岩土工程中试验数量与可靠指标的关系

基于小样本理论,分析了岩土工程中试验数量与参数统计均值间的关系、参数统计均值与可靠指标间的关系、试验数量与可靠指标间的关系,指出试验数量对参数统计均值及可靠指标均有影响.在相同的置信度及变异系数情况下,试验数量越小,参数统计均值及可靠指标的相对误差就越大.随着试验数量的增加,这种影响程度随之减弱.试验数量对可靠指标的影响还与参数的敏感性有关,参数的敏感性系数越大,在相同的置信度及变异系数情况下,试验数量对可靠指标的影响程度也越大.因此,可靠指标不是定值,它与试验数量、参数统计时的置信度及参数的变异系数有关.在进行岩土工程的可靠度分析时,一定要将概率的概念贯穿于从试验设计到可靠度分析的全过程,而不仅仅局限于可靠指标的分析计算阶段.

Relationship between number of test samples and reliability index in geotechnical engineering

Based on the small-sampling theory,several relationships were studied,such as the relationship between the number of test samples and the statistical mean value,the relationship between the statistical mean value and the reliability index,and the relationship between the number of test samples and the reliability index. It was shown that the number of test samples affect the statistical mean value and the value of reliability index. At the same confidence level and the same coefficient of variation,the relative error of the statistical mean value and the value of reliability index will increase if the number of test samples decreases. However,the degree of the influence will decrease with the increase in the number of test samples. The influence of the number of test samples on the value of reliability index is also affected by the sensitivity of parameters. If the sensitivity of a parameter is large,this parameter will have a large influence on the value of reliability index under the same condition of confidence level and coefficient of variation. Therefore,the value of reliability index is not a constant; it changes with the value of confidence level and coefficient of variation,which means that we should adopt the concept of probability for all the stages of the reliability analysis of geotechnical engineering,not just for the calculation stage of the reliability index.