Probabilistic slope stability analysis based on conditional random field

Abstract

Slope stability is always among the most important and attended geotechnical research topics. The heterogeneity and uncertainty of the properties of geotechnical materials and the complexity of actual slope engineering highlight the significance of studying slope stability at the probabilistic level. Yet most existing evaluation systems are based on deterministic conceptions. Superior to a definite safety factor (FS) provided by the deterministic analysis, statistical evaluation indexes obtained from the probabilistic analysis usually offer a more scientific, reliable, and realistic estimation on the slope safety. The random field theory is the most widely used methodology for characterizing the spatial variability and uncertainty of soils, and the application of conditional random field (CRF) is an improvement on it, which is adopted herein.In this study, the random fields of soil properties are generated using the Covariance matrix decomposition (CMD) method, and according to related theory, the heterogeneous and uncertain characteristics are defined by several statistical parameters. Further, with the application of CRF, some known soil property values at certain conditioning locations are taken into account when generating random fields. Since CRF can make better use of known information of the geotechnical object, it is supposed to provide a more realistic and convincing result. The generation of CRF is realized through the Kriging technique. Then for each single simulation of the soil property’s field, a corresponding safety factor and other failure consequences are calculated by adopting a numerical limit analysis (NLA) software OptumG2. At last, the probabilistic analysis is carried out through the direct Monte Carlo simulation (MCS), leading to some statistical results describing the slope safety, such as the distribution of FS, the failure probability (Pf), and the reliability index (β).There are several research emphases involved in this study, which are all based on the probabilistic analysis framework. At first, comparative analysis between the traditional unconditional random field method and the CRF method verifies the superiority of CRF, and the comparison between various sampling schemes reveals the effect of sampling points’ layout on the conditioning performance. Then the main part is parametric analyses concerning three different slope models. They are conducted to investigate the influence of statistical parameters of soil properties on the slope reliability, the form of random fields, and the overall state of slope stability. Involved slope models and soil properties include the undrained shear strength (Su) for an undrained slope, the cross-correlated cohesion (c) and internal frictional angle (φ) for a cohesion-frictional slope, and the hydraulic conductivity (Ks) for a dam slope. Furthermore, there is a discussion about if the additional consideration of failure consequence can improve the slope reliability definition which only incorporates the failure probability. In addition, with the CRF of Ks, the parametric sensitivity of the seepage situation in the slope is also studied.Through comparative analysis, the superiority of the CRF method lies in its more consistent estimations on the field form and the slope stability. Yet the effect on the estimation on the slope stability’s mean level is uncertain and much depends on the soil property level at the conditioning locations. Since Pf (characterizing the slope reliability) is an outcome of the distribution of FS (describing the variability and the mean level of slope stability estimation), the influence brought by applying CRF on the slope reliability estimation is also uncertain. Next, the evaluation of sampling schemes also adopts the standards just mentioned. It is found that increasing the number of sampling points and setting them at more influential locations (the locations where the failure is more likely to occur) lead to a better performance of the scheme.The statistical parameters covered in this study don’t significantly influence the mean level of slope stability, except that a higher coefficient of variation (COV) of Su brings a negative effect. The sensitivity of the variability of slope stability to the statistical parameters largely conforms with that of the variability of field form. Specifically speaking, the correlation length or the ratio between horizontal and vertical correlation lengths of Su has a two-sided effect on the variability of slope stability, so that as the two parameters increase, the variability first rises then turns gentle or even declines. Meanwhile, with increasing COV of Su, the variability keeps going up. Then for another slope model, with the cross-correlation between c and φ becoming less negative or more positive, the variability of slope stability increases. Next, the effects of the correlation length and COV of Ks qualitatively follow the laws concerning Su. Finally, the conclusions concerning slope reliability result from the above influence laws about the overall state of slope stability.For defining the slope reliability, taking the failure consequence into account in addition to the failure probability doesn’t bring significant improvement, so it is not recommended. Some other notable conclusions are about the seepage in the dam slope model. The correlation length and COV of Ks both negatively affect the overall flux level in the slope. Meanwhile, with the correlation length going up, the variability of seepage situation first increases then decreases, and with a rising COV, it constantly ascends. The above-mentioned conclusions are of great significance at both theoretical and practical levels.