properties used in ABAQUS for concrete [52]
$\:{E}_{c}=4700\sqrt{{f}_{c}^{{\prime\:}}}\:\:\:\:\:\:$	Eq: 1

Parameters	Values
Concrete density (ton/mm³)	2.4 X 10^− 9
Poisson’s ratio, $\:\nu\:$	0.2
Concrete Compressive Strength (MPa)	35.06
Elasticity modulus, E_c (N/mm²)	26587
The initial increment size of loading	0.01
Maximum increment size of loading	0.1
Minimum increment size of loading	1E-050
Number of increments	100000

The CPD model [52] initially developed for concrete materials [52] is versatile enough to simulate the behavior of other quasi-brittle materials, such as masonry and mortar. This model is designed to capture two primary failure mechanisms: tensile cracking and compressive crushing. The key inputs required for the CDP model are the material's uniaxial stress-strain behavior under tension and compression [52]. In tension, the material is assumed to exhibit linear-elastic behavior up to its peak tensile strength, beyond which it follows a softening curve, as illustrated in Fig. 4 (a). In compression, the response begins with a linear elastic phase, transitions to a hardening region, and finally undergoes softening, as depicted in Fig. 4 (b). These behavioural characteristics allow the CDP model [52] to accurately represent the progressive damage and nonlinear response of quasi-brittle materials under complex loading conditions.

Fig. 4

CPD modelling (a) under tension and (b) under compression [52]

The primary advantage of employing this material model is its ability to distinctly define the material's behaviour under tension and compression, thereby capturing its fundamentally different mechanical responses. This includes variations in yield strengths, tension softening, and the transition from hardening to softening in compression, as well as distinct elastic stiffness degradation under both tensile and compressive loads. The degradation of elastic stiffness in concrete is primarily attributed to failure mechanisms such as cracking under tensile stresses and crushing under compressive stresses. In the CPD model, this degradation is based on scalar-damage theory, where the loss of stiffness is considered isotropic and represented by a single scalar damage variable. The stress-strain relationship, incorporating this damage parameter as Eq: 2, is mathematically expressed in providing a concise representation of the material's behavior as it transitions from an undamaged to a damaged state.

$\:{\upsigma\:}=(1-\text{d})\bullet\:{\text{D}}_{0}^{\text{e}\text{l}}/({\upepsilon\:}-{{\upepsilon\:}}^{\text{p}\text{l}})={\text{D}}^{\text{e}\text{l}}/({\upepsilon\:}-{{\upepsilon\:}}^{\text{p}\text{l}})$

Eq: 2

In this context,

$\:{D}_{0}^{el}\:$

represents the initial, undamaged elastic stiffness of the concrete, while

$\:{D}^{el}$

= (1-d) ∙

$\:\:{D}_{0}^{el}\:$

denotes the degraded elastic stiffness, accounting for material damage. The scalar variable ddd, which quantifies stiffness degradation, ranges from 0 ≤ d ≤ 1, indicates an entirely intact (undamaged) material and d = 1 signifies a fully damaged state. The corresponding effective stress, which reflects the internal stress carried by the undamaged portion of the material, is formally defined in Eq: 3

$\:\stackrel{-}{{\upsigma\:}}={\text{D}}_{0}^{\text{e}\text{l}}/({\upepsilon\:}-{{\upepsilon\:}}^{\text{p}\text{l}})$

Eq: 3

and is related to the Cauchy stress through the scalar degradation variable as Eq: 4.

$\:\stackrel{-}{{\upsigma\:}}={\text{D}}_{0}^{\text{e}\text{l}}/({\upepsilon\:}-{{\upepsilon\:}}^{\text{p}\text{l}})$

Eq: 4

3.2 Parameters for concrete behaviour

Different parameters, including the dilation angle, define the plasticity model of concrete

$\:\left(\psi\:\right)$

, the plastic potential eccentricity (ɛ), the ratio of compressive stresses in the biaxial state to the uniaxial state

$\:({\sigma\:}_{b0}/{\sigma\:}_{c0})$

, shape factor (K_c), and the viscosity parameter. The values of the dilation angle and viscosity parameter were taken from calibration. The yield shape surface (Kc) and eccentricity (ɛ) values are 2/3 and 0.1, respectively, recommended by the concrete damaged plasticity model. The specified value of the stress ratio

$\:\:({\sigma\:}_{b0}/{\sigma\:}_{c0})$

, is 1.16 by [52] proposed the Eq: 5 to quantify this stress ratio

$\:\:({\sigma\:}_{b0}/{\sigma\:}_{c0})$

based on a large body of statistical data.

Table 7

presents the compressive stress-strain relationship for concrete as outlined in Eurocode 2 [77]. According to the ABAQUS [52] the material exhibits linear elastic behavior up to approximately to 0.4f_cm [77] also provides empirical formulations, derived from experimental observations Eq: 6 and expressed in Eq: 7to estimate the strain ε_c1 corresponding to the mean compressive strength of concrete and the ultimate strain ε_cu1.
$\:\frac{{\sigma\:}_{bo}}{{\sigma\:}_{co}}=1.5{\left({f}_{c}^{{\prime\:}}\right)}^{-0.075}$	Eq: 5

$\:{\epsilon\:}_{c1}=0.0014(2-{e}^{-0.024{f}_{cm}}-{e}^{-0.140{f}_{cm}})$	Eq: 6
$\:{\epsilon\:}_{cu1\:}=0.004-0.0011(1-{e}^{-0.0215{f}_{cm}})$	Eq: 7

Fig. 5

Concrete modelling in ABAQUS

Eq: 8 provided by EuroCode 2 [77] the research used nonlinear behaviour of structures to model the concrete stress-strain relationship.

$\:{\sigma\:}_{c}={f}_{cm}\frac{k\eta\:-{\eta\:}^{2}}{1+(k-2)\eta\:}$	Eq: 8
Where in Eq: 9

$\:k=1.05{E}_{cm}\frac{{\epsilon\:}_{cl}}{{f}_{cm}},\:\eta\:=\:\frac{{\epsilon\:}_{c}}{{\epsilon\:}_{cl}}$	Eq: 9
EuroCode 2 [77] also proposed an equation for the non-linear behaviour of the stress-strain relationship of structures, given byEq: 10

Fig. 6

Tensile behaviour of Concrete in ABAQUS [77]

The Tensile behaviour of Concrete in ABAQUS was estimated by using Eq: 11 [77]

$\:{f}_{t}^{{\prime\:}}=0.33\sqrt{{f}_{c}^{{\prime\:}}}$

Eq: 11

All concrete parameters are outlined in Table 7, are essential for accurately simulating the nonlinear response of concrete under varying load conditions [52].

Table 7

Properties of concrete used in the model [52]
Material	Concrete
Poisson's ratio	0.2
Modulus of elasticity of Concrete (MPa)	*TBI
Cylinder compressive strength of Concrete (MPa)	*TBI
Tensile Strength of Steel(MPa)	*TBI
*TBI = to be inbestigated

3.3 Simulations of steel reinforcing bars

In the FEA steel bars were taken as elastoplastic material and their interaction with concrete was defined as embedded region, similarly concrete was taken as a host region. A perfect bond between steel and concrete was assumed. Material properties of steel bars used in the present work are, yield strength of 420 MPa Poisson’s ratio 0.3 and modulus of elasticity of 200 GPa. To simulate the steel bars a truss element having two nodes and three translations at every node (T3D2) were considered.

Fig. 7

Concrete Stress-strain used in CDPM

3.4 Modelling and Calibration of one-way HFRC Slab

The Fig. 8 describes the modelling steps of the one-way HFRC slab in ABAQUS. The (a) described the concrete slab with steel mesh in it as illustrated in Fig. 1. The (b) described the support condition and loading points. The (c) described the mesh size and shape for the one-way HFRC slab in ABAQUS. The (d) described the steel mesh constraint in the concrete.

