ESTIMATING HYDRAULIC CONDUCTIVITY OF

ESTIMATING HYDRAULIC CONDUCTIVITY OF COMPACTED CLAY LINERS By Craig H. Benson, 1 Associate Member, ASCE, Huaming Zhai, 2 and Xiaodong Wang 3 ABSTRAC...
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ESTIMATING HYDRAULIC CONDUCTIVITY OF COMPACTED

CLAY LINERS

By Craig H. Benson, 1 Associate Member, ASCE, Huaming Zhai, 2 and Xiaodong Wang 3 ABSTRACT: A database is described that contains laboratory measurements of

hydraulicconductivity and associated soil properties that were extracted from construction reports for compacted soil liners. The database contains measurements conducted on a wide variety of soils from 67 landfills in North America. The database was used to evaluate relationships between hydraulic conductivity, compositional factors, and compaction variables and to identify minimum values for soil properties that are likely to yield a geometric mean hydraulic conductivity -7, the percent fines (30%, and the percent clay (15%. A multivariate regression equation was also developed that can be used to estimate the geometric mean hydraulic conductivityas a function of soil composition and compaction conditions. INTRODUCTION

Compacted soil liners are widely used as hydraulic barriers in wastecontainment facilities. To be effective, a c o m p a c t e d soil liner should have low hydraulic conductivity, which in m a n y cases is considered to be less than 1 • 10 -7 cm/s. In recent years, guidelines have been compiled for selecting appropriate soil properties and compaction methods that are likely to result in low hydraulic conductivity ( G o r d o n et al. 1984; Daniel 1990). These guidelines are typically based on experience and generally include minimum values or acceptable ranges for properties that describe composition of soil (e.g., A t t e r b e r g limits, particle-size distribution) and recommendations for selection of compaction criteria (i.e., control of water content and dry unit weight) and compaction machinery. The purpose of this p a p e r is to present data collected from actual soil liners that can be used to support and refine guidelines in current use. The paper is not meant to be a theoretical treatise on factors affecting hydraulic conductivity; numerous fundamental studies on hydraulic conductivity of compacted clay have been p r e s e n t e d elsewhere ( L a m b e 1954; Mitchell et al. 1965; Garcia-Bengochea et al. 1979; A c a r and Oliveri 1989; Benson and Daniel 1990). Instead, the p a p e r is m e a n t to be a practical guide that shows how basic soil properties and compaction conditions normally monitored during construction quality control of soil liners are related to hydraulic conductivity. A database is used to explore the relationship between hydraulic con1Asst. Prof., Dept. of Civ. and Envir. Engrg., Univ. of Wisconsin, Madison, WI 53706. aRes. Assoc., Dept. of Civ. and Envir. Engrg., Univ. of Wisconsin, Madison, WI. 3Res. Scientist, Dept. of Civ. and Envir. Engrg., Univ. of Wisconsin, Madison, WI. Note. Discussion open until July 1, 1994. To extend the closing date one month, a written request must be filed with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on May 14, 1992. This paper is part of the Journal of Geotechnical Engineering, Vol. 120, No. 2, February, 1994. 9 ISSN 0733-9410/94/0002-0366/$1.00 + $. 15 per page. Paper No. 4052. 366

ductivity, compositional factors of the soil, and compaction conditions. The data were collected from 67 landfills at various locations in North America. Graphs and multivariate regression are used to identify compositional and compaction variables that correlate with hydraulic conductivity. Results of the graphical and regression analyses are used to: (1) Define minimum values for soil properties that will yield hydraulic conductivity - 1 x 10 - 7 cm/s; (2) identify compaction conditions that yield low hydraulic conductivity; and (3) identify important variables to control during construction of soil liners. FACTORS AFFECTING HYDRAULIC CONDUCTIVITY

In his initial studies on the engineering behavior of compacted clay, Lambe (1954) stated that five factors had the greatest influence on hydraulic conductivity: (1) Soil composition; (2) permeant characteristics; (3) void ratio; (4) structure; and (5) degree of saturation during permeation. Subsequently, numerous other investigators have studied these factors in detail (Lambe 1954; Bjerrum and Huder 1957; Mitchell et al. 1965; Barden and Sides 1970; Garcia-Bengochea et al. 1979; Acar and Oliveri 1989; Benson and Daniel 1990). The scope of this paper is focused primarily on two of these factors, namely soil composition and structure. SOIL COMPOSITION

