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This paper develops an efficient algorithm that combines polynomial-chaos kriging (PCK) and adaptive radial-based importance sampling (ARBIS) for reliability analysis. The key idea of ARBIS is to adaptively determine a sphere with the center at the origin and radius equal to the smallest distance of the failure domain to the origin, also known as the optimal β -sphere, and only those samples outside the optimal β -sphere have a possibility of failure and thus need to evaluate the limit-state function to judge their states (safe or failure). In the proposed algorithm, both the PCK model and β -sphere are updated adaptively. In each iteration of determining the optimal β -sphere, the PCK model is updated sequentially based on an active learning function, which is used to select the most informative sample from the samples between the last and current β -spheres. Once the stopping criterion is met, the learning process of PCK in this iteration terminates, and the obtained PCK model is then used to determine the next β -sphere. The updating iteration of the β -sphere proceeds until the optimal sphere is found. Five representative examples are revisited, in which the results demonstrate the high accuracy and efficiency of the proposed PCK-ARBIS algorithm. [ABSTRACT FROM AUTHOR]

This work presents a probabilistic analysis of three-dimensional (3D) seismic active earth pressures acting on rigid retaining walls that are designed to support cohesive-frictional soil masses. The analysis is implemented using sparse polynomial chaos expansions (SPCE) to represent the physical model responses. The deterministic evaluation of 3D seismic active earth pressures is conducted with the application of the kinematic approach of limit analysis combined with a pseudo-static method. All of the input parameters are deemed as random variables. After the SPCE metamodels are determined, the method of Monte Carle simulations is applied to perform the probabilistic analysis of 3D seismic active earth pressures. The effects of uncertainty levels and correlation relationships of input parameters are investigated. Several illustrative examples of the reliability-based design of retaining walls are shown. Results indicate that uncertainties in input parameters possess a notable effect on 3D seismic active earth pressures, suggesting the need to investigate the problem from a stochastic perspective. In most cases, the soil cohesion, internal friction angle, and seismic coefficient are found to be three of the parameters that affect the final response the most significantly. It is also indicated that considering 3D effects and soil cohesion has a favorable effect on increasing the stability of retained slopes. [ABSTRACT FROM AUTHOR]