AI-driven sustainable strength prediction and experimental evaluation of high-performance fiber-reinforced concrete incorporating metakaolin

Abstract

This work developed an enhanced model to examine the High-Strength Fiber-Reinforced Concrete (HSFRC) that is replaced with 10% metakaolin as a sustainable cement replacement and four types of fibers at different dosages. Here, four types of fibers, Steel Fiber (SF), Glass Fiber (GF), Nylon Fiber (NF), and Polypropylene Fiber (PPF) wereincorporated, and concrete mixtures were designed with varying proportions of these Fibers. A 10%replacement of cement with Metakaolin was used as a Supplementary Cementitious Material (SCM). An M60 grade mix was selected, and the water-cement ratio (W/C) was maintained at 0.32.The most effective mix configuration was identified as High StrengthConcrete (HSC) (Concretewith 10% Metakaolin) combined with 1% steel fiber by cement weight.Then, the deep learning framework named Adaptive Pyramid Dilated Dense Long Short-Term Memorywith Sparse Attention (A-PDDLSTM-SA) is developed for predicting the compressive strength, split tensile strength, and flexural strength of concrete. To further optimize its performance, the model’s parameters are fine-tuned using the Updated Random Number-based Hiking Optimization Algorithm (URN-HOA). The manually collected experimental data is used for both training and evaluation of the predictive model, ensuring high reliability and generalizability across various mix compositions.The Mean Error Percentage (MEP) of the proposed model is 25.747 and the accuracy is 96.13%. Thus, it shows that the developed model proved notable improvement over other existing approaches in enhancing the accuracy and reducing the reliance on the wide-ranging destructive testing, providing a consistent supporting tool to develop enhanced and sustainable concrete mixes.

Introduction

Plain Cement Concrete is widely used in construction practices across the world. It is appreciated for its considerable properties, such as high compressive strength, adequate workability, and long-term durability. However, PCC is weaker in tension and very brittle¹. In recent developments, substantial structural flaws in concrete have been attributed to the propagation of cracks. These cracks expose the steel reinforcement within the concrete, leading to gradual corrosion. As the cracks progress over time, they compromise the stiffness and load-carrying capacity of the structure, ultimately impacting its structural safety, service life, and aesthetic quality. This deterioration is especially prominent in large infrastructures like bridges, where HSC presents a promising alternative. Achieving high strength in concrete involves reducing the porosity, inhomogeneity, and micro-cracks within the Hydrated Cement Paste (HCP) and the interfacial transition zone (ITZ). High Strength Concrete is defined as concrete in which the compressive strength lies between 60 and 150 MPa². Typically, HSC requires around 450 kg/m³ of cement, in contrast to conventional concrete, which uses between 280–360 kg/m³.To address these performance issues, the use of SCMs has been recommended to improve compressive strength without excessively increasing cement content³

SCMs such as Metakaolin, Silica Fume, Fly Ash, and Ground Granulated Blast Furnace Slag (GGBS) can enhance the strength properties of concrete. Among these, Metakaolin is selected in this study for its high pozzolanic activity, widespread availability, and better cost-efficiency compared to Silica Fume. By partially substituting cement with these SCMs, the density and weight-to-strength ratio of the concretematrix can be optimized. However, when comparing these SCMs, Silica Fume is often more beneficial for boosting concrete strength⁴. Generally, concrete that satisfies key performance criteria in terms of durability, impermeability, and mechanical strength is termed High-Strength Concrete^5,6.Because of its enhanced strength profile, HSC is extensively used in high-demand structures such as nuclear reactors, long-span bridges, and skyscrapers⁷. One viable alternative to Silica Fume in such high-performance mixes is Metakaolin⁸. Metakaolin is a white pozzolanic material produced by the calcination of kaolin at about 600°C–800°C⁹. Although Metakaolin can cost 3 to 4 times more than traditional cement in the national market, its economic feasibility remains favourable due to its overall impact on concrete performance.

Replacing Silica Fume with Metakaolin has proven to be a more adaptable and cost-effective option in the production of high-strength concrete. Although HSC provides excellent compressive strength, it is typically brittle, making it more prone to cracking¹⁰. Thus, improving the toughness, ductility, and crack resistance of HSC is a critical area of study to ensure sustained structural integrity and durability. Moreover, the recent research has spotted the resilience of improved cementitious composites within the extreme contexts, thus increasing the tensile strength of Strain-Hardening Ultra-High-Performance Concrete¹¹. The incorporation of fiber reinforcement in concrete is less noticeable. However, the integration of fibers significantly enhances post-peak behaviour during flexural testing¹². FRC has better performance than conventional concrete. Fibers help mitigate crack development and reduce crack widths, thereby improving overall durability. Many studies also highlight the impact of incorporating fiber in concrete. Fibers influence the residual strength of concrete after cracking and delay failure¹³. reported that fibers find major application in tunnelling segments, which can entirely substitute conventional concrete reinforcement. Hence, FRC finds its major application in pavements and tunnel segments¹⁴. Integrating fibers into HSC is a forward-looking strategy to improve both mechanical strength and service life.

Fibers actively suppress crack propagation, increase tensile capacity, and reduce the brittleness commonly associated with HSC. Initially, only steel and glass fibers were utilized. Over time, as the importance of fibers in concrete became evident, numerous companies began manufacturing them¹⁵. The primary mechanism by which fibers function is through uniform dispersion within the cement matrix, creating a reinforcing network that resists crack widening through mechanical interlocking or gripping action¹⁶. Concrete typically incorporates both synthetic and natural fibers. Natural fibers encompass materials such as jute, coir, ramie, sisal, hemp, and bamboo. On the other hand, syntheticfibers include options like glass, steel, polypropylene, nylon, aramid, and carbon fibers¹⁷. The performance of fiber-reinforced concrete is significantly influenced by fiber type, fibercontent, aspect ratio, and orientation¹⁸. Both synthetic and natural fibers offer advantages in terms of energy savings, cost-effectiveness, and environmental sustainability compared to traditional reinforcement methods.

Steel fibers boost the shearing capacity of reinforced concrete beams. The incorporation of fiber in the concrete mix began about 100 years ago¹⁹. Steel fibers help control diagonal cracking and enhance aggregate interlock, thus improving toughness. Recycled steel fibers are also used in concrete, often obtained from used tyres. Research on Carbon Fiber Reinforced Concrete (CFRC) is still limited. CFRC has good tensile and flexural properties and is commonly used in building special structures such as panels, curtain walls, roofing, etc²⁰. Glass Fiber Reinforced Concrete (GFRC) demonstrates improved impact resistance and energy absorption characteristics. The use of industrial glass waste increases the tensile as well as flexural strength and mitigates the environmental impact of glass disposal.Polypropylenefiber, derived from polymerized propylene, is widely used to reduce plastic shrinkage, control cracking, and improve impact resistance in concrete. It is a popular and reasonably priced building material that increases durability and offers builders a flexible, cost-effective option. Polypropylene fiber-reinforced concrete holds promising applications in public infrastructure projects. These areas often face challenges such as harsh environmental conditions, impact damage, surface wear, and vandalism, making the application of concrete with improved properties highly advantageous²¹. Nylonfiber (NF), when used in construction, improves crack control and accelerates construction timelines by eliminating the need for traditional reinforcement methods. This technique is particularly well-suited for applications in pavements, overlays, and precast elements. NF improves the tensile strength of concrete through bridging mechanisms but reduces the material’s flow characteristics²². Overall, the extensive literature survey affirms that incorporating various types of fibers into concrete matrices results in improved structural behavior, cost efficiency, and environmental performance²³. To further advance the sustainability goals, recent models applied the recycled fine aggregates, thus aiding in producing the strain-hardening by observing the enhanced ability of tensile strain²⁴.

