Soil Survey: Pedotransfer Function of Linear Extensibility Percent for Soils of the United States : Soil Science

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Soil Survey

Pedotransfer Function of Linear Extensibility Percent for Soils of the United States

Seybold, Cathy A.; Libohova, Zamir

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Soil Science 182(1):p 1-8, January 2017. | DOI: 10.1097/SS.0000000000000191
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Linear extensibility percent (LEP) is a measure of the linear volume change in soils as a result of a change in water content (Grossman et al., 1968; Burt, 2011). It is expressed on a whole-soil basis with units in percentages. Linear extensibility percent characterizes the shrink-swell capacity of soils and was designed for use in soil genesis and characterization studies (Hallberg, 1977). Shrink-swell arises from the movement of water into and out of interlayer spaces of primarily 2:1 phyllosilicate clay minerals that causes the mineral to expand and contract (Bohn et al., 1979; Vaught et al., 2006). Linear extensibility percent is calculated from the coefficient of linear extensibility (COLE) as LEP = 100 × COLE. The COLE is measured in the laboratory as follows (Grossman et al., 1968; Soil Survey Staff, 2014):


Where Dbd is bulk density at oven dryness (g cm−3), and Dbm is bulk density at -33 kPa (g cm−3) on natural fabric soil samples (clods). Bulk densities are corrected for any rock fragments to estimate COLE on a whole-soil basis.

Soil survey interpretations use LEP to assess potential shrinkage and swelling impacts in a wide range of rural and urban land uses and also for engineering and geotechnical purposes. Cracks created when soils shrink can affect soil infiltration rate and cause rapid movement of water downward into the soil, which can carry chemicals to the groundwater (de Jong et al., 1992). Soil swelling, on the other hand, can close cracks and reduce infiltration rates, possibly causing excessive soil surface runoff and erosion (Favre et al., 1997). Soils with high shrink-swell potentials can cause damage to plant roots, cracking or buckling of pavements, cracking of interior walls in buildings, foundation damages, slope failures, breakage of underground pipes, and complete structural collapse (Mbagwu, 1992; Mandal et al., 2005; US Department of Agriculture Natural Resources Conservation Service [USDA-NRCS], 2016). In engineering, LEP can be used for quantifying shrinkage factors such as the shrinkage limit, shrinkage ratio, and percent volume change (Hallberg, 1977). Shrink-swell is also important in the genesis of soil structure (Bronswijk, 1989), and linear extensibility (COLE multiplied by the layer thickness) is used as a criterion in soil taxonomy (Soil Survey Staff, 1999).

Linear extensibility percent is a basic soil property that is captured in the National Soil Information System (NASIS) database of the USDA-NRCS for soil map unit components (i.e., soils/series that make up the map unit). Field estimates of shrink-swell potential include observation of desiccation cracks, slickensides, gilgai, soil creep, and leaning utility poles and are placed in one of three classes of shrink-swell potential (USDA-NRCS, 2016). In soil survey, classes of shrink-swell are defined based on the LEP of the soil (USDA-NRCS, 2016). However, more accurate estimates require measurements, which are very time consuming and costly for an entire soil survey area. Therefore, estimation procedures or models are often used in soil survey, but there is no national model for estimating LEP. There are still areas where initial soil mapping is occurring, and there are many areas going through updates, especially on a major land resource area basis. To improve estimates of LEP, a model that is national in scope and uses available properties within the soil survey database is needed.

