Geotechnical and Geological Engineering (2005) 23: 43–60
# Springer 2005
Hydraulic conductivity of remolded fine-grained soils versus index properties A. SRIDHARAN1, and H. B. NAGARAJ2 $
1
Department of Civil Engineering, Indian Institute of Science, Bangalore 560 012, India; e-mail:
[email protected] 2 BMS College of Engineering, Bangalore 560 019, India (Received 3 April 2003; revised 14 October 2003; accepted 28 October 2003) Abstract. Hydraulic conductivity is a dominant parameter in the design of engineered waste disposal facilities such as landfill liners and covers, lagoon liners and slurry walls. It is of interest to a geotechnical or geo-environmental engineer to develop a predictive method of determining the hydraulic conductivity of fine-grained soils, in order to assess its suitability as a liner material. To predict the hydraulic conductivity of soils, researchers and geotechnical engineers have attempted to correlate it with index properties of the soils, such as the liquid limit, void ratio and specific surface. Based on the present study a predictive method has been developed in this paper to predict the hydraulic conductivity in terms of void ratio and shrinkage index (Liquid limit – shrinkage limit) for remoulded fine-grained soils. Though the initial conditions for the soil will affect the hydraulic conductivity behaviour to some extent, both the void ratio and soil characteristics are primary factors in affecting the hydraulic conductivity. Therefore for predictive purpose, the study of hydraulic conductivity behaviour of remoulded fine-grained soils as presented in this paper can be found to be useful for compacted soils also. Key words. clays, drainage, hydraulic conductivity, laboratory tests, permeability.
1. Introduction Hydraulic conductivity is one of the important basic engineering properties of soils. It governs such engineering problems as the ground water regime in stratified deposits, or near natural and excavated slopes, the flow of fluids through or around engineered structures, the consolidation of clay foundations under applied loads, or the migration of pollutants from waste disposal facilities (Tavenas et al., 1983). With increased industrialization and urbanization, the production of wastes has increased to a great extent. Disposal of wastes in an acceptable manner has been of growing concern to the public the world over. One of the most significant concerns has been the possible contamination of ground water by leachates generated by wastes. This leads to a change in the pore medium chemistry of the surrounding soil. The practice of containing contaminants in shallow land waste disposal facilities and the need to protect ground water against potential contamination have led to $
Corresponding author.
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A. SRIDHARAN AND H. B. NAGARAJ
construction of engineered disposal facilities such as landfill liners and covers, lagoon liners and slurry walls. The design of such facilities should ensure their structural integrity and minimize the potential dangers associated with migration of the contaminants. To contain the contaminants, compacted fine-grained soils are often used as earthen liners in these facilities. Hydraulic conductivity is a dominant parameter in the design of such disposal facilities. One of the main interests to a geotechnical or geo-environmental engineer is to develop a predictive method of determining the hydraulic conductivity of fine-grained soils, especially of clayey soils, in order to asses its suitability as a liner material. Fine grained soils, when used as a landfill liner material, are placed in a compacted condition to the required density. The hydraulic conductivity behaviour of such compacted soil depends on the fabric condition of the soil, which in turn depends on the moisture content at which the soil is compacted. If the soil is compacted dry of optimum, it results in a relatively flocculated structure that will result in a high hydraulic conductivity compared to a soil compacted to the same density but wet of optimum having a dispersed structure (Lambe, 1955). Sufficient literature can be found on the hydraulic conductivity behaviour of clays studied for various soil and environmental factors affecting it (e.g., Benson and Daniel, 1990, Benson et al., 1995; Daniel, 1984; Mitchell et al., 1965; Viklander, 1998). The hydraulic conductivity behaviour of compacted soils can be different from that of remoulded clays due to the fact that the initial placement conditions of the soil namely soil fabric and degree of saturation will be different. It may be noted that though the initial conditions of the soil will affect the hydraulic conductivity behaviour to some extent, both the void ratio and soil characteristics are primary factors in affecting the hydraulic conductivity of soils. Therefore for predictive purpose, the study of hydraulic conductivity behaviour of remoulded clays as presented in this paper can be found to be useful for compacted soils also.
