PSI - Issue 11

Pablo Benítez et al. / Procedia Structural Integrity 11 (2018) 60–67 Benítez et al./ Structural Integrity Procedia 00 (2018) 000 – 000

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( ) t corr insp icorr D D V t T    (2) Where 0 is the rebar diameter on its initial condition (cm), ( ) is the rebar diameter over time (cm); is the corrosion rate (cm/year 0.5 ), is the time of intervention (year) within the lifespan ( = 50 ), and is the time of corrosion initiation (year). It should be noted that for < the corrosion no longer exist and, therefore, the damage intensity must be equal to zero. Then, the detectability function can be formulated as a cumulative normal distribution function (CDF) for each inspection technique where is considered, besides the damage intensity, the medium damage intensity 0.5 for which a certain inspection technique has a 50% probability of detecting the damage. The values range for detectability is from zero to one and is related to a minimum ( ) and maximum ( ) damage degree in the structure (Frangopol, Lin, and Estes 1997). ( ) 0.5 ( ) min max t d for                   (3) Where Φ(. ) is the standard normal CDF, and is the standard deviation. Considering = 0.7 ∗ 0.5 and = 1.3 ∗ 0.5 , then the detectability will be equal to zero for ≤ and it will be equal to 1 for > . 3.2. Probability of failure by corrosion Corrosion in the reinforcement of concrete causes a section loss of the rebar that decreases its design resistance. Due to the high uncertainty of parameters involved in the study of structural failure, it is necessary to perform the analysis from a probabilistic approach. Monte Carlo Simulation (MCS) can be a useful method to performing the probability of failure for a structure given a failure function that describes the mechanism of degradation. Thereby, this simulation technique provides the probability density function (PDF) regarding the time to failure ( ) of the structure over its service life. In this paper, the failure function is obtained from Equation (1) and (2), where the damage degree is set to a critical damage degree to obtain the limit state function. For this purpose, it is possible to establish that when the rebar registers a section loss greater than 25%, it could present changes in its structural behaviour and reduce the margin of safety significantly (Cheung, So, and Zhang 2012). Therefore, can be said that when a damage degree reaches a value of 25%, corrosion-induced failure is expected in the structure. Thus, considering the variables of Equation (1) as random variables and developing a number of iteration in the MCS, the PDF for the probability of failure is obtained. One of the main objectives in the inspection schedule of structures is the need to detect the damage before the failure is reached. Achieve this goal depends mainly on the damage degree in the structure at the inspection time, as well as the detectability of the applied inspection technique. Therefore, the probability of damage detection before failure ( ) can be formulated considering both the ( ) and the PDF of (Soliman, Frangopol, and Kim 2013).       1 ( ) 1 ( ) 1 1 * , * , i i j j n BF insp f insp i insp j j i P P t T d t d t                       (4) Where is the number of inspections, ( ≤ ) is the probability that the i th inspection is performed before the corrosion failure, ( ) ( , ) is the probability of damage detection of an inspection technique at the time of inspection , and ( ) ̅̅̅̅̅ ( 0 , 0 ) = 1 . 3.4. Cost Analysis Cost analysis is very important in maintenance planning. Whether a building with a service life of 50 years is considered, approximately between 75% and 80% of the total costs are presented during the use and maintenance stage (Madureira et al. 2017). In this work, the total inspection cost is obtained from both the individual cost of each 0 2* 3.3. Probability of damage detection before failure