Dynamic Probabilistic Modeling of Concrete Strength: Markov Chains and Regression for Sustainable Mix Design
Bibliographic record
Abstract
Concrete is fundamental to modern construction, comprising 70% of all building materials and supporting an industry projected to reach $15 trillion by 2030. Predicting compressive strength—a key factor for structural safety and resource efficiency—remains a challenge, as conventional models often fail to capture the dynamic, time-dependent nature of strength development across mix compositions and curing intervals. This study proposes an integrated modeling framework using Markov Chain analysis and regression, validated on 135 samples from 27 mixtures with varying proportions of Portland Cement (PC), Fly Ash (FA), and Blast Furnace Slag (BFS) over curing periods from 3 to 180 days. The Markov Chain framework, integrated with regression analysis, models strength transitions across 10 states (9–42 MPa), with high accuracy (R2 = 0.977, standard error = 3.27 MPa). Curing time (β = 0.079), PC proportion (β = 0.063), and BFS proportion (β = 0.051) are identified as key drivers, while higher FA content (β = 0.019) enhances long-term durability. Model validation using Coefficient of Variation (CoV = 15.57%) and mean absolute error confirms robust and consistent performance across mix designs. The framework supports tailored mix strategies—PC for early strength, BFS for durability, FA for sustainability—empowering engineers to optimize mix selection and curing strategies for efficient and durable concrete applications.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".