Hybrid explainable machine learning models for predicting rapid chloride penetration test and sorptivity of self-compacting concrete with fly ash and silica fume under thermal exposure

Abstract

In this study, a comprehensive data set comprising 360 rapid chloride penetration test (RCPT) and 360 sorptivity measurements from 60 self-compacting concrete (SCC) mixtures with varying fly ash (FA) and silica fume (SF) contents and different temperature exposures was analyzed. To reduce reliance on labor-intensive experiments, four hybrid predictive models were developed by integrating eXtreme gradient boosting (XGBoost) with metaheuristic optimization algorithms, namely Particle Swarm Optimization, Whale Optimization Algorithm (WOA), and African Vultures Optimization Algorithm AVOA. While the primary focus is on enhancing predictive accuracy, with the XGBoost-WOA model achieving the best performance, the modeling framework also provides a foundation for future exploration of the influence of supplementary cementitious materials and curing conditions on SCC durability. Feature importance analysis identified temperature as the most critical variable influencing both RCPT (permutation score: 0.649, SHapley Additive exPlanations (SHAP): 110.626) and sorptivity (permutation score: 0.993, SHAP: 2.694). Furthermore, Monte Carlo simulations incorporating \pm5% input noise confirmed the accuracy under uncertain input variable. To enhance practical utility, a Python-based Graphical User Interface was developed using Tkinter, enabling users to predict RCPT and sorptivity values for SCC mixes containing FA and SF Beyond offering an efficient alternative to traditional laboratory testing, the developed artificial intelligence (AI) models have revealed new correlations between mix composition and durability performance.

Graphical abstract

Keywords

metaheuristic optimization technique / rapid chloride permeability / SCC / sorptivity / supplementary cementitious materials

1 Introduction

Infrastructure development is crucial for economic growth, urban expansion, and societal progress. Concrete, the most widely used construction material, plays a vital role in modern infrastructure. With the growing number of concrete structures, ensuring their durability is increasingly crucial. Reinforced concrete structures are highly susceptible to environmental degradation, especially in marine environments, industrial zones, and regions with extreme weather conditions. Enhancing concrete durability involves reducing porosity and internal pore volume, which minimizes permeability and increases resistance to environmental threats such as moisture ingress, freeze–thaw cycles, and chemical attacks. Proper compaction is essential for achieving a dense concrete matrix; however, traditional compaction techniques rely heavily on workforce skill and equipment quality. Poor compaction can lead to honeycombing, increased porosity, and reduced structural integrity. To address these challenges, Self-Compacting Concrete (SCC) was developed in Japan by Professor Okamura in the 1980s to address durability challenges in conventional concrete and has gained widespread attention [1,2]. SCC flows under its own weight and fills formwork, even in highly reinforced sections, without mechanical vibration or any external compaction. The properties of SCC such as high fluidity, deformability, and segregation resistance make it ideal for complex structural elements, such as heavily reinforced sections and intricate formwork. Nonetheless, SCC’s higher fine aggregate content typically demands increased cement dosage, contributing to a higher carbon footprint. Furthermore, the complexity of optimizing SCC mix design balancing workability, durability, and environmental impact poses a significant barrier to broader implementation. In this context, artificial intelligence (AI) offers a promising solution by enabling data-driven optimization of mix designs for SCC, reducing the reliance on costly trial-and-error procedures, and supporting more sustainable and efficient material development [3].

The penetration of chloride ions, which causes the corrosion of embedded steel reinforcement, is a major threat to the durability of reinforced concrete buildings. Corrosion significantly compromises structural integrity, reduces service life, and necessitates costly repairs, particularly in marine structures, bridges, and offshore platforms that are continuously exposed to aggressive chloride and sulfate environments. Studies have demonstrated that sulfate ions further exacerbate chloride-induced corrosion by modifying the microstructure of concrete, thereby expediting the initiation of corrosion processes. Numerical modeling of ion transport has revealed that sulfate penetration not only reduces the time before chloride-induced corrosion begins but also alters chloride concentration levels, affecting the long-term durability of reinforced concrete structures.

A promising strategy to enhance SCC’s resistance to chloride ingress and improve overall durability is the incorporation of supplementary cementitious materials (SCMs) such as fly ash (FA) and silica fume (SF) [4,5]. These materials have been widely acknowledged for their ability to refine the pore structure of concrete, thereby reducing permeability and enhancing resistance to aggressive environmental conditions [6,7]. The integration of FA and SF into SCC aligns with the construction industry’s shift toward sustainability, as these industrial by-products not only improve the mechanical and durability properties of concrete but also contribute to environmental conservation by reducing cement consumption [8]. The efficient utilization of FA and SF mitigates the environmental impact of concrete production while simultaneously immobilizing toxic heavy metals, thereby preventing hazardous leaching into the surrounding environment [9–12]. As the construction sector increasingly adopts sustainable practices, SCC incorporating SCMs is poised to gain broader acceptance, offering a durable, cost-effective, and environmentally responsible alternative for modern infrastructure development [13–16]. Several experimental studies have evaluated the durability properties of SCC containing FA and SF using the rapid chloride penetration test (RCPT) and sorptivity. The results show that fraction of FA and SF leads to a significant reduction in chloride ion ingress [17–19]. This improvement occurs due to the pozzolanic reactions of FA and SF, which produce additional calcium silicate hydrate (C-S-H) gel, thereby densifying the microstructure and reducing capillary porosity. As a result, not only does SCC with optimized SCM content enhance durability but it also contributes to the sustainability of construction by utilizing industrial by-products.

Beyond chloride resistance, high temperatures also affect the long-term performance of concrete structures. Exposure to elevated temperatures can alter permeability and reduce overall durability, making temperature-dependent assessments crucial. Studies by Pathak and Siddique [20,21] examined the permeability of SCC containing FA under varying temperatures (27, 100, 200, and 300 °C) and found that permeability increased with temperature. However, the increase was less pronounced in FA-modified SCC. Similarly, Kumar et al. [22,23] analyzed SCC mixtures with FA and SF at higher temperature ranges (30 to 180 °C). They found that the base mix without additives increased permeability by 26.5%, but the optimal combination of 20% FA and 4% SF increased permeability by only 18.2%, indicating an improvement of 8% in permeability resistance. These findings emphasize the role of SCMs in mitigating the adverse effects of temperature-induced durability loss. While laboratory experiments provide valuable insights, they are time-consuming and costly, especially when evaluating different environmental and temperature conditions. The need for repeated testing due to variations in materials, mix proportions, or test conditions further complicates experimental assessments. In response to these difficulties, AI methods have shown promise as an alternate approach for forecasting the resistance of SCC with FA and SF against chloride penetration under different temperature settings. AI-driven models can effectively simulate complex interactions between material properties, exposure conditions, and durability performance, significantly reducing reliance on physical testing while ensuring accurate and reliable predictions. The integration of AI into concrete research not only enhances efficiency but also accelerates the development of optimized SCC mixtures tailored for superior durability in aggressive environments.

Researchers across the world have been focusing a lot of emphasis on using AI approaches to evaluate the workability, durability, and other aspects of cementitious materials recently [24–31]. Among the various predictive modeling approaches, eXtreme Gradient Boosting (XGBoost) and its optimization algorithms have demonstrated exceptional efficiency due to their ability to 1) recognize complex patterns, 2) establish effective relationships between input variables and target outputs, 3) tolerate errors while maintaining accuracy, and 4) adapt flexibly to complex real-world problems through iterative learning processes [32–38]. Over the past decade, XGBoost, artificial neural network (ANN), multivariate adaptive regression spline (MARS), and several other machine learning (ML) models have been extensively employed to model the durability characteristics of concrete, particularly in predicting chloride penetration resistance and other performance-related attributes [39–45].

Recent advancements in computational intelligence have led to the integration of metaheuristic optimization techniques to enhance the predictive accuracy of AI models [46–49]. Recent studies have applied physics-informed and operator-based deep learning models, and variational or energy-based approaches, to solve partial differential equations with improved accuracy and interpretability [50–54]. These frameworks integrate physical principles with data-driven methods, reducing data requirements and enhancing robustness for complex engineering problems. Recent advances in machine learning have introduced several promising directions, for example, neural operators provide powerful tools for learning mappings between functional spaces [55], while physics-informed learning frameworks incorporate domain knowledge and governing equations directly into the training process [54], thereby improving interpretability and generalization. Other approaches, such as advanced structural modeling frameworks and alternative optimization algorithms further expand the applicability of AI in engineering problems [56–58].

