## 4 Results and Discussion
### Influence of Coefficient of Variation (COV) in the Random Field  
Figure 7 shows the development of the mean and standard deviation of the uniaxial horizontal and moment bearing capacity factors with the variation of COV in RFEM. It is found that the standard deviations of \(N_{CH}\) and \(N_{CM}\) increase with COV, for the fluctuation of the undrained shear strength is larger under conditions with higher COV, as illustrated in Figure 1a,b. In order to investigate the influence of COV of the soil undrained shear strength random field on the prediction performance of the proposed 2D-CNN model, the datasets consist of the random field data and corresponding bearing capacity factors from case Anti-1 to Anti-are trained separately with 480 samples and tested by the remaining 120 samples. The five-fold cross-validation method [51] is adopted to obtain more persuasive results, in which the total dataset is randomly divided into five subsets and each subset is taken as the prediction dataset while the remaining four subsets are taken as the training dataset to train five CNN models. In other words, the presented prediction performance is the average result of the five models. Figure 8 shows the root mean square error (RMSE) and coefficient of determination (R\({}^{2}\)) of the prediction dataset in the five cases. Specifically, the RMSE value reflects the degree to which the predicted result deviates from the actual value, where a smaller RMSE value represents better prediction accuracy. The R\({}^{2}\) value, varying between zero and one, reflects the global performance of the surrogate model. A larger R2 value indicates better prediction performance of the proposed model. It is visible in Figure 8 that the value of RMSE gradually increases when the COV extends from 0.1 to 0.5. Meanwhile, the value of R\({}^{2}\) slightly fluctuates with the increase in COV, which indicates that the performance of the proposed surrogate model is affected by the degree of variation of the random field when one considers the soil spatial variability in predicting the  
Figure 6: Influence of number of training samples on R\({}^{2}\) and RMSE values. Figure 7: Variation of the bearing capacity factors (\(N_{CH}\) and \(N_{CM}\) ) statistics with COV: (**a**) Mean; (**b**) Standard deviation. uniaxial bearing capacity of skirted foundation. The 2D-CNN model essentially captures the potential characteristics between the input and output vectors. The output value in the dataset contains a wider distribution range in the case of higher COV, resulting in a decrease in the average density of training data when the total number of samples remains unchanged. This is reflected in the surrogate model, which shows relatively poor prediction performance under higher COV. However, there are five surrogate models for the prediction of bearing capacity factors when COV varies from 0.1 to 0.5. These models are predetermined with the same structure (as shown in Figure 5), which contains the difference in the model parameters trained by different datasets. It is complicated to generate several datasets and train different surrogate models in dealing with the prediction of bearing capacity factors, considering the variation of COV in the random field. It is necessary to train a unified surrogate model in the stochastic analysis under different COV of random field without notably reducing the accuracy of prediction. Therefore, the samples from case Anti-1 to Anti-5 are composed to generate a mixed dataset to train a 2D-CNN model in predicting the bearing capacity factors of the skirted foundation. Specifically, there are 2100, 300 and 600 samples in the training, validation, and prediction datasets for the training process of the unified 2D-CNN model. Figure 9 presents the uniaxial bearing capacity factors predicted by the unified 2D-CNN model and calculated by the RFEM.