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Mathematics
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Numerical Simulation and Analysis of Rock Mechanics Engineering Geology
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Numerical Simulation and Analysis of Rock Mechanics Engineering Geology

A Special Issue of Mathematics (ISSN 2227-7390) belonging to the section "E2: Control Theory and Mechanics".

Deadline for manuscript submissions: 30 September 2026 | Viewed by 2746

Editor

Dr. Alireza Ahangar-Asr

E-Mail Website
Guest Editor
School of Computing, Science and Engineering, University of Salford, Salford M5 4WT, UK
Interests: geotechnical engineering and soil mechanics; computational geomechanics; machine learning and artificial intelligence in constitutive modelling of complicated civil and geotechnical engineering materials and systems; slope stability; saturated and unsaturated soils
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

We are pleased to announce this Special Issue of the Mathematics journal, entitled "Numerical Simulation and Analysis of Rock Mechanics Engineering Geology". With the increasing complexity of problems related to rock mechanics, from tunnel stability to earthquake-induced landslides, numerical simulations have become indispensable for understanding multi-scale, multi-physics phenomena. This Special Issue invites original research to advance our understanding of mathematical approaches and to address critical challenges in rock mechanics and engineering geology. Contributions should focus on innovative numerical methods—such as finite element analysis, discrete element modeling, or machine learning—applied to rock mass behavior, fracture dynamics, fluid–rock interactions, and geological hazard forecasting.

Dr. Alireza Ahangar-Asr
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-anonymized peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • numerical modeling of rock mechanics
  • machine learning-enhanced geomechanics
  • multiphase flow simulation (CFD-DEM coupling)
  • inverse problems in geological parameterization
  • uncertainty quantification in rock engineering

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Published Papers (2 papers)

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Research

29 pages, 15877 KB  
Article
Fracture Evolution in Rocks with a Hole and Symmetric Edge Cracks Under Biaxial Compression: An Experimental and Numerical Study
by Daobing Zhang, Linhai Zeng, Shurong Guo, Zhiping Chen, Jiahua Zhang, Xianyong Jiang, Futian Zhang and Anmin Jiang
Mathematics 2025, 13(24), 4035; https://doi.org/10.3390/math13244035 - 18 Dec 2025
Cited by 2 | Viewed by 755
Abstract
This study employs physical experiments and the RFPA3D numerical method to investigate the fracture evolution of rocks containing a central hole with symmetrically arranged double cracks (seven inclination angles β) under biaxial compression. The results demonstrate that peak stress and strain exhibit [...] Read more.
This study employs physical experiments and the RFPA3D numerical method to investigate the fracture evolution of rocks containing a central hole with symmetrically arranged double cracks (seven inclination angles β) under biaxial compression. The results demonstrate that peak stress and strain exhibit nonlinear increases with rising β. Tensile–shear failure dominates at lower angles (β = 0–60°), characterized by secondary crack initiation at defect tips and wing/anti-wing crack development at intermediate angles (β = 45–60°). At higher angles (β = 75–90°), shear failure prevails, governed by crack propagation along hole walls. When β exceeds 45°, enhanced normal stress on crack planes suppresses mode II propagation and secondary crack formation. Elevated lateral pressures (15–20 MPa) significantly alter failure patterns by redirecting the maximum principal stress, causing cracks to align parallel to this orientation and driving anti-wing cracks toward specimen boundaries. Three-dimensional analysis reveals critical differences between internal and surface fracture propagation, highlighting how penetrating cracks around the hole crucially impact stability. This study provides valuable insights into complex fracture mechanisms in defective rock masses, offering practical guidance for stability assessment in underground mining operations where such composite defects commonly occur. Full article
(This article belongs to the Special Issue Numerical Simulation and Analysis of Rock Mechanics Engineering Geology)
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22 pages, 7050 KB  
Article
Fractal-Based Modeling and Quantitative Analysis of Hydraulic Fracture Complexity in Digital Cores
by Xin Liu, Yuepeng Wang, Tianjiao Li, Zhengzhao Liang, Siwei Meng, Licai Zheng and Na Wu
Mathematics 2025, 13(17), 2700; https://doi.org/10.3390/math13172700 - 22 Aug 2025
Cited by 2 | Viewed by 1304
Abstract
Hydraulic fracturing in shale reservoirs is affected by microscale structural and material heterogeneity. However, studies on fracture responses to the injection rate across different microstructural types remain limited. To examine the coupled effects of microstructure and flow rate on fracture propagation and mineral [...] Read more.
Hydraulic fracturing in shale reservoirs is affected by microscale structural and material heterogeneity. However, studies on fracture responses to the injection rate across different microstructural types remain limited. To examine the coupled effects of microstructure and flow rate on fracture propagation and mineral damage, high-fidelity digital rock models were constructed from SEM images of shale cores, representing quartz grains and ostracod laminae. Coupled hydro-mechanical damage simulations were conducted under varying injection rates. Fracture evolution and complexity were evaluated using three quantitative parameters: stimulated reservoir area, fracture ratio, and fractal dimension. The results show that fracture morphology and mineral failure are strongly dependent on both the structure and injection rate. All three parameters increase with the flow rate, with the ostracod model showing abrupt complexity jumps at higher rates. In quartz-dominated models, fractures tend to deflect and bypass weak cement, forming branches. In ostracod-lamina models, higher injection rates promote direct penetration and multi-point propagation, resulting in a radial–branched–nested fracture structure. Mineral analysis shows that quartz exhibits brittle failure under high stress, while organic matter fails more readily in tension. These findings provide mechanistic insights into the coupled influence of microstructure and flow rate on hydraulic fracture complexity, with implications for optimizing hydraulic fracturing strategies in heterogeneous shale formations. Full article
(This article belongs to the Special Issue Numerical Simulation and Analysis of Rock Mechanics Engineering Geology)
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