岩石真三轴强度与Mohr-Coulomb准则形状函数修正方法研究

Study of true triaxial strength of rock and modified method of Mohr-Coulomb criterion shape function

基于颗粒流理论和PFC3D程序,建立Lac du Bonnet花岗岩的BPM模型,施加周期性边界条件。通过使周期性空间扭曲变形,保持恒定的平均应力p和Lode角q,进行真三轴试验,提出一种修正Mohr-Coulomb准则形状函数的新方法。建立试样的三维强度包络面,并从三轴平面、双轴平面和p平面3个角度,探讨Mohr-Coulomb准则的局限性:(1)Mohr-Coulomb准则预测的单轴抗拉强度偏大。(2)Mohr-Coulomb准则未考虑中间主应力的影响。(3)Mohr-Coulomb准则适用范围有限,在30 30s-°<q<°范围内,Mohr-Coulomb准则强度偏于保守。探索中间主应力对岩石强度的影响规律,结果表明:当2s处于低值时,1s随2s的增大而增大,而后达到了"平台期";当2s处于更高应力状态时,1s随2s的增大而减小。通过考虑中间主应力的影响,将Mohr-Coulomb准则形状函数修正为关于平均应力p的函数。将拟合的K值与修正的Lade-Duncan准则预测值进行比较,结果表明,本文的修正方法比修正的Lade-Duncan准则能更准确地描述岩石的常规三轴强度,研究方法及结论可为岩石强度研究提供有益参考,且具有一定的实际工程意义。

Based on particle flow theory and PFC3D software, a bonded particle model（BPM） for Lac du Bonnet granite is generated and periodic boundary condition is applied. True triaxial tests are conducted by distortion of the periodic space. Constant mean stress p and modifying Mohr-Coulomb criterion shape function constant Lode angle O, are maintained. A new method for is proposed. The three-dimensional failure envelope of sample is determined to study the limitations of Mohr-Coulomb criterion from three aspects： triaxial plane, biaxial plane, θσ plane. The limitations of Mohr-Coulomb criterion are as follows. （1） Uniaxial tension strength predicted by Mohr-Coulomb criterion is higher. （2） Mohr-Coulomb criterion ignores the impact of the intermediate principal stress on strength of rock. （3） In the range of -30°〈θσ〈30°, strength prediction made by Mohr-Coulombcriterion is smaller. According to the results of numerical tests, impacts of the intermediate principal stress on strength of rock are researched. Results show that, there is a general increase in 0-1 at the low level of 0-2 until a plateau is reached. Then value of 0-1 decreases at a higher level of 0-2. After taking impacts of the intermediate principal stress into account, Mohr-Coulomb criterion shape function is modified as a function of mean stress p, which can predict the strength of triaxial compression and extension more accurately by comparing K obtained from the fitting formula and the modified Lade-Duncan criterion. The research method and conclusion of this paper can provide a useful reference to the study of rock strength and have some practical significance for the engineering project.