Nowadays, the use of machine learning algorithms has revolutionized the prediction and simulation of concrete behavior, marking a paradigm shift in civil engineering practice²⁵. Over the past decade, machine learning algorithms, especially neural networks, have gained significant attention in civil engineering applications²⁶. Neural networks function as supervised learning algorithms, consisting of interconnected nodes (neurons), each capable of performing basic mathematical operations. These networks are structured into three main components: input layers, hidden layers, and output layers, and are trained to identify the relationship between inputs and desired outputs. This data-driven computational model often surpasses conventional regression-based techniques in capturing complex input–output dynamics.Although more models have been developed for the prediction of RDC, some challenges are present in the traditional approaches. Most of the models are developed by leveraging laboratory experimental evaluation. Though it is effective and optimal, the time requirement is more and sometimes, restricted to the limited terms of mix composition, thus making the model more challenging to widely analyze the kinds of fibres, supplementary materials and the curing ages. Similarly, the widely adopted regression and statistical-oriented models are not effective in capturing the interdependent patterns and the highly non-linear relationships that are present between the mathematical performance and the main constituents. These models basically consider the simplified linear patterns and have complexity when providing enhanced generalization to the new and unseen combination of the materials. Moreover, the traditional models that leverage machine learning mainly concentrates towards the single-strength characteristics thus minimize the practical application. Thus, all these significant issues highlight the requirement of enhanced data-based models, which can provide improved performance by learning the complicated and multivariate interactions from even a restricted numbers of databases. To address the challenge²⁷, employed hybrid frameworks integrating machine learning and multi-objective optimization to balance compressive strength, carbon emissions, and material costs. These models can extract non-obvious insights, revealing patterns that challenge traditional assumptions in material science.Deep learning frameworks, which use multi-layered architectures and automatic feature extraction, outperform shallow models in accuracy, adaptability, and generalization capabilities²⁸. Thus, this work developed effective models for the prediction of the FRC to provide a robust and scalable alternative.

Research objectives and contribution

Although more researchers have analyzed the mechanical strength of FRC and its corresponding use in cementitious materials, they have solely explored all these features, either through experimental testing or prediction models. Previous models have evaluated the impact on each type of fibres more extensively in terms of strength improvement and durability, while some others have concentrated on partially replacing metakaolin, thus enhancing the sustainability of the work. Only a few studies have used the combination of different fiber types with metakaolin in a unified experimental framework. Moreover, the existing literature proves the lack of combined systems by connecting the advanced prediction models with the experimental features. The combinedmodels make the prediction taskmore effective, leas to capture age-dependent strength development in high-performance in FRC. Since the traditional systems are based on a limited number of neural networks and linear statistical approaches, they are not effective in learning complicated patterns and providing reliable results in practical field decision-making. To address these gaps, the present study develops a sustainability-based and experimentally validated framework for high-strength FRC incorporating metakaolin and multiple fiber types. The primary objectives of this research are:

• Todevelop FRC by adding cement + metakaolin(10%), fine aggregate, coarse aggregate, superplasticizer, water, and fiberfor improving durability and strength. To enhance performance, four different fiber types, such as SF, GF, NF, and PPFare incorporated into the concrete matrix at varying dosages. Each fiber type contributes uniquely: steel fibers improve compressive and flexural strength, glass fibers aid in impact resistance, nylon fibers enhance tensile strength, and polypropylene fibers control shrinkage cracking. The experimental validation through standard tests (compressive, split tensile and flexural strength) confirms the mechanical superiority of the developed model over conventional approaches.

• To design and implement a hybrid deep learning framework called APDD-LSTM-SA, developed specifically for the strength prediction of FRC. This architecture effectively captures the complex nonlinear relationships between concrete mix parameters and their resulting mechanical strengths. It integrates Pyramid Dilated Convolutions to extract multiscale contextual features. Sparse Attention mechanism selectively emphasize influential input features such as fiber type, dosage, and curing age, making it a reliable tool for early assessment and optimization of FRC strength properties.

• To ensure maximum predictive performance, the APDD-LSTM-SA model is further optimized using the URN-HOA. This metaheuristic algorithm fine-tunes critical hyperparameters, including hidden neuron count, number of epochs, and learning rate. Minimizing prediction error and reducing model complexity enables the generation of reliable strength estimates from minimal data. This not only lowers the cost and time associated with physical testing but also supports sustainable construction practices by reducing material waste and promoting smart mix design strategies. The research framework thus bridges the gap between physical experimentation and AI-driven automation in modern civil engineering.

Literature survey

Recent studies highlight the growing integration of sustainable materials and artificial intelligence in concrete research. To forecast the effectiveness of the recycled powder, the machine learning²⁹ model can be used. It offers optimal results by carrying out the life cycle assessment. Some models evaluate the sustainability of the concrete through the incorporation of rubber waste fibres, along with the recycled aggregates, by concentrating on the strength characteristics of the concrete³⁰. The review conducted by³¹ summarizes the significance of using different waste materials to enhance the sustainable and mechanical features. Moreover, the machine learning models have also been used in the field of structural design³² to forecast the concrete’s flexural strength. Then, AI-based constitutive modeling³³ has been designed, which aids in simulating the axial load reflective behaviour of the made columns. AI has been widely used for prediction tasks to model the sustainable concrete strength properties³⁴. Finally, cycle assessment approaches³⁵ have been employed. This model evaluates the impacts on human health and the environmental impacts when recycling concrete materials. Together, these works highlight the use of AI techniques, aligning well with the direction of the present study.

Recently, in the AI sector, the machine learning models have provided growth towards concrete strength prediction. Some of the models based on machine learning are Random Forest (RF), Gradient Boosting Machines (GBM), Extreme Gradient Boosting (XGBoost), LightGBM, and CatBoost. Moreover, some researchers used Bayesian-NSGA-II³⁶, Back Propagation Neural Network (BPNN) with Extreme Gradient Boosting (XGB)³⁷, XGBoost-Bayesian Optimization (BO)³⁸ and Markov Chain Monte Carlo (MCMC) with Bayesian Model³⁹. These are intelligent in providing strong performance and are effective in reducing overfitting issues. To evaluate the tensile strength, durability, elastic modulus, high-performance, and sustainable mixes of the concrete and the compressive strength, these models can be successfully used. Some research works have unified the machine learning models with the optimization technique and the feature selection mechanism, thus enhancing the model’s stability while reducing the errors when doing prediction. Then, the hybridized models, which combine optimization mechanism and different algorithms, have recently gained significant attention, thus helping to enhance the generalization even performs using with heterogeneous and limited experimental datasets. Current developments also emphasize the need for explainable machine learning models, where the feature importance evaluation aids in identifying the most essential and effective mixing patterns affecting the durability and strength of the concrete.

Recent progress in machine learning has greatly improved the precision of predicting the mechanical properties of FRC. Kashyap et al.,2024⁴⁰ evaluated both supervised and unsupervised methods, including Support Vector Machine (SVM), Artificial Neural Network (ANN), M5 Prime (M5P), and Random Forest (RF), for coconut FRC, determining that SVM was most effective for compressive strength, while RF excelled in predicting tensile and flexural strength. Few studies concentrated on forecasting the early-age compressive strength of ultra-high-performance FRC using models like SVR, RF, Gaussian Process Regression (GPR), and ANN, with SVR and GPR showing the best results (R² > 0.90)⁴¹. Symbolic regression and hybrid ANN methods highlight the crucial factors such as superplasticizer dosage, cement content, and curing time through SHapley Additive exPlanations (SHAP) analysis^42,43. These models not only provided high accuracy but also offered interpretable insights to support sustainable and optimized mix designs.

Kazemi et al.,2025⁴⁴ and Rahane et al.,2025⁴⁵ examined how different AI models can be adapted to simulate the nonlinear behavior of FRC, emphasizing the importance of preprocessing and feature engineering. Certain practical applications by integrating predictive accuracy with explainable AI tools like SHAP and Graphical User Interface (GUI)basedLocal Interpretable Model-agnostic Explanations(LIME), for on-site implementation, were illustrated by^46[,47. Ensemble techniques such as Gradient Boosted Decision Trees (GBDT), Extreme Gradient Boosting (XGBoost), and Light Gradient Boosting Machine (LightXGBM)⁴⁸ consistently surpassed traditional models, particularly with large datasets, underscoring the impact of fiber on tensile strength and cement on compressive strength. Additionally, deep learning models like Recurrent Neural Network (RNN)⁴⁹, Gated Recurrent Unit(GRU)⁵⁰, SVM⁵¹, and LSTM (Chenet al.,2022) have demonstrated significant potential in modeling the complex behavior of FRC due to their strong generalization capabilities and proficiency in managing time-dependent and high-dimensional data.

