Pedotransfer functions to predict Atterberg limits for ...

Pedotransfer functions to predict Atterberg limits for SouthAfrican soils using measured and morphological properties

J. J. VAN TOL1, A. R. DZENE

2, P. A. L. LE ROUX1 & R. SCHALL

3

1Department of Soil, Crop and Climate Sciences, University of the Free State, Nelson Mandela Dr., Bloemfontein, 9300, South

Africa, 2Department of Agronomy, University of Fort Hare, King Williamstown Rd, Alice, 5700, South Africa, and 3Department of

Mathematical Statistics and Actuarial Science, University of the Free State, Nelson Mandela Dr., Bloemfontein, 9300, South

Africa

Abstract

Atterberg limits and indices, for example liquid limit (LL), plastic limit (PL), linear shrinkage (LS)

and plasticity index (PI), are important soil properties in engineering and land evaluation for

predicting soil mechanical behaviour. This study was conducted to develop and evaluate pedotransfer

functions (PTFs) to predict Atterberg limits using measured and morphological soil properties from a

large data set in South Africa covering a vast range of soils, geologies and climates. Five PTFs were

developed; the first four using measured properties from 2330 soil horizons including extractable Fe,

Al, Mn, Na, K, Mg and Ca; organic carbon (OC); pH (H2O); cation exchange capacity (CEC); and

sand, silt and clay fractions to predict LL, PL, LS and PI. Morphological descriptors such as colour,

structure (grade, size and type), consistency, occurrence of slickensides and cutans and abundance of

roots were included in the second PTF using data from 717 horizons to predict PI. For all PTFs,

two-thirds of the data were randomly selected and used for model development and the remainder for

validation. Prediction accuracies of R2 between 0.49 and 0.77 comparable to other studies on large

data sets but underperformed when compared to localized data sets. For engineering purposes, site-

specific PTFs for prediction of Atterberg limits should be developed.

Keywords: Engineering soil properties, linear shrinkage, liquid limit, plastic limit, plasticity index,

soil mechanics, soil morphology

Introduction

In 1911, Albert Atterberg qualitatively defined seven limits

that determine the mechanical behaviour of soils at

different water contents (Atterberg, 1911 in Haigh et al.,

2013). Three of these, namely liquid limit (LL), plastic limit

(PL) and linear shrinkage (LS), are frequently used to

quantify the physical activity of soils for engineering

purposes and for the estimation of other test indices such

as shear strength, bearing capacity, compressibility, swelling

potential and specific surface area (De Jong et al., 1990;

Fanourakis, 2012; Moradi, 2013). The LL is the water

content where a soil will begin to flow (become a viscous

fluid) under its own weight, the PL is the water content at

which a soil will crumble when rolled to a diameter of

3 mm (starts to behave like a semi-solid) and the LS is the

decrease in length of a soil sample when oven-dried,

starting with a moisture content of the sample at the liquid

limit (Atterberg, 1911; De Jong et al., 1990; SCWG, 1991).

The plasticity index (PI) is the numerical difference between

the LL and PL and is an indication of the workability of

the soil. In the South African Soil Classification System

(Soil Classification Working Group (SCGW), 1991), PI is a

diagnostic criterion to classify the diagnostic vertic topsoil

horizon.

Measurements of Atterberg limits are, however, time-

consuming and expensive and, despite the fact that they are

basic soil mechanical properties, are seldom recorded in soil

survey data (Ahmadi et al., 2012). Many researchers

consequently investigated relationships between other, more

available, easily and routinely measured properties and

Atterberg limits. These include inter alia the clay content (De

Jong et al., 1990; Schmitz et al., 2004; Fanourakis, 2012),

organic carbon (OC) and organic matter (OM) (Mbagwu &

Abeh, 1998; Zhang et al., 2005; Ahmadi et al., 2012;

Zolfaghari et al., 2015), cation exchange capacity (CEC)

(Mbagwu & Abeh, 1998; Yilmaz, 2004; Yukselen & Kaya,Correspondence: J. J. van Tol. E-mail: [email protected]

Received July 2015; accepted after revision September 2016

© 2016 British Society of Soil Science 1

Soil Use and Management doi: 10.1111/sum.12303

SoilUseandManagement

2006; Moradi, 2013), calcium carbonate (Smith et al., 1985;

Zolfaghari et al., 2015), Mg contents (Fanourakis, 2012) and

bulk density (Seybold et al., 2008). These relationships are

also termed pedotransfer functions (PTFs), which were

defined by Bouma (1989) as ‘translating data that we have

into what we need’. PTFs are generally developed for

inference of soil hydraulic properties from easily measured

properties and often make use of regression equations

(Vereecken & Herbst, 2004). Most of the previously

published PTFs on Atterberg limits made use of multiple

linear regression (e.g. De Jong et al., 1990; Seybold et al.,

2008; Fanourakis, 2012; Moradi, 2013).

