隧道岩土参数概率分布及取值数目探讨研究

Study on Probability Distribution and the Sampling Number of Geomechancial Parameters in Tunnel Engineering

摘要: 本研究选取南方某地铁某线路岩土试验测定值(粘聚力值、内摩擦角值、含水量、压缩系数、孔隙率、压缩模量和天然密度)为研究对象，利用统计学理论对测定值总体所服从的概率分布进行拟合分析，分别获得测定值正态分布、伽马分布、瑞利分布、泊松分布和威布尔分布下的分布参数，并利用柯尔莫哥洛夫–斯米洛夫检验对上述分布的拟合优度进行计算，进而获得测定值的最优分布函数，然后通过随机抽取的方式，从总体测定值中随机抽取4组子样，每组子样本含量分别为30个、20个、10个和6个，并在该基础上分析所抽取的子样是否服从与总体相一致的概率分布，再通过方差分析，检测上述子样间的显著性差异，最后分析样本含量对概率分布参数稳定性的影响。结果表明含水量的最优分布为正态分布，天然密度最优分布为威布尔分布，孔隙率最优分布函数为伽马分布，内摩擦角不服从上述任何一种分布，粘聚力值最优分布为伽马分布，压缩模量最优分布为伽马分布。此外，当子样数为6时，7项指标均与总样本空间KS检测结果不相符，即较少的子样数会导致数据服从多种分布模型从而造成土体指标统计值与实际值产生偏差，当子样本数大于等于10时，利用统计学原理得到的土体物理指标值及分布类型愈稳定。本研究成果对于隧道、边坡、基坑等工程勘察中的土工试样试验取值数目的确定具有一定的参考与指导价值。

Abstract: In this study, the determined values of soil sampled from a southern city sub-railway were selected as the tested objects (cohesive force, angle of internal friction values, water content, compressibility, porosity and compression modulus and density of natural). And these values were analyzed based on the theory of statistics to investigate their probability distribution patterns, such as normal distribution, gamma distribution, Rayleigh distribution, Poisson distribution, and Weibull distribution based on Kolmogorov test to obtain their optimal distribution. Afterwards, 4 sets of samples were randomly selected from the overall samples and the quantity of each group of subsample was 30, 20, 10 and 6 respectively, and based on these extracted subsamples, analysis was conducted to text whether these subsamples follow the same distribution function as their parent samples. Based on these, ANNOV was used to analyze their consistence of the parameter with that of the overall samples. The results show that the optimal distribution of water content is normal distribution, the optimal distribution of natural density is Weibull distribution, the optimal distribution function of porosity is Gamma distribution, the internal friction angle does not obey any of the above distribution, the optimal distribution of cohesion is Gamma distribution, and the optimal distribution of compression modulus is Gamma distribution. In addition, when the sample number is six, the seven indexes and total samples based on KS test result are not consistent, the less the number of the sample will lead to a variety of distributed data model, which lead to a deviation of soil physical parameter from their actual values. And when the sample is greater than or equal to 10, the values of soil parameters based on statistical principle are stable. The results of this study have certain reference and guiding value for determining the number of test values of geotechnical samples in tunnel, slope, foundation pit and other engineering investigations.