The strength of concrete is often estimated through linear or non-linear regression techniques⁵².Most conventional models struggle to represent nonlinear relationships between mix design parameters and resulting strength properties due to their limited memory, overfitting tendencies, and inability to focus on dominant features. In response to these limitations, AI models have come into the actions. The rationale for employing Artificial Intelligence (AI) in concrete strength prediction is well-supported by previous studies and arises from the limitations of traditional methods. The traditional regression and empirical systems are not effective in capturing the non-linear and complicated patterns that are present between the different mixing variables and the resulting strength properties owing to the limited dataset and the complexity of the model. However, the AI models, including the Artificial Neural Networks (ANNs), Support Vector Machines (SVMs), and deep learning frameworks, can learn the data effectively even with the presence of limited numbers. This can also handle the complicated feature interaction and provides high generalization towardsvarying fiber dosages and types, resulting in enhanced accuracy. The main intention of these models is to tackle the existing limitation by offering a more scalable and robust system, which can minimize the extensive time required for testing.

Moreover, the recent developments in deep learning models have created robust architectures, like Transformers⁵³ and Generative Adversarial Networks (GANs)⁵⁴, helping to model the complicated engineering actions. For the purpose of sequence modelling, transformer-based models have been developed. These models⁵⁵ have proved enhanced ability and performance to capture the spatial patterns and the long-term relationships that are present in the structural responsive data. The attention mechanism used within the transformer helps to provide selective concentration towards the essential features, thus helping to enhance the accuracy of the prediction even with highly non-linear systems. On the other hand, the models rely on the GAN as an intelligent tool to learn the high-dimensional data and create the real stress and strain distribution. Since the GAN can enhance the performance by augmenting thedatabases and improving the robustness of the model, the approaches centred on GAN are useful even with a limited number of experimental data. Therefore, the present study explores an alternative deep learning strategy for concrete mix data prediction.

Based on these advancements, a hybrid architecture calledAPDD-LSTM-SA is developed in this work. Compared to existing methods, the APDD-LSTM-SA model proposed in the present study, optimized using the URN-HOA algorithm, addresses several identified limitations. It leverages deep temporal feature learning and hierarchical dilation with attention mechanisms to enhance prediction accuracy, particularly in cases of limited and heterogeneous data. This positions the proposed model not only as a novel AI-based prediction tool but also as a scalable solution adaptable to broader FRC applications in civil infrastructure. Table 1 offers the key findings and the research gaps of the existing models.

Table 1.

Key findings and the research gaps of the existing models.

Study/model	Material/focus	Key findings	Research gap
40	SVM, ANN, M5P, RF	• Using SVM aids in enhancing the compressive strength, while the RF is effective in providing optimal tensile/flexural strength prediction in coconut FRC	• The performance is limited only to particular types of fibres • The generalization ability of this model is low
41	SVR, RF, GPR, ANN	• To precisely predict the compressive strength in its early stage, SVR and GPR can be used. It attains R2 > 0.90	• It has limited coverage of multi-fiber and high-strength FRC
42[,43	Symbolic regression, hybrid ANN	• It is effective in easily identifying the key parameters, like time taken for curing, superplasticizer dosage and the cement content	• It has only a limited field-scale application
44[,44	Various AI models	• It simulated nonlinear FRC behaviour and emphasized preprocessing and feature engineering	• It necessitates optimization mechanism and a hybrid multi-scale prediction model
46[,47	GUI + LIME	• It is practically available for on-site predictive AI implementation	• It is not effective and applicable for real-world adoption
48	GBDT, XGBoost, LightXGBM	• This ensemble approachoutscoredthe conventional traditional models • The use of fibers in this model greatly influencedthe tensile strength, while the cement influenced compressive strength	• It only has limited integration to the hybridized multi-fiber high-strength FRC
49	RNN	• It is effective in modelling even the complex FRC behaviour	• It has the necessity to use a multi-scale and sparse attention mechanism
50	GRU	• It aids in capturing the time-dependent behaviour	• It is not suitable to focus only on the relevant mix design due to the elimination of attention mechanisms
51	SVM	• Handles high-dimensional FRC data	• It has limited interpretability and multi-variable interaction
Chen et al., 2022	LSTM	• This model is effective for FRC mechanical property prediction	• It has the necessity to use the multi-scale feature learning as well as the attention mechanisms
Proposed APDD-LSTM-SA	Hybrid deep learning	• It always captures hierarchical material patterns • It adapts sparse attention for fiber influence, which is optimized via URN-HOA	• Novel solution bridging experimental and AI-based FRC prediction

Materials and testing methodology

Materials

The materials utilized in the study include cement, coarse aggregate, fine aggregate, water, superplasticizer, metakaolin, and fibers.

Cement and superplasticizer

For the study, OPC (Ordinary Portland Cement) of 53 grade, manufactured by UltraTech Cement Ltd., was used.A chemical admixture, Conplast WL Xtra, was incorporated at a dosage of 2.74%, functioning as a superplasticizer. This admixture was procured from ChettinadHardwares, Chennai.The physical properties of the OPC 53 grade cement were determined to be as follows: a bulk density of 1400 kg/m³, a specific gravity of 315, a Blaine fineness of 365 m²/Kg, a loss on ignition of 0.8% and a colour of grey. The chemical composition by percentage was determined to be 20% Silicon Dioxide (SiO2), 60% Calcium Oxide (CaO), 5% Aluminium Oxide (Al2O3), 3% Ferric Oxide (Fe2O3), 4% Magnesium Oxide (MgO), 2% Sulfur trioxide (SO3), and 0.5% Insoluble Residue (p. 7).

Coarse and fine aggregate

Both fine and coarse aggregates were sourced from CMR Materials,Chennai. Fine Aggregate consists of Manufactured Sand (M-Sand), which passes through a 4.75 mm IS sieve and is retained on the 150-micron sieve, ensuring suitability for construction-grade concrete. To maintain a balanced and uniform aggregate distribution, the coarse aggregate blend comprises 60% of 20 mm size and 40% of 10 mm size particles⁵⁶. Figure 1 depicts the particle size gradation curve for the combined aggregates, confirming compliance with standard grading requirements. The physical and mechanical properties of the fine and coarse aggregates used in the mix are presented here.The physical properties of the fine and coarse aggregates are different by varying types, with fine aggregate exhibiting a fineness modulus of 3.2 and a specific gravity of 2.69. Coarse aggregates had fineness moduli in the range of 3.05 to 3.08 and specific gravities between 2.55 and 2.69 (p. 8). Other properties like water absorption (0.9–12.5%), saturated density (1.3–2.8 Mg/m³), dry density (1.38–2.69 Mg/m³), shape index (11–31%), impact value (11–16%), and flakiness index (21–35%) were also recorded across the different aggregate sizes (p. 8).

Fig. 1.

Gradation of aggregates.

Metakaolin

To enhance the strength of concrete, Metakaolin is employed as an SCM.Metakaolin is a highly reactive, white, clay-based mineral derived from the thermal treatment of kaolin clay [78]. It is obtained by the calcination of kaolin at about 600–800 °C under controlled conditions.When combined with calcium hydroxide and water, it undergoes a pozzolanic reaction, resulting in the formation of additional cementitious compounds that improve the strength and durability of concrete⁵⁷. This fine, white clayey material constitutes more than 90% of the Metakaolin composition and contains a high concentration of siliceous and aluminous minerals^58,59. Due to its enhanced reactivity, Metakaolin is often referred to as High Reactivity Metakaolin (HRM)^5,6. The chemical composition of metakaolin consists predominantly of Silicon Dioxide (SiO2) at 50% and Aluminium Oxide (Al2O3) at 35%, 1% Iron Oxide (Fe2O3), 0.9% Calcium Oxide (CaO), and a 0.8% loss on ignition. Figure 2 illustrates the comparative particle size distribution curves of cement and Metakaolin, indicating its finer gradation.

Fig. 2 .

Particle size distribution of cement and metakaolin.

Fibers

Fibers are acquired from Fiber Source, Chennai. Their shapes and mechanical properties were tested in a verified strength of materials lab as per manufacturer guidelines. Properties of Fibers used are given in Table 2. In this table, the upper limits for the fibre dosages were selected primarily to balance the maximized mechanical performance and maintain adequate workability. Synthetic fibers enhance the performance of concrete primarily by bridging microcracks, thereby inhibiting their propagation once initiated⁶⁰. This crack-arresting mechanism becomes particularly effective under tensile and flexural loading conditions, leading to notable improvements in toughness, post-cracking energy absorption, and early-age crack mitigation.Numerous experimental and analytical studies have consistently confirmed the role of fibers in reducing shrinkage-induced cracking in both the plastic and hardened states,which is especially important in high-performance concretes that are susceptible to significant autogenous shrinkage⁶¹. In addition to increasing strength, fibers contribute significantly to enhancing ductility, a key property for structural applications subjected to seismic activity and impact forces^62[,63.