PTFs are, however, often only applicable and reliable for

the areas or soils where they were developed (Wagner et al.,

2001), with limited extrapolation value for other

environments, that is different climates, geologies and soils.

In South Africa, Fanourakis (2012) produced PTFs for five

soil forms occurring on approximately 4200 km2 in the

North West Province using Mg and the clay size fraction as

predictors of Atterberg limits. In this study, we aimed to

build on the work of Fanourakis (2012) and to develop

PTFs for estimating LL, PL, LS and PI from a large data

set covering most of South Africa. As South Africa is diverse

in terms of climate, geology and soils, it is hypothesized that

such PTFs can be useable internationally as well. Specific

objectives of this study were then (i) to explore relationships

between readily available soil properties and selected

Atterberg limits, (ii) to develop PTFs to estimate selected

Atterberg limits from readily measured soil properties and

(iii) to develop a PTF to assist soil surveyors to estimate PI

in the field.

Methodology

Land Type data set and data selection

Modal profiles from the Land Type database of South

Africa (Land Type Survey Staff, 1972–2002) were utilized. A

total of 3160 horizons with measured liquid limit (LL),

plastic limit (PL), linear shrinkage (LS) and plasticity index

(PI) values were identified, representing a large spatial

distribution (Figure 1). The horizons were broadly regrouped

into 10 diagnostic entities; for the topsoils, there were

distinguished between vertic, melanic, humic and orthic

horizons and for the subsoils between apedal, gleyed,

eluviated, plinthic, structured and saprolitic horizons. The

0 125 250 500 750 1 000Kilometers N

Figure 1 Location of soil profiles (and horizons) with measured Atterberg limits (Land Type Survey Staff, 1972–2002). [Colour figure can be

viewed at wileyonlinelibrary.com].

© 2016 British Society of Soil Science, Soil Use and Management

2 J. J. van Tol et al.

diagnostic horizons were only used to determine the

intercept terms. Data with obvious errors were eliminated

(e.g. negative or zero values of measured Atterberg limits

and abnormally high LL values, i.e. >100), as well as

horizons without geographical coordinates.

For quantitative analysis, the following explanatory

variables were considered: citrate–bicarbonate–dithionate(CBD) extractable Fe (%), Al (%) and Mn (%), percentage

organic carbon (OC) measured with the Walkley–Blackmethod, pH (H2O), extractable Na, K, Mg and Ca

(cmolc kg/soil), cation exchange capacity (CEC, cmolc kg/

soil), and particle size distribution (%) for three classes, that

is sand, silt and clay (initially measured with the pipette

method for five or seven classes but converted to the

aforementioned three classes). Any abnormal or spurious

values in explanatory variables were also identified, and the

specific variable was omitted from the data set. These

included horizons where the sum of the texture classes was

below and above 95 and 105%, respectively, CEC (cmolc kg/

soil) smaller than the sum of extractable Na, Mg, K and Ca

(cmolc kg/soil) any negative values and visually obvious

outliers. A total of 2230 horizons were included in the

quantitative analysis.

Qualitative data were selected based on pedogenetic

knowledge of variables possibly influencing Atterberg limits.

These included colour, field estimated texture class, terrain

morphological unit, soil structure (grade, size and type), field

estimated consistency, occurrence of slickensides and cutans,

abundance of roots and a description of the topography of

transition between horizons. To reduce the number of colour

classes, the Munsel colour value was translated into

descriptive colours.

Derivation of PTFs

Measured (quantitative) functions. Derivation of the PTFs

started with an analysis of data transformations with two

objectives, namely (i) to determine the optimal power

transformation of the dependent variables (the Atterberg

limits LL, PL, LS and PI) to normality and (ii) to

explore the functional relationship between the

(transformed) dependent variables and the 13 explanatory

variables.

