Seismic time-history response and system reliability analysis of slopes considering uncertainty of multi-parameters and earthquake excitations

Abstract

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 Pff, is proposed to describe the failure probability of the slopes, and can take the probability time histories intoaccount. 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.