Influences of anisotropic spatial variation of soils and sampling strategy on slope reliability evaluation

Abstract

In nature, soils are spatially variable. In the context of soil spatial variability, anisotropic spatial variation of soils is a significant topic, which has been widely investigated for horizontally deposited soils. However, rotated transverse anisotropy can often be observed in natural slopes with tilted stratification. Previous studies mainly considered rotated transverse anisotropy in two-dimensional (2D) probabilistic slope stability analyses using stationary random field (RF). However, in-situ observations usually show the non-stationarity of soils, where the trends of soil properties are not constant. Besides, the three-dimensional (3D) rotated transverse anisotropy of soil spatial variability has not been considered in probabilistic slope stability analyses up to the present. In practice, three-dimensional slope models often exhibit rotated transverse anisotropy associated with various stratigraphic occurrences, which can significantly influence the slope stability. The sampling effect is another important topic considering soil spatial variability, as the spatial uncertainty can be reduced by sampling points (i.e., known points) in a domain. Previous probabilistic slope stability analyses only considered the sampling effect in soils with horizontal bedding, while most of the studies were based on 2D slope models. In the few existing 3D studies related to the sampling effect, the influences of end boundary conditions and slope length (L) have not been investigated. This thesis aims to investigate those issues in probabilistic slope stability analyses and provide guidelines for engineering practice. The influence of rotated transverse anisotropy is first investigated in 2D probabilistic slope stability analyses, where the non-stationarity in soil property is also considered. In the study, two soil scenarios are simulated, where the undrained shear strength increases along depth or the direction perpendicular to bedding. The results show that when considering soil strength with an increasing trend with depth, the slope reliability is higher than that considering stationary random field. Meanwhile, when undrained shear strength increases along the direction perpendicular to bedding, the estimated slope reliability and sliding consequence are sensitive to the change of dip angle of strata (α). The rotated transverse anisotropy is then investigated in 3D probabilistic slope stability analyses, associated with three slope scenarios (i.e., cross-dip slope, reverse-dip slope and dip slope). In a cross-dip slope, the observations on the changes of slope reliability and failure patterns with spatial autocorrelation distance (θ) are different from those considering horizontally deposited soils. On the other hand, the changes of slope reliability with θ for a dip slope or a reverse-dip slope are similar to those under horizontal transverse anisotropy. In 2D probabilistic slope stability analyses considering the sampling effect, two conditional RF models are considered with various sampling strategies and dip angles of strata, the residual parts of which are simulated by Kriging interpolation and decomposing the conditional autocorrelation matrix, respectively. The method based on Sobol sensitivity index is also adopted. It is found that the conditional random field simulation method based on Kriging interpolation may result in higher standard deviation (σ) of factor of safety (FS) than that by unconditional random field simulation method. This issue may occur when sample points are distributed sparsely or the angle of the drilling direction of the borehole is near the dip angle of the strata, while such a problem cannot be found when using the conditional RF simulation method by decomposing conditional autocorrelation matrix and the Sobol index method. Besides, it is observed that the magnitude of uncertainty reduction by the various methods would decrease when the angle of the drilling direction of the borehole approaches the dip angle of the strata. For 3D probabilistic slope stability analyses considering the sampling effect, the computation effort would be quite demanding using conditional random field simulation method, as many trial sampling patterns need to be considered. Therefore, the Sobol index method is adopted to quantify the sampling efficiency. It is found that when the ratio of θ / L increases, the sampling efficiency increases. In the meantime, the optimal sampling efficiency for slopes with fixed end boundary condition would be higher than that with smooth end boundary condition, except for the cross-dip slope, where the smooth end boundary condition would indicate higher optimal sampling efficiency. This study reveals the significance of characteristics in 3D slope model [e.g., slope length (L) and end boundary conditions] in the reliability evaluation incorporating sampling effects, which cannot be explicitly considered in the 2D slope model.