Aimed at the problem of fuzzy uncertainty of geotechnical parameters in slope stability analysis, a non-probabilistic reliability analysis method for slopes based on fuzzy set theory is proposed. Geotechnical parameters are described as fuzzy numbers, which are transformed into interval numbers at different cut set levels by taking fuzzy sets. The corresponding non-probabilistic reliability indexes and failure degrees of the slope are calculated by the non-probabilistic reliability analysis method based on the ellipsoidal model, and then the overall failure degree of the slope is obtained by weighted average to judge the stability state of the slope. The feasibility of the method was verified by a case analysis. The results show that the type and shape parameters of the fuzzy affiliation function of geotechnical parameters have a great influence on the non-probabilistic reliability of the slope. The slope failure degrees obtained from trapezoidal fuzzy numbers were larger, the slope failure degrees obtained from triangular fuzzy numbers and normal fuzzy numbers were medium, and the slope failure degrees obtained from lognormal fuzzy numbers were smaller. When considering soil parameters as triangular fuzzy numbers, normal fuzzy numbers, or lognormal fuzzy numbers, with the reduction of the shape parameters, the non-probabilistic reliability indexes of the slope increased while the failure degrees decreased. Additionally, adopting the overall failure degree to evaluate the stability of the slope can effectively solve the problem where the calculation results are too conservative (if the non-probabilistic reliability index is greater than 1) to judge the stability state of the slope in the traditional non-probabilistic reliability method.

Aiming at the problem that the non-probabilistic reliability analysis method of slope engineering, which is based on an interval model, cannot consider the cross-correlation of geotechnical parameters, a non-probabilistic reliability analysis method of slopes based on a multidimensional parallelepiped model is proposed. This method can effectively alleviate the problem of difficult data survey in the field of geotechnical engineering. Using the limited sample data of soil parameters, the multidimensional parallelepiped model is constructed. The performance function of the slope is constructed based on Latin hypercube sampling and the quadratic response surface method. Then, the limit state equation of the slope can be standardized using the multidimensional parallelepiped model. The non-probabilistic reliability indexes of the slope are calculated based on the global optimal solution to judge the stability state of the slope. The example analysis verifies the feasibility of the proposed method. The results show that the correlation of shear strength parameters of soil has a great influence on the non-probabilistic reliability indexes of the slope. When the correlation coefficients of the shear strength parameters are between −1.0 and 0, the smaller the correlation coefficient is, the greater the non-probabilistic reliability index of the slope is; when the correlation coefficients of the shear strength parameters are between 0 and 1.0, the non-probabilistic reliability index of the slope does not change with the correlation coefficient. The non-probabilistic reliability indexes of the slope obtained using the multidimensional parallelepiped model are between the results obtained using an ellipsoid model and those obtained using an interval model, which are validated by Monte Carlo method and relatively more reasonable. In the absence of a large number of geotechnical sample data, this method provides a new way for slope stability analysis and expands the application field of calculation methods based on non-probabilistic theory.

Landslide risk assessment can quantify the potential damage caused by landslides to disaster-bearing bodies, which can help to reduce casualties and economic losses. It is not only a tool for disaster prevention and mitigation, but also a key step to achieve the coordinated development of the environment, economy, and society, and it provides important support for the realization of the global sustainable development goals (SDGs). In this study, a risk assessment method is proposed for an individual landslide based on the non-probabilistic reliability theory. The method represents an improvement to and innovation in existing risk assessment methods, which can obtain more accurate assessment results with fewer sample data points, refines the methods and steps of landslide risk assessment, and fully considers the destabilization mechanism of the landslide and the interaction with disaster-bearing bodies. A non-probabilistic reliability analysis of the slope was conducted, and the possibility of landslide occurrence was characterized by the failure value of the slope. Moreover, the influence range of the landslide was predicted using empirical formulas; space–time distribution probabilities of the disaster-bearing bodies were estimated by combining their location and activity patterns; and the vulnerability of the disaster-bearing bodies was calculated according to the landslide intensity and the resistance or susceptibility index of the disaster-bearing bodies. The method’s feasibility was verified through its application to the Xiatudiling landslide as a case study. In the process of performing slope stability calculations, it was found that the calculation results of the Monte Carlo method were consistent with those of the non-probabilistic reliability approach proposed in this paper, which was able to obtain more accurate results with less sample data. The personnel life and economic risks were 1.8499 persons/year and CNY 184,858/year (USD 25,448/year), respectively, under heavy rainfall conditions. The results were compared with the risk judgment criteria for geological disasters, and both risk values were unacceptable. After landslide treatment, the possibility of landslide occurrence was reduced, and the personnel life risk and economic risk of the landslide were also reduced. Both risk values then became acceptable. The effect of landslide treatment was obvious. The proposed method provides a new technique for assessing landslide risks and can help in designing mitigation strategies. This method can be applied to landslide risk surveys conducted by geological disaster prevention institutions, demonstrating enhanced applicability in data-scarce regions to improve risk assessment efficiency. It is particularly suitable for emergency management authorities, enabling rapid and comprehensive assessment of landslide risk levels to support informed decision making during critical response scenarios.