Table 2.

Parameters of the fibers.

Fiber types	Relative density (g/cm3)	Modulus of elasticity(GPa)	Diameter(m	Length(mm)	Aspect ratio (L/D)
SF	7.8	160	0.4	30	75
GF	2.7	80	0.112	9	80
NF	1.16	5	0.212	18	85
PPF	0.91	7	0.0875	7	80

Mix design and experimental testing

This section explains the mix design and the experimental testing. Table 3 presents the mix ratios for five distinct concrete formulations, all designed with a consistent water-to-cement ratio of 0.32 with an optimum fiber percentage. These mixes fall under the M60 grade classification, as per ACI guidelines.The initial mix design was formulated following the recommendations of⁶⁴ Fig. 3 illustrates the process of making HSFRC. The finalized mix proportion for M60 grade concrete in this study is 1:0.867:1.845:0.32. The experimental program includes one nominal mix (without fiber reinforcement) and four fiber-reinforced mixes, each of which uses a differentfiber type, such as steel fiber, glass fiber, nylon fiber, and polypropylene fiber incorporated at varying volume fractions.Specifically, SF was added in the range of 0.25% to 1.5%, while GF and NF were included at 0.10% to 0.35%, and PPF was used between 0.04% and 0.24% by volume of cement. These dosage levels were selected based on an extensive literature review, with particular emphasis on ensuring adequate workability and casting behaviour within the scope of the study⁶⁵.

Table 3.

Mix Design.

Mix	Cement + metakaolin (Kg)	FA	CA	Water + superplasticizer	Fiber
NC- control	616.13	534.58	1137.06	197.16	-
SF-(1%)	616.13	534.58	1137.06	197.16	6.16
GF- (0.3%)	616.13	534.58	1137.06	197.16	1.84
NF-(0.25%)	616.13	534.58	1137.06	197.16	1.54
PPF-(0.16%)	616.13	534.58	1137.06	197.16	0.985

Fig. 3.

High strength fiber reinforced concrete.

The workability of fresh concrete mixes was evaluated using the standard slump cone test, whereas the hardened concrete specimens underwent compressive strength, split tensile strength, and flexural strengthtesting. The mixing procedure involved an initial dry mixing of cement and aggregates for 2 min, followed by the addition of water and superplasticizer, which were mixed for another 3 min. Finally, fibers were gradually introduced and blended for an additional 3 min to ensure homogeneous dispersion throughout the mix. The fresh concrete was then cast into molds, compacted using a vibration table to eliminate entrapped air, and demolded after 24 h.Standard molds were used to prepare specimens, including cubes (150 × 150 × 150 mm), cylinders (150 × 300 mm), and beams (500 × 100 × 100 mm). All specimens were water-cured at a controlled temperature of 20 ± 2 °C for 7, 28, 56, and 90 days. For each fiber type and volume fraction—including the control mix—three specimens of each form (cube, cylinder, and beam) were cast for every curing age to ensure comprehensive evaluation of mechanical performance.

Analysis on the mechanical characteristics of hardened concrete

The evaluation of compressive, split tensile and flexural strengths is essential for understanding the mechanical response of FRC in structural applications. Compressive strength (cube specimens), assessed according to ASTM C39, determines the maximum axial force that the concrete can withstand before failure, thereby indicating its core load-bearing capacity. Split tensile strength (cylindrical specimens), tested as per ASTM C496, measures the concrete’s resistance to indirect tensile stress, which is critical for crack prevention and control. Flexural strength (beam specimens), evaluated using ASTM C1609, examines the material’s ability to resist initial cracking, maintain residual strength, and absorb energy under bending, especially under center-point loading conditions. HSFRC’s samples and testing are shown in Fig. 4.

Fig. 4.

Samples of HSFRC and testing.

Prediction of strength in concrete

A deep learning-based model for predicting FRC behavior was implemented using MATLAB 2020a. MATLAB, particularly with its deep learning toolbox, is a widely used platform for developing and deploying deep learning models in various engineering and scientific fields. The effectiveness of the developed model was proved by comparing it with existing optimization algorithms such as, Puma optimizer (PO)⁶⁶, Human Memory Optimization Algorithm (HMOA)⁶⁷, Hiking Optimization Algorithm (HOA)⁶⁸, and Addax Optimization Algorithm (AOA)⁶⁹, and benchmark models such as, Recurrent Neural Network (RNN)⁴⁹, Gated Recurrent Unit (GRU)⁵⁰, Support Vector Machine (SVM)⁵¹, and Long Short Term Memory (LSTM) (Chenet al.,2022) and Adaptive Pyramid Dilated Dense Long Short-Term Memory with Sparse Attention (A-PDDLSTM-SA).Here, APDDLSTM-SA outperformed all other models with higher accuracy.

Overview of the developed model

The proposed model is constructed to handle the intricate interactions between various mix parameters that influence concrete performance. The input to the model comprises a comprehensive set of features, such asthe proportionofcement + metakaolin, fine aggregate, coarse aggregate, superplasticizer, water, and the fibers(steel, glass, nylon, polypropylene). The output of the model includes predicted values of three key mechanical properties: compressive strength, split tensile strength, and flexural strength. Proposed model A-PDDLSTM-SA is designed with a pyramid dilated dense structure, allowing it to extract hierarchical features at multiple spatial and contextual resolutions. The LSTM layers are integrated to capture temporal dependencies and sequential patterns within the feature space, which is particularly beneficial when modelling interactions over varying mix compositions and proportions. To focus on the most influential parameters, a sparse attention mechanism is embedded, reducing redundancy and improving prediction sensitivity. For optimal performance, the model’s hyperparameters, including learning rate, number of hidden units, and number of epochs, are optimized using the URN-HOA. This metaheuristic optimizer enhances the model’s convergence rate and avoids local minima, leading to better generalization. This framework not only aids in reducing the time and cost associated with destructive testing but also provides engineers and researchers with a data-driven decision support tool for optimizing HSFRC mix designs, especially under varying structural and environmental demands. The step-by-step diagram of the developed model is given in Fig. 5.

Fig. 5.

Step-by-step diagram of the developed model.

Developed A-PDDLSTM-SA-based FRC prediction model

The architecture of the APDD-LSTM-SA represents a novel paradigm in deep learning applications for material property prediction. The model integrates three powerful concepts, such as pyramid dilated convolution, densely connected LSTM memory units, and sparse attention gating, into a seamless pipeline that emulates human decision-making during material design optimization. The input and output parameters are illustrated in Table 4.

Table 4.

Input and Output Parameters.

Input	Output
Proportion of cement, Metakaolin, fine aggregate coarse aggregate, superplasticizer& water	Compressive strength Split tensile strength Flexural strength
Fiber type and dosage
Fiber aspect ratio
Compressive strength at 7,28,56 and 90 days
Split tensile strength at 7,28,56 and 90 days
Flexural strength at 7,28,56 and 90 days

Novelty: The foundation of the proposed strength prediction model is built upon an LSTM network, selected due to its ability to effectively capture sequential dependencies and nonlinear temporal behaviors present in concrete curing and strength development. LSTM units, with their gated memory mechanisms (input, forget, and output gates), are capable of retaining important patterns over extended sequences, such as strength progression from early to late curing stages. This capability makes LSTM ideal for modeling how mix design parameters (e.g., fiber type, dosage, water-cement ratio, and curing age) influence the evolving mechanical properties of FRC over time. In the context of civil engineering, especially in predicting time-dependent behaviors of concrete, LSTM has proven effective due to its ability to model the temporal evolution of material properties such as strength development over curing periods. For instance, in FRC, parameters like curing age, fiber type, and water-cement ratio contribute to nonlinear and time-dependent strength characteristics. LSTM networks, when configured with appropriate layers and hyperparameters, can learn from these multivariate sequences to provide accurate predictions of compressive, tensile, and flexural strengths over time. The three gate components that comprise the LSTM (Zhang et al., 2023) are the input gate, forget gate, and output gate. The precise calculation for LSTM is as follows:

1

2

3

4

5

6

Here, the term indicates the input in time , is the invisible layer’s result at moment , is the hidden layer’s cell state at time , is the forget gate’s result at time , and is the input value at time for the input gate. The possible state memory segment of time is denoted by , is time output, stands for the cell state at time , for the output, stands for the weight matrix, and for the difference between the weights.

