Modified Kozeny-Carman Equation Research Articles

Applying machine learning for hydraulic flow unit classification and permeability prediction: case study from carbonate reservoir in the Southern part, Song Hong basin

Machine learning (ML) is an artificial intelligence (AI) that enables computer systems to classify, cluster, identify, and analyze vast and complex sets of data while eliminating the need for explicit instructions and programming. For decades, machine learning has become helpful for complex reservoir characterization such as carbonate reservoirs. Permeability prediction from well logs is a significant challenge, especially when the core data is rarely available due to its high cost. In this study, we aimed to bridge this gap by demonstrating the practical application of integrating Hydraulic Flow Units (HFU) and machine learning methods. Our goal was to provide a reliable estimation of permeability using core and wireline logging data in the complex Middle Miocene carbonate reservoir of the CX gas field in the southern part of the Song Hong basin. In the first step, due to the reservoir’s heterogeneity, the core plug dataset was classified into 5 HFUs based on the flow zone indicators (FZI) concept from the modified Kozeny-Carman equation using unsupervised machine learning - K-means method. The porosity - permeability for each HFU was defined after HFU clustering. In the second step, we designed three different workflows to predict permeability and HFU using supervised machine learning from a combination of core and log data. These workflows were rigorously test and compared with the core data. The most accurate result was chosen as the base, providing a high confidence level in our predictions’ reliability.

Assessing the impact of pore‐fracture structures on permeability sensitivity in tectonic coal using computerized tomography scanning

AbstractThe heterogeneity in permeability of coal reservoirs is primarily attributed to the considerable variation in the morphologies and structures of microscopic pore‐fractures, shaped by complex geological processes. This study emphasizes the necessity of understanding the impact and governance of these morphological and structural variations in pore‐fractures across different types of coal bodies on their permeability. Utilizing computerized tomography scanning and three‐dimensional imaging, we examined coal samples from the Datong coalfield in the southeastern Qinshui Basin, Shanxi Province, to characterize the pore‐fracture morphologies and structures distinct to various coal‐body types based on tomographic data. This introduces a methodology for assessing the influence of microscopic pore‐fracture parameters, such as porosity, specific surface area, tortuosity and fractal dimension, on permeability sensitivity. This is achieved through the application of the modified Kozeny–Carman equation and a fractal permeability model. Findings indicate a predominance of slab fractures in raw coal, whereas fragmented coal under weak brittle deformation exhibits small, isolated pore‐fractures with minimal diameter and volume and poor connectivity. In contrast, granular coal subjected to strong brittle deformation features extensive clusters of large pore‐fractures with significant diameter and volume, enhancing connectivity. Moreover, permeability predictions are refined by integrating the modified Kozeny–Carman equation with tomographic data, offering a more precise understanding of the permeability across different coal bodies.

A practical equation for predicting saturated hydraulic conductivity of fine-grained soils

The saturated hydraulic conductivity (ks) of soils plays a crucial role in various agricultural and environmental engineering applications, particularly in relation to pollution prevention and water migration. Firstly, the traditional Kozeny-Carman (KC) equation, which are commonly used to estimate ks, has limitations in predicting ks for different types of fine-grained soils based on the analyses of permeability test data in the literature. Secondly, to tackle this issue, a modified KC equation was proposed by introducing an expression for the shape parameter and establishing a relationship between the tortuosity equation and the plastic limit. Additionally, the validation of the proposed equation was conducted using ks values of 25 fine-grained soils obtained from other sources. Finally, a comparison was made with the four commonly used ks models to evaluate its performance. The results indicate that the proposed equation demonstrates a relatively high coefficient of determination and a low root mean square error. This suggests that the proposed equation has the potential to accurately assess ks for fine-grained soils. The predictions for ks using the modified equation showed good agreement with the experimental data mentioned in the literature.

