The geological complexity of the karst regions presents significant challenges, with the permeability coefficient being a critical parameter for accurately analyzing seepage behavior in hydraulic engineering projects. To overcome the limitations of traditional inversion methods, which often exhibit low computational efficiency, poor accuracy, and instability, this study utilizes a finite-element forward model and orthogonal experimental design to establish a sample set for permeability-coefficient inversion. A surrogate model for seepage calculation based on the Random Forest (RF) algorithm is subsequently developed. Furthermore, the Secretary Bird Optimization Algorithm (SBOA) is incorporated to propose an intelligent RF–SBOA inversion method for permeability-coefficient estimation, which is validated through a case study of the C-pumped storage power station. The results demonstrate that the RF model’s predictions for water levels at four boreholes closely align with the measured data, outperforming models such as CART, BP, and SVR. The SBOA effectively identifies the optimal geological permeability coefficient, with the borehole water-level inversion achieving a maximum relative error of only 0.128%, which meets the accuracy requirements for engineering applications. Additionally, the computed distribution of the natural seepage field is consistent with the typical distribution patterns observed in mountain seepage systems. During the normal water-storage phase, both the calculated seepage flow and gradient comply with engineering standards, while the seepage-field distribution aligns with empirical observations. This inversion model provides a rapid and accurate method for estimating the permeability coefficient of strata in the project area, with potential applicability to permeability inversion in other engineering geology contexts, thus demonstrating considerable practical value for engineering applications.
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