基于裂隙演化微分动力学机制的岩石损伤本构模型

A damage constitutive model of rock based on differential kinetic mechanism of fracture evolution

为研究天然岩石内部不同形态裂隙的演化行为与岩石累计损伤程度之间的关系,运用唯象理论将岩石分为完整岩石微元体、闭合裂隙微元体和开口裂隙微元体3组分。基于生物群落生长逻辑建立岩石的裂隙演化微分动力学方程,并利用半解析方式求解岩石闭合裂隙与开口裂隙在受压状态下的演化表达式,实现压缩过程中岩石不同微元体之间转化关系的量化。其中开口裂隙演化曲线呈先下降后上升趋势,反映初始开口裂隙在压密阶段前后的变化规律,符合压密阶段非线性的应力-应变曲线关系。随后,以岩石裂隙演化解析表达式定义岩石压缩破坏的全局损伤变量,精准量化岩石在初始阶段、压密阶段、弹塑性阶段以及峰后阶段的全过程损伤程度,并提出基于上述裂隙演化机制和全局损伤变量的损伤本构模型。最后,基于微分方程理论推导、强度准则以及多目标优化等多种手段确定损伤本构模型参数,完成对岩石三组分初始比例以及3种裂隙转化因子的稳定求解,进而实现岩石压缩过程中的应力应变曲线仿真。研究结果表明:在煤岩及炭质泥岩的实例分析中,所建立的损伤本构模型能够较好表征不同岩石在不同围压下的应力应变特征及裂隙扩展规律,模型仿真结果与试验结果基本吻合。

To study the correlation between the evolutionary behavior of different morphologies of fractures within natural rocks and the cumulative damage degree of the rocks,a phonomenology theory was applied to classify the rocks into three components:intact rock microelements,closed-form fracture microelements and open-form fracture microelements.The differential kinetic equations of rock fracture evolution were developed based on the logic of biotope growth,and the expressions for the evolution of closed-form and open-form fractures under compression were solved semi-analytically,so as to quantify the conversion relationships among different compoenents of microelements in the process of compression.The evolutional curves of the open-form fractures show a downward and then upward trend,reflecting the evolution rule of the initial open-form fractures before and after the compaction stage,which accords with the stress-strain curves during the nonlinear compaction stage.Subsequently,the semi-analytical expression of rock fracture evolution was used to define a global damage variable,which can precisely quantify the global damage degree of the rock during the initial stage,the compaction stage,the elastic-plastic stage,and the post-peak stage respectively,and the damage constitutive model was proposed based on the above fracture evolution mechanism and the global damage variable.Finally,based on the theoretical deduction of differential equations,strength criteria,and multi-objective optimization,the parameters of the damage constitutive model were determined by various means.The stable solutions for the initial proportions of the three components of the rock and the three fracture conversion factors are obtained,which enables the simulation of the stress-strain curve during the rock compression process.The results show that in the case study of coal rock and carbonaceous shale,the proposed damage constitutive model can well features the stress-strain characteristics and fracture evolutional law of different rocks under different confining stresses,and the simulation results of our model are basically in line with the experimental results.