Modified Kozeny-Carman equation for estimating hydraulic conductivity in nanoscale pores of clayey soils with active surfaces

Hydraulic conductivity is a critical parameter for studying the behavior of clay-water systems. However, accurately estimating saturated hydraulic conductivity k in clayey soil by using the Kozeny-Carman (KC) equation is challenging due to the neglect of its active surface properties and nanoscale pores. Clay surfaces can have diverse characteristics resulting from various physicochemical processes such as isomorphous substitution and are typically characterized by the Cation Exchange Capacity (CEC). These properties can significantly impact fluid transport through the clay matrix. To address this issue, this study modifies the KC equation by incorporating an adsorbed water proportion φ that considers the occurrence state of pore water and its correlation with pore diameter, making it applicable to clayey soils. Molecular dynamics (MD) models are established to investigate the influence of surface interaction (CEC) and nanopore size (r) on saturated hydraulic conductivity k of seepage flow in clayey soils. Based on the MD results, a specific function is proposed to quantify the adsorbed proportion φ, which is linearly related to the root of CEC and reciprocal of pore size (r), and then incorporated into a proposed hydraulic correction ratio k* to modify the classical KC equation. The modified KC equation is validated using experimental data from literature, showing a high R2 value of 0.96. This result demonstrates that the proposed correction ratio k* can extend the application scope of the classical KC equation to clayey soils.

Integrating hydraulic flow unit concept and adaptive neuro-fuzzy inference system to accurately estimate permeability in heterogeneous reservoirs: Case study Sif Fatima oilfield, southern Algeria

Formation characteristics are a crucial requirement for reservoir modeling and they need to be constantly updated as new static and/or dynamic reservoir-property details become available. This improves reservoir interpretation while achieving a good history-matching for a better representation of the reservoir. This paper proposes a new method to estimate reservoir permeability in an oil-producing reservoir by applying two distinct cases: partially cored and completely non-cored wellbores. The approach involves the determination of hydraulic-flow units (HFU) using a flow-zone indicator (FZI) distribution to consider the dynamic aspect of the permeability, which strongly influences fluid flow through porous media. The FZI is clustered by normal probability analysis to identify the optimum number of HFU clusters. The estimated reservoir permeability is validated in static and dynamic reservoir models. For an accurate prediction of the FZI over the entire reservoir thickness, an adaptive-neuro-fuzzy-inference system (ANFIS) is developed using conventional well-log variables: (i) gamma-ray (GR), (ii) sonic (DT), (iii) density (RHOB), (iv) deep resistivity (DLL), and (iv) neutron porosity (NPHI) calibrated with the available core data. The static regression parameters root-mean-squared error (RMSE), mean absolute error (MAE), coefficient of determination (R2), and R2adjusted are used to evaluate the performance of the ANFIS model in predicting FZI to determine HFU for estimating reservoir permeability. To validate this approach, a matching quality check of the downhole and reservoir pressure is carried out using a dynamic reservoir simulation model. Historical data collected from wellbore OPW-1 drilled in the Sif Fatima oilfield (Algeria) are used to evaluate the accuracy of the proposed permeability-prediction framework. The ANFIS model can accurately and efficiently predict the FZI exhibiting R2, R2adjusted, RMSE, and MAE of approximately (≈0.981, ≈0.979, ≈0.014, ≈4,600E-08)), (≈0.933, ≈0.891, ≈0.032, ≈1.615E-03), and (≈0.970, ≈0.968, ≈0.018, ≈2.381E-04)) for the training, testing and complete dataset, respectively. When applied to predict reservoir permeability, the Hydraulic Flow Unit concept was able to generate accurate results from the predicted FZI data by applying the modified Kozeny-Carman equation with, R2, RMSE and MAE values of approximately ≈0.9702, ≈0.969, ≈9.604, and ≈4.398, respectively. The calculated permeability was validated successfully at well and field levels. Additionally, it generated more accurate history matches of the well and the reservoir pressure trends than the previous permeability model, and consequently improved the reservoir modelling workflow.