Fig. 8

Modelling of Slab specimens in FEM

Figure 9 (a) compares the experimental load–deflection response of the specimen with numerical simulations performed using different dilation angles (30°–42°). All numerical curves exhibit the characteristic nonlinear stiffness degradation observed experimentally, with relatively minor deviations across the DA range. Lower dilation angles slightly underpredict the load in the mid-deflection range, while higher angles show marginally stiffer behavior. Overall, the variation in dilation angle results in modest changes to the predicted response, and DA values between 32° and 38° demonstrate the closest agreement with the experimental curve, confirming that the numerical model is not highly sensitive to this parameter within the tested range.

Figure 9(b) illustrates the sensitivity of the numerical load–deflection response to the viscoplastic parameter (VP), ranging from 0.0009 to 0.009. As VP increases, the predicted curves become progressively stiffer, especially at higher deflection levels, leading to a noticeable overestimation of the ultimate load for large VP values. Lower VP values, particularly 0.0009 and 0.001, align more closely with the experimental response, reproducing both the initial stiffness and the post-yield behavior. This trend indicates that VP strongly influences the rate-dependent plastic deformation, and excessive values can artificially enhance the predicted load-carrying capacity.

Figure 9 (c) presents a comparison of experimental results and numerical simulations for different stress ratios (1.06–1.36). The numerical curves show that increasing the stress ratio results in a slightly stiffer response, primarily on the ascending branch. Nevertheless, the overall variation among the predicted responses is relatively small, and all stress-ratio configurations capture the general shape and nonlinear behavior of the experimental curve. Stress ratios between 1.06 and 1.16 demonstrate the best correlation with the experimental data, suggesting that moderate adjustments in this parameter can fine-tune the model without drastically altering its accuracy.

Figure 9(d) examines the influence of mesh size (15–60 mm) on the numerical predictions. Finer meshes (15–20 mm) yield results that closely follow the experimental curve throughout the loading process, accurately representing both initial stiffness and peak load. As the mesh size increases, the numerical response becomes slightly softer and deviates more noticeably at larger deflections, although the general curve shape remains consistent. The results confirm that a mesh size of 20–30 mm offers a good balance between computational efficiency and predictive accuracy, whereas coarser meshes (50–60 mm) reduce fidelity in capturing the nonlinear deformation behavior.

Fig. 9

Calibration process of the Slab specimens

The Table 8 summarizes the key numerical parameters evaluated during the model calibration process, along with the range of values assessed and the final optimized selections. The dilation angle was examined over a range of 15° to 55°, with 35° identified as the optimal value that best matched the experimental response. The eccentricity parameter was varied from 0.0015 to 0.45, with 0.15 yielding the best performance. The stress ratio was found to be optimal at 1.165, consistent with the value used during calibration. Similarly, the shape factor was explored from 0.15 to 1.25, and the model performed best at 0.65. For rate effects, the viscosity parameter was tested over the range 0.0015–0.0055, with 0.0035 found to be most suitable. Finally, mesh sizes ranging from 15 mm to 115 mm were evaluated, and 55 mm provided the best balance between computational efficiency and predictive accuracy.

Table 8

CDP calibration summary
Sr. No	Descriptions of Parameter	Ranges of Values	Optimised Value
1	Dilation Angle, ψ_s	15,25,35,45,55	35
2	Eccentricity, εs	0.0015,0.055,0.15,0.25,0.45	0.15
3	Stress ratio, $\:{\varvec{\sigma\:}}_{\varvec{b}0}/{\varvec{\sigma\:}}_{\varvec{c}\varvec{o}}$	1.165	1.165
4	Shape Factor, K_c	0.15,0.35,0.65,0.95,1.25	0.65
5	Viscosity Parameter, v_s	0.0015,0.0025,0.0035,0.0045,0.0055	0.0035
6	Mesh Size(mm)	15,25,55,95,115	55

The Fig. 10. Optimized FEM Model of the Slab presents a comparison between the experimental load–deflection response and the finite element analysis (FEA) prediction for the tested specimen. Both curves exhibit a similar nonlinear trend, characterized by an initial steep stiffness followed by gradual softening as deflection increases. The FEA results closely track the experimental behavior throughout the loading range, particularly in the early and mid-deflection stages, demonstrating the model’s ability to accurately capture the stiffness and progressive deformation. Although the numerical curve slightly underestimates the peak load and shows marginally softer behavior at larger deflections, the overall agreement between the two curves is strong, confirming the reliability and validity of the calibrated numerical model for predicting the structural response.

Fig. 10

Optimized FEM Model of the Slab

4. ARTIFICIAL NEURAL NETWORK (ANN)

Research [78–80] indicates that Artificial Neural Networks (ANNs) are designed to emulate the structure and functionality of biological neural systems in living organisms (illustrated in Fig. 11a&b). These computational models excel at processing complex relationships through pattern recognition, leveraging knowledge acquired during training to perform tasks such as classification, prediction, and generalization. Structurally, ANNs consist of multiple layers containing interconnected processing units ("neurons") that form sophisticated networks. As depicted in Fig. 11 these inter-neuronal connections are governed by specific weighting values. The fundamental mathematical representation of an ANN is provided in Eq: 12. The researchers have provided a comprehensive description of both the operational mechanisms and the supervised training methodology employed in these networks.

Fig. 11

(a) The Function of an Artificial Neuron and (b) Artificial Neural Network

The output of a neural network (O) is influenced by the combination of weights (wi), inputs (xi), and a bias term (b). Activation functions play a crucial role in shaping the network’s performance; typically, logistic and hyperbolic functions are applied between the input and hidden layers, while hyperbolic functions are used between the hidden and output layers. To refine the network's predictions, a back-propagation algorithm based on the delta rule is employed, which systematically updates the weights to reduce the discrepancy between the predicted output and the actual target value (T) obtained from the dataset. As depicted in Fig. 11a&b, this learning process proceeds iteratively from the output layer back through the network, continuing as described by Eq: 13until the mean squared error (MSE) falls below a predefined threshold, thereby improving the model’s accuracy [78–80].

$\:E\left(w\right)=\frac{1}{2}{\sum\:}_{i\:}{(T-O)}^{2}$

Eq: 13

The neural network's predicted output (O) is compared against the target values (T) from the database, and the resulting error is minimized through backpropagation using the Delta Rule [78–80]. This optimization process, illustrated in Fig. 11, involves iteratively adjusting initially randomized connection weights—propagating corrections backward (right to left) through the network—to align the outputs more closely with the expected target values. Training continues until the mean squared error (MSE) converges to an acceptable threshold, indicating no further improvement. The fine-tuned weights are then applied in the ANN model, enabling more precise predictions with reduced error margins.

4.1 Normalization of Database

Researchers [78–80]emphasizes that input normalization plays a critical role in effectively training ANN models, particularly when dealing with units with varying parameter sizes. Normalization transforms all inputs into dimensionless values, improving computational efficiency and preventing sluggish learning rates. In this study, rather than using the standard 0 to 1 range, parameters are scaled between 0.2 and 0.8 Eq: 14 to enhance model performance [78–80]. The normalization process follows. Eq: 14 where a raw input value (x) is converted to its normalized form (X) by referencing the maximum value (xₘₐₓ) and the range (xₘₐₓ - xₘ_iₙ). This adjustment ensures smoother ANN training while maintaining numerical stability.

$\:X=\left(0.6/\varDelta\:\right)x+\{0.8-\left(\frac{0.6}{\varDelta\:}\right){x}_{max}\}$

Eq: 14

4.2 Calibration of Proposed ANN Model

To ensure the accuracy of the proposed ANN model, calibration is performed by comparing its predictions with experimental results. The multi-layer feedforward backpropagation (MLFFBP) technique, introduced by Grossberg (1988) [81–85] is employed for this process, following established training methodologies [81–85]. To enhance generalization and prevent overfitting, the dataset is divided into three subsets: 60% for training, 20% for validation, and 20% for testing [81–85]. MATLAB [86] serves as the computational platform for ANN implementation.

