###### Abstract  
Skirted foundations are widely used in offshore and subsea engineering. Previous studies have shown that soil undrained shear strength variability has a notable impact on probabilistic analyses of skirted foundation bearing capacity. This study proposes an efficient machine-learning method to predict the uniaxial bearing capacity factors of skirted foundations under pure horizontal and moment loads, without relying on traditional time-consuming random finite element methods. A two-dimensional convolutional neural network is adopted to capture the potential correlation between soil random fields and bearing capacity factors. The proposed CNN-based model exhibits satisfactory prediction performance with regard to coefficients of variation and scale of fluctuations in two directions. Specifically, coefficient of determination (R2) values exceed 0.97, while root mean square error (RMSE) values remain below 0.13 for the surrogate model. In addition, more than 96% of the predictions are associated with a relative error of 5% or less, providing evidence of the proposed 2D-CNN model's satisfactory prediction performance.  
convolutional neural network; spatial variability; skirted foundation; bearing capacity +
Footnote †: journal: Applied  
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under combined horizontal and moment loading. [PERSON] et al. [16] presented the probabilistic failure envelope of skirted foundations with surrounding soil undrained shear strength linearly increasing with depth. However, these studies are based on Monte Carlo simulation (MCS), which is time-consuming to obtain stochastic results. Usually, more than one hour was required for one MCS, while 500 simulations were necessary for a stochastic analysis [26]. To resolve this problem, there is a need to develop an effective method for probabilistic analysis of foundation bearing capacity.  
In recent years, machine learning has attracted significant attention for its unparalleled ability to model non-linear and exceedingly complex functions. Its efficacy in tackling geotechnical issues has been extensively studied and discussed [28; 29; 30; 31; 32]. For example, [PERSON] and [PERSON] [33] employed machine-learning techniques to predict the settlement of the ground near sloping terrain due to strip loading. [PERSON] et al. [34] proposed two hybrid machine-learning models that leveraged five input factors to predict the undrained shear strength of Finnish sensitive clays. [PERSON] et al. [35] developed a convolutional neural-network-based global response surface approach to support reliability-based design of a strip footing in soils that exhibit spatial variability. Furthermore, [PERSON] et al. [36] used multivariate adaptive regression splines to predict the bearing capacity of conical foundations in clays that are heterogenous and anisotropic. However, the accurate prediction of the bearing capacity of skirted foundations in spatially variable soils has not been studied using machine-learning methods, to date.  
This paper proposes an efficient machine-learning-based method to predict the bearing capacity of skirted foundation subjected to pure horizontal and moment loads. The proposed method employs a two-dimensional convolutional neural network (2D-CNN) to establish an efficient surrogate model, which replaces the time-consuming MCS. The input of the surrogate model is the non-stationary random field of soil undrained shear strength, while the output is the bearing capacity factor of the skirted foundation calculated by RFEM. The prediction performance of the proposed model is evaluated by comparing the prediction results with those generated from RFEM.