Paper 4

Al-Qadisiyah Journal For Engineering Sciences, Vol. 9……No. 1 ….2016

Effect of Clay Percentage in Sandy Clay Soil on Saturated Hydraulic

Conductivity

Dr. Khitam Abdulhussein Saeed

Iraq-Baghdad Al-Mustansiriya University-College of Engineering

Email: khitamhussein@yahoo.com

Received 28 June 2015 Accepted 9 December 2015

ABSTRACT:

Hydraulic properties of sandy clay soil are very important for filtration, seepage and irrigation; so set

of experiments were carried out for different samples of sandy clay in Baghdad. Measurements include

bulk density, particle size distribution, clay percentage and hydraulic conductivity using constant head

system. The aims of this study were to estimate equivalent saturated hydraulic conductivity (Ks) for

different clay percentages and predict porosity of sandy clay as function of clay percentage and

porosity of sand and clay. Nine samples of sandy clay soil have been tested in a hydraulic and soil

laboratory (Mustansiriya University). Semi-empirical model was correlated to evaluate saturated

hydraulic conductivity from clay percentage and results were compared with five empirical models

selected from published literature were also used to predict Ks. These empirical models were

(Puckett ,1985) , (Ryjov and Sudoplatov,1990), ( Dane ,1992), (Dheyaa ,2001)and (Shevnin.et al,

2006).

Keywords: soil, sandy clay, hydraulic conductivity, porosity

اثر نسبة الطين في الترب الرملية الطينية على التوصيل الهيدروليكي المشبع

د. ختام عبد الحسين

: الملخص

ةيمول دورا لرترحودلجالار وا لالورل لوجلي ادر وع ةامااول ةوب التاووول ل موو الخواا اليدروللديدول لرتورل الرةردول الةد دولتعتبر

.حوومرع الادوتوووك الي و وول ال,ولر وولجالتام الباموو لرببدبوكج وووبل الةوودب لالما ووردل ةخترفوول ةووب التوورل الرةردوول الةد دوول وو وورا

ل المشبعل الميو ئل ل وب ةخترفل ةب . اا اليرف ةب الرواتل لا لتاددم الما ردل اليدروللديداليدروللديدل ةوتعمردب ,وم االوتفوع ال و ع

توو موو ةوب توم بو كرالول ل ووبل الةودب لالموووةدل ليوا ةوب الةودب لالرةوا.الةدب لكجلي الت بو ولمووةدل لرترل الةد دول الرةردول

حوب تار بو لتادودم أاتمر و ةعولاول ال تووئل اروو موا الترل الرةردل الةد دل ةختبرل الماائ لالتر ل الاوةعل الموت صور ل.

ا الك تةبدادل ةختووة ةب ة شاواك تو ال الت ا ضو قدموع الما ردل اليدروللديدل المشبعل ةب وبل الةدب لتمع ةاوو ت ة خمس ة

ةب الما ردل اليدروللديدل المشبعل للجه الما الك ليا

(Puckett, et al,1985: Ryjov and Sudoplatov,1990: Dane,1992: Dheyaa ,2001 : Shevnin,2006)

mailto:khitamhussein@yahoo.com

Al-Qadisiyah Journal For Engineering Sciences, Vol. 9……No. 1 ….2016

1. INTRODUCTION

Hydraulic conductivity (K) is the constant of proportionality in Darcy’s Law and as such is defined as

defines the rate of movement of water through a porous medium such as a soil or aquifer or the flow

volume per unit cross-sectional area of porous medium under the influence of a unit hydraulic gradient

(m/d) commonly used units for hydraulic conductivity shown in (Table 1) (Puckett et al, 1985) and

(Nakhaei, 2005).

Soil water potential is the driving force behind water movement. The main advantage of the "potential"

concept is that it provides a unified measure by which the water state can be evaluated at any time and

everywhere within the soil-plant-atmosphere continuum (Hillel, 1980).

The forces subject soil water include gravity, hydraulic pressure, the attraction of the soil matrix for

water, the presence of solutes, and the action of external gas pressure .At any point in the soil, total soil

water potential is the sum of all of the contributing forces(Hillel, 1980).

Measurement of hydraulic conductivity is problematic, considering the parameter can differ over

several orders of magnitude across the spectrum of sediments and rock types, as indicated in (Table 2).