Cubic spline transformations of the explanatory variables

were fitted to the dependent variables; the splines had three

degrees of freedom and allowed for two knots. At the same

time, the dependent variable was transformed by a power

transformation (Box & Cox, 1964) which, as a limiting case,

includes the logarithmic transformation. For each dependent

variable, the optimal power parameter for transformation of

the dependent variable to normality and the optimal spline

transformation of the explanatory variables were determined.

The analysis was carried out using the SAS procedure

TRANSREG (SAS, 2013).

The optimal power parameter k for transformation to

normality of the four dependent variables was as follows:

k = 0.5 (square root transformation) for LL, k = 0.75 for

LS, k = 0.5 for PI and k = 0 (logarithmic transformation)

for PL.

Furthermore, the results of the transformation analysis

suggested that a polynomial of degree 3 (or lower)

approximated the optimal spline transformation of all

explanatory variables well. Thus, for all dependent variables,

a cubic polynomial regression model was chosen as a basis

for stepwise variable selection. Specifically, regression

variables available for selection were the following: the 13

explanatory variables as linear, quadratic and cubic terms

(3 9 13 = 39 variables); the 78 cross-terms between the 13

linear terms; and the intercept terms for the 10 horizons

(nine degrees of freedom).

Using the collection of independent variables described

above, stepwise model selection was performed as follows:

starting with the intercept, at each selection step that variable

was chosen whose inclusion in the model achieved the largest

decrease in the Schwarz Bayesian information criterion (SBC);

similarly, a variable already in the model could be chosen for

exclusion if the exclusion led to a decrease in the SBC. Among

various criteria for model selection, the SBC was chosen

because it generally led to the most parsimonious model

(model with fewest variables). At all stages during the stepwise

selection process, model hierarchy was observed, namely a

higher order polynomial term (quadratic, cubic or cross-term)

could enter the model only if all lower order terms contained

in the higher order term were already present in the model.

Similarly, a lower order term could leave the model only if

there were no higher order terms in the model which contained

the lower order term. In all cases, 75% of the data were

randomly chosen as a training sample, while the remaining

25% of the data were used for validation of the selected

model. The model selection was carried out using SAS

procedure GLMSELECT (SAS, 2013).

The final model identified by the model selection

procedure was fitted twice as follows: (i) if Y is the original

dependent variable, the model was fitted to the transformed

dependent variable Yk, where k is the parameter of the

optimal Box–Cox power transformation (k = 0.5, 0.75, 0.5

respectively, for the variables LL, LS and PI, and In(Y) for

the variable PL). The resulting regression coefficients are

reported, as well as the goodness-of-fit statistics R2 and root-

mean-square error (RMSE) of prediction. (ii) The final

model was also fitted to the transformed dependent

variableðYk � 1=ðk � Y ðk�1ÞÞ, where, as before, k is the

parameter of the power transformation, and Y is the

geometric mean of the dependent variable on the original,

untransformed, scale [for the variable PL, where k = 0, the

transformed variable is Y � lnðYÞ]. We carried out the second

fit because for this form of the dependent variable, the

RMSE values can usefully be compared to RMSE values


PTFs for Atterberg limits of SA soils 3

obtained from a fit of the untransformed variable Y. Thus,

we report the RMSE values for the second fit to facilitate

comparison with RMSE values reported in the literature

which are often based on the fit of untransformed dependent

variables (Atterberg limits).

Morphological (qualitative) function. Morphological data

were only used to predict PI. The effect of different classes

within a variable (e.g. apedal, weak, moderate and strong for

structure grade) on PI was identified using multiple linear

regression correlations between the individual morphological

variables (with various classes) and PI. The slope (m) of the

linear function of various classes was then coded from lowest

to highest with whole numbers starting at 1. Again, two-

thirds (477) of the horizons were randomly selected and used

to develop the PTF between morphological variables and PI,

and the remaining 240 horizons were used to evaluate the

PTF using R2 and RMSE. The number of horizons used for

the morphological PTF is considerably smaller than that

used for quantitative PTFs as not all morphological

variables were described for all the horizons.

Results

PTFs based on quantitative data

The selected horizons represent a healthy range within

measured soil properties (Table 1), for example clay contents

ranged from 9.7 to 84.5%, pH between 4.3 and 10.2 and OC

between 0.03 and 5.0%. The vast range of within measured

soil properties reflects the heterogeneity of South African

soils, climate and geology (Figure 1).

Significant correlations existed between most variables and

Atterberg limits (Table 1). Large positive correlations exist

between clay content and all Atterberg limits. The same

applies to CEC. Extractable cations (Mg, Ca, K and Na) are

well correlated with most of the Atterberg limits, especially

PI. Significant negative correlations exist between sand

content and all Atterberg limits, as well as between most

variables and PL. Interestingly, there is no significant

correlation between OC and PI.

