{"title":"Multilevel Model of Cleavage Fracture in Brittle Rocks in Compression","authors":"V. N. Odintsev, V. V. Makarov","doi":"10.1134/s1062739124020133","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>This study proposes a mathematical fracture model including processes of fracture of structural bonds on micro scale (tens microns) and meso scale (millimeters and centimeters), as well as interaction of structural fragments on macro scale (fractures longer then tens centimeters). The model uses two geometrical criteria of fracture growth, connected with the structure of rocks and governing transition between structural scale. The problem on the stress–strain behavior of an elastic medium near a fracture at the change in the fracture length and in the scale of its influence is solved. The limit equilibrium of a fracture is analyzed. For a meso-scale fracture, such condition is unstable, and the fracture, therefore, develops dynamically and up to a macro scale. Sufficiently long macro fractures can grow in the mode of quasi statics due to independent advance of fracture tips.</p>","PeriodicalId":16358,"journal":{"name":"Journal of Mining Science","volume":"75 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mining Science","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1134/s1062739124020133","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MINING & MINERAL PROCESSING","Score":null,"Total":0}
引用次数: 0
Abstract
This study proposes a mathematical fracture model including processes of fracture of structural bonds on micro scale (tens microns) and meso scale (millimeters and centimeters), as well as interaction of structural fragments on macro scale (fractures longer then tens centimeters). The model uses two geometrical criteria of fracture growth, connected with the structure of rocks and governing transition between structural scale. The problem on the stress–strain behavior of an elastic medium near a fracture at the change in the fracture length and in the scale of its influence is solved. The limit equilibrium of a fracture is analyzed. For a meso-scale fracture, such condition is unstable, and the fracture, therefore, develops dynamically and up to a macro scale. Sufficiently long macro fractures can grow in the mode of quasi statics due to independent advance of fracture tips.
期刊介绍：
The Journal reflects the current trends of development in fundamental and applied mining sciences. It publishes original articles on geomechanics and geoinformation science, investigation of relationships between global geodynamic processes and man-induced disasters, physical and mathematical modeling of rheological and wave processes in multiphase structural geological media, rock failure, analysis and synthesis of mechanisms, automatic machines, and robots, science of mining machines, creation of resource-saving and ecologically safe technologies of mineral mining, mine aerology and mine thermal physics, coal seam degassing, mechanisms for origination of spontaneous fires and methods for their extinction, mineral dressing, and bowel exploitation.
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