Atterberg Limits The Atterberg limits are indices of the quantity of clay-size particles and their mineralogical composition. Typically, higher liquid limit and plasticity index are associated with soils having a greater quantity of clay particles or clay particles having higher surface activity (Mitchell 1976). Consequently, a relationship between hydraulic conductivity and the Atterberg limits is expected (Terzaghi 1925). In particular, all other factors being equal, more plastic clays (i.e., having higher liquid limit or plasticity index) should have lower hydraulic conductivity. Lambe (1954) showed the sensitivity of hydraulic conductivity to plasticity by presenting hydraulic conductivities for several different clays. The hydraulic conductivity measurements were conducted in consolidometers on normally consolidated sedimented specimens. The data showed that for a given void ratio monovalent montmorillonite (e.g., sodium) had the lowest hydraulic conductivity, followed by divalent montmorillonite (e.g., calcium), attapulgite, and kaolinite. Although Atterberg limits for the clays were not presented by Lambe (1954), their plasticity typically decreases in the following order: monovalent montmorillonite > divalent montmorillonite > attapulgite > kaolinite (Mitchell 1976). A distinct trend of decreasing hydraulic conductivity with increasing plasticity was also presented by Mesri and Olson (1971). They investigated how the hydraulic conductivity of three clays was related to clay type, void ratio, and permeant chemistry. They back-calculated hydraulic conductivities from consolidation tests on normally consolidated specimens using Terzaghi's consolidation theory. The specimens were kaolinite, illite, or smectite and had plasticity indices of approximately 20, 60, and 500. The specimens were consolidated from homoionic slurries that were prepared by repeated washing with concentrated solutions of sodium chloride or calcium chloride. At a void ratio of 2.0, they measured hydraulic conductivities (when permeated with water) of 1.5 x 10 -6 (kaolinite), 2 x 10 -9 (illite), and 1 x 10 -11 (montmorillonite) cm/s. They explained that the clays with a higher plasticity 367

index had smaller particles, less aggregation, and thicker double layers. These factors combined to yield lower hydraulic conductivity. A similar relationship between hydraulic conductivity and plasticity should exist for clays compacted wet of optimum water content, where flow is affected primarily by the size and shape of microscale pores. Nevertheless, a trend of decreasing hydraulic conductivity with increasing plasticity cannot be assumed a priori, because sedimented clays and compacted clays are formed by vastly different processes. Ideally, data from studies in literature could be compiled to determine if a trend exists, but because procedures used for compaction and permeation have differed substantially over the years, a direct comparison between results obtained by various investigators is difficult to make. Particle-Size Distribution

The particle-size distribution of compacted clay affects hydraulic conductivity because the size of voids conducting flow is affected by the relative proportions of large and small particle sizes. Low hydraulic conductivity is likely to be achieved when the soil is well graded and the clay fraction governs the hydraulic behavior of the matrix.

Percentageof Clay Daniel (1987) presented a graph of hydraulic conductivity versus percent bentonite for a sand-bentonite mixture. He found that hydraulic conductivity decreased significantly (10 -4 to 10 -8 cm/s) as the percentage of bentonite was increased from 0% to 8%. At higher bentonite contents, however, little further reduction in hydraulic conductivity occurred. Similar results have been observed by Kenney et al. (1992), who compacted and permeated sand-bentonite mixtures at various molding water contents. For water contents wet of optimum, hydraulic conductivity was very sensitive to bentonite content when the bentonite content was less than 12% and insensitive for bentonite contents exceeding 12%. The low hydraulic conductivities achieved at bentonite contents exceeding 8-12% occurred because clay-size particles filled voids between the sand particles and controlled the hydraulic behavior of the soil. Effectively, the soil was behaving hydraulically as a clay even though it was principally composed of sand size particles. This behavior is consistent with findings of Seed et al. (1964), who found that mixtures of sand and bentonite changed from nonplastic to plastic at bentonite contents near 10%.

