THEORETICAL CHARACTERISATION OF EQUILIBRIUM SEDIMENT VOLUME OF CLAYS. D. S. Das 1, T.V. Bharat 2 ABSTRACT

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1 THEORETICAL CHARACTERISATION OF EQUILIBRIUM SEDIMENT VOLUME OF CLAYS D. S. Das 1, T.V. Bharat 2 ABSTRACT Equilibrium sediment volume is an important index parameter for understanding the behavior of expansive soils. The theoretical understanding of the influence of different pore fluid parameter and clay surface properties on sediment volume is, therefore, very much necessary in geotechnical engineering. This study presents a detailed theoretical analysis on the influence of various parameters on the equilibrium sediment volume in the light of diffuse double layer theory. Keywords: Sediment volume, characterization, diffuse double layer theory 1 Das, D.S., Department of civil engineering, IIT Guwahati, Guwahati, India, dhanx38@gmail.com 2 Bharat, T.V., Department of civil engineering, IIT Guwahati, Guwahati, India, tvb@iitg.ernet.in

2 THEORETICAL CHARACTERISATION OF EQUILIBRIUM SEDIMENT VOLUME OF CLAYS Dhanesh Singh Das, Indian Institute of Technology Guwahati, T. V. Bharat, Indian Institute of Technology Guwahati, Abstract: Equilibrium sediment volume is an important index parameter for understanding the behavior of expansive soils. The theoretical understanding of the influence of different pore fluid parameter and clay surface properties on sediment volume is, therefore, very much necessary in geotechnical engineering. This study presents a detailed theoretical analysis on the influence of various parameters on the equilibrium sediment volume in the light of diffuse double layer theory. INTRODUCTION Bentonite clays are receiving great importance for the application in municipal solid waste (MSW) repositories as landfill liner [2], in nuclear waste repositories as buffer and backfill material [13], in tunnel lining, in slurry trench cutoff walls as base liner and barrier [5] and many other geotechnical applications. Some characteristics features of these clays, such as high swelling capacity, ability to resist migration of contaminants due to very low hydraulic conductivity, and high adsorption capacity for ions are quite useful in engineering applications [13]. The wide variation in the geotechnical properties of these clays, through the complex clay-water-electrolyte interaction, attributes to the changes in the montmorillonite content, surface characteristics and composition of exchangeable cations [1, 6, 9, 11, 14]. The theoretical understanding of the physic-chemical behavior of naturally available clays, therefore, attach great importance in the geotechnical study. Equilibrium sediment volume (ESV) or free swell index (FSI) tests are routinely performed in laboratory for qualitative assessment of the geotechnical behavior of clays. The equilibrium sediment volume data were used for identifying different clay minerals [15, 4], classifying expansive soils [8, 10, 11], qualitative understanding of the swelling behavior of the clays [3] and correlating with different geotechnical properties of clays [7,8]. Theoretical framework for equilibrium sediment volume is required for basic understanding of the influencing parameters and interpretation of the test data. A detailed theoretical analysis on the various influencing parameters on the equilibrium sediment volume were carried out and presented in this study. THEORY The diffused electric double layers develops around the clay particles in presence of water or other electrolyte solutions attributing to the charged nature of the surface of clay particles. The distribution of the electric potential in the diffuse double layer (DDL) of a single clay platelet (Fig.1) is given by Poison-Boltzman equation [14]: (1) where, y is the scaled potential ( at any distance s, from the surface of the single clay plate, z is the scaled surface potential ( ), 1/k is the characteristics length or debye length,, e is the elementary electric charge ( ), v is the valence of ions, n is the ion concentration in the bulk fluid, is the dielectric constant, KT is the thermal energy per ion, F is the Faraday constant and φ is the electric potential at x.

3 Das, D.S. & Bharat, T.V... In a clay-electrolyte system, when two clay particles come close to each other, the non-interacting clay-electrolyte system where the electric potential becomes zero (Fig. 1). interaction of the diffuse double layers results in repulsive force between the particles. The values of were obtained iteratively using the following relation (Eq. 4) derived from Eq. 1. (4) Figure 1. Illustration of electric potential distribution around a non-interacting clay platelet system [14] This long range electrical repulsive force significantly dominates the sediment volume of clays as body forces are negligible and hence the inter-particle distance is in large scale compared to the size of the clay particles. When the separation distance increases the interaction between the clay platelet becomes negligible and under this condition the clay platelet behave individually, as a non-interacting system. The equilibrium sediment volume (ESV) or the equilibrium void ratio (EVR) characterize through the DDL thickness of a non-interacting system. In each iteration, was computed by assuming a very small value of scaled electric potential for a given pore-fluid and clay surface properties. If the computed distance between the particles is finite, the scaled electric potential was further reduced to find the limiting distance or void ratio. The limiting DDL thickness increased with decrease in the electric potential (Fig. 2). The smallest value of scaled electric potential corresponding to a finite value of DDL thickness (void ratio) was found to be for different pore-fluid and clay surface properties. Lower than this value could not be used in the computation as it resulted in an undefined value for DDL thickness or void ratio (Fig. 2). The variation of the limiting DDL thickness values for different pore-fluid concentrations is given in Fig. 3. The limiting DDL thickness varied nearly linear from to 80 Å over a pore-fluid concentration variation of 10-5 to 1 M (Fig. 3) Theoretical estimation of ESV The equilibrium sediment volume (ESV) or the equilibrium void ratio (EVR) can be obtained from the DDL thickness using the following relationships. (2) (3) Where, is the specific gravity of soil, is the density of water, SSA is the specific surface area and is the limiting DDL thickness of a Figure 2. Verification of infinity and calculation of DDL thickness corresponding to small pressure

