基于分叉理论的轴对称条件下岩石变形带分析

Analysis on deformation band in rock under axisymmetrical condition based on bifurcation theory

引入变形带描述轴对称状态下岩石应变局部化现象。采用通用形式的本构模型,基于分叉理论探讨了剪切带、压缩带和膨胀带3种变形带的出现条件,详细分析了轴对称状态下临界硬化模量和变形带方向角随本构参数的变化特性,发现现有的分叉理论分析不能预测压缩带和膨胀带是受所选用的本构模型的限制;同时在轴对称条件下,不管是采用关联还是非关联流动法则,预测到压缩带或膨胀带只能在软化阶段才能产生;而当采用非关联流动法则时,在特定范围内,预测到剪切带可以在硬化阶段产生。最后采用高孔隙岩石本构模型,分析了高孔隙岩石变形带角度随围压的变化规律,结果表明:岩石变形带的角度随围压的增大而减小;高孔隙岩石脆延转化是以压缩带的形成作为过渡,低围压下表现为脆性剪切带破坏,当围压达到临界围压后,随着围压继续增加,压缩带将会变得难以形成,宏观上表现为延性破坏。最后与已知试验结果进行对比,结果表明本文理论能合理描述岩石的应变局部化现象,预测结果与试验观察结果相符。

The concept of deformation band is introduced to describe the deformation localization phenomenon in rock under axisymmetric condition. Based on the conventional constitutive model, the bifurcation theory is applied to investigate the occurrence conditions of shear bands, compaction bands and dilation bands. The influences of model parameters and confining pressure on the critical hardening modulus and the inclination of deformation band are also discussed. The result shows that the bifurcation theory is not able to predict the compaction bands and dilation band due to adoption of irrational constitutive model. Under axisymmetrical condition, the compaction bands and dilation bands are always formed in the softening region, either based on associated flow rule or based on non-associated flOW rule. However, for certain geomaterials, shear band may be produced in the hardening region only if non- associated flow rule is used. In addition, by using a half elliptical plastic model, the theoretical approach for predicting the shear band inclination and critical confining pressure for transition from shear band to compaction band are given, which indicates that the shear band inclinations decrease with the increase of confining pressure. Compaction band is the transition localization from brittle to cataclastic flow in highly porous rock and forms at high confining pressure. The comparison shows that the prediction by model simulation is in good agreement with experimental data.