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中文摘要：
随着大量煤矿矿井开采深度的增加，在高围压的作用下，巷道围岩普遍出现破裂，而且围岩破裂范围在扩大的同时，往往出现继续破坏的现象。针对长的圆形巷道，将巷道围岩分成破裂区、塑性区和弹性区，采用Mohr-Coulomb准则，进行非关联弹塑性分析，获得其应力和变形的封闭解析解。通过利用在弹塑交界处应力连续的条件以及在破裂和塑性交界处径向应变连续的条件，获得确定围岩破裂区和塑性区半径的解析式。最后，给出一个算例，分析其破裂区和塑性区应力、应变的分布特点以及破裂区范围的影响。利用所获得的结果，可以为巷道的稳定性分析以及支护设计提供理论依据。
英文摘要：
With the increase of mining depth of a lot of coal mines, exerted by the high in-situ stress, the surrounding rocks in openings is fractured frequently. At the same time, the region of the cracked surrounding rocks enlarges; and the surrounding rocks re-crack. For a long and circular mine opening, the surrounding rocks are divided into three regions, i.e. the cracked region, the plastic region and the elastic region. With Mohr-Coulomb yield criterion, the mechanical behavior of the surrounding rocks is simulated by an elastoplastic model. The closed-form analytical solutions for the stress, strain and displacement in the three regions are derived in a theoretically consistency way by using a non-associated flow rule. According to the conditions that the stresses are continuous at the elastoplastic interface and that the radial strains are continuous at the plastic-cracked interface, the computational formulae to determine the radii of cracked and plastic regions are obtained. Finally, an example is analyzed to show the characteristics of stress and strain distributions in the cracked and plastic regions and the influence of cracked region radius on them. It provides theoretical foundations for the stability analysis of mine openings and reinforcement of the cracked surrounding rock.
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