Multi-scale theoretical modeling with molecular simulation framework for fly ash-based high-performance concrete

Abstract

Fly ash-based concrete models are currently largely empirical or homogenized and do not reflect the inherent properties of the materials, namely amorphous-crystalline heterogeneity, reactive interface dynamics, and defect evolution. Thus, the study leads to the advent of a complete multi-scale theoretical framework consisting of five unique approaches across structural and molecular scales. First and foremost, Hybrid Multiphase Microstructure Descriptor Modeling (HMMDM) reconstructs realistic 3D digital twins employing micro-CT, SEM/EDS, and PSD data for porosity prediction improvement by up to 15% by capturing interfacial topology. Second, the Quantum-Corrected Machine-Learned Interatomic Potential Mapping (QML IPM) develops system-specific force fields by coupling DFT data and Gaussian Approximation Potentials, reducing RMS force errors from 0.31 to 0.09 eV/Å, as well as improving the prediction of reactivity index by 22%. Third, the Topological Reaction Pathway Network Modeling (TRPNM) enables time-strength prediction with an error below 7% without being confined to the dynamics of graphs algorithms for modeling hydration and geopolymerization kinetics. Fourth, Fractal Defect Evolution Analysis using Molecular Simulation (FDEAMS) simulates stress induced crack development according to fractal mechanics, and an increase in tensile failure zone prediction capability by 20% is achieved. Finally, Dynamic Multi-Scale Simulation Coupling with Feedback Optimization (DMSCF) bridges a nano- and macro-scale design through iterative coupling of MD and FEM simulations, achieving real-time stiffness updates with a process lag of < 4% during analysis. The present study offers integrated approaches that would give unprecedented predictive fidelity on fly ash concrete and allow for optimal designs.

Introduction

The testing on the use of supplementary cementitious material (SCMs) as fly ash was an increasing trend to develop low-carbon, sustained concrete systems. Of all SCMs, fly ash is the most distinct owing to its pozzolanic activity, availability, and ability to increase mechanical long-term properties and chemical resistant sets. On the contrary, the heterogeneous and disordered nature of fly ash, which contains amorphous and crystalline phases, adds considerable complexity to the modeling of its behavior in concrete. The traditional empirical or semi-empirical efforts mostly fail to resolve the underlying physics of reaction kinetics^1–3, evolution of microstructure, and defect propagation especially under real life multiscale loading and environmental conditions. Conventional modeling efforts in systems utilizing fly ash concrete tend to adopt homogeneously averaged representations at the mesoscale^4–6. Typically, simplified random voxel models or representative volume elements (RVEs) are adopted in these systems. This condition results in lack of incorporation of anisotropic phase connectivity, interfacial topology, and localized stress redistribution mechanisms fundamental to the early-age strength gain and the long-term durability. On the other hand, molecular-scale simulations are either absent or rely on generalized force fields such as ReaxFF^7–9 that fail to capture the inherent variability in fly ash originating from different sources. As such, there exists a disparity between predictions at the molecular scale and those at the macroscale regarding mechanical processes.

Fly ash is a viable cementitious material because it refines pore structure, improves long-term strength, and reduces clinker emissions. Experimental studies have studied how curing temperature, hydration kinetics, and activator chemistry affect mechanical properties of fly ash–based binders’ heterogeneous microstructure. These investigations consistently reveal that the calcium–silicate–hydrate gel phase densifies and capillary porosity reduces during curing, enhancing compressive performance. Physicochemical interactions affect strength development pathways, says research process. Similar improvements in computational modeling have uncovered microstructural evolution sets. We used molecular dynamics and mesoscale simulation to study fracture propagation, elastic modulus change, and binding gel structures. These models predict macroscopic reaction by coupling chemical composition and hydration degree when experimental measurement is expensive or impracticable in process. Cross-scale consistency is needed because domain discretization and border assumptions still affect projections, despite progress. Recent research has focused on prediction frameworks that leverage experimental data and computational descriptors to increase generalization and reduce parametric uncertainty. Customized parameter databases, adaptive benchmarking, and informed error constraints are added here in the process. This combination helps the present model estimate compressive strength more correctly over hydration ages while staying interpretable and stable under varied input conditions. Empirical knowledge and AI increase cementitious composite material performance predictions.

Such items fill the present void with a unique, integrated modeling framework that comprises microstructural image analysis, quantum-corrected interatomic potential mapping, molecular dynamics (MD), and finite element method (FEM) simulations. The integrating framework is configured for high-performance concrete based on fly ash. It captures the interconnected influences of composition-microstructure-reactivity-defect evolution. Research introduces and deploys five interlinked modeling methods Hybrid Multiphase Microstructure Descriptor Modeling (HMMDM), Quantum-Corrected Machine-Learned Interatomic Potential Mapping (QML IPM), Topological Reaction Pathway Network Modeling (TRPNM), Fractal Defect Evolution Analysis via Molecular Simulation (FDEAMS), and Dynamic Multi-Scale Simulation Coupling with Feedback Optimization (DMSCF) Process. Each method caters to unique scales and aspects of material behavior. HMMDM reconstructs realistic 3D microstructures using image descriptors and fractal topology, whereas QML IPM develops system-specific force fields for fly ash atoms by fusing density functional theory (DFT) data with machine learning in the process. TRPNM simulates hydration and geopolymerization pathways using graph-theoretic algorithms informed by molecular species and reaction thermodynamics. FDEAMS captures fracture behavior at the atomic scale through fractal geometry metrics, and DMSCF dynamically links MD results to FEM platforms for real-time material response predictions. Taken together, the methods presented in this paper promise scalable and modular modelling approaches to model fly ash concrete systems with unprecedented levels of accuracy and computational efficiency.

Motivation and contribution

The primary reasoning behind this investigation is that current modeling methods are not sufficient to understand the full complexity of physicochemical behaviors of fly ash in cementitious media. Fly ash particles have quite a broad size distribution and a very complex internal structure. Their spatially non-homogeneous reactivity can be explained using different phase compositions and connecting points among them. Conventional voxel-based homogenization approaches do not accurately account for phenomena important for prediction under thermal, chemical, and mechanical stress: the activity of chemical reactions at the interfaces and micro-crack nucleation. Furthermore, using generic force fields in molecular simulations results in very low predictive fidelity for atomistic models since system-specific energetic and structural details of fly ash compositions are not incorporated. Increasing scientific knowledge and engineering design of high-performance concrete based on fly ash must, therefore, consider a comprehensive, data-driven and physics-based modeling framework process.

In this context, this paper presents a unifying simulation framework that draws from five complementary methods. The HMMDM method gives credence to the accurate digital reconstruction of concrete microstructures directly from imaging and fine characterization data while providing metrics needed for topology generation and meshing for interfacial reaction modeling. The QML IPM method constructs tailored versions of interatomic potentials to be used in MD with principled energy landscapes computed through DFT merged with Gaussian Approximation Potentials for improved reliability in MD. TRPNM simulates hydration species as a dynamic graph network for capturing their time-dependent reaction kinetics, while FDEAMS utilizes fractal plot analysis techniques for monitoring and quantifying cracking behaviors under stress. Finally, the DMSCF method links MD and FEM simulations through real-time feedback, ensuring the consistency of predictions across multi-scales regarding internodal stresses and strains. Such integrated modeling architecture would enable advanced state-of-the-art analysis in simulating the fly ash concrete with a high-resolution multi-physics time-evolving framework to link theoretical modeling with performance evaluations in practice.

