结构面粗糙度统计测量最小样本数确定方法

由于结构面粗糙度具有各质异性、各向异性、非均一性和尺寸效应等特征,结构面粗糙度系数(JRC)取值具有不确定性,工程中广泛采用统计方法来分析结构面粗糙度性质,然而以往研究往往忽略样本数不足对统计结果的影响。针对结构面粗糙度统计测量时无法确定合理样本数的问题,分别提出基于变异系数级比分析及简单随机抽样原理的最小样本数确定方法。以实际工程岩体结构面表面数据为研究对象,对比分析两种方法在系列尺寸下确定的统计测量最小样本数。实例分析表明:小尺寸样本的变异系数(CV)值明显大于大尺寸样本,且CV值随取样尺寸的增大而减小,取样尺寸为10~50cm的CV值基本稳定在0.31~0.47之间,取样尺寸为60~100cm的CV值基本稳定在0.21~0.31之间;最小样本数与取样尺寸基本满足幂函数关系,且最小样本数随取样尺寸的增大而减少;系列尺寸下级比分析方法在允许误差为±2%时确定的最小样本数与简单随机抽样原理在最大允许误差为10%、置信度为95%时计算的最小样本数是一致的,相似度大于0.997。该研究方法可为工程岩体中定量获取结构面粗糙度统计测量最小样本数提供依据,保证了JRC(结构面粗糙度系数)统计测量结果的准确性,对工程岩体稳定性评价中结构面力学参数的准确获取具有重要意义。

Methods of determining the minimum number of samples for statistical measurement of rock joint roughness

The rock joint roughness has many characteristics like heterogeneity,anisotropy,nonuniformity and scale effect.In engineering practice,different statistical methods are utilized for analyzing the rock joint roughness due to its uncertainty.However,previous studies often neglected the impact of insufficient samples on statistical results.To solve the problem that reasonable number of samples cannot be determined during the statistical measurement of joint roughness,the methods based on the coefficient of class ratio analysis and the simple random sampling principle are proposed for determining the minimum number of samples(MNS),respectively.In the case study,the MNS of statistical measurements is determined based on the proposed methods.The results of rock joint samples are compared and analyzed with different sample sizes.The results indicate that the coefficient of variation(CV)value of the small samples is significantly larger than that of large ones,and the CV value decreases with the size of samples.The CV values of the joint samples with the sizes of 10-50 cm basically are in a range of 0.31-0.47,and the values for those of 60-100 cm samples are between 0.21-0.31.The relationship between MNS and sample size basically satisfies the power function relationship,and the MNS decreases with the sample size.The MNS determined by the former method with an allowable error of±2%is consistent with that calculated by the latter with a maximum allowable error of 10%and a confidence level of 95%.The similarity of the results based on these two methods is greater than 0.997.This study can provide basis for quantitatively obtaining the MNS in rock joint roughness statistical measurement,and can ensure the accuracy of JRC statistical analysis.It is of great significance to accurately obtain mechanical parameters of rock joints in rock mass stability evaluation.