移动车辆作用下混凝土桥梁的裂缝开合效应及非线性振动机理研究

Cracks inevitably appear in concrete bridges during operation. Some cracks may be in close state under dead loads such as its self weight and prestressing force, but they will open under moving vehicles. The opening and closing make concrete bridges exhibit nonlinear behaviors, for example the contact nonlinearity of crack interfaces, the material nonlinearities of concrete and steel bar, the geometric nonlinearity caused by the change of vibration equilibrium position. According to these nonlinear characteristics, the method combined with theoretical analyses, model experiments and numerical simulations is used to study the behavior of concrete bridges with cracks. The three-dimensional analytical model of concrete crack is built, and solved by the contact mechanics to obtain the variation law of crack opening-closing degrees under moving vehicles. The relation model between the stiffness of crack regions and opening-closing degrees is set up to study the change law of the stiffness during the crack opening and closing. The influence mechanism of stiffness change on the vibration equilibrium position is investigated to analyze the geometric nonlinearity during the vibration. At last, a nonlinear method for vehicle-bridge coupling vibration is proposed, and the vibration responses of the concrete bridge with cracks are calculated to accurately evaluate the working state of the bridge during operation.

混凝土桥梁在运营过程中不可避免地出现各种裂缝，在结构自重、预应力等恒载作用下，有些裂缝处于闭合状态，但当移动车辆作用于桥梁上时，它们会张开；混凝土裂缝的这种“开合”使得混凝土桥梁结构产生一系列的非线性行为，如裂缝界面的接触非线性，混凝土与钢筋的材料非线性，振动平衡位置改变引起的几何非线性等。本项目针对这些非线性特点，使用理论分析、模型试验和数值模拟相结合的方法，研究带裂缝桥梁的结构行为。建立混凝土结构裂缝的三维分析模型，利用接触力学方法进行求解，获得移动车辆作用下裂缝开合度的变化规律；构建裂缝区域结构刚度与开合度的关系模型，分析结构刚度在裂缝开合过程中的变化规律；探讨刚度变化对结构振动平衡位置的影响机制，进而研究振动过程中产生的几何非线性效应，建立考虑裂缝开合效应的车-桥耦合振动非线性分析方法，计算带裂缝桥梁结构的车致振动响应，以准确评价既有混凝土桥梁的运营工作状况。

本项目围绕车辆荷载作用下开裂混凝土梁的振动特性开展系统深入的研究，从裂缝开合的精确模拟入手，提出开裂混凝土梁刚度计算方法和非线性车桥耦合振动分析方法。利用接触动力学，对混凝土裂缝在振动过程中状态变化进行精确模拟，总结了在不同荷载作用下裂缝状态变化规律。针对混凝土开裂区域，基于裂缝和钢筋的实际分布，提出了钢筋混凝土粘结破坏模型和非线性混凝土应变分布模型，利用内力平衡条件，求解这些模型中的关键参数；并基于这些模型，计算各个截面的惯性矩和结构刚度，进而分析裂缝深度与结构刚度之间的关系；结合裂缝状态的变化，得到结构刚度在振动过程中的变化规律。采用模态叠加方法，建立能够带开关型裂缝梁的车桥耦合分析模型，通过对裂缝开合时刻的结构响应进行重构分析，得到裂缝状态变化引起的结构响应非线性变化。研究算例表明呼吸裂缝会导致较大的加速度，进而改变各阶模态对位移贡献的斜率，会产生较大的位移；改变位移时程的方式，使得位移时程上增加一个的峰值; 同时裂缝开合会减小一阶模态对位移的贡献，但会增大二阶模态对结构响应的贡献。研究结果为既有混凝土桥梁行车性能评价提供了理论依据，保证桥梁在运营期间的适用性和安全性。