In this paper, the development and application of a new upper bound limit method for two- and three-dimensional (2D and 3D) slope stability problems is presented. Rigid finite elements are used to construct a kinematically admissible velocity field. Kinematically admissible velocity discontinuities are permitted to occur at all inter-element boundaries. The proposed method formulates the slope stability problem as an optimization problem based on the upper bound theorem. The objective function for determination of the minimum value of the factor of safety has a number of unknowns that are subject to a set of linear and nonlinear equality constraints as well as linear inequality constraints. The objective function and constrain equations are derived from an energy–work balance equation, the Mohr–Coulomb failure (yield) criterion, an associated flow rule, and a number of boundary conditions. The objective function with constraints leads to a standard nonlinear programming problem, which can be solved by a sequential quadratic algorithm. A computer program has been developed for finding the factor of safety of a slope, which makes the present method simple to implement. Four typical 2D and 3D slope stability problems are selected from the literature and are analysed using the present method. The results of the present limit analysis are compared with those produced by other approaches reported in the literature.Key words: limit analysis, upper bound, rigid finite element, nonlinear programming, sequential quadratic algorithm, slope stability.

Natural disasters, notably landslides, pose significant threats to communities and infrastructure. Landslide susceptibility mapping (LSM) has been globally deemed as an effective tool to mitigate such threats. In this regard, this study considers the northern region of Pakistan, which is primarily susceptible to landslides amid rugged topography, frequent seismic events, and seasonal rainfall, to carry out LSM. To achieve this goal, this study pioneered the fusion of baseline models (logistic regression (LR), K-nearest neighbors (KNN), and support vector machine (SVM)) with ensembled algorithms (Cascade Generalization (CG), random forest (RF), Light Gradient-Boosting Machine (LightGBM), AdaBoost, Dagging, and XGBoost). With a dataset comprising 228 landslide inventory maps, this study employed a random forest classifier and a correlation-based feature selection (CFS) approach to identify the twelve most significant parameters instigating landslides. The evaluated parameters included slope angle, elevation, aspect, geological features, and proximity to faults, roads, and streams, and slope was revealed as the primary factor influencing landslide distribution, followed by aspect and rainfall with a minute margin. The models, validated with an AUC of 0.784, ACC of 0.912, and K of 0.394 for logistic regression (LR), as well as an AUC of 0.907, ACC of 0.927, and K of 0.620 for XGBoost, highlight the practical effectiveness and potency of LSM. The results revealed the superior performance of LR among the baseline models and XGBoost among the ensembles, which contributed to the development of precise LSM for the study area. LSM may serve as a valuable tool for guiding precise risk-mitigation strategies and policies in geohazard-prone regions at national and global scales.