To further enhance the representational power of the base LSTM, a pyramid dilated dense convolutional module is integrated after the LSTM output. This module operates by applying multiple parallel convolutional layers with varying dilation rates (such as 1, 2, 4, and 8) on the temporal features extracted by LSTM. The rationale behind this design is to enable the model to capture multiscale contextual dependencies within the sequence data, small-scale interactions (e.g., impact of fiber volume on slump), as well as large-scale effects (e.g., strength trends over extended curing durations). The outputs from each dilated convolution path are densely concatenated, promoting a rich feature representation that retains both local and global contextual cues. DenseNet (Zhang et al., 2023) can extract more complex characteristics because of its properties, which are linked to all levels. The result of the preceding layer is typically used as the starting point of the succeeding layer in forwarding neural networks, and the calculation is as outlined below:

7

Here, the term is the layer input, while is the layer input, which is output. It makes it possible for the network to apply the features that were acquired in the preceding layer. The following formula represents the input–output connection between neighboring layers:

8

Based on Eq. (10), DenseNetenhances the reuse of characteristics from every layer by using a combination, which adds the input of the subsequent layer to the result of the preceding layer. Its links to networks are denser, though. All of the features acquired from the earlier layers may be processed by each DenseNet layer, and additional characteristics are added during learning to increase feature reuse. Equation (11) displays the DenseNet’s expression.

9

Here, the term is the concatenatedlayer. This structure not only enhances spatial resolution learning but also enables the network to learn hierarchical patterns without significantly increasing computational cost.

Following the convolutional stage of a densely connected network, a sparse attention mechanism is applied to refine the importance of each input feature. This selective feature prioritization enhances model interpretability and reduces the risk of overfitting, particularly in datasets with limited size or high dimensionality. Sparse Attention also improves convergence speed by directing the model’s capacity toward learning from the most influential variables.At the final stage, a fully connected regression head is employed to project the high-level feature representations into three continuous output predictions: compressive strength, split tensile strength, and flexural strength. To maximize the effectiveness of the LSTM backbone and the integrated modules, the model’s core hyperparameters are fine-tuned using the URN-HOA. The specific parameters optimized include:

• Hidden Neuron Count,

• Learning Rate,

• Number of Training Epochs.

URN-HOA is a metaheuristic search technique that improves traditional hiking optimization by dynamically updating random exploration values based on the evolving performance history of candidate solutions. It combines stochastic random walks with performance-aware memory, adaptively balancing global search (exploration) and local refinement (exploitation). By continuously adjusting its search path based on the best-known positions and fitness trends, URN-HOA avoids premature convergence and navigates complex, non-convex optimization landscapes efficiently. Figure 6 depicts the Structural Illustration of the A-PDDLSTM-SA-based FRC Prediction Model.

Fig. 6.

Structural illustration of the A-PDDLSTM-SA-based FRC prediction model.

URN-HOA for optimized prediction performance

A significant innovation of this research lies in the development and integration of the URN-HOA for hyperparameter optimization during the training of the APDD-LSTM-SA model. This URN-HOA is developed by modifying the traditional Hiking Optimization Algorithms (HOA)⁶⁸. It can effectively balance exploration of new areas with exploitation of promising paths, making it suitable for complex optimization problems with diverse search spaces. However, due to their reliance on static or arbitrarily selected random number components, traditional HOA often suffer from suboptimal convergence behavior, which may lead to premature convergence or entrapment in local minima. To overcome these drawbacks, the URN-HOA is introduced in this work by updating the random value in the HOA.

Novelty: The novelty of URN-HOA thus lies in its adaptive randomness regulation, problem-aware search behavior, and seamless integration into the model training loop, setting it apart from conventional optimization strategies used in AI-based concrete modeling. URN-HOA is a novel optimization algorithm, developed by the integration of a dynamic random value update mechanism given in Eq. (10) that adaptively modifies the exploration space based on real-time feedback from the solution’s fitness history. This update mechanism ensures a more balanced trade-off between exploration (global search) and exploitation (local refinement) throughout the optimization process.

10

Based on Eq. (10), the developed URN-HOA combines the strength of current fit, best fit, and worst fit to create a more efficient strategy. The URN-HOA is deployed to fine-tune critical hyperparameters of the APDD-LSTM-SA model, such as the hidden neuron count, number of epochs, and learning rate in the range of [5,255], [5,50] and [0.01,0.99], thereby minimizing the Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE). By leveraging URN-HOA, the optimization process becomes more resilient to overfitting and unstable gradient flows, particularly when dealing with highly nonlinear and limited concrete datasets. Moreover, the developed framework of deep learning fused with an adaptive metaheuristic optimizer not only enhances model accuracy but also demonstrates superior robustness in strength prediction across diverse FRC formulations.

Performance measures

This section shows the measures used for testing the performance of the developed model, and they are given in Table 5.

Table 5.

Measures used for testing the performance of the developed model.

Measures	Formula
Root Mean Squared Error (RMSE)
MEP
Symmetric Mean Absolute Percentage Error (SMAPE)
Mean Absolute Scaled Error (MASE)
L1-Norm	Represents the sum of the absolute differences between the elements of two vectors (representing different concrete mixes, based on their material proportions or test results)
L2-Norm	Calculates the straight-line distance between two points (vectors) in a multi-dimensional space, obtained by squaring the differences, summing them, and taking the square root
L-infinity Norm	Identifies the maximum absolute difference between corresponding elements of two vectors

Results and discussion

Flow characteristics of fresh concrete

The slump measurements for both nominal and FRCare illustrated in Fig. 7. Nominal concrete (NC)exhibitsthe highest slump value of 120 mm, indicating superior workability due to the absence of fibers. Among the fiber-reinforced options, steel fiberyieldsthe lowest slump, ranging from 85 to 53 mm, primarily due to the rigidity and higher density of steel fibers, which hinder flow and increase internal friction. Glass fiberdemonstrates slightly better workability, with slump values between 95 and 70 mm, as it is lighter and causes less resistance to flow. Nylon and polypropylene fibersexhibit moderate slump ranges between 65 and 100 mm, attributable to their flexibility and lower density, which minimally disrupts the mixture’s consistency. In general, adding fibers tends to decrease slump⁷⁰ due to the increased surface area and fiber-matrix interaction, which impedes the free movement of the concrete mix. This trend emphasizes the trade-off between mechanical enhancement and workability in FRC formulations.

Fig. 7.

Slump measurements for both nominal and FRC.

Impact of varying fiber content on compressive strength of concrete

The impact of fibres on the compressive strength of concrete has been experimentally given in Fig. 8. Depending on the type and percentage of fiber used, FRC’s compressive strength behavior varies greatly, providing crucial information about how fiber content, dispersion, and concrete matrix behavior interact.Among the fibers studied, steel fiber exhibited the greatest improvement in compressive strength, increasing by about 12.5% at a volume percentage of 1.0% when compared to nominal concrete. However, when the fiber content was increased to 1.5%, the strength dropped to 6.25%, probably as a result of fiber balling and poor dispersion, which negatively impactedthe mix’s overall workability and compaction efficiency^71,16. When GF dosage is increased from 0.10% to 0.35%, which are finer and lighter—helped to gradually boost strength, showing a substantial gain of 5.31% at 0.30% and a small improvement to 5.63% at 0.35%⁷². According to this pattern, glass fibers improve the cementitious matrix’s integrity without significantly reducing its workability by maintaining good dispersion and compatibility [] . Nylon fibers exhibited a comparable trend, showing a peak compressive strength gain of almost 9% at 0.30% before declining at greater levels, likely due to fiber clustering and reduced bonding efficiency within the mix⁷³. The strength of polypropylene fibers (PPF), which are renowned for their flexibility and light weight, increased steadily with increasing content, reaching 7.81% at 0.20% and slightly higher at 8.13% for 0.24%. This demonstrates PPF’s capacity to effectively distribute internal stresses and prevent the formation of microcracks.

Fig. 8.

Compressive strength analysis of different fibers.