Inclusion of diagnostic horizons made only a significant

contribution to the prediction of LL (Tables 2 and 3). The

PTFs for the estimation of Atterberg limits suggested

predictions of LL from measured properties are the most

accurate (R2 = 0.77 for training data, Table 3). This

supported by the highest Pearson correlation coefficients

(Table 1). All the PTFs were, however, significant

(P < 0.0001). Fe and CEC are present in all the PTFs and

texture (sand, silt and clay) also have a significant influence on

the Atterberg limits. The R2 for prediction of LS (0.56), PL

(0.53) and PI (0.62) are relatively low when compared to LL.

PTF based on qualitative data

Despite the low correlation coefficients, the relationships

between morphological properties and PI were significant

Table 1 Summary of explanatory variables and Pearson’s correlations between individual measured variables and Atterberg limits (n = 2230)

Explanatory variable Min Max Med Std. Dev.

Pearson’s correlation

LL PL LS PI

Clay (%) 9.700 84.500 40.385 14.221 0.673** 0.3789** 0.609** 0.558**

Silt (%) 0.300 61.800 21.110 11.696 NS 0.251** 0.112** �0.109**

Sand (%) 1.600 75.600 36.902 16.922 �0.605** �0.490** �0.585** �0.387**

CEC (cmolc kg/soil) 2.120 61.000 15.079 7.549 0.614** 0.204** 0.539** 0.619**

Mg (cmolc kg/soil) 0.040 28.600 4.518 3.989 0.413** NS 0.371** 0.623**

Ca (cmolc kg/soil) 0.050 69.600 6.396 6.501 0.308** �0.116** 0.293** 0.503**

K (cmolc kg/soil) 0.020 5.140 0.421 0.487 0.078** �0.113** NS 0.144**

Na (cmolc kg/soil) 0.010 14.830 0.661 1.099 0.193** �0.116** 0.100** 0.354**

pH (H2O) 4.290 10.200 6.686 1.183 NS �0.354** NS 0.290**

OC (%) 0.030 5.000 0.949 0.878 0.219** 0.371** 0.165** NS

Mn (%) 0.000 1.127 0.041 0.071 0.120** 0.056* 0.128** 0.108**

Al (%) 0.001 3.221 0.317 0.363 0.244** 0.510** 0.166** �0.095*

Fe (%) 0.030 17.320 2.567 2.131 0.336** 0.474** 0.250** 0.050**

Min 13.000 5.000 0.070 1.000

Max 92.000 50.000 26.000 64.000

Med 38.767 18.437 6.281 20.295

Std. De. 11.566 6.548 3.302 9.156

Significance levels of a = 0.05 and 0.01 indicated by * and **, respectively.



(P < 0.01) for all the properties (Table 3). The occurrence of

slickensides and cutans, structure (grade, type and size) and

the field estimated consistency proved to be the best

predictors of PI. Although texture was a key determining

factor of PI with measured data (Pearson’s

correlation = 0.56, Table 1), the field estimated texture

classes appear inadequate to predict PI, with the lowest R2

(Table 4).

Following the stepwise selection criteria, the best model to

predict PI with morphological data is as follows:

PI ¼ �4:831þ 2:028 x Structure gradeþ 2:519

xConsistencyþ 2:459 xRootsþ 5:368 x Slickensides:ð5Þ

With a model accuracy of R2 = 0.51 and RMSE = 7.47 it

was considerably lower than obtained from measured data

(Table 3). The validation data are presented in Figure 2, and

again regression correlations are much lower than those of

measured data (Table 3) with slight overestimations of high

PI values. The relatively high RMSE (7.03) is reflected by

the scattering as shown in Figure 2.

