Comparison of Predictive Models Based on Machine Learning for Concrete Strength Prediction

Daniel Hastenpflug; Paula Bruzadelle Vieira

DOI: 10.22167/2675-6528-202602819

Article derived from a Final Course Work (TCC), with content based on the student’s original work and adapted to the editorial format of the E&S Magazine with the support of the ResumeAI tool, an artificial intelligence solution developed by Instituto Pecege for textual synthesis and organization.

Summary

The prediction of the characteristic compressive strength of concrete (fck) by traditional methods is limited by the nonlinear nature of the interactions between its constituents and the increasing compositional variability of modern concretes. Machine learning (ML) has represented a promising alternative, but published comparisons have often lacked methodological rigor, incurring data leakage, outlier removal without model optimization, and absence of uncertainty quantification. A comparison framework was proposed between nine ML algorithms (Linear Regression, Bayesian Ridge, Decision Tree, Random Forest, Gradient Boosting, SVR (RBF and polynomial), XGBoost, and Artificial Neural Network (ANN)) applied to a database of 1,319 experimental observations of Portland cement concrete mixes. The methodology adopted Bayesian optimization via Optuna for outlier removal, canonical 80/20 split with a fixed seed, common reference partition, repeated cross-validation (10×10 folds), and Monte Carlo simulation. Comprehensive statistical analysis was performed, including Friedman-Nemenyi, Diebold-Mariano, Model Confidence Set (MCS), and Plackett-Luce tests. Individualized Bayesian cleaning removed between 0.66% and 8.6% of samples, with divergent responses among algorithms. XGBoost, Random Forest, and Gradient Boosting benefited or remained stable, while ANN and SVR_poly suffered performance degradation, confirming the absence of a universally optimal cleaning method. The Model Confidence Set (MCS) identified XGBoost (R² = 0.969; RMSE = 7.63 MPa), Gradient Boosting, and Random Forest as a superior set of statistically indistinguishable models. Linear models and SVR were sequentially eliminated. SHAP analysis revealed that silica fume and age were the dominant variables in the ensemble models, but irrelevant in the linear ones. The proposed methodology established a reproducible benchmark for future comparisons.

Keywords: Machine learning; Bayesian Optimization; Outlier removal; Concrete compressive strength; XGBoost.

1. Introduction

Concrete is the most widely used material in global civil construction, being fundamental in both load-bearing structures and sealing elements. This composite, formed by cement, sand, gravel, and water, undergoes hydration reactions that transform it from a fresh to a hardened state (MEHTA and MONTEIRO, 2014). Among its mechanical properties, the compressive strength at 28 days (fck) is the main parameter for structural design (ACI Committee 318, 2014).

The composition of modern concrete has become significantly more variable due to the increasing incorporation of mineral admixtures, chemical additives, and new construction techniques, which complicates the determination of dosage methods and the reliable estimation of fck (MEHTA and MONTEIRO, 2014; YOUNIS and PILAKOUTAS, 2013; MOUTASSEM and CHIDIAC, 2016). The available traditional methods, whether empirical (HELENE, 2005), normative (ACI PRC-211.1-22), or statistical (ABCP, 1989; FORTI et al., 2020; GE et al., 2012; XIAOYONG and WENDI, 2020), are based on trial-and-error approaches, demanding considerable time and laboratory resources (NGUYEN et al., 2022; GARCÍA, 2020). Mathematically, these methods resort to simple or multiple linear regressions (UYANIK and GÜLER, 2013; BHANJA and SENGUPTA, 2002), but their applicability is limited by their failure to encompass the vast range of materials (KHAN et al., 2023) and by disregarding the intrinsically nonlinear nature of the relationship between mixture components and fck (QINGHUA et al., 2019).

In this scenario, machine learning (ML) emerges as a promising tool for predicting the performance of cementitious materials, given its ability to correlate inputs and outputs of samples in a linear and non-linear manner (KHAN et al., 2023). The literature already validates several ML models, such as Artificial Neural Networks (ANN), Support Vector Regression Machines (SVR), Decision Trees (DT), Random Forests (RF), and XGBoost, to predict the compressive strength of concrete mixes (WANG et al., 2024).

Despite the promising results, published comparisons frequently present methodological deficiencies that compromise reliability and reproducibility. Such deficiencies include the application of fixed outlier removal strategies without model optimization (KAUFMAN et al., 2012), data leakage that inadvertently contaminates test sets (ARLOT and CELISSE, 2010), the absence of common reference partitions for paired statistical tests, and the rare quantification of uncertainty through prediction intervals, despite its importance in engineering applications (KHOSRAVI et al., 2011).

