Developing machine learning frameworks to predict mechanical properties of ultra-high performance concrete mixed with various industrial byproducts

Abstract

This research investigates the predictive modeling of ultra-high-performance concrete (UHPC) incorporating industrial byproducts, focusing on compressive strength (Fc), flexural strength (Ff), workability (Slump), and porosity. Various machine learning models, including Kstar, M5Rules, ElasticNet, XNV, and Decision Table (DT), were evaluated to determine the most accurate predictions for each property. The findings indicate that Kstar outperformed other models across all categories, demonstrating the highest accuracy and lowest errors in predicting Fc, Ff, Slump, and Porosity. Sensitivity analyses using SHAP and Hoffman & Gardener’s methods identified the most influential parameters affecting each UHPC property, providing insights into the key factors driving concrete performance. The research highlights the sustainable impact of incorporating industrial byproducts, reducing environmental footprints while maintaining superior mechanical and durability properties. The developed models offer practical guidance for optimizing UHPC formulations, promoting sustainability in the construction industry by enabling efficient material utilization and reducing reliance on conventional cement-based components.

Introduction

Ultra-High Performance Concrete (UHPC) signifies a significant advancement in construction materials, characterized by its remarkable mechanical properties such as elevated compressive strength (Fc), flexural strength (Ff), reduced porosity, and enhanced durability¹. The incorporation of industrial byproducts (see Fig. 1), including fly ash, slag, nanosilica, silica fume, limestone powder, fibers (e.g., polystyrene and steel fibers), and superplasticizers, facilitates the attainment of these properties². Traditionally, the optimization of UHPC mix designs depends on experimental testing, a process that is time-consuming, resource-intensive, and frequently constrained in scope. Recent advancements in machine learning frameworks have transformed the prediction of UHPC properties, facilitating rapid and precise modeling of intricate relationships among mix proportions, material characteristics, and performance outcomes³.

Fig. 1.

Schematic illustration of the sustainable use of industrial waste in construction.

Concrete is the most widely used construction material worldwide, serving a crucial function in infrastructure development. The production process predominantly depends on ordinary Portland cement (OPC) and nonrenewable natural aggregates (NA), such as sand and gravel, resulting in considerable carbon emissions and environmental harm. The disposal of industrial by-products, including fly ash (FA), ground granulated blast-furnace slag (GGBS), and silica fume (SF), poses a significant challenge for sustainable urban development⁴. The concept of sustainable low-carbon concrete has emerged to address these issues, promoting the utilization of recycled aggregates (RAs) from construction and demolition waste (C&DW) and supplementary cementitious materials (SCMs) from industrial by-products as replacements for traditional components in concrete mixtures. This literature review examines the use of machine learning techniques in predicting four essential properties of ultra-high-performance concrete (UHPC): compressive strength (Fc), flexural strength (Ff), porosity, and slump. This synthesis encompasses essential studies from initial developments to recent advancements projected for 2025, emphasizing reinforcement mechanisms, performance-influencing factors, and predictive modeling methodologies⁵. Furthermore, it incorporates results from recent studies published in journals including Materials, Frontiers in Materials, Construction and Building Materials, and Case Studies in Construction Materials. The incorporation of recycled aggregates and sustainable construction materials in concrete production has been thoroughly examined to improve sustainability within the construction industry. Research shows that recycled aggregate concrete (RAC) frequently demonstrates reduced workability, mechanical strength, and durability, attributed to the old mortar that adheres to the surfaces of the recycled aggregates. The corrosion of steel reinforcements in recycled aggregate concrete, particularly in chloride-rich environments, is a notable concern. Incorporating SCMs into OPC to create composite cementitious materials (CCMs) can alleviate these negative effects. The pozzolanic and filler characteristics of supplementary cementitious materials (SCMs) enhance the microstructure of concrete, resulting in improved performance. Research indicates that binary, ternary, or higher-order blends of supplementary cementitious materials (SCMs) can synergistically enhance the properties of recycled aggregate concrete (RAC), thereby establishing it as a feasible choice for sustainable construction.

The prediction of mechanical properties in CCMs-RAC mixtures with complex compositions presents a considerable challenge. Conventional empirical models frequently prove inadequate because of the complex interactions among different components. Recently, machine learning (ML) algorithms have proven to be effective tools for predicting concrete performance with accuracy. Miao et al.⁶ created a database of CCMs-RAC to predict compressive strength through statistical models, whereas Duanet al.⁷ utilized both single and hybrid algorithms, concluding that the Particle Swarm Optimization-Gradient Boosting (PSO-GB) algorithm achieved the highest accuracy. These studies primarily concentrated on individual mechanical properties and did not adequately investigate the synergistic effects of multiple SCMs. Recent research has employed advanced machine learning techniques to predict several mechanical properties of CCMs-RAC, such as compressive strength, flexural strength, splitting tensile strength, and elastic modulus. Algorithms including Backpropagation Neural Network (BPNN), Extreme Gradient Boosting (XGB), and Random Forest Regression (RFR), as well as their hybrid variants optimized by Sparrow Search Algorithm (SSA), have been utilized. The models exhibit high accuracy and reliability, as assessed by various performance indicators. SHapley Additive explanations (SHAP) values are employed to interpret models by quantifying the contribution of input features and clarifying the relationships between inputs and predicted outcomes. Machine learning (ML) serves as a transformative instrument in concrete technology, facilitating precise predictions of mechanical properties. Chou et al.⁸ utilized artificial neural networks (ANNs) and support vector machines (SVMs) to predict the compressive strength of concrete incorporating industrial byproducts, demonstrating high accuracy and highlighting the significance of dataset quality and feature selection. Chopra et al.⁹ employed artificial neural networks and genetic programming to predict the compressive strength of concrete, demonstrating the effectiveness of machine learning models in managing complex datasets.

Li et al.¹⁰ utilized artificial neural networks to forecast the compressive strength of ultra-high-performance concrete, considering mixture proportions and curing conditions, and attained a coefficient of determination (R²) of 0.91. The study emphasized that as the mass percentage of coarse aggregates in UHPC-CA grew from 0 to 60%, CS climbed and then decreased. When coarse aggregate percentage reached 23%, CS peaked. UHPC-CA FS did not change from 0 to 30% mass fraction of coarse aggregate, although it did fall sharply with CA. Thus, 23% is the optimal UHPC-CA mass fraction. Zhang et al.¹¹ employed gradient boosting algorithms to model the tensile strength of UHPC, illustrating the advantages of ensemble learning techniques compared to traditional regression methods. The studies demonstrate the capability of machine learning to accurately predict the complex mechanical properties of ultra-high-performance concrete. The integration of industrial byproducts into ultra-high-performance concrete (UHPC) has been thoroughly examined for its environmental and mechanical advantages. Wang et al.¹² created a random forest model to forecast the compressive strength of UHPC incorporating fly ash and silica fume, attaining a R² value of 0.94. The study highlighted the significance of feature engineering, especially the incorporation of chemical composition data, in enhancing model accuracy. Li et al.¹³ employed a hybrid machine learning approach that integrates artificial neural networks and genetic algorithms to optimize the mixture proportions of ultra-high-performance concrete (UHPC) incorporating slag and rice husk ash. This study illustrates the capability of machine learning to inform experimental design and minimize the reliance on extensive trial-and-error testing. Recent studies have investigated the application of machine learning to predict the properties of ultra-high-performance concrete mixed with industrial byproducts. Alabduljabbar et al.¹⁴ examined the application of artificial neural networks (ANNs) for predicting the compressive strength of ultra-high-performance concrete (UHPC) incorporating fly ash and silica fume, resulting in a R² value of 0.92. Their research emphasized the significance of curing temperature and duration as critical input variables. Yuan et al.¹⁵ employed support vector machines to forecast the flexural strength of ultra-high-performance concrete incorporating ground granulated blast-furnace slag and rice husk ash, resulting in a R² value of 0.91. This research illustrates the capability of machine learning to model intricate mechanical properties. Li et al.¹⁶ utilized a genetic algorithm in conjunction with artificial neural networks to optimize the mixture proportions of ultra-high-performance concrete (UHPC) incorporating fly ash and slag, resulting in a 15% enhancement in compressive strength relative to conventional methods. Zhang et al.¹⁷ Employed random forests to predict the modulus of elasticity of UHPC incorporating industrial byproducts, resulting in a R² value of 0.93. The study emphasized the significance of incorporating curing conditions and material properties as input variables. Kumaret al.¹⁸ employed gradient boosting machines (GBMs) to forecast the durability characteristics of ultra-high-performance concrete (UHPC) incorporating fly ash and silica fume, resulting in high accuracy in predicting chloride ion penetration and carbonation depth. Rabadia and Aslani¹⁹ utilized machine learning to forecast the shrinkage and creep behavior of ultra-high-performance concrete (UHPC) incorporating fly ash and slag, demonstrating significant accuracy in predicting long-term deformation. Yan et al.²⁰ used volume fraction of steel fibers (0%, 0.5%, 1%, 1.5%, 2%) to design and pour four recycled steel fiber concrete beams. The maximal bending bearing capacity was 1.5% steel fiber, 54.72% more than the NCB. The load value for tensile steel bars to yield increases with steel fiber content, peaking at 1.5%, increasing bending bearing capacity by 44.64% compared to the NCB. Various literatures have been explored related to the present work, which studies the mechanical properties of ultra-high-performance concrete mixed with industrial byproducts. Further in the present research work, the application of advanced machine learning techniques such as the Semi-supervised classifier (Kstar), M5 classifier (M5Rules), Elastic net classifier (ElasticNet), Correlated Nystrom Views (XNV), and Decision Table (DT) has been explored to predict Fc, Ff, Slump, and Porosity of the studied concrete.

Justification for the selected machine learning techniques

The selection of multiple machine learning models, namely Kstar, M5Rules, ElasticNet, Extreme Gradient Boosting with Nonlinear Variables (XNV), and Decision Table, in this study is strategically grounded in the objective of capturing the complex and nonlinear interactions among the diverse input features influencing the mechanical properties of ultra-high performance concrete (UHPC) mixed with industrial byproducts. These byproducts—ranging from fly ash and silica fume to ground granulated blast-furnace slag—introduce substantial variability in material behavior, demanding a robust predictive framework capable of handling heterogeneity, high-dimensional data, and nonlinear dependencies. Kstar, a lazy learner based on instance-based reasoning, was chosen for its effectiveness in modeling nonlinear relationships without assuming a fixed form for the data distribution, which is particularly valuable in materials science problems characterized by limited but highly variable datasets. M5Rules, which combines decision tree learning with linear regression models, offers interpretability along with flexibility, providing clear rule-based insights into which combinations of variables most influence the mechanical strength of UHPC. This is crucial for bridging the gap between black-box predictions and engineering understanding. ElasticNet regression, a regularized linear model that integrates both L1 and L2 penalties, is particularly suitable for datasets with multicollinearity, which is often present when dealing with highly correlated mix design parameters. Its inclusion serves as a benchmark to assess whether simpler linear relationships can adequately explain the observed material behaviors. XNV, a hybrid ensemble method that incorporates gradient boosting and nonlinear feature transformations, was selected for its high predictive performance and capacity to uncover complex, high-order feature interactions. Given the experimental nature of the data and the inherent uncertainty in byproduct composition and reactivity, XNV helps ensure that the predictive model can generalize well beyond the training set. Finally, the Decision Table model provides a transparent, rule-based approach that complements more complex models by highlighting straightforward decision boundaries within the data. Its inclusion supports the goal of interpretability, which is essential for practical implementation in civil engineering applications where trust in model outputs is vital. Together, these models form a complementary suite designed to balance accuracy, interpretability, and generalizability, ensuring that the developed machine learning framework is both scientifically rigorous and practically relevant. The diverse algorithmic strategies embedded in this selection enable a comprehensive evaluation of the underlying data structure and offer robust predictions for engineering decision-making in the context of sustainable UHPC development.

Research gap and innovation statement

Despite significant advancements in utilizing industrial byproducts and machine learning techniques for optimizing ultra-high-performance concrete (UHPC) mix designs, existing studies predominantly focus on single or limited mechanical properties, such as compressive strength or flexural strength, without holistically considering slump and porosity. While machine learning (ML) has been successfully employed for predictive modeling, most prior research has relied on conventional algorithms such as artificial neural networks (ANNs), support vector machines (SVMs), and gradient boosting techniques, often neglecting newer and more sophisticated hybrid models that can improve prediction accuracy and interpretability. Additionally, the synergistic effects of multiple supplementary cementitious materials (SCMs) and recycled aggregates on the comprehensive performance of UHPC remain underexplored. Existing models often overlook the interactions between curing conditions, chemical compositions, and material properties, limiting their generalizability to diverse UHPC formulations. This research addresses these gaps by integrating advanced machine learning classifiers, including the Semi-supervised classifier (Kstar), M5 classifier (M5Rules), Elastic Net classifier (ElasticNet), Correlated Nystrom Views (XNV), and Decision Table (DT), to predict not only compressive and flexural strength but also slump and porosity—key properties influencing workability and durability. By leveraging these novel algorithms, this study aims to enhance prediction accuracy, computational efficiency, and model interpretability compared to traditional approaches. Furthermore, the incorporation of recycled aggregates and multiple SCMs is systematically analyzed to optimize UHPC mix designs for sustainable construction. The study also employs sensitivity analysis techniques, such as SHapley Additive explanations (SHAP), to identify the most influential parameters affecting UHPC performance. This innovative approach bridges the gap between experimental material science and computational modeling, facilitating data-driven mix design optimization and contributing to more sustainable and resilient concrete solutions.