2. Literature review Study of the literature shows that only a limited study is done to correlate the hydraulic conductivity of fine-grained soils with simple index parameters. Atterberg limits are the most relevant index parameters or properties used for the prediction of fine-grained soil behaviour. Probably the correlative work to predict the hydraulic conductivity behaviour of fine-grained soils was that by Nagaraj et al. (1993). Based on the experimental work done on four normally consolidated clays, they have tried to generalize the prediction of the coefficient of hydraulic conductivity in terms of void ratio at the liquid limit given as: e ¼ 2:28 þ 0:233 log k eL
ð1Þ
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45
where e ¼ void ratio, eL ¼ void ratio at the liquid limit, and k ¼ hydraulic conductivity in cm/s. Stepkowsa et al. (1995) studied the hydraulic conductivity of dredged sludge and found that the generalized relation Equation (1) presented by Nagaraj et al. is not applicable to the sludges studied, and explained the reason being the difference by their microstructure. Recently, Sivappullaiah et al. (2000) have proposed a method for predicting hydraulic conductivity of sand–bentonite mixtures from their void ratio (e) and liquid limit (wL ) given by the following equation: log10 k ¼
e 0:0535ðwL Þ 5:286 0:0063ðwL Þ þ 0:2516
ð2Þ
where k ¼ hydraulic conductivity in m/s. However, the main limitation of the above equation is that it is valid for soils of liquid limit greater than 50%. Attempts have also been made to correlate hydraulic conductivity with surface area through the Kozeny–Carman equation (Santamarina et al., 2002) expressed as: k¼
S2
1 y gw e3 Z rs 2 1 þ e
ð3Þ
where k ¼ hydraulic conductivity, y ¼ shape and turtuosity factor, gw ¼ unit weight of water, e ¼ void ratio, S ¼ specific surface area, rs ¼ density of the material that makes up the grain and Z ¼ fluid viscosity. Researchers have also attempted to correlate specific surface with liquid limit (Farrar and Colmean, 1967; Muhunthan, 1991). One could try to predict hydraulic conductivity knowing liquid limit through a correlation between specific surface and liquid limit. Though specific surface of a soil is a valuable index property for the characterization of fine-grained soils and that liquid limit could be correlated with specific surface area, it has a serious limitation that, for the same soil with surface area, liquid limit could be different depending upon the exchangeable ion present. It can be seen that limited attempts have been made to predict the hydraulic conductivity of fine-grained soils through the index properties, and the generalization of the prediction has shown to be not fully satisfactory. In the light of the fact that soils having the same or nearly the same liquid limit but different plasticity properties are expected not to behave in the same way (Sridharan and Nagaraj, 2000), it is desirable to investigate which of the plasticity properties of soils indicated by Atterberg limits and the indices, namely plasticity index, shrinkage index (Liquid limit–shrinkage limit) (Sridharan and Nagaraj, 2000), correlate well with the hydraulic conductivity of soils. In this paper an attempt has been made in detail to examine which index property/consistency indices correlate better with the coefficient of hydraulic conductivity.
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3. Materials and methods Since soil type is also important in studying the hydraulic conductivity behaviour, ten soils including a number of natural soils along with commercially available kaolinite were selected covering liquid limits ranging between 37% and 74% and also representing the three extreme clay mineral types namely kaolinite, illite and montmorillonite. Also due attention was given to select pairs of soils with nearly the same liquid limit values, but having different plasticity properties. This was done to bring out the effect of plasticity characteristics on the hydraulic conductivity behaviour of fine-grained soils. The physical properties of the soils are reported in Table 1. The specific gravity was determined using a pycnometer (stoppered bottle having a capacity of 50 ml) as specified by British Standards BS 1377 (British Standards Institution, 1990). The specific gravity values are an average of three tests; individual determinations differed from the mean by less than 0.01. The liquid limit of soils was determined by the cone penetrometer method as specified by British Standards 1377 (British Standards Institution, 1990). The liquid limit tests were carried out to obtain a minimum of five points for plotting the flow curve. The consistency of the soil specimens was adjusted such that the cone penetration ranged between 15 and 25 mm. The plastic limit of the soil specimens was determined by the rolling thread method as outlined in the British Standards BS 1377 (British Standards Institution, 1990). The shrinkage limit of soil specimens was determined as per British Standards BS 1377 (British Standards Institution, 1990). The shrinkage limits reported are the average of three determinations; the variation between individual determination was less than 0.5%. Grain-size analysis was done as per British Standards BS 1377 (British Standards Institution 1990), by wet sieving of 100 g of oven dry soil using a 75 mm sieve. The portion retained on the 75 mm sieve was oven dried and sieved using sieves of 300, 212, and 150 mm sizes. The soil passing through 75 mm was collected carefully, air-dried, and the grain-size distribution analysis was performed by the hydrometer method. The results are presented in Table 1. The mineralogical analysis of the soils was performed using an X-ray diffractometer with Cu-ka radiation. The main clay minerals present in the soils are given in Table 1. 3.1.
