Mathematical Modelling and Optimization Methods in Geomechanically Informed Blast Design: A Systematic Literature Review

Fabian Leon (), Luis Rojas, Alvaro Peña, Paola Moraga, Pedro Robles, Blanca Gana and Jose García ()
Additional contact information
Fabian Leon: Doctorado en Industria Inteligente, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362804, Chile
Luis Rojas: Doctorado en Industria Inteligente, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362804, Chile
Alvaro Peña: Escuela de Ingeniería de Construcción y Transporte, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362804, Chile
Paola Moraga: Escuela de Ingeniería de Construcción y Transporte, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362804, Chile
Pedro Robles: Escuela de Ingeniería Química, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362804, Chile
Blanca Gana: Escuela de Ingeniería Química, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362804, Chile
Jose García: Escuela de Ingeniería de Construcción y Transporte, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362804, Chile

Mathematics, 2025, vol. 13, issue 15, 1-34

Abstract: 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 ( R 2 > 0.95 ) 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.

Keywords: rock blasting; geomechanical parameters; blast-design indices; fragmentation modelling; Kuz–Ram model; machine learning; numerical simulation; energy-based design (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/15/2456/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/15/2456/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:15:p:2456-:d:1713434

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().