Optimization of the Ternary Concrete Mix Design using Gaussian Process Regression

Technical Summary: Optimization of Ternary Concrete Mix Design Using Gaussian Process Regression

Problem Statement
The production of Ordinary Portland Cement (OPC) accounts for approximately 7–8% of global CO₂ emissions, necessitating the development of sustainable, low-carbon concrete alternatives. While supplementary cementitious materials (SCMs) like Ground Granulated Blast Furnace Slag (GGBFS) and Limestone Powder (LSP) offer viable pathways to reduce clinker content, their combined use in ternary blended systems presents complex, non-linear interactions. GGBFS enhances long-term strength through latent hydraulic activity but often delays early-age strength development. Conversely, LSP acts as a nucleation agent and filler, potentially compensating for early strength losses, yet excessive replacement can dilute cementitious phases and reduce mechanical performance. Conventional empirical modeling struggles to capture these synergistic effects and the inherent experimental noise in small-to-moderate datasets. Furthermore, there is a gap in applying probabilistic machine learning methods to predict multiple mechanical properties simultaneously for ternary GGBFS-LSP systems.

Methodology
This study employed a dual approach combining experimental characterization with advanced machine learning modeling:

• Experimental Program: Twenty-five distinct ternary concrete mix designs were prepared with a constant water-to-binder ratio of 0.40. The mixes varied GGBFS replacement levels from 0–40% and LSP replacement levels from 0–20% by binder mass. Specimens were cured at 23 ± 2°C and tested at 7, 14, 28, and 90 days for compressive strength, splitting tensile strength, and flexural strength.
• Machine Learning Modeling: Two algorithms were developed and compared:
  • Gaussian Process Regression (GPR): A non-parametric Bayesian method selected for its ability to provide both point predictions and uncertainty estimates (confidence intervals), making it suitable for noisy experimental data. The model utilized cement content, GGBFS %, LSP %, and curing age as input features.
  • Artificial Neural Network (ANN): A multi-layer perceptron (MLP) with three hidden layers (100, 50, and 25 neurons) using ReLU activation, trained with the Adam optimizer and L2 regularization to prevent overfitting.
• Validation: Both models were evaluated using 5-fold cross-validation. Synthetic oversampling was avoided to preserve the integrity of physical strength-mix relationships.

Key Results

• Mechanical Performance:
  • Compressive Strength: The binary mix with 30% GGBFS and 0% LSP (B0G30) achieved the highest 90-day compressive strength of 48.75 MPa, exceeding the OPC control by 7.0%. Ternary blends with 5–15% LSP and 20–40% GGBFS generally showed improved performance due to carboaluminate phase formation. However, LSP contents exceeding 20% resulted in strength reductions across all ages.
  • Splitting Tensile Strength: Strength generally improved with increasing GGBFS content. The ternary mix B10G40 (10% LSP, 40% GGBFS) achieved the highest 90-day tensile strength (3.58 MPa).
  • Flexural Strength: While early-age flexural strength was highest in binary GGBFS mixes, long-term performance was optimized in ternary blends. Mix B10G40 reached 6.31 MPa at 90 days.
• Model Performance:
  • Compressive Strength: GPR significantly outperformed ANN, achieving an $R^2$ of 0.848 (MAE = 1.755 MPa, RMSE = 2.289 MPa) compared to ANN's $R^2$ of 0.564.
  • Tensile and Flexural Strength: Prediction accuracy was lower for both models due to higher experimental scatter. Notably, ANN outperformed GPR for these properties ($R^2$ = 0.440 for tensile and 0.323 for flexural), suggesting its non-linear activation functions better captured the complex interactions governing these specific properties.
  • Uncertainty Quantification: A distinct advantage of GPR was demonstrated in its ability to generate 95% confidence intervals that widened in regions of sparse data (e.g., flexural strength with $n=100$), providing critical reliability metrics for structural design.

Key Contributions

1. Experimental Characterization: Provided a comprehensive dataset of 25 ternary GGBFS-LSP mixes evaluated across four curing ages for three mechanical properties.
2. Model Development: Developed individual GPR models for each mechanical property with integrated uncertainty quantification, a capability not previously reported for this specific ternary system.
3. Comparative Analysis: Systematically compared GPR and ANN, highlighting that while GPR is superior for compressive strength prediction and reliability assessment, ANN may be more effective for predicting tensile and flexural properties in this context.
4. Optimization: Identified four optimal mix designs based on specific performance criteria:
   • B0G30: Highest long-term compressive strength.
   • B0G40: Highest 28-day tensile strength.
   • B15G30: Most balanced performance across all three properties.
   • B15G10: Highest 28-day compressive strength.

Significance and Claims
The paper claims that the findings provide practical design guidance for sustainable ternary binder systems, demonstrating that moderate LSP replacement (5–15%) combined with GGBFS can balance early-age and long-term performance while reducing carbon footprints. The study emphasizes the complementary value of GPR and ANN: GPR is recommended as the primary model for compressive strength due to its probabilistic uncertainty bounds essential for reliability-based design, whereas ANN shows promise for capturing the non-linear complexities of tensile and flexural behaviors. The authors conclude that while prediction accuracy for tensile and flexural strength remains limited by dataset size and experimental scatter, the integration of GPR offers a robust framework for addressing uncertainties in concrete mix optimization. Future work is suggested to expand datasets and explore multi-output GPR for simultaneous multi-property prediction.