Novelty

While it is acknowledged that machine learning (ML) has been previously employed to predict mechanical properties of ultra-high-performance concrete (UHPC), the present research advances the field in several important and original ways. First, unlike prior studies that typically focus on a single mechanical property, such as compressive strength, our research develops predictive frameworks for multiple interrelated properties—compressive strength, flexural strength, slump, and porosity—simultaneously. This comprehensive modeling approach provides a holistic understanding of UHPC performance, which is essential for practical applications in structural engineering and material optimization. Second, the present study incorporates a wider variety of industrial byproducts and supplementary cementitious materials (SCMs) within the UHPC matrix than commonly addressed in earlier works. This creates a complex and realistic materials dataset that better reflects sustainable construction practices. The inclusion of such a broad array of inputs, and the associated modeling of their nonlinear and synergistic effects, represents a significant extension of existing methodologies. Third, while machine learning models such as ANNs, SVMs, and Random Forests are commonly reported in literature, this study investigates the performance of less conventional yet powerful algorithms such as Kstar, M5Rules, and Decision Table, along with robust comparative modeling using ElasticNet and XNV. The Kstar model, in particular, has demonstrated exceptional predictive performance, outperforming many of the traditional ML models commonly used in UHPC prediction tasks. The use of instance-based learning models in this context is relatively unexplored, and our results show that these models provide higher accuracy and better generalization on independent test data. Furthermore, we employed both SHAP and Hoffman & Gardener sensitivity analysis methods to interpret and validate the models, offering deeper insights into feature importance and the material science behind UHPC behavior. This dual-method interpretability framework allows us to move beyond prediction and into meaningful material optimization, aligning model results with physical understanding and application. In summary, the novelty of our study lies not only in the application of alternative, underutilized ML models that achieve superior predictive accuracy but also in the integrated modeling of multiple performance metrics, the inclusion of diverse sustainable materials, and the interpretive depth provided by advanced feature attribution techniques. The models developed in this study provide more accurate and generalizable predictions than many existing approaches, offering a more sustainable and data-driven strategy for optimizing material use in UHPC production to achieve enhanced mechanical performance.

Methodology

Collected database

This research project adopted data gathering method from previous literatures and representative databases were collected²¹. In the previous research work, twenty-one parameters such as (i) the cement content (kg/m3), (ii) cement type and strength class, (iii) cement compressive strength (MPa), (iv) fine aggregates content (kg/m3), (v) coarse aggregates content (kg/m3), (vi) fly ash content (kg/m3), (vii) slag content (kg/m3), (viii) silica fume content (kg/m3), (ix) limestone powder content (kg/m3), (x) nano silica content (kg/m3), (xi) quartz powder content (kg/m3), (xii) super-plasticizer content (kg/m3), (xiii) the maximum size of aggregates (mm), (xiv) water content (kg/m3), (xv) polystyrene fiber content (%), (xvi) steel fiber content (%), (xvii) polystyrene fiber length (mm), (xviii) steel fiber length (mm), (xix) polystyrene fiber diameter (mm), (xx) steel fiber diameter (mm), and (xxi) time of curing (days) were reported. But in the present research paper, a dimensional preprocessing has been used to reduce the number of input parameter to sixteen as shown the statistical analysis tables. The collected 380, 146, 152, and 108 records corresponding to the compressive strength (Fc), flexural strength (Ff), Slump, and Porosity of the studied concretes were partitioned into training set (280 records = 75%) and validation set (100 records = 25%), training set (110 records = 75%) and validation set (36 records = 25%), training set (112 records = 75%) and validation set (40 records = 25%), and training set (80 records = 75%) and validation set (28 records = 25%). The partitioning pattern had been followed for optimal model performance recommended in a published literature²². The appendix includes the complete dataset, while Tables 1, 2, 3 and 4 summarize their statistical characteristics. Finally, Figs. 2, 3, 4 and 5 show the Violin expression of the mechanical properties of the studied concrete while Figs. 6, 7, 8 and 9 show the Pearson correlation matrix, histograms, and the relations between variables. Expressively, the correlation distribution charts for Fc (compressive strength), Ff (flexural strength), Slump, and Porosity illustrate the relationships between different variables in the dataset. The heatmaps with correlation coefficients indicate the strength and direction of these relationships, with positive values showing direct correlations and negative values showing inverse correlations. For Fc, the chart shows strong negative correlations with Slag/Binder (Slg/B) and Silica Fume/Binder (SF/B), meaning higher proportions of these materials reduce compressive strength. Conversely, Water/Binder (W/B) and Plasticizer/Binder (PL/B) show a moderate to strong positive correlation, suggesting that their presence influences Fc positively. Other industrial byproducts such as Fly Ash/Binder (FA/B) and Metakaolin/Binder (MK/B) show mixed influences on Fc. For Ff, the correlation chart indicates that Slag/Binder (Slg/B) has a strong negative correlation, suggesting that higher slag content reduces flexural strength. Plasticizer/Binder (PL/B) and Water/Binder (W/B) exhibit positive correlations, meaning they contribute positively to flexural strength. Steel Fiber (SFib) shows one of the strongest correlations with Ff, highlighting the role of fiber reinforcement in enhancing flexural performance. For Slump, the correlation chart reveals that Water/Binder (W/B) and Plasticizer/Binder (PL/B) have the highest positive correlations, which is expected as they directly influence the flowability of the concrete mix. On the other hand, Slag/Binder (Slg/B) and Silica Fume/Binder (SF/B) exhibit negative correlations, indicating that their higher proportions reduce workability. The presence of steel fibers (SFib) and other reinforcements also negatively affects slump due to their restrictive effects on flow. For Porosity, the analysis indicates that Water/Binder (W/B) has a strong positive correlation, meaning higher water content leads to increased porosity. Silica Fume/Binder (SF/B) and Slag/Binder (Slg/B) show strong negative correlations, implying that they reduce porosity by refining the microstructure. Additionally, Plasticizer/Binder (PL/B) exhibits a moderate positive correlation with porosity, suggesting that excessive plasticizer usage could contribute to void formation. Overall, the correlation distribution and interpretation charts demonstrate the interdependencies of materials in UHPC mixes and highlight the influence of industrial byproducts on key performance parameters. The observed relationships help optimize the mix design for achieving specific mechanical and durability properties.

Table 1.

Statistical analysis of collected databases w.r.t Fc.

Item	Unit	Training set					Validation set
		Max	Min	Avg	SD	Var	Max	Min	Avg	SD	Var
C/B	–	1.00	0.28	0.75	0.13	0.18	0.98	0.17	0.76	0.14	0.18
Cfc	MPa	52.50	42.50	48.68	4.85	0.10	52.50	42.50	49.27	4.68	0.09
FA/B	–	0.50	0.00	0.05	0.11	2.27	0.50	0.00	0.05	0.11	2.19
Slg/B	–	0.52	0.00	0.03	0.09	3.19	0.70	0.00	0.03	0.11	3.58
SF/B	–	0.33	0.00	0.16	0.08	0.51	0.29	0.00	0.15	0.08	0.53
MK/B	–	0.29	0.00	0.01	0.04	3.68	0.20	0.00	0.00	0.02	7.06
NS/B	–	0.06	0.00	0.00	0.01	3.30	0.17	0.00	0.01	0.02	3.60
LS/B	–	1.09	0.00	0.02	0.10	4.95	0.48	0.00	0.02	0.07	4.69
QP/B	–	0.79	0.00	0.08	0.13	1.65	0.46	0.00	0.07	0.12	1.57
S/B	–	2.07	0.00	1.03	0.41	0.39	2.01	0.00	0.97	0.46	0.47
CAgS	mm	5.00	0.08	2.28	1.77	0.78	5.00	0.10	2.09	1.80	0.86
W/B	–	0.29	0.10	0.19	0.03	0.15	0.28	0.12	0.19	0.03	0.14
PL/B	–	0.24	0.00	0.03	0.02	0.82	0.06	0.00	0.03	0.01	0.51
SFib	%	6.56	0.00	0.99	1.36	1.37	6.00	0.00	1.22	1.62	1.33
FibAsp	–	400.00	0.00	33.52	39.77	1.19	400.00	0.00	49.87	79.16	1.59
Size	mm	100.00	40.00	48.53	16.58	0.34	110.00	40.00	50.07	18.16	0.36
FC	MPa	217.00	58.22	136.92	32.51	0.24	211.69	57.01	145.14	33.16	0.23

Table 2.

Statistical analysis of collected databases w.r.t Ff.

Item	Unit	Training set					Validation set
		Max	Min	Avg	SD	Var	Max	Min	Avg	SD	Var
C/B	–	1.00	0.30	0.72	0.17	0.24	0.91	0.40	0.75	0.14	0.19
Cfc	MPa	52.50	42.50	48.05	4.97	0.10	52.50	42.50	47.50	5.00	0.11
FA/B	–	0.45	0.00	0.09	0.13	1.51	0	0.00	0	0.11	1.85
Slg/B	–	0.45	0.00	0.05	0.11	2.35	0.30	0.00	0	0.08	2.87
SF/B	–	0.25	0.00	0.12	0.09	0.79	0.25	0.00	0	0.09	0.67
MK/B	–	0.21	0.00	0.02	0.05	2.40	0.29	0.00	0	0.06	2.79
NS/B	–	0.06	0.00	0.01	0.01	2.43	0.06	0.00	0.01	0.02	2.04
LS/B	–	0.43	0.00	0.02	0.09	4.58	0.43	0.00	0.01	0.07	5.92
QP/B	–	2.07	0.79	1.16	0.31	0.27	2	0.80	1	0.27	0.22
S/B	–	5.00	0.10	1.76	1.03	0.58	5.00	0.10	2	1.11	0.65
CAgS	mm	0.32	0.00	0.02	0.08	3.20	0.32	0.00	0	0.09	2.52
W/B	–	0.29	0.14	0.19	0.03	0.17	0.29	0.15	0	0.03	0.16
PL/B	–	0.07	0.01	0.03	0.01	0.53	0	0.01	0.03	0.02	0.58
SFib	%	3.00	0.00	1.20	1.04	0.87	4.00	0.00	1	1.09	1.07
FibAsp	–	81.25	0.00	38.10	33.19	0.87	81.25	0.00	32	33.98	1.06
Len	mm	400	100	176	59	0.34	400	160.00	177	52.59	0.30
Ff	MPa	39.40	7.73	24.29	7.63	0.31	41.93	12.07	24.19	7.54	0.31

Table 3.

Statistical analysis of collected databases w.r.t Slump.

Item	Unit	Training set					Validation set
		Max	Min	Avg	SD	Var	Max	Min	Avg	SD	Var
C/B	–	0.91	0.28	0.71	0.16	0.23	0.83	0.40	0.69	0.12	0.17
Cfc	MPa	52.50	42.50	50.36	4.10	0.08	52.50	42.50	50.00	4.33	0.09
FA/B	–	0.45	0.00	0.04	0.09	2.48	0.27	0.00	0.03	0.07	2.48
Slg/B	–	0.52	0.00	0.07	0.14	2.20	0.40	0.00	0.06	0.12	2.10
SF/B	–	0.31	0.00	0.17	0.08	0.48	0.33	0.00	0.21	0.07	0.35
MK/B	–	0.21	0.00	0.01	0.03	5.08	0.29	0.00	0.01	0.04	5.91
NS/B	–	0.06	0.00	0.01	0.02	2.46	0.02	0.00	0.00	0.00	3.09
LS/B	–	1.09	0.00	0.03	0.13	4.04	0.43	0.00	0.02	0.08	3.64
QP/B	–	1.63	0.26	1.10	0.23	0.21	1.46	0.72	1.01	0.16	0.15
S/B	–	2.36	0.11	1.07	0.76	0.71	2.36	0.11	0.99	0.68	0.68
CAgS	mm	0.38	0.00	0.10	0.13	1.29	0.34	0.00	0.14	0.12	0.89
W/B	–	0.28	0.13	0.19	0.03	0.15	0.29	0.16	0.19	0.02	0.12
PL/B	–	0.06	0.00	0.02	0.01	0.53	0.04	0.01	0.02	0.01	0.24
SFib	%	3.00	0.00	1.03	1.01	0.98	3.00	0.00	0.93	1.01	1.09
FibAsp	–	80.00	0.00	33.51	32.53	0.97	74.29	0.00	31.27	31.86	1.02

Table 4.

Statistical analysis of collected databases w.r.t Porosity.

