Probabilistic analysis of integrity inspection and dynamic evaluation of quality for bored piles

Based on the probability theory, the probability distribution of integrity inspection for piles is analyzed, and the analysis shows that the results of sampling inspection relate to the general unqualified rate and the number of sampling inspectionNSI). Therefore the general unqualified rate is suggested to be the criterion to judge the quality of all the bored piles. The prior distribution of the general qualified rate is deduced to follow the normal Beta distribution using the Bayesian method, and the posterior distribution also follows the Beta distribution according to the conjugate distribution theorem. The expectation and variance of the posterior distribution are studied, consequently. A conclusion is drawn that the posterior expectation is the weighted sum of the current sampling unqualified rate and the prior expectation, and the posterior variance is the current sampling unqualified rate and the prior variance. It is demonstrated through the analysis of the relation between the NSI and the weighted coefficients, and the posterior expectation and variance that the results of sampling inspection are sensitive to the NSI when the NSI is less than ten, but when NSI is greater than ten, especially, greater than twenty, the results of sampling inspection are insensitive to the NSI. Finally, a dynamic evaluation model of the general unqualified rate is established using the relation between the prior expectation and variance and the posterior expectation and variance. The results from the numerical example indicate that the general unqualified rate can be more accurately estimated using the dynamic evaluation model, which is significant in engineering practice.