Percentageof Fines D'Appolonia (1980) evaluated how the percentage of fines (particles smaller than the No. 200 sieve) affected the hydraulic conductivity of soil-bentonite slurries. He found that hydraulic conductivity decreased as the percentage of fines increased even when the percentage of fines was substantial (>30%). He also found that slurries containing plastic fines typically had hydraulic conductivities one order of magnitude lower than slurries containing primarily nonplastic fines. Similar results have been presented by Ryan (1987). D'Appolonia's results are consistent with changes in hydraulic conductivity occurring by adding bentonite (Daniel 1987; Kenney et al. 1992) or increasing plasticity. Additional fines will fill pores between coarser particles, reduce the size of pores controlling flow, and consequently decrease hydraulic conductivity. Furthermore, as the percentage of fines consisting 368

of clay-size particles increases, the pore spaces conducting flow decrease further in size and thus the hydraulic conductivity decreases. Coarse Fraction

Shakoor and Cook (1990) mixed various percentages of gravel with a low plasticity glacial till and compacted it slightly dry of optimum water content. They found little change in hydraulic conductivity for gravel contents less than 50%, but a rapid increase in hydraulic conductivity occurred when the gravel content was increased beyond 50%. Similar results have been presented by Shelley and Daniel (1993). They mixed varying quantities of subrounded concrete gravel with kaolinite or clayey mine spoil and compacted specimens at several water contents. The mine spoil was a well-graded soil with a classification of CL in the Unified Soil Classification System (USCS); it had 50% fines, 20% clay (


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effort and at similar water content relative to their respective optimum water contents, the dry unit weight of the low plasticity clay will be larger than the dry unit weight of high plasticity clay. Consequently, site-to-site comparisons between water contents or dry unit weights can be misleading. Site-to-site comparisons between water contents are further confounded by differences in compactive effort. When compactive effort is varied, optimum water content and maximum dry unit weight shift (Fig. 1). For a given water content, compaction may occur dry of optimum (low compactive effort) or wet of optimum (high compactive effort) depending on the compactive effort used during construction. Consequently, very different hydraulic conductivities can be realized for the same water content (Fig. 1). Thus, a fair comparison between water contents can be made only if the compactive effort (and the soil composition) is the same. Unfortunately, compactive effort is difficult to quantify in the field and varies from site to site (e.g., different compactor weights or number of passes are used). One way to avoid these confounding effects is to use "initial" (as-compacted) saturation (Si) as a combined measure of molding water content and dry unit weight; i.e.

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where wc = molding water content; ~/dc = dry unit weight during construction; ~tw = unit weight of water; and Gs = specific gravity of solids. The writers note that S~ represents the degree of saturation at compaction; it should not be confused with the degree of saturation during permeation. Initial saturation is useful for site-to-site comparisons because contours of initial saturation generally are parallel to the line of optimums (Fig. 1). Thus, initial saturation can be used as a measure of the location of combinations of water content and dry unit weight relative to optimum water content regardless of compactive effort. Also, initial saturation is not nearly as sensitive to soil composition as water content or dry unit weight (Benson and Boutwell 1992). Compaction conditions in the database and their effect on hydraulic conductivity can be examined using initial saturation because hydraulic conductivity generally decreases as the water content is increased beyond the line of optimums, regardless of compactive effort. As the water content is raised, initial saturation also increases. This effect is illustrated in Fig. 1; a decrease in hydraulic conductivity of approximately one order of magnitude occurs as S i is increased from 90% ( - l i n e of optimums) to 95% (3-4% wet of optimum), for each compactive effort. However, increases in initial saturation do not necessarily result in decreases in hydraulic conductivity. For example, if the water content is increased far above optimum, the hydraulic conductivity may increase, yet the initial saturation may remain essentially the same. Also, specimens compacted to the same initial saturation but with different compactive effort will have different fabrics and different hydraulic conductivities. Thus, initial saturation is not a unique measure of soil fabric. Nevertheless, when the average trend of the database is analyzed, these effects are expected to be less significant than the general trend of decreasing hydraulic conductivity with increasing initial saturation. Tables 1-4 show initial saturations for sites where water content and dry unit weight measurements were measured on the specimens used for hydraulic conductivity testing. Because values for Gs were rarely available, G~ 380