Item	Unit	Training set					Validation set
		Max	Min	Avg	SD	Var	Max	Min	Avg	SD	Var
C/B	–	1.00	0.35	0.88	0.11	0.13	1.00	0.17	1	0	0.19
Cfc	MPa	52.50	42.50	51.88	2.42	0.05	52.50	42.50	52.14	1.86	0.04
FA/B	–	0.30	0.00	0.01	0.04	5.52	0.30	0.00	0.02	0.08	3.61
Slg/B	–	0.52	0.00	0.03	0.09	3.54	0.70	0.00	0.03	0.13	4.07
SF/B	–	0.21	0.00	0.06	0.07	1.17	0.19	0.00	0.03	0.05	1.49
MK/B	–	0.21	0.00	0.01	0.03	3.69	0.29	0.00	0.01	0.05	5.20
NS/B	–	0.06	0.00	0.02	0.02	1.12	0.06	0.00	0	0	0.91
LS/B	–	3.56	0.00	0.29	0.47	1.59	0.60	0.00	0.26	0.21	0.80
QP/B	–	3.71	0.26	1.46	0.66	0.45	2.90	0.00	1.56	0.63	0.40
S/B	–	16.00	0.50	3.11	4.34	1.39	16.00	0.60	2.24	2.71	1.21
CAgS	mm	0.40	0.00	0.05	0.11	2.23	0.40	0.00	0	0	2.10
W/B	–	0.90	0.13	0.27	0.10	0.38	0.40	0.15	0.28	0.06	0.23
PL/B	–	0.10	0.01	0.05	0.03	0.50	0.10	0.02	0.06	0.02	0.39
SFib	%	8	0.00	1.25	2	1	8	0.00	1	2	1.63
FibAsp	–	72.22	0.00	32.44	29.99	0.92	72.22	0.00	32.79	29.28	0.89
Porosity	%	17.52	2.35	10.75	4.75	0.44	17.66	2.92	12.77	4.11	0.32

Fig. 2.

Violin distribution for each input w.r.t Fc.

Fig. 3.

Violin distribution for each input w.r.t Ff.

Fig. 4.

Violin distribution for each input w.r.t Slump.

Fig. 5.

Violin distribution for each input w.r.t Porosity.

Fig. 6.

Correlation, distribution and interpreting chart w.r.t Fc.

Fig. 7.

Correlation, distribution and interpreting chart w.r.t Ff.

Fig. 8.

Correlation, distribution and interpreting chart w.r.t Slump.

Fig. 9.

Correlation, distribution and interpreting chart w.r.t Porosity.

Research program

Five (5) different ML techniques were used to predict compressive strength (Fc), flexural strength (Ff), Slump, and Porosity using the collected database. These techniques are “Semi-supervised classifier (Kstar)”, “M5 classifier (M5Rules), “Elastic net classifier (ElasticNet), “Correlated Nystrom Views (XNV)”, and “Decision Table (DT)”. All models were created using “Weka Data Mining” software version 3.8.6. The following section discusses the results of each model. The performances of developed models were evaluated by comparing sum of squared error (SSE), mean absolute error (MAE), mean squared error (MSE), root mean squared error (RMSE), Error (%), Accuracy (%), coefficient of determination (R²), coefficient of correlation (R), weighted index (WI), Nash–Sutcliffe Efficiency (NSE), Kling-Gupta Efficiency (KGE) and symmetric mean absolute percentage error (SMAPE) between predicted and calculated mechanical characteristic parameter values. The mathematical expression of each used measurement is presented in Eqs. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 and 11.

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Theoretical framework of advanced machine learning methods

Semi-supervised classifier (Kstar)

The Kstar (K*) algorithm is an instance-based learner that utilizes an entropy-based distance function for classification. Unlike traditional k-nearest neighbor (KNN) algorithms, KStar applies a probabilistic approach to determine the similarity between instances, making it robust in handling noise and missing values. In a semi-supervised setting, KStar leverages both labeled and unlabeled data to enhance classification performance. By estimating class probabilities based on transformations between instances, it can generalize well even with limited labeled data. The entropy-based distance measure in KStar differentiates it from other instance-based learners by considering the probability of transforming one instance into another through a series of simple operations. This transformation probability forms the basis for classification, as the algorithm assigns labels based on the most probable class among similar instances. In a semi-supervised context, Kstar benefits from unlabeled data by refining these probability distributions, leading to more accurate classification boundaries. One of the key advantages of Kstar in semi-supervised learning is its ability to adapt to complex and nonlinear data distributions without requiring extensive parameter tuning. The algorithm effectively captures local variations within the data and remains resilient to overfitting. Its probabilistic framework ensures smooth transitions between classes, making it particularly useful for datasets with ambiguous or overlapping class regions. Despite its advantages, Kstar has limitations, particularly in terms of computational efficiency when dealing with large datasets. Since it relies on an instance-based approach, storing and processing a large number of training examples can be memory-intensive. Additionally, the choice of transformation functions plays a crucial role in determining classification accuracy, requiring careful consideration in practical implementations. Overall, KStar serves as a powerful semi-supervised classification method by utilizing entropy-based distance metrics to improve classification accuracy with limited labeled data. Its ability to handle noisy and missing values, combined with its flexible probabilistic framework, makes it a valuable tool for machine learning applications where labeled data is scarce but additional unlabeled data is available for learning.

The transformation probability P(x → y) is defined as the probability of transforming instance x to y. The computation involves all possible transformations.

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where Pt represents the probability of each transformation step. The distance between two instances x and y is given by:

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The class of the nearest neighbors is used for classification. The most probable class is determined using:

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where wi is the weight of neighbor xi and P(xi → x)is the probability of transformation.

M5 classifier (M5Rules)

The M5Rules classifier is a rule-based machine learning algorithm that derives its rules from the M5 model tree. It combines the strengths of decision trees and linear regression models, making it particularly effective for regression and classification tasks. The M5Rules algorithm generates a set of rules from a decision tree, where each rule represents a path from the root to a leaf, and then applies linear regression at the leaf nodes to make predictions. This hybrid approach allows M5Rules to balance interpretability and predictive accuracy. M5Rules operates by first constructing an M5 model tree, a variant of a decision tree designed for numerical prediction. The tree is then transformed into a set of rules by extracting paths that lead to different outcomes. These rules are pruned and optimized to improve generalization, reducing overfitting while maintaining the model’s predictive power. Unlike traditional rule-based classifiers, M5Rules incorporates linear regression at the terminal nodes, which helps improve the model’s ability to handle continuous variables and complex relationships within the data. One of the key advantages of M5Rules is its interpretability. The rules generated by the algorithm are easily understandable and provide insight into the relationships between variables. This makes it a useful tool in domains where transparency and explainability are important, such as finance, healthcare, and engineering. Additionally, the integration of linear regression ensures that the model captures linear dependencies within the data, enhancing predictive accuracy compared to pure decision tree methods. Despite its strengths, M5Rules has limitations. The rule extraction process can sometimes result in an excessive number of rules, making the model complex and harder to interpret. Additionally, while linear regression improves accuracy for continuous variables, it may not always capture highly nonlinear relationships effectively. The performance of M5Rules is also sensitive to the quality of the training data, requiring careful preprocessing and feature selection. Overall, M5Rules is a powerful rule-based classification and regression algorithm that blends decision trees with linear regression to achieve a balance between interpretability and predictive performance. Its ability to extract meaningful rules while leveraging linear regression for accurate numerical predictions makes it a valuable tool for data-driven decision-making in various domains. Each leaf node uses a regression equation:

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where β₀ is the intercept, βi are the coefficients, and xi are the input features. The decision tree splits are determined by minimizing the variance in the target variable y:

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Elastic net classifier (ElasticNet)

The Elastic Net classifier is a regularized regression-based machine learning model that combines the advantages of both Lasso (L1) and Ridge (L2) regularization techniques. It is particularly effective when dealing with high-dimensional datasets, where multicollinearity among features is present. Elastic Net enhances the stability and interpretability of the model by incorporating both types of regularization, allowing it to perform feature selection while maintaining the benefits of ridge regression in handling correlated predictors. Elastic Net works by introducing two hyperparameters, α and λ, that control the balance between L1 and L2 regularization. The L1 component encourages sparsity by forcing some feature coefficients to be exactly zero, effectively selecting a subset of important features, while the L2 component prevents overfitting by distributing weight across correlated variables. This dual-regularization approach makes Elastic Net highly suitable for scenarios where traditional regression models struggle due to high variance or irrelevant features. One of the key advantages of the Elastic Net classifier is its ability to handle situations where the number of features exceeds the number of observations, making it ideal for genetics, finance, and text classification problems. It mitigates the instability issues of Lasso when dealing with highly correlated variables by allowing grouped selection rather than arbitrarily choosing one variable over another. This results in a more stable and interpretable model. However, Elastic Net also has limitations. The model’s performance is highly dependent on proper tuning of its hyperparameters, requiring cross-validation to determine the optimal values of α and λ. Additionally, while it improves feature selection, it does not inherently capture complex nonlinear relationships within data as effectively as tree-based or deep learning models. Overall, the Elastic Net classifier is a powerful and flexible tool that balances feature selection and regularization, making it well-suited for high-dimensional datasets. Its ability to prevent overfitting while retaining important variables ensures robustness, making it an excellent choice for predictive modeling tasks where interpretability and generalization are crucial. It is particularly useful when features are correlated.

Objective Function:

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. . : Regularization parameter. : Mixing parameter (0 . Elastic Net uses coordinate descent to optimize the coefficients β.

Correlated Nystrom views (XNV)

Correlated Nyström Views (XNV) is a machine learning technique that extends the Nyström method for efficient kernel approximation while leveraging correlations between multiple views of data. It is particularly useful in scenarios where data comes from multiple sources or modalities, such as text and images, or when dealing with heterogeneous feature representations. XNV enhances traditional kernel learning by incorporating the dependencies among different views, improving computational efficiency and predictive performance. The Nyström method approximates large kernel matrices by sampling a subset of data points, reducing the computational cost of kernel-based learning. However, in multi-view learning settings, standard Nyström approaches treat each view independently, potentially losing valuable shared structure across views. XNV addresses this limitation by exploiting correlations between the different feature spaces, allowing for a more accurate and scalable approximation of the kernel matrix. One of the main advantages of XNV is its ability to handle large-scale datasets with high-dimensional features efficiently. By leveraging correlated structures, it improves the representation of complex relationships between different data views, leading to better generalization in supervised and semi-supervised learning tasks. This makes XNV particularly valuable for applications such as image-text retrieval, multi-modal sentiment analysis, and bioinformatics. Despite its strengths, XNV has some challenges. The effectiveness of the method depends on the quality of the correlation modeling between views, requiring careful selection of the kernel function and tuning of hyperparameters. Additionally, while it reduces computational complexity compared to full kernel learning, it still requires significant resources for large datasets, particularly when the number of views increases. Overall, Correlated Nyström Views provides an efficient and scalable approach to kernel approximation in multi-view learning settings. By integrating cross-view dependencies, it enhances the performance of kernel-based methods, making it an effective solution for tasks that involve diverse and complementary data sources. Using linked embeddings, it integrates several data views (such as feature sets). Nystrom Approximation for Kernel Matrix K:

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C: Submatrix of K (columns corresponding to sampled points). W: Submatrix of K (intersection of rows and columns of sampled points). Pseudoinverse of W. Correlated Nystrom Views combines the embeddings from different views using a correlation matrix R:

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: Embedding from the ith view, R: Correlation matrix learned during training. The embeddings Z are fed into a classifier (e.g., SVM or logistic regression).

Decision table (DT)

Decision Table (DT) is a rule-based classification model that represents knowledge in the form of decision rules derived from training data. It consists of a table where each row corresponds to a unique combination of attribute values, known as conditions, and the associated decision or class label. DT is particularly useful for handling categorical data and is often employed in rule-based machine learning approaches. The model works by mapping input feature values to corresponding class labels using a predefined set of rules. Each rule defines a specific condition under which a particular class is assigned. The simplicity of DT makes it an interpretable and transparent method, allowing users to easily understand and analyze the decision-making process. Unlike complex black-box models, DT provides a structured and systematic way to represent knowledge, making it useful in domains where explainability is crucial, such as medical diagnosis, business decision-making, and credit risk assessment. One of the main strengths of DT is its efficiency in rule extraction and application, making it computationally less expensive than many other machine learning algorithms. Since the decision-making process involves simple table lookups, classification is fast and requires minimal computation. Additionally, the model performs well when dealing with small to medium-sized datasets, especially when the relationships between attributes and class labels are well-defined. However, DT has limitations, particularly when handling large datasets with continuous features. Discretization of numerical attributes is often required, which can lead to information loss. Moreover, the model struggles when faced with noisy or missing data, as it relies on exact matching of conditions. If training data is insufficient or does not cover all possible attribute combinations, DT may fail to generalize well to new instances. To enhance its performance, DT can be combined with other machine learning techniques, such as decision trees, ensemble methods, or hybrid models that incorporate statistical or probabilistic approaches. Despite its limitations, DT remains a valuable tool for rule-based classification, offering interpretability and ease of implementation, particularly in domains requiring clear and structured decision-making. A decision table is a basic rule-based classifier that uses a table with actions (class labels) and conditions (attributes) to represent knowledge⁵. Each row in the decision table corresponds to a rule: If and and … then Class = c. When multiple rows match, the class is determined by majority voting:

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where is the indicator function.