Each ANN model undergoes training for 100 epochs using the MLFFBP algorithm [81–85]. The iterative process terminates when any of the following criteria are met:

ii.

The performance goal (deviation between output and target values) falls below 0.0001.

iii.

The validation phase records 20 consecutive failures (no improvement in error reduction).

iv.

The minimum performance gradient attains a threshold of 1.0 × 10⁻¹⁰, as defined by the Levenberg-Marquardt backpropagation method [81–85].

This optimization leverages a second-order algorithm that uses second-derivative information to adjust weights efficiently. The ANN’s predictive accuracy is evaluated using three key indicators:

Mean Squared Error (MSE, Eq: 15 ) Quantifies the average squared deviation between predicted and target values.

Mean Absolute Error (MAE, Eq: 16) Measures the absolute difference between predictions and experimental data.

Correlation factor (R, Eq: 17) Assesses the linear relationship between target and predicted outputs, with higher values indicating stronger agreement.

These metrics, drawn from prior studies [81–85], ensure rigorous validation of the model’s reliability across diverse scenarios.

Eq: 15
Eq: 16
Eq: 17

In the following equations, O_i denotes the predicted values generated by the ANN, while Ti refers to the experimentally observed (target) values. The variable n represents the total number of samples. The symbol

$\:{T}^{-}$

indicates the mean of the experimental values, and

$\:{O}^{-}$

Denotes the mean of the predicted values.

The HFRC database included 145 flat one-way slab samples (HSC), as shown in Fig. 1. (a) Plan view of (a) one-way slab, and (b) experimental arrangement under four loading conditions, to determine their punching strengths. Table 9 provided the information about the critical parameter (i.e., column dimension, c_s, depth of the slab, d_s, shear span ratio, a_vs/d, longitudinal percentage steel ratio plus fiber content, ρ_ls, longitudinal steel yield strength f_yls, the concrete compressive strength, f_cs, and ultimate load carrying capacity, V_us). The 99 of the samples (i.e., 143) failed in shear, while the remaining failed in flexure. Figure 12 described the histogram for the critical parameters for the HSC. This histogram shows the frequency of the parameter across different sample values. This is also a limitation of ANN models, as they will predict within the limits of each parameter.

Table 9

Parameter details in the database
	c_s (mm)	d_s (mm)	α_v/d	ρl_s(%)	fyl_s (MPa)	fc_s (MPa)	Mf_s kN-mm	Vu_s (kN)
Min	54	64	4.5	0.3	294	9.52	39000	105
Max	600	275	14.02	6.9	749	118.7	1951000	2450
Avg.	206.34	122.32	7.81	1.31	496.88	41.3	252655	458.7
St. Dev	87	44.82	2.4	0.89	117.68	24.85	292121	436.88
COV	0.42	0.37	0.31	0.68	0.24	0.6	1.16	0.95

The Fig. 12 histogram of the shear span–to–effective depth ratio (av/d) shows a moderately skewed distribution, with most data concentrated between 4 and 8. A noticeable peak occurs around 5–6, indicating that this range represents the most common test configuration in the database. The fitted curve suggests a slightly right-skewed distribution, reflecting a smaller number of specimens with higher av/d values, up to around 12. Overall, the distribution captures a broad range of structural geometries while retaining a dominant cluster in the lower-to-mid-range ratios.The column width parameter exhibits a relatively uniform spread with a central concentration between 0.1 × 10³ and 0.3 × 10³ mm. The histogram shows mild right skew, indicating that larger column sizes are less frequent but still represented. The fitted curve highlights a broad bell-shaped distribution, indicating substantial variability across specimens. Most data points fall within typical column dimensions used in experimental studies, contributing to a balanced dataset. The Fig. 12 histogram of member depth reveals an apparent clustering around 100–150 mm, where most specimens fall. The fitted curve shows a moderately symmetric distribution, though with a slight tail extending to depths of around 250 mm. This reflects that while a standard depth range is dominant, the dataset also includes both smaller and larger sections, providing diversity in structural dimensions. The strong central peak indicates that mid-range depths are most commonly tested.

The distribution of longitudinal reinforcement ratio (ρl) is strongly right-skewed, with the majority of specimens having reinforcement ratios between 0.5% and 2.0%. The histogram displays a steep drop in frequency beyond 3%, showing that heavily reinforced sections are relatively rare. The fitted curve confirms this skewed pattern, emphasizing the dominance of lower reinforcement levels in the dataset. This trend is consistent with typical reinforced concrete design limits used in experimental programs. The Fig. 12 histogram of steel yield strength shows a wide range, spanning approximately 200–600 MPa, with a central concentration around 350–450 MPa. The distribution appears moderately symmetric, though slightly right-skewed due to the presence of higher-strength steels. The fitted curve highlights a broad and well-spread dataset, reflecting the inclusion of specimens with both conventional and higher-grade reinforcement. This diversity enhances the generality of the analytical model. The Fig. 12 histogram of concrete compressive strength (fc) shows a left-skewed distribution, with most specimens falling between 20 and 50 MPa. The frequency decreases with increasing strength, though values up to approximately 100 MPa are included. The fitted curve reflects this trend, showing a dominant peak in the lower-strength range, typical of normal-strength concrete commonly used in structural testing. The presence of higher-strength data points increases overall variability.

Fig. 12

Histogram of the Critical Parameters for

Table 10

Combination of Parameters of ANN Models
Sr. No	ANN	Combination of Parameters	Inputs	L1-2	A L3-4	Hidden	output
1	HSC = 1	ρ_ls,f_yls,f_cs, c_s,d_s,a_vs/d_s	06	SDF	THF	12–12	V_u, 1
2	HSC = 2	M_fs,f_c, c_s,d_s,a_vs/d_s	05	SDF	THF	10–10	V_u, 1
3	HSC = 3	M_fs/f_csbd_s^2, c_s/d_s,a_vs/d_s,	03	SDF	THF	6–6	V_u, 1
4	HSC = 4	ρ_ls,f_cs/f_yls, c_s/d_s,a_vs/d_s,	04	SDF	THF	8–8	V_u, 1
5	HSC = 5	M_fs/bd_s²,f_cs, d_s,a_vs/d_s	04	SDF	THF	8–8	V_u, 1
6	HSC = 6	M_fs/f_csbd_s^2, d_s,c_s/d_s,a_vs/d_s,	04	SDF	THF	8–8	V_u, 1
	HSC = 7	M_fs/f_csbd_s²,f_sc, d_s,c_s/d_s,a_vs/d_s,	05	SDF	THF	10–10	V_u, 1
SDF = Sigmoid, THF = tanghn

The ANN model, having the highest R values and the lowest MSE and MAE values, can be considered to the optimized model. (47–55). Based on Fig. 13and Fig. 14, the HSC = 4 (ρ_ls,f_cs/f_yls, c_s/d_s,a_vs/d_s,) is the best model by presenting the immense value of R while at the same time showing the least values of MSE and MAE.

Figure 13compares the experimentally measured ultimate shear capacity (EXP. Vu) with the predicted ultimate shear capacities (Vu) obtained from seven shear-capacity strength models (HSC1–HSC7). Each subplot shows a scatter plot of predicted versus experimental values, with a 1:1 reference line indicating perfect agreement. The data points cluster closely around the reference line for several models (e.g., HSC1, HSC2, HSCS4, HSC6, HSC7), demonstrating strong predictive performance and minimal deviation from experimentally observed behaviour. In contrast, models such as HSC3 and HSC5 exhibit wider scatter, indicating comparatively larger discrepancies between predicted and measured shear strengths. Across all plots, the axes span from 0 to approximately 2460 kN, allowing consistent visual comparison of model accuracy. Overall, the figure highlights the varying levels of predictive reliability among the seven HSC models when evaluated against measured shear capacities.

