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A Method of Predicting Hydraulic Conductivity of Cohesive Soils Based on Kozeny-Carman Equation
ZHENG Yu-hao, MEI Zhi-ping, LIU Fu-yang, ZHOU Sheng-tao
Journal of Changjiang River Scientific Research Institute ›› 2026, Vol. 43 ›› Issue (5) : 164-173.
PDF(1673 KB)
PDF(1673 KB)
A Method of Predicting Hydraulic Conductivity of Cohesive Soils Based on Kozeny-Carman Equation
[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 (Ss) 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/Ss) 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.
cohesive soils / Kozeny-Carman equation / modified Kozeny-Carman equation / hydraulic conductivity / effective void ratio / liquid limit
| [1] |
Hydraulic conductivity is a parameter dictating groundwater recharge, having dependability on factors related to aquifer properties such as particle size, shape, degree of compaction, grain size distribution and fluid flow properties like viscosity and specific weight. The present study is focused on the effect of the grain size distribution of the particles of the aquifer material on its permeability. In order to investigate variation of permeability with respect to the grain size distribution, experimental investigations are conducted on natural borehole samples and those prepared by mixing borehole samples with known quantities of marble chips within a laminar flow regime. A power function model is developed for the estimation of permeability based on grain size distribution parameters σ (standard deviation) and D50 (median grain size). The results from the developed model show good agreement with experimental data as the values of R2, RMSE and MAE for the model are (0.99, 0.007, 0.005) for 5.08 cm dia., (0.99, 0.005, 0.004) for 10.16 cm dia. and (0.97, 0.004, 0.003) for 15.24 cm dia. permeameters respectively. The developed power function model provides an efficient tool to estimate the yield of wells, seepage below earthen structures and design of filters with reasonable accuracy.
|
| [2] |
|
| [3] |
樊贵盛, 邢日县, 张明斌. 不同级配砂砾石介质渗透系数的试验研究[J]. 太原理工大学学报, 2012, 43(3):373-378.
(
|
| [4] |
. In this paper, the results of permeability and specific surface area analyses as functions of granulometric composition of various sediments (from silty clays to very well graded gravels) are presented. The effective porosity and the referential grain size are presented as fundamental granulometric parameters expressing an effect of the forces operating on fluid movement through the saturated porous media. This paper suggests procedures for calculating referential grain size and determining effective (flow) porosity, which result in parameters that reliably determine the specific surface area and permeability. These procedures ensure the successful application of the Kozeny–Carman model up to the limits of validity of Darcy's law. The value of effective porosity in the referential mean grain size function was calibrated within the range of 1.5 µm to 6.0 mm. The reliability of the parameters applied in the KC model was confirmed by a very high correlation between the predicted and tested hydraulic conductivity values (R2 = 0.99 for sandy and gravelly materials; R2 = 0.70 for clayey-silty materials). The group representation of hydraulic conductivity (ranging from 10−12 m s−1 up to 10−2 m s−1) presents a coefficient of correlation of R2 = 0.97 for a total of 175 samples of various deposits. These results present new developments in the research of the effective porosity, the permeability and the specific surface area distributions of porous materials. This is important because these three parameters are critical conditions for successful groundwater flow modeling and contaminant transport. Additionally, from a practical viewpoint, it is very important to identify these parameters swiftly and very accurately.
|
| [5] |
苏立君, 张宜健, 王铁行. 不同粒径级砂土渗透特性试验研究[J]. 岩土力学, 2014, 35(5): 1289-1294.
(
|
| [6] |
杨兵, 刘一飞, 万奋涛, 等. 级配特性对砂土渗透系数影响试验研究[J]. 西南交通大学学报, 2016, 51(5):855-861.
(
|
| [7] |
张婧玮, 梁杏, 葛勤, 等. 江汉平原第四系弱透水层渗透系数求算方法[J]. 地球科学, 2017(5):761-770.