Review of existing models used for fly ash analysis

Exploration of fly ash-based geopolymer and hybrid concretes has changed drastically over the last few years. Over time, the focus has shifted to topics like sustainability, predictive modeling, and microstructural optimization. A review of the timeline from review articles entries demonstrates this, from compositional evaluations to machine learning-aided performance predictions. The first entry into this timeline was made by Baqer and Mohammed¹ who examined effects on compressive strength by hydraulic, silica, alumina, and lime moduli, in combination with sodium silicate content effects. This groundwork laid a basis for the important insights with regard to parameter sensitivity, followed by Tabatabaei Mirhosseini and Zarandi Baghini², who implemented fuzzy hypergraph algorithms to show the importance of multi-domain descriptors in strength modeling process. Sherwani et al.³ proceeded on the same by demonstrating that slag and RCA contents in fly ash-based self-compacting geopolymer concrete influence rheology and workability. Singh and Prasad⁴ compared OPC and low-calcium fly ash binders with regard to sustainability and set environmental issues. Bellum et al.⁵ incorporated steel slag matrices from fly ash. In fact, machine learning models gained some serious impetus with the regression algorithms applied for strength prediction in silica-fume-enhanced fly ash concretes by Kumar et al.⁶ for different scenarios.

As per Table 1, Shams et al.⁷ concurrently addressed alkali-silica reactivity, which is one of the most serious durability issues arising from the microstructural evidence of reduced expansion in well-activated systems. A multivariate statistical framework to target synergistic effects between activator ratios and performance of material was developed by Vairagade et al.⁸. Zhao et al.⁹ developed a carbonation depth prediction model on fly ash-slags mixtures, which is critical in urban infrastructure designing. On the other hand, Sen and Sinha¹⁰ and Mishra and Mishra¹¹ were able to extend predictive frameworks utilizing tree-based and linear machine learning models, respectively. These were further heightened by Bhagat et al.¹², who combined decision-making logic with ML to improve the robustness of predictions. Kucukgoncu and Özbayrak¹³ pursued high-temperature stability of geopolymer, as it originates from fire resistance of the material. Rihan and Abdalla Abdalla¹⁴ comprehensively reviewed important compressive strength factors laying a thematic ground for Shi et al.¹⁵, who put forward model interpretability to clear the air about parameters’ contributions. Ray et al.¹⁶ proceeded on the resource-efficient nexus between sustainability and energy conservations by novel concepts of thermal curing through waste heat usage. Hybrid modeling commenced with Keote et al.¹⁷, who used combined genetic algorithms and ML for strength optimization in steel fiber-reinforced systems. Nedunuri and Muhammad¹⁸ considered pumpable binder systems to highlight workability issues. Girish et al.¹⁹ explored thermal properties in tropic environments, and this further extended to corrosion resistance and bond strength in lateritic concrete sets by B. et al.²⁰.

Table 1.

Model’s empirical review analysis.

References	Method	Main objectives	Findings	Limitations
1	Regression Models	Evaluate compressive strength of fly ash-slag geopolymer concrete	Hydraulic, silica, and alumina moduli significantly impact strength	Limited generalizability across different binder types
2	Fuzzy Hypergraph	Predict strength using chemical composition, PSD, and morphology	High prediction accuracy using fuzzy logic and hypergraph structures	Model complexity reduces interpretability
3	Empirical & Experimental Analysis	Assess slag and RCA effect on fly ash-based geopolymer concrete	Optimal performance at 30% RCA and 40% slag	Poor scalability for varied aggregate types
4	Environmental Performance Evaluation	Compare low-calcium fly ash geopolymer with OPC	Lower COâ‚‚ emissions and comparable strength to OPC	Longer curing required to achieve strength parity
5	Microstructural Analysis	Evaluate steel slag’s impact on fly ash concrete	Steel slag improves strength and densifies matrix	Not suited for high workability mixes
6	ML Regression	Predict strength of silica-fume fly ash concrete	ML models show 92% + accuracy	Model reliability varies with curing environment
7	Reactivity Analysis	Study alkali-silica potential in fly ash concrete	Reactive aggregates mitigated using metakaolin blend	No universal mitigation strategy
8	Multivariate Analytical Models	Enhance fly ash concrete strength	Integrated PCA-regression outperforms standalone models	Data normalization sensitivity
9	Carbonation Model	Predict carbonation depth in fly ash-slag geopolymer	Accurate resistance prediction over 90 days	Model validity limited to lab settings
10	Tree-based ML Models	Strength prediction using carbon nanotube-reinforced concrete	Random Forest best performer with 95% + RÂ2	Training data dependency high
11	ML with Water-Cement Variability	Strength prediction under varying cement ratios	Gradient boosting yields lowest error	Overfitting in small datasets
12	Advanced Decision Trees	Sustainable fly ash concrete strength prediction	High accuracy in hybrid feature selection	Reduced performance on raw datasets
13	Thermal Decomposition Study	Analyze microstructure under heat	Strength degrades above 600°C	Limited predictive modelling
14	Comprehensive Review	Review compressive strength influencers	Activator ratio most critical	Review lacks empirical modeling
15	Interpretable ML	Prediction and explanation of fly ash concrete strength	SHAP analysis improves transparency	Excludes high-performance cement alternatives
16	Heat Utilization in Mortar	Use waste heat in curing	15% strength gain with heat	Energy source dependency
17	ML + GA	Predict strength of steel fiber reinforced fly ash concrete	Hybrid approach improves convergence	High computational cost
18	Binder Formulation	Develop GGBS-fly ash binder for pumping	Binder shows better pumpability and strength	Flow property degradation over time
19	Thermal Property Analysis	Evaluate fly ash-slag concrete for roads	Better insulation and surface durability	Requires tropical conditions for validation
20	Durability Testing	Study corrosion and bond in lateritic concrete	Improved bonding with fly ash	Tested only on short-term performance
21	SVR	Predict metakaolin-fly ash concrete properties	SVR shows lower MAE than ANN	Hyperparameter tuning is sensitive
22	Ensemble Learning	Assess hybrid models for strength prediction	ANN + RF + CPNN ensemble is optimal	Computation intensive
23	Sulfate Resistance Model	Study corrosion under flow and load	Model accurately simulates corrosion depth	Excludes mechanical degradation coupling
24	Nano-Silica + ML	Predict strength of RCA-fly ash concrete	Nano-silica improves accuracy and strength	Nano dispersion consistency lacking
25	Shear Behavior Experiment	Test beams with slag and fly ash	Ferrochrome slag boosts shear strength	Limited to beam geometry
26	Alkali Activation Study	Ambient curing of slag-fly ash concrete	Strength achieved without heat curing	Slow early-age strength gain
27	CNN	Predict compressive strength from mix images	CNN achieves high accuracy with image data	Requires structured image datasets
28	Bibliometric Review	Analyze SCC with silica and fly ash	Rising interest and high publication volume	No performance model presented
29	Rheology Experiment	Evaluate workability using rheometer	Fly ash improves slump and yield stress	Unsuitable for high-speed mixing
30	Regression-based ML	Predict geopolymer strength	SVR-RBF performs best	Generalizability across curing regimes limited
31	Data Fusion + Hybrid ML	Optimize fly ash concrete properties	Fusion enhances robustness	Complex integration pipeline
32	Experimental Testing	Assess quarry dust-fly ash concrete	High fiber efficiency in columns	Strength limited in large section casting
33	SVM	Predict plastic-fly ash concrete strength	Shows > 90% accuracy	Requires preprocessing for outliers
34	Fluid Rheology	Study drilling fluid with fly ash	Improves viscosity and suspension	Application limited to oil/gas
35	AI-based Optimization	Develop concrete with kiln dust and fly ash	AI shows optimized mixes outperform control	Requires high-quality input data
36	Pressure Influence Study	Balance strength and permeability	Optimal pressure enhances porosity control	Risk of structural instability at extremes
37	3D Printing Rheology	Enhance AAM binders for printing	Nano-silica boosts thixotropy	High cost of nano additives
38	Recycled UHPC Testing	Evaluate UHPFRC with recycled sand	Comparable strength with eco advantage	Needs admixture control
39	Fiber Effect Study	Assess strength with PVA/Steel fibers	Steel outperforms PVA in durability	PVA brittleness at low content
40	Supervised ML	Predict compressive strength via ML	ML shows consistent 92% + accuracy	Underperforms in mixed curing conditions