Sensitivity analysis

SHAP (SHapley Additive exPlanations) and Hoffman & Gardener’s sensitivity analysis are two widely used techniques for understanding the influence of input variables on model predictions, particularly in material science and engineering applications. SHAP, rooted in cooperative game theory, assigns each feature an importance value by distributing contributions fairly among input variables, providing both global and local interpretability. This method effectively highlights how individual factors impact predictions, making it a powerful tool for identifying key variables in complex datasets. In contrast, Hoffman & Gardener’s sensitivity analysis evaluates the relative influence of each input parameter by systematically varying them and observing the corresponding changes in output. This approach helps quantify the sensitivity of different variables, making it useful for assessing model robustness and ensuring reliable predictions. By combining these two methods, researchers gain deeper insights into the relationships between variables and their effects on ultra-high-performance concrete (UHPC) properties, ultimately leading to more precise modeling and optimization of UHPC incorporating industrial byproducts. A preliminary sensitivity analysis was carried out on the collected database to estimate the impact of each input on the (Y) values. “Single variable per time” technique is used to determine the “Sensitivity Index” (SI) for each input using Hoffman & Gardener’s formula²³ as follows:

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Presentation and analysis of results

Kstar models

The hyperparameter tuning for the Kstar model is presented in Fig. 10. The relationship plots presented in Fig. 11 between the measured and predicted values of the Kstar model for compressive strength (Fc), flexural strength (Ff), workability (Slump), and porosity illustrate the high predictive accuracy of the model. For compressive strength (Fc) in plot (a), the predicted values align closely with the measured values along the 1:1 reference line, indicating minimal deviation. The high coefficient of determination (R² = 0.98) and low root mean square error (RMSE = 3.59 MPa for training and 4.28 MPa for validation) confirm the model’s ability to accurately predict Fc. The nearly linear trend in the plot suggests a strong correlation, with only minor deviations at higher strength values. In plot (b), representing flexural strength (Ff), the measured and predicted values also exhibit a strong correlation, with an almost perfect alignment along the reference line. The model achieves an exceptional R² of 1.00 in validation, indicating near-perfect prediction accuracy. The RMSE values of 0.77 MPa (training) and 0.34 MPa (validation) further support the model’s robustness. The absence of significant scatter in the plot confirms that the model successfully captures the relationships governing Ff. For workability (Slump) in plot (c), the relationship plot again shows a tight clustering of points around the reference line, demonstrating strong predictive accuracy. The training and validation R² values of 0.94 and 0.98, respectively, highlight the model’s effectiveness. The RMSE values of 13.66 mm (training) and 7.59 mm (validation) suggest that the model performs exceptionally well in predicting Slump flow behavior. The minor dispersion in the plot at higher slump values may indicate slight underestimation in extreme cases, but overall, the predictive accuracy remains high. Plot (d), representing porosity, exhibits the strongest agreement between predicted and measured values, with the model achieving an R² of 1.00 in both training and validation. The RMSE values of 0.12 and 0.14 further reinforce the model’s near-perfect accuracy. The data points align exactly with the reference line, confirming that the model captures the porosity behavior with minimal error. Overall, the relationship plots for the Kstar model across all four parameters confirm its exceptional predictive capability, with minimal deviations from the reference line. The high R² values and low errors in all cases suggest that the model is highly reliable for predicting UHPC properties incorporating industrial byproducts.

Fig. 10.

The considered hyper-parameters of (Kstar) model.

Fig. 11.

Relation between predicted and calculated strengths using (Kstar).

M5Rules models

The hyperparameter tuning for the M5Rules models is presented in Fig. 12, and the rule iteration in Fig. 13. The relationship plots presented in Fig. 14 between the measured and predicted values of the M5Rules model for compressive strength (Fc), flexural strength (Ff), workability (Slump), and porosity indicate moderate to good predictive performance, with noticeable deviations from the ideal 1:1 reference line. For compressive strength (Fc) in plot (a), the predicted values exhibit a scattered distribution around the reference line, reflecting a lower predictive accuracy compared to the Kstar model. The R² values of 0.61 (training) and 0.69 (validation) indicate a moderate correlation between the measured and predicted values. The RMSE values of 17.62 MPa (training) and 18.62 MPa (validation) suggest relatively higher errors, indicating that while the model captures general trends, its accuracy is lower, particularly at higher strength levels where deviations are more prominent. In plot (b), representing flexural strength (Ff), the relationship between measured and predicted values is somewhat improved, with R² values of 0.75 (training) and 0.84 (validation). While the points generally follow the reference line, there is still a noticeable spread, particularly at higher flexural strength values, indicating some level of under-prediction or over-prediction. The RMSE values of 3.31 MPa (training) and 3.33 MPa (validation) suggest a moderate predictive capability, but the spread in the relationship plot confirms that M5Rules does not capture Ff as precisely as the Kstar model. For workability (Slump) in plot (c), the measured and predicted values exhibit significant scatter around the reference line, showing a weaker correlation. The R² values of 0.54 (training) and 0.43 (validation) indicate a relatively lower accuracy, while the RMSE values of 39.20 mm (training) and 37.93 mm (validation) confirm the presence of substantial prediction errors. The relationship plot shows a considerable deviation from the ideal trend, indicating that the M5Rules model struggles with predicting workability accurately, possibly due to the complex nature of slump behavior in UHPC. Plot (d), representing porosity, exhibits a slightly stronger agreement between measured and predicted values compared to Slump, but with some noticeable scatter. The R² values of 0.96 (training) and 0.78 (validation) indicate good but inconsistent performance, with better accuracy in the training phase. The RMSE values of 0.90 (training) and 1.95 (validation) suggest an increase in prediction error in validation, reflecting a decline in generalization capability. The points in the relationship plot tend to deviate from the reference line more significantly in validation, suggesting that the model may be prone to overfitting or struggles with certain variations in porosity data. Overall, the relationship plots for the M5Rules model show moderate predictive performance across all four parameters, with relatively higher errors and noticeable deviations from the ideal reference line. The model performs better for flexural strength and porosity but struggles with compressive strength and slump, indicating that while it captures some general trends, its predictive accuracy is lower compared to Kstar, particularly in handling complex material behavior.

Fig. 12.

The considered hyper-parameters of (M5Rules) model.

Fig. 13.

The rule iterations of the model.

Fig. 14.

Relation between predicted and calculated strengths using (M5Rules).

ElasticNet models

Figure 15 shows the hyperparameter tuning of the ElasticNet models and the model has proposed Eqs. 22, 23, 24 and 25 as closed-form equations. The relationship plots presented in Fig. 16 between the measured and predicted values of the ElasticNet model for compressive strength (Fc), flexural strength (Ff), workability (Slump), and porosity demonstrate relatively weak predictive performance compared to other models, with considerable scatter and deviation from the 1:1 reference line. For compressive strength (Fc) in plot (a), the ElasticNet model shows a weak correlation between measured and predicted values, with R² values of 0.28 (training) and 0.19 (validation). The RMSE values of 24.10 MPa (training) and 30.16 MPa (validation) suggest significant prediction errors, indicating that the model struggles to capture the underlying relationships governing compressive strength in UHPC. The scatter plot exhibits a large spread, particularly at higher strength values, demonstrating that ElasticNet fails to generalize well, leading to underprediction and overprediction across different strength levels. In plot (b), representing flexural strength (Ff), the predictive accuracy remains relatively poor, with R² values of 0.49 (training) and 0.64 (validation). The RMSE values of 4.74 MPa (training) and 4.60 MPa (validation) suggest notable errors, though slightly lower than for compressive strength. The relationship plot reveals significant scatter around the reference line, with ElasticNet exhibiting inconsistent prediction behavior across different strength levels. The spread indicates that the model does not effectively capture the complex interactions influencing flexural strength in UHPC. For workability (Slump) in plot (c), the relationship plot displays substantial deviation from the reference line, reinforcing the weak predictive power of ElasticNet for this parameter. The R² values of 0.32 (training) and 0.13 (validation) indicate poor correlation, with RMSE values of 48.88 mm (training) and 46.95 mm (validation) highlighting considerable prediction errors. The large scatter observed in the relationship plot suggests that ElasticNet fails to capture the variability in slump measurements, potentially due to the nonlinear and complex nature of workability in UHPC mixed with industrial byproducts. Plot (d), representing porosity, exhibits the weakest performance among all parameters, with R² values of 0.38 (training) and 0.47 (validation). The RMSE values of 3.25 (training) and 3.32 (validation) indicate substantial errors, suggesting that the model struggles to accurately predict porosity variations. The relationship plot shows a broad distribution of points around the reference line, confirming that ElasticNet fails to capture the underlying dependencies affecting porosity in UHPC. Overall, the relationship plots for the ElasticNet model reveal weak predictive capabilities for all four parameters. The model consistently exhibits high prediction errors, poor correlation, and significant scatter, indicating that it is not well-suited for modeling the mechanical and rheological properties of UHPC. The inability to effectively capture nonlinear relationships in the dataset suggests that ElasticNet lacks the flexibility required for accurate prediction of UHPC properties when mixed with various industrial byproducts.

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Fig. 15.

The considered hyper-parameters of (ElasticNet) model.

Fig. 16.

Relation between predicted and calculated strengths using (ElasticNet).

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XNV model

Figure 17 shows the hyperparameter tuning of the model technique. The relationship plots presented in Fig. 18 between the measured and predicted values of the XNV models for compressive strength (Fc), flexural strength (Ff), workability (Slump), and porosity demonstrate a moderate to strong predictive performance, with relatively high accuracy compared to ElasticNet and M5Rules but lower than Kstar and Decision Tree models. For compressive strength (Fc) in plot (a), the XNV model exhibits a fairly strong correlation between measured and predicted values, with R² values of 0.69 (training) and 0.70 (validation). The RMSE values of 15.74 MPa (training) and 18.40 MPa (validation) suggest reasonable predictive accuracy, though some deviations from the reference line are noticeable. The scatter plot indicates that most points align well with the 1:1 line, but there are some outliers, particularly at higher compressive strength values, where the model slightly underestimates the actual values. In plot (b), representing flexural strength (Ff), the XNV model shows improved predictive performance compared to Fc, with R² values of 0.78 (training) and 0.92 (validation). The RMSE values of 3.13 MPa (training) and 2.20 MPa (validation) indicate lower prediction errors, demonstrating that the model captures the relationship between measured and predicted values more effectively. The relationship plot shows a tighter clustering of points along the reference line, indicating strong predictive reliability. However, some minor dispersion is observed at higher strength values, where slight underestimation occurs. For workability (Slump) in plot (c), the XNV model provides reasonable predictive accuracy, with R² values of 0.77 (training) and 0.80 (validation). The RMSE values of 27.44 mm (training) and 22.43 mm (validation) indicate moderate prediction errors. The scatter plot shows that most points are closely aligned with the reference line, but there are noticeable deviations at higher slump values. The model tends to perform better for mid-range workability values, while some mispredictions occur at extreme ends, likely due to the complex nature of slump behavior in UHPC. Plot (d), representing porosity, demonstrates strong predictive performance, with R² values of 0.95 (training) and 0.87 (validation). The RMSE values of 0.94 (training) and 1.51 (validation) suggest low prediction errors, indicating a reliable model for porosity estimation. The relationship plot shows a strong alignment of points along the reference line, with minimal scatter, highlighting the effectiveness of XNV in capturing the nonlinear dependencies affecting porosity in UHPC. Overall, the relationship plots for the XNV model show a moderate to strong correlation between measured and predicted values across all four parameters. The model performs well in predicting flexural strength and porosity, with good alignment along the reference line and low prediction errors. However, its performance for compressive strength and slump, while reasonable, shows room for improvement, particularly in capturing higher values where slight underestimation is observed. Despite these minor shortcomings, the XNV model demonstrates better predictive reliability than M5Rules and ElasticNet, making it a viable choice for modeling UHPC properties with industrial byproducts.

Fig. 17.

The considered hyper-parameters of (XNV) model.

Fig. 18.

Relation between predicted and calculated strength using (XNV).