HYDRAULIC CONDUCTIVITY TESTS
The hydraulic conductivity test on soils was done by falling head test in the standard one-dimensional consolidation apparatus after the end of each pressure increment. Carrying out the hydraulic conductivity test using consolidation apparatus is quite simple, and one can get different values of void ratio for the sample by consolidating it to different pressures. The reproducibility of the results is also good. The hydraulic gradient, i, used in the tests was 35. The consolidation test on the selected soils was conducted in standard fixed ring consolidometers using stainless steel rings, 60 mm in diameter and 20 mm high as
Silty soil – 1 Kaolinite – 1 Red Earth – 2
Kaolinite – 2 Cochin clay Brown soil – 1
Kaolinite – 3 Illitic soil
B C soil – 1
2 3 4
5 6 7
8 9
10
2.70
2.65 2.58
2.64 2.61 2.66
2.65 2.65 2.70
2.70
Gs
73.5
58.7 73.4
55.0 56.4 58.5
39.0 48.0 48.0
37.0
wL (%)
35.6
45.2 51.9
31.4 38.1 32.1
29.5 35.6 23.2
18.0
wP (%)
11.9
46.4 39.0
33.1 21.0 13.5
27.4 39 15.5
14.7
wS (%)
37.9
13.5 21.5
23.6 18.3 26.4
9.5 12.4 24.8
19.0
IP (%)
61.6
12.3 34.4
21.9 35.4 45.0
11.6 9.0 32.5
22.3
IS (%)
1.98
1.56 1.89
1.45 1.47 1.56
1.03 1.27 1.29
0.99
eL
0.32
1.23 1.01
0.87 0.55 0.36
0.73 1.03 0.42
0.39
eS
13.0
0.0 0.9
1.0 18.0 19.5
36.5 16.0 8.0
35.5
Sand (%)
35.5
88.5 71.6
67.0 64.5 42.5
58.5 74.5 57.0
38.5
Silt (%)
51.5
11.5 27.5
32.0 17.5 35.0
5.0 9.5 35.0
26.0
Clay (%)
Grain size distribution
Kaolinite, montmorillonite, muscovite, quartz Illite, quartz Kaolinite, quartz Kaolinite, montmorillonite, muscovite, quartz Kaolinite, quartz Illite Montmorillonite, kaolinite muscovite, quartz Kaolinite, quartz Illite, kaolinite, quartz Montmorillonite, quartz
Mineralogy
Note: *G¼ s Specific gravity; wL ¼ Liquid limit; wP ¼ Plastic limit; wS ¼ Shrinkage limit; IP ¼ Plasticity index; IS ¼ Shrinkage index; eL ¼ Void ratio at liquid limit; eS ¼ Void ratio at shrinkage limit.
Red Earth–1
Soil type
Index properties of soils used
1
Soil no.