Estimation of hydraulic conductivity by the modified Kozeny–Carman equation considering the derivation principle of the original equation

The Kozeny–Carman (K–C) equation based on Poiseuille’s law is an efficient theoretical equation predicting hydraulic conductivity. Some modified K–C equations were proposed focusing on obtaining the uncertainty parameters in the original K–C equation. However, assumptions of some modified K–C equations are inconsistent with Poiseuille’s law. This study proposes a new modified K–C equation considering the derivation principle of the original K–C equation. By applying Poiseuille’s law in porous media, the concept of 2D porosity (ε) and a correction coefficient for permeation (f) are presented. During the derivation process, each section’s void distribution is assumed to be similar, and void pipes in various directions share similar characteristics, because the effective porosity (ne) is approximately equal to ε only when the change in the cross-section in porous media is small. The parameters in the new modified K–C equation include specific surface area (S0), tortuosity (1/cosθ), and ne. The prediction formulas of ne are presented according to the soil mineral and bound water features. The prediction formulas for S0 and 1/cosθ are deduced and verified by comparing them with established formulas proposed by other researchers and experimental data. The new modified K–C equation is adequate for predicting hydraulic conductivity for clay and sand by comparing it with the experimental value and theoretical equations, including the original and other established modified K–C equations.

A novel permeability model for hydrate-bearing sediments integrating pore morphology evolution based on modified Kozeny-Carman equation

Permeability of hydrate-bearing sediments is the key parameter to determine the gas production performance, which is mainly affected by the pore morphology and hydrate saturation. Existing models of permeability could not well capture the dynamic characteristic of permeability in sediments with changing hydrate saturation and pore morphology. In this paper, a novel normalized permeability model using logistic function linked different hydrate pore morphology evolution was established by modifying tortuosity, surface area and pore shape factor simultaneously in Kozeny-Carman equation. It was verified by different published data and compared with other models. The introduced critical hydrate saturation and transitional intensity of hydrate pore morphology were optimized by genetic algorithm. Results indicated that this model was more powerful than existed models and better captured the permeability evolution in hydrate-bearing sediments at various conditions. The critical hydrate saturation and transitional intensity of hydrate pore morphology dominated the characteristics of permeability evolution. In addition, the effect of porosity would not be ignored especially below the critical hydrate saturation when hydrate pore morphology changed from pore filling to grain coating. The proposed model brings reliable predictions and mechanistic understandings of the permeability evolution in hydrate-bearing sediments, and builds fundamental theory for development of natural gas hydrate in safety and efficiency.

Comparison of saturated hydraulic conductivity estimated by surface NMR and empirical equations

This study used eight empirical equations such as Kozeny-Carman (K-C), Terzaghi, Hazen, Slitcher, Kruger, Sauerbrei, NAVFACDM7, and Zamarin to estimate saturated hydraulic conductivity from soil particle size distribution and surface NMR porosity. The estimated empirical hydraulic conductivities were compared with the saturated surface nuclear magnetic resonance (surface NMR) hydraulic conductivity. It was found that most of the empirical equations showed poor correlation with the surface NMR hydraulic conductivity except Kozeny-Carman (KC), Hazen, and Zamarin equations. The value of the coefficient (β) of each equation is modified in such a way as to obtain a linear equation with the unit slope to improve the performance and accuracy of empirical equations. The modified Kozeny-Carman equation showed the maximum correlation R2=0.904, Pearson's r=0.951, and RMSE =6.36 in comparison with other empirical equations. The NAVFACDM7 and the Terzaghi equations showed the highest underestimated hydraulic conductivity data (64%) and overestimated hydraulic conductivity data (38%); however, the Zamarin equation showed the highest overlapped hydraulic conductivity data (44%), respectively, with the 1:1 line.

