Mathematical Modelling and Optimization Methods in Geomechanically Informed Blast Design: A Systematic Literature Review
Background: Rock–blast design is a canonical inverse problem that joins elastodynamic partial differential equations (PDEs), fracture mechanics, and stochastic heterogeneity. Objective: Guided by the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) protocol, a systematic r...
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2025-07-01
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| author | Fabian Leon Luis Rojas Alvaro Peña Paola Moraga Pedro Robles Blanca Gana Jose García |
| author_facet | Fabian Leon Luis Rojas Alvaro Peña Paola Moraga Pedro Robles Blanca Gana Jose García |
| author_sort | Fabian Leon |
| collection | DOAJ |
| description | Background: Rock–blast design is a canonical inverse problem that joins elastodynamic partial differential equations (PDEs), fracture mechanics, and stochastic heterogeneity. Objective: Guided by the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) protocol, a systematic review of mathematical methods for geomechanically informed blast modelling and optimisation is provided. Methods: A Scopus–Web of Science search (2000–2025) retrieved 2415 records; semantic filtering and expert screening reduced the corpus to 97 studies. Topic modelling with Bidirectional Encoder Representations from Transformers Topic (BERTOPIC) and bibliometrics organised them into (i) finite-element and finite–discrete element simulations, including arbitrary Lagrangian–Eulerian (ALE) formulations; (ii) geomechanics-enhanced empirical laws; and (iii) machine-learning surrogates and multi-objective optimisers. Results: High-fidelity simulations delimit blast-induced damage with ≤0.2 m mean absolute error; extensions of the Kuznetsov–Ram equation cut median-size mean absolute percentage error (MAPE) from 27% to 15%; Gaussian-process and ensemble learners reach a coefficient of determination (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>R</mi><mn>2</mn></msup><mo>></mo><mn>0.95</mn></mrow></semantics></math></inline-formula>) while providing closed-form uncertainty; Pareto optimisers lower peak particle velocity (PPV) by up to 48% without productivity loss. Synthesis: Four themes emerge—surrogate-assisted PDE-constrained optimisation, probabilistic domain adaptation, Bayesian model fusion for digital-twin updating, and entropy-based energy metrics. Conclusions: Persisting challenges in scalable uncertainty quantification, coupled discrete–continuous fracture solvers, and rigorous fusion of physics-informed and data-driven models position blast design as a fertile test bed for advances in applied mathematics, numerical analysis, and machine-learning theory. |
| format | Article |
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| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-07-01 |
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| series | Mathematics |
| spelling | doaj-art-fa1f4494b515417da8a55f87f595dee62025-08-20T03:36:27ZengMDPI AGMathematics2227-73902025-07-011315245610.3390/math13152456Mathematical Modelling and Optimization Methods in Geomechanically Informed Blast Design: A Systematic Literature ReviewFabian Leon0Luis Rojas1Alvaro Peña2Paola Moraga3Pedro Robles4Blanca Gana5Jose García6Doctorado en Industria Inteligente, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362804, ChileDoctorado en Industria Inteligente, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362804, ChileEscuela de Ingeniería de Construcción y Transporte, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362804, ChileEscuela de Ingeniería de Construcción y Transporte, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362804, ChileEscuela de Ingeniería Química, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362804, ChileEscuela de Ingeniería Química, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362804, ChileEscuela de Ingeniería de Construcción y Transporte, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362804, ChileBackground: Rock–blast design is a canonical inverse problem that joins elastodynamic partial differential equations (PDEs), fracture mechanics, and stochastic heterogeneity. Objective: Guided by the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) protocol, a systematic review of mathematical methods for geomechanically informed blast modelling and optimisation is provided. Methods: A Scopus–Web of Science search (2000–2025) retrieved 2415 records; semantic filtering and expert screening reduced the corpus to 97 studies. Topic modelling with Bidirectional Encoder Representations from Transformers Topic (BERTOPIC) and bibliometrics organised them into (i) finite-element and finite–discrete element simulations, including arbitrary Lagrangian–Eulerian (ALE) formulations; (ii) geomechanics-enhanced empirical laws; and (iii) machine-learning surrogates and multi-objective optimisers. Results: High-fidelity simulations delimit blast-induced damage with ≤0.2 m mean absolute error; extensions of the Kuznetsov–Ram equation cut median-size mean absolute percentage error (MAPE) from 27% to 15%; Gaussian-process and ensemble learners reach a coefficient of determination (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>R</mi><mn>2</mn></msup><mo>></mo><mn>0.95</mn></mrow></semantics></math></inline-formula>) while providing closed-form uncertainty; Pareto optimisers lower peak particle velocity (PPV) by up to 48% without productivity loss. Synthesis: Four themes emerge—surrogate-assisted PDE-constrained optimisation, probabilistic domain adaptation, Bayesian model fusion for digital-twin updating, and entropy-based energy metrics. Conclusions: Persisting challenges in scalable uncertainty quantification, coupled discrete–continuous fracture solvers, and rigorous fusion of physics-informed and data-driven models position blast design as a fertile test bed for advances in applied mathematics, numerical analysis, and machine-learning theory.https://www.mdpi.com/2227-7390/13/15/2456rock blastinggeomechanical parametersblast-design indicesfragmentation modellingKuz–Ram modelmachine learning |
| spellingShingle | Fabian Leon Luis Rojas Alvaro Peña Paola Moraga Pedro Robles Blanca Gana Jose García Mathematical Modelling and Optimization Methods in Geomechanically Informed Blast Design: A Systematic Literature Review Mathematics rock blasting geomechanical parameters blast-design indices fragmentation modelling Kuz–Ram model machine learning |
| title | Mathematical Modelling and Optimization Methods in Geomechanically Informed Blast Design: A Systematic Literature Review |
| title_full | Mathematical Modelling and Optimization Methods in Geomechanically Informed Blast Design: A Systematic Literature Review |
| title_fullStr | Mathematical Modelling and Optimization Methods in Geomechanically Informed Blast Design: A Systematic Literature Review |
| title_full_unstemmed | Mathematical Modelling and Optimization Methods in Geomechanically Informed Blast Design: A Systematic Literature Review |
| title_short | Mathematical Modelling and Optimization Methods in Geomechanically Informed Blast Design: A Systematic Literature Review |
| title_sort | mathematical modelling and optimization methods in geomechanically informed blast design a systematic literature review |
| topic | rock blasting geomechanical parameters blast-design indices fragmentation modelling Kuz–Ram model machine learning |
| url | https://www.mdpi.com/2227-7390/13/15/2456 |
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