Abstract
With the Stochastic Finite Element Method (SFEM), the spatial variability of soil properties can be incorporated into the analysis of geotechnical structures. Although this method is significantly superior in principle to the homogeneous analysis of soil parameters, generalizing the method in engineering practice is difficult due to its computational inefficiency. In this paper, we propose a new method for the fast calculation of convergence results. The proposed method introduces a distance space to the Monte Carlo Method (MCM) random field instances and, considering the importance of a safety margin in structures, uses selected spatial interpolation to predict the MCM instances to be solved. Two case study simulations are presented. The results show that compared to the full Monte Carlo Simulation, the fast calculation method proposed in this paper can achieve very accurate convergence results while substantially reducing the computational cost, and the simulation errors for the structure are on the safer side.
Highlights
Discretization of a random field requires that the autocorrelation function (ACF) be determined. e ACF is used to describe the magnitude of the correlation between points in space [5], and there are a number of alternative correlation functions [27, 28], such as the Markovian spatial correlation function, the square exponential correlation function, the second-order autoregressive model, and the cosine exponential correlation function
The convergence results obtained by the existing prediction method [26] and the proposed method are both larger than those obtained by the full MCS
A fast calculation method for Stochastic Finite Element Method (SFEM) convergence results based on spatial interpolation was presented in this study
Summary
Indicators that describe the spatial variability in soil parameters include the mean μ, standard deviation s, and scale of fluctuation δ. Discretization of a random field requires that the autocorrelation function (ACF) be determined. Considering the generality and simplicity of the Markovian spatial correlation function [29], this function (formula (2)) is used as the ACF in this study to discretize the random field. With reference to studies by other researchers [30,31,32], the generation of random fields in the present study is based on covariance matrix decomposition. E FISH language is used to generate random fields, and the specific steps are as follows:. Obtain n column vectors by varying i from 1 to n, and combine them using i as the row number to form a matrix Cn×n, which is the autocorrelation covariance matrix of the model: Cn×n. Repeat the previous steps M times to generate all the required MCM random field instances
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