Several soil properties have already been related to the shrink-swell capacity of soils. The type and amounts of clay in combination are known to affect the shrink-swell capacity of soils, with clay mineralogy being the dominant factor (Seed et al., 1962; Franzmeier and Ross, 1968; McCormack and Wilding, 1975; Kariuki and van der Meer, 2004). Smectite clay minerals have a high capacity to shrink and swell, because of their low layer charge (weak bonds) that allows water (a polar molecule) to enter between the mineral basal planes, causing an expansion or swelling (Bohn et al., 1979). Schafer and Singer (1976) found COLE to be highly correlated to the percent expandable clay, with a lower correlation to the ratio of expandable clay to total clay or total clay content. Franzmeier and Ross (1968) indicated that if clay is expressed on a volume basis (an effect of the arrangement of soil particles in space) the relationship between COLE and clay content could be improved. In addition to clay type, cations associated with the clay minerals have also been shown to have an effect on the swelling potential of soils, such as Na-montmorillonite (Al-Rawas, 1999). Zhang et al. (2016) showed Ca-montmorillonite to have greater swelling compared with Na-montmorillonite, which was attributed to a stronger hydration of the Ca-montmorillonite. The plastic index (PI) of soils is known to be highly correlated to the expansive property of soils (Seed et al., 1962; de Jong et al., 1992; Puppala et al., 2013). Other properties have been related to the shrink-swell potential such as specific surface area (Ross, 1978; de Jong et al., 1992; Grey and Allbrook, 2002) and cation-exchange capacity (CEC) (Gill and Reaves, 1957; Grey and Allbrook, 2002; Kariuki and van der Meer, 2004). The latter property integrates the total amount of clay and activity of the clay (Yule and Ritchie, 1980). In summary, several properties that are basic to soil survey such as total clay, CEC and PI would be useful in predicting LEP.

Several indexes or models that can predict the swelling or shrinkage capacity of soils have been developed. An artificial neural network model was developed by Ikizler et al. (2010) to predict lateral and vertical swelling pressures of soils. Seed et al. (1962) developed a swelling potential index for engineering purposes (on compacted clays) that used the percent total clay, clay activity, and an expansion coefficient depending on the clay type. Vertical shrinkage in Texas Vertisols using small cores was estimated by the CEC alone (R2 = 0.76) (Yule and Ritchie, 1980). Pruška and Šedivý (2015) predicted swelling pressures of expansive soils using a consistency index (PI) and a colloidal activity index on tuffaceous clays, mudstones, claystones, chalk marlites, and neogene clay soils in the Czech and Slovak Republic (R2 = 0.88). Schafer and Singer (1976) developed a prediction model for COLE using the expandable clay fraction and porosity for 16 California soils. Their validation results showed an R2 of 0.59 and very little bias for a wide variety of soils (using 160 soil samples from the Kellogg Soil Survey Laboratory [KSSL] database in Lincoln, NE). An expansive index was developed by Thomas et al. (2000) using 12 soils of various parent materials from Virginia. They used the swelling 2:1 minerals, PI, liquid limit, and a swell index and summed them into an index. However, none of the previously mentioned models are specific to the prediction of LEP. In the case where COLE was predicted, it was confined to only a few soils and used parameters that are not readily available in soil survey. This makes the previously mentioned models not suitable for use in predicting LEP for the diverse range in soils of the United States.

The objective of this study was to develop and validate a model for estimating LEP using general linear models and soil properties readily available within the NASIS soil survey database. The model would be limited to the basic soil properties captured in soil survey that are related to LEP such as total sand, silt, and clay; total organic matter; bulk density; and cation exchange properties. A prediction model that is national in scope will provide consistent and improved accuracy of LEP estimates, which will benefit all users of soil survey data and their interpretations, as soil survey data are being updated or through initial mapping.


Data Selection and Analysis

Soil horizons were selected from the KSSL characterization database (Lincoln, NE), which contains more than 37,000 pedons with measured chemical and physical properties representing geographically diverse soils from across the conterminous United States, Hawaii, and Alaska. The measured data prior to year 2000 were used for model development, whereas data from 2001 to 2010 were used for model validation. The data set starts around 1959 when the saran-coated clod method for determining bulk density was first used in soil survey (Brasher et al., 1966), and methodology has not changed. The following measured data were used: total sand (2–0.05 mm), total silt (0.05–0.002 mm), and total clay (<0.002 mm) (pipette method); carbonate clay (<0.002 mm); organic carbon content (acid-dichromate digestion method, discontinued in 2000); total C (dry combustion); CEC (1.0 N NH4OAc at pH 7); effective CEC (ECEC); bulk density at −33 kPa matric potential (Db,33, saran-coated clods); oven-dry bulk density (Db,o, saran-coated clods); water retention at −1,500 kPa (<2 mm sieved); gypsum content (<2 mm); CaCO3 equivalent (electronic manometer method); pH (in water and 0.01 M CaCl2 in 1:2 soil/solution suspensions); and LEP (between oven dryness and −33 kPa matric potential measured on saran-coated clods, calculated from COLE). All determinations, except those for bulk density and LEP, are made on air-dried (30°C–35°C), crushed, and sieved (<2 mm) soil samples. All of the previously mentioned methods are described in Soil Survey Staff (2014) and are reported on an oven-dry basis. Information on the soil taxonomic classifications from the soil profile descriptions was also used.