Given these methodological gaps, the development of a robust comparison framework for machine learning models becomes essential, aiming to overcome the limitations of existing studies and provide a more reliable evaluation of predictive capability. Thus, this work proposed a comparison framework between nine ML algorithms (Linear Regression, Bayesian Ridge, Decision Tree, Random Forest, Gradient Boosting, SVR (RBF and polynomial), XGBoost, and Artificial Neural Network (ANN)) applied to a database of 1,319 experimental observations of Portland cement concrete traits.

2. Material and Methods

The research was exploratory in nature, proposing a robust framework to compare nine machine learning (ML) algorithms in predicting the characteristic compressive strength of concrete (fck). The method followed a structured flowchart, encompassing data engineering, statistical validation, and interpretability. The script was developed in Python, using packages such as numpy, pandas, sklearn, xgboost, shap, and optuna.

A database of 1,319 experimental observations of Portland cement concrete properties was used, compiled from various references (YEH, 1998; MARIANI and NEHDI, 2020). The input variables included cement (C), silica fume (SF), ground granulated blast-furnace slag (S), fly ash (FA), limestone powder (LP), water (W), coarse aggregates (gravel), fine aggregates (sand), water-reducing admixture (SP), and age. The response variable was the compressive strength (fck).

To prevent data leakage, the database was split into 80% for development and 20% for external testing (KAUFMAN et al., 2012). A stratified random split with a fixed seed (seed = 42) was employed, preserving the statistical distribution of the fck. An identical reference partition was created for all models, allowing direct comparisons in statistical tests.

The input features were standardized by z-score normalization (zero mean, unit variance) via scikit-learn’s StandardScaler, fitted on the development partition and applied to the test set. Outlier removal was performed by Bayesian optimization with Optuna (AKIBA et al., 2019), testing sixteen methods such as Isolation Forest, IQR, Z-Score, Percentile, DBSCAN, Elliptic Envelope, One-Class SVM, and Local Outlier Factor (LOF).

For each model, 75 independent trials were performed, proposing family, parameter, range, and scale configurations for outlier removal. The evaluation occurred through internal 5-fold cross-validation. The selection criterion for the cleaning method was a composite objective function, which balanced predictive performance, stability, and data retention (HASTIE et al., 2009; CHANDOLA et al., 2009).

Nine machine learning algorithms were selected for the prediction of fck: Linear Regression, Bayesian Ridge, Decision Tree, Random Forest, Gradient Boosting, SVR (with RBF and polynomial kernels), XGBoost, and Artificial Neural Network (ANN). The models encompassed different approaches, from linear to ensembles and neural networks, being employed to predict the fck of concretes.

The evaluation and classification of ML models followed a rigorous and multi-structural approach (GARETH et al., 2021). Repeated K-Fold-CV with 10 folds and 10 repetitions (100 evaluations per model) was used (KUHN and JOHNSON, 2013). Monte Carlo simulation was also employed, with 30 repetitions and new random data splits into training (80%) and testing (20%), generating robust performance estimates.

For the comparative analysis, comprehensive statistical tests were applied: Friedman-Nemenyi, Diebold-Mariano, Model Confidence Set (MCS) (HANSEN et al., 2011), and Plackett-Luce Ranking (FAN et al., 2024). These methods allowed for the evaluation of the statistical significance of performance differences. The Prediction Interval Coverage Probability (PICP) was used to quantify the uncertainty associated with the estimates (GNEITING and RAFTERY, 2007; MURPHY, 2012).

A comprehensive analysis of residuals was conducted to verify the statistical assumptions of the models (BISHOP, 2006). Normality (Shapiro-Wilk, Jarque-Bera, Anderson-Darling), heteroscedasticity (Breusch-Pagan, White), and autocorrelation (Durbin-Watson, Breusch-Godfrey) tests were applied. For interpretability, SHapley Additive exPlanations (SHAP) (LUNDBERG and LEE, 2017) and Permutation Importance (BREIMAN, 2001) were employed, along with learning curves to diagnose overfitting.

The predictive capacity of the models was validated on 18 independent experimental concrete mixes. These mixes encompassed low (4.83–10.54 MPa), medium (19.69–45.94 MPa), and high (59.30–179.00 MPa) fck classes. This external validation step provided a practical assessment of the models’ generalization capability to unseen data.

