Deformation and failure analysis of heterogeneous slope using nonlinear spatial probabilistic finite element method

Slope failures in hilly terrain impact the social and economic balance of the community. The major reasons for these slope failures are steeper slopes, climate factors, seismic activity, nearby excavations, and construction. Natural slopes show significant heterogeneity due to the inherent randomness in material properties and geometric nonlinearities. Effective slope stability analysis solutions can be achieved by incorporating probabilistic approaches. We present a comprehensive method to develop and analyze a heterogeneous two-dimensional slope model, utilizing a non-linear-spatial-probabilistic-finite element method under a plane strain condition. The developed slope model encompasses geometrical and material nonlinearity with a uniform random distribution over the space. Also, the present slope model integrates the Mohr-Coulomb's constitutive model for elastoplastic analysis to capture more realistic and complex behavior. A benchmark soil slope problem was modeled using the spatial probabilistic finite element method, comprising all six material properties with uniform spatial uncertainties. These material properties are elastic modulus, unit weight, cohesion, friction angle, and dilation angle. During the numerical simulation, the detailed deformations, stress patterns, strain patterns, potential pre-failure zone, and failure characteristics of heterogeneous slopes were achieved under self-weight and step loading sequences. Nodal failure and probability of nodal failure were introduced as two novel quantitative parameters for more insights into failure investigations. The testbench slope model was subjected to self-weight load and external 100-step loading sequences with a loading increment of -0.1 kN/m. The percentage probability of nodal failure was obtained at 40.46% considering uniformly distributed material uncertainties with a 10% coefficient of variation. The developed testbench slope model was also simulated for different values of the coefficient of variation (ranging from 0% to 50%) and comparatively investigated. The detailed deformation patterns, thorough profiles of stresses-strains, failure zones, and failure characteristics provided valuable insights into geotechnical engineering practices.