This paper aims to propose a systematic quantitative method for system reliability evaluation of rock slope with plane failure involving multiple correlated failure modes. A probabilistic fault tree approach is presented to model system reliability of rock slope. An n-dimensional equivalent reliability method is employed to perform the system reliability analysis of the slope involving multiple correlated failure modes. Reliability sensitivity analyses at three different levels, namely, the single limit state function level, single failure mode level, and system reliability level, are carried out to study the effect of variables on reliability. An example is presented to demonstrate the validity and capability of the proposed approach. The results indicate that the system reliability of rock slope involving multiple correlated failure modes can be evaluated efficiently using the proposed approach. The system probability of failure is overestimated if the correlations between different failure modes are ignored. The relative importance of different failure modes to the system reliability can differ considerably. The sensitivity coefficients of basic random variables strongly depend on the selected sensitivity analysis level. The system reliability is sensitive to the location of the tension crack and the percentage of the tension crack filled with water.

A non-intrusive stochastic finite element method is proposed for reliability analysis of unsaturated slopes considering the spatial variability of hydraulic parameters and shear strength parameters. The Karhunen-Loève (KL) expansion technique is employed to discretize cross-correlated lognormal random fields. The factor of slope safety is explicitly expressed as input random parameters using the Hermite polynomial chaos expansion. The Latin hypercube sampling technique is used to calculate the unknown coefficients of polynomial chaos expansion. An example of reliability analysis of an unsaturated slope under the steady-state seepage flow is presented to demonstrate the validity of the proposed method. The results indicate that the proposed method can effectively evaluate the reliability of unsaturated slopes considering spatially varying soil properties. The polynomial chaos expansion combined with the Latin hypercube sampling technique can effectively estimate the probability of slope failure at a relatively low level.