Among these, Particle Swarm Optimization (PSO) [37,38], Whale Optimization Algorithm (WOA) [36,59], and African Vultures Optimization Algorithm (AVOA) [60–62] have been widely adopted in concrete research and engineering applications due to their computational efficiency, flexibility, and independence from derivative-based objective functions. These optimization techniques have demonstrated their effectiveness across a broad range of real-world engineering applications [45,63,64]. Despite the growing body of research in this domain, relatively few studies have specifically focused on predicting the RCPT and sorptivity of SCC mixtures incorporating SCMs. In these tests, chloride penetration resistance was evaluated only using RCPT data in C per ASTM C 1202 [6]. Several AI-based research have modeled the RCPT and sorptivity of SCC containing FA and SF at different temperatures. Kumar et al. [22] and Ge et al. [65] used AI to predict chloride infiltration in SCC treated to RCPT at different temperatures. However, the study by Kumar et al. [22] included only three input parameters FA percentage, SF percentage, and test temperature while neglecting key mixture design parameters such as water-to-cement ratio, cement content, and fresh property measurements (e.g., T-500 flow time, maximum spread diameter, J-ring, L-box, V-funnel, and temperature) critical influencing factors. In their study Kumar et al. [22], developed MARS and minimax probability machine regression (MPMR) model to predict the RCPT of SCC and found that the MARS model obtains the coefficient of determination (R²) value of 0.966 in training and 0.933 in testing followed by MPMR (R² = 0.937 in training and 0.935 in testing). After that, Kazemi and Gholampour [66] developed hybrid ANN model and found that the accuracy of developed models R² lies in the range of 0.968 to 0.9977 for developed models. In this study the developed models are more accurate compared to previous developed models in predicting the RCPT and sorptivity of SCC. The omission of these parameters reduced the validity and generalizability of the proposed model. Since AI models assign varying weights to input parameters during training, the inclusion of a limited number of variables can lead to biased attributions of significance, potentially skewing the predictive accuracy of the model. For this reason, it is essential to include environmental factors (i.e., temperature), basic mixture design parameters (i.e., cement content, FA, SF, coarse and fine aggregates, and water content), and a number of test measurements (such as the J-ring test, maximum spread diameter, L-box blocking ratio, and V-funnel time) as input features into the model in order to improve its reliability. Despite the advances in AI and metaheuristic optimization techniques for modeling concrete behavior, several critical gaps remain unaddressed in current literature. Hence, the specific gaps that this study seeks to fill are as follows.

1) Address the complexity and heterogeneity of SCC material behavior by incorporating a broad spectrum of mix design parameters (e.g., Ordinary Portland Cement (OPC), FA, SF, water content, aggregates) and fresh property measurements (e.g., T-500 flow time, maximum spread diameter, J-ring, L-box, V-funnel, and temperature) into the predictive modeling framework. These variables better represent the interrelated physical, chemical, and rheological characteristics of SCC.

2) Previously used single/hybrid AI models rely on simplified inputs, limiting their ability to capture the complex factors affecting durability, leading to poor generalizability. Proposing novel hybrid models by integrating XGBoost with metaheuristic optimizers (PSO, WOA, AVOA) to enhance prediction accuracy and robustness.

3) Improve both data quality and model architecture by tailoring the input feature set through a comprehensive feature selection process, ensuring high-quality, diverse, and representative input data that better reflect real engineering conditions.

4) Introduce a generalized framework for practical applications, moving beyond academic models by eliminating dependencies on specific Graphical User Interfaces (GUIs) and aiming for integration into practical decision-making tools for engineers.

Machine learning approaches offer a cost and time-efficient alternative to conventional laboratory methods while maintaining high accuracy. They promote sustainable construction by reducing material waste and enabling optimized mix designs that balance structural and environmental performance. By capturing complex relationships among variables, ML enhances decision-making in mix design, durability evaluation, and performance optimization, underscoring its transformative role in performance-based civil engineering.

2 Research significance

While previous studies on concrete prediction have focused mainly on simplified input variables and shows the algorithm performance, they often lack a unified framework for prediction, optimization, and practical application. This study addresses that gap by developing an optimized XGBoost model enhanced with PSO, WOA, and AVOA to predict RCPT and sorptivity of SCC. It incorporates data preprocessing, feature selection, and SHapley Additive exPlanations (SHAP) analysis for interpretability, and delivers a practical, open-source GUI for real-world use. This integrated approach advances interpretable, high-performance, and sustainable SCC mix design. The main objectives of the current study are summarized as follows.

1) Develop hybrid XGBoost models optimized using PSO, WOA, and AVOA to predict RCPT and sorptivity of SCC based on both mix design parameters and fresh property measurements collected from experimental study performed at laboratory.

2) Perform comprehensive feature selection and interpretability analysis using SHAP analysis to identify key input parameters.

3) Create a practical, open-source GUI tool for engineers to predict SCC durability properties accurately and efficiently based on constructed models.

4) Bridge the gap between ML research and real-world application by offering a complete, usable, and interpretable predictive framework for SCC design.

3 Properties of materials and mixture proportion

In this study, 43-grade OPC conforming to IS 8112-2013 [67] was used as the main binder (specific gravity: 3.15). SCMs included Class F FA and SF, selected for their pozzolanic properties and their ability to enhance the workability and durability of SCC. FA (specific gravity: 2.2), sourced from NTPC Kahalgaon per IS 3812-Part I [68], had a spherical shape and low lime content, contributing to improved workability and long-term strength. SF, obtained from Elkem South Asia Pvt. Ltd. and meeting IS 15388-2003 [69] standards, also had a specific gravity of 2.2 and helped densify the microstructure due to its high reactivity. The coarse aggregate used was crushed Pakur stone (max size 16 mm, specific gravity: 2.71, water absorption: 0.78%), while the fine aggregate was Sone River sand (specific gravity: 2.66, water absorption: 1.35%), both conforming to IS 383-2016 [70]. For mineralogical analysis, X-ray diffraction (XRD) using a Rigaku Ultima IV with CuKα radiation was conducted on finely ground samples of OPC, FA, SF, and the hardened high-volume FA-based self-compacting concrete (HVFA-SCC) mix. The XRD results, shown in Fig. 1, identified crystalline phases such as calcium hydroxide (CH), C-S-H, quartz, and unreacted FA, providing insights into hydration and microstructural development in ternary binder SCC.

4 Data and methodologies

4.1 Properties of fresh concrete

To assess the self-compatibility of the concrete mixes, the following tests were conducted within 30 min after mixing to minimize the influence of workability loss: slump flow, J-Ring flow (and height difference), V-funnel time, L-box. The following was the testing sequence: 1) slump flow, 2) height difference and J-Ring flow, 3) V-funnel time, and 4) L-box. When a typical slump cone is lifted and taken in two perpendicular directions, the slump flow test calculates the average spread diameter of the concrete. According to Khayat et al. [71] and Siddique [72], a slump flow between 500 and 700 mm indicates adequate self-compactability. Values above 700 mm may indicate segregation, while those below 500 mm suggest insufficient flowability for congested reinforcement. The V-funnel test was used to evaluate mix stability; as per Siddique [72], a flow time below 6 s is indicative of acceptable self-compacting behavior. Additionally, the compressive strength tests were conducted on three water-cured cube specimens (150 mm × 150 mm × 150 mm) for each mix at curing intervals of 14, 28, 56, and 90 d, following the guidelines of IS 516-2021 [73]. Besides, the split tensile strength was assessed at 28 d on cylindrical specimens measuring 150 mm in diameter and 300 mm in height, in accordance with the same standard [73].

4.2 Rapid chloride penetration test

The RCPT was employed to assess the chloride ion resistance of SCC mixes in accordance with ASTM C1202-12 [6]. Cylindrical specimens (100 mm in diameter and 50 mm in height) were cast and vacuum-saturated prior to testing, as per RILEM CPC-11.3:1984 [74], to ensure full saturation. Sodium hydroxide (NaOH) and sodium chloride (NaCl) solutions were applied to opposite sides of the specimen during the test. For six hours, a continuous voltage of 60 V DC was applied, and the total charge passed (in C) was recorded as a measure of the penetrability of chloride ions. Figure 2 shows the experimental setup.