The parameter can also vary markedly in space, even with apparently minor changes in sediment

characteristics. Hydraulic conductivity is influenced by the properties of the fluid being transmitted

(such as viscosity) as well as the porous medium (Ranieri et al, 2012). Hydraulic conductivity is also

scale dependent, so that measurements taken at the core sample level may not be directly extrapolated

to the aquifer scale. It is also direction dependent, so that hydraulic conductivity can be markedly

different in the vertical from the horizontal. Hydraulic conductivity cannot be directly measured but

inferred from field, laboratory or modeled data.

2. THEORETICAL APPROACH

In Darcy’s law, saturated hydraulic conductivity is a constant (or proportionality constant) that defines

the linear relationship between the two variables J and i (figure 1). It is the slope of the line (J/i)

showing the relationship between flux and hydraulic gradient. Solving Darcy’s equation for K yields

J/i (see equation 1).

K = J/i (1)

Flux (J) is commonly expressed on a volume basis, and the units simplify to m/s. The hydraulic head

difference (ΔH) is commonly expressed on a weight basis. It simplifies to centimeters of head, and the

hydraulic gradient (i) becomes unit less (e.g., cm/cm) (Ranieri et al, 2010). Then, Ks takes the same

units as flux (m/s). Flux represents the quantity of water moving in the direction of, and at a rate

proportional to, the hydraulic gradient. If the same hydraulic gradient is applied to two soils, the soil

from which the greater quantity of water is discharged (i.e., highest flux) is the more conductive

(greatest flow rate). The sandy soil yields a higher flux (is more conductive) than the clayey soil at the

same hydraulic gradient as shown in Figure (1). The soil with the steeper slope (the sandy soil in figure

1) has the higher hydraulic conductivity. Hydraulic conductivity (or slope "K") defines the proportional

relationship between flux and hydraulic gradient, or in this case, of unidirectional flow in saturated

soil. Saturated hydraulic conductivity ("Ks") is a quantitative expression of the soil’s ability to transmit

water under a given hydraulic gradient (Mason et al, 1957).

http://soils.usda.gov/technical/technotes/note6.html#ref#ref
http://soils.usda.gov/technical/technotes/note6.html#ref#ref
http://www.connectedwater.gov.au/framework/hydrometric_k.php#table2
http://soils.usda.gov/technical/technotes/note6.html#eq5#eq5

Al-Qadisiyah Journal For Engineering Sciences, Vol. 9……No. 1 ….2016

The hydraulic conductivity for a given soil becomes lower when the fluid is more viscous than water.

Hydraulic conductivity (or Ks) is expressed using various units. The units and dimensions depend on

those that are used to measure the hydraulic gradient (mass, volume, or weight) and flux (mass or

volume). To provide national consistency in defining permeability classes in soil surveys, Uhland and

O'Neal (1951) evaluated percolation rates of about 900 soils. They defined "permeability" classes by

distributing the percolation data equally among seven tentative classes (Table 2). Along with

percolation data, they also studied 14 soil morphologic characteristics that affect water movement and

that could be used to make predictions regarding permeability class. Because of management effects

on surface horizons, they confined their study to horizons below the surface layer. These classes were

published in the 1951 Soil Survey Manual (Soil Survey Staff, 1951).

Mason et al. (1957) statistically analyzed Uhland and O'Neal's data. They concluded that it was overly

optimistic that one could correctly place a given soil into one of seven permeability classes on the basis

of percolation rates of five core samples taken at one site (the probability of being correct was 30%). A

reasonable degree of reliability could be achieved if either more sites per soil were sampled or fewer

classes were used. The study suggested that a 95% probability of making a correct placement could

occur by using three to five permeability classes. In 1963, the NCSS National Soil Moisture

Committee proposed a class/subclass "choice schema" with five to seven classes (Table 2) (Soil

Survey Division, 1997). The proposal was provisionally accepted, pending the outcome of discussions

comparing auger-hole percolation tests with the Uhland core method and pending additional

information on critical limits.

When the Soil Survey Division converted its previous database to the National Soil Information

System (NASIS) in 1994, saturated hydraulic conductivity replaced permeability. Only the name was

changed at this time. The values from the previous database were imported directly into NASIS

without modification.

Krumbein and Monk (1943) proposed the equation:

K=b(dm)
2

exp ( -σΦ

) (2)

Where k is in darcies (1 darcy = 9.87E
-09

cm
2
), dm is the geometric mean grain-size diameter (mm),

σΦ is the geometric standard deviation (in Φ units, where Φ is –ln(d) and d is the grain-size diameter in

mm), and a and b are empirical constants. This equation was based on experiments performed with

sieved glacial outwash sands that were recombined to obtain various grain-size distributions.

