弱粘接复合梁与弱界面层状各向异性非饱和地基相互作用研究

The tracks of the high-speed railways, oil pipelines and so on can be simplified as the composite beams on the soil. It is important to study the interaction of the composite beams and the soil to make sure the safety of the high-speed railways and pipelines. In the system of the composite beams and the soil, defects, such as the microcracks, may occur in the interfaces of the composite beams and result in forming the weak interfaces. The soil often manifests multilayered, anisotropic and unsaturated features. Moreover, imperfect interfaces are formed between the soil layers due to defects such as voids. In the existing literature, some difficulties are encountered, for example the models and algorithms can’t accurately or efficiently calculate the mechanical responses of the composite beams and the soil. Based on the scaled boundary finite element method and the precise integration algorithm, the interaction between the composite beams and the multilayered anisotropic unsaturated soil is studied. The main contents include: (1) studying the static and dynamic responses of the weak interfacial composite beams and precisely and efficiently solving vibration frequencies and the distributions of the displacement and stress field; (2) investigating the responses of the multilayered anisotropic unsaturated soil with imperfect interfaces and accurately giving out the dynamic stiffness and change rules of displacements, stresses and the pore pressure; (3) researching the interaction between the weak interfacial composite beams and the multilayered anisotropic unsaturated soil with imperfect interfaces and precisely analyzing variations of displacements and stresses. This study will provide important theoretical reference and technical support for practical engineering projects.

高铁轨道、石油管线等均可简化为地基上的复合梁结构，研究复合梁与地基的相互作用对于保障其安全性至关重要。在复合梁与地基系统中，上部复合梁界面处易产生微裂纹等缺陷，形成弱粘接界面。下部地基往往表现出分层、各向异性和非饱和特性，并且地基层界面处由于孔洞等缺陷，形成弱界面。目前复合梁与地基耦合作用的研究尚不完善，存在着诸如现有模型与算法计算复合梁与地基力学响应的精度或效率不理想等问题。本项目拟运用比例边界有限元和精细积分方法研究上述问题，主要内容如下：（1）研究弱粘接复合梁的静动力响应，精确高效求解梁的自振频率和位移、应力的分布规律；（2）研究弱界面层状各向异性非饱和地基的力学特性，高精度求解地基的动力刚度和位移、应力、孔隙压力的变化规律；（3）研究弱粘接复合梁与弱界面层状各向异性非饱和地基的相互作用，精准分析梁和地基中位移、应力的变化规律。研究成果将为实际工程项目提供重要的理论参考和技术支持。

复合梁与地基相互作用是结构-地基耦合作用领域的重要组成部分，研究该课题对于节约建设成本和保障高铁、桥梁等结构的安全具有重要意义。上部复合梁在使用过程中梁层交界面处易出现粘接层老化等问题，产生微裂纹，形成弱粘接界面；下部土体含有孔隙，同时呈现出分层和各向异性特征，并且土层界面处易产生孔洞，形成弱界面。因此，本项目开展了弱粘接复合梁与弱界面层状各向异性非饱和地基相互作用的研究，包括：（1）将比例边界有限元和精细积分方法结合建立了精准分析弱粘接复合梁中位移、应力和自振频率变化规律的数值算法；（2）运用精细积分、对偶变量和积分变换方法高精度求解了弱界面层状各向异性非饱和地基的动力刚度矩阵，并揭示了地基中位移、应力和孔隙压力的分布规律；（3）根据梁与地基接触面处的连续性边界条件实现了上部梁与下部地基刚度矩阵的组装，精确求解了弱粘接复合梁与弱界面层状各向异性非饱和地基的动力相互作用，探究了梁与地基系统中位移和应力的变化规律。在本项目的基础上进一步开展了以下研究：提出了分析轴向功能梯度梁静力弯曲和自由振动响应的高效数值模型；建立了求解复合压电板力学响应的精确数值方法。以上成果将为结构-地基相互作用的学术研究和工程设计提供重要的参考。