Table 1
REMOLDED FINE-GRAINED SOILS VERSUS INDEX PROPERTIES
47
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A. SRIDHARAN AND H. B. NAGARAJ
per ASTM Standard Test Method for One-Dimensional Consolidation properties of soils (D 2435-90, 1995). The inside of the rings was lubricated with silicone grease to minimize side friction between the ring and the soil specimen. The consolidation tests were conducted in a room maintained at a uniform temperature of 20 1 C. Taking into consideration initial moisture content, which is an important parameter controlling the compressibility, the soil specimens were remoulded at their respective liquid limit. The initial water content was set equal to the liquid limit, primarily because, it is the extreme limiting water content above which the soil is about to flow. These soil specimens were hand remoulded in the consolidation rings to a thickness of 20 mm, taking care to prevent any air entrapment in the specimens. Filter papers were positioned on the top and bottom of the soil specimens to prevent particles from being forced into the pores of the porous stones placed on both sides of the specimen. The porous stones were kept in distilled water for sufficient time, and were used in damp condition to avoid absorption of water from the sample. Each ring with the sample prepared as described above was placed in a consolidation cell and screwed tightly to the close fitting metal jacket on top of the cell. The cell was next mounted and positioned on a loading frame with a vertical deflection dial gauge properly adjusted and fixed in position to give proper dial reading under application of load. The cell was inundated with distilled water and a nominal load of 6.25 kPa was applied. Care was taken to replenish any evaporated water. After equilibrium was attained as indicated by the nearly constant readings on the dial gauge, conventional oedometer tests were carried out. A load increment ratio of unity was adopted and each load maintained until near equilibrium had been attained. For each load increment after the nearly the end of primary consolidation was completed i.e., after nearly 24 hours, the hydraulic conductivity measurements were done and continued for a maximum of two days to obtain sufficient readings. Each soil specimen was loaded to a maximum of 800 kPa and later unloaded with a load decrement ratio of unity.
4. Results and discussion In this investigation apart from liquid limit, wL , plasticity index, IP and shrinkage index, IS (which is equal to the difference between liquid limit and shrinkage limit) (Sridharan and Nagaraj, 2000) have been studied in the correlation with the hydraulic conductivity. Based on the results from an extensive experimental program, Sridharan and Prakash (1998, 2000) have shown that the shrinkage limit of a soil is not controlled by the plasticity characteristics of the soil. Further, they have shown that shrinkage limit of a natural soil is primarily a result of the soil packing phenomenon, which in turn is a function of the grain size distribution of the soil, irrespective of the main clay mineral of the soil. Thus, the shrinkage index may be viewed as representing both the water holding capacity of the soil represented by the liquid limit of the soil on one extreme and the grain size distribution of the soil represented by the shrinkage limit on the other extreme, and hence, the soil type.
REMOLDED FINE-GRAINED SOILS VERSUS INDEX PROPERTIES
49
Figure 1 shows typical log k–e plots of two pairs of soils having nearly the same liquid limit (39%, 37% and 58.7%, 58.5%) but different plasticity properties. It can be seen that there is more than one order of variation in log k–e behaviour of the two soils even though their liquid limits are nearly equal. Similar variations were obtained for 3 more pairs of soils having nearly the same liquid limit namely 48%, 48%; 55%, 56.4%; and 73.4%, 73.5%, but differing in their plasticity properties.
Figure 1 Hydraulic conductivity versus void ratio relationship for two sets of two soils each having liquid limit approximately 38% and 58%
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A. SRIDHARAN AND H. B. NAGARAJ
Figure 2 Hydraulic conductivity versus void ratio relationship for two sets of two soils each having plasticity index approximately 19% and 24%
Figure 2 shows log k–e plots of two pairs of soils having nearly the same plasticity index. These figures also show variation in the hydraulic conductivity, but the variation is less as compared with the variation in the hydraulic conductivity for soils of nearly the same liquid limits. Figures 3a,b show log k–e plots of pairs of soils having nearly the same shrinkage index, from which it can be observed that all the soils having nearly the same shrinkage index have almost similar log k–e behaviour. Also it can be observed that the log k–e curves are non-linear as reported in the literature
REMOLDED FINE-GRAINED SOILS VERSUS INDEX PROPERTIES
51
Figure 3 (a) Hydraulic conductivity versus void ratio relationship for a set of two soils having shrinkage index approximately 22%; (b) Hydraulic conductivity versus void ratio relationship for a set of two soils having shrinkage index approximately 34%
for remoulded fine-grained soils (Ansary et al., 1999; Mesri and Olsen, 1971; Raymond, 1966; Samarasinghe et al., 1982; Tavenas et al., 1983). Further, to verify which of the index properties correlates well with the hydraulic conductivity, the values of hydraulic conductivity for all the ten soils at the void ratios e ¼ 0:75 and e ¼ 1:0 were selected from the log k–e plots, and plotted against the liquid limit, plasticity index and shrinkage index as shown in Figures 4a,b; 5a,b
52
A. SRIDHARAN AND H. B. NAGARAJ
Figure 3 (Continued)
and 6a,b, respectively. From these figures, it is clear that there is a good correlation of hydraulic conductivity with shrinkage index, better than with the plasticity index. However, the correlation of hydraulic conductivity with the liquid limit is poor. Thus, it is clear that the shrinkage index correlates well with the hydraulic conductivity of soils with water as the pore medium. However, the limitation of the correlation of hydraulic conductivity with shrinkage index is that the correlation equations (Figures 6a,b) are applicable at that particular void ratios of e ¼ 0:75 and e ¼ 1:0. If the hydraulic conductivity is required at any other void ratio, it is
REMOLDED FINE-GRAINED SOILS VERSUS INDEX PROPERTIES
53
Figure 4 Hydraulic conductivity versus liquid limit relationship (a) at void ratio, e ¼ 0:75 and (b) at void ratio, e ¼ 1:0
not possible to predict the hydraulic conductivity. This shortcoming can be overcome by adopting the model suggested by Samarasinghe et al. (1982), incorporating in it the correlation of hydraulic conductivity with shrinkage index of soils, as described in the following paragraphs.
