基于Drucker-Prager屈服准则的煤壁内塑性区宽度的确定

The Determination of Plastic Zone Width in the Coal Wall Based on Drucker-Prager Yield Criterion

根据Drucker-Prager准则,考虑中间主应力对煤壁内塑性区宽度的影响,从理论上研究分析了塑性区的范围及受力情况,推导出塑性区宽度的计算公式及在塑性区内能够反映应力分布规律的表达式,并与经典的Mohr-Coulomb准则导出的公式计算结果进行对比,详细讨论了各因素对塑性区宽度的影响。结果表明,中间主应力对塑性区宽度具有重要的影响,并且表现出了中间主应力效应的区间性,而且计算结果说明将Drucker-Prager准则导出的公式应用于工程实践中比Mohr-Coulomb准则导出的公式安全性更大。

According to Drucker - Prager criterion, considering the influence of the intermediate principal stress on the width of the plastic zone in the coal wall, the ranges of the plastic zone and the force bearing status are studied, the mathematical formula of the plastic zone width and stress expression which can reflect the stress distribution in the plastic zone are deduced, and also the calculated results are compared with the results deduced from the classic Mabr - Coulomb criterion derivation formula. At the same time, the major factors for the width of the plastic zone are discussed in detail. The results prove that the intermediate principal stress has significant effects on the width of the plastic zone in the coal wall and shows the interval of effect. The calculated results indicate that the Drucker - Prager criterion derivation formula is safer than the Mohr - Coulomb criterion derivation formula when used in engineering practice.