SMP准则在计算煤柱极限强度中的应用

基于黏性材料的SMP（spatially mobilized plane）破坏准则，分析了煤柱在三维应力状态下的应力问题，并推导了煤柱极限强度的计算公式。通过改变煤体的内摩擦角? 和凝聚力c，与Mohr-Coulomb准则下煤柱极限强度以及简化的A. H. Wilson公式得到的煤柱极限强度进行对比，结果表明，Mohr-Coulomb准则和A.H.Wilson公式由于忽略了煤柱中主应力的影响，其得到的极限强度计算公式低估了煤柱实际极限强度，说明基于黏性材料的SMP准则下的煤柱极限强度计算符合实际，对于分析煤柱的稳定性具有一定的现实指导意义。

Application of SMP failure criterion to computing limit strength of coal pillars

Based on the spatially mobilized plane (SMP) failure criterion of the coherent material, the stress problem for the coal pillar under the three-dimensional stress states was analyzed; and the formula of limit strength of the coal pillar was derived. Through changing the internal friction ? and the cohesion c of the coal, compared with the limit strength of the coal pillar using the Mohr-Coulomb failure criterion and the simplified A. H. Wilson formula, it is shown that because of neglecting the influence of the intermediate principal stress in the Mohr-Coulomb failure criterion and A.H.Wilson formula of the limit strength of coal pillar underestimate the actual limit strength; and it also is shown that limit strength computing of the coal pillar based on the SMP failure criterion of the coherent material has certain practical significance.