Figure 5 Hydraulic conductivity versus plasticity index relationship (a) at void ratio, e ¼ 0:75 and (b) at void ratio, e ¼ 1:0
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A. SRIDHARAN AND H. B. NAGARAJ
Figure 6 Hydraulic conductivity versus shrinkage index relationship (a) at void ratio, e ¼ 0:75 and (b) at void ratio, e ¼ 1:0
Samarasinghe et al. (1982) suggested a model to predict the hydraulic conductivity of normally consolidated remoulded clays. The relationship is as follows: x e ð4Þ k¼C 1þe They named the exponent x and C as permeability parameters. A plot of log ½kð1 þ eÞ versus log e may be interpreted as a straight line with a slope x and an intercept log C (e.g. Figure 7a). This model gives a linear relationship between the hydraulic conductivity and ex =1 þ e as compared to the non-linear relationship got by log k e plot. However, to use this model as a predictive tool, it is essential to know the coefficients x and C. If these coefficients could be correlated with any of easily determinable index parameters, then the above model would be very handy in the prediction of hydraulic conductivity of fine-grained soils. Figure 7(a) is a plot of log ½kð1 þ eÞ versus log e for soil 1. The slope of the straight line fit gives the parameter x ¼ 5:16. With x ¼ 5:16, the values of ex =1 þ e at different void ratios as obtained from the experimental results are calculated. Then a plot of the measured hydraulic conductivity versus the corresponding values of ex =1 þ e as calculated above are plotted as shown in Figure 7(b). The slope of the straight-line fit gives the parameter C, which has the same units as that of the hydraulic conductivity, k. The same procedure was repeated for the other nine soils. The values of x and C for the ten soils are tabulated in Table 2. From the table, it can be seen that x values are found to vary from 3.97 to 6.39, with an average value approximately
55
REMOLDED FINE-GRAINED SOILS VERSUS INDEX PROPERTIES
Figure 7 (a) log ½kð1 þ eÞ versus log e plot and (b) k versus ex =ð1 þ eÞ plot for red earth-1 (Soil No.1)
equal to 5. C values range from 0:68 1010 m/s to 684 1010 m/s. While x varies marginally (1.6 times), C varies more than 1000 times. Figures 8(a) to (c) show the plot of the parameter C versus the liquid limit, plasticity index and shrinkage index, respectively. It can be seen that the parameter C correlates best with shrinkage index (Figure 8c), given by the equation: C ¼ 2:5 104 ðIS Þ3:69
ðin m=sÞ
ð5Þ
The correlation of the permeability parameter, C with the plasticity index (Figure 8b) is also good, but not as good as with the shrinkage index. The correlation of C with the liquid limit is poor (Figure 8a). Table 2 Permeability parameters of the fine-grained soils used in the study of hydraulic conductivity of normally consolidated reconstituted soils by Samarasinghe’s method
Soil no. 1 2 3 4 5 6 7 8 9 10
Soil description
Exponent x
Factor C ð1010 m/s)
Red earth – 1 Silty soil – 1 Kaolinite – 1 Red earth – 2 Kaolinite – 2 Cochin clay (oven dried) Brown soil – 1 Kaolinite – 3 Illitic soil BC soil – 1
5.16 4.04 3.97 4.40 4.10 6.39 5.74 4.42 6.37 5.92
13.90 444.00 684.00 5.80 36.20 5.18 2.70 240.00 4.49 0.68
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A. SRIDHARAN AND H. B. NAGARAJ
Figure 8 Relationship between the permeability parameter, C obtained by Samarasinghe et al’s method and (a) Liquid limit (b) Plasticity index (c) Shrinkage index