= 2.7 was used for all computations. In one case, this resulted in S i > 1.0, which is physically impossible for an average value of initial saturation. The writers believe, however, that using a single Gs was a consistent way to analyze the data without introducing artificial bias by variable and artificially selected values for G,. Fig. 5 is a graph of hydraulic conductivity versus initial saturation; it shows a trend of decreasing hydraulic conductivity with increasing initial saturation. The data also exhibit significant variability (Fig. 5); for a given initial saturation, the hydraulic conductivity can vary by an order of magnitude or more. Variability is expected because soils of various composition comprise the database and initial saturation is not uniquely related to soil fabric or hydraulic conductivity. Nevertheless, the trend (Fig. 5) suggests that focusing on compaction conditions that result in higher initial saturation (i.e., increasing compactive effort and molding water content) will, on average, tend to reduce hydraulic conductivity. The writers caution, however, that higher initial saturation should be obtained without decreasing compactive effort (i.e., compactor weight and number of passes). Decreases in compactive effort concurrent with increases in initial saturation may offset any benefits obtained by increasing initial saturation. Weight and Type of Compactor The weight and type of compactor used at each site was extracted from construction documentation reports or by interviewing persons involved in construction. In most cases, the weight of the compactor could be estimated based on the model type or on descriptions. Furthermore, in most cases, several compactors were used concurrently. In these cases, an average weight was used to describe the weight of the compactor. Fig. 6(a) shows the relationship between hydraulic conductivity and weight of compactor. As expected, a wide range of hydraulic conductivities is realized for a given weight of compactor because numerous other factors (Atterberg limits, particle size distribution, water content, compactor type, etc.) affect hydraulic conductivity. Nevertheless, a trend of decreasing hydraulic conductivity with increasing weight of compactor is evident. This trend is expected, because increasing the weight of the compactor generally 10 -6

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results in greater compactive effort, more shear deformation, smaller more uniform pores, and lower hydraulic conductivity. Compactors were also categorized into two types: "sheepsfoot" (SF) and "rubber tire" (RT), Compactors classified as sheepsfoot were footed compactors that would normally be classified as sheepsfoot compactors by geotechnical engineers (Holtz and Kovacs 1981). Typical compactors in this category included padfoot compactors, tamping foot compactors, and traditional sheepsfoot compactors. Rubber tire compactors were generally scrapers loaded with soil, but this category also included wheeled dozers and other types of earth-moving equipment with inflated rubber tires. Admittedly, classifying compactors into two basic groups is simplistic and may have masked some differences in hydraulic conductivity that occur as a result of variations in compactor type. However, specific details associated with compactor type were difficult to obtain and thus more descriptive categories were not possible. A comparison of hydraulic conductivities obtained using compactors classified as sheepsfoot and rubber tire is shown in Fig. 6(b). The data are presented as box plots, which show the median (center bar), 25th and 75th percentiles (outer edges of center box), and 10th and 90th percentiles (outer bars). The box plots show that the median hydraulic conductivity for compactors classified as sheepsfoot (K = 1.4 x 10 -8 cm/s) is approximately 4 times lower than the median hydraulic conductivity of compactors classified as rubber tire (K = 6.0 • 10 -8 cm/s). A t-test was performed to test the hypothesis that both groups have the same mean. Before the test was performed, the data were transformed logarithmically (base 10 log) because the group of lOgl0KS for each category was approximately normally distributed. The t-statistic was computed to be 2.84 corresponding to a p-value of 0.003 (62 degrees of freedom). Thus, the hypothesis was rejected at the 0.05 level (i.e., p = 0.003 < 0.05, the means are not the same). REGRESSION MODEL

The graphical analysis showed correlations between hydraulic conductivity, several compositional factors, and compaction variables. However, some of these variables are correlated to each other (e.g., percent fines and percent clay) and hence the hydraulic conductivity of the soils in the database 382

may be described using only a select subgroup of these variables. This subgroup was identified by multivariate regression. The regression model was developed for estimating hydraulic conductivities that can be obtained for different soil types and compaction conditions. Stepwise Regression Stepwise linear regression was used to select the variables to be included in the model and their coefficients. The model takes the form lnKg

= ao + a l X 1 + a2X2 + 9 . .

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whet;e the ai = coefficients; Xi = independent variables; and e = a meanzero Gaussian random error term. In stepwise regression, a decision is made to add or delete an independent variable based on its correlation with the dependent variable and a statistic called the "partial-F." Variables are added to the model in accord with their correlation to In Kg; i.e., variables with greatest correlation to In K g are added first whereas those with poorer correlation are added later. Two correlated independent variables will be included only if both variables independently provide significant information to explain variability of In Kg. Thus, using stepwise regression minimizes the effects of masking and overemphasis. After a new variable is added to the model, its significance is checked with the partial-F statistic. The partial-F is a measure of the variance explained by an additional variable relative to the residual error remaining in the data; it is similar to the F-statistic used to analyze trends [(1)]. If the partiaI-F is large enough, the variable is added to the equation. For the model described herein, the partial-F was required to exceed 4 for a variable to be incorporated in the model. A minimum partial-F of 4 corresponds to a significance level of 0.05, which is a consistent with the significance level used to analyze trends. Greater details regarding stepwise regression can be found in Draper and Smith (1981). The model developed by stepwise regression is 894 In Kg = -18.35 + ~ - 0.08PI -2.87Si + 0.32~/-G + 0.02C + e . . . (4) where Kg is in centimeters per second; W = compactor weight in kilonewtons; G = percent gravel; C = percent clay; and S~ = initial saturation (decimal form, Gs = 2.7). Partial-Fs for the variables were compactor weight (F = 59.7), PI ( F = 50.1), percentage gravel ( F = 13.8), initial saturation (F = 5.1), and percentage clay ( F = 4.9). Other functional forms for these variables could have been used (e.g., S~, log PI, etc.) as has been done by others (Wang and Huang 1984; Boutwell and Hedges 1989), but the writers found that these forms provided no improvement in fit. The model has an R 2 of 0.78, meaning that 78% of the variance in hydraulic conductivity is explained by the model. The error term (e) has a variance (~r~) of 0.25. Fit of the model was checked by comparing predicted and measured In K g and by examining the residuals for normality and for correlation with predicted In Kg. Details of the validation procedure can be found in Benson et al. (1992). Comment on Model Eq. (4) is a functional relationship between In K g and five variables that describe composition and compaction conditions for soils compiled in the 383