Impact of varying fiber content on split tensile strength of concrete

The impact of fibres on the split tensile strength of concrete has been experimentally given in Fig. 9. In all types of fibers, increasing the fiber dosage generally resulted in enhanced split-tensile strength compared to the nominal (non-fiber-reinforced) concrete. However, the degree of improvement varied depending on the fiber type and its volume fraction.Steel fibers showed the most notable increase in split-tensile strength⁷⁴. At a fiber volume content of 1.25%, the split-tensile strength improved by approximately 76.32%, further rising to 89.47% at 1.5% fiber dosage compared to the control specimen. At 0.30%, the increase in split-tensile strength was 26.32%, and at 0.35%, it slightly rose to 28.96%⁷⁵. These improvements are mainly due to the alkali-resistant characteristics of glass fibers, which preserve their structural integrity within the cementitious matrix and efficiently help redistribute tensile stresses.Polypropylene Fibers (PPF) exhibited the least improvement among the evaluated fibers¹⁸. At 0.20% content, the split-tensile strength improved by 18.42%, increasing slightly to 23.68% at 0.24%⁷⁶. Although PPF offers excellent chemical resistance and effective crack control during the plastic phase, its relativelylow elastic modulus limits its ability to significantly improve the hardened-state tensile.Nonetheless, PPF still offers secondary reinforcement benefits by minimizing shrinkage cracks and improving the ductility of the composite.

Fig. 9.

Split tensile strength analysis of different fibers.

Impact of varying fiber content on flexural strength of concrete

The impact of several fiber types and varying dosages, steel, glass, nylon, and polypropylene fiber on the flexural strength of concrete was examined as given in Fig. 10. Although the degree of improvement varied depending on the fiber type and volume percentage, the results consistently demonstrated an overall enhancement in flexural strength with increasing fiber content. Steel fibers, known for their superior tensile strength and excellent crack-bridging capacity, showed the most significant influence, with improvements of 9.59% at 0.25%, 41.10% at 1.25%, and up to 47.95% at 1.5%. However, the flexural strength gain beyond 1.25%, suggesting that higher fiber content may lead to aggregation, decreased workability, or reduced fiber dispersion. Nylon fibers, valued for their flexibility, ductility, and strong bonding with the cement matrix, showed notable improvements, 2.74% at 0.10%, 17.81% at 0.30%, and 19.81% at0.35%, effectively mitigating microcrack propagation and enhancing post-cracking behavior²². Although PPF is considered the least effective in boosting flexuralstrength due to its lower stiffness, it still contributed positively, particularly in improving ductility, toughness, and crack reistance, with recorded improvementsof 1.37% at 0.04%, 10.96% at 0.16%, 13.70% at 0.20%, and 15.07% at 0.24%²³. Among all, steel fiber at 1.25% was identified as the optimal dosage, delivering the highest mechanical benefit without significantly compromising workability. PPFexhibited its best performance at 0.24%⁷⁷, whereas glass and nylon fibers performedoptimally at 0.35%.These findings underscore the importance of fiber selection and dosage optimization in fiber-reinforced concrete to achieve the desired flexural performance without negatively impacting workability or dispersion characteristics.

Fig. 10.

Flexuralstrength analysis of different fibers.

Convergence evaluation on the developed model

The convergence behavior of the URN-HOA during the hyperparameter tuning process of the APDD-LSTM-SA model is presented in Fig. 11. In Fig. 11a, the x-axis represents the number of iterations (or optimization epochs), while the y-axis denotes the fitness value obtained during validation. The curve effectively demonstrates how the URN-HOA progresses toward minimizing prediction error as it fine-tunes critical hyperparameters, namely the hidden neuron count, learning rate, and number of training epochswithin the LSTM-based framework.At the outset (initial iterations), the RMSE values fluctuate significantly, indicating the algorithm’s exploratory behavior in searching a broad solution space. This stage reflects the random-walk component of URN-HOA, which allows for dynamic exploration without prematurely settling on suboptimal regions. Around the 15th–25th iteration, the curve begins to show a steady decline in RMSE, marking the transition from exploration to exploitation. Unlike static or gradient-based optimizers, URN-HOA dynamically adjusts its search behavior, ensuring both diversity in early iterations and refinement in later stages, which is particularly advantageous when working with limited experimental datasets and highly nonlinear FRC strength data.

Fig. 11.

Convergence evaluation on the developed model based on (a) compressive strength, (b) split tensile strength, and (c) flexural strength.

Compressive strength evaluation on the model

Figure 12 illustrates a comparative performance analysis between the proposed APDD-LSTM-SA model and several baseline models and optimization algorithms for predicting the compressive strength of FRC. The evaluation is conducted using standard metrics to measure the prediction accuracy, reliability, and explanatory power of each model.In the graphs mentioned below, the x-axis shows the learning percentages, typically ranging from 35 to 85%. These ranges are chosen, since it aids in evaluating the learning curve of the model and the corresponding ability towards the generalization. Similarly, the different ranges are used in y-axis, which helps to ensure the high-resolution and statistical view of the performance gaps. For the L1-Norm measure, scale ranges from 0–700, 0–100 for L2-Norm, and 0–160 for MASE. Selection of these rages aids in encompassing the full range of baseline model fluctuations, thus helping to highlight the proposed model’s consistent reduction in total error volume. Moreover, when considering the L-Infinity, 0–20 range was taken and 0–15 for MAE, thus proving that the average prediction score and the worst-case error remain good within the strict structural tolerances. Then, to offer the granular perspective to the prediction biases, the range 0–50 was chosen for MEP, while 0–2 for SMAPE, thus helping to emphasize the stability of the designed model.In Fig. 12h, the SMAPE of the developed URN-HOA-A-PDDLSTM-SA is 0.25, which is better than existing models such as RNN (1.28), SVM (0.9), GRU (1.2), and LSTM (0.75) at the 35^th learning percentage. This demonstrates the developed URN-HOA-A-PDDLSTM-SA model’s high reliability in predicting concrete compressive strength by achieving superior SMAPE compared to other models. This indicates the model’sability to capture the complex relationships within concrete data and provide accurate predictions. Moreover, Fig. 12d presents a comparative evaluation of the MAE in predicting the compressive strength of FRC using various machine learning and deep learning models across different learning percentages (35%, 45%, 55%, 65%, 75%, and 85%). Across all learning percentages, the URN-HOA-A-PDDLSTM-SA model (depicted in black bars) consistently outperforms the other models, achieving the lowest MAE values, which indicates superior prediction accuracy and robustness. The clear margin by which the proposed model outperforms traditional and neural network-based models underlines its effectiveness in handling complex, nonlinear mix-property relationships in modern concrete design.

Fig. 12.

Compressive strength evaluation on the proposed model based on (a) L1-NORM, (b) L2-NORM, (c) L-INF-NORM, (d) MAE, (e) MASE, (f) MEP, (g) RMSE, and (h) SMAPE.

Split tensile strength analysison the proposed model

The performance analysis of the developed model in predicting the split tensile strength is given in Fig. 13. It is observed that the SMAPE analysis of various optimization-based PDDLSTM-SA models for predicting the split tensile strength of FRC across multiple learning percentages (35%, 45%, 55%, 65%, 75%, and 85%) is given in Fig. 13h. The models evaluated include PO-A-PDDLSTM-SA (green), HMO-A-PDDLSTM-SA (brown), HOA-A-PDDLSTM-SA (violet), AOA-A-PDDLSTM-SA (orange), and the proposed URN-HOA-A-PDDLSTM-SA (black). Among these, the URN-HOA-A-PDDLSTM-SA model consistently exhibits the lowest SMAPE values across all learning percentages, scaled from 0 to 2, emphasizing its superior accuracy and resilience against training data variations. At 35% learning, the URN-HOA model achieves an SMAPE of 0.47, which is significantly lower than that of HMO-A-PDDLSTM-SA (1.81) and HOA-A-PDDLSTM-SA (1.42). Even at higher learning rates (75% and 85%), where overfitting often becomes a risk, the URN-HOA model delivers SMAPE values of 0.45 and 0.59, whereas HOA-A-PDDLSTM-SA sharply increases to 1.78 and AOA-A-PDDLSTM-SA to 1.53, further validating the robustness of the proposed framework. It demonstrates not only superior accuracy but also remarkable consistency and stability across all learning percentages.

Fig. 13.

Split tensile strength evaluation on the proposed model based on (a) L1-NORM, (b) L2-NORM, (c) L-INF-NORM, (d) MAE, (e) MASE, (f) MEP, (g) RMSE, and (h) SMAPE.