REMOLDED FINE-GRAINED SOILS VERSUS INDEX PROPERTIES
57
Figure 9 Relationship between the permeability parameter, x obtained by Samarasinghe et al’s method and (a) Liquid limit (b) Plasticity index (c) Shrinkage index
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A. SRIDHARAN AND H. B. NAGARAJ
Figure 10 Predicted hydraulic conductivity for x ¼ 4 versus measured hydraulic conductivity
Figures 9(a) to (c) show the plot of the parameter x versus the liquid limit, plasticity index and shrinkage index, respectively. It can be seen that the best correlation is that with the shrinkage index (Figure 9c) as compared to the liquid limit or the plasticity index as is given by: x ¼ 3:79 þ 0:044 IS
ð6Þ
Samarasinghe et al. (1982) carried out direct permeability tests and incremental loading consolidation tests on artificially sedimented normally consolidated sandy clay to verify their model represented by Equation (4) and also compared the data from Raymond (1996). For the soils from their study and data from the literature, they found the value of x to be fairly constant, around 5. Statistically the most suitable or probable value of x to be used for prediction of the hydraulic conductivity was determined as explained in the following paragraph. The hydraulic conductivity was predicted as calculated from Equation (4): In Equation (4), different values of x varying around the average value of 5, namely x ¼ 3; 4; 4:5; 5; 6 and 7 have been chosen for all soils. The value of x has also been evaluated using Equation 6 and used in Equation (4). The value of C for the
REMOLDED FINE-GRAINED SOILS VERSUS INDEX PROPERTIES
59
Table 3 Standard Error of Estimate for various values of exponent Exponent x x ¼ 3:79 þ 0:044 IS 3 4 4.5 5 6 7
Standard error of estimate (m/s) 23:26 1010 32:15 1010 24:34 1010 27:13 1010 33:19 1010 50:67 1010 85:63 1010
respective soils was obtained from Equation (5). Thus, using Equation 4, the values of k were calculated for various values of x and a particular value of C for each soil (Equation 5). The values of predicted hydraulic conductivity ðkP Þ thus obtained were plotted against the measured values of hydraulic conductivity ðkM Þ for the different values of x. A typical plot for x ¼ 4 is presented in Figure 10. Table 3 shows the standard error of estimate for various values of x chosen here. It can be seen from Table 3 that the SEE is the lowest for the x value obtained from the equation relating the shrinkage index (Equation 6), being equal to 23:26 1010 m/s, and is the maximum for x ¼ 7, being equal to 85:63 1010 m/s. As already discussed, the x value is found to vary within a narrow range, so, it was felt by the authors that a better value of x could be selected, avoiding the use of the correlative equation (Equation 6) with the shrinkage index to determine x without sacrificing the predictive accuracy of the hydraulic conductivity. From Table 3, it can be seen that x ¼ 4 has the least Standard error of estimate, being equal to 24:34 1010 m/s, as compared with the standard error of estimate obtained with x ¼ 3; 4:5; 5; 6 and 7, indicating that x ¼ 4 is the most suitable value. Hence, the value of x ¼ 4 is recommended for prediction of the hydraulic conductivity. However, the parameter C is obtained from Equation 5 knowing the value of the shrinkage index of the soil.
