斜交各向异性隧洞围岩与衬砌相互作用的力学解析研究

Natural rock masses are complex geological bodies which exhibit evident anisotropic characteristics. At present, the complex conditions of rock masses involved in mechanical analysis of tunnels and supporting structures are mainly orthotropic, and little analytical analyses have been conducted on non-orthogonal anisotropic conditions, which are more common in practical engineering. In this study, the skew anisotropic rock mass with only one elastic symmetry plane is taken as the research object. According to the conversion formulas of the elastic constants between the coordinate systems, the determining method of compliance matrix is studied, and the compliance matrices under different conditions are obtained. Based on anisotropic mechanics and conformal transformation method of complex function, analytical study on stress and displacement fields of an arbitrary shaped tunnel in skew anisotropic rock mass is carried out, and the distribution law of stress and displacement is analyzed. Considering different contact conditions between skew anisotropic surrounding rock mass and lining, the expression of contact conditions and boundary conditions using complex variable function is studied. Analytical solutions for stress and displacement on the inner boundary of lining and the interface of surrounding rock mass and lining are derived. On this basic, optimization for shape of the lining section is conducted to reduce stress concentration of the surrounding rock mass and lining. This research fully considers the skew anisotropic property of rock mass, and is more in accordance with the engineering condition. The research results will improve the theoretical system of mechanical analysis of anisotropic surrounding rock mass and supporting structure of tunnel, and provide theoretical basis for engineering practice.

自然界的岩体是非常复杂的天然地质体，具有明显的各向异性。目前采用解析方法开展隧洞围岩及支护结构的力学研究，分析的岩体复杂工况大都是正交各向异性，但是对于工程实际中常见的非正交的更复杂工况却鲜有研究。本项目以只存在一个弹性对称面的斜交各向异性岩体为研究对象，利用坐标系旋转时弹性常数的转化，研究柔度矩阵的求解方法，进而对不同工况下岩体的柔度矩阵进行计算；基于各向异性体力学和复变函数中的保角变换方法，开展斜交各向异性岩体开挖任意形状隧洞后应力场、位移场的解析研究，揭示其应力、位移分布规律；针对斜交各向异性围岩与衬砌不同的接触条件，研究接触条件和边界条件的复变函数表达，推导出围岩衬砌接触面以及衬砌内边界上的应力、位移解析解，进而对衬砌的断面形状进行优化。本项目充分考虑岩体的斜交各向异性，更符合岩体的实际工况，研究成果将完善各向异性隧洞围岩和支护结构力学分析的理论体系，为工程实践提供理论依据。

自然界的岩体是非常复杂的天然地质体，具有明显的各向异性。目前采用解析方法开展隧洞围岩的力学研究，分析最复杂工况大都是正交各向异性，但是对于工程实际中常见的非正交的更复杂工况却鲜有研究。本项目的主要研究内容为：(1)以只存在一个弹性对称面的斜交各向异性岩体为研究对象，获得其柔度系数矩阵的理论求解方法，进而对不同工况下岩体的柔度矩阵进行计算；(2)基于各向异性体力学和复变函数中的保角变换方法，开展斜交各向异性岩体开挖任意形状隧洞后应力场、位移场的解析研究，揭示其应力、位移分布规律；(3)针对斜交各向异性平板结构中的开孔问题，完成弹性常数的求解和板中开设任意形状孔的应力解析解的推导，并开展不同工况下带孔斜交各向异性板的力学特性研究；(4)研究不同因素下切顶沿空留巷高强锚注控制技术对围岩稳定性的影响，开展不同切顶角度、高度、注浆加固范围和参数等影响因素下切顶沿空留巷围岩控制数值对比试验。研究表明：斜交各向异性围岩的应力和位移分布具有明显不对称性，且孔边最大切向应力远大于各向同性结构；外荷载为压应力时，孔边应力也以压应力为主，拉应力非常小，且由于材料的各向异性特性，拉应力区域偏离孔洞边界与y轴的交点；单向均布荷载作用下，孔边总有4个点的位移和切向应力值为零。本项目充分考虑材料的斜交各向异性特性，更符合实际工况，研究成果将完善各向异性隧洞围岩力学分析的理论体系，为工程实践提供理论依据。