Issue 37

Z. Hongping et alii, Frattura ed Integrità Strutturale, 37 (2016) 352-359; DOI: 10.3221/IGF-ESIS.37.46 354 are the functions of service time; and ( ) sj k t stands for coordination coefficient of jth steel reinforcement, and it is also the function of service time. Uncertainty Statistical Parameters of Resistance Uncertainty of reinforced concrete resistance includes uncertainty of calculation mode, material performance and geometrical parameters. Uncertainty of calculation mode refers to variability induced by basic assumption adopted by resistance analysis and evaluation, uncertainty of material performance refers to variability induced by durability degeneration, such as concrete carbonization, cross section loss induced by steel reinforcement corrosion, corrosion expansion, cracking and separation of concrete cover and mechanical property degeneration of corroded steel reinforcement. Considering the uncertainty of calculation mode, the resistance of reinforcement concrete structure can be expressed using the following formula ( ) ( ) r r P t K P t  (2) Where ( ) P t stands for random process of resistance and r K stands for random variable of uncertainty of calculation mode. According to relevant methods of mathematical statistics and considering the uncertainty of model parameters, probability statistic characteristic of resistance can be obtained from the following formula. ( ) ( ) P K P r r t t     (3) 2 2 ( ) ( ) P K P r r t t      (4) ( ) ( ) ( ) P P P t t t     (5) where K r  and K r  stand for the average value of random variable r K and variable coefficient of calculation mode uncertainty respectively; ( ) Pr t  and ( ) Pr t  stand for the function of average value and the function of variable coefficient respectively. It can be known from formula (6), (7) and (8) that ( ) [ ( ), ( ), ( )] P f aj d K r j sj t P t t t      (6) ( ) ( ) ( ) Pr Pr Pr t t t     (7) 2 2 ( ) ( ) ( ) P P Z r j j j t t t Z                (8) where j Z stands for relevant random variable influencing resistance and ( ) P j t Z     stands for result of partial derivative when the average value was used. It can be seen from the above deduction process that, some statistical characteristics of basic parameters of resistance needs to be determined at first before acquisition of statistical characteristics of final resistance. Depending on the current test means and research conditions, we can obtain some statistical characteristics of parameters easily. Using mathematical method, we can obtain uncertainty statistical rules of final model.