Discussion

Measured data

Significant positive correlations existed between clay

fractions and most of the Atterberg limits studied, with

significant negative correlations between sand fractions and

all Atterberg limits (Table 1). These correlations are

expected and agree with other studies (e.g. De Jong et al.,

1990; Ahmadi et al., 2012) as clay is the major contributor

to plasticity in soils and inversely correlated to the sand plus

silt content. Large positive correlations also existed between

CEC and all Atterberg limits. The CEC is largely controlled

by the amount of swelling clay in most soils and therefore

Table 2 PTFs for estimating Atterberg limits from measured soil properties

Prediction equation for LL0.5 Prediction equation for LS0.75 Prediction equation for logPL Prediction equation for PI0.5

Parameter Estimate P-value Parameter Estimate P-value Parameter Estimate P-value Parameter Estimate P-value

Intercept 4.757 <0.001 Intercept 4.459 <0.001 Intercept 4.095 <0.001 Intercept 0.741 0.003

Humic-A*1 �0.601 <0.001 Fe 0.292 <0.001 Fe 0.198 <0.001 Fe 0.126 <0.001

Melanic-A �0.352 0 pH �1.331 <0.001 Al 0.136 <0.001 OC �0.068 <0.001

Orthic-A �0.402 <0.001 K �0.638 <0.001 OC 0.022 0.3022 Na �0.041 0.282

Apedal-B*2 �0.141 0.124 Mg 0.04 0.001 pH �0.364 <0.001 Mg 0.075 <0.001

Eluvial-B �0.495 <0.001 CEC 0.068 <0.001 CEC 0.005 0.005 CEC 0.027 <0.001

Gleyed-B 0.05 0.613 Si 0.049 <0.001 Sa �0.017 <0.001 Clay 0.134 <0.001

Plinthic-B 0.017 0.864 Cl 0.061 <0.001 (Fe)2 �0.01 <0.001 (Fe 9 Cl) �0.002 <0.001

Saprolitic B/C 0.054 0.563 (Fe 9 Cl) �0.004 <0.001 (Fe 9 OC) �0.016 <0.001 (Na 9 CEC) 0.005 0.002

Structured-B �0.102 0.227 (pH)2 0.086 <0.001 (Fe 9 pH) �0.013 <0.001 (Cl)2 �0.001 <0.001

Fe 0.411 <0.001 (K)2 0.116 0.002 (OC)2 0.018 0.002 (Cl)3 0.001 <0.001

Al 0.192 <0.001 (Si)2 �0.001 <0.001 (pH)2 0.025 <0.001

OC 0.277 <0.001 (CEC 9 Sa) 0.001 <0.001

pH �0.186 <0.001 (Sa)2 0.001 <0.001

Na �0.026 0.398 (Fe)3 0.001 0.004

Ca �0.107 <0.001

Mg 0.059 <0.001

CEC 0.062 <0.001

Sa 0.003 0.075

Cl 0.025 <0.001

(Fe 9 OC) �0.035 <0.001

(Fe 9 Sa) �0.003 <0.001

(Fe 9 Cl) �0.005 <0.001

(pH 9 Ca) 0.015 <0.001

(Na 9 Ca) �0.006 0.005

(Na 9 CEC) 0.007 <0.001

(CEC 9 Cl) �0.001 <0.001

(Clay)2 0 <0.001

Fe and Al: CBD iron and aluminium content (%); OC: organic carbon content (%); Na, Ca, K and Mg: pH: pH (H2O); extractable sodium,

calcium, potassium and magnesium (cmolc kg/soil); CEC: cation exchange capacity (cmolc kg/soil); Sa, Si and Cl: sand, silt and clay fractions

(%). *1-A refers to topsoil horizons and *2-B to subsoil horizons.



related to clay mineralogy (Moradi, 2013). Higher CEC

values are typically associated with soils dominated by 2:1

clay minerals which are plastic by nature. The role of

magnesium (Mg) in the structure of montmorillonitic clay

implies a link to CEC and an indirect, although strong,

correlation with PI. Fanourakis (2012) found that Mg in the

clay-sized fraction can predict LL, PI and LS sufficiently in

apedal subsoils with r values of 0.92, 0.72 and 0.82,

respectively (albeit for a much smaller, localized data set).

Positive correlations between Atterberg limits and cations

were also reported by De Jong et al. (1990), Ahmadi et al.

(2012) and Moradi (2013). The lack of impact by OC on the

indicators of PI may be due to a contribution to CEC of the

soil imitating higher physical activity but is actually

physically stabilizing the soil. Zolfaghari et al. (2015) also

reported no significant correlations between LL and PI and

OC, but Seybold et al. (2008) considered OC an important

predictor of PI.

The PTFs developed (Tables 2 and 3) have low predictive

value when compared to other studies with smaller data sets

and localized studies. For example, Ahmadi et al. (2012),

using 26 samples, obtained R2 of 0.87, 0.77 and 0.84 for LL,

PL and PI, respectively. The RMSE (%) was below 3 for all

these predictions. The modelling accuracy of Fanourakis

(2012) reported earlier was obtained on 30 samples of the

same diagnostic horizon.