(
|
| [8] |
王婷, 张爱军, 刘宏泰, 等. 不同酸度渗透溶液对重塑黄土渗透特性影响研究[J]. 长江科学院院报, 2013, 30(2): 35-40.
通过对杨凌黄土进行三轴渗透试验和常规渗透试验，分析了不同干密度的重塑黄土分别在pH=7.0的无气纯水及pH=3.0, 4.0, 5.0的乙酸溶液渗透下渗透系数的变化规律,研究了黄土在含酸渗透水流作用下的劣化性质，为分析黄土在酸溶液渗透作用下强度变化以及黄土构筑物的稳定变化特性提供依据。试验结果表明：①饱和黄土的渗透系数随着干密度的增加而减小。②在一定的干密度下，黄土的渗透系数随围压的增大而减小。③饱和黄土在pH=3.0酸溶液短期渗透下的渗透系数最大，随着酸溶液pH值的增大，渗透系数随之减小，因为酸溶液中的氢离子溶解了黄土中的难溶盐形成了新的渗流通道；而纯水pH=7.0渗透下土样的渗透系数介于pH=3.0和pH=4.0渗透下土样的渗透系数之间，是因为纯水采用的是煮沸过的无气水，相比之下试验配置的酸溶液本身存在少量的气体，从而影响了渗透系数的大小。④渗透系数随时间的增加而出现减小的趋势。试样进行三轴渗透和常规渗透，得出渗透系数都有随时间的延长而减小的规律。
(
|
| [9] |
肖桂元, 张达锦, 雷云, 等. 氯化钙溶液对红黏土渗透系数变化的影响[J]. 长江科学院院报, 2023, 40(3):80-84,92.
为探究CaCl<sub>2</sub>溶液对红黏土渗透系数的影响,通过X射线衍射(XRD)试验、渗透试验、热分析试验和扫描电镜(SEM),对红黏土试样受不同浓度(0.0、0.1、0.3、0.5、1.0 mol/L)的CaCl<sub>2</sub>溶液饱和后的渗透性进行了试验分析。结果表明:当孔隙溶液浓度从0.0 mol/L增加到0.5 mol/L时,红黏土的渗透系数先降低后升高;此后随着孔隙溶液浓度的增加,渗透系数呈下降趋势;利用热分析试验,得到红黏土在加入不同浓度CaCl<sub>2</sub>溶液后强结合水的含量,其强结合水含量的变化与红黏土渗透系数的变化有着紧密的联系;利用扫描电镜(SEM)观测了不同浓度CaCl<sub>2</sub>溶液下土样的微观结构,Ca<sup>2+</sup>增大了红黏土矿物结合水膜厚度,导致土的有效孔隙减少,从而降低了土体的渗透性。该研究成果可为红黏土作为隔离墙隔离污染物提供数据参考。
(
|
| [10] |
|
| [11] |
|
| [12] |
崔德山, 项伟, 曹李靖, 等. ISS减小红色黏土结合水膜的试验研究[J]. 岩土工程学报, 2010, 32(6): 944-949.
(
|
| [13] |
王平全. 粘土表面结合水定量分析及水合机制研究[D]. 成都: 西南石油学院, 2001.
(
|
| [14] |
|
| [15] |
Correlations have been developed which relate the compressibility, undrained shear strength, and permeability of remoulded clays to their Atterberg limits and activity. The relationships can be used to model a hydraulic fill, such as fine-grained dredged material or mine tailings, prior to deposition. They can also be used to estimate the engineering properties of normally consolidated natural clay, such as marine sediments. The correlations cover a wide range of plasticity index and liquidity index for a wide variety of clays. It was found that the activity plays a major role in the compressibility and undrained shear strength, and is thus also related to the sensitivity of clays. The activity apparently does not affect the permeability, but other factors remain to be investigated. Because compressibility, undrained shear strength, and permeability are interrelated, it can be concluded that if one is known, then the other two can be derived. Hence, these three engineering properties are seen as different expressions of the same physical phenomenon, rather than as independent variables.
