具有复杂层次结构的二维离散块系岩体中摆型波与旋转波研究  

Research on pendulum-type and rotational waves in 2D discrete blocky rock masses with complex hierarchical structures

作　　者：姜宽 卢春生 戚承志[4,5] 王泽帆 JIANG Kuan;LU Chunsheng;QI Chengzhi;WANG Zefan(Faculty of Architecture,Civil and Transportation Engineering,Beijing University of Technology,Beijing 100124,China;School of Civil,Environmental and Mining Engineering,The University of Western Australia,Perth,6009,Australia;School of Civil and Mechanical Engineering,Curtin University,Perth,Western Australia 6845,Australia;Beijing Advanced Innovation Center for Future Urban Design,Beijing University of Civil Engineering and Architecture,Beijing 100044,China;Beijing International Scientific and Technological Cooperation Base of Construction of Urban Traffic Infrastructure,Beijing University of Civil Engineering and Architecture,Beijing 100044,China)

机构地区：[1]北京工业大学城市建设学部,北京100124 [2]西澳大学土木、环境与采矿工程学院,澳大利亚珀斯6009 [3]科廷大学土木与机械工程学院,澳大利亚珀斯6845 [4]北京建筑大学北京未来城市设计高精尖中心,北京100044 [5]北京建筑大学城市交通基础设施建设北京国际科技合作基地,北京100044

出　　处：《岩石力学与工程学报》2024年第2期424-438,共15页Chinese Journal of Rock Mechanics and Engineering

基　　金：国家自然科学基金资助项目(51774018,12172036);国家留学基金管理委员会资助项目(202206540052)。

摘　　要：岩体是由软弱结构层分割的各种尺度的岩块相互嵌套形成,具有复杂的层次结构,对岩体动力变形及应力波传播具有显著影响。针对具有复杂层次结构的块系岩体,基于Cosserat理论建立摆型波与旋转波的动力模型,确定层次结构对动力变形的影响。进一步,针对摆型波的低频、低速特征,基于Bloch定理确定并求解不同层次结构中波的频散方程,研究波的频散关系及速度特征。最后,基于固体能带理论揭示摆型波低频特性的力学机制,并基于研究结果讨论摆型波及旋转波诱发冲击地压的可能性。研究表明:忽略岩体高阶层次结构将低估岩体的位移及其整体变形,计算结果偏于不安全。长波扰动作用下,高阶层次结构中第一模态摆型波(对应声学支)频散现象不显著,其传播速度降低,岩体内部高阶层次结构阻碍波的传播;其他波(对应光学支)频散现象极其显著,几乎不能独立存在并传播;低频摆型波为波的主要形式,比高阶模态波及传统的P波、S波衰减速度更慢、传播距离更远。Rock masses consist of nesting rock blocks with various scales separated by weak structural layers,and their complex hierarchical structures play a significant role in dynamic deformation and stress wave propagation.In this paper,based on the Cosserat theory,a dynamic model of pendulum-type and rotational waves in blocky rock mass with complex hierarchical structures is established to determine the influence of hierarchical structures on dynamic deformation.Then,aiming at low-frequency and low-velocity characteristics of pendulum-type waves,dispersion equations of waves are determined and solved in different hierarchical structures based on the Bloch theorem,and furthermore,the dispersion relation and velocity characteristics of waves are investigated.Finally,mechanism of low-frequency characteristics of pendulum-type waves is revealed on the basis of solid energy band theory,and the possibility of pendulum-type and rotational waves inducing rock bursts is discussed based on the research results.It is indicated that ignoring higher-order hierarchical structures of rock masses may underestimate displacement and overall deformation of rock masses,resulting in unsafe numerical results.Under the action of long wave disturbance,for the first mode pendulum-type waves(the acoustic branches),the dispersion is not significant and propagation velocity decreases,and higher-order hierarchical structures inside rock masses hinder the wave propagation.However,the dispersion of other waves(the optical branches)is significant so that they hardly exist and propagate independently.The low-frequency pendulum-type waves are dominant,which have slower attenuation and longer propagation distance than the high-order mode waves and traditional P and S-waves.

关 键 词：岩石力学 块系岩体 摆型波 旋转波 层次结构 频散关系 COSSERAT理论 

分 类 号：TU45[建筑科学—岩土工程]