Influence of Pore Morphology on Permeability through Digital Rock Modeling: New Insights from the Euler Number and Shape Factor

The microscopic pore shape and topology significantly affect fluid transport and occurrence in porous permeable rock. A quantitive characterization of the impact of pore morphology on permeability is currently lacking, which limits the efficient development of underground hydrocarbon resources. This work introduces the Euler number and shape factor to characterize the pore topology and shape of heterogeneous sandstone based on CT imaging. The pore morphology under different pore sizes and the correlation of the Euler number, shape factor, fractal dimension, and surface area are analyzed. Furthermore, a modified Kozeny–Carman equation is established to explain the influence of the Euler number and shape factor on permeability. The results show that with the increase of pore diameter, the Euler number decreases while the shape factor increases. In a connected pore system, the smaller Euler number corresponds to the complex pore network, which leads to the increase in the surface area, shape factor, and fractal dimension. At constant porosity, the shape factor is negatively correlated with permeability, and with increasing Euler number, the heterogeneity of the pore structure increases, resulting in an increase of flow resistance and a decrease of permeability. The results provide a new pore morphology characterization method for digital rock and help to understand the flow mechanism of hydrocarbons in complex pore networks.

A modified Kozeny–Carman equation for predicting saturated hydraulic conductivity of compacted bentonite in confined condition

Kozeny–Carman (KC) equation is a well-known relation between hydraulic conductivity and pore properties in porous material. The applications of KC equation to predicting saturated hydraulic conductivities of sands and non-expansive soils are well documented. However, KC equation is incapable of predicting saturated hydraulic conductivity of expansive soil (e.g. bentonite) well. Based on a new dual-pore system, this study modified KC equation for improving the prediction of saturated hydraulic conductivities of bentonites. In this study, an assumption that inter-layer space (micropore) has limited effect on fluid flow performance of compacted bentonite was adopted. The critical parameters including total porosity and total tortuosity in conventional KC equation were replaced by macroporosity and tortuosity of macropore, respectively. Macroporosity and microporosity were calculated by basal spacing of compacted bentonite, which was estimated by assuming that specific surface area is changeable during saturation process. A comprehensive comparison of bentonite's saturated hydraulic conductivity predictions, including modified KC equation proposed in this study, conventional KC equation, and prediction method based on diffuse double layer (DDL) theory, was carried out. It was found that the predicted saturated hydraulic conductivity of bentonites calculated using modified KC equation fitted the experimental data better than others to a certain extent.

A New Modified Model of the Streaming Potential Coupling Coefficient Depends on Structural Parameters of Soil-Rock Mixture

The streaming potential effect in soil-rock mixture (SRM) is related to the compactness and rock content, but there is no model to quantitatively describe this behavior. In this paper, the Kozeny–Carman (KC) equation is modified by using the compactness and rock content. Then, the modified KC equation is substituted into the equation of streaming potential coupling coefficient. A new modified model of streaming potential coupling coefficient that depends on the compactness, rock content, particle shape, and particle gradation is proposed. The reliability of the new modified model is tested by experiments, and the applicable scope of the model is obtained. The results show that when the rock content is 30%, the permeability coefficient prediction accuracy of the modified KC equation is higher in the range of 85–95% compactness. The new modified model of the streaming potential coupling coefficient represents well the control of the compactness (75–95%) on the coupling coefficient. When the compactness remains 85%, the permeability coefficient calculated by the modified KC equation in the range of 10–70% rock content is consistent with the experimental data. The influence of the rock content (10–90%) on the coupling coefficient is well described by the new modified model of the streaming potential coupling coefficient. The new modified model of streaming potential coupling coefficient is helpful to quantitatively evaluate the internal structure evolution of embankment dam by using streaming potential phenomenon.

