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.

土壤性质的固有空间变异性是现场调查中不确定性的主要来源，通常使用随机场理论来表征。在随机场背景下，波动尺度（SOF）是反映土壤性质两点间空间相关性的重要参数。然而，准确估计 SOF 值具有挑战性，特别是当只有有限的项目特定测试结果时，例如锥入度测试 (CPT) 数据。本研究旨在开发一种卷积神经网络 (CNN) 方法，以基于有限的 CPT 数据估计垂直 SOF。CNN 模型是通过使用随机场模拟的 15,000 个 CPT 样本构建和训练的。结果表明，CNN模型在估计垂直SOF方面具有出色的性能。该方法通过新模拟的 CPT 数据、从文献中获得的八个真实 CPT 数据以及从上海站点收集的三个 CPT 数据得到验证和说明。提出的比例因子方法可以解决实际CPT深度与CNN模型输入数据所需深度不匹配的问题，使得CNN模型的应用更加广泛。