To evaluate the thermal degradation impact, specimens from each mix were subjected to elevated temperatures ranging from 30 to 180 °C at a uniform heating rate of 1 °C/min, based on the recommendations of RILEM Technical Committee TC-129 [75]. Each target temperature was sustained for two hours to ensure homogeneity of thermal exposure. Post-heating, the RCPT was repeated to determine changes in chloride permeability due to thermal effects. The chloride ion permeability was categorized according to ASTM C1202 [6], as presented in Table 1.

RCPT results showed that all SCC mixtures exhibited negligible to moderate chloride permeability under ambient conditions, indicating adequate durability. However, increased exposure temperatures led to higher charge passed, reflecting pore structure degradation. Permeability notably increased above 150 °C, shifting classifications from ‘very low’ to ‘moderate’, emphasizing the negative impact of heat on SCC’s chloride resistance and the need to consider thermal stability in durability assessments.

4.3 Sorptivity

Sorptivity is a key transport property that quantifies a material’s capacity to absorb and transmit water through capillary suction. It serves as an indicator of concrete’s resistance to water ingress; lower sorptivity values signify enhanced durability due to reduced capillary absorption. The schematic representation of the test setup is illustrated in Fig. 3.

Cylindrical specimens were used to determine sorptivity, following a procedure that ensures unidirectional water flow from the base. Each specimen was partially submerged in a shallow water tray so that the bottom surface remained in contact with water up to a height of approximately 3–5 mm. To restrict lateral water ingress, the sides of the specimens near the base were sealed with adhesive tape to a height of 35–40 mm. This sealing technique ensures that water enters only through the bottom face, thereby enhancing the reliability of the results. To maintain consistent testing conditions, the total water surface area in the tray was kept at least ten times greater than the cross-sectional area of the specimen, minimizing water depletion effects. The specimens were removed from the water and weighed at specified time intervals of 0, 60, 300, 600, 1200, 1800, 3600, 7200, and 10800 s. The amount of water absorbed was calculated by measuring the weight gain and expressed per unit cross-sectional area. Sorptivity (S) was then determined as the slope of the linear portion of the graph plotting cumulative water absorption (mm) against the square root of time (min^0.5).

4.4 Microstructural property tests

XRD analysis was employed to investigate the mineralogical composition of the paste present within the interfacial transition zone (ITZ) of various concrete mixes. Samples of OPC, SF, FA, and HVFA-SCC were finely ground into powder using a mortar and pestle to ensure uniform particle size suitable for XRD analysis. Each powdered sample was subjected to XRD examination to identify the crystalline phases present. The scanning was conducted over an appropriate 2θ range to capture relevant diffraction peaks, enabling the qualitative identification of mineralogical constituents such as CH, C-S-H, ettringite, quartz, and other pozzolanic reaction products. For phase identification and quantitative phase analysis, the X’Pert HighScore Plus software was utilized. This analysis was critical for understanding the microstructural changes within the ITZ, particularly the influence of SCMs such as SF and FA on the refinement of the microstructure and the reduction of deleterious phases that may affect long-term durability.

In this study, all input and output data were obtained through controlled laboratory experiments to ensure consistency, reliability, and accuracy. The selected parameters were grouped into three main categories based on their role in influencing SCC durability. First, material composition parameters (e.g., OPC, FA, SF, water, coarse, and fine aggregates) govern the pore structure and chemical resistance of the hardened concrete. Second, fresh property measurements (e.g., T-500 flow time, spread diameter, J-ring height difference, L-box blocking ratio, V-funnel time) reflect the workability and compaction quality, which significantly impact permeability. Third, environmental conditions (e.g., curing temperature) affect hydration rate and microstructure development. The output parameters RCPT and sorptivity were chosen as standard indicators of ion penetration and capillary absorption, respectively.

5 Details of machine learning models

The methodology flowchart for predicting the RCPT and sorptivity of SCC using XGBoost and its optimization algorithms namely XGBoost-PSO, XGBoost-WOA, XGBoost-AVOA is illustrated in Fig. 4.

5.1 eXtreme gradient boosting

XGBoost represents a sophisticated evolution of the traditional Gradient Boosting Regression Trees (GBRT), originally introduced by Friedman [76] and further refined by Chen and Guestrin [77]. XGBoost introduces a highly efficient tree-based boosting framework designed to balance model complexity and predictive performance through regularization techniques. Unlike standard GBRT, XGBoost incorporates two significant mathematical enhancements that improve both its robustness and scalability. The first enhancement involves the formulation of an objective function that includes both a differentiable convex loss function and a regularization term. This objective function can be defined as Eq. (1):

(1)Obj=\sum L(y_i,\widehat{y_i})+\sum \mathit{\Omega }(f_k),

where L(y_i,\widehat{y_i}) represents the loss between the true label y_i and the predicted value \widehat{y_i}, which can be any convex and differentiable function suited to the problem domain. The term \mathrm{\Omega }(f_{\mathrm{k}}) quantifies the complexity of each tree f_k, expressed as Eq. (2):

(2)\mathrm{\Omega }(f_k)=\gamma T+\frac{1}{2}\lambda \sum w_j^2.

In this formulation, T denotes the count of leaves, w_j denotes the weight of leaf, and \lambda and \gamma denotes the regularization parameters that penalize complexity. The term \lambda \sum w_j^2 imposes L2 regularization on the leaf weights, while \gamma T adds a constant cost per leaf to discourage overly complex models. This regularization framework encourages the construction of simpler, more generalizable trees by minimizing both the loss and the complexity term. Additionally, XGBoost improves the optimization process by utilizing a second-order Taylor approximation of the loss function, in contrast to GBRT, which relies solely on first-order derivatives. This higher-order approach enhances convergence speed and accuracy, especially in complex prediction tasks [77].

5.2 Particle swarm optimization-eXtreme gradient boosting

PSO is a population-based optimisation method, inspired by the social behavior of creatures like ant colonies and bird flocks. Concept of PSO algorithm was proposed by Kennedy and Eberhart [78]. In nature, a group of birds searching for food in an unknown area adjusts their movements based on their own experiences and interactions with nearby birds. This collaborative and adaptive behavior is mathematically modeled in PSO to solve complex nonlinear optimization problems. PSO uses a particle model where each possible solution is defined by its location and speed in the search space. Each particle evaluates its position using a fitness function derived from the optimization objective. It retains knowledge of its best-found position (pbest) and also shares information about the best position found by the entire swarm (gbest). The particles adjust their velocity and position over successive iterations, influenced by both personal and global experiences. The update equations governing particle movement using Eqs. (3) and (4):

(3)\begin{array}{rl}{V}_{i,j}\left(t+1\right)=& w\times V_{i,j}\left(t\right)+c_1{r}_1\left(X_{\mathrm{p}\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t}}\left(t\right)-X_{i,j}\left(t\right)\right)\\ & +c_2{r}_2\left(X_{\mathrm{g}\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t}}\left(t\right)-X_{i,j}\left(t\right)\right),\end{array}

(4)X_{i,j}\left(t+1\right)=X_{i,j}\left(t\right)+V_{i,j}\left(t+1\right),

where V_{i,j}\left(t\right) and X_{i,j}\left(t\right) are the velocity and position of the ith particle in the jth dimension at iteration t, w is the inertia weight controlling exploration vs. exploitation, c_1 and c_2 are cognitive and social acceleration coefficients, r_1 and r_2 are random numbers in [0,1], X_{\mathrm{p}\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t},j} and X_{\mathrm{g}\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t},j} represent the best-known positions for the individual particle and the swarm, respectively. The algorithm initializes particle positions and velocities randomly, then iteratively updates them until convergence or a maximum iteration is reached. PSO achieves optimization through a balance of individual learning and collective intelligence.

5.3 Whale optimization algorithm-eXtreme gradient boosting

The WOA which is swarm intelligence-based metaheuristic algorithm was first presented by Mirjalili and Lewis [79]. It was inspired by the cooperative hunting methods of humpback whales. It is especially known for its simple structure, strong global search capability, and fast convergence rate. The algorithm mimics three primary behaviors observed in nature: encircling prey, the bubble-net feeding method, and random search for prey. These behaviors are translated into mathematical operations that guide the search for optimal solutions in a given problem space.

