Effects of spatial autocorrelation structure of permeability on seepage through an embankment on a soil foundation

Theoretical autocorrelation functions (ACFs) are generally used to characterize the spatial variation of permeability due to the limited number of site investigation data. However, many theoretical ACFs are available in the literature, and there are difficulties in selecting a suitable ACF for general cases. This paper proposes using the random finite element method to investigate the effects of ACF on the seepage through an embankment. Five commonly used ACFs-the squared exponential (SQX), single exponential (SNX), second-order Markov (SMK), cosine exponential (CSX) and binary noise (BIN) ACFs in the literature-are compared systematically by a series of parametric studies to investigate their influences on the seepage flow problem. Both stationary and non-stationary random fields are considered in this study. The results show that the commonly used SQX and SNX ACFs may overestimate and underestimate the seepage flow rate, respectively. It is also known that the maximum exit gradient associated with the SNX ACF is larger than those obtained using the other four ACFs. Additionally, it is proved that the deterministic approach-based design is on the conservative side and tends to be too conservative when dealing with soils with greater variation in the properties. It is also found that the SQX ACF has a higher probability of providing a more conservative design in practice. Overall, the differences between different ACFs are not significant and are within acceptable ranges.