Integration of strength-reduction meshless numerical manifold method and unsupervised learning in stability analysis of heterogeneous slope

•Integrating the meshless numerical manifold method with unsupervised learning is formulated for slope stability analysis.•The Weibull distribution is deployed to describe the heterogeneity in physical and mechanical parameters for the slopes.•Unsupervised learning is employed to automatically extract critical sliding surfaces with displacement and strain fields.•The effects of two parameters in the Weibull distribution function on slope heterogeneity and stability are investigated. The rock-soil mass, subjected to complex and lengthy geological processes, exhibits heterogeneity which induces variations in mechanical properties, thereby affecting the overall stability of slopes. In this paper, a novel numerical model that incorporates the Weibull distribution function into the meshless numerical manifold method based on the strength reduction method (MNMM-SRM) to account for the slope soils heterogeneity and their influence on the factor of safety (Fs) and the critical sliding surface (CSS). Initially, the Weibull distribution is introduced into the MNMM-SRM model based on the complementary theory of subspace tracking, addressing the issue of multiple yield surface corners in the Mohr-Coulomb framework while simultaneously considering the heterogeneous nature of rock and soil formations. Subsequently, an intelligent method based on unsupervised learning is proposed to obtain reasonable CSS, utilizing the total displacement field at slope nodes and the equivalent plastic strain field as input variables. The results serve as criteria for terminating the strength reduction in the MNMM-SRM. The applicability of this method is verified through three typical examples, demonstrating its potential for widespread application in the assessment of heterogeneous slope stability.