相似角θ与Lode角θ_δ的相互关系及其在岩土力学中的作用

The relationship and function in geotechnical mechanics of similar angle θ and lode angle θ_δ

岩土力学中的摩尔 -库仑 (Mohr-Coulomb)屈服准则是在工程实践中经得起考验的屈服准则 ,由于该屈服函数的导数不连续而不能用于有限元分析中 ,从而限制摩尔 -库仑屈服准则的应用范围 ,用D -P(Druck -Prager)类屈服准则去逼近摩尔 -库仑屈服准则可以克服这些困难 ,但由于两者之间没有建立明确的物理关系 ,因此逼近效果还不够理想 .利用主应力空间与偏平面的几何关系 ,给出相似角θ与主偏应力s1和偏应力r之间的关系 ,再依照Lode角θδ 的定义 ,得出两者之间的关系 ,最后给出了相似角在岩土力学屈服准则中的一个应用 ,为今后建立更好的屈服准则打下基础 .

The Mohr-Coulomb yield criterion in geotechnical mechanics was amenable to engineering,for the discontinuity of its derivative,it can't be used in the analysis of finite element method,therefore the application of the Mohr-Coulomb yield criterion was limited.These difficulty can be overcome by using D-P yield criterion to approach the Mohr-Coulomb yield criterion, but there was no specific physical relationship between the Mohr-Coulomb yield criterion and D-P yield criterion,thus the approach effect was not good.The relationship among similar angle θ,principal deviation stress s and deviation stress r was given by using the geometric relationship of principal stress space and deviation plane in this paper,then the relationship between similar angle θ and Lode angle θ δ was obtained according to the definition of Lode angle θ δ.Finally,an application of similar angle θ in geotechnical mechanics yield criterion was given.This will be a base for establishing better yield criterion in the future.