5. Conclusions Soils having nearly the same liquid limit but different plastic and shrinkage limits have shown to have wide variation in their k–e relationship. At any void ratio, the correlation of the hydraulic conductivity of soils is best with shrinkage index fIS ¼ ðwL wS Þg, irrespective of their liquid and plastic limits. A method based on Samarasinghe et al’s model (1982) has been proposed to predict the hydraulic conductivity of the soils taking into consideration its void ratio, liquid limit and shrinkage limit. Shrinkage limit happens to be a function of grain size distribution only in terms of the shrinkage index. The relationship between the hydraulic conductivity and the void ratio could be expressed as Equation (4). x e k¼C 1þe
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A. SRIDHARAN AND H. B. NAGARAJ
where x ¼ 4 and C ¼ 2:5 104 ðIS Þ3:69 and C is the soil parameter represented by the shrinkage index, IS ¼ ðwL wS Þ.
References Ansary, M.A., Siddique, A. and Sarullah, A.M.M. (1999) Compressibility and permeability characteristics of selected coastal soils of Bangladesh, Indian Geotechnical Journal, 29(2), 162–185. Benson, C.H. and Daniel, D.E. (1990) The influence of clods on the hydraulic conductivity of a compacted clay, Journal of Geotechnical Engineering ASCE, 116(8), 1231–1248. Benson, C.H., Abichou, T., Olson, M. and Bosscher, P. (1995) Winter effects on the hydraulic conductivity of compacted clay, Journal of Geotechnical Engineering ASCE, 121(1), 67–79. British Standards Institution. (1990) British standard methods of test for engineering purposes, BS 1377, Part 2: Classification tests. British Institution, London. Daniel, D.E. (1984) Predicting hydraulic conductivity of clay liners, Journal of Geotechnical Engineering ASCE, 110(2), 285–300. Farrar, D.M. and Coleman, J.D. (1967) The correlation of surface area with other properties of nineteen British clay soils, Journal of Soil Science, 18, 118–124. Lambe, T.W. (1955) The permeability of compacted fine grained soils, ASTM, Special Technical Publication No. 163. Mesri, G. and Olson, F.E. (1971) Mechanisms controlling the permeability of clays, Clay and Clay minerals, 99, 151–158. Mitchell, J.K., Hooper, D.R. and Campanella, R.G. (1965) Permeability of compacted clay, Journal of Soil Mechanics and Foundations Division ASCE, 91 (SM4), 41–65. Muhunthan, B. (1991) Liquid limit and surface area of clays, Geotechnique, 41(1), 135–138. Nagaraj, T.S., Pandian, N.S. and Narasimha Raju, P.S.R. (1993) Stress state-permeability relationships for fine-grained soils, Geotechnique, 43(2), 333–336. Raymond, G.P. (1996) Laboratory consolidation of some normally consolidated soils, Canadian Geotechnical Journal, 3(4), 217–234. Samarasinghe, A.M., Huang, Y.H.F. and Drnevich, V.P.M. (1982) Permeability and consolidation of normally consolidated soils, Journal of the Geotechnical Engineering Division, Proceedings of ASCE, 108(6), 835–850. Santamarina, J.C., Klein, K.A., Wang, Y.H. and Prencke, E. (2002) Specific surface: determination and relevance, Canadian Geotechnical Journal, 39(2), 233–241. Sivappulaiah, P.V., Sridharan, A. and Stalin, V.K. (2000) Hydraulic conductivity of bentonite-sand mixtures, Canadian Geotechnical Journal, 37(2), 406–413. Sridharan, A. and Prakash, K. (1998) Mechanism controlling the shrinkage limit of soils, Geotechnical Testing Jl., 21(3), 240–250. Sridharan, A. and Prakash, K. (2000) Shrinkage limit of soil mixtures, Geotechnical Testing Jl., 23(1), 3–8. Sridharan, A. and Nagaraj, H.B. (2000) Compressibility behaviour of remoulded, fine-grained soils and correlation with index properties, Canadian Geotechnical Journal, 37(2), 712–722. Stepkowsa, E.T., Thorborg, B. and Wichman, B. (1995) Stress state-permeability relationships for dredged sludge and their dependence on microstructure, Geotechnique, 45, 307–316. Tavenas, F., Leblond, P., Jean, P. and Leroueil, S. (1983) The permeability of natural soft clays. Part I: Methods of laboratory measurement, Canadian Geotechnical Journal, 20, 629–644. Viklander, P. (1998) Permeability and volume changes in till due to cyclic freeze-thaw. Canadian Geotechnical Journal, 35(3), 471–477.
