D-P准则的性能评估及其在强度折减分析中的适用性研究

将D-P准则对M-C准则的近似视为连续函数逼近问题,据此建立了最佳平方逼近的误差解析表达式,并提出了一个最佳D-P准则。同时,利用该误差表达式分析了各种常用D-P准则对于M-C准则的最佳平方逼近误差。分析结果表明,在所有的D-P准则中,采用大外接圆的D-P准则误差最大,等面积圆准则与本文所提出的最佳准则的误差相近,内切圆、小外接圆和中径圆的误差基本上处于同一水准。同时,通过利用强度折减分析方法对各准则的适用性作了进一步的研究,结果表明,在系统处于相对稳定状态时等面积准则和最佳准则与M-C准则具有较好的接近程度,但当系统将进入不稳定状态时M-C准则却与内切圆准则接近。

Research on the Performance of the D-P Criteria and the Applicability in Strength Reduction Analysis

The Drucker-Prager(D-P) criterion,which is used to approximate the Mohr-Coulomb(M-C) hexagon with a circle on the π plane and adopted by most general numerical analysis programs,has been researched by using the least square approximate theory.A close-form formulation about the square error has been gained.At the same time,an optimal D-P criterion,which corresponds to the minimum square error,has been proposed.The analysis of square error indicated that the D-P criterion matched with the compressive meridian of the M-C generates more errors than others,and the square error of the equivalent area criterion is the closest to that of the optimal criterion,as well as the rest are nearly same.Furthermore,according to the curves of reduction factor(RF) vs.iterative number gained by strength reduction analysis,it can be found that the curves of the equivalent area criterion and the optimal criterion are closer to that of the M-C criterion when the system is in stable condition.However,the curve of the M-C criterion will approaches the inscribed circle when the system is in unstable condition.