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混凝土在重复荷载作用下的疲劳寿命由于不可避免的随机因素的干挠,具有较大的离散性,因此有必要把概率的方法引入混凝土疲劳寿命的研究中去。本文根据混凝土在疲劳荷载下的损伤机理,提出以应变做为表征其损伤程度的量度。并由疲劳损伤过程与马尔可夫过程的数学相似性,认为可以考虑混凝土的疲劳损伤过程具有马尔可夫性。通过求解FOKKER-PLANCK方程,找出疲劳损伤状态的转移概率密度函数,求出在指定时间下疲劳损伤分布,也可求出在给定的临界损伤后的疲劳寿命分布。经与试验相比较,可知由此方法推出的寿命分布函数较对数正态分布更为接近试验数据,且具有较大的适用范围。该方法在进行铁路桥梁疲劳可靠性分析中是有用的。
The fatigue life of concrete under repeated load due to the unavoidable stochastic factor, has large dispersion, so it is necessary to introduce probability method into the study of fatigue life of concrete. In this paper, based on the damage mechanism of concrete under fatigue loading, the strain is taken as a measure of its damage degree. From the mathematical similarity between the fatigue damage process and the Markov process, it is considered that the fatigue damage process of concrete can be considered Markovian. By solving the FOKKER-PLANCK equation, the transition probability density function of the fatigue damage state is found out, the fatigue damage distribution is obtained at the specified time, and the fatigue life distribution after a given critical damage can also be obtained. Compared with the test, it can be seen that the life distribution function introduced by this method is closer to the test data than the lognormal distribution, and has a larger range of application. This method is useful in the fatigue reliability analysis of railway bridges.