Abstract:Due to the complexity of reliability analysis of subgrade slopes, establishing a fast estimation method of reliability index β is of great help for the promotion of probability theory in engineering practice. Using the Fellenius limit equilibrium method and Monte Carlo simulation, the reliability analysis of simple soil slopes with typical slope gradients was carried out, and the change laws of β with slope height h and the coefficient of variation of strength parameters, i.e., δ_c and $\delta_\varphi $, were investigated. Using dimensionless and multiple nonlinear regression techniques, a β estimation function based on safety factor F_s and mean strength parameters, i.e., $\overline c $ and $\overline \varphi $, was developed. The relationships between regression coefficients and slope height as well as the coefficient of variation were analyzed, and subsequently, the impact of F_s, $\overline c $, and $\overline \varphi $ on the estimation bias of β was explored. The results indicate that: 1) β displays a negative power-law increasing trend with increasing $ {F}_{\mathrm{s}} $. The limit value of β satisfies $\; \beta _{\text{d}}^{\text{u}}$=$ a_{\text{d}}^{\text{u}} $(1−$ F_{\text{s}}^{{{ - }}b_{\text{d}}^{\text{u}}} $), in which $ a_{\text{d}}^{\text{u}} $ and $ b_{\text{d}}^{\text{u}} $ are mainly affected by the variation level of strength parameters, indicating negative exponential power and negative linear laws respectively; 2) By nondimensionalizing the internal friction angle and cohesion, the β estimation model consisting of power and logarithm functions can well consider the influence of slope height, strength variability, and safety factor on β. 3) The estimation bias Δβ is affected by the variation level of strength parameters more than slope height. When $\overline \varphi $≤18.52+1.5$\overline c $–0.17${\overline c ^2}$, the estimation bias of β is slightly large, i.e., Δβ≥0.5, and accordingly F_s ≤1.377 for this case. The proposed method can assist engineers to assess the reliability of soil subgrade slopes rapidly and accurately.