1) Encircling the prey

At the beginning of the optimization, whales assume that the current best candidate solution is the target prey. Each whale updates its position relative to this best solution. The distance between the whale and the prey is calculated using Eq. (5):

(5)\overrightarrow{D}=\left|\overrightarrow{C}\cdot {{\overrightarrow{X}}^{\ast }}_t-\overrightarrow{X}\left(t\right)\right|,

where \overrightarrow{X}\left(t\right) is the current position vector of the whale, {{\overrightarrow{X}}^{\ast }}_t is the best position found so far, \overrightarrow{C} is a coefficient vector, ∣\cdot∣ represents the absolute difference (element-wise). Using the distance vector, the new position of the whale is updated using Eq. (6):

(6)\overrightarrow{X}\left(t+1\right)={{\overrightarrow{X}}^{\ast }}_t-\overrightarrow{A}\cdot \overrightarrow{D},

where \overrightarrow{A} and \overrightarrow{C} are coefficient vectors defined using Eqs. (7) and (8) as follows:

(7)\overrightarrow{A}=2\overrightarrow{a}\cdot \overrightarrow{r_1}-\overrightarrow{a},

(8)\overrightarrow{C}=2\cdot \overrightarrow{r_2},

where \overrightarrow{r_{}} is a random vector with values in the range of [0,1], vector \overrightarrow{a} is a linearly decreasing factor from 2 to 0 over iterations. The role of the coefficient vector \overrightarrow{A} is to make a balance between exploration and exploitation. If , whales move closer to the best solution; if \mid \overrightarrow{A}\mid \ge 1, whales search away from the best solution.

2) Bubble-Net attacking mechanism

The second phase simulates the Bubble-Net hunting strategy, a unique feeding technique used by humpback whales. In WOA, this is represented by a spiral movement toward the prey. Mathematically, this behavior is captured by the Eq. (9):

(9)\overrightarrow{X}\left(t+1\right)=\overrightarrow{D}\cdot {\mathrm{e}}^{b\cdot l}\cdot \cos \left(2\pi l\right)+\overrightarrow{X^{\ast }}\left(t\right),

where b is a constant defining the spiral’s shape, and l is a random number in the range [−1,1]. The term {\mathrm{e}}^{b\cdot l}\cdot \cos \left(2\pi l\right) defines the logarithmic spiral and the multiplication with \overrightarrow{D} ensures the spiral path is centered around the prey. This spiral update allows the whales to gradually approach the prey using a nonlinear and adaptive path. The algorithm probabilistically decides between the encircling mechanism and the spiral motion using a random variable, as follows from Eq. (10):

(10)

As per the above Eq. (10), if , the encircling update is used; otherwise, the spiral motion guides the whale’s movement.

3) Searching for prey (Exploration phase)

The third and final phase is exploration, designed to avoid local optima and improve global search efficiency. When the absolute value of vector \overrightarrow{A} is greater than or equal to 1, the algorithm triggers a global search by allowing a whale to update its position based on a randomly chosen peer rather than the current best solution. The distance vector is redefined using Eq. (11):

(11)\overrightarrow{D}=\left|\overrightarrow{C}\cdot {\overrightarrow{X}}_{\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{d}}\left(t\right)-\overrightarrow{X}\left(t\right)\right|,

where {\overrightarrow{X}}_{\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{d}}(t) is the position of a randomly selected whale from the population. The new position is then calculated using Eq. (12).

(12)\overrightarrow{X}\left(t+1\right)={\overrightarrow{X}}_{\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{d}}(t)-\overrightarrow{A}\cdot \overrightarrow{D}.

This mechanism encourages diversity in the search space and helps prevent premature convergence by introducing randomness into the movement patterns. It can be observed that the WOA iteratively updates whale positions through a blend of exploitation and exploration, with adaptive parameters controlling the trade-off between the two phases. These biologically inspired strategies make WOA a robust tool for solving complex, multidimensional, and nonlinear optimization problems.

5.4 African vultures optimization algorithm-eXtreme gradient boosting

The AVOA is a nature-inspired, swarm-based metaheuristic that mimics the cooperative foraging and scavenging behaviors of African vultures. AVOA achieves a balance between exploration (global search) and exploitation (local refinement) by simulating the soaring, circling, and cooperative search strategies of vultures. The population consists of two behavioral categories: leaders (high-fitness individuals) and followers. Each vulture represents a candidate solution with a distinct hyperparameter configuration. The best-performing vultures guide the population toward promising regions, while others maintain diversity by probing unexplored areas. The movement of each vulture V_i at iteration, t is governed by a cooperative strategy based on Eq. (13).

(13)V_i^{\left(t+1\right)}=V_i^{\left(t\right)}+\alpha \left(V_{\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t}}-V_i^{\left(t\right)}\right)+\beta \left(V_{\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{n}\mathrm{e}\mathrm{r}}-V_i^{\left(t\right)}\right)+\gamma \overrightarrow{r},

where V_{\mathrm{b}\mathrm{e}\mathrm{s}\mathrm{t}} is the current best solution, V_{\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{t}\mathrm{n}\mathrm{e}\mathrm{r}} is a selected influential vulture, \alpha and \beta are attraction coefficients, \gamma \overrightarrow{r} introduces stochasticity for exploration, with \overrightarrow{r} being a random vector. Fitness evaluation is based on a predefined objective, such as classification accuracy or RMSE. High-fitness vultures reinforce the search direction, while random perturbations encourage broader search space coverage. The XGBoost-AVOA process begins with the random initialization of N candidate solutions (vultures), each representing a unique set of XGBoost hyperparameters. The algorithm iteratively updates these positions using AVOA’s cooperative and competitive strategies, evaluates fitness, and checks stopping criteria (e.g., maximum iterations or convergence). Upon termination, the best-performing hyperparameter set is used to train the final XGBoost model, typically resulting in improved predictive accuracy and reduced error.

5.5 Performance evaluation metrics

To thoroughly assess model performance, a comprehensive set of statistical performance metrics is employed: Coefficient of Determination (R²), Weighted Mean Absolute Percentage Error (WMAPE), Nash–Sutcliffe Efficiency (NS), Root Mean Square Error (RMSE), Willmott’s Index (WI), Mean Absolute Error (MAE), Mean Square Error (MSE), Theil’s Inequality Coefficients (TIC), Index of Agreement (IA), and Index of Scatter (IOS), as presented in Table 2. These metrics capture various dimensions of model accuracy, robustness, and error distribution, offering a holistic evaluation of prediction quality.

6 Data description

6.1 Data set characteristics and insights of experimental data

A statistical summary of experimental data sets is vital for developing robust ML models, as it provides essential insights into the data’s central tendency, variability, and distribution. Descriptive statistics for the experimental data set were assessed, such as the minimum, maximum, mean, median, and standard deviation (SD), to identify outliers, skewed distributions, and inconsistencies that may affect model performance. Measures like skewness and kurtosis further reveal distributional characteristics, highlighting potential deviations from normality that could impact training and generalization. Table 3 illustrates such a statistical summary for an experimental data set related to concrete mix design and performance parameters. Variables include components like OPC, FA, SF, coarse, and fine aggregates, water content, and several test measurements such as T-500 flow time, maximum spread diameter, J-ring test, L-box blocking ratio, V-funnel time, temperature, RCPT, and sorptivity.