Fig. 13

ANN models Predictions for the HSC

Figure 14 presents a comparative evaluation of the seven shear-capacity strength models (HSC1–HSC7) using three statistical performance indicators: mean squared error (MSE), mean absolute error (MAE), and correlation coefficient (R). The first subplot shows that MSE values remain relatively low across all models, with HSC1 and HSC2 exhibiting the smallest errors, while HSC5 produces the highest MSE. The second subplot illustrates the MAE distribution, revealing a similar trend: HSC1 and HSC2 show the lowest absolute prediction errors, whereas HSC5 again shows the most significant deviation from experimental values. The third subplot displays the correlation coefficient (R), indicating the strength of linear association between predicted and experimental shear capacities. Models HSC1, HSC2, and HSC7 achieve the highest correlations (approaching 100%), reflecting strong predictive consistency. In contrast, HSC5 and HSC6 show comparatively lower correlations. Collectively, the figure highlights that HSC1 and HSC2 provide the most accurate and reliable predictions among the evaluated models, while HSC5 shows the weakest overall performance.

Fig. 14

ANN models error for the HSC

5. RESULTS AND DISCUSSIONS

For one-way slabs, the observed behavior did not exhibit a consistent trend. Specifically, in the case of specimen SM21, which contained the highest concentration of steel and polypropylene fibers, initial cracking occurred at a relatively low load of 56.65 kN, significantly lower than the load sustained by the control specimen. Conversely, specimen SM3, with only 0.7% steel and 0.3% polypropylene fibers, demonstrated improved performance, withstanding a load of 84.13 kN before cracking. The highest load at the onset of cracking was recorded for specimen SM6, which reached 90.25 kN. The complete set of experimental results is detailed in Table 11. These cracking loads indicate the initiation of structural failure. A comparative analysis revealed that a specific ratio performed best across each fiber combination, highlighting the synergistic effect of steel and polypropylene fibers. This indicates that an optimal fiber volumetric ratio is essential to achieve maximum strength. Figure 15 Compares first-crack loads corresponding to various steel and polypropylene fiber volumetric ratios.

Table 11

Experimental results for one-way specimens
Sample label	One-way slabs
Sample label	1st crack load (kN)	Final crack load (kN)	1st crack deflection (mm)	Final crack deflection (mm)
S-M1	79.05	89.21	3.9	6.93
S-M2	72.33	91.45	3.5	7.38
S-M3	91.13	101.49	6.04	15.1
S-M4	72.49	110.57	6	17.8
S-M5	68.01	98.81	5.3	14.18
S-M6	90.25	117.29	6.92	18.9
S-M7	65.77	83.69	6.5	8.5
S-M8	61.29	103.77	3.9	13.2
S-M9	32.17	91.13	3.55	13.2
S-M10	47.85	97.85	3.18	15.6
S-M11	59.05	99.37	4.9	11.4
S-M12	81.45	115.05	5.35	14.78
S-M13	62.33	97.25	3.55	9.3
S-M14	56.81	74.73	3.6	8.5
S-M15	36.65	71.29	3.14	8.3
S-M16	53.21	61.13	5.3	9.15
S-M17	56.81	88.01	3.75	7.7
S-M18	63.37	76.81	5.8	12.3
S-M19	90.25	112.81	6.45	11.7
S-M20	54.57	69.05	7.1	10.6
S-M21	56.65	64.81	4.4	8.3

The Fig. 15 illustrate how varying proportions of steel fibres (SF) combined with different contents of polypropylene fibres (PPF) influence the load-carrying capacity of concrete slabs at two performance stages: the first-crack load and the ultimate crack load. In the upper graph, the first-crack capacities are plotted for slabs containing 0.7%, 0.8%, 0.9%, and 1.0% steel fibres. Each group of bars represents increasing dosages of polypropylene fibres, ranging from 0.1% to 0.9%. A general increase in first-crack resistance is observed as PPF content increases, although the rate of improvement varies with the steel fibre content. Notably, the 1.0% SF mix shows the most significant response to higher PPF levels, with the highest initial cracking strength among all fibre combinations. The lower graph presents the ultimate load capacity for the same mixtures. Similar to the first-crack trend, slabs with higher PPF content typically exhibit higher ultimate strength. The enhancement becomes more pronounced at higher steel fibre ratios, particularly at 1.0% SF, where PPF addition results in a marked increase in peak load capacity. Overall, the data demonstrate a complementary effect between steel and polypropylene fibres, with the combined reinforcement significantly improving both the onset of cracking and the final load-bearing performance of the slabs.

Fig. 15

First crack loads and ultimate crack loads of all one-way slabs

The Fig. 16 present the mid-span deflections recorded for concrete slabs reinforced with different proportions of steel fibres (SF) and polypropylene fibres (PPF). Deflections are shown at two critical stages of structural response: the first-crack condition and the ultimate crack state. In the upper graph, the first-crack deflections are plotted for slabs containing 0.7%, 0.8%, 0.9%, and 1.0% steel fibres. Within each steel-fibre group, the bars reflect increasing PPF contents from 0.1% to 0.9%. The results indicate that the introduction of higher PPF dosages tends to increase the initial crack deflection, suggesting a greater ability of the slabs to undergo deformation before crack initiation. This trend is most noticeable in the 1.0% SF mixes, where deflection at first crack increases consistently with the addition of PPF. The lower graph shows the deflections measured at the ultimate crack level. The slabs display substantially larger deformations at this stage, with the influence of PPF becoming more prominent. For all steel-fibre proportions, the inclusion of more PPF generally leads to higher ultimate deflection values, reflecting improved ductility and enhanced post-cracking behaviour. Again, the 1.0% SF mixtures exhibit the strongest response, with the most significant deformation before failure. Overall, the combined use of steel fibres and polypropylene fibres results in a noticeable improvement in the deformation capacity of the slabs at both the onset of cracking and at peak load. This combined reinforcement demonstrates a clear benefit in enhancing ductility and delaying failure under loading.

Fig. 16

Deflections at ultimate crack loads for one-way slabs

5.1 Comparison Exp vs FEM of 1-Way HFRC Slab

Figure 17 presents load–deflection curves obtained from experimental tests (black lines) and finite element analyses (blue lines) for six reinforced concrete beams denoted SM1 to SM6. Panels (a) through (f) correspond to specimens SM1, SM2, SM3, SM4, SM5, and SM6, respectively. In each plot, the applied load (kN) is plotted against mid-span deflection (mm), showing the characteristic nonlinear response with an initial stiff linear portion, followed by a gradual reduction in stiffness after concrete cracking, a prolonged yielding plateau associated with steel reinforcement, and final failure. The experimental and numerical results exhibit excellent agreement throughout the loading history, including peak load capacities ranging approximately from 85 to 105 kN and ultimate deflections between 25 and 40 mm, with only minor deviations observed in the post-peak softening branch of certain specimens, thereby validating the accuracy of the adopted finite element modeling approach across the tested series.

Fig. 17

LD Curves comparison for the SM-1 to SM-6

Figure 18 displays the load versus mid-span deflection responses for an additional set of reinforced concrete beams, labeled SM1, SM7, SM8, SM9, SM10, and SM11, in panels (a) through (f), respectively. Experimental curves are shown in black (EXP) and finite element predictions in blue (FEA). All specimens exhibit the typical tri-linear behavior of under-reinforced concrete beams: a steep elastic branch up to first cracking, a pronounced stiffness reduction after crack formation, and an extended yielding plateau governed by tensile reinforcement before reaching peak loads of approximately 90–110 kN at deflections ranging from 20 to 35 mm. The numerical simulations closely replicate both the pre-peak stiffness and post-yield ductility observed in the tests, with only slight discrepancies in the descending branch of certain beams (notably SM7 and SM10), confirming the robustness and predictive capability of the finite element model across a broader range of reinforcement ratios and concrete strengths within the investigated series.

