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The scale of fluctuation (SOF) is the critical parameter to describe the soil spatial variability, which significantly influences the embedded geostructures. Due to the limited data in the horizontal direction, horizontal SOF estimation is relatively challenging and not well studied yet. This paper aims to develop an efficient convolutional neural network (CNN)-based approach for estimating the horizontal SOF by coupling random field and limited CPT data. Two or three columns (i.e. pseudo-CPT) were selected from the simulated 2D random field with prescribed SOF at the same spacing and combined into a two-dimensional matrix as input data to train the CNN model, namely CNN2 and CNN3 models. The dataset of CNN2 and CNN3 models contains 196,670 and 149,420 samples. Results on the training and testing datasets show that the trained CNN model has a good estimation performance as the mean squared error value is less than 0.1 and the correlation coefficient value is larger than 0.99. The effectiveness of trained CNN models was further verified by the new simulated CPT data with untrained SOF from the random field and CPT data from real site in Hollywood, South Carolina. The excellent agreement indicates that the trained CNN model has the ability to capture the horizontal SOF for limited CPT data from the actual project. Finally, the collected CPT data from the Shanghai site was applied for application. The COV of the estimated results of CNN3 and CNN2 models for the Shanghai site is 0.09 and 0.40, indicating the estimation performance of the CNN3 model has less variability than the CNN2 model. The proposed method provides the potential to characterize the soil spatial variability using very limited CPT data. [ABSTRACT FROM AUTHOR]

The inherent spatial variability of soil properties is the main sauces of uncertainties in the site investigation, and it is commonly characterized using random field theory. In the context of random fields, the scale of fluctuation (SOF) is a significant parameter to reflect the spatial correlation between the two points of soil properties. However, it is challenging to estimate the SOF value accurately, especially when there are only limited project-specific test results, such as cone penetration test (CPT) data. This study aims to develop a convolutional neural network (CNN) approach to estimate the vertical SOF based on limited CPT data. The CNN model was constructed and trained by the simulated 15,000 CPT samples using random fields. The results show that the CNN model has excellent performance for estimating vertical SOF. The approach is validated and illustrated through newly simulated CPT data, eight real CPT data obtained from the literature, and three CPT data collected from the Shanghai site. The proposed scale factor method can solve the mismatch between the actual CPT depth and the required depth for input data of the CNN model, making the CNN model more widely applicable. • A CNN approach is developed to estimate vertical SOF for soil properties. • The approach is validated and illustrated using both real and simulated data. • The proposed scale factor method can make CNN model more widely applicable. • Promising estimation performance is achieved. [ABSTRACT FROM AUTHOR]