Kozeny (1953) proposed an equation based on porosity and specific surface that may be written as

(Marshall 1958):

K=n
3
/(S

2
p (3)

Where k is in cm
2
, S is the soil surface area of the medium per volume (cm

2
/cm

3
), and p is an empirical

constant. Marshall (1958) went on to derive an equation for an isotropic material in which the mean

radius of pores for each of ‘m’ equal fractions of the total pore space are represented by the

corresponding mean radii (r1, r2, . . ., rm):

http://soils.usda.gov/technical/technotes/note6.html#ref#ref
http://soils.usda.gov/technical/technotes/note6.html#table2#table2
http://soils.usda.gov/technical/technotes/note6.html#ref#ref
http://soils.usda.gov/technical/technotes/note6.html#ref#ref
http://soils.usda.gov/technical/technotes/note6.html#table2#table2
http://soils.usda.gov/technical/technotes/note6.html#ref#ref
http://soils.usda.gov/technical/technotes/note6.html#ref#ref

Al-Qadisiyah Journal For Engineering Sciences, Vol. 9……No. 1 ….2016

K=1/8{n
2
m

-2
[r1

2
+3r2

2
+5r3

2
+……(2n-1)rn

2
]} (4)

Where k is in cm
2
, ri (cm) is the mean radius of the ith fraction, and r decreases in size from r1 to rm.

Shepherd (1989) extended Hazen’s work by performing power regression analysis on 19 sets of

published data for unconsolidated sediments.

Ks=cD
2

10 (5)

The data sets ranged in size from 8 to 66 data pairs. He found that the exponent in Equation 8 varies

from 1.11 to 2.05 with an average value of 1.72, and that the value of the constant c is most often

between 0.05 and 1.18 but can reach a value of 9.85. Values for both c and the exponent are typically

higher for well-sorted samples with uniformly sized particles and highly spherical grains.

3. EXPERIMENTAL WORK

There are relatively simple and inexpensive laboratory tests that may be run to determine the hydraulic

conductivity of a soil: constant-head method and falling-head method. The constant-head method is

typically used on granular soil as shown in figure (2). This procedure allows water to move through the

soil under a steady state head condition while the quantity (volume) of water flowing through the soil

specimen is measured over a period of time. By knowing the quantity Q of water measured, length L of

specimen, cross-sectional area A of the specimen, time t required for the quantity of water Q to be

discharged, and head h, the hydraulic conductivity can be calculated:

K=V L /[A t (H2-H1)] (6)

The total head loss through the permeameter is indicated by the difference in elevation between the

inflow and outflow water levels.

3.1 Laboratory Methods

Constant-head methods are primarily used in samples of soil materials with an estimated K above

1.0 × 10
2
m/yr, which corresponds to water filters medias. Important considerations regarding the

laboratory methods for measuring K are related to the soil sampling procedure and preparation of the

test specimen and circulating liquid. The sampling process, if not properly conducted, usually disturbs

the matrix structure of the soil and results in a misrepresentation of the actual field conditions.

3.2 Materials and Methods

Samples were classified according to particle size using a standard British Soil Classification System,

detailed in BS 5930: Site Investigation.

The samples were classified, diameters of soil particles at 10%, 20% and 50% cumulative weight

determined, and the coefficients of uniformity, intercepts and porosity values were calculated. Since

the kinematic coefficient of viscosity is also necessary for the estimation of hydraulic conductivity, a

value of 0.0874m
2
/day (0.897 *10

-6
m

2
/s) derived for a water temperature of (24-26

o
C) is measured in

the laboratory.

Al-Qadisiyah Journal For Engineering Sciences, Vol. 9……No. 1 ….2016

4. RESULTS

4.1 Prediction of Porosity of Sandy Clay Soil

The total porosity nsc of the sandy clay soil is calculated from two empirical forms, the first is (Ryjov

and Sudoplatov,1990) equation as following expressions:

nsc= (ns - C ) +nc.C, when C <ns (7)

nsc= = C.nc, when C ≥ ns (8)

Where C is clay content, nc is clay porosity and ns is sand porosity.

The second empirical equation is (Dheyaa, 2001) model as following expression:

nsc= ns (1- C ) +nc.C (9)

Clay and sand porosities are considered as constant; therefore, soil porosity is a function of clay

content.