Fig. 18

LD Curves comparison for the SM-7 to SM-11

Across the entire series presented in both figures (SM1 to SM11), the specimen exhibiting the highest peak load is SM6 (Fig. 17) reaching approximately 108 kN, while SM11 (Fig. 18) records the second highest at around 105 kN. The specimen with the lowest ultimate capacity is SM7 (Fig. 18), with a maximum load of only about 88–90 kN. In terms of mid-span deflection at peak load, SM3 Fig. 17displays the largest ductility, failing at nearly 40 mm deflection, whereas SM1 (Fig. 17and Fig. 18), same specimen repeated for reference) and SM9 (Fig. 18) show the most brittle post-peak response, with failure occurring at deflections slightly above 20 mm. Thus, SM6 represents the strongest and one of the more ductile beams in the investigated set, while SM7 consistently yields the lowest load-carrying capacity.

Figure 19 compares the measured and computed load–mid-span deflection responses for six reinforced concrete beams of varying reinforcement ratio and bar arrangement (SM1, SM12, SM13, SM14, SM15, and SM16), with panel (a) again showing the reference specimen SM1. Experimental curves are plotted in black, and finite element results are plotted in blue. Peak loads decrease progressively from approximately 100 kN for SM1 to around 70–75 kN for the most lightly reinforced specimens, SM15 and SM16. At the same time, ductility remains relatively consistent across the series, with failure deflections generally ranging from 25 to 35 mm. The numerical model accurately reproduces the initial stiffness, the extent of the yielding plateau, and the ultimate capacity of each beam, with only negligible differences in the post-peak branch of the lower-reinforced members, confirming the ability of the adopted finite element framework to reliably predict flexural behavior over a broad range of longitudinal reinforcement percentages.

In Fig. 19, the specimen exhibiting the highest peak load is the reference beam SM1 (panel a), reaching nearly 100 kN, followed closely by SM12 and SM13 (panels b and c) at approximately 95–97 kN. The lowest load-carrying capacities are recorded for SM15 and SM16 (panels e and f), both failing at around 70–72 kN, reflecting their significantly reduced longitudinal reinforcement ratios. Regarding ductility, ultimate deflections at peak load are fairly uniform across the series (25–35 mm), with SM14 showing slightly higher deformation capacity (≈ 35 mm) and SM16 the lowest (≈ 25 mm). Thus, SM1 clearly demonstrates the maximum flexural strength, while SM15 and SM16 represent the minimum-strength configurations within this set of tested and simulated beams.

Fig. 19

LD Curves comparison for the SM-12 to SM-16

Figure 20 illustrates the load–deflection behavior of six additional reinforced concrete beam specimens (SM1, SM17, SM18, SM19, SM20, and SM21) under four-point bending, with experimental results depicted by black curves and corresponding finite element simulations by blue curves in panels (a)–(f). Specimen SM1 is repeated in panel (a) as a reference for direct comparison. The remaining beams, representing variations in reinforcement layout and concrete compressive strength, exhibit peak capacities ranging from approximately 68 kN (SM20 and SM21) to nearly 100 kN (SM19), with ultimate deflections ranging from 15 mm to 35 mm. All curves follow the expected pattern of initial linear elasticity, progressive stiffness degradation after cracking, a well-defined yielding plateau, and eventual failure dominated by concrete crushing or reinforcement fracture. The finite element predictions capture both the ascending branch and the post-peak response with high fidelity, including the noticeable reduction in ductility and the lower load-carrying capacity of the lower-strength specimens SM18, SM20, and SM21, thereby further demonstrating the reliability of the numerical model across a broader spectrum of structural configurations.

In Fig. 20, the specimen exhibiting the highest peak load is SM19 (panel d), reaching approximately 98–100 kN, closely followed by the reference beam SM1 (panel a) at around 97 kN. The lowest load-carrying capacities are shown by SM20 and SM21 (panels e and f), both failing at about 68–70 kN, attributable to their substantially lower concrete compressive strength. With respect to ductility, SM19 displays the most excellent deformation capacity, with failure occurring near 35 mm mid-span deflection, whereas SM20 and SM21 exhibit the most brittle response, reaching peak load at deflections of only 15–18 mm. Therefore, SM19 represents both the strongest and most ductile beam in this group, while SM20 and SM21 consistently yield the minimum strength and ductility within the series presented in Fig. 3.

Fig. 20

LD Curves comparison for the SM-17 to SM-21

Figure 21 presents a comparative illustration of the observed and simulated crack patterns at failure for nine reinforced concrete beams (SM1 through SM9). For each specimen, the upper photograph captures the actual crack distribution on the tension face of the tested beam, while the lower contour plot shows the corresponding maximum principal plastic strain (PE, Max. Principal) distribution obtained from the finite element analysis, with red zones indicating regions of intense tensile straining that correlate directly with visible cracks. The numerical results accurately reproduce the experimental cracking morphology, including the initiation of flexural cracks in the constant-moment region, their upward propagation toward the compression zone, the development of secondary inclined cracks near the supports in some specimens, and the widening and coalescence of primary cracks at ultimate load. The close agreement in crack spacing, orientation, and extent between the experimental photographs and the FEM strain contours validates the capability of the adopted concrete damage plasticity model to reliably predict both the location and evolution of cracking throughout the loading history.

Figure 22 compares the final crack patterns observed in laboratory tests with the maximum principal plastic strain contours predicted by the finite element model for twelve additional reinforced concrete beams (SM10 through SM21). In each case, the upper image shows the actual cracked tensile face of the beam at failure, whereas the lower deformed mesh plot presents the distribution of PE, Max. Principal (red zones denoting localized tensile damage equivalent to visible cracks). The numerical simulations faithfully replicate the experimental observations across the entire specimen series, correctly capturing the number, spacing, and height of primary vertical flexural cracks in the pure bending zone, the emergence of flexural-shear cracks near the loading points in several beams, and the pronounced widening of central cracks immediately before collapse. Even in beams with markedly different reinforcement ratios or lower concrete strength (e.g., SM18, SM20, SM21), where crack density and damage localization vary considerably, the finite element results maintain excellent qualitative and quantitative agreement with the photographed crack maps, further confirming the robustness of the concrete damaged plasticity formulation in simulating distributed cracking and localized failure mechanisms under flexural loading.

Fig. 21

Cracks pattern comparison from SM-1 to SM-9

Fig. 22

Cracks pattern comparison from SM-10 to SM-21

5.2 Comparison of Exp vs FEM vs ANN of 1-Way HFRC Slab

Figure 23 offers a bar chart comparison of ultimate flexural loads for the complete set of 21 reinforced concrete beams (SM1 through SM21), contrasting experimental measurements (EXP, blue bars) against predictions from finite element modeling (FEA, orange bars) and artificial neural network forecasting (ANN, yellow bars). The experimental capacities fluctuate notably across the specimens, starting at roughly 90 kN for SM1, climbing to peaks near 110–115 kN around SM6 and SM11, then tapering off to lows of about 65–70 kN for the weaker configurations like SM20 and SM21, which underscores the dominant roles of reinforcement density, bar diameter, and concrete grade in governing failure loads. FEA outcomes closely track the EXP data, rarely deviating by more than 3–5 kN, and faithfully replicate trends in strength enhancement from added steel or higher compressive strength, thereby affirming the model's aptitude for simulating complex damage accumulation and bond-slip phenomena. ANN estimates, derived from a machine learning framework calibrated on partial experimental inputs, align tightly with both EXP and FEA for most beams—particularly those with standard setups (e.g., SM3-SM5)—but show minor overpredictions in heavily reinforced cases (e.g., SM12-SM14, up to 8 kN excess) and subtle underpredictions in low-capacity outliers (e.g., SM17-SM18, around 5 kN short), suggesting strong generalization yet room for improved training on diverse failure modes. Collectively, the overlapping bar heights illustrate the complementary strengths of these methods, positioning FEA as a detailed mechanistic tool and ANN as an efficient data-driven approximator for rapid parametric studies in beam design optimization.

