层状岩石横观各向同性蠕变损伤本构模型研究  

Transversely isotropic creep damage constitutive model for layered rocks

作　　者：朱元广[1,2] 王璇尧 刘滨 刘学伟[1,2] 薛皓元 耿志[1,2] ZHU Yuan-guang;WANG Xuan-yao;LIU Bin;LIU Xue-wei;XUE Hao-yuan;GENG Zhi(Institute of Rock and Soil Mechanics,Chinese Academy of Sciences,Wuhan,Hubei 430071,China;University of Chinese Academy of Sciences,Beijing 100049,China)

机构地区：[1]中国科学院武汉岩土力学研究所,湖北武汉430071 [2]中国科学院大学,北京100049

出　　处：《岩土力学》2025年第4期1095-1108,共14页Rock and Soil Mechanics

基　　金：国家自然科学基金(No.U22A20234);湖北省自然科学基金杰出青年项目(No.2022CFA084)。

摘　　要：我国中西部深埋隧道建设穿越大量层状岩体,在高地应力作用下层状岩石呈现出横观各向同性性质和显著的蠕变现象,极易引发隧道掌子面坍塌、支护结构破坏等工程灾害。为准确表征岩层倾角和时间效应对层状岩石力学性质的影响,基于分数阶微积分理论和蠕变柔量替代法,以元件组合模型为基础,建立了一种考虑损伤和岩层角度的横观各向同性非线性蠕变模型(T模型),并推导了一维和三维蠕变本构方程。T模型采用分数阶Kelvin模型描述减速蠕变阶段特征,采用Abel黏壶描述稳态蠕变阶段特征,采用瞬时塑性元件和分数阶非线性损伤黏壶并联来反映加速蠕变阶段特征。基于炭质板岩蠕变试验数据,采用最小二乘法对蠕变本构方程进行了参数识别。通过RMSE(均方根误差)、MAE(平均绝对误差)和R2(决定系数)的误差分析及与现有横观各向同性蠕变模型的对比,验证了T模型本构方程的拟合效果,表明T模型能更加准确地描述层状岩石各蠕变阶段的特性。研究结果为层状岩石隧道围岩长期稳定性分析提供理论依据。Deep-buried tunnels in the central and western China pass through a large number of layered rock masses.Under the action of high in-situ stress,the layered rocks exhibit transversely isotropic properties and significant creep phenomena,which are highly likely to trigger engineering disasters such as tunnel face collapses and support structure failures.To accurately characterize the impact of bedding angles and time effects on the mechanical properties of layered rocks,based on the fractional calculus theory and the creep compliance substitution method,taking the component combination model as the foundation,this study established a transversely isotropic nonlinear creep model(T model)that takes into account damage and rock layer angles,and derived the one-dimensional and three-dimensional creep constitutive equations.The T model uses the fractional-order Kelvin model to describe the characteristics of the decelerating creep stage,the Abel dashpot for the steady-state creep stage,and connects the instantaneous plastic element and the fractional-order nonlinear damage dashpot in parallel to reflect the characteristics of the accelerating creep stage.Based on the creep test data of carbonaceous slate,the least square method was used to identify the parameters of the creep constitutive equations.Through the error analysis of RMSE(root mean square error),MAE(mean absolute error)and R²(coefficient of determination),as well as the comparison with the existing transversely isotropic creep models,the fitting effect of the constitutive equation of the T model was verified,which indicates that the T model can describe the characteristics of each creep stage of layered rocks more accurately.The research results provide a theoretical basis for the long-term stability analysis of the surrounding rock of layered rock tunnels.

关 键 词：层状岩石 横观各向同性 蠕变 本构方程 分数阶 

分 类 号：TU452[建筑科学—岩土工程]