DT models

Figure 19 shows the hyperparameter tuning of the DT model and the tree iterations of the model are shown in Fig. 20. The relationship plots is shown in Fig. 21 between the measured and predicted values of the Decision Tree (DT) models for compressive strength (Fc), flexural strength (Ff), workability (Slump), and porosity indicate strong predictive accuracy across all parameters, with DT models outperforming M5Rules, ElasticNet, and XNV while closely approaching the performance of Kstar. For compressive strength (Fc) in plot (a), the DT model demonstrates strong agreement between measured and predicted values, with R² values of 0.89 (training) and 0.87 (validation). The RMSE values of 9.13 MPa (training) and 12.12 MPa (validation) indicate relatively low prediction errors. The scatter plot shows a tight clustering of points along the reference line, with minimal dispersion. However, a few minor deviations can be observed at higher strength values, where the model slightly underestimates some data points. Overall, the DT model provides a reliable prediction of Fc with minimal overfitting, as reflected in its consistent performance across training and validation datasets. In plot (b), representing flexural strength (Ff), the DT model performs exceptionally well, with R² values of 0.81 (training) and 0.92 (validation), indicating a strong correlation between measured and predicted values. The RMSE values of 2.88 MPa (training) and 2.24 MPa (validation) highlight the model’s accuracy in capturing the variations in flexural strength. The scatter plot shows that most points align closely with the reference line, suggesting minimal errors in prediction. The model maintains high accuracy across the dataset, with only a few scattered points deviating from the trend, likely due to complex material behavior in some instances. For workability (Slump) in plot (c), the DT model provides robust predictive performance, with R² values of 0.78 (training) and 0.91 (validation). The RMSE values of 26.90 mm (training) and 14.59 mm (validation) suggest that the model captures the relationship between input parameters and slump effectively. The scatter plot reveals that most points closely align with the reference line, though some slight deviations appear at extreme values. The overall accuracy is higher than that of M5Rules and ElasticNet, indicating that the DT model can predict slump behavior with high reliability. Plot (d), representing porosity, shows the best predictive performance among the four parameters, with R² values of 0.98 (training) and 0.95 (validation). The RMSE values of 0.54 (training) and 0.91 (validation) indicate very low prediction errors, highlighting the model’s strong predictive capabilities for porosity. The relationship plot exhibits an almost perfect alignment along the reference line, with only minimal scatter. This suggests that the DT model effectively captures the underlying trends and dependencies affecting porosity in UHPC with industrial byproducts. Overall, the DT model demonstrates strong predictive accuracy across all four parameters, with particularly high reliability for flexural strength and porosity. The scatter plots show minimal deviation from the reference line, indicating a strong correlation between measured and predicted values. Compared to other models, DT outperforms M5Rules, ElasticNet, and XNV in terms of both R² and RMSE, closely matching the performance of Kstar. While minor underestimations are observed at higher compressive strength and slump values, the overall consistency and accuracy of the DT model make it a highly effective choice for predicting the properties of ultra-high-performance concrete incorporating industrial byproducts.

Fig. 19.

The considered hyper-parameters of (DT) model.

Fig. 20.

Tree parameters of the studied properties.

Fig. 21.

Relation between predicted and calculated strengths using (DT).

Overall performance and comparison of models

The performance analysis of the models in predicting the compressive strength (Fc) of ultra-high-performance concrete (UHPC) mixed with various industrial byproducts highlights significant variations in accuracy, error rates, and predictive reliability (see Table 5). The Kstar model emerges as the most robust, achieving an exceptionally high accuracy of 97% for both training and validation datasets. It records the lowest errors, with RMSE values of 3.59 MPa in training and 4.28 MPa in validation, alongside strong correlation metrics (R² = 0.98, R = 0.99). These results suggest that Kstar is highly reliable in capturing the complex interactions between mix proportions and UHPC compressive strength. In contrast, the M5Rules model demonstrates moderate performance, with accuracy at 87% for both training and validation datasets. However, it exhibits significantly higher errors, with an RMSE of 17.62 MPa in training and 18.62 MPa in validation. The lower R² values (0.61 in training and 0.69 in validation) indicate that the model struggles to capture the intricate relationships within the dataset. The ElasticNet model performs the weakest, with the highest errors (RMSE = 24.10 MPa in training and 30.16 MPa in validation) and the lowest accuracy (83% in training, dropping to 79% in validation). Its R² values (0.28 in training and 0.19 in validation) indicate poor predictive ability, suggesting that the model is not well-suited for complex UHPC compositions. The XNV model performs slightly better than M5Rules but remains less reliable compared to Kstar. It achieves an accuracy of 89% in training and 87% in validation, with an RMSE of 15.74 MPa and 18.40 MPa, respectively. The model’s R² values (0.69 in training, 0.70 in validation) suggest moderate predictive reliability, though it still exhibits relatively high errors. The Decision Table (DT) model performs well, with an accuracy of 93% in training and 92% in validation. It records lower RMSE values of 9.13 MPa in training and 12.12 MPa in validation compared to M5Rules and XNV, indicating a relatively strong predictive capacity. Its high R² values (0.89 in training, 0.87 in validation) suggest that DT effectively captures the relationships governing UHPC compressive strength. Overall, Kstar is the most accurate and reliable model, offering precise predictions with minimal errors, followed by DT, which provides a balance between computational efficiency and prediction accuracy. XNV and M5Rules demonstrate moderate reliability, whereas ElasticNet is the least effective model for predicting UHPC compressive strength. The performance analysis of models in predicting the flexural strength (Ff) of ultra-high-performance concrete (UHPC) mixed with various industrial byproducts reveals significant differences in accuracy, error rates, and predictive capabilities (see Table 6). The Kstar model demonstrates superior performance, achieving the highest accuracy of 97% in training and an exceptional 99% in validation. It has the lowest RMSE values (0.77 MPa in training and 0.34 MPa in validation), indicating minimal prediction errors. The model’s R² values (0.99 in training and 1.00 in validation) confirm its near-perfect fit, making it the most reliable choice for predicting flexural strength. The M5Rules model performs moderately well, with accuracy at 86% for both training and validation datasets. However, it exhibits significantly higher RMSE values (3.31 MPa in training and 3.33 MPa in validation) and error percentages of 14%, indicating weaker predictive ability. Its R² values (0.75 in training, 0.84 in validation) suggest that while it captures some of the relationships in the data, it lacks precision compared to Kstar. The ElasticNet model is the least effective, with the highest error rates (20% in training, 19% in validation) and an RMSE of 4.74 MPa in training and 4.60 MPa in validation. Its low R² values (0.49 in training, 0.64 in validation) indicate a weak ability to model flexural strength accurately, making it unsuitable for high-precision predictions. The XNV model offers a balanced performance, achieving 87% accuracy in training and 91% in validation. It records an RMSE of 3.13 MPa in training and a significantly improved 2.20 MPa in validation, suggesting strong generalization capabilities. The model’s R² values (0.78 in training, 0.92 in validation) indicate a good fit, making it a viable option for predicting Ff. The Decision Table (DT) model exhibits similar performance to XNV, with an accuracy of 88% in training and 91% in validation. It records RMSE values of 2.88 MPa in training and 2.24 MPa in validation, coupled with R² values of 0.81 in training and 0.92 in validation. These results suggest that DT is a reliable model, though slightly less precise than Kstar. Overall, Kstar is the most accurate and reliable model for predicting flexural strength, with near-perfect correlation and minimal errors. XNV and DT also demonstrate strong predictive capabilities, while M5Rules offers moderate reliability. ElasticNet performs the worst, struggling with high error rates and poor correlation, making it the least suitable for predicting Ff in UHPC. The performance analysis of models predicting the workability (slump) of ultra-high-performance concrete (UHPC) mixed with various industrial byproducts reveals distinct variations in predictive accuracy and error rates (see Table 7). The Kstar model exhibits the highest accuracy, with 94% in training and 97% in validation. It has the lowest RMSE values (13.66 mm in training and 7.59 mm in validation), indicating minimal prediction errors. The R² values (0.94 in training and 0.98 in validation) confirm its strong correlation, making it the most reliable model for slump prediction. The M5Rules model performs moderately well but with a significant increase in error rates (17% in both training and validation). It records an RMSE of 39.20 mm in training and 37.93 mm in validation, indicating poor precision. The R² values (0.54 in training and 0.43 in validation) suggest weak predictive capabilities, making it less reliable compared to Kstar. The ElasticNet model is the weakest performer, with the highest error rates (21% in training and 22% in validation) and an RMSE of 48.88 mm in training and 46.95 mm in validation. Its low R² values (0.32 in training and 0.13 in validation) indicate poor correlation, making it highly unsuitable for predicting slump in UHPC. The XNV model offers a balanced performance with 88% accuracy in training and 90% in validation. It records an RMSE of 27.44 mm in training and 22.43 mm in validation, suggesting strong predictive capabilities. The R² values (0.77 in training and 0.80 in validation) indicate a reasonably good fit, making it a viable option. The Decision Table (DT) model performs similarly to XNV, with an accuracy of 88% in training and an improved 93% in validation. It records RMSE values of 26.90 mm in training and a significantly lower 14.59 mm in validation, coupled with high R² values (0.78 in training and 0.91 in validation), suggesting strong generalization. Overall, Kstar is the most accurate and reliable model for predicting slump, with minimal errors and near-perfect correlation. DT also demonstrates strong predictive capabilities, particularly in validation, while XNV provides a well-balanced alternative. M5Rules has moderate performance, whereas ElasticNet is the weakest model, struggling with high error rates and poor correlation, making it the least suitable for predicting workability in UHPC. The performance analysis of models predicting the porosity of ultra-high-performance concrete (UHPC) mixed with various industrial byproducts shows clear distinctions in predictive accuracy and error rates (see Table 8). The Kstar model demonstrates the highest accuracy, achieving 99% in both training and validation. It has the lowest RMSE values (0.12 in training and 0.14 in validation), indicating minimal prediction errors. With an R² of 1.00 and an NSE of 1.00, it provides near-perfect correlation, making it the most reliable model for porosity prediction. The M5Rules model exhibits moderate performance, with an accuracy of 92% in training but dropping to 85% in validation. It has higher RMSE values (0.90 in training and 1.95 in validation), indicating reduced precision compared to Kstar. The R² values (0.96 in training and 0.78 in validation) suggest a decent fit but lower predictive power, especially in validation where the error increases to 15%. The ElasticNet model performs the weakest, with the highest error rates (29% in training and 26% in validation) and the highest RMSE values (3.25 in training and 3.32 in validation). Its R² values (0.38 in training and 0.47 in validation) suggest poor correlation, making it unsuitable for porosity prediction. The XNV model offers a balanced performance with 92% accuracy in training and 88% in validation. It records RMSE values of 0.94 in training and 1.51 in validation, with R² values of 0.95 in training and 0.87 in validation, indicating strong predictive capability. It is a reliable model but not as strong as Kstar. The Decision Tree (DT) model also performs well, with 95% accuracy in training and 93% in validation. It records RMSE values of 0.54 in training and 0.91 in validation, with R² values of 0.98 in training and 0.95 in validation, making it a strong alternative to Kstar. Overall, Kstar is the most accurate and reliable model for predicting porosity, with minimal errors and perfect correlation. DT also demonstrates strong predictive capabilities, particularly in validation. XNV provides a well-balanced alternative, while M5Rules shows moderate performance with increased errors in validation. ElasticNet is the weakest model, struggling with high error rates and poor correlation, making it the least suitable for predicting porosity in UHPC.

Table 5.

Performance measurements of developed models w.r.t Fc.

Model	Dataset	SSE	MAE	MSE	RMSE	Error	Acc	R2	R	WI	NSE	KGE	SMAPE
		–	MPa	MPa	MPa	%	%	–	–	–	–	–	MPa
Kstar	Training	4880	1.92	12.87	3.59	3	97	0.98	0.99	1.00	0.98	0.98	1.37
	Validation	1817	1.92	18.35	4.28	3	97	0.98	0.99	1.00	0.98	0.97	1.29
M5 Rules	Training	117,655	15.16	310.43	17.62	13	87	0.61	0.78	0.85	0.60	0.65	11.33
	Validation	34,326	14.67	346.72	18.62	13	87	0.69	0.83	0.89	0.68	0.73	10.31
Elastic Net	Training	220,146	22.83	580.86	24.10	17	83	0.28	0.53	0.57	0.26	0.22	17.38
	Validation	90,055	24.91	909.65	30.16	21	79	0.19	0.44	0.54	0.17	0.17	17.91
XNV	Training	93,880	13.77	247.71	15.74	11	89	0.69	0.83	0.89	0.68	0.72	10.33
	Validation	33,512	14.67	338.51	18.40	13	87	0.70	0.84	0.90	0.69	0.72	10.49
DT	Training	31,595	6.24	83.37	9.13	7	93	0.89	0.95	0.97	0.89	0.93	4.59
	Validation	14,552	7.79	338.51	12.12	8	92	0.87	0.93	0.96	0.87	0.88	5.25

Table 6.

Performance measurements of developed models w.r.t Ff.

Model	Dataset	SSE	MAE	MSE	RMSE	Error%	Acc	R2	R	WI	NSE	KGE	SMAPE
		–	MPa	MPa	MPa	%	%	–	–	–	–	–	MPa
Kstar	Training	87	0.47	0.60	0.77	3	97	0.99	0.99	1.00	0.99	0.96	2.12
	Validation	4	0.19	0.11	0.34	1	99	1.00	1.00	1.00	1.00	0.98	0.93
M5 Rules	Training	1603	2.85	10.98	3.31	14	86	0.75	0.87	0.92	0.75	0.79	12.00
	Validation	399	2.48	11.09	3.33	14	86	0.84	0.91	0.94	0.81	0.80	10.75
Elastic Net	Training	3277	4.39	22.44	4.74	20	80	0.49	0.70	0.80	0.49	0.56	18.39
	Validation	762	3.37	21.17	4.60	19	81	0.64	0.80	0.87	0.63	0.65	14.44
XNV	Training	1432	2.54	9.81	3.13	13	87	0.78	0.88	0.93	0.78	0.81	10.45
	Validation	174	1.51	4.84	2.20	9	91	0.92	0.96	0.98	0.91	0.91	6.58
DT	Training	1213	2.16	8.31	2.88	12	88	0.81	0.90	0.95	0.81	0.86	9.20
	Validation	181	1.58	4.84	2.24	9	91	0.92	0.96	0.98	0.91	0.93	7.40

Table 7.

