柱状节理岩石的旋转椭球纤维丛力学模型

A Micromechanical Model of Rotating Ellipsoid from Cluster of Fiber for Columnar Jointed Rocks

根据柱状节理岩石形成的地质特征,基于细观层面,将单根柱状岩石在重力方向上视为纤维丛,轴对称状态下,纤维丛将根据外荷的变化有机地进行调整,假设纤维丛根据变形协调条件排列为细观椭球体胞群,则通过分析典型椭球体胞的本构行为即可进一步探讨整个岩石的宏观力学性质。根据纤维椭球体胞的几何方程,通过Banach不动点定理和Brouwer不动点定理证明了轴对称状态下椭球体胞中存在着旋转效应并给出了旋转附加应力的表达式,揭示了柱状岩石存在通过周界粘滞剪切耗散局部应变能的过程;通过引入Freudenthal率相关方程并联合有旋转效应的平衡方程构建了分析椭球体胞的本构微分方程组并对之进行了Laplace变换;根据纤维丛细观本构模型及理论并结合泥巴山柱状流纹岩的岩石试验分析了不同应力路径下椭球体胞的几何特征与宏观破坏结果之间的内在联系。

Based on its geological characters,the columnar jointed rock could be regarded as vertical clusters of fiber that could be adjusted to ellipsoid cells organically when external load was changing. The micromechanical model about rotating ellipsoid made of cluster of fiber could rationally illustrate the splitting and shearing of columnar rock,and different phenomena in triaxial rock tests could also be explained. According to the geometrical function of ellipsoid cell,we could see that there existed rotating effects based on Banach and Brouwer immobile point theory in columnar jointed rock leading to reducing the potential energy by shearing around ellipsoid perimeter. A series of differential equations are established which consist of the Freudenthal equation and the constitutive equilibriums of columnar rock and we can analyze rock’s constitutive action through their Laplace-transforming forms. The micromechanical model was turned to be reasonable by two different rock tests about Niba Mountain that different ellipsoid microstructures caused different effects in triaxial compression and triaxial unloading confining pressure rock tests.