一种扩展的Drucker-Prager准则及数值应用  

An Alternative Modified Drucker⁃Prager Criterion and Its Numerical Application

作　　者：许胜才[1] 蒙东林[1] 范理云 邓礼娇 XU Shengcai;MENG Donglin;FAN Liyun;DENG Lijiao(College of Architecture and Electric Engineering,Hezhou University,Hezhou 542899,Guangxi,China)

机构地区：[1]贺州学院建筑与电气工程学院,广西贺州542899

出　　处：《力学季刊》2023年第3期759-769,共11页Chinese Quarterly of Mechanics

基　　金：广西自然科学基金(2018GXNSFBA281129);广西高校中青年教师科研基础能力提升项目(2020KY18018)。

摘　　要：已有Mohr-Coulomb(M-C)准则的匹配圆Drucker-Prager(D-P)准则只能在有限的应力点与M-C准则等效,且不具备应力角效应,在工程数值分析中受到限制.因此,对D-P准则设置了角隅函数来反映应力角效应,采用与M-C准则在π平面上面积等效的方法构建了等面积扩展D-P准则,进一步对等面积扩展D-P准则在中主应力影响下的强度特性进行了分析,最后通过三个算例比较了不同等效D-P强度准则在岩土工程分析中的适用性.结果表明:等面积扩展D-P准则相比其它D-P准则和M-C准则的强度离差更小,整体上在和M-C准则的等效性上表现更佳;数值模拟算例表明等面积扩展D-P准则能够适应各种应力状态,在数值模拟结果上和M-C准则具有更好的等效性,且在计算收敛性上还具有较好的表现,可作为M-C准则的替代.The existing matching circle Drucker-Prager(D-P)criteria of Mohr-Coulomb(M-C)criterion are only equivalent to the M-C criterion at finite stress points,and lack of stress angle effect,thus are limited in engineering numerical analysis.Therefore,a corner function is set up in the D-P criterion to reflect the stress angle effect,and then the equal area extended D-P criterion is constructed by using the area equivalence principle with the M-C criterion in theπplane.Furthermore,the influence of medium principal stress on the strength of the equal area extended D-P criterion is analyzed.Finally,three examples are given to compare the applicability of different equivalent D-P strength criterion in geotechnical engineering analysis.Results show that the equal area extended D-P criterion has obviously smaller strength deviation with the M-C criterion than other D-P criteria,and good equivalence performance with the M-C criterion as a whole.Numerical simulation examples indicate that the equal area extended D-P criterion can adapt to various stress states,and has better equivalence performance with the M-C criterion in the numerical simulations.Moreover,the equal area extended D-P criterion also has good performance in computational convergence,hence can be used as an alternative to the M-C criterion.

关 键 词：扩展D-P准则 M-C准则 等面积 参数有效性 强度 

分 类 号：TU443[建筑科学—岩土工程]