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.

蒙特卡洛模拟方法是一种强大的工具，可用于考虑岩土工程问题中土壤特性的固有变异性。但是，为了充分揭示变化性并获得收敛的结果，需要进行大量的蒙特卡洛模拟，这需要大量的计算能力和时间，尤其是对于具有多个随机变量的复杂岩土问题。在本文中，为了减少蒙特卡洛模拟的数量并确保结果的准确性，使用一小部分蒙特卡洛实例（GK）修改了现有过程，以基于相似性预测实例的其余部分（GP）。矩阵P（来自GP）和矩阵之间的差分矩阵D的弗罗宾尼斯范数（|| D || _F）K（来自GK），以及P和K的平均值和标准偏差的相对差（RD）被认为可以比较两个矩阵P和K的相似性。来自GK的合格实例，具有最小的RD和可接受的|| D || 选择_F以预测实例P的结果。修改后的过程包括两个主要步骤：获取关键||。D || _F，并使用||限定的实例结果来预测单个实例的结果 D || _F小于临界|| D || _˚F。使用两个示例将修改后的过程的性能与现有方法和完整的蒙特卡洛模拟的性能进行比较，这两个示例是浅层基础的沉降和隧道的收敛性。比较结果表明，改进后的程序比现有方法执行得更好，并且预测结果与从完整的蒙特卡洛模拟获得的结果可比。根据参数研究，在改进的方法中至少需要60个样本才能通过完整的蒙特卡洛模拟获得可比的结果。