Drucker-Prager准则参数有效性及第二主应力对强度的影响分析  

Validness analysis of parameters in Drucker-Prager criterion and effects of the second principal stress on strength

作　　者：张信贵[1,2,3] 许胜才[1] 严利娥[1] 孔祥刚[1] 易念平[1] 

机构地区：[1]广西大学土木建筑工程学院,南宁530004 [2]工程防灾与结构安全教育部重点实验室,南宁530004 [3]广西防灾减灾与工程安全重点实验室,南宁530004

出　　处：《应用力学学报》2015年第5期810-816,898,共7页Chinese Journal of Applied Mechanics

基　　金：国家自然科学基金(51268003);广西防灾减灾与工程安全重点实验室开放课题(2012ZDK08);广西重点实验室系统性研究项目(2013ZDX11)

摘　　要：由于非粘性土在现实中不能承受拉应力的作用,在使用D-P准则描述岩土材料时,其强度参数的范围受到了限制。通过坐标变换,对粘性土与非粘性土建立了统一的D-P准则表达式;在π平面上从几何关系角度对D-P准则的参数有效性进行了分析,结果表明D-P准则参数α的有效范围为0≤α≤3/6;并进一步求出了D-P系列屈服准则的有效φ值范围。分析了第二主应力对D-P系列屈服准则强度的影响,建立了/b oφφ-b关系曲线,结果表明:相对于M-C准则,D-P1准则高估了材料的强度,而D-P3准则低估了材料的强度,D-P2准则的强度特性介于D-P1和D-P3之间;在oφ小于10o时,D-P4、D-P5和D-P6准则都与M-C准则有较好的近似;而当oφ大于10o时,这三个准则在靠近三轴拉伸区强度得到增长的同时,总是伴随着在三轴压缩区的弱化;D-P5准则在参数α的有效范围内,进行复杂三维应力状态的数值模拟时可以得到与M-C准则相近的结果;由于其在数学处理上的方便,D-P5准则具有广阔的应用前景。As the cohesionless soil is not able to bear tensional stress,the range of strength parameters for Drucker-Prager criterion is limited while the criterion is applied to describe geotechnical materials. A unified Drucker-Prager criterion is established for cohesion soil and cohesionless soil by transforming the coordinates, and an analysis on validness of parameters of Drucker-Prager criterion is made via the geometrical relationship on π-plane. Results show that the valid range of parameter α in Drucker-Prager criterion is 0 ≤ α≤3/6. Further, valid range of parameter φ can be obtained. The effects of the second principal stress on the strength of Drucker-Prager criterion is analyzed and the relationship curve of ? b/?o- b is established. Results show that, compared with Mohr-Coulomb criterion, D-P1 overestimates the strength of the material, while D-P3 underestimates it. The strength property of D-P2 Criterion is between that of D-P1 Criterion and D-P3 Criterion. When φois less than 10°, D-P4, D-P5 and D-P6 are relatively approximate to Mohr-Coulomb criterion. However, when φo exceeds 10°, the strengths of the three criteria increase at the triaxial tensile area, and weaken at the area of triaxial compression. Within the valid range of parameters of D-P5, a similar result as Mohr-Coulomb criterion can be obtained by making a complex numerical simulation on three-dimensional stress state. There is an extensive prospect for practical application because of its convenience in mathematical processing.

关 键 词：DRUCKER-PRAGER准则 MOHR-COULOMB准则 参数有效性 第二主应力 强度 

分 类 号：TU443[建筑科学—岩土工程]