考虑双剪中主应力影响系数的D-P系列屈服准则研究  

Research on D-P series yield criteria considering the influence coefficient of double shear intermediate principal stress

作　　者：高江平[1] 杨继强 孙昕 GAO Jiangping;YANG Jiqiang;SUN Xin(Key Laboratory of Highway Engineering in Special Areas,Chang'an University,Xi'an,Shaanxi 710064,China)

机构地区：[1]长安大学特殊地区公路工程教育部重点实验室,陕西西安710064

出　　处：《岩石力学与工程学报》2021年第6期1081-1091,共11页Chinese Journal of Rock Mechanics and Engineering

摘　　要：双剪统一强度理论考虑了中间主应力的影响,但其屈服面不光滑,不利于数值分析。为了解决Mohr-Coulomb屈服面奇异性问题,已有研究推导得到与Mohr-Coulomb有特殊位置关系的一系列D-P屈服准则。为了解决双剪统一强度理论角点奇异性问题,参考传统的D-P系列屈服准则的推导过程,推导得到了考虑中间主应力影响系数b的D-P系列屈服准则。根据双剪统一强度理论得到的π平面极限线有12个,它们在π平面上两两相交组成了关于3个主应力轴对称的十二边形,与这些极限线有特殊关系的圆有6个,这些圆在空间中是与双剪统一强度理论屈服面有特殊位置关系的圆锥,根据理论分析和数学推导分别得到6个圆锥面的屈服函数表达式,分别为DDP1,DDP2,DDP3,DDP4,DDP5和DDP6。利用经典的强度折减法,分别计算了匀质边坡和非匀质边坡在考虑b时的D-P屈服准则下边坡稳定性系数,结果表明考虑b的D-P系列屈服准则可以适用于边坡稳定性分析,与传统的D-P系列屈服准则相比,能够充分发挥材料的强度潜力。The yield surface of the double-shear unified strength theory considering the influence of the intermediate principal stress is not smooth and hence,is not conducive to numerical analysis. In order to solve the problem of the singularity of the Mohr-Coulomb yield surface,some scholars derived a series of D-P yield criteria that have a special positional relationship with the Mohr-Coulomb yield surface. In order to solve the corner singularity problem of the double-shear unified strength theory,this paper refers to the derivation process of the traditional D-P series yield criterion and derives the D-P series yield criterion considering the influence coefficient b of the intermediate principal stress. According to the double-shear unified strength theory,there are 12 limit lines on the π plane,which intersect in pairs on the π plane to form a dodecagon that is symmetric about the three principal stress axes. There are six circles that have a special relationship with these limit lines,and these circles are cones in space that have a special positional relationship with the yield surface of the double-shear unified strength theory. According to theoretical analysis and mathematical derivation,the yield function expressions of the six cone surfaces are obtained,namely DDP1,DDP2,DDP3,DDP4,DDP5 and DDP6. Using the classic strength reduction method,the stability coefficients of a homogeneous slope and a non-homogeneous slope under the D-P yield criterion considering b are calculated separately. The results show that the D-P yield criterion considering b can be applied to slope stability analysis and compared with the traditional D-P series yield,can give full play to the strength potential of the material.

关 键 词：边坡工程 D-P系列屈服准则 π平面极限线 边坡稳定性分析 强度折减法 

分 类 号：P642[天文地球—工程地质学]