3. Results and Discussion

The research compared nine machine learning (ML) algorithms for predicting the characteristic compressive strength of concrete (fck), focusing on a robust methodology to overcome gaps in previous studies. The results revealed that outlier removal optimization had a differentiated impact on the models, confirming that there is no universally optimal cleaning approach. Ensemble methods, such as XGBoost, Random Forest, and Gradient Boosting, demonstrated superior performance and greater resilience compared to linear and kernel-based models, especially after data preprocessing. This comprehensive evaluation provided an in-depth understanding of the predictive capabilities and limitations of various ML algorithms in estimating concrete strength.

Overall Model Performance and Data Cleansing Optimization

The optimization of data cleaning, performed through Bayesian optimization via Optuna, resulted in the removal of 0.66% to 8.6% of the training samples and generated divergent responses between algorithms. This variability reinforced the central hypothesis that there is no universally optimal cleaning method for all ML models. Models such as XGBoost, Random Forest, and Gradient Boosting benefited from or remained stable in their performance, indicating greater robustness or adaptability to changes in the dataset. In contrast, the Artificial Neural Network (ANN) and the polynomial SVR (SVR_poly) suffered substantial performance degradation, highlighting the sensitivity of these algorithms to data topology and the removal of extreme points.

The XGBoost model has consolidated itself as the highest-performing architecture, presenting the most favorable response to database refinement. A conservative cleaning configuration, which resulted in the exclusion of only 0.85% of the samples, provided an 8.2% increase in the IFI index and an 8.3% rise in the Plackett-Luce probability, from 33.9% to 42.2%. This gain ratified that the selective removal of low-density noise favored the stability of gradients in XGBoost (Chen and Guestrin, 2016; Shwartz-Ziv and Armon, 2022). Analogous trends, although of smaller magnitude, were observed for Random Forest and Gradient Boosting, suggesting that models based on boosting and bagging presented greater resilience and direct benefit in optimized data panoramas.

Conversely, the Decision Tree exhibited paradoxical behavior after cleaning. Although it maintained a high training coefficient of determination (R²) (0.9993 before cleaning, 0.9992 after cleaning), its test performance degraded significantly, with R² dropping from 0.9660 to 0.9465, a reduction of 2.0%. The mean squared error (RMSE) increased by 25.4%, and the mean absolute percentage error (MAPE) rose from 11.77% to 12.34%. The Plackett-Luce capacity for the Decision Tree drastically reduced from 21.1% to 3.8%, a drop of 17.3%. This phenomenon suggested that outlier removal inadvertently eliminated informative support vectors that defined critical decision thresholds, resulting in a model with severe overfitting to the central distribution data (Kuhn and Johnson, 2013).

The most pronounced deterioration was observed in the Artificial Neural Network (ANN), whose test R² decreased to 0.9048, a drop of 4.2%, accompanied by a 30.9% jump in RMSE. The application of the Z-score method with a threshold of five proved counterproductive, reducing Plackett-Luce’s capacity by 94%. Unlike tree models, ANN convergence depends on the density of information in the transition regions of the feature space. The exclusion of extreme cases distorted the non-linear decision boundary, confirming that the sensitivity of neural networks to data topology requires preprocessing strategies that preserve the variability of the studied physical phenomenon (Goodfellow et al., 2016).

The linear models, Linear Regression and Bayesian Ridge, demonstrated a convergence of performance, maintaining stable error metrics with almost no variation compared to data optimization methods, with a test R² of 0.819 and MAPE of 30.3. This stability suggests that the performance limiter for these algorithms was not the presence of noise or outliers, but the very linear nature of their base functions, which proved insufficient to map the complex non-linear interactions of the concrete fck database (Uyanik and Güler, 2013; Qinghua et al., 2019). The structural rigidity of the linear models was not mitigated by pre-processing, maintaining Plackett-Luce probability scores of approximately 8.5 × 10^-6 and IFI indices ranging from 0.0862 to 0.0954.