|
| [16] |
|
| [17] |
|
| [18] |
|
| [19] |
|
| [20] |
|
| [21] |
|
| [22] |
The saturated hydraulic conductivity of a soil can be predicted using empirical relationships, capillary models, statistical models, and hydraulic radius theories. A well-known relationship between permeability and the properties of pores was proposed by Kozeny and later modified by Carman. The resulting equation is largely known as the Kozeny\u0096Carman (KC) equation, although the two authors never published together. In the geotechnical literature, there is a large consensus that the KC equation applies to sands but not to clays. This view, however, is supported only by partial demonstration. This paper evaluates the background and the validity of the KC equation using laboratory permeability tests. Test results were taken from publications that provided all of the information needed to make a prediction: void ratio, and, either the measured specific surface for cohesive soils, or the gradation curve for noncohesive soils. The paper shows how to estimate the specific surface of a noncohesive soil from its gradation curve. The results presented here show that, as a general rule, the KC equation predicts fairly well the saturated hydraulic conductivity of most soils. Many of the observed discrepancies can be related to either practical reasons (e.g., inaccurate specific surface value; steady flow not reached; unsaturated specimens, etc.) or theoretical reasons (some water is motionless; hydraulic conductivity of soils is anisotropic). These issues are discussed in relation to the predictive capabilities of the KC equation.Key words: permeability, prediction, gradation curve, specific surface.
|
| [23] |
An activated-state model for the flow of aqueous bentonite suspensions has been used to match rheology data taken over a wide range of temperatures and shear rates. The parameters used in the theory all have physical significance and their values are consistant with estimates made independently. The activated state for clay flow appears to be the state where the clay plates are parallel and just passing each other. The main barrier to activation is the loss of rotational entropy associated with this alignment of the plates.
|
| [24] |
|
| [25] |
|
| [26] |
吕海波, 钱立义, 常红帅, 等. 黏性土几种比表面积测试方法的比较[J]. 岩土工程学报, 2016, 38(1):124-130.
(
|
| [27] |
崔德山. 离子土壤固化剂对武汉红色黏土结合水作用机理研究[D]. 武汉: 中国地质大学, 2009.
(
|
| [28] |
|
| [29] |
|
| [30] |
|
| [31] |
晏红波, 周斌, 卢献健, 等. 基于EEMD-GA-BP模型的大坝变形监测数据预测[J]. 长江科学院院报, 2019, 36(9): 58-63.
针对大坝自动监测数据序列存在的不稳定性和测值漂移问题,提出了基于集合经验模态分解(EEMD)和遗传(GA)BP神经网络的大坝变形监测数据预测方法。采用EEMD技术提取反映大坝真实变形的低频信号,剔除自动监测系统数据中存在的噪声和野值,利用遗传算法优化的BP神经网络对真实信号进行学习与外推,据此构建EEMD-GA-BP模型。利用本文模型计算得到大坝变形的预测值,将其与实测变形值进行对比,并根据残差大小比较了本文方法与其它方法的预测效果。算例表明,本文提出的组合模型能有效地提高大坝变形预测精度。
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A prediction model of dam deformation monitoring data integrating Ensemble Empirical Mode Decomposition (EEMD), Genetic Algorithm (GA) and Back Propagation (BP) neural network is built to tackle the unstable performance and the drift of measured value of automatic monitoring data of dam deformation. The EEMD is used to extract the low-frequency signals which reflect the true deformation of dam and to remove the noise and outliers in the data of the automatic monitoring system; the GA-optimized BP neural network is employed to learn and extrapolate the real signals. The model-predicted deformation values are compared with measured values and also predicted values of some other methods in terms of residual error. Case study demonstrates that the proposed model could improve the prediction accuracy of dam deformation effectively.
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| [32] |
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