Earthquake is one of the important driving factors that induce slope instability. Accurate evaluation of the stability of three-dimensional (3D) loess slopes under earthquake needs further study. To address the stability of loess slopes under nonlinear conditions

this study develops a theoretical calculation method for the seismic stability of 3D loess slopes that incorporates the effect of tension cut-off (T-C). Based on the upper bound theorem of limit analysis

a multi-tangent technique is employed to approximate the nonlinear strength criterion in a piecewise manner. The modified strength envelope of tensile strength accounting for the cut-off effect is derived in Mohr space

upon which a novel 3D multi-cone failure mechanism is constructed. In addition

this method employs the pseudo-dynamic approach to characterize seismic loading

which can accurately and comprehensively evaluate the influence of T-C and seismic effects on slope stability. The results indicate that T-C significantly affects slope stability and the contours of sliding surfaces

with particularly notable effects in slopes characterized by high width-to-height ratios or steep gradients. As the degree of T-C increases

both slope stability coefficients and safety factors decrease markedly

and tensile failure characteristics at the slope crest become increasingly prominent.