Across the complete dataset of 21 reinforced concrete beams depicted in Fig. 23, the experimental (EXP, blue bars) ultimate loads reach their maximum at approximately 115 kN for specimen SM11, with SM6 closely behind at about 112 kN, while the minimum occurs at roughly 65 kN for both SM20 and SM21, highlighting the superior capacity of optimally reinforced high-strength configurations versus those with reduced concrete grades. For the finite element analysis (FEA, orange bars), the peak value is similarly attained by SM11 at around 114 kN, followed by SM6 at 110 kN, and the lowest capacities are again noted for SM20 and SM21 near 66–68 kN, demonstrating the model's close fidelity to physical tests across varying parameters. The artificial neural network (ANN, yellow bars) predictions exhibit their highest load at approximately 118 kN for SM11, with SM12 registering a secondary maximum of about 110 kN. In contrast, the minima dip to around 62 kN for SM21 and 64 kN for SM20, though with occasional deviations such as overestimation in SM19 (≈ 105 kN versus EXP's 98 kN) and underestimation in SM15 (≈ 70 kN versus EXP's 75 kN), underscoring ANN's overall accuracy but sensitivity to training data extremes in capturing nuanced effects of reinforcement and material variations.

Fig. 23

Exp vs FEM Ultimate Load values for all HSC

Figure 24 presents a grouped bar chart comparing the ultimate mid-span deflection at peak load for the entire series of 21 reinforced concrete beams, with experimental values (EXP, blue), finite element predictions (FEA, orange), and artificial neural network estimates (ANN, yellow). Experimental ultimate deflections vary widely from approximately 15–18 mm for the brittle low-strength specimens SM20 and SM21 to a maximum of nearly 38 mm exhibited by SM3 and SM19, reflecting the strong influence of reinforcement ratio and concrete compressive strength on post-yield ductility. The finite element results follow the experimental trend almost exactly, reproducing both the highest deflections (37–38 mm for SM3 and SM19) and the lowest values (15–17 mm for SM20–SM21) with deviations rarely exceeding 2 mm, thereby confirming the ability of the numerical model to capture the full extent of inelastic deformation and damage localization prior to failure. The ANN predictions also track the overall pattern satisfactorily, correctly identifying SM3, SM6, and SM19 among the most ductile members and SM20–SM21 as the least deformable; however, slight overpredictions are observed in moderately reinforced beams (SM12–SM14) and minor underpredictions in several high-ductility cases (SM5, SM11), indicating that, while the trained network provides rapid and reasonably accurate ductility estimates across a broad parametric space, the finite element approach remains superior for precise quantification of large-displacement response and failure deformation in reinforced concrete flexural members.

In Fig. 24, the experimental ultimate mid-span deflections (EXP, blue bars) show the maximum values for specimens SM3 and SM19, both reaching approximately 38 mm, followed closely by SM6 and SM11 at 35–36 mm; these beams benefited from balanced reinforcement ratios and higher concrete strength, promoting extensive yielding and large plastic deformation before crushing. The minimum experimental deflections are recorded for SM20 and SM21 at only 15–16 mm, and for SM18 at around 18 mm, where significantly lower concrete compressive strength led to premature compression-zone failure and brittle post-peak behavior. Finite element predictions (FEA, orange bars) reproduce these extremes with excellent precision: maximum deflections of 37–38 mm again for SM3 and SM19, and minimum values of 15–17 mm for SM20 and SM21, with differences from experiment never exceeding 1–2 mm across the entire series. The artificial neural network (ANN, yellow bars) correctly identifies SM3 and SM19 as the most ductile (predicted 36–37 mm) and SM20–SM21 as the least ductile (15–17 mm), although it slightly underestimates the peak ductility of SM6 and SM11 (by 2–4 mm) and marginally overestimates deflection in a few intermediate cases (SM12–SM14), confirming that both FEA and ANN reliably rank ductility across the 21 specimens, with FEA providing virtually identical quantitative values to the experiments while ANN offers a close but marginally less precise approximation.

Fig. 24

Exp vs FEM Ultimate deflection values for all HSC

6. CONCLUSIONS

In this study, a total of 42 reinforced concrete slabs (21 one-way ) incorporating varying proportions of steel fibers (SF) and polypropylene fibers (PF) were fabricated and tested under flexural loading. The specimens were evaluated based on their load-carrying capacity, deflection at initial and ultimate cracking, and observed failure modes. The major conclusions are as follows:

1. An increase in fiber dosage does not consistently lead to proportional gains in flexural strength. The optimum fiber content is significantly influenced by factors such as mix proportion and mixing procedure. Excessive fiber addition may result in fiber balling, a phenomenon in which fibers agglomerate, thereby reducing workability. This occurs because the concrete matrix becomes stiffer and water films on the fiber surfaces hinder their uniform dispersion. Thus, while hybrid fibers can improve mechanical properties, careful control of fiber content is essential to balance workability and structural performance.

2. The load-carrying capacity of hybrid fiber-reinforced concrete (HFRC) one-way slabs was substantially enhanced with specific SF–PF combinations. Among the tested mixes, the combination of 0.7% SF and 0.9% PF exhibited the best performance, achieving 115% of the ultimate load capacity of the control specimen (without fibers). This demonstrates that optimized fiber combinations can considerably increase the flexural resistance of one-way slabs.

3. Crack pattern comparison confirms that the numerical model correctly predicts the number, spacing, orientation, and propagation height of flexural and flexural-shear cracks for every specimen, including heavily damaged and lightly reinforced members, validating its ability to simulate distributed cracking and localized failure mechanisms.

4. Both Finite Element Analysis (FEA) and Artificial Neural Network (ANN) predictions demonstrated strong agreement with experimental results for the ultimate flexural load and mid-span deflection of 21 reinforced concrete beams. FEA demonstrated exceptional quantitative fidelity, with minimal deviation from experimental data and accurate simulation of complex mechanical behaviors such as damage accumulation and ductility.

5. While both predictive methods were reliable, they exhibited complementary characteristics. FEA proved to be a precise mechanistic tool for detailed simulation and quantification of failure modes. In contrast, ANN served as an efficient, data-driven approximator, capably generalizing trends across a broad parametric space but with slightly reduced precision at extremes, indicating its suitability for rapid design optimization studies.

Competing interests

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Data Availability

The datasets used during the current study available from the corresponding author on reasonable request

Author Contribution

Conceptualization, P.S., B.C., Q.H., G.S., P.C., C.S., A.A.; Methodology, P.S., B.C., Q.H., G.S., P.C., C.S., A.A.; Data curation, P.S., B.C., Q.H., G.S., P.C., C.S., A.A.; Writing-original draft, P.S., B.C., Q.H., G.S., P.C., C.S., A.A.; Writing-review & editing, P.S., B.C., Q.H., G.S., P.C., C.S., A.A. All authors have read and agreed to the published version of the manuscript.

Funding:

No Funding

REFERENCES

Gu, D-S., Wu, Y-F., Wu, G. & Wu, Z. Plastic hinge analysis of FRP confined circular concrete columns. Constr. Build. Mater. 27, 223–233 (2012).

Barrera, A., Bonet, J., Romero, M. L. & Miguel, P. Experimental tests of slender reinforced concrete columns under combined axial load and lateral force. Eng. Struct. 33, 3676–3689 (2011).

Bayramov, F., Taşdemir, C. & Taşdemir, M. Optimisation of steel fibre reinforced concretes by means of statistical response surface method. Cem. Concr. Compos. 26, 665–675 (2004).

Mohammadi, Y., Singh, S. P. & Kaushik, S. K. Properties of steel fibrous concrete containing mixed fibres in fresh and hardened state. Constr. Build. Mater. 22, 956–965 (2008).

Chen, B. & Liu, J. Residual strength of hybrid-fiber-reinforced high-strength concrete after exposure to high temperatures. Cem. Concr. Res. 34, 1065–1069 (2004).

Sun, W., Chen, H., Luo, X. & Qian, H. The effect of hybrid fibers and expansive agent on the shrinkage and permeability of high-performance concrete. Cem. Concr. Res. 31, 595–601 (2001).

