|Title:||Efficient and conditional reliability analysis of slopes in spatially variable soils|
|Advisors:||Cheng, Y. M. (CEE)|
|Subject:||Hong Kong Polytechnic University -- Dissertations|
Slopes (Soil mechanics)
|Department:||Department of Civil and Environmental Engineering|
|Pages:||xxiv, 197 pages : color illustrations|
|Abstract:||Spatial variability in soil properties has been widely recognized as an important issue. The influence of spatially variable soils on geotechnical structures such as a slope has attracted increasing notice in the past years. However, it is not a trivial task to accurately estimate the slope reliability with sufficient efficiency when the spatial variability of soil properties is incorporated into the slope stability model, because there are a great number of discretized random variables within the framework of random field theory. In addition, site investigation data, despite not much, are actually the exact values of the soil properties at some particular positions which are independent of the simulation methods. The traditional unconditional random field discards such known data, which is actually a serious drawback and a waste of site investigation effort. Neglecting the known data would also increase the simulation variance ofthe underlying random fields, which subsequently affects the responses of the whole slope system, such as the FS and the probability of failure (Pf). Furthermore, there is another kind of uncertainty—stratigraphic boundary uncertainty (SBU)—which widely exists in layered soils but is missing in most of the previous studies. However, how the SBU influences the slope stability is still an open question. This will subsequently affect the assessment of the estimated results based on the deterministic boundary assumptions. In view of these problems, this thesis mainly focuses on proposing an efficient approach for slope reliability analysis with consideration of the soil spatial variability and incorporating borehole/measurement data (i.e., conditional information) into slope reliability analysis. Firstly, a simplified framework for efficient system reliability analysis of slopes in spatially variable soils is proposed based on multiple response surface method (MRSM) and Monte Carlo simulation (MCS). Within this framework, the equivalent spatially constant parameters, calculated from an explicit random variable model, are used to characterize the soil spatial variability such that the MRSM can be efficiently performed. In addition, a variance reduction strategy is proposed to enable the framework applicable to slope reliability problems involving more than one type of shear strengths. The results show that the proposed simplified framework can well deal with slope reliability analysis in spatially variable soils, providing sound results that are comparable with those by MCS as reported in the literature. It is robust against changes of various cross-correlations, COVs and ACDs, which provides a practical tool for system reliability analysis of slopes in spatially variable soils.|
Secondly, some attempts are made to estimate the failure probability of a slope characterized by soil spatial variability conditioned on a certain number of cored samples (or known data) from site investigation. Kriging method is used in combination with the Cholesky decomposition technique (CDT) to model the conditional random fields (CRFs) such that the simulated CRFs can be constrained by the measured data at particular locations. Then, the probability of slope failure is calculated by Subset simulation (SS). An example application is performed on a nominally "homogeneous" cohesion-frictional (c-φ) slope to illustrate the proposed approach. A series of parametric studies are conducted to investigate the influence of the layout of the cored samples on the Pf, FS, and the spatial variability of the critical slip surface (CSS). It is found that whether the CRFs can be precisely modelled relies highly on the relationship between the sample distance and the underlying auto-correlation distance (ACD). A smaller ratio of the sample distance to the ACD would provide a better simulation result. Moreover, compared with unconditional random field simulations, the simulation variance can be substantially reduced by CRF simulations. This finally produces a narrower variation range of the FS and the corresponding CSS location as well as a much lower Pf. The results also highlight the major significance of the CRF simulation at relatively large ACDs. Thirdly, the influence of the system SBU on the system Pf and risk of a layered slope with spatially varied soil properties are studied. Within this contribution, the inherent soil spatial variability is modelled by non-stationary random fields that are obtained by using an extended CDT, while the random nature of the stratigraphic boundary location is simulated by a discrete random variable model. A series of comparative studies on the probabilistic analysis results obtained from considering and neglecting the system SBU have been conducted with respect to different statistics of soil properties. It is found that the system SBU has a significant influence on the slope failure mechanism. In addition, the slope failure risk would be overestimated for various statistics if the system SBU is not considered, except for small values of COVφ (i.e., COV of φ), where the results are underestimated. Finally, efforts are made to incorporate the inherent SBU into the reliability analysis of slopes in spatially variable soils using one-dimensional conditional Markov chain model, so as to investigate the influence of different borehole layout schemes on slope reliability analysis with and without considering the spatial soil variability. Detailed procedure for implementing the proposed approachon commonly used commercial software (e.g., ABAQUS and MATLAB) is described. It is found that both the location and number of boreholes have significant influence on the stratigraphic boundary simulation. Whether the soil spatial variability is neglected or not, the FS statistics and Pf do not increase or decrease with the borehole number, because there is an influence zone in the slope body and the boreholes located in this zone play a dominant role in the stability of the slope. However, the FS statistics and Pf can converge to the correct results if more and more boreholes are drilled. In addition, it is found that the conventional reliability analysis with an implicit assumption of DSB condition may overestimate the slope reliability. The difference between the DSB and RSB decreases with the increase of the vertical SOF. Compared with the effect of the system SBU, the inherent SBU is far more important to be considered in slope reliability analysis.
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