Statistical Analysis of Undrained Strength as Linear Function of Depth

The undrained shear strength of clay often increases in an approximately linear manner with depth. This trend can be characterized by an undrained strength at the top of the soil layer (s_u0) and a change in undrained strength with depth (ρ). Because naturally occurring soils are rarely homogeneous and consequently show high variability in undrained shear strength, the measured properties will exhibit scatter about the linear trend. While many studies have examined the variability in undrained shear strength itself, statistical data for describing undrained shear strength as a function of soil depth is sparse to nonexistent in the geotechnical literature. In addition, the slope and intercept parameters would be expected to show significant correlation, which has not been investigated. The analysis presented in this paper estimates the intercept, slope, and statistics of published data sets of undrained shear strength and generates smaller synthesized data sets based on that information. The synthesized data is then used to estimate the mean and standard deviation of the slope and intercept parameters from the linear trends, and to estimate the correlation coefficient between these two parameters. A strong negative correlation is found between s_u0 and ρ. The stability of a homogenous clay slope with linearly increasing undrained shear strength is examined probabilistically. The negative correlation between s_u0 and ρ substantially reduces the calculated probability of failure for the example.