Model accuracy of PTFs conducted on larger data sets is

more comparable to our results (Table 3). De Jong et al.

(1990) working with approximately 260 samples reported R2

of 0.86, 0.35 and 0.35 for LL, PL and PI, respectively. The

prediction of LL of Seybold et al. (2008) on 4332 samples

(R2 = 0.79; RMSE = 6.694) is comparable with our results

(R2 = 0.77; RMSE = 5.38). Likewise, our prediction of PI

(R2 = 0.62; RMSE = 5.19) is analogous with that of Seybold

et al. (2008) on 2797 samples (R2 = 0.69; RMSE = 5.429).

The higher R2, in comparison with De Jong et al. (1990), for

prediction of PL and PI, and lower RMSE, compared to

Seybold et al. (2008), might be attributed to a more complex

model structure (Tables 2 and 3).

Morphological data

Physical activity leaves conspicuous signatures in the soil.

The expression of these signatures could be related to the

parameters of PI. Slickensides, cracks in the dry state and

structure are commonly known as inherently part of swelling

soils and therefore used as classification criteria for

extremely swelling soils.

The relationship with terrain relates to hydrology. The

distribution of swelling clays is related to wetness.

Pedological wetness of a terrain position is dependent on

climate as locally manipulated by hydrology. A very large

area of South Africa is semi-arid with a long boundary to

the arid climate zone. Climatically the dry semi-arid climates

are too dry for the development of swelling clays either by

weathering of basic igneous rock to swelling clay or the

neoformation of clay. Hydrological redistribution of water to

valley bottoms results in the crest of the hillslope being to

dry and the valley bottom wet enough for the formation

of swelling clay. This is in agreement with the results of

Zolfaghari et al. (2015) who recorded greater plasticity at

deeper positions in the profile. A positive correlation

between swelling properties and structure, specifically coarse

angular blocky and prismatic, and slickensides confirms tacit

knowledge in every soil surveyor working with a variety of

swelling soils (Table 4). The positive correlation of physical

Table 3 Characteristics of final selected regression models for Atterberg limits (n = 2230)a

Atterberg

limit (dependent

variable) to

be predicted

Exponent of

optimal power

Transformation of

dependent variablebHighest

term selected

Intercept

terms for

horizon

selected?

Number of

model parameters

(excl overall

intercept) R2 (training data)

RMSE

(training data)cRMSE

(validation data)c

LL k = 0.5 Quadratic Yes 27 0.774 5.380 5.160

0.439 0.430

LS k = 0.75 Quadratic No 11 0.563 2.10 2.050

1.050 1.020

PL k = 0. (logarithm) Cubic No 14 0.526 4.130 4.610

0.229 0.255

PI k = 0.5 Cubic No 10 0.624 5.19 5.130

0.614 0.607

aOf the total sample (n = 2230), 75% of observations (nT = 1669) were randomly selected as training sample, and 25% (nV = 561) as validation

sample. bPower parameter k of Box–Cox transformation of dependent variable (Box & Cox, 1964). cFor each model, the first line provides

RMSE values for the transformed dependent variable scaled as ðYk � 1=ðk � Y ðk�1ÞÞ, where k is the parameter of the power transformation, and Yis the geometric mean of the dependent variable on the original scale (these RMSE values can usefully be compared to RMSE values obtained

from a fit of the untransformed variable Y); the second line (in italics) provides RMSE values for the transformed dependent variable Yk. When

k = 0, the transformed dependent variables, respectively, are given by Y � lnðYÞ and ln(Y).



Table

4Morphologicalsoilproperties,regressionslopes

andassociatedcodingusedin

developmentofPTF

Texture

(R2=0.014)

Class

(N)

SiLm

(41)

Sa(5)

Si(1)

SiClLm

(73)

SaLm

(84)

SaCl(225)

Lm

(100)

SaClLm

(580)

SiCl(115)

ClLm

(283)

Cl(873)

m0.000

0.011

0.018

0.045

0.052

0.080

0.099

0.111

0.176

0.181

0.273

Code

12

34

56

78

910

11

Structure

type

(R2=0.163)

Class

(N)

Mass

(981)

Crumb(76)

Granu(45)

Platy

(17)

Sanbl(1064)

Colum

(20)

Prism

(185)

