中文摘要：

针对小尺度的各态历经假设的失效，研究小尺度上多孔介质特性参数统计特征。利用基于K·L（Karhunen-Loeve）展开和混沌展开的谱模型，分析了尺度大小对地下水流动的影响。结果表明，尺度大小导致了特征值系列和特征函数系列的变化，尺度的变化对水头、含水量、流速影响程度不同；水头和流速方差与尺度相关，尺度越大，水头和流速方差越大；研究尺度的变化对水头、含水量、流速均值产生的影响较小。

英文摘要：

The ergodic hypothesis will become invalid in a small domain. Therefore, the modified covariance functions of aquifer parameters are evaluated from the ensemble average, and an improved numerical model is developed based on the K-L （Karhunen-Loeve）expansion and chaos expansion. This study analyzes the impact of the domain scale on groundwater flow. The results show that the investigation scale causes the change of the eigenvalue and eigenfunction series, and the investigation scale impacts the total head, water content and velocity in different degree. The variances of total head and velocity increase as the investigation scale increases, and the mean of total head, velocity and water content are scaled independent.