基于能量耗散理论的岩石塑性-损伤本构模型  

Rock plastic-damage constitutive model based on energy dissipation

作　　者：马秋峰 刘志河[1] 秦跃平[2] 田静 王树立 MA Qiu-feng;LIU Zhi-he;QIN Yue-ping;TIAN Jing;WANG Shu-li(School of Resources and Environmental Engineering,Shandong University of Technology,Zibo,Shandong 255000,China;School of Emergency Management and Safety Engineering,China University of Mining and Technology(Beijing),Beijing 100083,China;Department of Mechanical Engineering,Zikuang University,255120,Zibo,Shandong 255120,China)

机构地区：[1]山东理工大学资源与环境工程学院,山东淄博255000 [2]中国矿业大学(北京)应急管理与安全工程学院,北京100083 [3]淄矿大学机械工程系,山东淄博255120

出　　处：《岩土力学》2021年第5期1210-1220,共11页Rock and Soil Mechanics

基　　金：国家自然科学基金青年科学基金项目(No.51904177);国家自然科学基金(No.50904071)。

摘　　要：将Mohr-Coulomb准则与能量耗散理论相结合,考虑了加载过程中岩石的硬化、软化特性,采用非关联塑性流动法则描述岩石的塑性变形,通过损伤过程中耗散能与损伤耗能率相除的方法求解损伤变量,建立了损伤-塑性本构模型。通过常规三轴加-卸载试验,分析了岩石损伤过程中耗散能-损伤变量的关系,建立了损伤耗能率表达式,同时标定了模型参数。利用所提的新模型模拟岩石的常规三轴试验,将模拟结果与试验结果进行对比,探究了模型的合理性。在此过程中得到如下结论:(1)损伤耗散能在线弹性阶段随着轴向应变的增长,呈现上凹型曲线,增长速率不断增大,在应力峰值附近增长速率达到最大值,在峰后残余阶段,损伤耗散能与轴向应变近似呈现线性关系;(2)采用与弹性模量相关联的损伤变量定义方法,试验结果表明,存在一个小于或等于1的损伤变量极限,随着围压的增大,损伤变量极限逐渐减小;(3)所提的新模型能够反映出在加载过程中不同围压条件下岩石的强度、硬-软化特性,数值模拟结果能够描述应力-应变关系、损伤耗散能规律以及损伤演化规律。In this paper,the dissipative energy in the damage process was employed to solve the damage variable while the damage constitutive model was established.In this model,the Mohr-Coulomb criterion and the energy dissipation theory were introduced.Considering the hardening and softening characteristics of rock during loading,the non-associated plastic flow rule was applied to describe the plastic deformation of rock,and the damage variable was calculated by quoting the dissipation energy and damage energy dissipation rate in the damage process.Based on the conventional triaxial loading-unloading experiments,the energy consumption and damage evolution law of rock was analyzed.The expression of damage energy dissipation rate was established,and the parameters in the model were calibrated.Simulation was conducted by this model and the simulation results were compared with the experimental results to validate the model.In this process,the following conclusions were obtained:(1)in the elastic stage,the damage dissipation energy increases slowly with the axial strain,showing an upward concave curve,and the growth rate reaches the maximum near the peak-stress.In the residual stage,the relationship between damage dissipation energy and axial strain is linear;(2)based on elastic modulus associated damage definition,the experimental results show that there is a damage variable limit less than 1,and the damage variable limit gradually decreases with the increase of confining pressure;(3)the model in this paper can be used to investigate the strength,hardening,softening characteristics and strain law of rock under different confining pressures during the loading process.The numerical simulation results can describe the stress-strain relationship and damage evolution law of rock.

关 键 词：损伤 能量耗散 MOHR-COULOMB准则 本构模型 损伤耗能率 

分 类 号：TU452[建筑科学—岩土工程]