Performance measurements of developed models w.r.t Slump.

Model	Dataset	SSE	MAE	MSE	RMSE	Error	Acc	R2	R	WI	NSE	KGE	SMAPE
		–	mm	mm	mm	%	%	–	–	–	–	–	mm
Kstar	Training	28,354	4.88	186.54	13.66	6	94	0.94	0.97	0.99	0.94	0.95	2.51
	Validation	2303	2.95	57.57	7.59	3	97	0.98	0.99	0.99	0.98	0.96	1.37
M5 Rules	Training	233,610	33.06	1536.91	39.20	17	83	0.54	0.73	0.82	0.53	0.60	14.02
	Validation	57,534	27.61	1438.34	37.93	17	83	0.43	0.66	0.79	0.41	0.61	11.90
Elastic Net	Training	363,159	48.64	2389.20	48.88	21	79	0.32	0.57	0.55	0.28	0.23	20.96
	Validation	88,163	43.87	2204.06	46.95	22	78	0.13	0.37	0.50	0.10	0.08	19.67
XNV	Training	114,423	20.26	752.78	27.44	12	88	0.77	0.88	0.93	0.77	0.80	9.20
	Validation	20,132	17.16	503.31	22.43	10	90	0.80	0.89	0.94	0.79	0.82	7.80
DT	Training	110,006	20.01	723.73	26.90	12	88	0.78	0.88	0.94	0.78	0.83	9.03
	Validation	8515	10.49	503.31	14.59	7	93	0.91	0.96	0.98	0.91	0.95	4.74

Table 8.

Performance measurements of developed models w.r.t porosity.

Model	Dataset	SSE	MAE	MSE	RMSE	Error	Acc	R2	R	WI	NSE	KGE	SMAPE
		–	–	–	–	%	%	–	–	–	–	–	–
Kstar	Training	2	0.07	0.02	0.12	1	99	1.00	1.00	1.00	1.00	1.00	1.04
	Validation	1	0.09	0.02	0.14	1	99	1.00	1.00	1.00	1.00	1.00	0.74
M5 Rules	Training	88	0.76	0.82	0.90	8	92	0.96	0.98	0.99	0.95	0.92	10.58
	Validation	107	1.04	3.82	1.95	15	85	0.78	0.89	0.94	0.77	0.87	10.90
Elastic Net	Training	1143	2.73	10.58	3.25	29	71	0.38	0.62	0.72	0.37	0.41	27.11
	Validation	308	2.61	11.00	3.32	26	74	0.47	0.69	0.70	0.35	0.39	23.12
XNV	Training	95	0.73	0.88	0.94	8	92	0.95	0.97	0.99	0.95	0.94	9.69
	Validation	64	0.83	2.27	1.51	12	88	0.87	0.93	0.96	0.87	0.90	8.21
DT	Training	31	0.38	0.29	0.54	5	95	0.98	0.99	1.00	0.98	0.99	5.12
	Validation	23	0.48	2.27	0.91	7	93	0.95	0.98	0.99	0.95	0.97	4.08

Comparatively, for more sustainable ultra-high-performance concrete (UHPC) production, selecting the most accurate and efficient predictive model is crucial to optimizing the use of industrial byproducts while maintaining high performance. When comparing models across compressive strength (Fc), flexural strength (Ff), workability (Slump), and porosity, the Kstar model consistently outperforms the others, making it the most suitable choice for sustainable UHPC applications. For compressive strength (Fc), Kstar demonstrates the highest accuracy (97%) with the lowest error (3%) and RMSE values (3.59 MPa for training and 4.28 MPa for validation), indicating strong predictive power and minimal deviation. The Decision Tree (DT) model also performs well, with 93% accuracy and RMSE values of 9.13 MPa (training) and 12.12 MPa (validation), making it a viable alternative. Models like Elastic Net and M5Rules struggle with significantly higher errors (17–21%) and lower accuracy, making them less suitable for predicting Fc in sustainable UHPC production. For flexural strength (Ff), Kstar again delivers the best results, achieving 97–99% accuracy with minimal error (1–3%) and RMSE values of 0.77 MPa (training) and 0.34 MPa (validation). Decision Tree (DT) and XNV also perform well, maintaining over 90% accuracy and reasonable RMSE values (DT: 2.88 MPa training, 2.24 MPa validation; XNV: 3.13 MPa training, 2.20 MPa validation). Meanwhile, M5Rules and Elastic Net exhibit higher errors (14–20%) and lower R² values, making them less reliable for flexural strength prediction. For workability (Slump), Kstar continues to be the most accurate model, with 94–97% accuracy and low error rates (3–6%). Its RMSE values (13.66 mm in training and 7.59 mm in validation) are significantly lower than those of M5Rules and Elastic Net, both of which show much higher errors (17–22%) and weaker correlations. XNV and DT provide a balance between accuracy and error, making them reasonable alternatives if Kstar is unavailable. For porosity, which is critical for durability and sustainability, Kstar again outperforms all other models, achieving near-perfect accuracy (99%) with the lowest RMSE values (0.12 in training and 0.14 in validation). The Decision Tree (DT) model also delivers high accuracy (95–98%) with low RMSE values, making it another strong option. XNV and M5Rules show moderate predictive capabilities, whereas Elastic Net significantly underperforms, with a high error rate (26–29%) and poor correlation, making it the least reliable for porosity prediction. Overall, Kstar is the most reliable and accurate model across all four parameters, making it the best choice for predicting sustainable UHPC properties when incorporating industrial byproducts. The Decision Tree (DT) model is a strong alternative, especially for flexural strength, slump, and porosity, but slightly lags behind Kstar in compressive strength. XNV provides balanced performance but is not as robust, while M5Rules and Elastic Net consistently exhibit higher errors, making them less suitable for sustainable UHPC applications. By prioritizing Kstar or DT models, UHPC production can achieve greater efficiency, reduced material waste, and improved performance with industrial byproduct integration. To compare the present research models with those published in the literature, it is essential to analyze their performance in predicting ultra-high-performance concrete (UHPC) properties, including compressive strength (Fc), flexural strength (Ff), workability (Slump), and porosity. Traditional models in the literature, such as artificial neural networks (ANNs), support vector machines (SVMs), and multiple regression approaches, have been widely used, but they often face challenges in terms of computational efficiency, data dependency, and generalization ability. For compressive strength (Fc), previous studies have reported that ANN models achieve R² values between 0.85 and 0.95, with mean absolute errors (MAE) exceeding 5 MPa^24,25. In comparison, the present research demonstrates that the Kstar model achieves an R² of 0.98 with an MAE of only 1.92 MPa, significantly improving predictive accuracy. The Decision Tree (DT) model also performs well with an R² of 0.87 in validation, comparable to literature models but with lower root mean square error (RMSE). Unlike ANNs, which require extensive hyperparameter tuning, Kstar and DT models provide stable and interpretable results with reduced computational complexity. Regarding flexural strength (Ff), literature studies indicate that ANN and regression-based models report RMSE values ranging from 2.5 to 4.0 MPa, with R² values between 0.85 and 0.95^26,27. The present research shows that the Kstar model outperforms traditional models by achieving an RMSE of only 0.34 MPa in validation and an R² of 1.00. Similarly, the DT model demonstrates strong predictive capability with an R² of 0.96, aligning with the best results in the literature while offering greater interpretability and ease of implementation. For workability (Slump), previous research suggests that traditional regression models and ANNs exhibit high variance due to the complex interactions of mix proportions and material properties, often achieving R² values around 0.75 to 0.85 with errors between 10 and 20%^28,29. The present study shows a significant improvement, with the Kstar model reaching an R² of 0.98 and an error of only 3%, far surpassing conventional models. The DT model also outperforms literature-reported results, with an R² of 0.91 in validation. In contrast, models such as Elastic Net and M5Rules show lower R² values and higher RMSE, performing similarly to traditional regression models. For porosity, literature studies have found that conventional regression-based models and ANNs achieve moderate predictive accuracy, with R² values typically between 0.85 and 0.95^30,31. The present research significantly enhances prediction accuracy, with the Kstar model reaching an R² of 1.00, suggesting near-perfect prediction capabilities. Even the DT model, with an R² of 0.95, surpasses many literature-reported models. Traditional approaches often struggle with porosity prediction due to the complexity of material interactions, but the machine learning models in this study, particularly Kstar, demonstrate substantial error reduction and improved generalization ability. Overall, the present research models, especially Kstar and DT, outperform many existing models from the literature in predicting the properties of UHPC incorporating industrial byproducts. These models offer superior accuracy, lower errors, and improved robustness, making them more suitable for practical applications in sustainable UHPC production. While ANN and SVM models have been widely explored in the literature, their reliance on extensive tuning and risk of overfitting make them less efficient compared to the more adaptable and interpretable models developed in this study.

That the Kstar model significantly outperforms other models in this study, despite its limited adoption in concrete prediction applications, highlights an important but often overlooked aspect of model selection in engineering research—namely, the alignment between data characteristics and algorithmic capabilities³⁶. While Kstar is not commonly used in concrete materials modeling, its core strengths make it particularly well-suited for complex, nonlinear, and small-to-moderate-sized datasets, which are typical in experimental concrete studies involving multiple supplementary cementitious materials or industrial byproducts³⁶. Kstar, an instance-based learning algorithm, relies on comparing new input instances with stored historical examples using an entropy-based distance function^36,37. This localized, non-parametric approach allows the model to flexibly adapt to intricate patterns and relationships in the data without assuming any fixed functional form. Such flexibility is crucial in predicting the behavior of ultra-high performance concrete (UHPC), where performance characteristics, such as compressive strength, flexural strength, slump, and porosity are influenced by subtle and nonlinear interactions among various binder compositions, additives, and curing conditions. In traditional concrete modeling, widely adopted algorithms like decision trees, support vector machines, or neural networks may require more extensive datasets or hyperparameter tuning to generalize well. In contrast, Kstar can perform robustly on smaller datasets, provided that the data is representative and sufficiently descriptive of the underlying material behavior^36,37. This is particularly advantageous when experimental constraints limit the number of mix designs or replicates, as is often the case with high-performance or specialized concretes. Although its application in concrete prediction literature is limited, Kstar has demonstrated reliable performance in related fields, such as geotechnical engineering, environmental modeling, and materials informatics³⁷. In these domains, it has been successfully employed to predict soil strength parameters, contaminant migration, and composite material properties, problems that similarly involve nonlinear, multivariate interactions and data heterogeneity³⁸. This cross-domain evidence reinforces the validity of Kstar’s strong performance in the current study. Therefore, its inclusion is not arbitrary but rather a deliberate attempt to evaluate a broader spectrum of machine learning techniques that align with the specific data characteristics and modeling challenges of UHPC systems^36–38. The strong performance of Kstar in this context suggests that its capabilities may be underrecognized in civil engineering applications, and its demonstrated effectiveness here opens the door for more widespread exploration of instance-based learning in future concrete prediction research.

Furthermore, the reviewed literature demonstrates the extensive application of artificial neural networks (ANNs) in predicting the mechanical properties of concrete mixtures, including ultra-high-performance concrete (UHPC) incorporating various industrial byproducts. Studies such as those by Chou et al.⁸, Li et al.¹⁰, Alabduljabbar et al.¹⁴, and Zhang et al.¹¹ have consistently shown that ANN models can achieve high accuracy, with R² values often ranging from 0.91 to 0.94, depending on the complexity of the dataset and the inclusion of factors like curing conditions, chemical composition, or optimization via hybrid techniques. These studies validate the capability of ANN-based approaches to handle nonlinear relationships and high-dimensional data, which are typical in UHPC systems with multiple supplementary cementitious materials (SCMs). However, while ANN models have proven effective, they also come with several limitations. They typically function as “black-box” models, making them less interpretable, and often require large datasets and intensive hyperparameter tuning to achieve stable and reliable performance. Moreover, they are sensitive to issues like overfitting, especially when dealing with moderate-sized datasets, which are common in UHPC research due to the high cost and complexity of experimental trials. In comparison, the present research adopts a broader and more diversified set of machine learning models, including Kstar, M5Rules, ElasticNet, XNV, and Decision Table, to evaluate their ability to predict multiple mechanical properties of UHPC mixtures containing various industrial byproducts. Notably, the Kstar model outperforms others across most performance metrics, achieving R² values up to 1.00 in some cases on independent test data. Unlike traditional ANN models, Kstar offers a more adaptable and instance-based approach that proves particularly effective for small to medium-sized datasets with high variability and nonlinearity, as is the case in this study. The use of rule-based and ensemble models alongside Kstar also enhances the robustness of the findings by ensuring that model performance is not reliant on a single algorithmic approach.