The data set shown in Table 3 includes key variables essential for concrete mix design and performance evaluation. For instance, OPC varies from 180.30 to 515.14 kg, averaging 363 kg, with near-symmetric distribution and light tails, indicating consistent use across samples. FA, ranging from 0 to 515.14 kg with a mean of 237 kg, shows slight positive skewness, reflecting varying replacement levels that influence workability and durability. SF, ranging from 0 to 51.51 kg (mean 25.76), has a balanced distribution, highlighting selective use to enhance strength. Coarse Aggregate (617.50–799.00 kg) and Fine Aggregate (686.47–888.25 kg) both have mild negative skewness, indicating fairly uniform proportions that affect volume and workability. Water content is tightly controlled between 203.69 and 205.02 kg, showing minimal variation due to its critical role in strength development. T-500 time, measuring fresh concrete flow, varies from 1.80 to 5.40 s (mean 3.27) with positive skewness, suggesting some mixes are more viscous. Maximum Spread Diameter (634–755 mm, mean 705) shows negative skewness, indicating generally high fluidity. The J-ring test, which assesses passing ability around reinforcement, ranges from 2.00 to 6.60 mm (mean 4.14) with slight positive skewness, signifying acceptable flow in most mixes. L-box blocking ratio (0.81–1.00, mean 0.89) and V-funnel time (8.40–12.00 s, mean 10.31) exhibit consistent flow properties with low variability. These rheological indicators reflect workability and homogeneity, both essential to achieving a dense and durable matrix. Temperature varies widely from 30 to 180 °C (mean 105), representing diverse curing conditions. RCPT values range from 633 to 2160 C (mean 1170) with mild positive skewness, indicating variability in durability related to chloride ion penetration. Sorptivity, measuring water absorption rate, ranges from 52.28 to 72.14 (mean 60.92) and shows slight positive skewness, both RCPT and Sorptivity directly assess durability, indicating variability in resistance to chloride ingress and capillary suction. From the above discussion it can be observed that these variables effectively capture the variability in mix composition and performance of SCC, which is essential for training reliable machine learning models. Notably, no outlier was detected in the experimental data set, indicating data consistency and suitability for modeling.

6.2 Data preprocessing and analysis

Data preprocessing is crucial for ensuring model reliability and accuracy. The data set was structured in Excel, with standardized feature names and clearly defined input and output variables. Inputs included fresh and hardened SCC properties such as binder content, admixtures, and test values (T500, J-ring, V-funnel, L-box) while RCPT and sorptivity served as outputs. The data was split into 80% training and 20% testing to balance learning and evaluation. To reduce variance and overfitting, the process was repeated 30 times with different random seeds. Additionally, 5-fold cross-validation (CV) was employed to assess model generalization, enhancing performance stability across varied data subsets

Prior to constructing the ML models, all input and output variables in the data set underwent a normalization process. Specifically, the min-max normalization technique was applied to scale the values of each variable into a standardized range between 0 and 1, as recommended in previous studies [31,47,80,81]. This method adjusts the scale of the data without distorting differences in the ranges of values, using the transformation equations outlined in Eqs. (14) and (15). The primary purpose of data normalization is to eliminate the influence of differing units and magnitudes across variables, ensuring that each feature contributes equally to the modeling process. Without normalization, variables with larger numeric ranges could disproportionately influence the learning algorithm, potentially leading to biased or suboptimal model performance. By transforming all variables to the same scale, min-max normalization enhances the stability, convergence, and accuracy of machine learning algorithms.

(14){Input}_{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{z}\mathrm{e}\mathrm{d},i}=\frac{{Input}_{\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{u}\mathrm{a}\mathrm{l},i}-Inpu{t}_{min,i}}{Inpu{t}_{max,i}-Inpu{t}_{min,i}},

(15)Outpu{t}_{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{z}\mathrm{e}\mathrm{d},i}=\frac{{Output}_{\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{u}\mathrm{a}\mathrm{l},i}-Outpu{t}_{min,i}}{Outpu{t}_{max,i}-Outpu{t}_{min,i}}.

The model training and evaluation of the current study can be summarized in bullets points as follows. 1) The whole data set was randomly divided into 80% training and 20% testing as mentioned above. The 20% means testing data set was kept aside and used only for developed model evaluation. 2) The 80% means training data set was subjected to 5-fold CV during hyperparameter tuning, ensuring reliable optimization without data leakage. 3) To account for randomness in the splitting process, the entire 80/20 split + 5-fold CV process was repeated 30 times with different random seeds. This provided 30 independent estimates, which were averaged to yield stable and unbiased performance results. This technique of 5-fold CV ensured that hyperparameter optimization was based solely on training data while still providing a rigorous and reproducible evaluation of model generalization on unseen test data. Cumulative frequency histograms (Fig. 5) provide insights into the distribution of SCC data set variables. Most inputs, such as OPC, FA, and SF, exhibit negative kurtosis and low skewness, indicating uniform distributions without outliers. Water content and temperature show near-perfect symmetry with low standard deviations, reflecting measurement consistency. Slight skewness is observed in properties like T-500 flow time, J-ring, and L-box ratio. RCPT values are primarily concentrated between 1000 and 1300 C, while sorptivity clusters around 60 \times 10⁻⁴ mm/\sqrt{\mathrm{s}}, highlighting key data concentration zones.

6.3 Correlation analysis

Correlation coefficient is a valuable statistical measure used for the initial assessment of the degree of interrelation between the selected variables. In this study, the Spearman’s rank correlation coefficient (r_{\mathrm{s}}) was employed to evaluate pairwise relationships among all considered features, shown in heatmap matrix Fig. 6.

The r_{\mathrm{s}} value ranges from –1 to 1, where values closer to \pm 1 indicate stronger correlation. A positive r_{\mathrm{s}} suggests a direct association, whereas a negative value implies an inverse relationship. Notably, the main diagonal of the heatmap reflects perfect self-correlation (r_{\mathrm{s}} = 1). To simplify interpretation, Table 4 categorizes the absolute r_{\mathrm{s}} values based on their strength of correlation. Analysis of the correlation matrix reveals strong positive relationships among parameters such as OPC content with T-500 and V-funnel time, while fine aggregate shows high inverse correlation with L-box and J-ring results. Parameters such as temperature and water exhibit very weak associations with most other variables, indicating minimal interdependence.

The multicollinearity of the data set was assessed for the prediction of key performance parameters to evaluate the impact of input variable interdependence on the reliability of regression-based models. Multicollinearity is a statistical phenomenon that commonly arises in regression analysis when two or more input variables are highly correlated, potentially affecting model accuracy and interpretability [82,83]. For instance, OPC showed a very strong correlation with both T-500 (r_s = 0.83) and V-funnel time (r_s = 0.81), indicating a consistent directional association. Similarly, T-500 and J-ring (r_s = 0.93), and J-ring with V-funnel (r_s = 0.94) also exhibited very strong correlations Following the approach proposed by Khatti and Grover [84], the degree of multicollinearity was determined using the Variance Inflation Factor (VIF), calculated using the formula:

(16)VIF=\frac{1}{1-R_i^2},

where R_i^2 is the coefficient of determination obtained by regressing the ith variable on all other independent variables. A VIF value exceeding 1 suggests some degree of multicollinearity, with values above 5 or 10 typically considered problematic.

Despite the presence of high monotonic trends among certain pairs, the multicollinearity analysis following the researchers VIF classification as presented in Table 5 [82,83].

Following the Table 5 classification for multicollinearity level among the variables as presented in Table 6, it can be observed the acceptable independence among variables. For both RCPT and sorptivity prediction models, no input variables exceeded a VIF value of 5. The highest VIF (4.93) was observed for OPC, indicating moderate multicollinearity, while L-box blocking ratio (VIF = 4.85), J-ring test (3.71), V-funnel time (3.15), and T-500 (3.02) also exhibited moderate but acceptable multicollinearity. All other features, including FA, SF, aggregates, and water, had VIF values below 2.87, suggesting low multicollinearity. Particularly, water had a VIF of 1.04, and temperature remained the lowest at 1.26 in both models.

6.4 Check for outliers in experimental data set

The constructed models might be skewed by outliers, which are values of the target variable that are extremely tiny or extremely big in comparison to the average experimental values. Figure 7 presents notched box plots of RCPT (C) and sorptivity (× 10⁻⁴ mm/√s) values, displaying key statistical features including the median, upper quartile (Q3), lower quartile (Q1), and calculated upper and lower limits. The Q1 and Q3 values represent the 25th and 75th percentiles of the respective variables. The upper and lower limits were calculated using Eqs. (17) and (18):

(17)\mathrm{U}\mathrm{p}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{L}\mathrm{t}.=Q3+1.5(Q_3-Q_1),

(18)\mathrm{L}\mathrm{o}\mathrm{w}\mathrm{e}\mathrm{r}\mathrm{L}\mathrm{t}.=Q3-1.5(Q_3-Q_1).

These thresholds were further bounded by the actual maximum and minimum values observed in the data set, ensuring all data points fall within the computed limits. Notably, the plots show no outliers, as all RCPT and sorptivity values lie within their respective lower and upper bounds. This confirms that the data set is free from extreme values and is representative of the true behavior of both parameters.

