<p>Slope stability is crucial to engineering safety, and traditional single safety factor design methods fail to account for parameter variability and nonlinear strength characteristics. This study employs the nonlinear Mohr-Coulomb (M-C) failure criterion to establish safety factor and reliability index constrained optimization models for searching potential slip surfaces. It also proposes a theoretical analysis method for reinforcing slopes with anchor bolts based on reliability theory. The study reveals that potential slip surfaces vary under different failure criteria, with those derived from the nonlinear M-C failure criterion exhibiting deeper slip surfaces. The nonlinearity of strength parameters and their variability significantly impact anchoring force calculations, resulting in notable discrepancies between anchoring forces determined through reliability theory analysis and traditional deterministic analysis. Incorporating the variability and nonlinearity of parameters is of importance for geotechnical engineering computations and design practices. When reinforcing slopes based on reliability theory, it is essential to search for slip surfaces corresponding to the minimum reliability index to ensure slope safety.</p>