土体渗透系数是量化流体在土壤中渗透能力的关键参数,能直接影响边坡稳定性分析、地基处理及防渗工程设计。当前,粗粒土渗透系数能基于一些常规参数准确估算,而黏性土在这方面的研究相对缺乏。传统的柯森-卡门方程为粗粒土渗透系数估算提供了有效途径,但在黏性土渗透系数预测上表现不佳。基于此,利用统计方法,结合土体液限构建土体总孔隙比与有效孔隙比的关系,进而对柯森-卡门方程进行改进,得到了适用于黏性土的渗透系数计算方法。选用大量黏性土的相关参数,分别利用原方程及改进方程对黏性土渗透系数进行计算,并与实测值进行对比。研究结果表明,传统的柯森-卡门方程的预测可靠度为56.2%,柯森-卡门改进方程的预测可靠度高达81.9%,相比于原方程精度提高了25.7%。孔隙比和液限是影响黏性土渗透系数预测结果的关键参数。黏土矿物类型对建立的计算模型性能影响不大,建立的计算模型对渗透系数实测值在10^-9、10^-10 m/s数量级的预测效果具有更好的适用性。提出的柯森-卡门改进方程能为岩土工程实践中黏性土渗透系数的估算提供可靠的理论参考。

[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 (R²) 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 R²=0.83. Parameter C in the Kozeny-Carman equation exhibited a power-law relationship with soil specific surface area, with R²=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.