Flexural strength evaluation on the proposed model

The performance analysis of the developed model in predicting the flexural strength is depicted in Fig. 14. In terms of evaluation with existing models and optimization algorithms, the SMAPE Fig. 14h of the developed URN-HOA-A-PDDLSTM-SA (0.3) is comparatively lower than RNN (0.92), GRU (1.35), SVM (1.2), and LSTM (1.38), and PO-A-PDDLSTM-SA (1.02), HMO-A-PDDLSTM-SA (1.1), HOA-A-PDDLSTM-SA (1.24), and AOA-A-PDDLSTM-SA (0.86) when used for predicting flexural strength at 45^th learning %. Thus, it suggests that APDD-LSTM-SA is a promising model for predicting flexural strength, achieving better performance (lower SMAPE) compared to several established models and optimization techniques. Figure 14c illustrates the comparative evaluation of the L-INF-NORM metric for predicting the flexural strength of FRC using various machine learning and deep learning models, such as RNN, GRU, SVM, LSTM, and the proposed URN-HOA-A-PDDLSTM-SA across different learning percentages (35% to 85%). The proposed URN-HOA-A-PDDLSTM-SA model significantly outperforms RNN, GRU, SVM, and LSTM models by achieving the lowest L-INF-NORM values across all learning percentages, effectively minimizing extreme prediction deviations.

Fig. 14.

Flexural strength evaluation on the proposed model based on (a) L1-NORM, (b) L2-NORM, (c) L-INF-NORM, (d) MAE, (e) MASE, (f) MEP, (g) RMSE, and (h) SMAPE.

RADAR chart analysis for the developed model

The RADAR chart presented in Fig. 15 provides a comprehensive comparative evaluation of the proposed APDD-LSTM-SA model. It presents a thorough assessment of the proposed URN-HOA-A-PDDLSTM-SA and the PDDLSTM model across five essential performance metrics: MEP, SMAPE, MASE, MAE, and RMSE. When analyzing Fig. 15a, for compressive strength, the proposed APDD-LSTM-SA model exhibits superior performance across all measured dimensions, occupying the outermost boundaries of the radar plot. The outer pentagon, normalized to a score of 1 across all axes, signifies the ideal performance benchmark (i.e., minimal error). The inner polygon, representing the actual performance of the proposed model, indicates a strong alignment toward this benchmark. The proposed URN-HOA-A-PDDLSTM-SA outscored the baseline PDDLSTM model on all the metrics, thus proving that it attained enhanced performance. The PDDLSTM provided 0.67 of MASE and shows moderate performance when considering the MEP of 0.33. On the contrary, the designed URN-HOA-A-PDDLSTM-SA model reaches the maximum values across all five metrics.The radial spread of APDD-LSTM-SA clearly establishes it as a reliable and scalable solution for strength prediction in advanced concrete systems.

Fig. 15.

RADAR Chart analysis for the developed model (a) Compression (b)Split tensile strength (c)Flexural strength.

Statistical evaluation on the developed model

Table 6 presents a comparative statistical evaluation of the developed model with various optimization strategies used to train predictive models for FRC strength estimation. The tested models include PO-A-PDDLSTM-SA, HMO-A-PDDLSTM-SA, HOA-A-PDDLSTM-SA, AOA-A-PDDLSTM-SA, and the proposed URN-HOA-A-PDDLSTM-SA. Among these in compressive strength prediction, the URN-HOA-A-PDDLSTM-SA model outperformed all others, achieving the lowest best-case value of 5.301, which indicates the smallest deviation between predicted and actual values. In contrast, the other models exhibited higher values: 5.610 for PO, 5.666 for HMO, 5.548 for HOA, and 5.603 for AOA, highlighting the superior error minimization achieved by URN-HOA. This enables the model to fine-tune critical parameters such as the number of hidden neurons, learning rate, and epoch count with high precision. This reinforces the model’s practical value in enabling high-precision prediction of compressive, tensile, and flexural strengths in FRC formulations.

Table 6.

Statistical assessment on the developed model.

Terms	PO-A-PDDLSTM-SA66	HMO-A-PDDLSTM-SA67	HOA-A-PDDLSTM-SA68	AOA-A-PDDLSTM-SA69	URN-HOA-A-PDDLSTM-SA
Compressive strength
Best	5.610	5.666	5.548	5.603	5.301
Worst	6.069	5.906	7.877	5.782	8.728
Mean	5.695	5.769	5.670	5.620	5.371
Median	5.610	5.690	5.624	5.603	5.301
Standard deviation	0.166	0.117	0.318	0.051	0.370
Split tensile strength
Best	5.635	5.549	5.563	5.554	5.331
Worst	6.363	6.026	7.066	7.218	9.126
Mean	5.693	5.684	5.641	5.607	5.376
Median	5.635	5.713	5.605	5.554	5.331
Standard deviation	0.112	0.088	0.184	0.248	0.381
Flexural strength
Best	5.789	5.585	5.570	5.553	5.319
Worst	8.430	8.185	8.368	8.347	5.909
Mean	6.041	5.669	5.626	5.628	5.353
Median	5.817	5.585	5.570	5.570	5.319
Standard deviation	0.559	0.267	0.392	0.333	0.135

Overall comparative study on the proposed model

Tables 7 and 8 offer the overall comparative evaluation of the proposed model in predicting the compressive, split tensile, and flexural strength with existing optimization algorithms and models, while Table 9 shows the state-of-the-art evaluation with the recent models. When evaluating the compressive strength in Table 8, the MEPof the proposed model in predicting the mechanical properties of FRC is evaluated with models includingRNN, SVM, GRU, and LSTM. The MEP metric is a critical indicator of a model’s average deviation from actual observed values, with lower values representing higher prediction accuracy and consistency.Among all models, the proposed model achieves the lowest MEP of 25.747, significantly outperforming traditional models such as RNN (43.774) and SVM (41.629), as well as more advanced architectures like GRU (47.582) and LSTM (45.702). This substantial reduction in error of approximately 40% compared to the next best modelunderscores the effectiveness of the proposed architecture, which integrates long-term temporal learning via LSTM, multiscale spatial feature extraction through Pyramid Dilated Convolution, and selective feature focusing using Sparse Attention.

Table 7.

Overall comparative study on the proposed model with existing optimization algorithms.

Terms	PO-A-PDDLSTM-SA66	HMO-A-PDDLSTM-SA67	HOA-A-PDDLSTM-SA68	AOA-A-PDDLSTM-SA69	URN-HOA-A-PDDLSTM-SA
Compressive strength
MEP	49.047	48.291	46.275	45.019	25.747
SMAPE	0.936	0.907	0.633	0.918	0.157
MASE	151.780	135.280	134.090	133.590	110.480
MAE	10.376	11.018	12.862	14.206	5.625
RMSE	9.772	11.092	11.352	14.307	4.860
L1-NORM	550.650	661.340	617.660	689.650	474.510
L2-NORM	85.312	81.045	86.468	85.105	69.746
L-INF-NORM	16.090	14.200	17.095	14.353	11.133
Split tensile strength
MEP	48.218	47.802	40.144	41.117	31.295
SMAPE	1.251	1.310	0.686	1.640	0.106
MASE	131.630	134.320	147.730	149.000	120.110
MAE	9.820	13.013	11.122	14.338	4.387
RMSE	11.829	10.610	14.023	12.099	5.264
L1-NORM	606.350	603.230	537.080	522.560	466.140
L2-NORM	81.589	85.658	83.003	82.532	67.676
L-INF-NORM	14.932	15.565	16.129	14.436	11.627
Flexural strength
MEP	44.087	42.608	46.848	45.157	31.685
SMAPE	1.690	1.167	1.329	0.913	0.456
MASE	157.580	155.680	134.240	136.950	111.310
MAE	8.849	13.071	8.555	14.297	4.695
RMSE	11.848	9.294	13.695	13.907	5.571
L1-NORM	584.740	548.310	595.680	628.660	473.200
L2-NORM	85.754	82.964	83.901	82.922	63.972
L-INF-NORM	16.042	17.363	15.795	16.335	10.452

Table 8.

Overall comparative evaluation on the proposed model with existing models.