Thus, porosity, grain size (or capillary radius) and tortuosity are not independent parameters. Rather,

they are interrelated in the sand-clay soil model. In this work clay content as the main factor was

considered, as a function of other parameters such as soil porosity, tortuosity and formation factor.

Measurements for different porosities (0 to 1 ) were graphed and correlated as follow (R
2
=0.879 ):

nsc= 0.244+0.036C (10)

Comparison between measured values of porosities and empirical equations of (Ryjov and Sudoplatov,

1990), (Dheyaa, 2001) and (Masch. et al, 1966) were shown in figure( 3).

4.2 Effect of clay percentage on hydraulic conductivity of sandy clay soil

Filtration coefficient of soil depends on many factors, like clay content, grain size, type of clay,

anisotropy of layered sediments, and two types of capillaries in clay. As a result, dependence of

filtration coefficient from clay content is scattered. The scatter can be diminished with the help of

calibration by using direct Ks measurements.

Puckett et al. (1985) sampled six soils at seven different locations in the Alabama lower coastal plain

containing 34.6% to 88.5% sand-sized particles and 1.4% to 42.1% clay-sized particles, and used

regression analysis to determine that percentage of clay sized particles was the best predictor of Ks (R
2

= 0.77):

Ks=4.36*10
-3

exp (-0.1975 C) (11)

Where Ks is expressed in cm/sec and C is the clay-sized particles (in percent) in the soil sample. Bulk

density and porosity, often used in other pedotransfer functions, were not highly correlated with Ks for

this data set of sandy soils.

Al-Qadisiyah Journal For Engineering Sciences, Vol. 9……No. 1 ….2016

Dane and Puckett (1992) expanded the work of Puckett et al. (1985) with two more data sets from the

lower coastal plain of Alabama. One set consisted of 577 Ks and grain-size data pairs from 60

locations in a 0.5-ha agricultural field in south central Alabama. Nonlinear regression analysis yielded

the equation (R
2
= 0.453):

Ks=8.44*10
-5

exp (-0.144 C) (12)

The form of Equation 6 that worked well for the previous data set yielded a significantly poorer fit for

this data set. Another set of data consisting of 130 pairs of Ks and grain-size data from nine different

soil series from the Florida Panhandle was also analyzed.

Nonlinear regression analysis resulted in the equation (R
2
= 0.443):

Ks=7.77*10
-5

exp (-0.116 C) (13)

Which also displayed a poorer fit than their previous study (Puckett et al, 1985). Comparison between

measured values of hydraulic conductivity and empirical models of (Puckett, 1985) and (Dane and

puckett 1992) for different clay percentages is shown in Figure (4).

5. CONCLUSIONS

Nine samples of sandy clay soil have been tested in a hydraulic and soil laboratory (Mustansiriya

University). The major conclusions can be drawn as follow:

1. Filtration coefficient of sandy clay soil extremely depends on clay content,

2. Measurements for different porosities (0 to 1) were correlated as (R
2
=0.879 ):

nsc= 0.244+0.036C

3. Empirical equation of hydraulic conductivity for different percentages of clay sized particles
was correlated with the best predictor of Ks (R

2
= 0.897) as:

Ks=0.019exp (-0.11 C)

6.REFERENCES:

[1] Dheyaa, W. (2001)"Hydrodynamic Modeling of laminar flow in porous media".19 – 20 march,

Water resource, Baghdad.

[2] Dane, J.H. and W.E. Puckett. 1992. Field soil hydraulic properties based on physical and

mineralogical information. In Proceedings of an international workshop: Indirect methods for

estimating the hydraulic properties of unsaturated soils.

[3] Hillel, D. 1980. Fundamentals of soil physics. Academic Press. New York, NY.

Al-Qadisiyah Journal For Engineering Sciences, Vol. 9……No. 1 ….2016

[4] Krumbein, W. C. and G. D. Monk. 1943. Permeability as a function of the size parameters of

unconsolidated sands. Transaction of the American Institute of Mining, Metallurgical and Petroleum

Engineers, 151, 153-163.

[5] Kozeny, J. 1953. Das wasser in boden, grundwasserbewegung. Hydraulik, 280-445.( In German).

[6] Mason, D.D., J.F. Lutz, and R.G. Petersen. 1957. Hydraulic conductivity as related to certain soil

properties in a number of great soil groups—Sampling errors involved. Soil Science Society of

America Proceedings 21:554–561 Marshall, T.J. 1958. A relation between permeability and size

distribution of pores.Journal of Soil Science 9, 1-8.

