# Non-Probabilistic Reliability Analysis of Slopes Based on a Multidimensional Parallelepiped Model
## 1 Introduction  
Slope stability analysis [1; 2; 3; 4; 5; 6; 7] is one of the most important research techniques in the field of geotechnical engineering. Slope stability analysis methods are mainly divided into qualitative analysis methods, quantitative analysis methods, and uncertainty analysis methods. Since most of the geotechnical parameters affecting slope stability have uncertainties, such as randomness, fuzziness, and variability, an uncertainty analysis method is more appropriate for actual slope projects. The non-probabilistic reliability method, as one of the uncertainty analysis methods, does not require detailed parametric probabilistic statistical characterization to take into account the uncertainty of influencing factors. Therefore, it is suitable for use when sample data are small. It also has the advantages of less computational workload and relatively simpler operation than probabilistic reliability analysis methods. The correlation between geotechnical parameters is a result of long-term geological evolutionary processes and an important factor affecting slope stability. When using the non-probabilistic reliability method to analyze slope stability, the influence of the correlation between geotechnical parameters needs to be considered. Currently, domestic research in China and international research on non-probabilistic reliability analysis of slopes can be divided into two categories according to the convex set model used: (1) The first is non-probabilistic reliability analysis based on an interval model. [PERSON] et al. [8], [PERSON] et al. [9], and [PERSON] [10] used an interval mathematical method to calculate the interval of safety coefficient of slopes, and then calculated a non-probabilistic reliability index of slopes using an interval model. This kind of method only needs to determine the upper and lower boundaries of the interval of geotechnical parameter values, and the calculation process is relatively simple. However, its limitation is that it cannot take into account the correlation between geotechnical parameters. In some cases, the interval expansion problem will arise during the calculation process. (2) The second category is non-probabilistic reliability analysis based on an ellipsoid model. [PERSON] et al. [11], [PERSON] et al. [12], and [PERSON] et al. [13] used an ellipsoid model to construct the uncertainty domain of geotechnical parameters, and calculated the non-probabilistic reliability index of slopes using a direct iterative method to assess the stability of slopes. This type of method considers the correlation between geotechnical parameters, but the calculation process is relatively complicated. Therefore, in the field of non-probabilistic reliability analysis of slopes, it is of great significance to develop a method that can take into account the correlation of geotechnical parameters and has a relatively simple calculation process. The multidimensional parallelepiped model proposed by [PERSON] [14] is a class of models that can take into account the correlation between interval variables. A multidimensional parallelepiped model can be used to express the situation where the parameters under consideration are independent or correlated, or where both correlation and independence coexist [15]. [PERSON] et al. [16] introduced a multidimensional parallelepiped model to deal with the case of coexistence of correlation and independence of system parameters. Combining it with the Monte Carlo method, they proposed a method to analyze the uncertainty in the intrinsic characteristics of automotive powertrain suspension systems. [PERSON] et al. [17] applied a multidimensional parallelepiped model to the interval analysis of complex-valued domains, which significantly alleviated the interval overestimation problem. [PERSON] et al.