A reexamination of the permeability index of clays

NOTE A reexamination of the permeability index of clays G . L. SIVAKUMAR BABU, N. S. PANDIAN, AND T. S. NAGARAJ Department of Civil Engineering, Indian Institute of Science, Bangalore 560 012, India Received April 8, 1992 Accepted September 23, 1992 The permeability index C,, similar to the compression index, is the slope of the void ratio - coefficient of perme- ability relationship. Literature shows that, in general, for sensitive clays it can be related to initial void ratio by C, = 0.5eo. The possibility of obtaining such a relationship for Cochin marine clays in terms of liquid limit void ratio is indicated in this paper. Analysis of permeability behaviour of Cochin marine clays and the test results available in published literature using generalized state parameter approach show that, in principle, these forms of equations for the permeability index are tenable, even though they were obtained based on experimental observation alone. Key words: permeability index, initial void ratio, void ratio at liquid limit, generalized state parameter approach. L'indice de permCabilitC (Ck) similaire a l'indice de compression est la pente de la relation indice de vide - coeffi- cient de permkabilite. La litterature montre qu'en gCnCral pour les argiles sensibles, cet indice peut Ctre mis en relation avec l'indice des vides initial par Ck = 0,5e0. La possibilitC d'obtenir une telle relation pour les argiles marines de Cochin en termes de l'indice des vides a la limite de liquidit6 est indiquCe dans cet article. L'analyse du comportement de la permkabilite des argiles marines de Cochin et les rCsultats d'essais disponibles dans la 1ittCrature utilisant l'approche de parambtre d'Ctat genCralisC montrent qu'en principe ces formes d'equations pour I'indice de permCabilitC sont soutenables, mCme si elles ont CtC obtenues en partant d'observations experimentales seulement. Mots clPs : indice de permCabilitC, indice des vides initial, indice des vides a la limite de liquiditk, approche de parametre d'Ctat gCnCralisC. Can. Geotech. J. 30, 187-191 (1993) Introduction Permeability is one of the fundamental soil properties, and its importance is increasingly realized with the increas- ing interest in environmental geotechnical problems. In addi- tion, aspects like seepage, rate of settlement, and the associated stability and drainage problems are also basically controlled by this property. In the early stages, when engineers were concerned with augmenting groundwater sup- plies, they were primarily interested in measuring the per- meability of coarse-grained soils. The fine-grained soils from which extraction of groundwater is not economically feasi- ble were treated as almost impervious. However, in recent years, the need for understanding the permeability behav- iour of fine-grained soils has assumed considerable impor- tance, owing to their use in the construction of clay liners and slurry walls which impede the movement of leachates contaminating the groundwater. The accurate determination of coefficient of permeabil- ity is involved, time consuming, and difficult. Hence, often, recourse is taken to correlate the coefficient of permeabil- ity with some physical characteristics of soils which are easy to determine. For sands, the coefficient of permeability has been related with some success to the characteristics of grain- size distribution (Hazen 191 1; Loudon 1952; Kenny et al. 1984). However, attempts to find similar relationships for fine-grained soils, taking into consideration the effects of shape, tortuosity, and pore-size distribution (Olsen 1962; Garcia-Bengochea and Love11 198 1 ; Juang and Holtz 1986), have been less successful. Lapierre et al. (1990) conclude that, though there are a number of models for predicting the permeability of fine-grained soils, they are often not Printed in Canada / Imprime au Canada realistic. According to Lapierre et al., permeability is a global parameter and a function of many factors such as size of pores, shape of pore channels, tortuosity, mineralogy of the clay, and direction of flow. It is more advantageous to examine the permeability behaviour in terms of void ratio - coefficient of permeability relationships. Samaras- inghe et al. (1982) suggest that the relationship between coef- ficient of permeability and void ratio is not linear in all ranges of pressure and proposed a modified version of the Kozeny-Carman equation. By doing so, they intend to take into account the slight curvature observed in the e - log k data of some soils, particularly for larger variation of pressures. Mesri and Tavenas (1983) contend that, since many natural soils are seldom subject to such large varia- tions in stress, equations of the form proposed by Samaras- inghe et al. (1982) are seldom justified. According to Mesri and Tavenas, the merit of a linear e - log k relationship is to define permeability in terms of permeability index, defined as the slope of e - log k path, and relate it to changes in void ratio. The results presented by Mesri and Choi (1987) also show the existence of nonlinear behaviour between e and log k. Since the nonlinearity is not pro- nounced, it can be linearized without much loss of accuracy. Permeability index Tavenas et al. (1983a) studied the variation of coefficient of permeability with void ratio for Champlain clays, Canadian clays, and Swedish clays. They have suggested that in the range of strains normally encountered in practice, there exists a linear relationship between the void ratio and C an . G eo te ch . J . D ow nl oa de d fr om w w w .n rc re se ar ch pr es s. co m b y D ep os ito ry S er vi ce s Pr og ra m o n 11 /1 8/ 14 Fo r pe rs on al u se o nl y. 188 CAN. GEOTECH. J. VOL. 30, 1993 Initial void ratio, e,, 1.50- FIG. 1. Relationship between initial void ratio and permeabil- ity index. 