岩样单轴抗压强度区间估计分析

基于岩石单轴抗压强度为正态分布随机变量,利用数理统计理论对岩样单轴抗压强度置信区间、置信度等问题进行了系统的分析研究,整理并推导出了岩样单轴抗压强度"区间估计指标"的理论计算公式,并分析了岩样单轴抗压强度样本均值、样本标准差、总体均值置信区间、总体标准差置信区间等与岩样数量之间的关系,最后利用前人试验数据进行了验证应用与分析。结果表明:现有"单值点指标"方法给出的数据"信息不足",导致不同试验条件下得到的各组试验数据之间的横向比较的可靠性得不到保证,而"区间估计指标"可克服其不足,且在岩样数量较小时仍可使用,只是其置信度会较低(置信区间宽度会较大);当岩样数量较小时,样本标准差的波动性比样本均值的波动性约高一个数量级,样本标准差的随机性与离散性更大且达到收敛稳定所需的岩样数量也更大;岩样单轴抗压强度的"区间估计指标"置信区间、置信度等与岩样数量、岩样非均质性、岩样强度分布的随机性等有关。

Interval estimation of uniaxial compressive strength of rock samples

Based on the fact that the uniaxial compressive strengths (UCS) of rock are normally distributed random variables, we first used mathematical statistics to analyze the scattering and the interval parameters of UCS of rock samples, then deduced a theoretical calculation formula about interval parameters of UCS of rock spamles and analyzed the relationship between the sample size and the mean of uniaxial compressive strength, the sample standard deviation, the confidence interval for population mean, and the confidence interval for population standard deviation of UCS of rock samples, and finally employed the previous test data to verify and analyze the interval parameters. The results show that the present single value method doesn''t contain enough information and cannot guarantee the reliability of the comparison between tests data obtained under different test conditions. However, the interval estimation method can overcome the deficiency and can be used even if the sample size is small, but its confidence level will be lower (confidence interval width will be greater). When the sample size is small, the volatility of the sample standard deviation is one order of magnitude higher than that of the sample mean, the randomness and the discreteness of the sample standard deviation is greater, and the sample size for achieving stable convergence is larger. The confidence interval and the confidence level of UCS of rock samples are related to sample size, heterogeneity of rock sample, and randomness of rock strength distribution, etc.