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Compressibility behaviour of clays at large pressures
Snehasis Tripathy and Tom Schanz

Abstract: In this study, a method is proposed on the basis of the diffuse double layer theory to determine the compressibility of clays for one-dimensional conditions for vertical pressures far greater than the testing range of conventional oeodometer tests. Experimental e–p curves of several reported bentonitic clays were considered to verify the proposed method. It is shown that the parameters required to use the diffuse double layer theory can be obtained from the experimental e–p data for a low range of pressure and those can in turn be used to compute void ratios at higher vertical pressures. The stepwise procedure to calculate the e–p relationships at high pressure is given. The results showed that the agreement between the calculated and experimental compression characteristics at large vertical pressures is very good for the clays considered in this study. Key words: clays, compressibility, consolidation, expansive soils. Résumé : Dans cette étude, on propose une méthode basée sur la théorie de la double couche diffuse pour déterminer la compressibilité des argiles pour des conditions unidimensionnelles de pressions verticales beaucoup plus grandes que la plage des pressions utilisées dans les essais oedométriques conventionnels. On a étudié des courbes expérimentales e–p de plusieurs argiles bentonitiques publiées pour vérifier la méthode proposée. Il est montré que les paramètres requis pour utiliser la théorie de la double couche diffuse peuvent être obtenus à partir des données expérimentales e–p pour une plage de pressions basses et celles-ci à leur tour peuvent être utilisées pour calculer les indices de vide aux pressions verticales plus élevées. On donne la procédure étape par étape pour calculer les relations à forte pression. Les résultats montrent qu’il y a une très bonne concordance entre les caractéristiques de compression calculées et expérimentales à de fortes pressions verticales pour les argiles considérées dans cette étude. Mots-clés : argiles, compressibilité, consolidation, sols gonflants. [Traduit par la Rédaction] Tripathy and Schanz 362

Introduction
The compressibility of clays is primarily governed by the physico-chemical forces present in a clay–water electrolyte system (Bolt 1956). The type of clay minerals, the type and amount of exchangeable cations, and the properties of the fluid to which the clay is exposed to and interacts with, are some of the factors that contribute to the physico-chemical forces. One-dimensional consolidation tests are generally carried out to determine the compressibility behaviour of
Received 12 May 2006. Accepted 17 November 2006. Published on the NRC Research Press Web site at cgj.nrc.ca on 2 May 2007. S. Tripathy1,2 and T. Schanz. Scientific Researcher and Professor, Laboratory of Soil Mechanics, Bauhaus University Weimar, Coudraystrasse 11C, D-99421 Weimar, Germany.
1 2

Corresponding author (e-mail: TripathyS@cf.ac.uk). Present address: Lecturer, Geoenvironmental Research Centre, Cardiff School of Engineering, Cardiff University, Queens Buildings, The Parade, Newport Road, Cardiff, CF24 3AA, Wales, UK.

soils. Commonly, the tests are conducted up to a vertical pressure of about 800 kPa. The toxic waste disposal facilities in several countries are planned to be at great depths ranging from 500 to about 1000 m below ground level surrounded by intact host rock (Atomic Energy of Canada Limited (AECL) 2002; Enviros 2003). Considering the average overburden density of 1.8 Mg/m3, the geostatic stress at such depths is expected to be about 9.0 to 16.0 MPa. Densely compacted bentonites are considered to serve as isolation for the toxic wastes at these depths. In addition, compacted bentonites are proposed for use as backfilling materials for sealing the excavated tunnels and the access galleries. The dry density of the compacted bentonites that are commonly considered in such applications is in the range of 1.2 to 2.0 Mg/m3, corresponding to a range for void ratio of 1.3–0.4. Compacted bentonites exhibit swelling upon imbibing fluid from the saturated host rock. The stress convergence of the host rock becomes an important issue in this case and hence so is the pressure – void ratio relationship of the compacted saturated bentonites. Therefore, considerable research studies on the hydromechanical behaviour of expansive clays covering a wide
© 2007 NRC Canada

Can. Geotech. J. 44: 355–362 (2007)

