Structure-constrained continuous probabilistic modelling method of three-dimensional karst spatial distribution for construction control

Reliable characterisation of concealed karst caves is essential for construction safety, yet sparse borehole data make their three-dimensional distribution difficult to reconstruct continuously. This study proposes a structure-constrained probabilistic modelling method for karst spatial distribution and construction control. A stratigraphic triangulated irregular network defines the prediction domain and reconstruction topology, while a Monte Carlo dropout back propagation neural network estimates karst occurrence probability and prediction uncertainty. The stochastic predictions are reconstructed as continuous probability and uncertainty fields within the target stratum, and a classification and coding structure links stable cave attributes with dynamic risk attributes. The method was applied to a foundation pit project using 253 boreholes. Among seven supervised learning models, the Monte Carlo dropout back propagation neural network achieved the highest recall and F1 score, with values of 0.78 and 0.72, respectively. The reconstructed fields revealed continuous zones with high karst probability and internal variations in concealed karst risk, while the karst information model linked verified caves and predicted risk zones with investigation, treatment, monitoring, and status updating. The proposed method transforms probabilistic karst information into actionable construction control information, thereby bridging geological modelling and construction management.