Soil samples with −1,500 kPa water-to-clay ratios greater than 0.6 were removed from the database, except those with the following mineralogy classes: ferritic, gibbsitic, allitic, sesquic, parasesquic, ferruginous, magnesic, halloysitic, amorphic, ferrihydritic, glassy, and isotic. When the ratios are greater than 0.6, incomplete dispersion during the particle size determinations introduces inaccuracies, especially in soils dominated by silicates (Stolpe and Lewis, 1990; Soil Survey Staff, 1999; Burt, 2011). Incomplete dispersion has less of an impact on the accuracy of low clay content soils. Soil samples with more than 3% organic carbon were also removed from the database to reduce potential error associated with irreversible shrinkage from organic matter. Organic matter represents a nonreversible shrinkage portion of the soil, and LEP characterizes the reversible shrinkage of soils (Soil Survey Division Staff, 1993). Soils with fragments were also removed from the database as COLE is calculated on a whole-soil basis. If coarse fragments are present, they are corrected for in the calculation of COLE and thus LEP (Holmgren, 1968). For this study, soils without coarse fragments were desired in order to estimate COLE on a <2-mm basis, which would be consistent with the properties used in predicting LEP. Percent carbonate clay was subtracted from the percent total clay to get noncarbonate clay (nclay) because carbonate clay has less of an influence on the shrink-swell properties than silicate clays (Nettleton et al., 1991). Subtracting out the carbonate clay removes the disadvantage of the particle-size measurement by giving only silicate clay amounts. The database was further screened for obvious inconsistencies, and samples with Db,33 > Db,o, negative values of water contents retained at −1,500 kPa, ECEC > CEC, and the sums of sand, silt, and clay less than 100% were removed.

In the final database, only pedons that had a correlated soil classification based on laboratory data were used. Within a pedon, horizons were used only if they met the previously listed criteria. The family mineralogy class was extracted from the soil classification. Pedon depths varied, ranging up to 200 cm. Organic C ranged from 0% to 3%. Horizons contained no rock fragments. The −1,500 kPa water-to-clay ratios were all less than 0.6 except for those horizons in the mineralogy classes listed previously. There were no missing values for total sand, silt, and nclay. There were no missing values for LEP and CEC or ECEC. The statistics describing the development data set are presented in Table 1.

Statistical Properties of the Development Data Set

Data Stratification

The database was partitioned into more homogeneous soil groups to improve the accuracy of the LEP predictions. The data set for model development was stratified by taxonomic mineralogy class. It is well established that clay mineralogy governs the shrink-swell behavior of soils (Franzmeier and Ross, 1968; Nettleton and Brasher, 1983; Kariuki and van der Meer, 2004; Burt, 2011). The major taxonomic clay mineralogy classes used were smectitic, kaolinitic, vermiculitic, and illitic, as well as the major mineralogy classes of mixed, siliceous, and carbonatic (Fig. 1). Most of the remaining taxonomic mineralogy classes are dominated by Fe and Al oxides, hydroxides, amorphous materials, and other less common minerals and are of minor extent and so were grouped together. Mineralogy classes included in this group are ferritic, gibbsitic, allitic, sesquic, parasesquic, ferruginous, magnesic, halloysitic, amorphic, ferrihydritic, glassy, and isotic and will be referred to as the “other” mineralogy group. In soil taxonomy, a mineralogy class is assigned to all mineral soils, except Quartzipsamments (USDA-NRCS, 2016). The LEP concept is not applicable to organic layers, but they are assigned to mineral layers of organic soils (Soil Survey Staff, 2016). All mineral horizons that do not fit into the mineralogy groups defined previously (including those mineral horizons in Histosols and Histels) are assigned to the “mixed” mineralogy group. Complete coverage of all soils is necessary for a national model. Similar to calcium carbonate, gypsum does not have a CEC, and thus, it is corrected for in the sample. Soils with greater than 5% gypsum were also grouped into a separate data set, which was split further into two data sets at a threshold of 40% gypsum. In most cases, NASIS does not contain clay content (particle size information) for soils with greater than 40% gypsum. Therefore, a separate group is needed because clay content cannot be used as a predictive variable. Visual examination of scatter plots of LEP versus nclay content for the smectitic and mixed mineralogy groups showed a change in the relationship at approximately 35% and 20% clay, respectively. To improve predictions, the smectitic group was split at 35% clay, and 20% clay for the mixed mineralogy group.

