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.

In recent years, infrared detection technology for embankment leakages has become a popular research topic. The seepage and heat transfer characteristics of embankments under seepage failure conditions form the theoretical basis of infrared detection technology for leakage hazards. Nevertheless, a majority of prior research has relied on predetermined seepage pathways, which fail to accurately simulate the actual scenarios encountered in engineering practice. Accordingly, taking a typical soil embankment in the Dongting Lake area as the research object, a seepage damage test of the embankment body and surface soil of the embankment foundation was conducted. The mechanical and seepage damage of the embankment soil was established. FLAC3D6.0 software was used to develop a coupled numerical model of the unsaturated seepage, temperature, and stress of the embankment based on the damage model. The distribution laws of the seepage and temperature fields in the embankment body and foundation were calculated and analyzed. The results of this study show that there is a strong correlation between seepage, temperature, and structure during local seepage failure and even the overall structural failure of the embankment. Moreover, the evolution of the downstream embankment toe and surface temperature shows a phased change. By capturing this feature, it is possible to quickly screen the seepage location of an embankment to thereby provide a basis for determining the infrared detection indicators of the embankment.