Determining the bound water content of montmorillonite from molecular simulations

The physical, chemical and engineering properties of clay, particularly for strength, deformation and permeability, largely depend on the characteristics of bound water. The bound water has been a hotspot research focus on the matter in soil mechanics, engineering geology and so on. Despite numerous studies on bound water of clay, a unified theory for the quantitative determination of bound water film thickness has not been proposed yet. This paper put forwards a point of view that the boundary of bound water in clay is located at the position of the water layer closest to the shear plane in the electrical double layer (EDL). Molecular dynamics (MD) was adopted to determine the thickness of bound water in Na-montmorillonite. The thickness of bound water in the pore containing two water layers was determined as about 6 Å regarded as tightly bound water after verifying by experimental data. The physical properties of bound water were also investigated showing that the bound water suffers compressive stress more than 103 kPa from the clay surface and has shear viscosity several times greater than bulk water. Additionally, an application for predicting the hydraulic conductivity of clay by considering the bound water was introduced. A modified Kozeny-Carman equation with the variable viscosity of the seepage fluid was proposed, satisfying accuracy compared with experimental data. The findings in this study are helpful for revealing the mechanism of bound water on the surface of soil particles.

Characterization of macropore structure of remolded loess and analysis of hydraulic conductivity anisotropy using X-ray computed tomography technology

The pore structure of loess is crucial for understanding the transport of water in soil and affects soil permeability. In this study, X-ray computed tomography (X-ray CT) technology was used to establish the macropore structure of remolded loess, and analyze the influence of macropore on permeability. A new specific and efficient workflow for constructing macropore structure of loess samples was established. The workflow improves the precision of image segmentation and provides a new method for creating 3D soil macropore structure. The macropore structure showed that the macro-porosity variation of loess sample was clearly anisotropic. Based on the macropore structure model, a modified Kozeny–Carman equation was suggested to investigate the hydraulic conductivity anisotropy of the loess sample. Subsequently, permeability test was used to verify the results calculated by equation. Both the results showed that hydraulic conductivity was positively correlated with the uniformity of the porosity changes in each direction. It provides a new method to estimate the anisotropy of hydraulic conductivity based on macropore structure model.

Evaluation of coal petrophysics incorporating fractal characteristics by mercury intrusion porosimetry and low-field NMR

Mercury intrusion porosimetry (MIP) and low-field nuclear magnetic resonance (NMR) were combined to investigate pore-fracture structure and fractal characteristics of coals (0.93% < Ro,m < 2.77%), and their impacts on coal permeability were assessed using two newly-proposed models. The results indicate that coals with type I mercury intrusion/extrusion curve are beneficial to gas flow due to well-developed micro-fractures (73.9–86.74%) and high pore-fracture connectivity, whereas coals with type II and III curves are less conducive to gas flow because of non-uniform pore-fracture structure and poor connectivity. Based on NMR analysis, pore-fracture structure of low-rank bituminous coals (0.9% < Ro,m < 1.2%) presents irregular three T2 peaks, whereas two and irregular three T2 peaks simultaneously exist in other coals (1.2% < Ro,m < 2.8%). The variation of coal composition and gas generation process may have complex effects on pore-fracture structure during the coalification process. Moreover, MIP fractal dimension ranges from 2.265 to 2.873, whereas NMR fractal dimension varies from 2.744 to 2.976. Due to different sample morphology and fractal estimation methods, most of MIP fractal dimension is larger than NMR fractal dimension. A modified Kozeny-Carman equation was used to calculate MIP permeability, ranging from 3.62 × 10−4 to 1.229 mD. The effect of mesopores on MIP permeability may be related to the gas flow pathway and interlinkage mechanism of adsorption pores and fractures. The NMR permeability was estimated by a movable porosity-permeability model (kN=0.0045∗eϕNM0.6851+0.037), ranging from 0.043 to 2.767 mD. The NMR permeability should be related to movable fluid space and pore-fracture connectivity, and micro-fractures can largely contribute to free fluid volume.

