基于热力学框架的碳质页岩弹塑性各向异性损伤模型研究

Elastoplastic Anisotropic Damage Model of Carbonaceous Shale in Thermodynamic Framework

碳质页岩是隧道工程建设中常见的一类脆性岩石,具有典型的非线性各项异性特性,工程建设中面临的关键问题是如何建立合适的本构模型描述该类岩石的复杂力学行为。基于热力学框架建立了碳质页岩的弹塑性各向异性损伤本构模型。该模型中屈服准则采用基于改进的Mohr-Coulomb准则,用于描述应变硬化/软化行为,利用非关联流动法则来控制塑性流动;提出了一种考虑各向异性损伤演化的指数函数形式损伤准则来描述岩石材料力学性能的退化,并基于相互独立的屈服准则和损伤准则函数实现了塑性与各向异性损伤之间的耦合。为了验证模型的有效性,开展了碳质页岩的常规三轴压缩试验研究,通过模型预测结果和试验结果的对比,表明模型可以很好地描述碳质页岩在不同应力水平下的损伤演化规律和非线性力学行为,特别是塑性变形和各向异性损伤耦合行为。提出的模型可嵌入大型有限元/有限差分软件,为隧道围岩稳定安全分析提供理论支撑。

Carbonaceous shale is a kind of brittle rock encountered in the construction of tunnel engineering,which has typical nonlinear anisotropy characteristics.It is significantly important to established suitable constitutive model to approach the complicated mechanical behavior of this kind of rock.In this paper,an elastoplastic anisotropic damage constitutive model was proposed within the framework of thermodynamic.The plastic hardening/softening response is described by an improved Mohr-Coulomb yield criterion and the plastic flow is controlled by a non-associated flow rule.An exponential function form of damage criterion accounting for the anisotropic damage evolution was adopted to describe the degradation of stiffness.Plastic deformation and anisotropic damage evolution were coupled through combing“two surfaces”plastic yield criterion and damage criterion.Conventional triaxial compression tests were conducted on carbonaceous shale to exam the efficiency of the model.The comparison between the predictive result and experimental data suggests that the proposed model is capable to reproduce the damage evolution at different stress conditions and non-linearly mechanical behavior under compression of carbonaceous shale.In addition,the coupling between plastic deformation and anisotropic damage evolution was well produced.The proposed model can be implemented into FEM/FDM software to provide the theoretical support for stability and safety analysis of tunnel surrounding rock.