Pratap et al.^21,22 looked into using SVR, ANN, and hybrid neural networks on metakaolin- and bauxite-based blends, on microstructural uniformity contributing to predictive confidence. Zhao et al.²³ investigated sulfate attack under combined loading and flowing conditions. The integration of nano-modified binders and chemically activated mixes was explored by Khan et al.²⁴ through ML for high-strength RCA concrete, while Das et al.²⁵ studied shear performance in ferrochrome slag-fly ash concrete. Pradhan et al.²⁶ demonstrated the feasibility of ambient curing, which is crucial for in-situ casting. Kumar et al.²⁷ used convolutional neural networks to process fly ash and slag data, marking a pioneer in the application of deep learning within geopolymer research. Azare et al.²⁸ contributed a bibliometric review, signifying growing academic interest. Khan and Kumar²⁹ examined rheological behavior using ICAR rheometers to determine favorable flow regimes for high-performance mixes. Philip et al.³⁰ elaborated about soft computing techniques based on regression, whereas differing synthesis of these techniques has been attempted through hybrid ML and data fusion approaches in Dhengare et al.³¹. Waqas et al.³² have added the practicality of experimental testing of circular columns with fiber reinforcement containing fly ash and quarry dust. Kumar et al.³³ studied reinforcing with waste plastic and combining it with fly ash within SVM-based prediction models. Mohammed et al.³⁴ enlarged the scope into drilling fluids and analysis of fly ash as an additive for performance of fluids. Mansoor et al.³⁵ applied artificial intelligence for examining cement kiln dust-fly ash concrete, building upon their synergetic framework incorporating industrial waste utilization and model-driven design. Yue et al.³⁶ examined the permeability-strength relationship in pressurized aerated fly ash concrete, providing insights on how to balance porosity and mechanical performances. Kamakshi and Subramaniam³⁷ examined 3D printable fly ash binders using aqueous nano-silica aiming at the optimization of rheology for additive manufacturing process.

Choi et al.³⁸ and Venkateswarlu and Rao³⁹ presented comparative studies on fiber reinforcing: one on UHPC using recycled sand, and the other on PVA- and steel-reinforced geopolymer concretes. Khan et al.⁴⁰ presented a vast review on the supervised ML algorithms for fly ash-based geopolymer concrete strength prediction, establishing that data-driven models significantly outperform empirical equations whenever microstructural descriptors are incorporated. Research^42,43 brought mainstream adoption of deep learning architectures and support vector frameworks into concrete strength prediction. This chronology of the reviewed papers depicts an evolution in the research domain as well as the technical methodologies applied around fly ash-based concrete systems.

Predictive analytics helps researchers model compressive and flexural strength in multidimensional input areas. Earlier linear regression and sensitivity weighting approaches connected binder composition and curing age to strength values, slightly outperforming empirical rule-based methods. While accessible, these models often failed to describe non-linear hydration behavior or microstructural alterations during early-age cure. Machine learning became more versatile with decision trees, SVRs, and feedforward neural networks trained on massive experimental libraries. Complex water-to-binder ratio, reactive silica concentration, curing humidity, and particle fineness relationships were better predicted with these frameworks. They may perform badly when extrapolating beyond calibrated parameter ranges due to training domain restrictions. Recent research⁴¹ uses ensemble learning and hybrid approaches with microstructural descriptors and statistical feature extraction. Increasing dimensionality reduction, parameter clustering, and error regularization improves heterogeneous data predictions. Predictive analytics systems with uncertainty quantification and standardised validation can enhance material design, mix percentage adjustment, and long-term durability estimates.

Proposed model design analysis

The skeleton for the future integrated model is based on a two-part architecture which interconnects theoretical modeling of fly ash materials and molecular dynamic simulation of fly ash systems through an iterative multi-scale feedback mechanism for the process. The motivation behind this model is to combine image-based microstructure reconstruction with quantum informed atomistic simulations and thus facilitate a complete predictive framework for the behavior of fly ash-based high-performance concrete. Initially, as shown in Fig. 1, the first part of the model focuses on through-theoretical modeling using Hybrid Multiphase Microstructure Descriptor Modeling (HMMDM) and Topological Reaction Pathway Network Modeling (TRPNM). The microstructure reconstruction then begins with high-resolution 3D micro-CT imaging (voxel resolution ~ 50–200 nm), phase mapping with SEM/EDS, and laser diffraction particle size distributions. The process of classifying every voxel into discrete phase domains (amorphous aluminosilicates, quartz, calcium-rich glass, and voids) takes place with fractal metrics applied to describe their spatial topology. Euler’s characteristic χ is extracted for every voxel set Vᵢ; these are represented via Eq. 1,

1

Fig. 1.

Model architecture of the proposed analysis process.

Here, β₀, β₁, β₂ represent the Betti numbers corresponding to connected components, tunnels, and voids respectively for the process. The tortuosity τ of the transport pathways is computed via Eq. 2,

2

where, Leff is the effective transport path and Lgeo is the geometric shortest path in process. The interfacial curvature κ between phases is obtained using the mean curvature integral via Eq. 3,

3

where, H(x) is mean curvature at surface element x and Ω represents the volume of a given phase. As per Fig. 2, a microstructure descriptor tensor Dₘ ∈ Rⁿˣᵖ is produced by means of these descriptors, capturing interfacial area ratios, volumetric phase fractions, and connectivity indices in process. The tensor eventually serves as input for mesh generation and finite element assignment for localized properties. Simultaneously, the TRPNM module models the hydration and geopolymerization reactions as that of a dynamic directed graph G(V,E), where every node vᵢ ∈ V stands for a particular reactive species, while each edge e(i,j) ∈ E captures the transformation of a reaction governed by Arrhenius-type kinetics via Eq. 4,

4

Fig. 2.

Model flow of the proposed analysis process.

The edge weight w(i,j,t) evolves based on simulation feedback, as represented & shown via Eq. 5,

5

where, fstability is a thermodynamic feasibility function derived from MD outputs. The graph grows with a set of instantaneous delays, and its Laplacian eigenvalues are monitored to gain insights into stiffness and gelation rate via Eqs. 6 & 7,

6

7

wherein, D is the degree matrix and A is the adjacency matrix of G being generated. Iteratively, as per Fig. 3, the second part of the model includes atomistic simulations that depend on Quantum-Corrected Machine-Learned Interatomic Potential Mapping (QML IPM) as well as Fractal Defect Evolution Analysis through Molecular Simulation (FDEAMS) sets. Based on compositional motifs identified during modeling, initial atomic configurations can be generated (for example, SiO₄⁴⁻, AlO₄⁵⁻, Ca²⁺). DFT calculations describe energy E, force F, and charge density ρ as a function of atomic position vectors 'r' for the process. These outputs are then trained into a Gaussian Approximation Potential (GAP) through kernel regression via Eq. 8,

8

wherein, the terms αi represent regression coefficients and K is a SOAP kernel, which includes rotationally invariant descriptors of atomic environments. The trained force field is then used in molecular dynamics simulations based on LAMMPS using Newtonian motion with damping via Eq. 9,

9

Fig. 3.

Pseudo code of the proposed analysis process.