Terms	RNN49	GRU50	SVM51	LSTM(Chen et al., 2022)	URN-HOA-A-PDDLSTM-SA
Compressive strength
MEP	43.774	41.629	47.582	45.702	25.747
SMAPE	1.545	1.659	1.705	0.998	0.157
MASE	139.150	136.670	143.990	146.730	110.480
MAE	10.236	8.585	13.509	10.098	5.625
RMSE	13.102	8.479	10.747	9.034	4.860
L1-NORM	610.670	658.520	689.870	639.750	474.510
L2-NORM	82.088	86.541	80.011	85.474	69.746
L-INF-NORM	16.857	16.888	17.827	17.090	11.133
Split tensile strength
MEP	43.158	41.728	46.403	43.064	31.295
SMAPE	0.958	1.578	1.612	0.903	0.106
MASE	140.350	158.790	141.210	157.480	120.110
MAE	12.664	13.391	13.367	12.305	4.387
RMSE	13.597	13.688	9.093	8.606	5.264
L1-NORM	657.120	532.130	613.550	632.990	466.140
L2-NORM	87.007	85.174	85.020	81.536	67.676
L-INF-NORM	17.398	15.264	16.784	17.030	11.627
Flexural strength
MEP	41.045	46.480	49.150	42.068	31.685
SMAPE	0.611	1.221	1.098	1.299	0.456
MASE	131.770	136.970	138.690	140.430	111.310
MAE	10.259	13.179	12.423	13.024	4.695
RMSE	13.067	13.778	9.920	8.182	5.571
L1-NORM	580.390	674.770	631.970	532.030	473.200
L2-NORM	84.957	84.776	80.380	87.417	63.972
L-INF-NORM	17.872	16.554	17.879	14.342	10.452

Table 9.

State-of-the-art evaluation with the recent models.

Terms	Bayesian-NSGA-II36	BPNN-XGB37	XGBoost-BO38	MCMC with Bayesian39	URN-HOA-A-PDDLSTM-SA
Compressive strength
MEP	41.858	43.747	42.354	49.711	25.747
SMAPE	0.822	0.751	1.115	1.573	0.157
MASE	140.250	143.050	147.080	145.180	110.480
MAE	14.530	8.641	8.430	9.952	5.625
RMSE	10.539	11.995	11.226	12.853	4.860
L1-NORM	569.180	521.980	635.620	562.650	474.510
L2-NORM	81.216	84.586	81.770	87.659	69.746
L-INF-NORM	15.549	17.080	17.265	16.419	11.133
Split tensile strength
MEP	47.579	45.884	44.390	43.039	31.295
SMAPE	1.048	1.708	1.499	1.156	0.106
MASE	142.880	132.580	134.450	140.130	120.110
MAE	14.694	11.503	12.339	13.589	4.387
RMSE	11.724	11.390	9.694	14.419	5.264
L1-NORM	672.950	536.230	600.220	548.630	466.140
L2-NORM	82.211	87.237	86.752	81.895	67.676
L-INF-NORM	16.427	17.449	14.765	16.739	11.627
Flexural strength
MEP	41.835	46.708	48.988	44.241	31.685
SMAPE	1.448	1.202	1.680	0.992	0.456
MASE	150.900	138.960	154.460	146.240	111.310
MAE	13.439	12.928	8.010	14.483	4.695
RMSE	11.262	10.480	8.020	9.940	5.571
L1-NORM	596.590	622.180	535.740	580.860	473.200
L2-NORM	84.890	87.103	82.086	86.876	63.972
L-INF-NORM	17.338	17.288	14.089	15.328	10.452

Ablation study

Table 10 shows the ablation study of the proposed model. In the table, the traditional LSTM attained 81.26% of accuracy, while the inclusion of dense connections enhanced the accuracy value to 84.91%. Moreover, the incorporation of pyramid dilated dense connections with the LSTM further enhanced the accuracy value of the model, which may result in 88.37%. However, when the sparse attention network was used, it provided 91.82% by focusing only on the selective features. Removing the optimization algorithm but retaining the full architecture still achieved 93.45%. Finally, the inclusion of A-PDDLSTM-SA and the URN-HOA delivered an accuracy to be 96.13%. Thus, it proved that each element in the designed model can be contributed towards the optimal performance.

Table 10.

Ablation study of the proposed model.

Model variant	Accuracy (%)
Baseline LSTM	81.26
LSTM + dense connectivity	84.91
PDDLSTM	88.37
PDDLSTM + sparse attention	91.82
PDDLSTM-SA (No optimization)	93.45
A-PDDLSTM-SA (proposed)	96.13

Conclusion

This study successfully investigated the mechanical performance of FRC using both experimental methods and advanced deep learning techniques. The experimental phase confirmed that the inclusion of steel, glass, nylon, and polypropylene fibers significantly influences the strengths of concrete. The selection of fiber type depends on the nature of the structure and its service environment. Steel fibers are preferred for load-bearing structural components. Nylon and glass fibers can be used in moderate exposure conditions or where surface finish and dimensional stability are required.Moreover, APDD-LSTM-SA was designed, which aided in predicting the behavior of the concrete mixes. It has the efficiency to comprehensively learn the relationships present between the types of fibers, mixing parameters and the strength properties. It also incorporated the sparse attention mechanism with it to find the most influential and effective input data, thus enhancing the reliability of the prediction process. This model was tuned using the URN-HOA to enhance the accuracy and the convergence speed. Finally, the combination of an enhanced optimization algorithm and the deep learning model offered the predicted outcome. When comparing the designed system with the traditional approaches, it proved to have better predictive performance.

• By achieving the lowest RMSE values of 4.860 for compressive strength, 5.264 for split tensile strength, and 5.571 for flexural strength, the proposed model demonstrated superior generalization capability.

• Moreover, for Compressive Strength, the developed model achieved an MEP of 25.747 and a SMAPE of 0.157, which is lower than the models, such as the GRU at 41.629 MEP.

• For Split Tensile Strength, the developed model registered an MEP of 31.295 and a SMAPE of 0.106, outperforming alternatives, which had MEPs above 41.

• For Flexural Strength, the URN-HOA-A-PDDLSTM-SA model maintained superior performance with an MEP of 31.685 and a SMAPE of 0.456, compared to competitor MEP values that ranged from approximately 41 to 49.

These results confirm that the developed framework can serve as a reliable tool for estimating concrete strength and reducing the need for extensive experimental testing. This validates the effectiveness of integrating sparse attention, pyramid dilated convolution, and URN-HOA optimization in capturing complex nonlinear dependencies, establishing the model as a state-of-the-art predictive framework for FRC mechanical behavior. This framework bridged the gap between empirical material testing and AI-driven prediction, enabling intelligent strength forecasting for FRC applications.

Real-world application: The developed model has acted as an innovative, field-applicable decision-support and practical tool to support the engineers and researchers in developing a more efficient solution. The practitioners can employ this model to test the different fibre proportions and their supplementary materials virtually, rather than carry out the expensive and wide-ranging physical investigation for the combination of each possible combination. This enables to detectionofthe optimal set of concrete composition more rapidly that meets the requirements of specific strength by minimizing the cost and material wastage. Finally, the proposed model directly supports resource-constrained construction, thus enhancing the assessment durability and providing intelligent planning for real-world infrastructure projects.

Limitation

Though the developed model provides enhanced and optimal results, it has some limitations, and they are expanded in this section. The dataset used by this work was limited in size to train the model, which impacts the generalizability to all the corresponding mix designs, the curing and the fiber combination. Then, this research work concentrated on using only the M60 concrete grade and the particular dosage of fibre, which may not be effective in representing the full range of high-performance concrete applications. Further, only under the controlled laboratory contexts, the experimentation was done on the developed model, resulting in varied results and prediction solutions when concerning varying temperature, loading circumstances and humidity. Moreover, the proposed solution does not evaluate the long-term durability aspects of the concrete, like shrinkage, creep and the resistance to environmental attacks. Finally, the predictive performance of the proposed AI model is highly dependent on the quality and diversity of the input data, and the absence of large-scale multi-source datasets may limit its robustness when applied to unfamiliar concrete compositions.

Future scope

Future research will extend further to use the hybrid fiber-reinforced concrete, which aids in exploring the lower and the higher concrete dosage, optimized combination of the fiber and the alternative concrete grades, resulting in enhanced mechanism performance and durability. Using more and large database in the upcoming work will help to improve the generalizability of the designed AI-based predictive models for fiber-reinforced concrete. Future research could expand the dataset to include a wider range of mix designs, curing environments, and additional fiber types such as carbon, aramid, basalt, etc. The proposed model could be extended to predict other durability parameters, such as permeability, chloride resistance, and shrinkage. Incorporating real-time sensor data and field performance metrics would further enhance the model’s practical relevance.Finally, actionable plans for cross-laboratory extrapolation and systematic on-site data collection will be outlined to improve the model’s practical applicability.

Author contributions

Ninu Praseetha N.S: Writing—original draft, Conceptualization Validation, Software. P.Kaythry: Review & editing, Supervision. P.Sangeetha: Review & editing, Supervision.

Data availability

The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

Declaration

Competing interests

The authors declare no competing interests.