横观各向同性岩石弹塑性本构模型与参数求解方法研究

地层中普遍存在层理状岩石,这些岩石细观结构具有显著的方向性,从而引起了其变形与强度具有横观各向同性。采用弹性力学与广义塑性力学基本理论,建立了岩石横观各向同性弹塑性本构模型:弹性部分采用广义胡克定律描述,塑性部分采用基于广义八面体剪应力的屈服准则和势函数、非关联流动法则和应变硬化准则描述。该模型屈服面为外凸的非等截距椭圆截面角锥体,在各向同性条件下可退化为米塞斯屈服准则。提出了模型参数求解方法:弹性参数采用三轴压缩和扭转试验联合求解;塑性参数采用不同层理方向试样的三轴压缩试验求解。以炭质板岩为例,验证了所提出的横观各向同性弹塑性模型和参数求解方法,验证结果表明所提模型较好地反映了岩石的横观各向同性,参数求解方法简单有效。此外,还根据试验数据分析了炭质板岩塑性势方向性和弹塑性参数耦合特征。研究成果将为丰富岩石力学基本理论和解决相关工程问题提供理论基础。

Elastoplastic constitutive model and parameter determination for transversely isotropic rocks

Layered rocks are widely distributed in formations. The macro-structure of the layered rocks is characterized with transversely isotropy, which will induce the transverse isotropy in deformation and strength. Based on the basic theory of elasticity and generalized plastic mechanics, an elastoplastic constitutive model for transversely isotropic rock is proposed. In the model, the generalized Hooke's law is adopted for the elastic behavior. For the plastic behavior, the yield criterion and potential function formulated as a function of the generalized octahedral shear stress, the non-associated flow rule and the stress-dependent hardening criterion are used. The yield surface of the model is convex with non-equal intercept elliptical cross-section pyramid, which can be simplified under isotropic condition as that for the Mises yield criterion. A method for determination of the model parameters is proposed, that is, the elastic parameters are obtained by combining the triaxial compression tests with a torsion test. The plastic parameters are obtained by using the triaxial compression tests on samples with different bedding directions. Taking the carbonaceous slate as an example, the proposed transversely isotropic elastic-plastic model and the parameter determination method are verified. The results show that the proposed model can reflect the transversal isotropy of the rock well, and the parameter determination method is simple and effective. The direction of plastic potential and the coupling between elastic and plastic behaviors of carbonaceous slate are also discussed according to the test data. This research provides a theoretical basis for enriching the basic theory of rock mechanics and solving engineering problems.