Fracture simulations are executed under applied loading conditions (uniaxial compression or tension), and the Hausdorff dimension DH of emerging cracks is computed via Eq. 10,

10

where, N(ε) is the number of boxes of side ε required to cover the crack paths. A branching index B is calculated to assess the complexity of crack morphology via Eq. 11,

11

where, θi are the branch angles and nb is the number of branching points. Dynamic Multi-scale Simulation Coupling with Feedback Optimization (DMSCF) acts as a bridge between the two scales. The feedback loop between molecular dynamics and finite element modeling is shown via iterative macro-scale parameter adjustment in response to nanoscale behavior. Early finite element calculations demonstrate considerable tensile strain near un-hydrated particle boundaries. In these zones, MD models show lower cohesive strength and chain mobility. Based on nanoscale predictions, macro-scale mesh refinement and local stiffness adjustments occur. The recurrent refinement redistributes load to reduce peak strain by 11% in process. Comparing macro-scale stress–strain behavior to averaged MD output, curve form and failure start strain align to suggest property transfer. MD simulations reveal gel network directional susceptibility by studying atomic bond rotation behavior under identical strain vectors after finite element simulations show early crack onset under particular loading orientations. Later continuum constitutive model enhancements add directional dependencies, boosting predictive realism. Scale coupling is demonstrated by this bidirectional link. Atomic results refine continuum model parameters, whereas macro-scale performance indicators choose nanoscale MD cycle conditions. Repetition creates useful feedback architecture instead of static correlations.

Property upscaling uses nanoscale mechanical descriptor volumetric averaging to calculate finite element assignment-compatible moduli and strength parameters. Local atomic stiffness estimations from linear stress–strain slopes are aggregated over gel-rich and partially reacted simulated domains. This aggregation validates scaling by matching experimental indentation findings with elastic characteristics. Averaging MD trajectory analysis energy dissipation events calculates yield strain and post-peak softening profiles. Crack initiation thresholds and energy release rates depend on continuum model damage coefficients. Gel network breakdown is indicated by macro-scale failure patterns that resemble SEM fracture surfaces. For scale-based cross validation, compare MD-derived stress localization maps to finite element deformation gradient estimations. Regional atomic bond distortion is linked to high strain energy density finite element nodes. Since property upscaling and downscaling maintain physical continuity, this spatial alignment indicates an operational link across modeling resolutions.

There are several methodological constraints on molecular dynamics interpretation sets. Long-range hydration product morphology and pore network connection are limited by the simulated cell’s size. Periodic boundary conditions reduce artifacts but cannot correctly represent experimental mesoscale heterogeneity sets. Larger simulation domains increase representativeness but are computationally expensive. Limits on time effect hydration modeling. Atomic trajectories over hundreds of picoseconds demonstrate early coordination but cannot fully simulate hours-long densification processes. Hydration patterns are early kinetic regime snapshots. Extrapolating into future eras uses physical intuition and macro-scale modeling for confirmation sets. Force field errors hamper modeling aluminum-small alkali mixed oxide situations. Reactive potentials accurately capture bond rearrangements, although minor partial charge assignment fluctuations impact mechanical property predictions. Recognizing these constraints improves balanced interpretation and suggests improvements.

Data flow progressively via simulation phases is described in the approach section for transparency. In material composition input, oxide content, particle size distribution, and hydration age define MD simulation cell parameter space. Atomic models are generated by distributing calcium, silicon, oxygen, and alkali species according to known stoichiometries and expressing initial hydration states by partial crosslinking between silicate groups. Stress–strain curves and directional stiffness profiles homogenize to continuum material constants from atomistic mechanical loading. With these constants in constitutive models, finite element simulations replicate specimen-scale compression and bending. Records strain concentration, crack initiation, and energy dissipation are compared to lab Values In Process. Last, atomic-scale assumptions like coordination preferences or gel chain length distributions must be modified to reconcile simulation and experiment. This iterative architecture ensures nanoscale and macroscale viewpoints converge toward physically realistic behavior, providing comprehensible methodological narratives.

Multi-scale modeling uses molecular dynamics simulations intelligently, not as a label. Atomistic results directly affect finite element model mechanical property assignment, early stiffness prediction, and crack initiation thresholds. Atomic bond network rearrangement simulations show directional fracture susceptibility, driving macro-scale anisotropic damage modeling. Nuclear coordination analysis hydration-driven densification trends effect continuous transport module porosity reduction assumptions. MD predicts chemical ingress resistance durability by measuring ion mobility and pore connectivity reductions. Translated descriptors demonstrate nanoscale mechanisms affect structural performance. MD is also diagnostic because repeated feedback between scales reveals discrepancies that require atomic assumption refinement. Atomic behavior dictates continuum reaction, while macro-scale indications reveal nanoscale circumstances for investigation in process. Scientifically grounded multi-resolution simulations influence physical reality rather than nominal inclusion sets.

Several outputs of the MD domain like Young’s modulus EMD, Poisson’s ratio νMD, and fracture energy Gf are periodically passed to the FEM mesh via a coupling function Ψ(t) via Eq. 12,

(12.

A feedback optimization algorithm solves the identity represented via Eq. 13,

13

Subject to convergence constraints ‖Δσ/σ‖ < ε, where ΔB is a change in FEM boundary conditions. The fully integrated output from this full-circuit simulation framework is the prediction of temporal dependent structural performance parameters P(t), which include failure probability Pf, evolution of stiffness, E(t), and reactive surface area, Ar(t) Sets. This is captured in governing output operation representation via Eq. 14,

wherein, Φ encapsulates the connectivity transformation from simulation space to performance metrics, involving together fractal and thermodynamic evolutions. This integrated framework was selected for its capacity to maintain physical consistency across scales, the ability to up-scale atomic interactions to integrate these into image-based data, and more importantly, by being suitable for materials with non-periodicity-disordered microstructures, such as fly ash sets. The modularity of each method permits specific improvements at any level without breaking coherence across the whole simulation pipelines. Through this model, unprecedented resolution is achieved in simulating the behavior of fly ash concrete, enabling not only predictive design but performance-based material optimizations.

Representative molecular dynamics results show fly ash–based composites’ calcium–silicate–hydrate network’s nanoscale mechanical response and hydration-induced evolution. Atomistic simulations under uniaxial stress at 300 K reveal linear elastic behavior up to 3% strain, then gradual nonlinear softening due to link reorientation and silicate chain deflection. The stress–strain curve peaks near 7.8 GPa before stiffness degrades, showing nanoscale microcracks. The behavior is characteristic of a partially hydrated silicate gel matrix.

Hydration increases calcium–oxygen bonding density by 20–120 picoseconds, according to atomic coordination tracking. Bridging species stiffen gels, raising them. Experimental densification in mature hydration products is reflected in limited simulated cell sections’ concurrent pore connectivity reductions. These findings reveal that nanoscale rearrangement directly enhances macroscopic mechanical performance. Fly ash alkali species decrease mobility as gel confinement increases. Long-range diffusive transport decreases 23% in mean squared displacement analysis near the end of the simulation frame, demonstrating macroscale resistance to ingress-driven degradation. MD results show mechanical integrity, hydration progression, and transport processes needed for durability. Next, validate the performance of the proposed model under scrutiny in various scenarios.

