边坡在地震作用下的动力响应研究目前主要关注单一主震作用，而没有考虑余震的影响，且材料参数的空间变异性往往被忽略。本文充分考虑土体强度参数的空间变异性，提出了一种基于Newmark方法和概率密度演化方法（PDEM）的可靠度分析框架来量化余震及空间变异性对边坡动力可靠度的影响。首先，将物理随机函数模型、Copula函数和窄带谐波群叠加方法相结合生成主余震序列。此外，基于谱表示法生成随机场并根据对应坐标将参数赋值到有限元模型中。然后，采用Newmark位移法批量计算了主余震序列作用下考虑材料参数空间变异性的边坡的永久位移，并通过位移均值分析了粘聚力和摩擦角的变异系数（COVC和COVF）、余震和峰值加速度（PGA）对边坡永久位移的影响。最后，基于PDEM，从概率的角度解释了变异系数（COV）和余震对边坡动力可靠度的影响。研究结果表明:随着COV增大，边坡的永久位移均值呈现逐渐增大的趋势。相比之下，COVF对边坡的永久位移影响更明显。此外，与单一主震相比，地震序列作用下边坡的位移均值更大。若忽略材料参数的空间变异性和余震的影响，将明显高估边坡的抗震性能。

The research on the dynamic response of slopes under seismic action is currently focused on the action of a single mainshock without considering the effect of aftershocks, and the spatial variability of material parameters is always ignored. In this paper, the spatial variability of parameters is fully considered, and a reliability analysis framework based on the Newmark method and probabilistic density evolution method (PDEM) is proposed to quantify the effects of aftershocks and spatial variability on the dynamic reliability. First, the physical random function model, Copula function and narrowband harmonic group superposition method are combined to generate the mainshock-aftershock sequence (MAS). In addition, the random field is generated based on the spectral representation and the parameters are assigned to the finite element model based on the corresponding coordinates. Then, the permanent displacement of the slope considering the spatial variability of parameters subjected to the MAS were batch calculated based on the Newmark method, and the effects of the coefficient of variation of cohesion and friction angle (COVC and COVF), aftershock, and peak ground acceleration (PGA) on the permanent displacement of the slope were analyzed by the mean of the displacement. Finally, based on PDEM, the effects of COV and aftershocks on the dynamic reliability of the slope are explained from a probabilistic point of view. The results of the study show that the mean of displacement shows a gradual increase with the increase of coefficient of variation (COV). In contrast, the COVF has a more pronounced effect on the displacement of the slope. In addition, the mean of displacement of the slope subjected to the MAS are larger compared to the single mainshock. If the spatial variability of parameters and the influence of aftershocks are ignored, the seismic performance of the slope will be overestimated.

国家重点研发项目(2023YFC3011400)；国家自然科学基金(52379117, 52279096, 52279125)；水利工程仿真与安全国家重点实验室开放基金( HESS-2302)；海岸和近海工程国家重点实验室青年学者创新基金(LY2301)