Reliability Analysis of Infinite Slopes Subjected to Seismic Loadings Considering Spatially Variable Shear Strength Parameters

ObjectiveEvaluating seismic slope stability is a critical research topic in the field of geotechnical engineering. Natural soils exhibit spatial variability, with properties varying from point to point. This characteristic significantly affects slope stability, necessitating a statistical approach to its investigation. The infinite slope model evaluates the stability of long slopes running down a hillside and analyzes the mechanics of shallow landslides. This study focuses on the reliability of infinite undrained slopes and cohesive-frictional soil slopes subjected to seismic loadings using the random field method.MethodsThe random field method was adopted to investigate the effects of horizontal and vertical seismic loadings on the reliability of infinite slopes. The deterministic method was also employed to verify the results obtained by the random field method. For deterministic stability analyses of infinite undrained slopes with linearly increasing strength, the infinite slope equation was utilized to evaluate the factor of safety <italic>F</italic>_S and derive the analytical formula for the critical slope angle <italic>β</italic>_min, which leads to the minimum factor of safety <italic>F</italic>_S. An algorithm generating 1D non-stationary random fields of undrained strength was applied to assess the probability of slope failure pf and determine the critical slope angle <italic>β</italic>_min, which corresponds to the maximum probability of slope failure <italic>p</italic>_f. For deterministic analyses of infinite cohesive-frictional soil slope stability, the infinite slope equation was employed to analyze the factor of safety <italic>F</italic>_S, with the critical slope angle min obtained by calculating the factor of safety <italic>F</italic>_S at intervals of 0.01. The random field method was then applied to compute the probability of slope failure <italic>p</italic>_f and determine the critical slope angle <italic>β</italic>_min.Results and DiscussionsFor the infinite undrained slopes subjected to horizontal and vertical seismic loadings, the results showed that as the slope angle <italic>β</italic> increases, the factor of safety <italic>F</italic>_S initially decreases and then increases, indicating the existence of a critical slope angle <italic>β</italic>_min. As the value of <italic>λ</italic> (ratio of the vertical seismic coefficient kv to the horizontal seismic coefficient <italic>k</italic>_h) increases, the critical slope angle min gradually rises, and the effect of the vertical seismic loading on the critical slope angle <italic>β</italic>_min becomes more significant as the horizontal seismic coefficient <italic>k</italic>_h increases. The results also indicated that as the value of <italic>λ</italic> increases, the probability of slope failure pf increases significantly, highlighting that the effect of the vertical seismic loading on the reliability of infinite undrained slopes cannot be ignored.In addition, the probability of slope failure <italic>p</italic>_f decreases as the nondimensional spatial correlation length <inline-formula><alternatives><math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mi>Θ</mi></math><graphic specific-use="big" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/D92153EE-869E-412e-9911-AFB18226FA42-M001.jpg"><?fx-imagestate width="2.11666679" height="2.11666679"?></graphic><graphic specific-use="small" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="alternativeImage/D92153EE-869E-412e-9911-AFB18226FA42-M001c.jpg"><?fx-imagestate width="2.11666679" height="2.11666679"?></graphic></alternatives></inline-formula> increases and eventually converges asymptotically on the first-order second moment (FOSM) solution, demonstrating that the traditional reliability method may provide unconservative results for infinite undrained slopes subjected to seismic loadings. The analysis further reveals the existence of a critical slope angle <italic>β</italic>_min, which leads to the maximum value of the probability of slope failure <italic>p</italic>_f, a phenomenon that can also be verified by the deterministic method. For the infinite cohesive-frictional soil slopes subjected to horizontal and vertical seismic loadings, the results showed that as the slope angle <italic>β</italic> increases, the value of <italic>F</italic>_S/tan <italic>ϕ'</italic> initially decreases and then increases, indicating the existence of a critical slope angle min. The value of <italic>F</italic>_S/tan <italic>ϕ'</italic> increases as the nondimensional parameter <italic>S</italic> = <italic>c</italic>/(<italic>H </italic>tan <italic>ϕ'</italic>) increases, while the critical slope angle <italic>β</italic>_min decreases as the nondimensional parameter <italic>S</italic> increases. When the horizontal seismic coefficient <italic>k</italic>_h is relatively small, the effect of the vertical seismic loading on the stability of infinite cohesive-frictional soil slopes is not significant. However, as the horizontal seismic coefficient <italic>k</italic>_h increases, the effect of the vertical seismic loading becomes more pronounced. In addition, the influence of the vertical seismic loading on the stability of infinite cohesive-frictional soil slopes is affected by the horizontal seismic coefficient <italic>k</italic>_h, the slope angle <italic>β</italic>, and the nondimensional parameter <italic>S</italic>. The critical slope angle <italic>β</italic>_min increases as the value of <italic>λ</italic> increases, and the effect of the vertical seismic loading on the critical slope angle <italic>β</italic>_min for infinite cohesive-frictional soil slopes becomes more evident as the horizontal seismic coefficient <italic>k</italic>_h increases. The critical slope angle <italic>β</italic>_min decreases as the nondimensional parameter <italic>S</italic> increases and eventually stabilizes. The critical slope angle <italic>β</italic>_min increases as the value of <italic>λ</italic> rises. As the horizontal seismic coefficient <italic>k</italic>_h improves, the effect of the vertical seismic loading on the critical slope angle <italic>β</italic>_min becomes increasingly significant, particularly for higher values of the nondimensional parameter <italic>S</italic>. Some results indicate that the probability of slope failure <italic>p</italic>_fincreases as the value of <italic>λ</italic> increases. In contrast, others show a decrease in the probability of slope failure <italic>p</italic>_f as the value of <italic>λ</italic> increases. This phenomenon can also be confirmed by the deterministic method. There exists a critical slope angle <italic>β</italic>_min that leads to the maximum probability of slope failure <italic>p</italic>_f, with the critical slope angle <italic>β</italic>_min being consistent with previous results.ConclusionsFor infinite slopes subjected to seismic loadings, the effect of the vertical seismic loading on the probability of slope failure pf remains significant even when the horizontal seismic coefficient <italic>k</italic>_h is small. Both horizontal and vertical seismic loadings must be considered when performing seismic reliability analyses of infinite slopes. There exists a critical slope angle <italic>β</italic>_min that results in the maximum probability of slope failure <italic>p</italic>_f for infinite slopes. In addition, the influence of the vertical seismic loading on the critical slope angle <italic>β</italic>_min becomes increasingly apparent as the horizontal seismic coefficient <italic>k</italic>_h increases.