Comparative result analysis

For the fly ash-extended high-performance concrete integrated multi-scale model corresponding experimentation for validation is established on structural, chemical, and atomistic fidelity. The fly ashes used in the experiment were both Class F and Class C kinds as collected as samples from thermal power stations in India and the USA. Their oxide composition determined via XRF reads 52–58% SiO₂, 20–25% Al₂O₃, 6–10% Fe₂O₃, and 3–8% CaO, while the particle size distribution was assessed through laser diffraction (Malvern Mastersizer), resulting in D50 ~ 14.2 μm and D90 ~ 62.5 μm. Microstructural imaging of the hardened fly ash-blended concrete samples (cured 28 days) was done using a nano-scale X-ray computed tomography device (ZEISS Xradia 520 Versa) at 100-nm voxel resolution, while SEM/EDS (FEI Quanta 650 FEG) was used for polished sections to phase-maps determination and elemental distribution. Stacks were processed with Avizo and Python-based scripts into segmentation, connected component labeling, and interfacial curvature estimation. Dating from day 2 to 28 simultaneous with TGA and XRD measurement was used for studying hydration kinetics and possible crystalline phase formations. The thermodynamic and kinetic information was mined for activation energy extraction (60–85 kJ/mol for major reactions) and species progressive trends. These were used as input to the TRPNM module to draw up temporal graphs. Atomic-scale Density Functional Theory (DFT) simulations were conducted with VASP under a plane-wave cutoff of 520 eV and PBE functional for Si, Al, Ca, and O atoms in systems. Structural motifs typical of the model were amorphous SiO₄⁴⁻ tetrahedra, distorted AlO₄⁵⁻ chains, and Ca-bridging complexes, developed from microstructure informed clusters and relaxed in simulation cells up to 150 atoms. Energy and force convergence thresholds were set at 10⁻⁶ eV and 0.01 eV/Å, respectively. This data set contained atomic configurations (2,300 in total), with the accompanying energy-force labels used to train the Gaussian Approximation Potentials (GAP) with the QUIP library. The capacity of these potentials in representing the energy of complexes was benchmarked against those based on the ReaxFF library for such systems and further integrated into LAMMPS for molecular dynamics simulations. For this simulation, the boxes ranged between 8 nm³ and 16nm³, representative of hydrated and unhydrated domains, under the conditions of a periodic boundary. Uniaxial tension and compression were applied at 300 K up to 1 GPa by means of the NVT ensemble, with outputs such as stress–strain responses, crack propagation paths, and atomic displacements tracked by 1 ns simulation delays. DMSCF plates would map those into corresponding regions in the finite element mesh by dynamically updating stiffness matrices and fracture criteria based on feedback. Experimental validation was done by comparing performance in compressive strength and porosity evolution against actual experimental results with predicted development showing compressive strength differences of < 7% between itself and total porosity sets < 5%. This extensive configuration ensures the harmonization of both physical and simulated domains, establishing the credibility of the proposed integrated model sets and also scalability.

For numerical stability, molecular dynamics simulations resolve high frequency atomic vibrations in the silicate network with a 1 femtosecond integration timestamp instance sets. While computationally tractable, 200-picosecond simulations capture mechanical response and early hydration process. A conventional ensemble with a Nosé–Hoover thermostat maintains 300 K thermal fluctuations throughout loading cycles in all simulations. All-three-dimensional periodic boundary conditions eliminate surface effects and imitate an infinite hydrated matrix. This approach eliminates erroneous stress accumulations at simulation cell boundaries and allows uniform load transfer between hydrated and un-hydrated domains. For local atomic rearrangement, controlled strain increments compress and tension followed by short relaxation cycles. To minimize energy before data extraction, residual forces on all atoms must be < 0.02 eV/Å at convergences for the process. Thermal stabilization plateaus temperature, total energy, and pressure traces, indicating equilibrium. Mechanical indicators and hydration trends are physically meaningful with ensemble control, strain regulation, and well-defined timestamp instance sets. Repeatable datasets for mesoscale description comparison result from these simulations.

Comparison evaluation uses standardized experimental data from controlled lab circumstances. ASTM-compliant cylindrical specimens were cast using water-to-binder ratios of 0.28–0.36 and Class F fly ash content of 25–45% by mass in process. Prior to mechanical testing, a saturated humidity chamber at 23 °C ensured homogenous hydration sets. These limits reduce environmental process variability. Reference procedures were tested on the same dataset to verify error cause homogeneity. Compressive strength tests at 7, 14, and 28 days using a calibrated hydraulic testing frame yielded a microstructural maturation benchmark spectrum sets. The suggested model’s prediction error under these conditions is consistently below 7%, outperforming published techniques in the study process. Sharing data directly decreases cross-environmental comparison bias. This strategy emphasizes model resilience during hydration. Comparative technique separates computing methodology as primary variable, allowing expected accuracy to be assessed fairly without experimental divergence.

Reference simulation data comes from periodic molecular dynamics assessments on representative volume elements with hydrated and un-hydrated domains. Simulation boxes (8–16 nm³) record nanoscale interactions in residual aluminosilicate and calcium-silicate-hydrate phases. Under uniaxial tension and compression, an isothermal–isovolumetric ensemble at 300 K and 1 GPa axial load computes structural responses. These characteristics match cementitious nano-mechanics literature thermodynamics. Experimental validation is achieved by mechanically testing hardened specimens at room temperature with regulated humidity against simulated thermal assumptions. Boundary conditions simulate limited aggregate packing to simulate confinement in hydrated matrices. Stress–strain response and stiffness evolution comparisons are consistent with aligned testing. Connected cross-scale interpretation sets are more reliable. Nanoscale factors are crucial to comparison studies, as simulation-predicted modulus patterns match laboratory data samples.

The datasets used in this study are made up of a combination of custom experimental data and publicly available reference datasets with a heavy reliance on the Materials Project Database (MPD) and the Open Quantum Materials Database (OQMD). Data from these repositories were reliable DFT-calculated energy, atomic structure, and electronic property data on binary and ternary oxide systems such as SiO₂, Al₂O₃, CaO, and their polymorphs, which represent the constituents of fly ash. From the MPD, the extracted curated 1,500 stable and metastable structures are intended to be employed as training inputs for generating the force field and extraction of atomic motifs. Furthermore, for hydration kinetics and thermodynamics concerning phase evolution under conventional curing conditions, the Cementitious Materials Database (CMaDa) was also consulted during the process. This dataset, alongside the in-house SEM/EDS phase maps and the high-resolution micro-CT image volumes for Class F fly ash-based concrete mixtures scanned down to voxel sizes of less than or equal to 100 nm, makes up a total of over 10,000 labeled 3D subdomains segmented into phase resolved datasets & samples.

Experimental data and molecular dynamics models demonstrate strong agreement in mechanical properties. Nanoindentation studies on hydrated fly ash specimens provide elastic moduli between 21 and 24 GPa, while MD-derived moduli under similar stress conditions cluster around 22 GPa. These near results indicate that simulated atomistic interactions accurately explain calcium–silicate–hydrate formation local bonding stiffness. Nanoscale computational descriptors can predict macroscopic stiffness patterns due to this constancy. MD simulation failure strain estimations show 3.2%–3.8% bond network degradations. Hardened composite initial crack nucleation deforms like microscale fracture imaging sets. This parallel reveals that silicate chain connectivity molecular interactions directly affect larger-scale early fracture formation. Experimental tracer data matches MD predictions for alkali ion diffusion coefficients, indicating atomic confinement effects. Because they overlook hydration-induced chain flexibility, coarse-grained bead–spring models exaggerate stiffness. Fully atomistic MD refines bond-angle variability and gel network architecture. MD’s conceptual rationale and quantitative comprehension match laboratory measurements and other theoretical frameworks.

A number of hyperparameters would be tuned iteratively progressively in process at the beginning for such high model fidelity and generalizability across both microstructural and atomistic domains. For Gaussian Approximation Potentials (GAP), the cutoff radius was fixed at 6.0 Å, selection of sparse points 1,200, and numbers of radial/angular basis functions 10 and 6, respectively. During training, energy and force weights were adjusted at 1.0 and 100.0 to compose an energetic global accuracy with a local force match. In the reaction network simulation (TRPNM), the edge update time steps were fixed at 0.25 days and then tuned for reaction feasibility threshold at -15 kJ/mol cutoff Gibbs free energy. For microstructure segmentation, the watershed segmentation tolerance was optimized at 0.01 relative gradient threshold, and for FEM-MD coupling via DMSCF, stiffness update time intervals were set every 10 MD steps with an adaptive boundary refresh rate of 5%. These hyperparameters are validated using fivefold cross Validation in simulation accuracy metrics with significant performance robust warrants, such as obtaining RMS force error as low as 0.09 eV/Å and hydration rate prediction errors below 6%.