The SVR models exhibited the most extreme and divergent behaviors. The SVR_rbf model, which received no cleaning, maintained weak but stable performance with an R² of 0.598 and a capability of 9.84 × 10^-10. In stark contrast, SVR_poly underwent aggressive cleaning, removing 8.6% of the data, and suffered a significant performance drop. Its test R² decreased from 0.5873 to 0.4658, a 20.7% reduction, and the RMSE increased from 27.87 to 31.71 MPa, a 13.8% increase. The Plackett-Luce capability for this model fell from 4.95 × 10^-10 to 1.47 × 10^-11, a 97% decrease. This result demonstrated that, for certain kernel methods, aggressive cleaning can be extremely detrimental, removing essential support vectors for defining the decision boundary in the significant feature space (Smola and Schölkopf, 2004).

These results provide compelling evidence for the central hypothesis of this study: there is no universally optimal database cleaning method applicable to all models. The differential responses observed ranged from beneficial for XGBoost, Random Forest, and Gradient Boosting, to neutral for linear models, and detrimental for ANN and SVR. The Friedman test was applied to verify if there are statistically significant differences between the evaluated models, and the results indicated a p-value of 6.53627 × 10^-91. Thus, it can be stated, with 95% confidence, that there were statistically significant differences between the evaluated models.

The Model Confidence Set (MCS) procedure (Hansen et al., 2011), with a 95% confidence level and using the Mean Squared Error (MSE) on the common test partition as the loss function, identified XGBoost (MSE = 25.10), Gradient Boosting (MSE = 30.15), and Random Forest (MSE = 40.20) as the Superior Model Set (SMS). These three ensemble-based algorithms exhibited equivalent predictive accuracy, with XGBoost achieving an R² of 0.969 and an RMSE of 7.63 MPa. In contrast, Decision Tree (MSE = 80.25), ANN (MSE = 180.30), linear models (MSE ≈ 340), and both SVR specifications (MSE > 760) were sequentially eliminated, confirming their significantly inferior performance.

Additionally, the Nemenyi Critical Difference (CD) diagram, constructed with CD = 1.475 for α = 0.05 and a p(Friedman) ≈ 0.000, indicated statistically significant global differences among the models. Based on this criterion, XGBoost, Decision Tree, and Random Forest were considered statistically indistinguishable in terms of average ranking, although MCS identified a slightly different superior set of models based on absolute performance. The learning curves, which compared the behavior of the models on the original and optimized datasets, revealed that the impact of individualized Bayesian cleaning was influenced by the model architecture.

Ensemble methods, including XGBoost, Random Forest, and Gradient Boosting, exhibited stable convergence on both datasets, with validation gaps (∆Gap) below 0.005, confirming excellent generalization capability regardless of preprocessing. Among these, XGBoost showed the most pronounced improvement after outlier removal (∆Val = +0.0004 | ∆Gap = −0.0004), while Random Forest and Gradient Boosting maintained practically unchanged performance, evidencing the robustness of these algorithms to the presence of discrepant values. Decision Tree also responded positively to cleaning (∆Val = +0.0014 | ∆Gap = −0.0015), with a slight gain in validation and a reduction in the generalization gap.

In contrast, the SVR and ANN models reacted negatively to the optimization procedure. SVR_poly was the most affected model, showing a significant drop in validation (∆Val = −0.0135 | ∆Gap = −0.0032), a result attributable to the removal of 8.6% of the training samples. This removal eliminated essential samples for defining the decision boundaries in the space transformed by the polynomial kernel. ANN showed the most pronounced worsening among all models (∆Val = −0.0461 | ∆Gap = −0.0019), with high instability along the validation curves, suggesting that the removal of outliers distorted transition regions of attributes essential for adjusting the network weights.

Residual Analysis

The comprehensive analysis of residuals was crucial to verify if the models met the main statistical assumptions, as even models with good performance can present structural problems that compromise their reliability (Bishop, 2006). The normality of residuals, an important assumption for inference and construction of confidence intervals, was evaluated through the Shapiro-Wilk (Shapiro and Wilk, 1965), Jarque-Bera (Jarque and Bera, 1980), and Anderson-Darling (Uh and Yi, 2021) tests, along with visual diagnostics, such as Q-Q plots. All models showed statistically significant deviations from normality (p < 0.05), confirming that Gaussian homoscedastic prediction intervals are invalid for the entire portfolio of models, making non-parametric methods, such as Conformal Prediction or Quantile Regression, necessary.

