基于贝叶斯理论的灌注桩多个缺陷统计特性分析

Evaluation of statistics of multiple defects in bored piles using Bayesian theory

由于施工技术水平、岩土工程条件等不确定性因素的影响,基桩中经常出现各种缺陷。为此,提出了基于贝叶斯理论的灌注桩多个缺陷统计特性的分析方法。在考虑钻芯法检测不确定性的基础上,采用泊松分布模型模拟基桩中多个缺陷的出现概率,推导了缺陷平均出现率后验分布的计算公式。提出了估计缺陷尺寸修正的贝叶斯抽样方法,给出了评价钻芯法检测概率的方法。算例分析表明,钻芯法的检测概率对准确地估计缺陷平均出现率有明显的影响,如果不考虑检测不确定性因素的影响,缺陷平均出现率将被低估。随着检测到缺陷数目的增加,更新的缺陷平均出现率的均值逐渐增加,更新的变异系数逐渐减小。此外,先验的信息能够有效地减小缺陷平均出现率和缺陷尺寸估计的不确定性。

Due to errors in handling slurry, concrete, casings, reinforcement cages and other factors, minor or major defects in piles can be introduced during or after pile construction. Therefore this paper aims to propose a procedure to estimate the statistics of multiple defects in bored piles using the Bayesian theory. A Poisson process is adopted to model the occurrence of multiple defects in bored piles. Moreover the formulae of updated mean rate of occurrence are derived with a consideration of detection uncertainties for coring examination. A modified Bayesian sampling method is presented to update the distribution of mean defect size. Then, a method to evaluate the detection probability of coring examination is formulated. Results from numerical example indicate that the detection probability has a significant influence on the Bayesian estimator of mean rate of occurrence. The mean rate of occurrence will be highly underestimated without consideration of detection uncertainties. The updated mean of mean rate of occurrence increases with increasing values of the number of detected defects, while the updated coefficient of variation of mean rate of occurrence decreases. In addition, the uncertainties in mean rate of occurrence and mean defect size can be reduced substantially through the use of prior information.