基于柯森-卡门方程的黏性土渗透系数预测方法研究

[Objective] Research on predicting the hydraulic conductivity of cohesive soils is relatively lacking. The classical Kozeny-Carman equation provides an effective method for estimating the hydraulic conductivity of coarse-grained soils, but it performs poorly in predicting the hydraulic conductivity of cohesive soils. This study aims to improve the Kozeny-Carman equation and establish a method for calculating the hydraulic conductivity of cohesive soils. [Methods] We first constructed a relationship between bound water content and liquid limit (LL) in cohesive soils using statistical methods based on their correlation analysis. With this relationship as a bridge, we established a correlation between the total void ratio and the effective void ratio of the soil. Accordingly, the Kozeny-Carman equation was modified to develop a method for calculating the hydraulic conductivity of cohesive soils. Considering that parameter C in the modified equation was difficult to obtain in engineering practice, we developed a calculation model for specific surface area of cohesive soils, incorporating bound water, free water, and soil particles, in order to establish an engineering-friendly equation. A semi-empirical equation relating the specific surface area (S s) of soil particles to liquid limit was derived, leading to a formula that calculated parameter C based on specific surface area. Data of 105 cohesive soils from published literature were employed to calculate hydraulic conductivity using both the original and modified equations, and the results were compared with measured values. After predicting the saturated hydraulic conductivity of cohesive soils using the improved model, we further evaluated the model’s predictive performance using two error metrics: Mean Absolute Error (MAE) and Root Mean Square Error (RMSE). Subsequently, the sensitivity of each input parameter was analyzed using the cosine amplitude method. Finally, the influence of the main clay mineral types and the order of magnitude of the measured hydraulic conductivity values on the model’s predictive performance was analyzed. [Results] (1) As the water content increased in cohesive soils, the hydration of clay minerals proceeded sequentially through tightly bound water, loosely bound water, and free water phases. A strong linear correlation existed between the ineffective void ratio and the logarithm of liquid limit (lgLL), with a coefficient of determination (R 2) of 0.98. A discernible linear correlation was observed between the reciprocal of specific surface area (1/S s) and the reciprocal of liquid limit (1/LL), with R 2=0.83. Parameter C in the Kozeny-Carman equation exhibited a power-law relationship with soil specific surface area, with R 2=0.85. The prediction reliability of the classical Kozeny-Carman equation was 56.2%, while that of the improved equation achieved 81.9%, representing a 25.7% improvement in accuracy. However, predictions exhibited divergence, primarily due to the heterogeneity of the experimental data sources, the error propagation from the indirect estimation of specific surface area data, and the fact that the improved formula relied solely on void ratio and liquid limit, potentially neglecting factors like particle size distribution and pore channel tortuosity. (2) Sensitivity analysis revealed that both void ratio and liquid limit were the primary parameters affecting the prediction accuracy of hydraulic conductivity. The model’s performance metrics for the database were MAE=0.29 and RMSE=0.36. For kaolinite-dominated clay, prediction reliability reached 72.4% (MAE=0.29, RMSE=0.38); that of montmorillonite-dominated clay achieved 94.4% (MAE=0.30, RMSE=0.32); and that of illite-dominated clay showed 77.8% (MAE=0.35, RMSE=0.38). Overall, the type of clay mineral had little influence on model performance. When the measured hydraulic conductivity value was within the 10-9 m/s order of magnitude, the prediction reliability was 88.2% (MAE=0.24, RMSE=0.29);when it was within the 10-10 m/s order of magnitude,the prediction reliability was 93.3% (MAE=0.20,RMSE=0.25);when it was within the 10-11 m/s order of magnitude, the prediction reliability was 65.9% (MAE=0.42,RMSE=0.47). [Conclusion] These results show that the prediction reliability of hydraulic conductivity at the 10-11 m/s order of magnitude is significantly lower than at the 10-9 and 10-10 m/s order of magnitude, with the errors and divergence much higher for the 10-11 m/s order of magnitude. Therefore, the magnitude of hydraulic conductivity has a great impact on model performance, and the model has better applicability for predictions within the 10-9 to 10-10 m/s order of magnitude. The modified Kozeny-Carman equation proposed in this study provides a reliable theoretical reference for estimating the hydraulic conductivity of cohesive soils in geotechnical engineering practice.