The taxonomic mineralogy classes of the continental United States in this study. The “other” mineralogy class includes ferritic, gibbsitic, allitic, sesquic, parasesquic, ferruginous, magnesic, halloysitic, amorphic, ferrihydritic, glassy, and isotic.

Statistical Analysis

Linear extensibility percent was estimated using general linear model procedures in SYSTAT Software (2009). For each stratum (data group), the best fit model (with the lowest root mean square error [RMSE]) was developed. The RMSE gives the accuracy of the estimations in terms of S.D.; the smaller the RMSE, the more accurate the model. Pearson correlation coefficients were computed to help in the selection of predictive variables. Only data elements that contributed significantly (P = 0.05) to predicting LEP and that contributed more than 5% to the overall improvement of the coefficient of determination (R2) were included in the equations. The R2 value represents the proportion of total variability in LEP data that is explained by a model. Scatter plots of the residuals versus the fitted values of each model were used to determine whether there were nonlinearity, unequal variances, and outliers in the data. All outliers, as identified by the studentized residual in SYSTAT Software (2009), were removed from the data groups.


The validation data set consisted of 2,176 soil samples from KSSL corresponding to pedons sampled throughout the United States (Table 2). All properties of the validation data set were within the range of the development data set. Organic C in this data set was estimated from the difference between the total and CaCO3-C (Soil Survey Staff, 2014). Model performance was evaluated by comparing measured versus predicted LEP values and by calculating the prediction RMSE (RMSEP) and mean error (ME) as defined in McBratney et al. (2011). Confidence intervals (P = 0.05) were calculated for the slope and intercept of the least squares estimate line.

Statistical Properties of the Validation Data Set


Model Development and Comparisons

The data set used to develop the prediction models had a broad range in soil properties and represents the soils of the United States (Fig. 2). Clay content ranged from 1.5% to 95%, and CEC ranged from 0.1 to 100.6 cmol(+) kg−1 (Table 1). The range in LEP varied from 0% to 29.6%. Given the wide range of soil properties, the LEP for the complete unstratified data set was highly correlated with CEC (r = 0.834), ECEC (r = 0.708), nclay (r = 0.813), and total clay content (r = 0.743). The high correlations with these properties were expected and are similar to what others have found between clay, CEC, and some measure of the soil shrinkage and/or swelling potential (Gill and Reaves, 1957; Seed et al., 1962; Franzmeier and Ross, 1968; McCormack and Wilding, 1975; Grey and Allbrook, 2002; Kariuki and van der Meer, 2004). The CEC and ECEC can give an indication of the clay mineralogy (Burt, 2011). In an example, Puppala et al. (2013) used a high CEC value to indicate the presence of smectite clay minerals and a low CEC to indicate the presence of nonexpansive clay minerals such as kaolinite. In the present study, LEP weakly correlated with calcium carbonate (r = −0.196) and organic carbon (r = 0.158) contents. Similarly, others have shown no relationship between COLE and organic C (Schafer and Singer, 1976; de Jong et al., 1992) and have found COLE to have no correlation or to be negatively correlated with the carbonate content of the soil (de Jong et al., 1992; Dinka et al., 2013). The high correlations with CEC and nclay suggest they would be the most useful in predicting LEP.

Sample location of pedons (continental United States only) that make up the development data set used in the prediction of LEP.

