Hybrid machine learning model with random field and limited CPT data to quantify horizontal scale of fluctuation of soil spatial variability

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.