0 0 0 Champlain clays 0 Other Canadian clays * Other clays ." /' - logarithm of coefficient of permeability given by [I] Ae = Ck A(log k) They termed the slope of this relationship the permeabil- ity index Ck, which is similar to the compression index C, and dependent on initial void ratio. Mesri and Rokshar (1974) have observed that the ratio of permeability index to compression index is in the range of 0.5-2.0 for a wide variety of natural soils. Tavenas et al. (1983a) and Leroueil et al. (1990) analyzed a considerable volume of data and as a first approximation suggest an equation of the form [2] Ck = o.5e0 where Ck is the permeability index, and eo is the initial void ratio. Figure 1 shows this relationship. This relationship is derived for sensitive soils (with liquidity indices more than unity). A similar relationship can be developed for normally consolidated soils. In this paper, the viability of these forms of equations is established from the generalized state parameter approach. 1 /' 0 z 1.00- u C .- >. d . - 4 . - 13 CI E k- 0.50- a, a Generalized state parameter approach The basis for the generalized state parameter approach is the experimental observation (Wroth and Wood 1978) that the liquid limit of all fine-grained soils corresponds to near- constant values of consolidation-suction pressures (5-6 kPa) and the shear strength properties (1.7-2.2 kPa) associated with it. This approach has received considerable attention in recent years and is found to be successful in explaining the consolidation and shear strength behaviour of normally consolidated soils (Nagaraj and Srinivasa Murthy 1983; Srinivasa Murthy et al. 1988; Pandian et al. 1991) and over- consolidated soils (Nagaraj and Srinivasa Murthy 1986). The near-unique values of shear strength and consolidation pressure at liquid limit water content are attributable to the existence of the same pattern of pore geometry at liquid limit. Analysis of the data of Griffiths and Joshi (1989) giv- ing pore-size distribution patterns at liquid limit state for four different soils suggests that at liquid limit state the pore- size distributions have the same pattern (Nagaraj et al. 1990). This indicates that coefficient of permeability, an indirect reflection of pore geometry, should also be in the same range for different soils at this state. This lends credence to using liquid limit as the normalizing parameter with respect to which permeability behaviour of fine-grained soils can be examined in the form of an equation given by e [3] - = c + d log k eL where c and d are constants, and eL is the value of void ratio at liquid limit water content. In the case of sensitive soils, the in situ void ratios are often more than liquid limit void ratios. These higher void ratios are as a result equilib- rium between the internal stresses, bonding among the aggregates of particles, and the external conditions. Hence, the in situ void ratio can be considered to represent the overall potential of the soil for further deformations and changes in coefficient of permeability. Hence [3] can be modified to e [4] - = cl + dl log k eo to represent the permeability behaviour of sensitive soils. The postulation that the coefficient of permeability is an indirect reflection of microstructure can be further strength- ened from the data of Tavenas et al. (1983a). They presented consolidation and permeability paths for sensitive clays. Their results indicate that there is no change in coefficient of permeability due to loading up to yield stress, since loading within this zone resulted in negligible changes in void ratio. In other words, there is no change in the effective pore geometry influencing the permeability. Beyond the yield stress, upon loading, there is appreciable compression affect- ing the pore geometry, leading to changes in the coefficient of permeability. This suggests that coefficient of permea- bility can be considered to represent the overall pore geometry of the soil under equilibrium conditions. Analysis of data pertaining to Cochin marine clays in the light of above postulations and the data available in published literature for sensitive soils, besides showing that these forms of equations are, in general, tenable, also permit the reexamination of the permeability index. Materials and methods Most of the area near Cochin in India consists of marine clays that have water contents close to liquid limit values. The samples were collected from two locations, viz., Parur and Wypeen, which are within 20 km of Cochin city. The peculiarity of these clays is that they are prone to changes in plasticity characteristics upon drying. Hence, samples from the natural state were collected using an auger and immediately transferred to polythene bags without permit- ting any