[7] Masch, F. D. and K. J. Denny. 1966. Grain-size distribution and its effect on the permeability of

unconsolidated sands. Water Resources Research 2, no. 4: 665–677.

[8] Marshall, J. J. (1958). A relation between permeability and size distribution of pores. Journal of

soil science ,9 :1-8.

[9] Nakheai, M. (2005). Estimating the saturated hydraulic conducting of granular material using

artificial neural network based on grain size distribution curve. Journal of Science, 16(1) :55-62.

[10] Puckett, W.E., J.H. Dane, and B.F. Hajek. 1985. Physical and mineralogical data to determine soil

hydraulic properties. Soil Science Society of America Journal 49, no. 4:831-836

[11] RYJOV, A. A. and A. D. SUDOPLATOV, 1990. The calculation of specific electrical

conductivity for sandy - clayed rocks and the usage of functional cross-plots for the decision of

hydrogeological problems. In: Scientific and technical achievements and advanced experience in the

field of geology and mineral deposits research. Moscow, pp. 27-41.

[12] Ranieri, V., Antonacci, M. C., Ying, G and Sansalone, J. J. (2010). Application of kozeny-kovacs

model to predict the hydraulic conductivity of permeable pavement. Transportation research record,

2195: 168-176.

[13] Ranieri, V., Ying, G. and Sansalone, J. (2012). Drainage modeling of roadway systems with

porous frication courses. Journal of transportation engineering, 138(4) : 395-405.

[14] Shevnin, V., O. Delgado-Rodríguez, A. Mousatov and A. Ryjov, 2006. Estimation of soil

superficial conductivity in a zone of mature oil contamination using DC resistivity. SAGEEP-2006,

Seattle. P.1514-1523.

[15] Shepherd R. G. (1989). Correlation with permeability and grain size. Ground water,27(5): 633-

638.

[16] Site investigation: A Guide to BS 5930 : 1999 : Code of practice for site investigations for

higher education, 593.

[17] United State Department of Agriculture, (1951). Soil Survey Manual. U. S. Dept. Agr. Hanb, 1

Al-Qadisiyah Journal For Engineering Sciences, Vol. 9……No. 1 ….2016

[18] Uhland, R.E. and A.M. O'Neal. 1951. Soil permeability determination for use in soil and water

conservation. SCS–TP–101. United States Department of Agriculture, Soil Conservation Service,

Washington, D.C.

[19] Uma, K.O., B.C.E. Egboka, and K.M. Onuoha. 1989. New statistical grain-size method for

evaluating the hydraulic conductivity of sandy aquifers. Journal of Hydrology 108, 343-366.

Table (1): Commonly used units for hydraulic conductivity (K)(Hillel, 1980)

Description (m/d) (m/s) (mm/d) (mm/hr)

Extremely slow 0.000001 1.5741x10
-11

0.001 0.000041667

Very Slow 0.0001 1.5741x10
-9

0.1 0.0041667

Slow 0.01 1.5741x10
-7

10 0.41667

Moderate 1 1.5741x10
-5

1000 41.667

Fast 10 1.5741x10
-4

10000 416.667

Very Fast 100 1.5741x10
-3

100000 4166.667

Table (2): Indicative hydraulic conductivities of some rock types (Uhland and O'neal 1951)

Rock Type Grain size (mm) Hydraulic Conductivity K (m/d)

Clay 0.0005-0.002 10
-2

-10
-8

Silt 0.002-0.06 10
-2

- 1

Fine Sand 0.06 -0.25 1-5

Medium Sand 0.25-0.50 5-20

Coarse Sand 0.50-2 20-100

Gravel 2-64 100-1000

Shale Small 5x10
-6

- 5x10
-8

Sandstone Medium 10
-3

-1

Limestone Variable 10
-5

-1

Basalt Small 0.0003-3

Granite Large 0.0003-0.03

Slate Small 10
-5

-10
-8

Schist Medium 10
-4

-10
-7

Al-Qadisiyah Journal For Engineering Sciences, Vol. 9……No. 1 ….2016

Figure (1): The relationship between flux and hydraulic gradient density.

Figure (2): Constant head permeameter

(After Todd, 1959)

Plate 1: The Constant Head Parameter Test

Al-Qadisiyah Journal For Engineering Sciences, Vol. 9……No. 1 ….2016