Ground seismic response analysis based on the probability density evolution method

• A series of earthquake time history samples with given probabilities was generated.
• The high accuracy of PDEM was verified by a SDOF system with random excitation.
• Abundant earthquake probability information for a specific engineering site was obtained.
• The amplification effect for the engineering site was verified by the stochastic method PDEM.
• The reliability of the seismic performance for the engineering site was assessed.

Based on an overview of pertinent literature, the work presented in this paper focuses on the simulation of non-stationary ground motion processes and the stochastic seismic response analysis of site-specific soils. Using the random process orthogonal expansion method and the concept of random functions, initial earthquake ground motion is expressed as a random process based on only one random variable. Then, by discretizing the random acceleration process, we obtained 628 non-stationary earthquake acceleration time history samples with assigned probabilities. By comparing second-order statistical quantities of the random acceleration process between the sampled ensembles and an initial random targeting process, we demonstrate the advantages and effectiveness of this hybrid approach. The first part of this process also laid a foundation for subsequent stochastic seismic response analysis. Then, during the next part of the procedure, the calculation accuracy of the probability density evolution method (PDEM) was verified for a single-degree-of-freedom system with random excitation. The site-specific stochastic seismic response of the ground was then analyzed using the PDEM with the previously mentioned 628 acceleration time history samples. Abundant information was obtained on the probability of the ground seismic response, and the amplification effect on the target soil was verified from a random viewpoint. According to the performance-based method and PDEM, the reliability of the Shanghai soft engineering site was determined to be 0.7959. Furthermore, this new research introduces the use of PDEM techniques for modern geotechnical engineering problems.