Banthia, N. & Sappakittipakorn, M. Toughness enhancement in steel fiber reinforced concrete through fiber hybridization. Cem. Concr. Res. 37, 1366–1372 (2007).

Atiş, C. D. & Karahan, O. Properties of steel fiber reinforced fly ash concrete. Constr. Build. Mater. 23, 392–399 (2009).

Fu, C-Q., Ma, Q-Y., Jin, X., Shah, A. & Tian, Y. Fracture property of steel fiber reinforced concrete at early age. Computers and Concrete. Int. J. 13, 31–47 (2014).

10.

Yazıcı, Ş., İnan, G. & Tabak, V. Effect of aspect ratio and volume fraction of steel fiber on the mechanical properties of SFRC. Constr. Build. Mater. 21, 1250–1253 (2007).

11.

Sivakumar, A. & Santhanam, M. Mechanical properties of high strength concrete reinforced with metallic and non-metallic fibres. Cem. Concr. Compos. 29, 603–608 (2007).

12.

Cagatay, I. H. & Dincer, R. Modeling of concrete containing steel fibers: Toughness and mechanical properties. Computers Concrete. 8, 357–369 (2011).

13.

Thomas, J. & Ramaswamy, A. Mechanical properties of steel fiber-reinforced concrete. J. Mater. Civ. Eng. 19, 385–392 (2007).

14.

Ahmad, A., Tahir, F., Mehboob, S. & Raza, A. Proposed equation of elastic modulus of hybrid fibers reinforced concrete cylinders. Tech. J. 24, 9–20 (2019).

15.

Ali, B. et al. Influence of glass fibers on mechanical properties of concrete with recycled coarse aggregates. Civ. Eng. J. 5, 1007–1019 (2019).

16.

Banthia, N. & Gupta, R. Influence of polypropylene fiber geometry on plastic shrinkage cracking in concrete. Cem. Concr. Res. 36, 1263–1267 (2006).

17.

Afroughsabet, V. et al. The influence of expansive cement on the mechanical, physical, and microstructural properties of hybrid-fiber-reinforced concrete. Cem. Concr. Compos. 96, 21–32 (2019).

18.

Pourfalah, S. Behaviour of engineered cementitious composites and hybrid engineered cementitious composites at high temperatures. Constr. Build. Mater. 158, 921–937 (2018).

19.

Li, Y., Tan, K. H. & Yang, E-H. Synergistic effects of hybrid polypropylene and steel fibers on explosive spalling prevention of ultra-high performance concrete at elevated temperature. Cem. Concr. Compos. 96, 174–181 (2019).

20.

Pourfalah, S., Suryanto, B. & Cotsovos, D. M. Enhancing the out-of-plane performance of masonry walls using engineered cementitious composite. Compos. Part. B: Eng. 140, 108–122 (2018).

21.

Pourfalah, S., Cotsovos, D. M. & Suryanto, B. Modelling the out-of-plane behaviour of masonry walls retrofitted with engineered cementitious composites. Comput. Struct. 201, 58–79 (2018).

22.

Padanattil, A., Karingamanna, J. & Mini, K. Novel hybrid composites based on glass and sisal fiber for retrofitting of reinforced concrete structures. Constr. Build. Mater. 133, 146–153 (2017).

23.

Barluenga, G. & Hernández-Olivares, F. Cracking control of concretes modified with short AR-glass fibers at early age. Experimental results on standard concrete and SCC. Cem. Concr. Res. 37, 1624–1638 (2007).

24.

Denneman, E., Kearsley, E. P. & Visser, A. T. Splitting tensile test for fibre reinforced concrete. Mater. Struct. 44, 1441–1449 (2011).

25.

Kayali, O., Haque, M. N. & Zhu, B. Some characteristics of high strength fiber reinforced lightweight aggregate concrete. Cem. Concr. Compos. 25, 207–213 (2003).

26.

ZHANG, P. & LI, Q. Experiment and study on tensile strength of polypropylene fiber reinforced cement stabilized macadam. Highway 4, 175–179 (2008).

27.

Kakooei, S., Akil, H. M., Jamshidi, M. & Rouhi, J. The effects of polypropylene fibers on the properties of reinforced concrete structures. Constr. Build. Mater. 27, 73–77 (2012).

28.

Naaman, A. E., Wongtanakitcharoen, T. & Hauser, G. Influence of different fibers on plastic shrinkage cracking of concrete. ACI Mater. J. 102, 49 (2005).

29.

Song, P. S., Hwang, S. & Sheu, B. C. Strength properties of nylon-and polypropylene-fiber-reinforced concretes. Cem. Concr. Res. 35, 1546–1550 (2005).

30.

Han, C-G., Hwang, Y-S., Yang, S-H. & Gowripalan, N. Performance of spalling resistance of high performance concrete with polypropylene fiber contents and lateral confinement. Cem. Concr. Res. 35, 1747–1753 (2005).

31.

Pelisser, F., Neto, A. B., da SS, H. L. & de Andrade Pinto, R. C. Effect of the addition of synthetic fibers to concrete thin slabs on plastic shrinkage cracking. Constr. Build. Mater. 24, 2171–2176 (2010).

32.

Hsie, M., Tu, C. & Song, P. Mechanical properties of polypropylene hybrid fiber-reinforced concrete. Mater. Sci. Engineering: A. 494, 153–157 (2008).

33.

Sun, Z. & Xu, Q. Microscopic, physical and mechanical analysis of polypropylene fiber reinforced concrete. Mater. Sci. Engineering: A. 527, 198–204 (2009).

34.

Cui, K. et al. Mechanical behavior of multiscale hybrid fiber reinforced recycled aggregate concrete subject to uniaxial compression. J. Building Eng. 71, 106504 (2023).

35.

Qian, C. X. & Stroeven, P. Development of hybrid polypropylene-steel fibre-reinforced concrete. Cem. Concr. Res. 30, 63–69 (2000).

36.

Selina Ruby, G., Geethanjali, C., Varghese, J. & Muthu Priya, P. Influence of Hybrid Fiber on Reinforced Concrete. Int. J. Adv. Struct. Geotech. Eng. 3, 40–43 (2014).

37.

Manolis, G. D., Gareis, P. J., Tsonos, A. D. & Neal, J. A. Dynamic properties of polypropylene fiber-reinforced concrete slabs. Cem. Concr. Compos. 19, 341–349 (1997).

38.

Mashayekhi, A., Hassanli, R., Zhuge, Y., Ma, X. & Chow, C. W. Synergistic effects of fiber hybridization on the mechanical performance of seawater sea-sand concrete. Constr. Build. Mater. 416, 135087 (2024).

39.

Aydin, A. C. Self compactability of high volume hybrid fiber reinforced concrete. Constr. Build. Mater. 21, 1149–1154 (2007).

40.

Guo, H., Wang, H., Li, H., Wei, L. & Li, Y. Effect of whisker toughening on the dynamic properties of hybrid fiber concrete. Case Stud. Constr. Mater. 19, e02517 (2023).

41.

He, F., Biolzi, L. & Carvelli, V. Effects of elevated temperature and water re-curing on the compression behavior of hybrid fiber reinforced concrete. J. Building Eng. 67, 106034 (2023).

42.

Afshar, A. et al. Corrosion resistance evaluation of rebars with various primers and coatings in concrete modified with different additives. Constr. Building Mater. 262, 120034 (2020).

43.

Leblouba, M., Barakat, S., Altoubat, S., Maalej, M. & Awad, R. Resistance factors for reliability based-design of fiber reinforced concrete suspended slabs in flexure. J. Building Eng. 57, 104911 (2022).

44.

Soufeiani, L. et al. Influences of the volume fraction and shape of steel fibers on fiber-reinforced concrete subjected to dynamic loading–A review. Eng. Struct. 124, 405–417 (2016).

45.

Lee, D. H., Park, J., Lee, K. & Kim, B. H. Nonlinear seismic assessment for the post-repair response of RC bridge piers. Compos. Part. B: Eng. 42, 1318–1329. https://doi.org/10.1016/j.compositesb.2010.12.023 (2011).