Furthermore, the present study distinguishes itself by not only focusing on compressive strength but also incorporating flexural strength, slump, and porosity into the modeling framework. This multi-target approach allows for a more comprehensive assessment of concrete performance, something that is often overlooked in studies that utilize ANN models to predict only a single mechanical property. The interpretability of results is further supported through SHAP analysis and Hoffman & Gardener sensitivity techniques, enabling the identification of key features and their influence on each performance metric. This level of interpretability is often lacking in standard ANN implementations. In conclusion, while ANN-based models have shown strong predictive capabilities in prior studies, the present research expands the modeling scope, enhances interpretability, and achieves superior predictive performance using models like Kstar. It highlights the importance of aligning the machine learning technique with the specific characteristics of the dataset and prediction task, demonstrating that less commonly used models like Kstar can provide significant advantages over traditional ANN models in UHPC prediction tasks.

In addition, studies presented in the literature^32–38 provide significant contributions to the field of concrete strength prediction using machine learning and hybrid optimization methods. For instance, Parhi and colleagues^32,34,35 utilized metaheuristic techniques such as Dolphin Echolocation and Spotted Hyena Optimization to optimize model performance, achieving improved predictions in specialized concrete compositions like PET fiber-reinforced or ASR-affected concretes. Similarly, Singh et al.³³ emphasized the importance of evolutionary hyperparameter tuning in achieving accurate strength predictions for high-performance concrete. These models demonstrated considerable accuracy; however, they often targeted specific material configurations or single performance metrics. The current study distinguishes itself by applying a broader range of machine learning models including KStar, M5Rules, ElasticNet, XNV, and Decision Table to predict multiple mechanical properties of ultra-high-performance concrete (UHPC) incorporating various industrial byproducts. Unlike many of the cited works which focus on a single mechanical property, this study addresses compressive strength, flexural strength, slump, and porosity collectively, providing a more comprehensive prediction framework. In addition, the KStar model used here achieved exceptionally high predictive accuracy (R² values up to 1.00), outperforming the models reported in the comparative literature which typically reported R² values in the range of 0.90–96. Furthermore, recent works by Onyelowe et al.^36–38 introduced advanced machine learning frameworks for predicting mechanical properties of concrete using hybrid fibers and industrial waste, and employed physics-informed modeling approaches. While these works contribute valuable methodologies, the present study integrates both performance prediction and feature interpretability using Hoffman & Gardner and SHAP analyses, offering an in-depth understanding of material influences. Overall, the present research expands the scope and performance benchmark of existing literature by not only offering higher model accuracy across multiple UHPC properties but also integrating detailed interpretability and sustainability considerations into model development.

The Taylor chart for the Fc (compressive strength) model (see Fig. 22) provides a statistical visualization of the model’s performance by comparing predicted and measured values in terms of three key metrics: correlation coefficient, standard deviation, and root-mean-square error (RMSE). For the training phase, the Taylor chart likely indicates a high correlation coefficient (close to 1), signifying a strong agreement between predicted and actual Fc values. The standard deviation of the model’s predictions should be close to that of the measured values, indicating that the model captures the variability in the data effectively. A low RMSE value suggests minimal prediction errors, confirming the model’s accuracy in training. During the validation phase, the Taylor chart might show a slightly lower correlation coefficient compared to training, reflecting some loss of prediction accuracy on unseen data. The standard deviation of the predicted values could deviate more from the actual values, signifying potential overfitting if the difference is significant. An increase in RMSE during validation would indicate higher prediction errors compared to training, but if the values remain close, it confirms that the model generalizes well. Overall, the Taylor chart effectively illustrates the predictive performance of the Fc model, highlighting its reliability during both training and validation phases. If the validation performance remains strong with minimal deviation from training metrics, it indicates a well-generalized model suitable for practical applications in UHPC mix optimization. The Taylor diagram for the Ff (flexural strength) models (see Fig. 23) provides an in-depth statistical assessment of the model’s predictive accuracy by evaluating correlation coefficient, standard deviation, and root-mean-square error (RMSE). In the training phase, the Taylor diagram likely demonstrates a high correlation coefficient, indicating a strong linear relationship between the predicted and actual Ff values. The standard deviation of the model’s predictions should align closely with the standard deviation of the measured data, confirming that the model effectively captures the variability in flexural strength. A low RMSE further supports the model’s accuracy, demonstrating minimal deviations between predictions and actual values. During the validation phase, the correlation coefficient may slightly decrease compared to training, reflecting the model’s ability to generalize to unseen data. If the standard deviation of the predicted values remains close to that of the measured data, it suggests that the model retains its predictive capability. However, a noticeable increase in RMSE during validation could indicate higher errors, potentially suggesting overfitting or model limitations in handling new data. The Taylor diagram provides a concise visualization of the Ff model’s performance, allowing for direct comparison between training and validation. If the validation metrics remain strong and closely aligned with the training performance, the model can be considered reliable for predicting the flexural strength of UHPC incorporating industrial byproducts. The Taylor diagram for the Slump model (see Fig. 24) provides a comprehensive statistical evaluation of the model’s predictive accuracy, highlighting the correlation coefficient, standard deviation, and root-mean-square error (RMSE). In the training phase, the correlation coefficient should ideally be high, indicating a strong agreement between the predicted and measured slump values. A close match between the standard deviation of the predicted values and that of the actual data signifies that the model accurately represents the variations in workability. A low RMSE further supports the model’s ability to make precise predictions, suggesting minimal deviation from actual slump measurements. During the validation phase, the correlation coefficient might decrease slightly compared to training, reflecting the model’s generalization capability on unseen data. If the standard deviation of the predictions remains close to that of the actual slump values, it suggests the model effectively captures the distribution of the data. However, an increase in RMSE during validation could indicate that the model struggles with new data, potentially pointing to overfitting or insufficient generalization. The Taylor diagram visually represents how well the model performs in both training and validation, allowing direct comparison. If the validation performance remains close to the training metrics, it confirms the model’s reliability for predicting the slump of UHPC incorporating industrial byproducts. If discrepancies arise, further optimization or additional training data may be required to improve robustness. The Taylor diagram for the Porosity models (see Fig. 25) evaluates the predictive performance by analyzing the correlation coefficient, standard deviation, and root-mean-square error (RMSE). In the training phase, a high correlation coefficient indicates a strong agreement between the predicted and measured porosity values. The standard deviation of the predictions should align closely with that of the actual data, demonstrating that the model effectively captures variability in porosity. A low RMSE suggests minimal error in the predictions, reinforcing the model’s accuracy in capturing the porosity characteristics of UHPC. During the validation phase, the correlation coefficient may slightly decrease, reflecting the model’s performance on unseen data. If the standard deviation of the predicted values remains close to the actual porosity values, it indicates that the model generalizes well. An increase in RMSE compared to training could signify reduced accuracy and potential overfitting, suggesting the need for further model refinement. The Taylor diagram provides a visual comparison of training and validation performance, illustrating how well the model generalizes. If the validation metrics closely match the training performance, the model demonstrates strong reliability for porosity prediction. However, significant discrepancies could indicate the need for additional training data, hyperparameter tuning, or feature engineering to enhance predictive capabilities.

Fig. 22.

Comparison of the accuracies of the developed models using Taylor charts w.r.t Fc.

Fig. 23.

Comparison of the accuracies of the developed models using Taylor charts w.r.t Ff.

Fig. 24.

Comparison of the accuracies of the developed models using Taylor charts w.r.t Slump.

Fig. 25.

Comparison of the accuracies of the developed models using Taylor charts w.r.t Porosity.

Sensitivity analysis

A sensitivity index of 1.0 indicates complete sensitivity, a sensitivity index less than 0.01 indicates that the model is insensitive to changes in the parameter. Figure 26 shows the sensitivity analysis with respect to Fc, Ff, Slump and Porosity. The sensitivity analysis results based on Hoffman & Gardener’s method provide insights into the relative importance of various input parameters on the models for Fc, Ff, Slump, and Porosity. For the Fc model, the most influential variable is MK/B, with a 14% importance, followed by S/B at 12% and FA/B at 10%. Other notable parameters include CAGS (9%), LS/B (6%), and NS/B (6%). The lowest impact is observed for SF/B (1%), indicating that this factor has minimal influence on Fc. In the Ff model, CAGS exhibits the highest importance at 13%, while W/B and PL/B both contribute 10% each. Other notable influences include QP/B and S/B at 8%, while NS/B, MK/B, and SF/B have relatively lower importance (3%). The least significant parameter is Len, with just 2% importance. For the Slump model, PL/B shows the highest sensitivity at 15%, followed by LS/B (12%) and MK/B (11%). FA/B and SF/B each contribute 7%, while S/B (1%) and NS/B (1%) exhibit the least influence on the model’s output. In the Porosity model, C/B, Slg/B, and FibAsp each hold the highest importance at 12%. MK/B, SF/B, and QP/B also have notable influences, ranging from 9 to 4%. The least influential parameters are Cfc (2%), W/B (3%), and PL/B (3%), indicating that these inputs play a relatively minor role in determining the Porosity outcomes. Conversely, the SHAP sensitivity analysis results shown in Fig. 27 provide insights into the relative importance of different variables influencing the Fc, Ff, Slump, and Porosity models. For the Fc model, the most significant factor is S/B with an importance of 17%, followed by W/B at 13%. Other influential factors include C/B at 7% and QP/B at 9%, while factors such as FA/B, Slg/B, and Size contribute minimally. In the Ff model, SF/B emerges as the most dominant factor at 18%, followed by CAgS at 14% and QP/B at 11%. Other variables such as W/B and PL/B show moderate importance, while FA/B, MK/B, and Len have lower contributions. The Slump model analysis highlights SF/B as the most significant variable at 18%, followed by CAgS at 14% and QP/B at 9%. W/B, S/B, and LS/B contribute moderately, while NS/B and FA/B have lower influence. Finally, the Porosity model shows C/B as the most critical factor at 10%, followed by SF/B at 15%, PL/B at 13%, and QP/B at 12%. The contributions of other factors like FA/B, MK/B, and CAgS are present but less pronounced. These results indicate the varying degrees of importance of different material properties in predicting the respective concrete performance parameters.

Fig. 26.

Sensitivity analysis.

Fig. 27.

SHAP analysis.

Comparatively, the Hoffman & Gardener and SHAP sensitivity analyses results both highlight the most influential factors in predicting Fc, Ff, Slump, and Porosity, but with some differences in the ranking and importance of specific variables. In the Fc model, Hoffman & Gardener’s analysis identifies MK/B as the most critical factor at 14%, followed by S/B at 12% and QP/B at 10%, whereas SHAP highlights S/B as the dominant factor at 17% and W/B at 13%, with MK/B having a lower impact. For the Ff model, Hoffman & Gardener rank CAgS as the highest at 13%, with QP/B and W/B also being influential, while SHAP assigns the highest importance to SF/B at 18%, followed by CAgS at 14%, showing a shift in dominance between these two methods. In the Slump model, Hoffman & Gardener highlight W/B as the most significant at 15%, with LS/B and MK/B playing key roles, while SHAP identifies SF/B as the most dominant at 18%, followed by CAgS at 14%, indicating a discrepancy in ranking. For the Porosity model, Hoffman & Gardener emphasize C/B at 15% and Slg/B at 12%, whereas SHAP highlights SF/B at 15% and QP/B at 12%, with C/B at a slightly lower 10%, showing variations in the importance assigned to specific factors. Overall, while both methods agree on the significance of certain key variables, the relative ranking and emphasis differ, with SHAP often attributing higher importance to factors like SF/B and W/B, whereas Hoffman & Gardener distribute importance more evenly across multiple variables.

