基于Neumann展开随机有限元的混凝土重力坝结构可靠度分析

Structure reliability analysis of concrete gravity dams using Neumann expansion stochastic finite element method

针对混凝土重力坝等大体积混凝土结构中,受原材料、混凝土拌合过程以及浇筑施工影响而产生的材料特性空间分布的随机性问题,采用平稳随机场局部平均法离散理论,推导了基于Neumann展开随机有限元的重力坝结构随机响应计算公式,提出了重力坝可靠度计算方法,并开发了相应Matlab计算程序。通过悬臂梁算例对该方法进行验证,并运用该方法研究了随机场离散单元尺寸及相关偏度对结构可靠度的影响,进而计算了典型重力坝坝踵抗拉可靠度。结果表明,相关偏度取值对大坝的可靠度影响显著,可靠度随相关偏度的减小而增大,仅将坝体弹性模量视为单一随机变量时所得可靠度较实际值低;随机场离散单元尺寸应依据相关偏度确定且不宜过大,建议取值不大于相关偏度的1/10～1/8。

For massive concrete structures such as concrete gravity dams,the materials have random spatial distribution properties due to the influences of raw materials and their mixing,as well as the pouring construction.Using the discretization theory of the local average method for a stationary random field,a computational formula of the structural random response for gravity dams is derived based on Neumann expansion stochastic finite element.Corresponding calculation method for the reliability of gravity dams is proposed together with a programmed Matlab code.A cantilever beam is given for the validation of the method and the influence of element size and fluctuation scale of the random field on structural reliability is discussed.The tensile strength reliability of the dam heel is also calculated.The results show that the reliability of a dam can be influenced significantly by the fluctuation scale.Reliability increases with a decreasing fluctuation scale,and it is undervalued if the elastic modulus is considered as a single random variable.In addition,the discretized element size of the random field should be determined by the fluctuation scale and it should not be too large.The suggested element size is less than 1/10~1/8 of the fluctuation scale.