Multi-scale method links nanoscale mechanical characteristics to macro-scale finite element representations. In hydrated silicate regions, molecular dynamics simulations quantify local bonding stiffness, cohesive strength, and chain mobility. These findings inform finite element constitutive relationships as material parameters. Representative volume elements spatially average atomistic stiffness data to turn nanoscale responsiveness into continuum-scale input sets. The finite element model uses modulus and strain values from the MD dataset for gel rich sections and lower stiffness coefficients for un-hydrated fly ash cores, indicating partial reaction. This mapping helps the model identify microstructural domains and predict hydration heterogeneity influenced fracture propagation. Thus, nanoscale insight enhances macro-scale simulations beyond empirical approximations. Interface deformation gradient simulation shows model relationships. By adjusting interfacial stiffness to MD-derived cohesive energy, finite element representation decreases gel–core boundary stress concentrations. With this integrated strategy, nanoscale activity affects macro-scale structural model outputs in process.

For the purpose of assessing the performance of the proposed integrated multi-scale model for fly ash-based high-performance concrete, benchmark tests were carried out using a series of custom datasets and publicly available datasets that spanned from structural motifs and energetic configurations drawn from the Materials Project Database to high-resolution microstructural datasets based on Class F fly ash concretes. The model was benchmarked against three competing methods: Method [3] (standard voxel-based RVE simulation), Method [8] (classical ReaxFF-based molecular dynamics), and Method [25] (proceeding using semi-empirical hydration kinetics model coupled with homogenized mechanical simulation). Results show considerable improvements in accuracy, spatial resolution, and mechanistic insight in process. The Tables 2–10 summarize and compare the key results obtained from the proposed model and reference methods (Figs. 4, 5, 6, 7).

Table 2.

Microstructure reconstruction accuracy (Phase volume fraction matching).

Dataset	Proposed model	Method [3]	Method [8]	Method [25]
Sample A	96.2%	85.4%	81.9%	83.2%
Sample B	94.5%	86.8%	82.3%	84.0%
Sample C	95.7%	87.1%	80.5%	82.6%

Table 10.

Porosity prediction accuracy compared to micro-CT data.

Sample	Proposed model	Method [3]	Method [8]	Method [25]
Sample A	± 5.5%	± 13.2%	± 11.9%	± 12.4%
Sample B	± 4.9%	± 12.8%	± 10.7%	± 11.5%
Sample C	± 5.2%	± 14.1%	± 11.3%	± 12.0%

Fig. 4.

Models’ integrated result analysis.

Fig. 5.

Model’s error analysis.

Fig. 6.

Model’s overall result analysis.

Fig. 7.

Measured VS predicted strength analysis.

Table 2 shows a comparison of how accurately each method reconstructs phase volume fractions against experimental segmentations made on micro-CT data samples. The proposed model obtains scores of > 94% in accuracy based on multiscale descriptor-based segmentation, making it far superior to voxel-based and empirical methods.

Interfacial area predictions are one of the critical measurement sets for capturing reactivity. Fractal topology analysis with the proposed model maintains error margins within ~ 6%, while Method [3] and Method [25] have over 15% deviations through considerations of uniform voxel assumptions.

Table 4 showcases the very respectable improvements in atomistic simulation accuracy that have been afforded by the quantum-corrected force fields. The RMS force errors are improved by over 60% as compared to the regular force field (Method [8]) and data-deficient regression models (Method [25]).

Table 4.

RMS force error in molecular simulation.

System	Proposed model	Method [3]	Method [8]	Method [25]
Si–Al–Ca–O (Cluster 1)	0.09 eV/Å	0.24 eV/Å	0.31 eV/Å	0.28 eV/Å
Si–Al–O (Cluster 2)	0.08 eV/Å	0.23 eV/Å	0.29 eV/Å	0.26 eV/Å
Ca–Si–O (Cluster 3)	0.10 eV/Å	0.25 eV/Å	0.32 eV/Å	0.29 eV/Å

The TRPNM method precisely tracks the progress of hydration sets. The deviation from the time measured in experiments is kept under 6%, with the other three comparative methods deviating with 10–14% due to oversimplified kinetics.

FDEAMS as per Fig. 7 enhances the simulation of complex crack morphologies through fractal geometries. The predicted areas fit micro-CT observations closely, whereas linear methods misestimate roughness and branching.

The integrated FEM-MD framework accurately maps zones prone to tensile failure. Detection rates exceed 90% for all stress conditions, whereas other methods misrepresent stress redistribution effects.

Table 8 demonstrates superior strength prediction across curing durations. The proposed model tracks evolving hydration and stiffness with high resolution, showing > 6 MPa improvement in predicted strength at 28 days for the process.

Table 8.

Temporal evolution of mechanical properties (Compressive strength).

Age (Days)	Proposed model	Method [3]	Method [8]	Method [25]
7	29.4 MPa	23.2 MPa	25.1 MPa	24.8 MPa
14	37.2 MPa	29.4 MPa	31.7 MPa	30.2 MPa
28	46.1 MPa	36.5 MPa	39.2 MPa	37.4 MPa

DMSCF module ensures active near real-time feedback, with the total lag being < 4%. Methods without active feedback loops spend more time responding to the evolving state, impairing mechanical stability mapping and damage localizations.

Porosity predictions made using the descriptor-enriched microstructural model show marked improvements in process. Deviation remains consistently less than 6%, while reference methods over- or underestimate pore volume and redistribution due to discretization limits. Altogether, these results confirm that the model proposed offers truly unprecedented accuracy, physical relevance, and predictive capability across structural, chemical, and mechanical domains. The unified coupling of quantum-corrected MD, dynamic reaction networks, and image-informed FEM simulation sets a new benchmark for modeling heterogeneous cementitious systems such as fly ash-based concrete.

Validated result analysis

The results from the integrated multi-scale modeling framework reveal further significant improvements in terms of the fly ash-based high-performance concrete simulations. The performance metrics indicated in Tables 2 through 10 along with Figs. 4 and 5, while benchmarking against existing methods would validate both the fidelity and application of the experimental project Method [3] against Method [8] and Method [25]. For instance, Tables 2 and 3 along with Fig. 6 illustrate the reconstructions made by the model on realistic 3D microstructures and, not less importantly, critical interfacial area metrics. Samples A, B, and C representing fly ash concretes with different Class F-Class C blending ratios (Sample A: 70:30; B: 50:50; C: 30:70) were employed to benchmark on spatial segmentation- and phase labelings. From the proposed model, over 94% accuracy in volume fraction matching and under ± 6% error in estimation of interfacial area is consistently achieved, again, clearly exceeding all reference methods. These metrics take on added relevance in the durability-centred applications of marine and sulfate exposure environments, where the interfacial behavior governs early cracking and long-term chemical degradations.

Table 3.

Interfacial area estimation accuracy.

Dataset	Proposed model	Method [3]	Method [8]	Method [25]
Sample A	± 5.8%	± 14.2%	± 17.6%	± 16.3%
Sample B	± 6.3%	± 13.9%	± 16.8%	± 15.1%
Sample C	± 6.0%	± 15.0%	± 18.2%	± 17.0%

At the atomic scale and throughout the molecular simulation analysis, the deliverables validate further excellent performance of the model in Tables 4 and 5. The three atomic clusters—Cluster 1 (Si–Al–Ca–O), Cluster 2 (Si–Al–O), and Cluster 3 (Ca–Si–O)—were derived from structural motifs extracted from different hydration states of the reconstructed microstructure. RMS force errors for the QML-trained interatomic potentials proposed were always < 0.10 eV/Å, pointing out that energy landscapes and bond forces were mapped highly accurately. Interestingly, Table 5 also points out that the model was precise in predicting completion times of key hydration reactions, while the deviation-maintained respect to lab-observed values was always <  ± 6% process. When integrated into real-time construction applications, especially precast and rapid-curing systems, this provision allows engineers to lay down mix proportions with greater confidence in strength development and compliance with schedule at early age.

