基桩完整性检测的概率分析及质量动态评估

基于概率理论，对基桩完整性检测的概率分布进行了详细的分析，分析表明抽检结果与总体不合格率和抽检桩数有关，因此建议将总体不合格率作为评价整批桩质量的标准。利用 Bayesian 方法推导出总体不合格率的先验分布服从标准的 Beta 分布，由共轭分布原理得出后验分布也服从 Beta 分布。然后分析了总体不合格率后验分布的期望和方差，得出结论：后验分布的期望是先验分布的期望和当前抽样检测不合格率的加权和；后验分布的方差是当前抽检不合格率及先验分布方差的加权和。通过分析抽检桩数对加权系数和后验分布的期望和方差的影响，结果表明：当抽检桩数小于 10 时，抽检桩数对检测结果有显著影响；当抽检桩数大于 10 时，抽检桩数对抽检结果的影响变小；尤其当抽检桩数大于 20 时，对抽检结果无显著影响。最后利用先验分布的期望和方差与后验分布的期望和方差的关系建立起质量检测的动态评估模型。算例分析表明该动态模型可更准确地估计出总体不合格率，具有较重要的工程实际意义。

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 inspection(NSI).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.