7 Results and discussion

7.1 Fresh state results

For all SCC mixtures evaluated, slump flow values were consistently achieved within the target range of (750 ± 20) mm, in accordance with the guidelines specified by EFNARC (2005) [60], indicating adequate flowability for self-compaction without external vibration. T₅₀₀ time increased with higher FA content, indicating a reduced flow rate due to FA’s lower reactivity and spherical particles, which enhance lubrication but delay stiffening. In contrast, V-funnel flow time decreased with more FA, reflecting lower viscosity and improved flowability, attributed to FA’s smooth texture and low water demand. However, incorporating SF with FA and OPC in ternary systems increased viscosity. The high fineness and pozzolanic activity of SF enhance particle packing and water absorption, resulting in thicker, more cohesive mixtures. These trends highlight the distinct rheological impacts of FA and SF in SCC formulations. Figure 8 illustrates a strong correlation between T₅₀₀ and J-ring test results (R² = 0.8854) as well as the maximum spread diameter (R² = 0.9393), affirming the robustness of the SCC in navigating congested reinforcement scenarios.

The combination of SF and FA effectively minimized segregation and surface bleeding, enhancing mixture homogeneity. SF’s fine particles filled microvoids, while FA’s spherical shape improved packing density and flowability, resulting in synergistic improvements in fresh concrete performance. Ternary binder SCC mixtures exhibited uniformly viscous flow and consistent results across flowability tests, reflecting stable fresh-state behavior. These enhancements are attributed to the complementary physical and geometric properties of SF and FA, which optimize particle distribution and rheology. As shown in Fig. 9, polynomial regression was used to model the relationship between T₅₀₀ time and the results of both the V-funnel and L-box tests. The resulting regression curves demonstrate strong fits, with R² values of 0.9595 for the V-funnel and 0.9658 for the L-box test. These high coefficients of determination further support the conclusion that ternary cementitious blends promote well-balanced SCC mixtures, exhibiting superior flowability and enhanced resistance to segregation.

7.2 Result of X-ray diffraction

XRD analysis of OPC revealed the presence of key cementitious phases, including tricalcium silicate (\alpha), dicalcium silicate (\beta), tricalcium aluminate (\gamma), tetra calcium aluminoferrite (\delta), and gypsum (\eta). Among these, the XRD pattern exhibited prominent high-intensity peaks corresponding to \alpha, and \beta, indicating their significant contribution to the crystalline composition and hydration potential of the cement. Both of these minerals react with water (process a pozzolanic reaction) and result in gaining compounds. Moreover, it helps to improve strength in structure. From Fig. 1(a) it can be observed that the minerals \alpha diffraction peaks are at positions of 2θ = 29.40, 32.6, 41.3 42.95, 51.80, and 62.35 (d = 3.037, 2.745, 2.183, 2.107, 1.762, and 1.488 Å, respectively). Further, minerals \beta diffraction peaks are at positions of 2θ = 34.35 and 39.35(d = 2.611 and 2.286 Å) and \gamma peaks are at positions of 2θ = 23, 36.7, and 60.05 (d = 3.864, 2.446, 1.540 Å, respectively). For materials FA (Fig. 1(b)), the peak for Quartz is found at 2θ = 20.75 and 26.6 with interplanar spacings of d = 4.278 and 3.349 Å. In the SF sample (Fig. 1(c)), portlandite was observed at 2θ = 21.7, 31.5, 36.8, 40.5, and 44.3 corresponding to d = 4.093, 2.839, 2.443, 2.227, and 2.045 Å, respectively, for silicate 2θ = 28.35, 30.5, 31.5, and 35.6 with corresponding spacings of d = 3.147, 2.930, 2.839, and 2.519 A˚, while calcium carbonate was also detected at 2θ = 28.35, and 35.6, sharing the same d-spacings. A peak at 2θ = 30.4 (d = 2.940 Å) was attributed to the presence of ettringite and ferrite. In the SCC mixture without SF (Fig. 1(d)), quartz peaks were identified at 2θ = 20.74 and 26.54, CH appeared at 2θ = 27.74 and 34.04, for ettringite 2θ = 29.34, 47.04, and 68.2. In addition, mullite was identified by peaks at 2θ = 32.5 and 42.78, and for the mixture of HVFA-SCC without SF (Fig. 1(c)), the peak for quartz is found to be at 2θ = 20.74, 26.58, 47.06, and 59.9, for CH peak is at 2θ = 29.36, 34, 39.38, and 68.25.

7.3 Microstructural properties

The microstructural characteristics of HVFA-SCC incorporating OPC, with and without SF, were examined through SEM, as shown in Figs. 10–12. Microstructure is a key determinant of mechanical strength, workability, and durability, and SEM images provide insight into the observed performance trends of SCC mixes. Figure 10 presents the SEM micrograph of the control mix (HVFA-SCC with OPC only), revealing a poorly developed ITZ between the aggregate and mortar. The presence of visible cracks and voids indicates a weak internal bond, contributing to reduced mechanical performance compared to the binary and ternary mixes. In contrast, the binary mix (Fig. 11), which contains FA but no SF, exhibits a more refined microstructure with a denser mortar phase and a well-formed ITZ. The spherical FA particles are uniformly dispersed, acting as micro ball bearings that enhance workability and durability of mixes. At later curing ages, this mix displays a lower content of CH and ettringite, but a noticeable increase in C-S-H gel. The SEM image shows fibrous C-S-H growing over the plate-like CH crystals, forming larger aggregates that contribute to strength gain over time. The evolving microstructure appears progressively denser, with fewer and finer pores, which improves resistance to water absorption, capillary suction, and chloride ion penetration and hence enhance the durability properties. Figure 12 shows the ternary mix of HVFA-SCC incorporating both FA and SF. This mix demonstrates the most compact and refined microstructure among the three, with minimal voids and a dense, net-like arrangement of C-S-H gel an indication of secondary C-S-H formation. The presence of SF nanoparticles likely restricts the formation of large CH crystals, promoting more uniform and beneficial hydration. These nanoparticles act as nucleation sites, further enhancing the hydration process and contributing to a stronger, more durable matrix. As a result, this ternary mix exhibits superior mechanical performance and long-term durability due to optimized pore structure, reduced permeability, and enhanced resistivity.

7.4 Configuration of the developed models

The configuration and tuning of the XGBoost model and its hybrid variants XGBoost-PSO, XGBoost-WOA, and XGBoost-AVOA were carried out meticulously to improve predictive accuracy for the durability properties of SCC, particularly RCPT and sorptivity. The baseline XGBoost model was initially configured using manually selected hyperparameters, such as 301 estimators, a learning rate of 0.1, and default values for maximum depth and sampling ratios. While this provided a reasonable benchmark, it lacked optimization, leaving room for performance enhancement through intelligent hyperparameter tuning. These algorithms PSO, WOA, and AVOA offer efficient global search capabilities, improving model accuracy and robustness by avoiding local minima. The hybrid approach demonstrates a novel application in SCC modeling, with results showing clear improvements over the standalone XGBoost model. To overcome this limitation, PSO was first applied. PSO, inspired by the social behavior of bird flocking, works by evolving a population of candidate solutions (particles) toward the best-known positions in the search space. It iteratively minimized the RMSE of the XGBoost model predictions on testing data by adjusting five key hyperparameters: learning rate, number of estimators, maximum tree depth, subsample ratio, and column sampling ratio.

The hybrid algorithms, PSO, WOA, and AVOA, offer efficient global search capabilities that help avoid local minima, thereby improving accuracy and robustness. In each hybrid approach, five key hyperparameters were optimized: learning rate, number of estimators, maximum depth, subsample ratio, and column sampling ratio. PSO algorithm is inspired by the social behavior of birds was implemented with a swarm size of 35 and 300 iterations. Inertia weight was set to 0.7, and the acceleration coefficients (c1, c2) were both set to 1.5. WOA, which mimics the bubble-net hunting strategy of humpback whales, was executed with 30 agents and 300 iterations. Control parameters a and b were linearly decreased from 2 to 0 and from 1 to 0, respectively, as recommended in the original formulation. AVOA was employed with 30 agents, 300 iterations, and standard control parameters (\alpha =0.5, \beta =0.5) to balance exploration and exploitation. To ensure reproducibility, all experiments were conducted with a fixed random seed (42). After combining the optimization algorithm with XGBoost model it can be observed that the final developed hybrid algorithms substantially outperformed the manually configured XGBoost model, with XGBoost-WOA achieving the lowest and most consistent prediction errors for both RCPT and sorptivity. Table 7 below summarizes the final optimized hyperparameters for each model. These values reflect the tuning achieved through the respective optimization algorithms and indicate how hybrid approaches can significantly outperform manually configured models in predicting RCPT and sorptivity of SCC. The hybrid models setting summarized in Table 8.

