Advances in Civil Engineering

Volume 2018, Article ID 6846584, 11 pages

https://doi.org/10.1155/2018/6846584

## Hydraulic Conductivity Variation of Coarse-Fine Soil Mixture upon Mixing Ratio

Correspondence should be addressed to Taesik Kim; rk.ca.kignoh@mik.kiseat

Received 7 August 2017; Revised 15 November 2017; Accepted 2 January 2018; Published 22 March 2018

Academic Editor: Kirk Hatfield

Copyright © 2018 Choong-Ki Chung et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This paper presents the theoretical and experimental investigations of the hydraulic conductivity variation of the soil mixture that contains two distinct particle size distributions, coarse and fine soils. A new model for the hydraulic conductivity is introduced that focuses on the relationship between the coarse-fine soil mixing ratio and the hydraulic conductivity of the mixture. For the model verification, permeability tests were conducted. The glass beads and quality-controlled standard sand and soils obtained from fields were used for the specimen. The experiment results showed that the hydraulic conductivity of the soil mixture strongly depends on the mixing ratio. As the amount of the coarse soil contained in the fine soil increased, the hydraulic conductivity of the mixture decreased from that for the fine soil until the critical mixing ratio. This ratio is defined as the fine soils perfectly fill the voids between the coarse soils without remains. When the ratio is greater than the critical mixing ratio, the hydraulic conductivity is drastically increased with the mixing ratio up to that of the coarse soil. The comparison between the computed values and the test results shows that the introduced model successfully describes the measurements.

#### 1. Introduction

The hydraulic conductivity of soil is important in geotechnical projects related to the determination of seepage, stability analyses, and settlement prediction. Many researchers have found that the hydraulic conductivity of soil is affected by many factors such as density, water contents, degree of saturation, void ratio, grain size distribution, and particle structure. Some examples are Hazen [1], Kozeny [2], Carman [3, 4], Burmister [5], Lambe [6], Olson [7], Mitchell et al. [8], Horn [9], Garcia-Bengochea et al. [10], Hauser [11], and Wang and Huang [12], to name a few.

A frequently cited theoretical model was suggested by Kozeny [2] and Carman [3, 4]. Kozeny [2] developed the model using analogy to pipe flow and flow in capillaries. Carman [3, 4] verified the Kozeny equation. He considered the water move around irregularly shaped particles, introduced the hydraulic radius concept, and used the wetted surface area per unit volume of particles, *S*_{0}. The Kozeny–Carman equation has taken several forms including the following one:where *k* is the hydraulic conductivity, *C*_{s} is a coefficient of the shape and tortuosity of channels, is the viscosity, is the density of water, *S* is the degree of saturation, *R* is the hydraulic radius, and *n* is the porosity. The hydraulic radius can be computed bywhere is the volume of water, *V*_{s} is the volume of solid, and *e* is the void ratio. As noted by Chapuis and Aubertin [13], the Kozeny–Carman equation is not frequently used in practice due to the difficulty in determination of *S*_{0}. Several methods can be used to measure the specific surface of the soil particles to evaluate *S*_{0} but they are not commonly used in soil mechanics and hydrogeology [13]. Freeze and Cherry [14] present the Kozeny–Carman equation with *d*_{m} instead of *S*_{0} in (2). This *d*_{m} is called a representative grain size without any indication of how to calculate this equivalent diameter.

In the various models, the tortuosity is considered as an important factor. The tortuosity is used to describe the difference between the actual distance traveled by fluids and the macroscopic travel distance, owing to the sinuosity and interconnectivity of pore spaces [4, 15, 16]. In general, tortuosity depends on various factors including the shape, size, type of grains, pores, and grain size distribution [16]. Accordingly, there is ambiguity associated with the derivation of the actual distance traveled by fluids [17]. Many researchers have made an effort to find a simple relationship between the tortuosity and the porosity [18–22]. Among the proposed relations describing the relationship tortuosity versus *n*, is the most frequently used, where *m* is a value in the range of approximately 0.4 to 0.5 [19].