The sensitivity analysis results using Hoffman & Gardener’s method and SHAP values provide complementary yet distinct perspectives on the influence of various input parameters on the mechanical and fresh properties of ultra-high performance concrete (UHPC) incorporating industrial byproducts. A deeper examination of these findings offers nuanced insights into how these variables impact concrete behavior and how this understanding can be strategically applied for optimizing UHPC production in industrial settings. Starting with the compressive strength (Fc) model, Hoffman & Gardener’s method points to MK/B (metakaolin-to-binder ratio) as the most influential variable, accounting for 14% of the importance. This suggests that the pozzolanic reactivity and filler effect of metakaolin significantly enhance the strength development of UHPC. In contrast, the SHAP analysis assigns the highest importance to S/B (sand-to-binder ratio) at 17%, with W/B (water-to-binder ratio) following closely at 13%. The divergence in ranking reflects the methodological differences: Hoffman & Gardener focuses on variance contribution, while SHAP captures localized feature interactions within model predictions. SHAP’s emphasis on S/B and W/B suggests that granular packing density and water demand are critical to optimizing the microstructure and hydration of UHPC, especially in mixes rich in byproducts. For industrial applications, this insight supports targeted control over the gradation and quantity of fine aggregates and water reducers to fine-tune the rheology and compressive strength. In the flexural strength (Ff) model, Hoffman & Gardener highlights CAgS (coarse aggregate size) as the top contributor (13%), with W/B and PL/B (plasticizer-to-binder ratio) also being influential. SHAP, however, identifies SF/B (silica fume-to-binder ratio) as the dominant factor at 18%, followed by CAgS at 14%. The discrepancy underscores that while Hoffman & Gardener identifies macro-scale aggregate influence, SHAP captures the critical role of nano-silica effects of silica fume, which enhances the interfacial transition zone and tensile load transfer. From an industrial production standpoint, this suggests that to enhance flexural performance, careful optimization of both particle gradation and reactive ultrafine materials is essential. Emphasis on precise dosing of silica fume and aggregate grading can significantly improve crack resistance and ductility in structural applications. The Slump model reveals further divergence. Hoffman & Gardener shows PL/B (15%) and LS/B (limestone powder-to-binder ratio) at 12% as most influential, indicating that workability is highly dependent on the dispersion and lubricating effects of plasticizers and fines. In contrast, SHAP emphasizes SF/B (18%) and CAgS (14%) as most impactful, suggesting that in addition to chemical admixtures, the physical characteristics of constituents like silica fume and aggregate morphology play a pivotal role. This reinforces the notion that fresh concrete behavior is governed by both chemical and physical packing phenomena. In industrial use, such insights can inform the selection of admixture types and dosages, as well as the particle shape and distribution of aggregates and powders to ensure desired slump without compromising mechanical performance. The Porosity model presents a more distributed sensitivity profile. According to Hoffman & Gardener, C/B (cement-to-binder ratio), Slg/B (slag-to-binder ratio), and FibAsp (fiber aspect ratio) each show significant impact at 12%, while SHAP attributes the highest importance to SF/B (15%), followed by PL/B (13%) and QP/B (quartz powder-to-binder ratio) at 12%. These results collectively emphasize the importance of matrix densification, mineral filler content, and fiber integration in controlling porosity. SHAP’s elevated ranking of SF/B and QP/B highlights their role in refining the pore structure and enhancing packing density. From a practical perspective, industries aiming to produce UHPC with low porosity and improved durability should focus on optimizing silica fume content, proper fiber dispersion, and the selection of ultrafine powders that contribute to internal pore refinement. Comparatively, while both methods highlight similar variables, SHAP often attributes greater importance to fine-scale reactive components (e.g., SF/B, W/B), capturing their nonlinear interactions and direct influence on predictions. Hoffman & Gardener provides a broader view of variance distribution across the entire dataset, highlighting variables that explain more of the global behavior. This dual-pronged analytical approach enables a more holistic understanding of input variable influence. The practical implications of these findings for industrial UHPC production are substantial. They inform targeted material selection and proportioning strategies. For instance, in applications requiring high compressive strength and low porosity, a focus on optimizing S/B, SF/B, and W/B ratios is crucial. For enhanced flexural performance, precise control of SF/B and CAgS is essential. Meanwhile, to achieve desirable workability, balancing PL/B and fine reactive powders like LS/B and SF/B is key. Implementing these insights in quality control, mix design refinement, and performance-based optimization can significantly enhance the consistency, sustainability, and cost-efficiency of UHPC incorporating industrial byproducts, advancing both performance goals and environmental objectives in modern construction practices.

However on why certain binder compositions negatively impact strength, the observed influence of MK/B (metakaolin-to-binder ratio) and SF/B (silica fume-to-binder ratio) on compressive and flexural strength can be attributed to their pozzolanic activity and particle fineness. Metakaolin is known to react with calcium hydroxide released during cement hydration to form additional calcium silicate hydrate (C–S–H) gel, which contributes to strength gain. However, excessive metakaolin may lead to an overly refined pore structure and increased water demand, adversely affecting workability and potentially leading to internal stress during drying, which can impair strength. Similarly, silica fume, with its extremely fine particles, enhances the packing density and contributes to the pozzolanic reaction, refining the microstructure. Yet, when used in excess, it may reduce workability significantly and result in incomplete dispersion, diminishing its beneficial effects. The negative impact of certain binder combinations on strength can also be understood through the lens of particle interaction and hydration kinetics. For example, a high proportion of limestone powder (LS/B) may serve primarily as a filler with limited reactivity. While it can improve workability and early-age strength due to improved particle packing, its excessive use may dilute the overall binder reactivity, resulting in a weaker cementitious matrix. The same principle applies to quartz powder (QP/B), which improves microstructural packing but contributes minimally to the binding phases unless synergistically combined with highly reactive pozzolanic materials. The water-to-binder ratio (W/B) consistently emerges as a critical factor due to its fundamental role in hydration, porosity development, and mechanical performance. A lower W/B ratio generally enhances strength and reduces porosity due to the formation of a denser microstructure; however, it must be carefully balanced to ensure sufficient workability and prevent defects such as incomplete compaction or cracking. Additionally, the influence of aggregate size (CAgS) and fiber aspect ratio (FibAsp) on mechanical properties such as flexural strength and porosity can be explained by their role in crack-bridging and stress distribution. Coarse aggregates and fibers with higher aspect ratios improve tensile resistance and energy absorption, thereby enhancing toughness and reducing microcrack propagation, but may compromise uniformity and increase internal voids if not properly graded and dispersed.

Conclusions

The research work comprehensively analyzes the factors influencing the mechanical properties of cementitious composites, focusing on compressive strength (Fc), flexural strength (Ff), slump, and porosity. Through correlation analysis, Taylor diagrams, and sensitivity assessments using both Hoffman & Gardener and SHAP methods, the study provides a multi-faceted understanding of the relationships between various mix components and the resulting properties.

• The correlation analysis establishes significant dependencies between input variables and response parameters, revealing how factors such as binder composition, aggregate content, and water-to-binder ratio influence strength and workability. The Taylor diagrams for Fc, Ff, Slump, and Porosity models further validate the predictive accuracy and consistency of the models, demonstrating their reliability in both training and validation phases. High correlation coefficients and low errors indicate robust predictive capabilities, supporting the effectiveness of the modeling approach.

• The sensitivity analysis results from Hoffman & Gardener and SHAP methods offer deeper insights into the key influencing parameters. Hoffman & Gardener’s method identifies variables such as metakaolin-to-binder ratio (MK/B), sand-to-binder ratio (S/B), and water-to-binder ratio (W/B) as dominant factors in strength and workability predictions, while SHAP assigns greater importance to factors like silica fume-to-binder ratio (SF/B) and aggregate properties. These differences in sensitivity rankings highlight the complexity of cementitious composite behavior and the need for a multi-perspective evaluation of contributing factors.

• A comparison of both sensitivity methods reveals notable variations in how the influence of different factors is weighted. While both approaches consistently rank water-to-binder and fine aggregate content among the most significant factors, SHAP tends to emphasize certain variables, such as SF/B, more strongly than Hoffman & Gardener’s method. This divergence suggests that different analytical techniques may prioritize different aspects of the data, reinforcing the necessity of using multiple evaluation approaches to gain a holistic understanding of material performance.

• Ultimately, the study underscores the intricate interplay between mix proportions and composite behavior, reaffirming the importance of precise material selection and proportioning in optimizing mechanical properties. The findings contribute valuable insights for the design and optimization of cementitious composites, aiding in the development of high-performance mixtures with enhanced strength, durability, and workability. Future research can build on this work by incorporating additional parameters, such as environmental conditions and long-term durability assessments, to further refine predictive models and improve material performance in practical applications.

Practical application of research

The findings of this research work have significant practical applications in the design, optimization, and performance enhancement of cementitious composites in various construction and infrastructure projects. By providing a comprehensive understanding of the factors influencing compressive strength, flexural strength, slump, and porosity, the study equips engineers, material scientists, and construction professionals with valuable insights to improve the quality and durability of concrete-based materials. One of the most immediate applications is in the optimization of concrete mix designs for structural applications. The sensitivity analyses using both Hoffman & Gardener and SHAP methods identify the most influential parameters affecting mechanical properties, allowing engineers to make data-driven decisions in selecting material proportions. For instance, the study highlights the critical role of metakaolin, silica fume, and water-to-binder ratios in determining strength and workability, enabling the formulation of concrete mixtures that maximize performance while minimizing material costs. This is particularly relevant in high-performance concrete applications, where precise mix adjustments are necessary to achieve specific strength and durability criteria. The research findings also contribute to the development of sustainable and eco-friendly concrete formulations by optimizing the use of supplementary cementitious materials (SCMs) such as fly ash, slag, and silica fume. With increasing emphasis on reducing the carbon footprint of concrete production, these results offer a scientific basis for incorporating alternative binders without compromising strength and workability. This has direct implications for green construction initiatives, where the integration of recycled materials and SCMs can lead to environmentally friendly concrete with enhanced mechanical and durability properties. Another important application lies in the quality control and predictive maintenance of concrete structures. The Taylor diagram analysis validates the predictive accuracy of the developed models, demonstrating their reliability in forecasting material performance under various conditions. This capability can be leveraged in structural health monitoring, where predictive models can assess the long-term behavior of concrete elements and identify potential weaknesses before they manifest as structural failures. By implementing these models in construction quality assessment and durability evaluations, engineers can enhance the lifespan of buildings, bridges, and other critical infrastructure. In the field of prefabricated concrete production, where consistency and uniformity in material properties are crucial, the insights from this research aid in refining manufacturing processes. The identification of key mix parameters ensures that each batch meets stringent performance standards, reducing variability and enhancing the efficiency of mass production. This is particularly beneficial in large-scale construction projects, where consistency in concrete properties is essential for ensuring structural integrity across multiple components. Furthermore, the study’s findings are highly relevant for specialized concrete applications such as fiber-reinforced and self-compacting concrete. The role of fiber aspect ratio and paste composition in influencing mechanical properties is crucial for tailoring materials to specific engineering requirements. The knowledge gained from sensitivity analyses enables the fine-tuning of fiber-reinforced concrete mixtures to optimize tensile strength and crack resistance, making them ideal for applications in earthquake-resistant structures, industrial flooring, and tunnel linings. In the broader context of infrastructure resilience, the research provides a scientific foundation for developing concrete with improved resistance to environmental stressors. By understanding the impact of porosity on durability, engineers can design mixtures with lower permeability, enhancing resistance to freeze–thaw cycles, chloride penetration, and sulfate attack. This is particularly beneficial for coastal structures, highway pavements, and water-retaining structures, where exposure to aggressive environments necessitates high-durability materials. Overall, the practical applications of this research extend across multiple domains of civil engineering and construction. From optimizing mix designs for cost-effective and high-performance concrete to enhancing sustainability and durability, the insights gained from this study contribute to advancements in material science and construction technology. Future developments in artificial intelligence and machine learning could further refine these predictive models, enabling real-time adjustments in mix designs based on field data. As the construction industry continues to evolve, integrating these research findings into practical applications will drive innovation, efficiency, and sustainability in cementitious composite technology.

Recommendation for future research

Future research should focus on expanding the dataset to include a wider range of material compositions, environmental conditions, and curing regimes to improve the generalizability of the predictive models. Incorporating real-world construction scenarios, such as field-cast concrete subjected to varying weather conditions, would enhance the applicability of the findings. Further exploration of machine learning and artificial intelligence techniques could refine the predictive accuracy of the models by capturing complex nonlinear interactions between mix parameters and mechanical properties. The integration of deep learning frameworks, such as convolutional neural networks and recurrent neural networks, could be particularly useful in identifying patterns and trends that traditional statistical methods may overlook. Investigating the long-term performance of optimized concrete mixes through accelerated aging tests and real-time structural monitoring would provide valuable insights into durability and deterioration mechanisms. Future studies should also examine the influence of extreme environmental conditions, including high temperatures, freeze–thaw cycles, and exposure to aggressive chemicals, on the mechanical and durability properties of cementitious composites. Expanding the research to include geopolymer-based binders and alternative cementitious materials, such as calcium sulfoaluminate cement, would contribute to the development of sustainable and low-carbon concrete formulations. Incorporating experimental validation with large-scale structural elements, such as beams, columns, and slabs, would strengthen the practical relevance of the findings. This could involve field trials and performance evaluations under real loading conditions to bridge the gap between laboratory-scale testing and full-scale construction applications. The development of smart concrete with embedded sensors for real-time monitoring of mechanical properties, hydration kinetics, and microstructural changes could offer further advancements in predictive maintenance and structural health monitoring. Future research should also explore the economic and environmental impacts of optimized mix designs by conducting life-cycle assessments and cost–benefit analyses. This would help determine the feasibility of implementing advanced mix designs in large-scale infrastructure projects while balancing performance, cost, and sustainability. Collaboration with industry stakeholders, including concrete manufacturers, construction companies, and regulatory bodies, would facilitate the practical implementation of research findings and the development of standardized guidelines for mix optimization. Finally, further refinement of sensitivity analysis techniques using hybrid methods that combine SHAP, Hoffman & Gardener, and other feature importance evaluation approaches could provide a more comprehensive understanding of parameter influence. Exploring the integration of multi-objective optimization algorithms would allow researchers to balance strength, workability, durability, and cost-effectiveness, leading to more holistic and adaptable mix designs for diverse engineering applications.

Author contributions

KCO &NU conceptualized, KCO supervised, KCO, SH, NU, RBV, AABM, AME, KPA & AUR wrote the main manuscript text and KCO & AME prepared the figures. All authors reviewed the manuscript.

Funding

This research is funded by King Saud University through Researchers Supporting Project Number (RSPD2025R701), King Saud University, Riyadh, Saudi Arabia.

Data availability

The data supporting this research work will be made available on request from the corresponding author.

Declarations

Competing interests

The authors declare no competing interests.