Study on pore size effect of low permeability clay seepage

Low-permeability clays are characterized by a large amount of clay minerals and a special distribution of pore sizes, so their seepage behavior shows an obvious pore size effect. Therefore, conventional seepage theories show deviations in describing the seepage behavior of low-permeability clays. This paper analyzes two reasons for the pore size effect in low-permeability clay seepage: the pore distribution property and the electric double layer effect of the clay surface. Considering these two factors, the seepage theory of the pore size effect based on the microscale seepage of the circular tube model is proposed. The rationality of this theory is tested by the seepage experiments of natural undisturbed clay and artificial clay, and from these experiments, three beneficial conclusions are drawn: (1) The results of the pore size effect seepage theory are in good agreement with the experimental results and are better than the modified Kozeny-Carman equation; (2) The properties of the electric double layer have a certain regular influence on the seepage behavior of the clay; (3) Considering the properties of the soil pore size distribution, the results obtained by using the pore size effect theory are much closer to the experimental results than the results calculated using the average pore diameter of the clay.

Analysis of filtration and electrical properties anisotropy of terrigenous reservoir rocks (for DDB axial zone reservoirs)

The paper focuses on the filtration and electrical anisotropy coefficients and relationship between vertical and horizontal permeability in sandstone reservoir rocks. Field case study of DDB reservoir rocks. Petrophysical properties and parameters are estimated from core and log data from a Moscovian and Serpukhovian stages of Dnipro-Donetsk Basin (West-Shebelynka area well 701-Bis and South-Kolomak area well 31). Routine core analysis included estimation of absolute permeability, open porosity, irreducible water saturation and electrical resistivity (on dry and saturated by mineralized solution) of 40 core samples along two orthogonal directions. Shale fraction is estimated using well logging data in wells which are analyzed. The authors report that reservoir rocks are represented by compacted poor-porous (φ &lt;10 %), low permeable (k&lt;1mD) laminated sandstone with different ratios of clay minerals (Vsh from 0,03 to 0,7) and high volume of micaceous minerals (in some cases 20-30 %). Research theory. One of the main objectives of the work is to develop empirical correlation between vertical permeability and other capacitive and filtration properties for compacted sandstone reservoirs. A modified Kozeny-Carman equation and the concept of hydraulic average radius form the basis for the technique. Results. Coefficients of the anisotropy of gas permeability (IA) and electrical resistivity (λ) are defined based on the results of petrophysical studies. The experiments proved that IA lies in a range from 0,49 to 5 and λ from 0,77 to 1,06. Permeability and electrical resistivity anisotropy in most cases have horizontal distribution. It has been shown that in West-Shebelynka area sample №1 (depth 4933 m) there is probably no fluids flow in vertical direction and in samples №№3 and 15 fractures have the vertical orientation. We have also found that the values of electrical and filtration anisotropy for all samples of South-Kolomak area are similar, this characterized the unidirectionality in their filtration properties, as well as the fact that the motion of the fluid flow mainly in the horizontal direction. In the studied rocks the degree of anisotropy has been concluded to depend on the volume of clay and micaceous minerals, their stratification, fractures, density, and their orientation. New correlation between vertical permeability, horizontal permeability and effective porosity are developed for Late Carboniferous DDB intervals that are analyzed.

Frost heave in freezing soils: A quasi-static model for ice lens growth

Frost heave can have a very destructive impact on infrastructure in permafrost regions. The complexity of nanoscale ice-mineral interactions and their relation to the macroscale frost heave phenomenon make ice lens growth modeling an interesting but challenging task. Taking into account the limiting assumption of the constant segregation temperature in the segregation potential model, we propose here a new quasi-static model for ice lens growth under a time varying temperature based on the water activity criterion. In this model, the conventional pressure potential gradient in Darcy's law is replaced by a water activity based chemical potential gradient for the calculation of water flow velocity, which provides a better prediction of ice lens growth and is useful to describe the ice nucleation and the state of water at a specific temperature. Moreover, based on the analysis of the new developed model, a mathematical description of the segregation potential is provided here. The modified Kozeny-Carman equation is applied to determine the water permeability of a given soil. In our new model, the effects of the equivalent water pressure are taken into account to modify the freezing characteristic function. Hence, the temperature- and equivalent water pressure- dependent hydraulic permeability in the frozen fringe is mathematically determined and improved. By coupling the quasi-static model with the modified hydraulic permeability function, the numerical calculation of ice lens growth is validated based on the experimental data of the temperature of the ice lens measured in the laboratory. The prediction of ice lens growth using the proposed method contributes and facilitates the simplified calculation of frost heave in the field and/or laboratory scenarios at a quasi-static state, and thus enables a better understanding of phase change and fluid flow in partially frozen granular media (soils).