46.

Zhang, J. & Foschi, R. O. Performance-Based Design And Seismic Reliability Analysis Using Designed Experiments And Neural Networks. Probab. Eng. Mech. ;19:259–267. https://doi.org/10.1016/j.probengmech.2004.02.009. (2004).

47.

Ali, A., Abbas, S. M. S. M. & Statically-Indeterminate, S. F. R. C. Columns under Cyclic Loads. Adv. Struct. Eng. 17, 1403–1417 (2014).

48.

Balouch, D. S. U. SFRC Modelling and Non-Linear Analysis of Beam- Column Joint Under Cyclic Loading. CTCSE 2021;7. https://doi.org/10.33552/CTCSE.2021.07.000671

49.

Elshamandy, M. G., Farghaly, A. S. & Benmokrane, B. Experimental behavior of glass fiber-reinforced polymer-reinforced concrete columns under lateral cyclic load. ACI Struct. J. 115, 337–349 (2018).

50.

Greifenhagen, C. & Lestuzzi, P. Static cyclic tests on lightly reinforced concrete shear walls. Eng. Struct. 27, 1703–1712 (2005).

51.

Hadad, H. S., Metwally, I. M. & El-Betar, S. Cyclic Behavior Of Braced Concrete Frames: Experimental Investigation And Numerical Simulation. HBRC J. (2015).

52.

Abaqus Abaqus 6.12 documentation. Simulia (Dassault Systemes, 2012).

53.

ADINA System 9. 2 Documentation. vol. 9.2. R&D, Inc. 71 Elton Avenue Watertown (MA 02472 USA, 2015).

54.

SAP C. Computers and Structures Inc. (2013).

55.

Tim Stratford and Chris Burgoyne. Shear Analysis of Concrete with Brittle Reinforcement. J. Compos. Constr. 7, 323–330. https://doi.org/10.1061//ASCE/1090-0268/2003/7:4/323 (2003).

56.

Cotsovos, D. M. Cracking of RC beam/column joints: Implications for the analysis of frame-type structures. Eng. Struct. 52, 131–139. https://doi.org/10.1016/j.engstruct.2013.02.018 (2013).

57.

Guner, S. & Vecchio, F. J. Pushover Analysis of Shear-Critical Frames: Verification and Application. ACI Struct. J. 107, 72–81 (2010).

58.

Sharma, A., Reddy, G. R., Eligehausen, R. & Vaze, K. K. Experimental And Analytical Investigation On Seismic Behavior Of Rc Framed Structure By Pushover Method. Struct. Eng. Mech. 39, 125–145 (2011).

59.

Vecchio, F. J. & Emara, M. B. Shear Deformations In Reinforced Concrete Frames. ACI Struct. J. 89, 46–56 (1992).

60.

Lai, B-L., Tan, W-K., Feng, Q-T. & Venkateshwaran, A. Numerical parametric study on the uniaxial and biaxial compressive behavior of H-shaped steel reinforced concrete composite beam-columns. Adv. Struct. Eng. 25, 2641–2661 (2022).

61.

Zhou, Z., Qian, J. & Huang, W. Shear strength of steel plate reinforced concrete shear wall. Adv. Struct. Eng. 23, 1629–1643 (2020).

62.

Ali Al-Tameemi, S. K. et al. Simulation and design model for reinforced concrete slabs with lacing systems. Adv. Struct. Eng. 27, 871–892 (2024).

63.

Abbas, A. A., Mohsin, S. M. S. & Cotsovos, D. M. A simplified finite element model for assessing steel fibre reinforced concrete structural performance. Comput. Struct. 173, 31–49 (2016).

64.

Abbas, A. A., Syed Mohsin, S. M. & Cotsovos, D. M. Numerical modelling of fibre-reinforced concrete, p. 473. (2010).

65.

Afifi, M. Z., Mohamed, H. M., Chaallal, O. & Benmokrane, B. Confinement model for concrete columns internally confined with carbon FRP spirals and hoops. J. Struct. Eng. 141, 04014219 (2014).

66.

Ahmad, S. & Shah, A. Evaluation of shear strength of high strength concrete corbels using strut and tie model (STM). Arab. J. Sci. Eng. 34, 27–35 (2009).

67.

Chaallal, O., Shahawy, M. & Hassan, M. Performance of axially loaded short rectangular columns strengthened with carbon fiber-reinforced polymer wrapping. J. Compos. Constr. 7, 200–208 (2003).

68.

Foster, S. J., Powell, R. E. & Selim, H. S. Performance of high-strength concrete corbels. Struct. J. 93, 555–563 (1996).

69.

Krawinkler, H. & Seneviratna, G. D. P. K. Pros And Cons Of A Pushover Analysis Of Seismic Performance Evaluation. Engineering Structures. ;20:452–64. https://doi.org/Doi%252010.1016/S0141-0296(97)00092-8. (1998).

70.

Sipos, T. K. & Earthquake Performance Of Infilled Frames Using Neural Networks And Experimental Database. Eng. Struct. ;51:113–127. https://doi.org/10.1016/j.engstruct.2012.12.038. (2013).

71.

ASTM A. C150/C150M-17, standard specification for Portland cement (Am Soc Test Mater West Conshohocken, 2017).

72.

Standard, A. ASTM C33/C33M–18 Standard Specification for Concrete Aggregates. West Conshohocken, PA. (2018).

73.

ASTM International. ASTM A820/A820M-16, Standard Specification for Steel Fibers for Fiber-Reinforced Concrete. West Conshohocken (2016).

74.

Söylev, T. & Özturan, T. Durability, physical and mechanical properties of fiber-reinforced concretes at low-volume fraction. Constr. Build. Mater. 73, 67–75 (2014).

75.

Standard, A. C494/C494M-17 Standard specification for chemical admixtures for concrete (ASTM International, 2017).

76.

Astm, C. others. Standard practice for making and curing concrete test specimens in the field. C31/C31M-12 2012.

77.

EC2. Eurocode 2: Design Of Concrete Structures - Part 1–1: General Rules And Rules For Buildings. Management Centre: Avenue Marnix 17, B-1000 Brussels: (2004).

78.

Raza, A., Khan, Q. U. Z. & Ahmad, A. Prediction of Axial Compressive Strength for FRP-Confined Concrete Compression Members. KSCE J. Civ. Eng. 24, 2099–2109. https://doi.org/10.1007/s12205-020-1682-x (2020).

79.

Ahmad, A., Plevris, V. & Khan, Q-Z. Prediction of Properties of FRP-Confined Concrete Cylinders Based on Artificial Neural Networks. Crystals 10, 811 (2020).

80.

Ahmad, A. & Cotsovos, D. M. Reliability analysis of models for predicting T-beam response at ultimate limit response. Proceedings of the Institution of Civil Engineers - Structures and Buildings. ;176:28–50. (2023). https://doi.org/10.1680/jstbu.20.00129

81.

Anderson, D. McNeill. G. Artificial Neural Networks Technology. Kaman Sciences Corporation 258 Genesse Street Utica, New York 13502 – 4627: (1992).

82.

LeCun, Y., Bottou, I., Orr, G. B. & Muller, K. R. Efficient Backprop (Red Bank, NJ 07701 – 703, 1998).

83.

Jong, K. D. & Fogel, D. B. Schwefel. H. P. Handbook of Evolutionary Computation (IOP Publishing Ltd and Oxford University: IOP;, 1997).

84.

Adeli, H. Neural Networks In Civil Engineering: 1989–2000. Computer-Aided Civil and Infrastructure Engineering. ;16:126–42. https://doi.org/Doi%252010.1111/0885-9507.00219. (2001).

85.

Rojas, R. The Backpropagation Algorithm. Neural Networks, Verlag, Berlin, : Springer; 1996, pp. 151–84. (1996).

86.

MathWorks., M. A. T. L. A. B. MathWorks; (2022).

Yes