The Linear and Bayesian Ridge models showed the highest p-values in normality tests (Shapiro-Wilk: 0.35 and 0.30, respectively), indicating they were the least non-normal, which is consistent with their moderate performance in Prediction Interval Coverage Probability (PICP). The Decision Tree, in turn, exhibited extreme non-normality (p < 0.01), reflecting its gradual prediction surface. Despite the superior accuracy of the points, XGBoost (p = 0.12), Random Forest (p = 0.08), and Gradient Boosting (p = 0.15) also rejected normality, explaining their severe PICP undercoverage. Heteroscedasticity, where the variance of the residuals is not constant, was assessed by the Breusch-Pagan and White tests (Hameed and Matanmi, 2021; Li et al., 2022), indicating inconsistency in model errors and the need for respecification (Chaabene et al., 2020; Verma, 2025).

The Durbin-Watson, Breusch-Godfrey, and Residual Autocorrelation tests were employed to verify the dependence of residuals on each other, indicating that the model did not capture the entire data structure, generating erroneous predictions and loss of reliability (Uyanto, 2020). In addition to statistical tests, graphical methods such as Q-Q Plots, residual histograms, and autocorrelation functions (ACF and PACF) were used for qualitative analysis (Rigby and Stasinopoulos, 2005). The histograms showed sharp central peaks with rapid decay, consistent with narrow prediction intervals, but a subset of observations presented prediction problems, invalidating the parametric intervals for all models.

The scatter plots, known as Parity Plots, illustrated the correlation between the experimental and predicted values of fck. XGBoost exhibited a tight clustering around the diagonal, with randomly scattered residuals, indicating minimal bias and adequate generalization. In contrast, the Linear and Bayesian Ridge models showed a systematic downward bias at higher strengths, with residuals becoming progressively negative. The Decision Tree presented a stepwise pattern, reflecting overfitting, while SVR_rbf produced predictions limited between 25 and 75 MPa, indicating an inability to extrapolate. SVR_poly exhibited virtually uncorrelated predictions, confirming a severe model specification error after cleaning.

Residual plots revealed a striking contrast between Linear Regression and XGBoost. The Linear model exhibited a systematic downward trend, with residuals becoming increasingly negative at higher predicted fck values, ranging from -10 to -30 MPa. This indicated that the linear functional form failed to capture the inherent non-linearity in the fck development process (Lundberg and Lee, 2017; Molnar, 2022). In contrast, XGBoost’s residuals showed random scatter centered around zero across the entire prediction range (0-120 MPa), with values uniformly distributed between -15 and +15 MPa and no systematic trends. This evidence reinforces the capability of ensemble methods to capture complex non-linear relationships between concrete constituents, a capability that linear models lacked.

The influence of input variables on the fck predictions was elucidated through SHapley Additive exPlanations (SHAP) (Lundberg and Lee, 2017) and Permutation Importance (Breiman, 2001) analyses. These analyses revealed differences in feature prioritization for each model. For the ensemble models, the most influential variables were active silica (SF), age (Age), and cement. In contrast, for the linear methods, cement, gravel (Gravel), and fly ash (FA) were the dominant variables. This difference in feature prioritization is indicative of the ensemble models’ ability to capture non-linear interactions and curing phenomena that linear models cannot represent.

Active silica, which showed low importance in linear models (approximately 6.3%), had a significantly higher position in XGBoost (15.8%). Similarly, age, which was the second most important variable in the ensemble methods (Random Forest with 0.220, XGBoost with 0.211, and Gradient Boosting with 0.216), had minimal importance in linear models (approximately 0.055). This change in variable relevance confirmed that ensemble methods successfully captured non-linear interaction effects and time-dependent curing phenomena. The SHAP heatmap quantitatively confirmed this divergence, showing the dominance of active silica in all tree-based models and its insignificance in linear models.

The Permutation Importance analysis showed that the influence of active silica depended on its interactions with other variables, rather than operating as an independent influencer. Although SHAP identified active silica as the most important feature for XGBoost and Random Forest, Permutation Importance showed more moderate values, indicating that the contribution of active silica to predictive accuracy depended on the presence and values of other variables, especially cement and age. This divergence between SHAP and Permutation Importance highlighted the complementary nature of these analyses: SHAP captures local contributions, considering interactions, while Permutation Importance provides a global and independent assessment of feature relevance. Together, they confirmed that the superior performance of ensemble methods stemmed from their ability to model how features interact in determining concrete fck (Lundberg and Lee, 2017; Molnar, 2022).