doi:10.1139/T06-123

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principal equations are used to determine the void ratio – range of void ratios owing to large pressure and suction pressure relationships (i.e., e–p relationships) for clays changes have been reported recently by several researchers (Sridharan and Jayadeva 1982; Tripathy et al. This(Al-Mukhtar et al.copy of V2SLet al. 2002; Marcial et al. is evaluation 1999; Fleureau PDF Password Remover. It only decrypts first two pages. 2004). 2002). In most cases, the volume change behaviour of ini[1] p = 2 n 0 kT (cosh u − 1) Purchase PDF Passwordwater content to removethe liqtially saturated clays with Remover greater than Limitations. http://www.v2softlogic.com uid limit served as the reference behavioural pattern. 1/ 2  2 n e′ 2 v 2  Considering the range of void ratios that is of interest to  0  [2] K=  ε 0 DkT  practicing geotechnical engineers, it is necessary that very   high pressure must be applied in the laboratory environment to determine the volume-change characteristic of the clays. It is to be noted that establishing the compressibility behaviour at very high pressures needs specialized heavy equipment and loading mechanisms. Also, the time involved in carrying out the test is significantly high because of an increase in the number of loading steps. Attempts have been made in the past to predict the compressibility behaviour of natural soils (Nagaraj and Srinivasa Murthy 1986; Burland 1990). The methods have been applied for a limited range of pressure and plasticity characteristics of the soils. In this study, a method is proposed on the basis of the diffuse double layer theory to determine the compressibility of clays for one-dimensional conditions for vertical pressures far greater than the testing range of conventional oeodometer tests. Experimental e–p data of several reported bentonitic clays were considered for verification of the proposed method. It is shown that the e–p relationships of highly plastic clays for very high vertical pressures can be established by knowing the compressibility behaviour of the clays for pressures within the oeodemeter test pressure range. The parameters required to use the diffuse double layer theory can be derived from the experimental data for a low range of pressures, and those can in turn be utilized for calculating void ratios at higher pressures. [3] e = Gγ w Sd × 106

Interacting diffuse double layers
The Gouy–Chapman diffuse double layer theory (Gouy 1910; Chapman 1913) has been used the most to understand the behaviour of clay–water electrolyte systems (Mitchell 1993). The diffuse double layer theory is applicable for single clay platelet systems and for interacting clay platelet systems. In the case of single clay platelet systems, the clay platelets are considered to be separated by a large distance such that the individual double layers do not overlap. The interference of the individual diffuse double layers and the associated interaction forces are important for the range of pressures and the void ratios commonly dealt with in geotechnical engineering, and hence the equations proposed for the interacting clay platelet systems are widely used (Bolt 1956; Sridharan and Jayadeva 1982; Mitchell 1993). According to the diffuse double layer theory, a clay–water electrolyte system is said to be in equilibrium under a given pressure, p, such that the difference in the osmotic pressure at the midplane between two parallel clay platelets and the osmotic pressure in the bulk fluid surrounding the clay is balanced by the external pressure. For a clay monotonically loaded from the saturated slurried state and at equilibrium under a given pressure, the applied pressure (i.e., the effective pressure), p, is termed as the repulsive pressure or the swelling pressure (Bolt 1956; Mitchell 1993). The following

where p is the swelling pressure in N/m2, K (1/m) is the diffuse double layer parameter, n0 is the ionic concentration of the bulk fluid in ions/m3, e′ is the elementary electric charge (= 1.602 × 10–19 C), v is the valency of exchangeable cations, ε 0 is the permittivity of vacuum (= 8.8542 × 10–12 C2 J–1 m–1), D is the dielectric constant of the bulk fluid (= 80.4 for water), k is Boltzmann’s constant (= 1.38 × 10–23 J/K), T is the absolute temperature in Kelvin, d is half the distance between clay platelets in meters, e is the void ratio of the clay specimen, G is the specific gravity of soil solids, S is the specific surface area, and γw is the unit weight of water (= 1.0 Mg/m3). Prediction of void ratios for a range of vertical pressures is done by relating the u values obtained from eq. [1] with the values of the nondimensional distance function, Kd. Kd values for various u values are determined from a table or a chart that is pre-established for a known mineralogical properties of the clay and the pore-fluid properties using another set of equations (Sridharan and Jayadeva 1982; see also Tripathy et al. 2004); the discussion of which is beyond the scope of this study. For parallel clay platelets, Bolt (1956) proposed eq. [3] to relate the clay platelet spacing to the void ratio of the system. Knowing the Kd values and K from eq. [2], e values are determined from eq. [3]. A review of the literature strongly suggests that the diffuse double layer theory is a valid way to predict the compressibility behaviour of montmorillinitic clays (Bolt 1955, 1956; Warkentin et al. 1957). These studies have clearly brought out the applicability of the diffuse double layer theory for a pressure range of 10 to 5000 kPa. Nevertheless, some differences have been observed between the theoretical predictions and experimental results for certain situations. In general, it has been shown that the experimental compression curves remained above that of the predicted ones, whereas the experimental decompression and recompression curves were very nearly in agreement with that of the predicted from the diffused double layer theory, particularly so, when the clay predominantly contains sodium as the exchangeable cation. The insufficient and qualitative matching between the theory and the experimental results was attributed to several factors, notably the difference in the fabric and structure of the clay system from that of the parallel plate arrangement (Bolt 1956; Warkentin et al. 1957). There are a number of phenomena believed to be responsible for the compressibility behaviour of saturated clays depending upon the spacing between the clay platelets (Verwey and Overbeek 1948; van Olphen 1977; Mitchell 1993): (i) The long-range repulsive pressure and attractive pressure dominate at clay platelet distances beyond 1.0 nm. (ii) The interference of the outer electron shells of mole© 2007 NRC Canada