Assessment of water inrush hazards in tunnels using the inversion method of full-decay induced polarization with physical law constraints

Water hazards pose significant risks in complex geological conditions encountered during tunnel construction. Therefore, it is necessary to assess and detect water hazards in tunnels with greater precision. This paper proposes an inversion method of full-decay induced polarization (FDIP) with physical law constraints for assessing water inrush hazards. This method innovatively adds physical law constraints to the conventional FDIP inversion method based on equivalent resistivity. The physical law constraints comprise time-smoothing, the Weibull growth model, and spatial smoothing three constraints. Initially, the study presents two constraints for calculating equivalent resistivity, time-smoothing, and Weibull growth model constraints, to ensure smooth and monotonical resistivity changes over time. Additionally, the study incorporates a spatial smoothing constraint when deriving FDIP multi-parameters which guarantees gradual transitions of subsurface properties to avoid abrupt changes. The efficacy of the inversion method of FDIP with physical law constraints was confirmed by numerical simulations and a water diverting tunnel in Southwest China.