4 Effect of pore fluid parameters The dependency of d lt and EVR on different clay surface properties and pore-fluid parameters were analyzed (Fig. 4-7). Fig. 4a shows the effect of valence of ions on the DDL thickness at different ion concentrations. The DDL thickness decreases with increases in the valence of ions and shows a linear relationship at all the concentration of ions. When the charge on the exchangeable cations is more, the diffusion tendency decreases as the attractive force become stronger. Similar influences are reflected on EVR at different concentration (Fig. 4b). Figure 3. Limiting DDL thickness of noninteracting system vs pore fluid concentration Fig. 3 &4a. shows the variation of DDL thickness in non-interacting system with the change in the ion concentration in the pore fluid. The thickness decreases with increase in the ion concentration. The tendency of the counter-ions to diffuse away from the surface reduces as the ion concentration in the bulk solution increases, which results in compression of the diffuse double layer developed around the surface of a clay particle. Figure 4b. EVR vs ion concentration in the pore fluid for different valence in a non- interacting system Figure 5a. Limiting DDL thickness of noninteracting system vs dielectric constant of pore fluid for three different valences Figure 4a. Limiting DDL thickness of noninteracting system vs ion concentration in the pore fluid for different valence The electric permittivity of the pore fluid has a significant effect on the thickness of diffuse

5 Das, D.S. & Bharat, T.V... double layer. The ability of the counter-ions to At higher concentration dielectric constant has a diffuse away from the surface decreases as the minor effect on the DDL thickness while at permittivity or the dielectric constant of the pore lower concentration, DDL thickness changes fluid medium decreases. Limiting thickness and considerably with the change in dielectric therefore, consequently the EVR decreased with constant (Fig. 6a). At higher concentration the decrease in the dielectric constant of pore fluid tendency of the counter-ions to diffuse away is (Fig. 5a & 5b). very less or negligible due to which the permittivity of the medium does not get to play much role, whereas on decreasing the ion concentration, the tendency of the counter-ions to diffuse away from the surface increases due to which the effect permittivity becomes more pronounce towards the lower concentrations. Similar trends were observed for EVR also (Fig. 6b). Figure 5b. EVR vs dielectric constant of the pore fluid three different valences Dielectric constant has more prominent effect on the DDL thickness and EVR at lower valence than higher valence (Fig. 5a & 5b). Similarly Fig. 6a shows the influence of dielectric constant on the DDL thickness at various pore fluid concentration. Figure 6b. EVR vs dielectric constant of the pore fluid for three different ion concentrations Figure 6a. Limiting DDL thickness vs dielectric constant of the pore fluid for different concentrations Figure 7a. Limiting DDL thickness vs ion concentration in the pore fluid for two different SSA values

6 Figure 7b. Electric potential distribution around the surface of clay particle for two different SSA values Influence of surface properties of clays The influence of specific surface area was not observed on the limiting DDL thickness and, therefore, on d lt vs. n relationship (Fig. 7a). Even though SSA influenced the surface potential and the potential distribution in the diffused layer, the limiting DDL thickness did not show any variation (Fig. 7b). The specific surface area, however, influenced the relationship between EVR vs. n (Fig. 7c) as the equilibrium void ratio is a direct function of specific surface area (Eq. 2). Figure 7d. Limiting DDL thickness vs ion concentration in the pore fluid for three different CEC values. Similarly the cation exchange capacity showed no influence on both dlt vs.n and e lt vs. n. The dlt vs.n plot is shown in the Fig. 8 for three different valences. CONCLUSION The influence of specific surface area and cation exchange capacity of the soil were not observed on the limiting DDL thickness in a sediment volume of clays. However, the equilibrium void ratio was linear dependent on the specific surface area of the clay. The cation exchange capacity does not have any effect on the equilibrium void ratio as well, whereas the percentage of each individual cation seemed to have great influence which is evident from the influence of valence on both limiting DDL thickness and equilibrium void ratio. REFERENCES Figure 7c. EVR vs ion concentration in the pore fluid for two different SSA values 1. Abdullah, W.S., Al-Zou bi, M.S., and Alshibli, K.L. (1997), On the physicochemical aspects of compacted clay compressibility, Canad. Geotech. Jl., 34,

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