A new model of pore structure typing based on fractal geometry

Abstract In this study, we report a physics-based model for pore structure typing in which a generalized model is also derived to calculate the specific surface area of the grains. In this model, a new pore-structure-type indicator is defined to characterize the discrepancies of pore structures based on the fractal geometry theory and a modified Kozeny-Carman equation. We compared the proposed model with the conventional model by comprehensive experimental tests in 130 low permeability sandstone cores from the Dongfang gas reservoir in the South China Sea. The fractal dimension of the grain Dg was first accurately calculated through thin section analysis. The results show that grains of low-permeability sandstone indeed have the bifractal distribution with constant radius boundaries of approximately 30 μm, potentially accounting for the multiscale of pore spaces. Compared with the conventional model, considering the complex pore and grain size distributions as well as irreducible water saturation, the developed model as a generalized expression performs better in pore structure typing with higher correlation coefficients in porosity-permeability and structural coefficients-pore radius relationships due to the newly identified indicator with a wider range. Finally, a multiscale workflow was proposed to analyze the petrological and structural features of pore structures by two-dimensional core images, thin sections, scanning electron microscope, mercury intrusion tests and three-dimensional micro-computed tomography. This work enables us to explain the genetic types and differences of the pore structure and may help to characterize the internal connection of the grain structure-pore structure-flow mechanism in hydrocarbon exploration and development.

Experimental and numerical investigation of the effect of soil type and fineness on soil frost heave behavior

The type and fineness of soil are commonly recognized as the two major factors affecting the frost heave behavior of foundation. This paper aims to study the effect of soil type and fineness on frost heave behavior by experimental and numerical methods. Optical and scanning electron microscopes were employed to study the microstructure of kaolin and montmorillonite soils. A finite volume method, considering the changes of thermal and water fields simultaneously, was used to model the frost heave behavior of finely grained soil. By coupling the rigid ice model with the modified Kozeny–Carman equation and estimating the hydraulic conductivity, the relationship between the frost heave ratio and specific surface area of fines was established. Based on the modeling results, a region of proportion range of three typical soil (silty, clay and sandy soil) was proposed based on the ternary plot of frost heave values. Microscopic test results show that the multilayer microstructure of kaolin results in high content of bonded water compared with that of montmorillonite, leading to higher frost heave value. This model is proved to be reliable by a good agreement between the predicted and measured frost heave values.

Comprehensive investigation of permeability characteristics of pervious concrete: A hydrodynamic approach

Pervious concrete (PC) mixtures were designed and prepared to measure and study permeability characteristics at varying head levels using a falling head permeameter. A total of 1092 readings was used to study the permeability properties of eighteen PC mixtures whose porosity was in the range of 15–37%, and permeability in the realm of 0.076–3.5cm/s. The permeability reduced as the head of water increased, and gradually attained an asymptotic relation with the head. Cement-to-aggregate ratio had largest contribution in controlling permeability of PC mixtures. Nonlinearity in Darcy’s law was observed in respect of permeability of PC mixes, which was modelled using Izbash/power law, and was prominent for gradations consisting of larger sized aggregates due to inconsequential tortuous pore structure. Modified Kozeny-Carman equation was fitted for PC gradations to compare the results with Izbash law, which showed good agreement. This study is deemed to assist in understanding the hydrodynamics of water flow in pervious concrete, which in turn will aid in rational pervious concrete pavement system designs.