External Validation

To validate the predictive capability of machine learning models in practical scenarios, 18 independent experimental concrete mixes were tested, covering low (4.83–10.54 MPa), medium (19.69–45.94 MPa), and high (59.30–179.00 MPa) fck classes. The external validation results corroborated the performance classification obtained in the internal analyses. The XGBoost model demonstrated the highest accuracy when compared with laboratory measurements for all fck classes, showing variations less than 5% for most mixes. This consistency established it as the most reliable model for practical applications in predicting concrete compressive strength, confirming its robustness and generalization capability across different strength ranges.

Gradient Boosting and Random Forest also showed similar assertiveness to XGBoost for medium and high fck compositions, but showed a slight overestimation for low fck concretes. In contrast, SVR models exhibited a very inaccurate prediction capacity, with SVR_Rbf, for example, estimating 86.85 MPa for concretes that should have 179 MPa, a reduction of 51.5%. This demonstrated that this type of model could not extrapolate beyond the training domain. Linear models significantly underestimated high fck mixtures, about 16.8%, although they performed acceptably for low to medium fck. The Decision Tree presented adequate predictions for various mixtures due to memory-based learning, but in some ranges indicated inadequate fck, such as 45.94 MPa for a laboratory fck of 52.20 MPa, revealing a limitation in prediction capacity for concrete classes with a larger number of samples.

In summary, the research demonstrated that outlier removal optimization should be specific to each model, with XGBoost, Gradient Boosting, and Random Forest benefiting or remaining stable, while ANN and SVR_poly suffered degradation. The Model Confidence Set identified XGBoost, Gradient Boosting, and Random Forest as the superior set of statistically indistinguishable models. Residual analysis revealed that no model met the normality assumption, invalidating parametric prediction intervals. Silica fume and age were the most important variables for the ensembles, highlighting their ability to capture non-linear interactions and curing phenomena, which did not occur in the linear models. External validation confirmed the superiority of XGBoost, establishing a robust benchmark for future comparisons in predicting concrete compressive strength.

4. Conclusion

This study proposed a robust framework for comparing nine machine learning algorithms in predicting the characteristic compressive strength of concrete (fck), addressing methodological gaps in previous research. It was found that the optimization of outlier removal impacted the models differently, confirming the absence of a universally optimal cleaning method. Ensemble-based algorithms, such as XGBoost, Random Forest, and Gradient Boosting, demonstrated superior performance and greater resilience. The Model Confidence Set identified these three as a superior set of statistically indistinguishable models, with XGBoost standing out with an R² of 0.969 and an RMSE of 7.63 MPa. In contrast, linear models and SVR proved inadequate for the non-linear complexity of the data. SHAP analysis revealed that silica fume and age were the most influential variables in the ensemble models, highlighting their ability to capture non-linear interactions and curing phenomena that linear models did not represent. External validation corroborated the superior assertiveness of XGBoost across various fck classes. This methodology established a reproducible benchmark for future comparisons, contributing significantly to the reliability and reproducibility in predicting the performance of cementitious materials.

Despite the predictive performance achieved, residual analysis indicated that none of the models met the normality assumption, invalidating the use of Gaussian parametric prediction intervals. This limitation suggests the need to employ non-parametric methods, such as Conformal Prediction or Quantile Regression, for a more precise quantification of uncertainty in predictions. Furthermore, it was observed that the Decision Tree exhibited overfitting after cleaning, and the SVR_rbf and SVR_poly models demonstrated an inability to extrapolate beyond the training domain, especially after aggressive cleanings. For future studies, it is recommended to deepen the investigation into the application and development of uncertainty quantification techniques that are robust to deviations from the normality of residuals, further consolidating the reliability of fck predictions in engineering scenarios.

Bibliographic References

AMERICAN CONCRETE INSTITUTE (ACI). ACI Committee 318-14, Building code requirements for reinforced concrete, . Farmington Hills, MI, ACI, 2014.

AMERICAN CONCRETE INSTITUTE (ACI). ACI PRC-211.1-22: Selecting proportions for normal-density and high-density concrete – guide. Farmington Hills, MI: ACI, 2022

ASSOCIAÇÃO BRASILEIRA DE CIMENTO PORTLAND (ABCP). Parâmetros de dosagem do concreto. São Paulo: ABCP,1989

HELENE, P. Dosagem do Concreto de Cimento Portland. In: ISAIA, G. C., Editor. Concreto: Ensino, pesquisa e realizações. São Paulo: IBRACON, 2005. v. 1, p. 75-107

MOUTASSEM, F., CHIDIAC, S.E., Assessment of concrete compressive strength prediction models, KSCE J. Civ. Eng. 20 (2016) 343–358

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