In practical geotechnical engineering of slopes, it is well-known that the uncertainty of soil properties and ground motions need to be considered for the safety of the project. The effect of uncertain parameters and stochastic ground motions on seismic responses as well as dynamic failure probabilities of slopes are analyzed and discussed in this study. A recently proposed generalized probability density evolution method (GPDEM) is formulated to investigate the system reliability of complex slopes with consideration to uncertainty in multiple slope parameters and in ground motions. Firstly, the fundamental theory of dynamic stability, GPDEM, dynamic system reliability, generation of random samples and stochastic ground motion model are described. Then, the efficiency and accuracy of proposed GPDEM are verified and a novel evaluating index is presented. Four complex slopes, each with multi-parameter uncertainties, are examined in separate study cases. Each study case uses GPDEM to study the random dynamic responses as well as probability responses of slopes while considering deterministic ground motion. The efficiency and accuracy of GPDEM used in complex slopes are validated by comparing with the Monte Carlo method (MCM). In addition, a novel evaluating index called the average large failure probability P_ff, is proposed to describe the failure probability of the slopes, and can take the probability time histories into account. Finally, the seismic system reliability of complex slopes is evaluated using the time-history method, and randomness in earthquakes, parameters and their coupling are investigated. The stochastic dynamic responses and probability responses of deterministic parameters subjected to stochastic earthquake excitations, and random parameters subjected to stochastic earthquake excitations are also discussed and are compared based on study case 3. The results demonstrate the high accuracy and validity of the GPDEM. Furthermore, the probability of failure and the degree of safety for the slopes can be directly estimated through probability analysis. In addition, the results also indicate that randomness in ground motions have a much larger influence than randomness in slope parameters, but randomness in slope parameters cannot be completely neglected.

在实际的边坡岩土工程中，众所周知，为保证工程的安全性，必须考虑土壤特性和地震动的不确定性。分析和讨论了不确定参数和随机地震动对边坡地震响应以及动态破坏概率的影响。考虑到多个边坡参数和地面运动的不确定性，制定了最近提出的广义概率密度演化方法（GPDEM），以研究复杂边坡的系统可靠性。首先，描述了动态稳定性，GPDEM，动态系统可靠性，随机样本的产生和随机地震动模型的基本理论。然后验证了提出的GPDEM的效率和准确性，并提出了一种新的评价指标。在单独的研究案例中检查了四个复杂的斜坡，每个斜坡都具有多参数不确定性。每个研究案例都使用GPDEM研究斜坡的随机动力响应以及概率响应，同时考虑确定性地面运动。通过与蒙特卡洛方法（MCM）进行比较，验证了复杂斜坡中GPDEM的效率和准确性。另外，提出了一种新的评价指标，称为平均大破坏概率P _ff，来描述边坡的破坏概率，并且可以考虑概率时间历史 。最后，采用时程方法对复杂边坡的地震系统可靠性进行了评估，并对地震的随机性，参数及其耦合进行了研究。在研究案例3的基础上，还讨论了随机地震激励确定性参数的随机动力响应和概率响应，以及随机地震激励随机参数的概率响应。结果表明，GPDEM具有较高的准确性和有效性。此外，可以通过概率分析直接估计斜坡的破坏概率和安全程度。此外，结果还表明，地面运动的随机性比坡度参数的随机性具有更大的影响，但不能完全忽略坡度参数的随机性。