Abstract: Herein, a method characterizing the spatial effects of deep large-diameter shaft structures in water resource allocation projects is established. Based on a three-dimensional finite element model, a database is constructed to capture the influence of typical geological conditions and structural dimensions on shaft deformation. To further predict the overall structural deformation during the construction process, a multi-output prediction model for shaft displacement is proposed. Two algorithms, gradient boosting trees and random forest, are selected, and three combinations of single-target models, multi-output models, and regressor chain models are employed. This results in the creation of six prediction models: single-target gradient boosting, multi-output gradient boosting (MO-GB), regressor chain gradient boosting, single-target random forest, multi-output random forest, and regressor chain random forest. The results indicate that: (1) The MO-GB model considers multiple prediction indicators, and its corresponding maximum deformation E_RMS is 0.457, smaller than other models; it performs the best in terms of predictive accuracy, with a determination value R² for maximum displacement and its corresponding location exceeds 0.98. (2) The maximum deformation value and its corresponding location using MO-GB model align well with three-dimensional finite element model results, providing guidance for design of shaft structure.

Key words: deep and large shaft, spatial foundation pit model, gradient boosting algorithm, multi-output, deformation prediction