A modified method for the prediction of Monte Carlo simulation based on the similarity of random field instances

Monte Carlo simulation method is a powerful tool to consider inherent variability of soil properties in geotechnical problems. However, to fully reveal the variability and obtain convergent results, a large number of Monte Carlo simulations are required, which need great computational power and time, especially for complicated geotechnical problems with multiple random variables. In this paper, to reduce the number of Monte Carlo simulations and ensure the accuracy of the outcomes, an existing procedure is modified using a small part of Monte Carlo instances (GK) to predict the remaining part of instances (GP) based on similarity. Both the Frobenius norm (||D||(F)) of the difference matrix D between a matrix P (from GP) and a matrix K (from GK), and the relative difference (RD) of the mean values and standard deviations of P and K are considered to compare the similarity of the two matrices P and K. A qualified instance from GK having minimum RD and acceptable ||D||(F) is selected to predict the outcome of the instance P. The modified procedure contains two main steps: to obtain the critical ||D||(F), and to predict the outcomes of individual instances using the results of instances qualified with ||D||(F) less than the critical ||D||(F). The performance of the modified procedure is compared with that of the existing method and full Monte Carlo simulation using two examples: the settlement of a shallow foundation and the convergence of a tunnel. The comparison indicates that the modified procedure performs better than the existing method, and the predicted outcomes are comparable with those obtained from full Monte Carlo simulations. According to parametric study, at least 60 samples are required in the modified method to get a comparable result with a full Monte Carlo simulation.