7.5 Performance analysis of developed models

The performance comparison of the developed models for predicting the RCPT values of SCC, as shown in Table 9, highlights the superior predictive capabilities of hybrid XGBoost models enhanced by metaheuristic optimizers. Prior to computing the performance metrics, all model predictions were reconverted to the original units of RCPT and sorptivity using Eqs. (14) and (15). This procedure ensures that the reported RMSE, MAPE, and other evaluation metrics accurately reflect the true physical scales of the outputs. The baseline XGBoost model achieves respectable results with an R² of 0.9125 (train) and 0.8984 (test), but the optimization using XGBoost-PSO, XGBoost-WOA, and XGBoost-AVOA significantly improves the model accuracy and robustness. Among these, XGBoost-WOA stands out with the highest R² values of 0.9892 and 0.9709 for training and testing, respectively, indicating excellent fit and generalization. It also reports the lowest error metrics, including WMAPE at 0.0361 (train) and 0.0462 (test), RMSE at 0.0163 (train) and 0.0263 (test), and MAE at 0.0128 (train) and 0.0158 (test). This demonstrates the WOA’s superior hyperparameter tuning capability, yielding highly accurate and consistent predictions. XGBoost-PSO and XGBoost-AVOA also show substantial improvements over the base model, with R² values exceeding 0.94 in testing and reduced error measures. For example, XGBoost-AVOA attains R² of 0.9769 (train) and 0.9534 (test) and maintains low RMSE and MAE values, showcasing its efficacy in balancing exploration and exploitation during optimization. Additional metrics such as NS, WI, and TIC further confirm these trends, with XGBoost-WOA consistently achieving the best scores, indicating superior predictive accuracy, reliability, and minimal bias. The IA and IOS similarly favor the optimized models, especially XGBoost-WOA. In summary, while all metaheuristic-augmented XGBoost models outperform the baseline, XGBoost-WOA provides the most precise and reliable predictions for RCPT of SCC, validating the effectiveness of advanced optimization algorithms in enhancing machine learning model performance for complex concrete durability assessment.

The performance comparison of the developed models for predicting the sorptivity of SCC, as shown in Table 10, reveals significant improvements when the base XGBoost model is hybridized with optimization algorithms. The standalone XGBoost model demonstrates solid performance with a test R² of 0.9166 and a WMAPE of 0.1193, indicating good predictive accuracy but leaving room for improvement. When coupled with the PSO algorithm, the model’s test R² improves to 0.9416, and WMAPE reduces to 0.1021, reflecting better model fitting and error reduction. The XGBoost-WOA hybrid shows the most remarkable enhancement, achieving the highest test R² of 0.9792 and the lowest WMAPE of 0.0540. The XGBoost-AVOA model also demonstrates strong performance, with a test R² of 0.9454 and WMAPE of 0.1009, slightly lower than WOA but better than the base XGBoost and XGBoost-PSO models. Other metrics like RMSE (0.0530) and WI = 0.9856 further reinforce its effectiveness in sorptivity prediction. Finally, it can be observed that the all hybrid models significantly outperform the baseline XGBoost, with XGBoost-WOA emerging as the best model in terms of predictive accuracy, error minimization, and overall agreement with experimental data.

7.6 Scatter plots

The scatter plots of the developed models for predicting RCPT values provide clear visual evidence of each model’s predictive performance, as shown in Fig. 13. The base XGBoost model exhibits moderate dispersion of predicted values around the equality line (y = x), indicating reasonable but less precise predictions, particularly at extreme values. In contrast, models optimized with metaheuristic algorithms XGBoost-PSO, XGBoost-AVOA, and especially XGBoost-WOA demonstrate significantly enhanced accuracy, with predicted values more closely aligned to the y = x line and reduced scatter. Among these, XGBoost-WOA shows the most concentrated clustering around the equality line, reflecting superior prediction fidelity. Furthermore, when assessed against the ±20% error margin boundaries (y = 0.8x and y = 1.2x), the XGBoost model presents few RCPT predicted data points beyond the error margin. Conversely, the metaheuristic-enhanced models, particularly XGBoost-WOA, contain most predictions within this margin, indicating improved generalization and reliability. Thus, the scatter plot analysis confirms that XGBoost-WOA outperforms all other models in both accuracy and consistency for RCPT prediction.

The scatter plots for the developed models predicting sorptivity visually illustrate the relationship between the observed (experimental) and predicted values shown in Fig. 14. Ideally, points should lie close to the equality line (y = x), indicating perfect prediction accuracy where predicted values exactly match the measured sorptivity. The hybrid models (XGBoost-PSO, XGBoost-WOA, and XGBoost-AVOA) display tighter clustering around the equality line, indicating better fit and reduced error. Among them, XGBoost-WOA shows the closest adherence to y = x, reflecting its superior R² (0.9792) and lowest error metrics. For the XGBoost-WOA model, the majority of points fall within the 20% error margin band, illustrating reliable prediction capability.

7.7 Feature importance evaluation

The results obtained from the combined application of permutation importance and SHAP analysis offer a robust and nuanced understanding of the key variables influencing the RCPT and sorptivity performance in SCC. Both methodologies, despite their distinct conceptual foundations, converge in highlighting temperature as the most dominant predictor affecting RCPT outcomes, thereby underscoring the critical role of thermal conditions in determining the durability characteristics of SCC. Permutation importance assesses feature relevance by evaluating the change in model performance when the values of a given feature are randomly permuted. This process disrupts the original structure of the feature and quantifies the corresponding drop in model accuracy (measured by R²), with larger drops indicating greater feature importance. In this analysis, temperature yielded the highest permutation importance score of 0.649, signaling its substantial influence on the model’s predictive accuracy, as shown in Fig. 15. SHAP analysis, on the other hand, is grounded in cooperative game theory and attributes a fair contribution of each input feature to the final prediction by computing marginal effects across all possible combinations of features. The SHAP value for temperature was also the highest, with a mean contribution of 110.626, reaffirming its central role in shaping RCPT values, as shown in Fig. 16.

In addition to temperature, OPC content and maximum spread diameter also emerged as critical factors. OPC displayed a permutation importance score of 0.291 and a mean SHAP value of 75.125, reflecting its pivotal contribution to the binding matrix and the resistance to chloride ion penetration. Maximum spread diameter, a measure of workability and mix homogeneity, was ranked next (permutation importance = 0.129; SHAP = 34.672), indicating that flow behavior significantly influences pore structure and hence chloride resistance. SF and fine aggregates also demonstrated moderate impact, with SHAP values of 31.934 and 25.873, respectively. These materials are known for improving matrix densification and mitigating permeability. Other variables such as coarse aggregate (SHAP = 19.711), L-box blocking ratio (SHAP = 9.835), and water content (SHAP = 6.403) contributed modestly to the model’s predictions. Notably, features like V-funnel time, J-ring test, T-500, and FA were found to have minimal influence, as evidenced by their low permutation importance scores and SHAP values. This suggests that, under the studied mix conditions and performance criteria, these factors exert a negligible direct impact on RCPT outcomes. Overall, the alignment between the global insights from permutation importance and the local interpretability offered by SHAP enhances the credibility of the findings. Together, these analyses confirm that optimizing temperature conditions, OPC dosage, and flowability parameters such as maximum spread diameter are essential for improving the chloride penetration resistance of SCC. Such insights are critical for both the practical design of durable SCC mixes and the strategic prioritization of variables in predictive modeling frameworks.