Anbl(492)

m�0

.232

�0.063

�0.019

�0.011

0.000

0.008

0.107

0.236

Code

12

34

56

78

Colour

(R2=0.071)

Class

(N)

Yellow

(29)

Red

(550)

Brown(1740)

Grey(146)

Black

(129)

m0.000

0.011

0.085

0.219

0.221

Code

12

34

5

TMU

(R2=0.016)

Class

(N)

Crest

(340)

Midsl(1559)

Valbt(273)

Ftsl(829)

m�0

.095

�0.085

0.000

0.030

Code

12

34

Structure

grade

(R2=0.224)

Class

(N)

Aped

(1001)

Weak(819)

Modr(572)

Strng(501)

m�0

.087

0.000

0.271

0.415

Code

12

34

Structure

size

(R2=0.121)

Class

(N)

None(898)

Fine(519)

Med

(857)

Coar(488)

m0.000

0.206

0.301

0.338

Code

12

34

Consistency

(R2=0.150)

Class

(N)

Loose

(45)

Frbl(613)

Firm

(1026)

VFrm

(221)

m�0

.596

�0.407

�0.218

0.000

Code

12

34

Cutans

(R2=0.164)

Class

(N)

None(531)

Few

(542)

Cmn(520)

Many(283)

m0.000

0.233

0.378

0.459

Code

12

34

Roots

(R2=0.060)

Class

(N)

Many(253)

Cmn(498)

Few

(635)

None(141)

m�0

.147

�0.131

�0.120

0.000

Code

12

34

Transitiontopo

(R2=0.015)

Class

(N)

Broke(33)

Smoo(1566)

Tong(93)

Wavy(387)

m�0

.122

�0.077

�0.022

0.000

Code

12

34

Slickenside

(R2=0.361)

Class

(N)

None(554)

Few

(91)

Many(103)

m0.000

0.319

0.517

Code

12

3

SiLm,Silty

Loam;Sa,Sand;Si,Silt;SiClLm,Silty

ClayLoam;SaLm,SandyLoam;Lm,Loam;SaClLm,SandyClayLoam;SiCl,Silty

Clay;ClLm,ClayLoam;Cl,Clay;Mass,

Massive;

Granu,Granular;Sanbl,Sub-angularblocky;Colum,Columnar;Prism

,Prism

atic;

Anbl,Angularblocky;Midsl,Midslope;

Valbt,Valley

bottom;Ftsl,Footslope;

Aped,

Apedal;Modr,Moderate;Strng,Strong;Med,Medium;Coar,Coarse;

Frbl,Friable;VFrm

,Veryfirm

;Cmn,Common;Smoo,Smooth;Tong,Tongey;Topo,Topography;TMU,

Terrain

MorphologicalUnit.



activity with soil colour is also a confirmation of tacit

knowledge. The selection of data across all soil types brings

another element to the front. Black colours are commonly

associated with increased clay in a calcium-rich environment

and grey colours with water logging; yet, both are positively

correlated with the parameters of physical activity. The

positive correlation with consistence confirms the

relationship between vertic soils and gleyed subsoils. Gleyed

subsoils are generally waterlogged or at least wet, and

typical vertic morphology does not occur. It indicates an

impact of soil water regime on the development of vertic

properties often overlooked.

The negative correlation of roots and horizon transition

with parameters of physical activity is indirect (Table 4).

Stunted growth of trees on soil with extremely high physical

activity is claimed to be from root pruning related to

shrinking in the dry state.

Although the accuracy of PTF to estimate PI from

morphological data is not comparable to those developed

from measured properties (Table 3), and especially not to

those developed from measured properties on local scale

(e.g. Fanourakis, 2012), it might be able to assist pedologist

to quantify PI in the field with a degree of accuracy.

Conclusion

Atterberg limits are generally used for engineering purposes,

which by nature requires site-specific information. Although

the PTFs presented are comparable with other studies

working on large data sets, it is clear that PTFs for specific

areas are more accurate and hence more applicable in

practice. For engineering purposes, PTFs of Atterberg limits

should therefore be developed for specific areas. The

presented PTFs can, however, be valuable for reconnaissance

purposes, for example identifying areas likely to pose

structural challenges on large-scale developments.

Although the PTF developed from morphological

properties has a low prediction accuracy, it does suggest that

there is potential to use these properties in PTFs. Future

research should therefore aim to combine morphological

properties and routinely measured soil properties to improve

PTFs.

