基于八面体理论的岩石循环加-卸载本构模型及修正

Study and Correction of Cyclic Loading-Unloading Constitutive Model of Rock Based on Octahedral Theory

探究岩石的受力特点及破坏特性是研究岩石地下工程安全性的关键,诸多学者都期望能在岩石本构模型的研究上取得突破性进展。在此背景下,提出了一种能够描述循环加-卸载条件下岩石的本构模型。首先,假设岩石的微元强度服从八面体剪应力理论并且微元破坏服从Weibull概率公式,将岩石本构中的损伤变量以及岩石微元强度表达式里包含的损伤因子进行本构变换,得到关于应力、应变等其他表现加-卸载下岩石损伤本构模型的参数,表示出岩石微元强度和损伤变量,再将得到的岩石微元强度和损伤变量代入所提出的岩石本构模型中,并进行等式变换得到一个函数表达式。通过将其与实验数据进行拟合对比分析,得出修正后的拟合参数,将其代入函数式中,得到损伤本构模型的修正式。最后将拟合参数进行必要的敏感性分析,得出各拟合参数的实际物理意义。

Exploring the stress and failure characteristics of rock is the key to study the safety of rock underground engineering,thus many scholars expect to make breakthrough in the study of rock constitutive model.In this paper,a constitutive model is proposed to describe the rock under cyclic loading and unloading.Firstly,it is assumed that the micro-unit strength of rock obeys Octahedral shear stress theory and the micro-unit failure of rock obeys Weibull probability formula,and the damage variables in rock constitution and the damage factors contained in micro-unit strength of rock expression are transformed into the constitutive equation.Then the parameters such as stress,strain and others representing the damage constitutive model of rock under loading and unloading can be obtained and are used to express the microunit strength and damage variables.Substituting the micro-unit strength and damage variables into the proposed rock constitutive model,a function expression can be carried out by an equation transformation.Through the comparison and analysis of the fitting data with the experimental results,the modified fitting parameters are acquired,and can be substituted into the function to revise the damage constitutive model.Finally,the necessary sensitivity analysis of the fitting parameters is implemented to obtain the practical physical significance of each fitting parameter.