Experimental and empirical methods have also been employed to make the better prediction [1, 23–25]. Considering the relationships between the grain size and the hydraulic conductivity, Hazen [1] reported that the hydraulic conductivity of granular soils with uniform particles is proportional to the square of the effective particle size, *D*_{10} [1]. Burmister [5] reported that the range of the grain size, shape of the gradation curve, and *D*_{10} should be considered. Chen et al. [26] found that the hydraulic conductivity is strongly related to the median diameter *D*_{50}. Boadu [27] proposed the multivariate regression model to overcome the difficulty in the previous models. However, if soils are artificially mixed and compacted with selected particle sizes, those conductivity models for natural soils composed with various particle sizes are limited.

In practice, the binary mixtures such as compacted sand-clay mixtures are often used as blankets or liners to form seepage barriers against fluids, including leachates from disposal facilities [28]. In this type of binary mixture, fine soils provide impermeability and coarse soils provide constructability, compaction efficiency, and better deformation control. The characteristics of binary granular mixtures were investigated by many researchers [29–34]. Fragaszy et al. [29] proposed a theoretical method to evaluate the effects of oversized particles in the clean granular soils, but they emphasized the effects on the density of soil mixture rather than on the hydraulic conductivity. Shakoor and Cook [30] compacted mixtures of poorly plastic soils with gravel by varying percentages of gravel. They found that the hydraulic conductivity was slightly increased when the gravel percentage was less than 50% and a significant increase for higher percentages. Marion [31] also found that the effects of the fraction of fine-grained soils on the hydraulic conductivity of the soil mixtures were complex based on the measured permeability of the soil mixture. Shelley and Daniel [32] investigated the influence of the percentage of gravel on the hydraulic conductivity of kaolinite and of mine spoil. They found that the hydraulic conductivity increased significantly with percentages of gravel higher than 60%. Koltermann and Gorelick [33] proposed the hydraulic conductivity model for the binary granular mixture. They modified the ideal packing model concept by introducing a weighting coefficient that reflects the relative proportions of coarse and fine packing. Kamann et al. [34] proposed the hydraulic conductivity model for poorly sorted sands and gravely sands by expanding the model proposed by Koltermann and Gorelick [33].

The objective of this paper is to introduce a new simple model that describes the variations of hydraulic conductivity and dry density of the binary soil mixture that contains two distinct particle sizes, coarse and fine soils. Note that coarse and fine soils are defined by their relative particle sizes in the mixture. For example, sand is regarded as the fine soil in the gravel-sand mixture but is regarded as the coarse soil in the sand-silt mixture. The hydraulic conductivity variation is theoretically analyzed with respect to the coarse soil mixing ratio. The permeability test results are presented for the model verification. The mixtures of glass beads-Joomunjin sand, Joomunjin sand-kaolinite, and Gwanak granite soil-Songdo silty clay were used for the model verification tests.

Existing models use many variables to estimate the hydraulic conductivity such as void ratio, particle size distribution, temperature, chemical components of soil, and viscosity of fluid. The introduced model herein focuses on the relationship between the mixing ratio and the hydraulic conductivity of the mixture, so the mixing ratio is the only variable. The average porosity and the hydraulic conductivities of the pure coarse soil and pure fine soil are used as given parameters.

#### 2. Two-Particle Model for Hydraulic Conductivity

Fluid flow through soils finer than coarse gravel is laminar, and the hydraulic conductivity equations were derived from Poiseuille’s law for flow through a round capillary [35]. Based on this, the starting point for the new derivation is the Kozeny–Carman equation (1), and this can be simplified as follows:where *A* is a constant defined as and the converted porosity *n*^{∗} for the hydraulic conductivity prediction is defined as .

Figure 1 shows three possible cases when the two different particle size soils are mixed. Note that the subscripts *c* and *f* indicate the index for the pure coarse soil and the pure fine soil, respectively. For example, the model parameters *n*_{c} and *n*_{f} are the porosities of the pure coarse soil and the pure fine soil, respectively. The hydraulic conductivities of *k*_{c} and *k*_{f} are expressed as