loss of fines and exposure to the atmosphere. Polythene bags were sealed immediately, transported to the laboratory, and preserved under humid conditions. All the tests were conducted in a fully remolded condition. Permeability tests were carried out using conventional consolidation (fixed ring) cells. The sample is 60 mm in diameter and 20 mm in height. The soils were initially mixed at liquid limit state in the form of slurry and allowed for uniform distribution of moisture. They slurry was trans- C an . G eo te ch . J . D ow nl oa de d fr om w w w .n rc re se ar ch pr es s. co m b y D ep os ito ry S er vi ce s Pr og ra m o n 11 /1 8/ 14 Fo r pe rs on al u se o nl y. NOTE S o i l Wypeen clay Coefficient of permeability, k (cm/s) FIG. 2. (a) Relationship between void ratio and logarithm of coefficient of permeability for Cochin clays. (b) Relationship between (e/e,) and logarithm of coefficient of permeability. ferred to the consolidation rings and pressures applied. According to Tavenas et al. (1983b), analysis of clay foun- dations is better achieved in terms of consolidation and per- meability characteristics determined directly, rather than using the Terzaghi's solution based on compounded coeffi- cient of consolidation. Mesri and Tavenas (1983) showed that the magnitude of error involved in computing the coef- ficient of permeability using coefficient of consolidation is greater than that obtained using falling-head permeability test results. Hence, falling-head permeability tests were con- ducted in the present investigation. The samples were allowed to consolidate under each pressure and the falling- head permeability test performed. The flow is assumed to be entirely vertical and the coefficient of permeability calculated using the formula where a is the cross-sectional area of the burette, A is the cross-sectional area of the sample, L is the height of the sam- ple, ho is the initial excess head of water applied through the permeability burette at time t = 0, and hl is the excess head of water after time t. Load increment ratio of one was adopted for consolidation. Coefficient of permeability was measured at every load increment only after equilibrium is achieved. Results and discussion Figure 2a shows the e - log k paths for the two locations. The results when normalized with respect to the void ratios at the respective liquid limit values are shown in Fig. 2b. The normalized plot can be represented by an equation of the form with a correlation coefficient of 0.97. Differentiation of the above normalized equation gives This shows that, in principle, the permeability index can be determined from liquid limit void ratio also. The clays under examination are fully remoulded, and hence [8] can be taken to give the permeability index for uncemented soils. The data pertaining to sensitive soils from Tavenas et al. C an . G eo te ch . J . D ow nl oa de d fr om w w w .n rc re se ar ch pr es s. co m b y D ep os ito ry S er vi ce s Pr og ra m o n 11 /1 8/ 14 Fo r pe rs on al u se o nl y. CAN. GEOTECH. J. VOL. 30, 1993 FIG. 4. Relationship between (e/e,) and logarithm of coefficient of permeability for sensitive clays. Symbols as ir 1.0- 0.8 0.6 0.4 L Fig. 3. ---(go) ~ 3 . 7 5 rO.41 log k - - - I I I I 1 l I l l I I I I 1 l l l l I I I (1983a) and Leroueil et al. (1990) are examined in the fol- form lowing section. Figure 3 shows the e - log k paths presented e by Tavenas et al. and Leroueil et al. The path pertaining - = 3.75 + 0.41 log to each soil is distinct and all put together, there has been eo considerable scatter between the paths. As proposed earlier, and is in Fig. 4. eo represents the overall potential of these soils and can be Differentiation of the above normalized equation gives de considered as the normalizing parameter. The normalized - = 0.41 d(log k) path of these clays can be represented by an equation of the eo 1 0 - ~ lo-8 Coefficient of permeabil i ty, k (cm 1 s ) C an . G eo te ch . J . D ow nl oa de d fr om w w w .n rc re se ar ch pr es s. co m b y D ep os ito ry S er vi ce s Pr og ra m o n 11 /1 8/ 14 Fo r pe rs on al u se o nl y. NOTE 191 is close to the value given by [ 2 ] . Analysis of a greater volume of data in these lines would improve the numerical values given by [8] and [lo] presented in this paper. Concluding remarks The equation available for the permeability index can be said to be tenable, and its rationale can be established from the generalized state parameter approach. Further, in prin- ciple, the permeability index can be determined either from the void ratio at liquid limit for normally consolidated soils or from initial void ratio for sensitive soils. Further work in this direction with due recognition of the nature of cemen- tation bonds in normally consolidated and overconsolidated states and partially saturated states is required and can pro- vide a framework for examining the permeability behaviour of in situ soil systems. Acknowledgements This paper forms a part of the work carried out under the scheme Engineering Behaviour of Tropical Soils of India sponsored by the Central Board of Irrigation and Power, Ministry of Water Resources, New Delhi. The financial sup- port given by them is gratefully acknowledged. Garcia-Bengochea, I., and Lovell, C.W. 1981. 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