随机-区间混合不确定性下FRP桁架桥多尺度可靠性分析

桁架结构是FRP材料在新建桥梁结构中应用的主要形式之一,然而由于缺乏设计规范、分析方法和数据信息等,FRP桥梁结构存在真实安全度模糊的问题。针对FRP桁架桥在细-宏观尺度参数均存在不确定性,且同时存在随机不确定性和由于概率信息缺乏而表达为非概率不确定性的问题,提出一种多尺度混合可靠性分析方法,该方法能够处理在概率和非概率不确定性并存的FRP结构中的可靠性分析问题。首先,综合运用多尺度方法及随机-区间混合可靠性分析方法等建立多尺度混合可靠度分析模型,并给出可靠度计算公式。其次,通过理论算例验证所提出算法的有效性和精确性。然后,方法应用于一座GFRP桁架桥,通过有限元分析和参数敏感性分析识别对宏观响应影响最显著的不确定性参数,根据显著参数概率信息的完整性,将其划分为区间变量和随机变量。进一步对桁架桥进行位移控制的可靠性分析和以应力控制的可靠性分析,结果表明细观尺度的材料力学性能对桥梁位移控制的可靠性影响较大,而对应力控制的可靠性影响不明显;对桥梁位移控制和应力控制的可靠性影响最大的参数分别为外荷载和抗拉/压强度。最后,比较了方法与其他3种区间变量的处理方法(不考虑区间变量、作为截断正态分布、作为均匀分布)的可靠性,表明不确定性处理的不合理将导致结构可靠性预测的不准确。

Multi-scale Reliability Analysis of FRP Truss Bridges with Hybrid Random and Interval Uncertainties

The truss structure is one of the main forms of application of full FRP bridges. However, due to the lack of design specifications, analysis methods, probability data information, etc., FRP bridges have the problem of ambiguity in the true safety. In order to accurately quantify the reliability of FRP truss bridges with considerations hybrid probability and interval uncertainties at various length scales, a multi-scale hybrid reliability analysis method was proposed. First, a multi-scale hybrid reliability analysis model was established by combining the multi-scale analysis method with the hybrid random-interval reliability analysis method, and the reliability calculation formula was given. Secondly, the feasibility and accuracy of the proposed method were verified through theoretical examples. Then, the method was applied to a GFRP truss bridge to identify the most significant uncertain parameters affecting the macroscopic response through the finite element analysis and parameter sensitivity analysis. According to the availability of probability information, these identified parameters were divided into interval variables and random variables. Further, the reliabilities of the truss bridge were analyzed by using the displacement dominated limit state function and the stress-based limit state function, respectively, and the results show that the microscale material mechanical properties significantly affect the reliability index for the displacement based limit state function, but have no obvious influence on the reliability index for the stress based one. The parameters that have the greatest influence on the reliability are external load and tension/pressure strength. Finally, the method was used to calculate the reliability indices when the interval variables were considered alternatively, which includes without considering interval variables, as truncated normal distribution and as uniform distribution, and the comparison demonstrates that unreasonable considerations of uncertainties may lead to an inaccurate estimate of the structural reliability.