# Dimensional Reduction-Based Moment Model for Probabilistic Slope Stability Analysis
## 1 Introduction  
Stability analysis and design are essential to safety in slope construction. Various traditional methods have been applied to slope stability analysis, such as limit equilibrium [1], limit analysis [2], numerical method [3], and intelligent method [4]. A field-testing program investigated five expansive soil slopes with different inclinations subjected to artificial rainfalls and calibrated based on a numerical model [5]. The characteristics and prevention mechanisms of artificial slope instability were explored with field investigation in a typical watershed using a neural network [6]. The soilbag-protected slopes in expansive soils were designed to consider the swelling pressure based on the balance between the soilbag friction and the active lateral earth pressure [7]. A limit analysis was used to evaluate the stability of expansive soil slopes stabilized by anchor cables based on the kinematic limit analysis theorem [8]. The uncoupled and hydro-mechanical coupled analyses were conducted to deal with the hydraulic and hydro-mechanical responses of the surficial layer of soil slopes [9]. However, the traditional slope stability analysis does not deal with uncertainty. Obviously, this does not conform to the reality of slope engineering. Uncertainty is the intrinsic feature of slope engineering due to the complex property of geomaterials,complicated and changeable geological conditions, unclear failure mechanisms, etc. How the uncertainty to deal with is one of the biggest challenges in slope engineering. Recently, many researchers have paid more attention to the uncertainty analysis of slope [10]. The reliability analysis method has been widely used in slope stability analysis for considering the uncertainty in the past decades [11; 12; 13; 14; 15; 16; 17]. [PERSON] et al. integrated the random finite element method (RFEM) with an advanced Monte Carlo Simulation and developed an efficient RFEM for the reliability analysis and risk assessment of soil slopes [18]. Various reliability methods have been developed for slope reliability analysis such as first order second moment (FOSM) [19; 20], first-order reliability method (FORM) [19; 20; 21; 22; 23], and second-order reliability methods (SORM) [21; 24]. A Bayesian approach was developed to characterize the soil-water retention curve and hydraulic conductivity and was illustrated through a slope example [25]. The above methods need the gradient of the limit state function. However, it is difficult to obtain the explicit limit state function for practical slope engineering. To overcome this problem, the response surface method (RSM) has been developed to estimate the reliability of slopes by combining it with stability analysis methods such as the limited equilibrium method, or the numerical method [26; 27; 28; 29]. A genetic algorithm optimized Taylor Kriging surrogate model was developed for the system reliability analysis of soil slopes [30]. [PERSON] et al. reviewed the application of RSM in slope reliability analysis [31]. Polynomial-based RSM was commonly used in slope reliability analysis which is time-consuming when practicing engineering problems dealing with a high-order polynomial. Other methods, such as artificial neural networks (ANN), support vector machines (SVM), and Relevance vector machine (RVM) overcome this problem [20; 24; 32; 33; 34]. Those methods have the advantage of providing high-order approximations with fewer samples than polynomial functions of comparable order; however, they have some inherent drawbacks, such as their slow convergence, a less generalized performance, arriving at a local minimum, over-fitting problems, and the selection of a suitable kernel function. The limits of the above reliability methods hindered the application of the reliability method to practical geotechnical engineering. The moment methods have been the most popular method to find an approximate solution in uncertainty analysis [35].