基于莫尔–库仑准则的岩石峰后应变软化力学行为研究

STUDY OF POST-PEAK STRAIN SOFTENING MECHANICAL PROPERTIES OF ROCK BASED ON MOHR-COULOMB CRITERION

岩石类材料的应力–应变曲线关系分为峰值前区和峰值后区2个部分。在岩石应力–应变曲线峰前部分,一般将岩石视为弹性体,在此阶段采用线弹性本构关系;而在峰后部分,由于不能确定岩石的破坏形态和应力的跌落方式,其力学行为难以用经典理论来描述,因此确定岩石峰后模量的变化是研究岩石峰后力学行为的关键。基于莫尔–库仑强度准则,以内摩擦角?作为中间变量,通过理论推导,将峰后弹性模量E pp表征为应变ε的函数,建立峰后岩体力学非线性应力–应变关系。通过数值算例得到大理岩在不同围压下的全应力–应变曲线,其数值计算结果与试验结果吻合较好,表明所提出的非线性本构模型是正确合理的,同时也表明该模型可以较好的描述不同围压下大理岩的峰后力学行为。

The stress-strain curves of rocks are composed of two parts,which are pre-peak region and post-peak region.In the pre-peak region of stress-strain curve,rocks are usually regarded as elastomer.At this stage,the constitutive relationship is linearly elastic.However,in the post-peak region,the curve could not be determined by classical theory because the fracture morphology and the stress drop of the rocks are hard to describe.Thus,the post-peak modulus is the key of the mechanical behavior research.Based on Mohr-Coulomb criterion,the paper uses internal friction angle as intermediate variable to propose post-peak elastic modulus.The nonlinear post-peak stress-strain relationship of rock is established.In numerical cases,the stress-strain curves under different confining pressures are obtained and they agree well with the test data.It is concluded that the fitting curve model proposed by this paper is reasonable and the model could describe the post-peak mechanical behavior of marbles under various confining pressures preferably.