For sorptivity prediction, the combined results of permutation importance and SHAP analysis reveal that temperature is the most influential variable affecting the water absorption behavior of SCC. Specifically, temperature achieved a permutation importance score of 0.993 and a mean SHAP value of 2.694, indicating its dominant role in governing sorptivity performance, as shown in Fig. 17. This outcome suggests that even minor fluctuations in curing or ambient temperatures can significantly alter the capillary suction and pore structure of SCC, directly impacting its capacity to absorb water over time. Elevated temperatures can accelerate hydration kinetics and densify the microstructure, while lower temperatures may result in higher porosity, both of which influence sorptivity. Following temperature, SF emerged as the second most influential factor, with a permutation score of 0.236 and a mean SHAP value of 1.355 (refer to Figs. 17 and 18). SF is known for its pozzolanic activity and ultra-fine particles, which contribute to pore refinement and reduced permeability, thus having a notable effect on sorptivity reduction. Similarly, the J-ring test, typically used to evaluate the passing ability and segregation resistance of fresh SCC, also showed a meaningful contribution (permutation importance = 0.145; SHAP = 0.594). This result implies a connection between the fresh-state performance and the uniformity of the hardened matrix, which in turn affects water ingress. Other moderately significant contributors include water content (permutation = 0.023; SHAP = 0.343) and maximum spread diameter (permutation = 0.022; SHAP = 0.238). These factors influence mix consistency, workability, and the eventual formation of capillary pores, which are critical in sorptivity behavior. Additionally, fine aggregates (permutation = 0.016; SHAP = 0.219) and OPC (permutation = 0.014; SHAP = 0.193) also demonstrated minor but consistent impacts, likely due to their effect on the paste matrix and pore distribution. In contrast, features such as coarse aggregate, L-box blocking ratio, V-funnel time, T-500, and FA were found to have negligible contributions, both in terms of permutation scores and SHAP values. Their limited influence suggests that, within the tested SCC compositions, these parameters do not substantially alter the water transport properties once the concrete has hardened. Collectively, the analysis underscores that thermal conditions and micro-filler content (like SF) are the most critical drivers of sorptivity, while traditional workability or mix parameters related to segregation and flow resistance play a less pronounced role. These insights are vital for the targeted design of SCC mixes in applications where controlling moisture ingress and durability is essential.

7.8 Uncertainty analysis

A predictive uncertainty analysis was carried out using Monte Carlo simulations to assess the dependability and robustness of the suggested XGBoost-WOA ensemble model when subjected to input variability. All test input characteristics were enhanced with \pm5% Gaussian noise in order to mimic actual measurement mistakes. To provide a wide variety of prediction scenarios, the analysis utilized 72 test samples (20% of the data set). Each sample was then exposed to 100 noise-perturbed simulations. For each sample, the prediction spread the gap between the greatest and least expected RCPT values and was computed to quantify local uncertainty. The average spread was then compared to two practical RCPT thresholds, ±600 and ±800 C, commonly used to assess chloride penetration in SCC. For each sample, Figs. 19(a) and 20(a) show the original forecast (black), mean noisy prediction (blue dashed), and prediction range (red shaded). Even with noisy inputs, the model stays directionally stable since the original and mean predictions coincide closely. See Figs. 19(b) and 20(b) for sample spreads. Most forecasts are within realistic tolerance limits, with an average spread of 435.78 C and 5.69 ({\times 10}^{-4}\mathrm{m}\mathrm{m}/\sqrt{\mathrm{s}}). These results confirm that the XGBoost-WOA model is robust and exhibits minimal sensitivity to moderate input uncertainties. The model maintains consistent predictive performance and is thus reliable for real-world durability assessments and thermal analyses of SCC structures. This underscores its practical utility in engineering scenarios where input variability is inevitable.

7.9 Graphical user interface

The developed GUI offers an intuitive and efficient platform for predicting the durability characteristics of SCC incorporating FA and SF. Specifically, the GUI has been designed to estimate two critical durability indicators RCPT values and sorptivity based on a variety of input parameters related to concrete mix design and fresh properties. These include cementitious materials (OPC, FA, and SF), aggregate quantities, water content, and workability tests such as T-500 time, maximum spread diameter, J-ring flow, L-box blocking ratio, and V-funnel time, along with ambient temperature. The GUI integrates the best performing hybrid model XGBoost-WOA to ensure highly accurate predictions. The interface was built using Python’s Tkinter [84] library and features a clean layout for all labels and inputs, adhering to a professional presentation standard. Users input values into designated fields, and upon clicking the ‘Predict’ button, the GUI returns predicted RCPT and sorptivity values. This functionality provides a fast, user-friendly alternative to traditional laboratory testing, which can be time-consuming and resource intensive. To assess the accuracy of the developed system, a case study was conducted wherein a known SCC mix produced an experimental RCPT value of 1207 C and a sorptivity value of 64.26. The GUI predicted these values as 1199.95 C and 64.28, respectively. The absolute error for RCPT was 14.15 C, corresponding to a remarkably low percentage error of 1.17%, while the error in sorptivity prediction was only 0.07241, yielding a percentage error of just 0.10%. These low errors show the model’s great predictive power and capacity to generalize across new data. The hybrid XGBoost-WOA model's dependability and practicality are confirmed by the excellent agreement between predicted and experimental results. Figure 21 illustrates the GUI for RCPT and sorptivity predictions emphasizing the visual clarity and functionality of the interface. The developed GUI represents a notable advancement in SCC mix design, facilitating rapid and informed decision-making with reduced experimental effort.

8 Conclusions

In this research, four predictive models XGBoost, XGBoost-PSO, XGBoost-WOA, and XGBoost-AVOA were developed to estimate the RCPT and sorptivity of SCC based on experimental datset. Based on the analysis and findings, the following key conclusions have been derived.

1) Experimental results show that incorporating FA and SF together in SCC reduced bleeding, segregation, and enhances durability by significantly lowering both chloride ion penetration and sorptivity. SCC with FA alone exhibited a low chloride penetrability (1000–2000 C), while mixes with both FA and SF achieved a very low rating (< 1000 C). Sorptivity results also confirmed improved resistance to water absorption in ternary blends compared to binary mixes, which confirms the combined use of FA and SF in SCC improves its resistance to chloride ingress and water absorption, even under thermal exposure.

2) Among the four models, the XGBoost-WOA exhibit the strongest agreement with experimental values, highlighting its superior accuracy in estimating RCPT and sorptivity. The performance improvement arises due to WOA’s efficient global search strategy, which enhances hyperparameter tuning and promoting better generalization.

3) Comparative analysis of statistical metrics and the scatter plot between experimental and predicted values demonstrates that the XGBoost-WOA model delivers more accurate and consistent predictions, with a smaller error margin compared to the other three models.

4) The combined permutation importance and SHAP analysis confirm temperature as the most dominant factor influencing both RCPT (score: 0.649; SHAP: 110.626) and sorptivity (score: 0.993; SHAP: 2.694). Secondary influential factors included OPC content (0.291; 75.125) and maximum spread diameter (0.129; 34.672) for RCPT, and SF (0.236; 1.355) and J-ring flow (0.145; 0.594) for sorptivity, highlighting the importance of binder composition and fresh-state properties in optimizing SCC mix design.

5) The developed GUI, powered by the hybrid XGBoost-WOA model, demonstrates high predictive accuracy for RCPT and sorptivity, offering a practical, time-efficient alternative to conventional testing methods and supporting more informed SCC mix design decisions.

This study presents a robust hybrid AI model for predicting RCPT and sorptivity in SCC, aiming to reduce reliance on time-intensive laboratory tests and skilled personnel. The model is specifically validated for SCC mixtures incorporating FA and SF, with RCPT values ranging from 600 to 2000 C, SF replacement levels between 0%–10%, and elevated temperatures up to 180 °C; it remains applicable across all FA replacement levels. Additionally, the framework offers potential for broader application in predicting other concrete properties under diverse materials and conditions. However, to enhance model generalizability and reliability, further data collection is necessary. The integration of XGBoost with optimization algorithms enhances model robustness against noisy or inconsistent data, ensuring reliable predictions under practical conditions. However, its accuracy is best within the input ranges shown in Table 4. Predictions beyond this range may be less reliable due to limited extrapolation. As more data becomes available, the model can be retrained to improve generalization and extend its applicability. Future research is encouraged to perform more laboratory experiment and develop advanced AI models while also considering variables such as exposure duration and environments with varying concentrations of aggressive ions. Additionally, a potential direction for future research is the application of physics-informed deep learning models to incorporate underlying physical principles, thereby reducing data requirements while maintaining predictive accuracy.

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