Acknowledgements

We would like to express our gratitude towards all Land

Type personnel who classified the soils and collected soil

samples as well as towards the Agricultural Research

Council of South Africa for availing the data.

References

Ahmadi, A., Talaie, E. & Soukoti, R. 2012. Pedotransfer functions

for estimating Atterberg limits in semi-arid areas. International

Journal of Agriculture: Research and Review, 2, 491–495.

Atterberg, A. 1911. Die Plastizit€at der Tone. Internationale

Mitteilungen f€ur Bodenkunde, 1, 10–43. (in German).

Bouma, J. 1989. Using soil survey data for quantitative land

evaluation. Advances in Soil Science, 9, 177–213.

Box, G.E.P. & Cox, D.R. 1964. An analysis of transformations.

Journal of the Royal Statistical Society, Series B, 26, 211–234.

De Jong, E., Acton, D.F. & Stonehouse, H.B. 1990. Estimating the

Atterberg limits of Southern Saskatchewan soils from texture and

carbon contents. Canadian Journal of Soil Science, 70, 543–554.

Fanourakis, G.C. 2012. Estimating soil plasticity properties from

pedological data. Journal of the South African Institution of Civil

Engineering, 2, 117–125.

Haigh, S.K., Vardanega, P.J. & Bolton, M.D. 2013. The plastic limit

of clays. Geotechnique, 63, 435–440.

Mbagwu, J.S.C. & Abeh, O.G. 1998. Prediction of engineering

properties of tropic soils using intrinsic pedological parameters.

Soil Science, 163, 93–102.

Moradi, S. 2013. Effects of CEC on Atterberg limits and Plastic

Index in Different Soil Textures. International Journal of

Agronomy and Plant Production, 4, 2111–2118.

50

50

R2 = 0.485

RMSE = 7.03

40

40

30

30

Mea

sure

d P

I

20

20

10

10

45

45

35

35

25

25

Estimated PI

15

15

5

50

0Figure 2 Validation of measured versus

estimated PI based on predictions from

qualitative (morphological) data.



SAS Institute Inc. 2013. SAS/STAT 13.1 User’s Guide. SAS Institute

Inc., Cary, NC

Schmitz, R.M., Schroeder, C. & Charlier, R. 2004. Chemo-

mechanical interactions in clay: a correlation between clay

mineralogy and Atterberg limits. Applied Clay Science, 26, 351–358.

Seybold, C.A., Elrashidi, M.A. & Engel, R.J. 2008. Linear regression

models to estimate soil liquid limit and plasticity index from basic

soil properties. Soil Science, 173, 25–34.

Smith, C.W., Hadas, A., Dan, J. & Koyumdjisky, H. 1985.

Shrinkage and Atterberg limits in relation to other properties of

principle soil types in Israel. Geoderma, 35, 47–65.

Soil Classification Working Group (SCGW). 1991. Soil classification:

a taxonomic system for South Africa. Memoirs on the

Agricultural Natural Resources of South Africa no. 15.

Department of Agricultural Development, Pretoria.

Vereecken, H. & Herbst, M. 2004. Statistical regression. In:

Development of pedotransfer functions in soil hydrology (eds Y.A.

Pachepsky & W.J. Rawls), pp. 415–429. Elsevier, Amsterdam.

Wagner, B., Tarnawski, V.R., Hennigs, V., Muller, U., Wessolek, G.

& Plagge, R. 2001. Evaluation of pedo-transfer functions for

unsaturated soil hydraulic conductivity using an independent data

set. Geoderma, 102, 275–297.

Yilmaz, I. 2004. Relationship between liquid limit, cation exchange

capacity and swelling potential of clayey soils. Eurasian Soil

Science, 37, 506–512.

Yukselen, Y. & Kaya, A. 2006. Prediction of cation exchange

capacity from soil index properties. Clay Minerals, 41, 827–837.

Zhang, B., Horn, R. & Hallett, P.D. 2005. Mechanical Resilience of

degraded soil amended with organic matter. Soil Science Society

of America Journal, 69, 864–871.

Zolfaghari, Z., Mosaddeghi, M.R. & Ayoubi, S. 2015. ANN-based

pedotransfer and soil spatial prediction functions for predicting

Atterberg consistency limits and indices from easily available

properties at watershed scale in western Iran. Soil Use and

Management, 31, 142–154.



Pedotransfer functions to predict Atterberg limits for ...

Documents

Transcript of Pedotransfer functions to predict Atterberg limits for ...