The development data set was stratified into 12 data sets based on their gypsum content, taxonomic mineralogy class, and clay content (Table 3). For each data set, a general linear model was developed for a total of 12 prediction equations (Table 3). The CEC and nclay content were found to be the most useful in predicting LEP. The CEC and nclay content alone explained between 43% and 86% of the variability in LEP for nine of the equations (Table 3). For soils with greater than 5% gypsum, nclay (on a gypsum-free basis) and CEC explained 88% of the variability in LEP. For soils with greater than 40% gypsum, CEC alone explained 75% of the variability in LEP. Noncarbonate clay, CEC, and (CEC)2 explained 78% of the variation in LEP for the siliceous mineralogy group (Table 3). No other combination of predictor variables provided equations with a higher R2 and lower RMSE for either of the data sets.

Model to Predict LEP for Soil Layers With <3% Organic Carbon

In soil survey, CEC is available only for soils that have a pH greater than 5.5, and ECEC is available for low pH layers (USDA-NRCS, 2016). To make the prediction of LEP available for low pH soils, a second set of eight prediction equations was developed that use ECEC as a predictor variable in place of CEC (Table 3). Because gypsum generally does not occur in low pH soils, no additional equations were needed. In low pH soils, the ECEC and nclay content were the most useful variables in predicting LEP. For six of the equations, the ECEC and nclay content explained between 42% and 67% of the variability in LEP (Table 3). Noncarbonate clay, (nclay)2, and ECEC explained 51% of the variation in LEP for the kaolinitic mineralogy group (Table 3). Similarly, for the “other” mineralogy data set, nclay, (nclay)2, and ECEC explained 61% of the variation in LEP. No other combination of predictor variables provided equations with a lower RMSE.

The RMSEs ranged from 0.25 to 2.86 among all the equations (Table 3). In general, the RMSEs were slightly higher for the smectitic equations compared with the other groups. They also have the greatest range in LEP values among the mineralogy groups, because RMSE depends on the scale or range of the data.

The numbered models serve as a guide to help select the correct equation in predicting LEP (Table 3) and provide flexibility for the user. Based on the properties of the soil and taxonomic classification, the user selects the prediction equation from Table 3 starting with Model 1. If gypsum is present in the soil and whether total clay is available will determine which gypsum equations to use in predicting LEP (Table 3). Next, if gypsum is not present in the soil, then the taxonomic mineralogy class and total clay content are used to determine which equation to use (Table 3). For example, if the soil has mixed mineralogy and the clay content is less than 20%, then the appropriate equation is used to predict LEP (depending whether CEC or ECEC is available). The models provide an LEP estimate for every soil sample that has an organic carbon content of 3% or less, given that the CEC or ECEC, nclay content, and the soil classification are known. If rock fragments are present in the soil, then the predicted LEP is adjusted to a whole-soil basis: (1 − volume fraction of fragments) × LEP.

Model Validation

Each soil sample from individual pedons in the validation data set was run through the appropriate predictive model to estimate LEP, based on the models in Table 3. All developed prediction models were used as indicated by the breakdown of the soil taxonomic mineralogy classes in the validation data set (1% has >5% gypsum, 24% smectitic, 5% kaolinitic, 61% mixed, 3% siliceous, 0.5% vermiculitic, 1% illitic, 2% carbonatic, and 2.5% other). This is very similar to the mineralogy class breakdown of the development data set (1.5% has > 5% gypsum, 21% smectitic, 3.5% kaolinitic, 60% mixed, 7% siliceous, 0.5% vermiculitic, 1% illitic, 2% carbonatic, and 3.5% other). A plot of measured versus predicted LEP values for all other equations is presented in Fig. 3. The collective model (all equations using CEC) explained 87% of the variation in the LEP data. Accuracy of the predictions produced an RMSEp of 1.44% and ME of −0.16% (Fig. 3).

A scatter plot of the measured versus predicted LEP representing prediction equations that use CEC as one of the predictor variables, as listed in Table 3.

