Slopes have a significant impact on the ground motion characteristics, which can aggravate the damage degree of building structures during a strong earthquake. However, many studies have focused on the design response spectra under flat site conditions and fewer researchers have investigated the impact of slope topography on the design response spectra. In this study, the numerical simulation is used to obtain the seismic response of slopes and the differential evolution algorithm is used to obtain the standardized response spectra of the acceleration time histories along the ground surface behind the slope crest. The impacts of slope height (H), slope gradient (i), average shear wave velocity in the top 30 m (VS30) and distance from the slope crest (x) on the characteristic parameters of the design response spectra are then investigated. The results show that H, i, VS30 and x have a little influence on the normalized second inflection point period (mean(Tg/Tg,ff)) but a great influence on the normalized plateau value (mean(alpha max/alpha max,ff)). Specifically, both mean(Tg/Tg,ff) and mean(alpha max/alpha max,ff) show a trend from increasing first to decreasing and stabilizing finally as x increases; the mean(alpha max/alpha max,ff) shows an increasing trend as H increases, but a decreasing trend as i or VS30 increases. Finally, to provide some guidance for the seismic design of building structures near slopes, two approximate relationships are proposed: (1) between mean(Tg/Tg,ff) and x, and (2) between mean(alpha max/alpha max,ff) and H, i, VS30, x. The main innovation of this paper is that the relationship between the characteristic parameters of the design response spectra and the slope site characteristic parameters is clearly summarized and quantified for the first time.

The construction of the 'Dayangyun' Expressway has generated a large number of engineering landslide disaster chains, mainly due to the lack of consideration of the influence of soil sediment anisotropy and slope geometric characteristics on slope stability, instability risk, and failure characteristics. It is urgent to propose a reasonable geometric optimization design method for slopes to prevent the occurrence of such disasters. This study established a random field model that incorporates rotational anisotropy-related structures of strength parameters. Subsequently, the slope reliability index(beta) was computed to evaluate slope stability. Additionally, failure modes were classified, introducing the shallow failure probability (PL) to assess failure risk. Finally, a comprehensive probability analysis framework with two indexes(the beta and PL) was designed to determine the optimal platform width of the slope(Lopt), and two slope cases were utilized for research and application purposes. The results indicate that rotation angles(theta) and platform width (L) significantly impact slope stability and instability risk. As the theta increases, the beta and PL exhibit S and M shaped trends, respectively. Specifically, the beta and PL display a logarithmic and exponential increasing trend with the increase of the L, respectively, this trend determines the Lopt. The dual-index comprehensive probability analysis framework can be employed to assess slope excavation stability and risk, as well as optimize slope geometry design. The research results can be used to prevent the occurrence of excavation slope disasters.