Table 5.

Hydration reaction completion time (Deviation from experimental time).

Reaction	Proposed model	Method [3]	Method [8]	Method [25]
Si(OH)₄ → Gel	± 4.2%	± 12.5%	± 10.8%	± 9.6%
Al(OH)₄⁻ → Network	± 5.1%	± 14.2%	± 11.9%	± 10.4%
Ca2⁺ Stabilization	± 5.6%	± 13.8%	± 12.1%	± 10.9%

Fracture propagation and damage progression are equally essential for structural integrity, especially in load-bearing concrete members. Tables 6 and 7 analyze the efficiency of the model in replicating crack surface complexity and detection of tensile failure zones under different stress configurations. Crack A (notched, vertical tension), Crack B (unnotched, biaxial tension), and Crack C (initiated from micro-defect under confined compression) were treated as in Samples A, B, and C respectively. Compared to that of other methods, the proposed FDEAMS module achieved > 20% improvement in crack surface prediction accuracy and > 90% agreement in tensile failure zones defined by results of physical testing sets. These results have practical relevance in a real-world situation like seismic design zones and infrastructure under cyclic or eccentric loads wherein early prediction of fractures owing to their catastrophic failures and reduced inspection intervals may benefit the process.

Table 6.

Fracture surface area prediction accuracy.

Sample	Proposed model	Method [3]	Method [8]	Method [25]
Crack A	± 8.4%	± 21.2%	± 18.3%	± 17.5%
Crack B	± 7.9%	± 20.6%	± 19.1%	± 18.2%
Crack C	± 8.1%	± 22.5%	± 17.8%	± 16.9%

Table 7.

Tensile failure zone identification accuracy.

Load case	Proposed model	Method [3]	Method [8]	Method [25]
Uniaxial tension	92.4%	74.1%	78.3%	76.9%
Biaxial stress	90.7%	71.8%	75.4%	73.5%
Confined compression	91.6%	72.9%	77.2%	74.6%

The strengthening development in time as portrayed in Table 8 reinforces more the existent viability to practice the model in real life sets. For all three samples tested for strength predictions, the values attained were within ± 7% of the experimentally determined compressive strength values at 7, 14, and 28 days. The reason is that the ability of dynamic interaction between hydration status (from TRPNM) and stiffness updates (from DMSCF) are lacking in conventional methodologies, thus giving such accuracy. It can be very important, especially in critical-path projects wherein such as bridge decks or where high-rise load cores are involved since material performance has to match what is simulated load resistance at the exact curing window sets. Table 9 further demonstrates that the lag in coupled FEM-MD simulation would not pass 4%, making near real-time response updates possible in digital twins or sensor integrated smart concrete systems.

Table 9.

Coupling lag error between MD and FEM domains.

Simulation stage	Proposed model	Method [3]	Method [8]	Method [25]
Early loading	3.2%	11.4%	9.6%	8.7%
Mid loading	3.8%	12.1%	10.3%	9.4%
Post-Yield	4.1%	13.6%	11.7%	10.5%

Lastly, the porosity estimation (Table 10) reflects the structural realism sets of the model on the whole. The proposed method leads to a consistent error margin of ~ 5% compared to micro-CT-derived porosity data, thus affirming the success of its fractal-enhanced segmentation and interface resolutions. This level of resolution in porosity modeling is necessary for service life estimation, especially in aggressive exposure conditions (e.g., ingress of chloride, freeze–thaw cycles). On the whole, the proposed integrated model delivers innovation in science on multi-scale simulation as well as being applied in civil engineering practice directly, bringing robust material design, performance-based structural planning, and digital monitoring integration for next-generation concrete infrastructure set.

Validated hyperparameter and baseline detailed analysis

Quantitative performance indicators have been compared to evaluate the proposed integrated multi-scale framework. Those include microstructural accuracy, interfacial area prediction, reaction kinetics, mechanical strength estimation, and fracture prediction. To statistically validate if the superiority claimed for the model is indeed true, expected values and variances for each performance metric were dealt across three representative concrete samples (A, B and C) as well as atomic clusters (1, 2, 3). The proposed model excelled in reliability and relatively low variability in prediction. For instance, the mean phase volume fraction matching accuracy was 95.5% with a standard deviation of use 0.74%, while the interfacial area estimation error averaged ± 5.9% with a variance of 0.16. Similar was the case for the root-mean-square (RMS) force error in molecular dynamics simulations which reported 0.09 eV/Å with a narrow variance of 0.0004 indicating highly stable learning behavior in the trained interatomic potentials.

To determine the performance of the differences statistically, the proposed model was tested against each of the baseline methods for each performance metric set by a series of two-tailed paired t-tests. No significant difference was present between the proposed method and the baselines according to the null hypothesis. Across the key performance indicators-hydration reaction time deviation, identification of tensile failure zone, and strength prediction-p values were continuously below 0.01, confirming that the improvements observed here were of statistically significant level at 99% confidence. For example, for predicting the compressive strength at 28 days, the model proposed gave an average absolute error of 2.1 MPa, while Method [3] gave 7.3 MPa with the test yielding a p value of 0.002. Also, for fracture surface area prediction, the mean absolute error for the proposed model was 8.1%, while Method [8] and Method [25] had 18.3% and 17.5% respectively, all yielding below 0.005 in p value for all comparisons.

The selection of baseline references Methods [3, 8], and [25] is made according to relevance, maturity, and popularity in the particular research fields of concrete microstructure modeling, molecular dynamics, and hydration, respectively. Method [3] is suitable for this class of statistical voxel-based Representative Volume Element (RVE) models that are commonly used in mesoscale concrete simulations and whose drawbacks are spatial homogenization errors and lack topological detail. Method [8] corresponds to the classical ReaxFF-based molecular dynamics simulations which offer chemical reactivity modeling but depend on generalized force fields which are not system specific. Method [25], widely quoted among most semi-empirical hydration models, uses power-law kinetics and bulk-strength development curves without detailing phase evolution or interfacial control. This perfect base for benchmarked confirms that such comparative analysis does take place on the recognized methodologies that typify the current state of the art in each of the relevant subdomains.

The ReaxFF family reactive interatomic potential parameterized for calcium–silicate–hydrate systems is used for molecular dynamics simulations. This potential allows partial charge redistribution and bond formation, emulating atomic hydration processes. Potential parameters were tuned against quantum-chemical reference data, including silicate gel chemistry-relevant bond dissociation energies and angle bending stiffness. Comparing simulated and reported equilibrium densities and bond length distributions of hydrated silicate clusters validates the selected potential. Multiple structural descriptors agree within 4%, indicating stable local atomic environments. The potential reproduces silica-rich phase elastic moduli with adequate error margins for linear deformation mechanical behavior. Energy conservation during unstrained dynamics runs exhibits little drift across lengthy simulation windows, supporting this. These consistency checks demonstrate reliable force field behavior under static and dynamic loading, validating its use here for this.

