基于Bootstrap-AIC的隧道围岩参数不确定性表征与最小样本数研究  

Uncertainty Characterization of Surrounding Rock Parameters for Tunnels and the Study of Minimum Sample Size Based on Bootstrap-AIC

作　　者：方砚兵 封坤[1] 李博[1] 张景轩 何川[1] FANG Yan-bing;FENG Kun;LI Bo;ZHANG Jing-xuan;HE Chuan(Key Laboratory of Transportation Tunnel Engineering,Ministry of Education,Southwest Jiaotong University,Chengdu 610031,Sichuan,China)

机构地区：[1]西南交通大学交通隧道工程教育部重点实验室,四川成都610031

出　　处：《中国公路学报》2024年第11期26-37,共12页China Journal of Highway and Transport

基　　金：国家重点研发计划项目(2021YFB2600900);国家自然科学基金项目(52078430,52408447)。

摘　　要：围岩参数不确定性表征是隧道长寿命设计的基础,其中如何在有限数据样本条件下获得足够精度是关键。为此,结合Bootstrap方法和赤池信息量准则(AIC),提出了一种隧道围岩参数不确定性表征方法,并以此研究获得足够精度所需的最小样本数。该方法先通过Bootstrap抽样计算小样本条件下围岩参数概率特征值;然后利用AIC方法识别概率分布类型;其次计算统计特征值落入95%置信区间的频率,确定目标准确率(如90%)所需的最小样本数,从而确保获取足够精度的围岩参数不确定性表征。以Hoek软岩参数为例演示了该方法,研究了软岩参数的不确定性表征与最小样本数;结果表明,满足90%精度需求时软岩参数均值和标准差所需的最小样本数分别为12和22。利用2处软岩实际数据对该方法进行了验证,结果表明在上述最小样本数条件下软岩参数不确定性表征精度满足要求。结合三倍标准差准则,应用该方法对岩体分级标准中的三、四级围岩进行不确定性表征分析,得到了重度、变形模量、黏聚力、内摩擦角和泊松比等围岩参数所需的最小样本数,可为工程实际中三、四级隧道围岩参数不确定性表征的采样提供有益参考,从而助力于隧道可靠性评估与长寿命设计。Uncertainty characterization of surrounding rock parameters is the fundamental cornerstone of tunnel long-life design,and the key is to obtain sufficient accuracy under limited data samples.To address this,a novel method for uncertainty characterization of surrounding rock parameters has been proposed by combining the Bootstrap method and the Akechi Information Criterion(AIC),studying the minimum sample size required to obtain sufficient accuracy.Firstly,the mean and standard deviation of surrounding rock parameters was obtained by the Bootstrap method.Secondly,the probability distributions of the sample under this resampling size were identified by the AIC.Thirdly,the confidence intervals for the mean and standard deviation of the parameters with a confidence level of 95%were calculated.Subsequently,the minimum numbers of samples required for an accuracy of 90%were determined.By this way,the curacy of the uncertainty characterization of surrounding rock parameters was ensured.The proposed method was illustrated through Hoek's classical weak rock parameters.Results indicated that the minimum sample sizes for the mean and standard deviation of weak rock parameters are 12 and 22,respectively.These minimum sample sizes derived from the proposed method were validated by real data of weak rocks from two different places,and the results agreed well with the real data.Furthermore,by incorporating the triple standard deviation criterion,this proposed method was applied to conduct uncertainty characterization of surrounding rocks for the third and fourth level rock mass in the rock mass classification standards.The minimum number of samples for weight,deformation modulus,cohesion,internal friction angle,and Poisson's ratio,were obtained.These could provide valuable insights for the uncertainty characterization of surrounding rock parameters in engineering practices,which in turn would aid in tunnel reliability assessments and long-term design considerations.

关 键 词：隧道工程 围岩参数 BOOTSTRAP方法 最小样本数 不确定性表征 AIC准则 

分 类 号：U452.2[建筑科学—桥梁与隧道工程]