database. Other variables appearing significant in the graphical exploration could have been added to the regression, but they did not provide any additional information with statistical significance. Correlations and other functional relationships also exist among the "independent" variables used in the regression analysis. Hence, the linear model should be interpreted as a linear approximation. Eq. (4) suggests that increasing compactor weight, PI, or initial saturation will result in lower geometric mean hydraulic conductivity. It also shows that increasing the quantity of gravel results in an increase in the geometric mean hydraulic conductivity. Similar trends were observed in the graphical analysis. The model also suggests that increasing clay content corresponds to higher hydraulic conductivity, a result directly opposite the trend shown in Fig. 3(d). An increase in hydraulic conductivity with increasing clay content occurs, however, only if all other variables are held constant. Hence, if PI is held constant and the clay content is increased, then the activity is decreasing. Increasing hydraulic conductivity with decreasing activity is consistent with the relationship between hydraulic conductivity and activity in the database (Fig. 4).

Practical Applications Eq. (4) can be used to make inferences from the database. For example, if the properties of a candidate borrow soil are known and compaction conditions (initial saturation and compactor weight) are specified, then an estimate can be made of the hydraulic conductivity that can be achieved provided the liner is properly compacted (e.g., >85% of water contentdry unit weight measurements falling wet of the line of optimums, sufficient number of compactor passes, etc.). The probability of excessive hydraulic conductivity can also be computed using the normal distribution with mean = In Kgand variance = ~r~. Another use of (4) is to estimate the compactor weight necessary to achieve a specified hydraulic conductivity for given compaction conditions and a given borrow source (Fig. 7). The curves shown in Fig. 7 were computed using (4) assuming average values for clay content (40%) and gravel

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content (2%) and specifying Si = 0.85. If the plasticity index of the borrow soil is known, then the compactor weight necessary to achieve hydraulic conductivity below a specified threshold can be estimated. However, reasonable estimates can be obtained with (4) only if conditions existing during construction are consistent with the conditions at sites included in the database. That is, construction specifications must be stipulated that: (1) Require compaction wet of the line of optimums; (2) ensure a sufficient number of compactor passes are applied to ensure complete remolding of the clay; and (3) address other factors necessary to ensure proper compaction (e.g., lift thickness, hydration time, documentation and testing, etc.). Furthermore, the writers note that hydraulic conductivities computed using (4) are only estimates for use in preconstruction planning or for rapid construction quality control assessments; testing is necessary to ensure sufficiently low hydraulic conductivity is achieved. CONCLUSION

In this paper, a database is described that contains laboratory-measured hydraulic conductivities and associated index measurements collected during construction of compacted soil liners. Screening was conducted to eliminate sites where scale-dependent hydraulic conductivities were known or likely to exist. Only liners compacted wet of the line of optimums were included. Thus, the following conclusions are relevant only for well-compacted soil liners constructed with naturally formed clays (i.e., liners constructed with soil-bentonite mixtures, mine tailings, etc. were excluded) such as those represented in the database. Soil liners with construction defects or liners constructed with soils not represented in the database may have much different hydraulic conductivity at field-scale than would be expected based on the data presented in this paper. The graphical and regression analyses showed that the geometric mean hydraulic conductivity is correlated to the Atterberg limits, the percentage of fines and clay, and activity. The analyses suggest that the index properties shown in Table 5 are likely to be necessary if a geometric mean hydraulic conductivity -

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