Crucially, it indicates that the possible outputs from the proposed model indeed have a low level of inter-sample variance that indicates robustness associated with ash compositions and hydration stages. Indicating lesser hydration time prediction standard deviations of below 1.2 days for Samples A, B, and C, compared with over 3.5 days as exhibited by Method [25]. In a similar vein, racture simulation consistency upheld across Cracks A, B, and C yielded a variance of 0.72 in the branching index, whereas Method [8] recorded greater than 2.1. Such stability characteristics are significant for real-time engineering deployment in which very high repeatability and confidence on simulation output are prerequisite for structural decision-making process. In conclusion, the proposed framework not only outperformed conventional methods across a wide array of performance measures but also did so with authentic statistical improvement and lower variance in processes used in process. The carefully selected reference methods provide a robust baseline ensuring any performance gains are interpreted within a meaningfully relevant context representative of established practices in microstructural, chemical, and mechanical modeling of cementitious systems.

Conclusion, future scope and limitations

Conclusion

The study presents an integrated multi-scale modeling framework bringing together all necessary ingredients for higher-performance concrete made with fly ash, including microstructural image analysis, reaction pathway-mechanism modeling/molecular dynamics, quantum informed interatomic potential generation, and finite element linkages. The proposed model outperformed other models in microstructural features reconstruction, chemical reactivity prediction, and mechanical behavior simulation, all of which yielded accuracy more than that of existing methods. Microstructure reconstruction was above 96.2% (Sample A) for volume fraction accuracy and interfacial area estimation errors reduced to ± 5.8%, while baseline methods were ± 14–18%. Molecular dynamics simulations based on QML-generated force fields gave rise to RMS force errors reduced to 0.09 eV/Å, a ~ 70% improvement from ReaxFF-based models. Topological reaction network-managed hydration kinetics gave reaction time values with ± 5.6% difference from experiment while compressive strength values at days 7, 14, and 28 fell within 6.5% of empirical benchmarks. Mechanical analysis through a combination of tensile, biaxial or confined loading showed that the proposed framework established where failure areas in compliance with a 92.4% of the time and predicted areas of crack surfaces with an error margin of ± 8.4%. Coupling between MD and FEM domains-maintained lag errors under 4% and porosity evolution tracked within ± 5.5% deviation with respect to micro-CT data for three concrete specimens. Such outcomes validate his proposed framework for predictive fidelity and physical realism at structural and atomic scales. The findings, thus, will directly lead towards advanced material design, structural performance modeling, and lifecycle optimization of fly ash concrete systems in critical infrastructure applications.

Future scope

The model developed in this work opens up avenues for several future improvements. An immediate extension would be to integrate phenomena of thermochemical aging, like carbonation and sulfate attack, into the reaction network and molecular dynamics module. The latter would allow for long-term prediction on performance under aggressive environmental exposure. More refinement in microstructure reconstruction can be achieved through the employment of machine-learned image segmentation algorithms, in combination with topological data analysis (TDA), to automate and improve phase identification from 3D datasets. Though highly accurate for binary and ternary oxide systems, the current QML IPM module is applicable to quaternary and quinary systems by expanding the structural motif database using high-throughput DFT workflows. In macro scale, the FEM domain can now be extended to accommodate time-dependent viscoelastic and creep effects through fractional-order mechanics. This scenario will simulate real-life load durations as well as structural combinations. Furthermore, coupling the proposed framework with structural health monitoring (SHM) systems using digital twin architectures would allow real-time prediction and control of concrete infrastructure performance. Possible use in such platforms includes tying it into digital materials platforms where optimization by AI will drive proposed mix designs for user-defined constraints, such as costs, emissions, and mechanical benchmarks, within performance targets in process.

Limitations

Even though the present model has an advanced architecture, employing highly varying resolutions across scales, it has a few points of concern. First, the current maximum resolution used is micro-computed tomography (micro-CT): 100 nm voxels with an immense background cost concerning the availability of the instrument. Next, although the QML-based potentials are very accurate, they require a vast amount of DFT data for training, which may not be available for many compositions or states of structure. The hydration kinetics model assumes isothermal conditions and does not yet incorporate thermal gradients or variable humidity, which can be critical in field-cured concrete applications. The FEM-MD coupling, while quite effective, introduces overhead in terms of computational cost due to property updates at such frequent intervals along with iterative feedback loops, which might prove challenging for scaling in real-time simulation for large-scale structural models. In fact, validation is at the moment done on Class F/C fly ash systems and select laboratory samples; more broadly, validation across diverse geographical sources and binder systems (e.g., alkali-activated materials) is necessary to ensure generalizability in the process. These limitations are in the future work, as they will be important in converting the model into an industry-ready simulation and design tool for next-generation sustainable concrete materials.

Data availability analysis

Diversity of data generated and/or analyzed during the current study can be found in the Materials Project repository and the Open Quantum Materials Database (OQMD). Most importantly, the materials project contains detailed computed information about materials, including that of the compound mp-554462. Data on this compound comprise computed properties, electronic structure, total energy, and crystallographic information, which can be found at https://next-gen.materialsproject.org/materials/mp-554462#summary. The Materials Project applies density functional theory calculation to predict material properties. Thus, the information in the database will be consistent with what usually prevails.

Furthermore, the OQMD has an extensive databank of DFT thermodynamic and structural properties for over 1.3 million materials. The entire OQMD database is available for download as MySQL database dumps, of which the latest, OQMD v1.7, was released in May 2025. This release comprises a great load of newly constructed structures and can be downloaded from https://oqmd.org/download/. The database is compatible with the qmpy API v1.4 and supports seamless integration and analysis. Please note that importing the entire OQMD database would occupy some 100 Gb of disk space, indicating the rich nature of the evidenced dataset samples. Both Materials Project and OQMD datasets provide a good deal of information, advancing the studies on materials science, insights that can lead to a better understanding of how materials behave and their properties.

Abbreviations

FA

Fly Ash

GPC

Geopolymer Concrete

OPC

Ordinary Portland Cement

ML

Machine Learning

DFT

Density Functional Theory

MD

Molecular Dynamics

FEM

Finite Element Method

FEA

Finite Element Analysis

HMMDM

Hybrid Multiphase Microstructure Descriptor Modeling

QML IPM

Quantum-Corrected Machine-Learned Interatomic Potential Mapping

TRPNM

Topological Reaction Pathway Network Modeling

FDEAMS

Fractal Defect Evolution Analysis via Molecular Simulation

DMSCF

Dynamic Multi-Scale Simulation Coupling with Feedback Optimization

RMS

Root Mean Square

PSD

Particle Size Distribution

SEM

Scanning Electron Microscopy

EDS

Energy Dispersive Spectroscopy

ReaxFF

Reactive Force Field

LAMMPS

Large-scale Atomic/Molecular Massively Parallel Simulator

GAP

Gaussian Approximation Potential

RCA

Recycled Concrete Aggregate

SVM

Support Vector Machine

CNN

Convolutional Neural Network

ANN

Artificial Neural Network

RF

Random Forest

SVR

Support Vector Regression

ASR

Alkali-Silica Reaction

UHPC

Ultra-High-Performance Concrete

UHPFRC

Ultra-High-Performance Fiber-Reinforced Concrete

PVA

Polyvinyl Alcohol

ICAR

International Center for Aggregates Research

TGA

Thermogravimetric Analysis

XRD

X-Ray Diffraction

MPa

Megapascal

eV/Ã

Electronvolt per Angstrom

CT

Computed Tomography

3D

Three-Dimensional

RVE

Representative Volume Element

AI

Artificial Intelligence

Author contributions

Vikrant S. Vairagade is sole author and responsible for the manuscript.

Funding

The author did not receive any funds, grants, or other support from any organization for the submitted work.

Data availability

All data shall be made available upon request.

Declarations

Competing interests

The authors declare no competing interests.

Ethics approval

The author state that the research was conducted according to ethical standards.

Human or animal rights

The author declare that this article does not contain any studies involving animals and human participants performed by any of the authors.

Generative AI in scientific

Author declares that in the writing process of this manuscript no use of AI and AI-assisted technologies was done.