Equations using ECEC as a predictor variable were validated as a separate group. Validation of the equations using ECEC as a predictor variable for low pH soils is shown in Fig. 4. The collective model explained 77% of the variation in the LEP data. Accuracy of the predictions produced an RMSEp of 1.29% and ME of −0.034% (Fig. 4). Prediction accuracy for equations using ECEC was slightly lower than that for equations using CEC. It should be noted that the range in LEP is smaller for equations using ECEC than that for equations using CEC. Validation results from Schafer and Singer (1976) on a model developed from 16 California soils could predict LEP within 1% to 2%. Also, simple linear regressions using total clay for predicting LEP were developed from laboratory characterization data for each of the taxonomic mineralogy groups (montmorillonitic, mixed, and kaolinitic) that resulted in R2 ranging from 0.44 to 0.77 (Soil Survey Laboratory Staff, unpublished data, 1981). There are no other published studies that attempted to predict LEP or addressed such a wide range of soils as in the present study.

A scatter plot of the measured versus predicted LEP representing prediction equations that use ECEC as one of the predictor variables, as listed in Table 3.

In the plots of measured versus predicted LEP in Fig. 3, the 95% confidence intervals for the slope (0.825, 0.856) do not include 1, suggesting a significant difference from unit 1 slope. The 95% confidence intervals for the intercept (0.574, 0.787) do not include 0, which indicates the intercept is significantly different from 0. Similarly, in plots of measured versus predicted LEP in Fig. 4, the 95% confidence intervals for the slope (0.760, 0.836) do not include 1, and the 95% confidence intervals for the intercept (0.410, 0.739) do not include 0. For both plots, this means that more than 95% of the time similarly constructed intervals will not contain unit 1 slope and 0 intercept. In other words, the model slightly overestimates LEP starting at the intercept (0 LEP), then crosses over the 1:1 line at some point, and beyond that point, the model underestimates LEP as LEP increases. The crossover point is at LEP of 4% in Fig. 3 and at 2.75% in Fig. 4. However, the overall ME is small, −0.16% for equations using CEC and −0.034% for equations using ECEC. The small negative ME indicates an overall underestimation.

Validation results for the different mineralogy groups are presented in Table 4. The RMSEp ranged from 0.42% to 1.80% among the mineralogy groups, with the smectitic group having the largest RMSEp. However, the smectitic group also has the largest range in LEP. The siliceous group had the lowest RMSEp. In general, the lower clay content groups tended to have lower RMSEp. The range in the RMSEp was lower than that for the RMSE of the estimate and tended to be lower or similar for most of the mineralogy groups. The MEs or bias ranged from −0.689 to 0.609 among the different mineralogy groups (Table 4). The “other” mineralogy group had the largest positive ME of 0.609, which indicates an overestimation, whereas the carbonatic group had the largest negative ME of −0.689, which indicates an underestimation of LEP. Six of the nine mineralogy groups had a small negative ME (Table 4). In general, the MEs were small, indicating that these models can predict LEP reasonable well for the wide variety of soils of the United States.

Validation Results for the Prediction of LEP for Each of the Mineralogy Groups


Models were developed for predicting LEP that can be applied to soils of the United States. The data were stratified based on the taxonomic mineralogy class and pH, which resulted in 20 general linear models for predicting LEP. The models apply to mineral soils with less than 3% organic carbon. Noncarbonate clay and CEC were the variables most highly correlated with LEP. Noncarbonate clay and CEC were able to explain between 43% and 86% of the variation in LEP for nine of the models, whereas nclay and ECEC (low pH soils) explained between 42% to 67% of the variability in LEP for six of the models. Validation results showed a prediction accuracy (RMSEp) of 1.44% with an ME of −0.16% for equations using CEC as a predictor variable and an RMSEp of 1.29% with an ME of −0.034% for equations using ECEC as a predictor variable. The RMSEp ranged from 0.42% to 1.80% among the different mineralogy groups, which were generally lower than the RMSE of the estimate. The models are considered adequate for use in soil surveys.

The LEP prediction models developed in this study are an improvement over previous estimation procedures based on visual estimations of shrink-swell potential and on a discrete class assignment. The models will be made available as a calculation within the NASIS database for field soil scientists to use when measured data are not available. Initial soil mapping is still being conducted in the United States, and many areas are undergoing updates. Improvements in LEP estimates will improve interpretations generated from soil survey data, which benefits all users of soil survey information.


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COLE; linear extensibility percent; prediction; shrink-swell; soil survey

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