一种考虑主应力空间的岩石非线性真三轴强度准则

A nonlinear true triaxial strength criterion for rocks considering principal stress space characteristics

为评估岩石的真三轴强度特性,首先根据常规三轴试验岩石强度的变化规律,提出基于偏应力极值的非线性强度准则,并与12种岩石试验强度和4种典型岩石强度准则进行对比,发现该强度准则的预测值与试验强度非常接近,相关性系数R^(2)均在0.98以上,平均相对误差(MAPE,E_(MAP))均小于4%(除7号岩石为6.83%);该强度准则、指数准则、H-B准则、MM-C准则和D-P准则对所有12种岩石预测E_(MAP)的平均值分别为2.32%、2.43%、5.28%、7.39%和13.74%,说明该强度准则能够很好地预测不同类型岩石的强度,其预测精度略优于指数准则(岩石力学界认为预测精度较高的强度准则),远好于其他3种强度准则。在上述所建常规三轴强度准则的基础上,通过引入中主应力参数和罗德应力参数,构建考虑中主应力效应的真三轴强度准则,并与8种岩石的真三轴试验强度进行对比,该强度准则很好地反映了大主应力随中主应力的增加呈先增大后减小的变化规律,所得R^(2)均在0.9以上,其中5种岩石的R^(2)大于0.96;除了13和14号岩石(E_(MAP)分别为7.79%和4.84%),其余6种岩石的平均相对误差E_(MAP)均小于4%,说明该强度准则能够较好地预测岩石的真三轴试验强度,很好地反映了中主应力效应,具有良好的普遍适用性。子午面和偏平面的应力空间特征也说明该强度准则很好地反映了岩石的静水压力效应和中主应力对大主应力的影响规律。

In order to evaluate the true triaxial strength properties of rocks,according to the variation of rock strength measured using conventional triaxial tests,a nonlinear strength criterion was developed based on the maximum value of deviatoric stress.The proposed strength criterion was compared with the measured strengths of 12 kinds of rocks and four typical rock strength criterions.The predicted results of the new strength criterion were close to the measured strengths of 12 kinds of rocks,and all the regression coefficients R^(2) were larger than 0.98 and mean absolute percentage errors(MAPE,E_(MAP))less than 4%(except 6.83%for No.7 rock).The average E_(MAP)of the 12 rocks were 2.32%,2.43%,5.28%,7.39%,and 13.74%,calculated by the new strength criterion,exponential criterion,Hock-Brown(H-B)criterion,modified Mohr-Coulomb(MM-C)criterion,and Drucker-Prager(D-P)criterion,respectively.It shows that the strength criterion proposed in this paper could well predict the strength of different types of rocks,and its prediction accuracy was slightly better than that of exponential criterion,an outstanding criterion in rock mechanics,and was far better than the other three typical strength criterions.Based on the conventional triaxial strength criterion,considering the effect of intermediate principal stress,a true triaxial strength criterion was developed by introducing the intermediate principal stress parameter and Rhode stress parameter.Compared with the true triaxial test results of eight rocks,the proposed true triaxial strength criterion well reflected the variation that the maximum principal stress increased firstly and then decreased with the increase of the intermediate principal stress.The R^(2) values of the eight types of rocks were all above 0.9,among which the R^(2) values of five rocks were greater than 0.96.Except for rocks No.13 and No.14 with E_(MAP)being 7.79%and 4.84%,the E_(MAP)of the other six rocks were all smaller than 4%.It shows that the proposed strength criterion could well predict the true triaxial test strength of rocks,and reflect the effect of intermediate principal stress well with good universal applicability.The stress spatial characteristics of meridian plane and deviatoric plane also explained that the proposed strength criterion well reflected the effects of hydrostatic pressure and intermediate principal stress on the maximum principal stress.