Journal of Hydrology 519 (2014) 1649–1659

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Journal of Hydrology

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A laboratory method to determine the hydraulic conductivityof mountain forest soils using undisturbed soil samples

http://dx.doi.org/10.1016/j.jhydrol.2014.09.0450022-1694/� 2014 Elsevier B.V. All rights reserved.

⇑ Corresponding author. Tel.: +48 12 662 5111; fax: +48 12 411 9715.E-mail addresses: a.ilek@wp.pl (A. Ilek), j.kucza@ur.krakow.pl (J. Kucza).

Anna Ilek ⇑, Jarosław KuczaDepartment of Forest Engineering, Faculty of Forestry, University of Agriculture in Cracow, Al. 29 Listopada 46, 31425 Cracow, Poland

a r t i c l e i n f o

Article history:Received 23 May 2014Received in revised form 30 August 2014Accepted 17 September 2014Available online 28 September 2014This manuscript was handled byPeter K. Kitanidis, Editor-in-Chief, with theassistance of Markus Tuller, Associate Editor

Keywords:Forest hydrologyStony forest soilsLaboratory methodHydraulic conductivityUndisturbed soil samples

s u m m a r y

Determination of infiltration properties of soils under laboratory conditions necessitates the collection ofsoil samples in a way that maintains their natural physical properties. Mountain forest soils, containingrock fragments, root systems and a significant amount of organic matter, make it extremely difficult totest their hydraulic conductivity using both laboratory and field methods. A widely used technique ofsampling by driving a cylinder into the ground in this type of soils causes damage to their structureresulting from the displacement of root systems and rock fragments as well as reduction of soil porosity.Thus, subsequent results contain an error that is difficult to estimate. The aim of the present researchwas: (1) to develop a laboratory method for testing the hydraulic conductivity of mountain forest soils,and in particular a method of collection of undisturbed soil samples, (2) to determine the influence of theapplied method of collecting samples on the thickening of their peripheral layer and on elimination ofincreased infiltration at the boundary between the soil medium and the cylinder, (3) to determine theextent of the impact of the irregular shape of a sample on its hydraulic conductivity and (4) to developan empirical method for determining the actual values of hydraulic conductivity, taking into account theerror associated with the flow of water through samples with different shapes. The method of soil sam-pling consists in gradual formation of a cylindrical soil monolith and filling the free space between themonolith and the tri-cylindrical container with low-pressure assembly foam. This method ensures pres-ervation of the natural physical properties of the examined samples and elimination of errors during themeasurement of the hydraulic conductivity, caused by increased infiltration at the boundary between thesoil medium and the cylinder. It was shown that the mean error of hydraulic conductivity determination,related to the irregular shape of samples, amounts to 11.57%. The error may be eliminated by the appli-cation of conversion coefficients.

� 2014 Elsevier B.V. All rights reserved.

1. Introduction

Hydraulic conductivity is one of the basic measures of the flowof water in the ground. Field and laboratory methods widelyreported in the literature indicate the existence of numerous waysand instruments for measuring hydraulic conductivity (Ohte et al.,1989; Plagge et al., 1990; Ankeny et al., 1991; Hendrayanto et al.,1998; Youngs, 2001; Bagarello et al., 2004; Meadows et al., 2005;Lassabatère et al., 2006; Schindler and Müller, 2006; Peters andDurner, 2008; Price et al., 2008). Their use is usually dependenton the type of soil material being tested. Numerous studies showthat the values of hydraulic conductivity determined by laboratorymethods are rarely in accordance with the values of hydraulic con-ductivity determined by in situ measurements (Ankeny et al., 1991;

Mohanty et al., 1994; Fallico et al., 2005; Price et al., 2010). This isdue to the fact that both field and laboratory research is burdenedwith errors which may account for the differences in the obtainedhydraulic conductivity values (Ankeny et al., 1991). The selectionof an appropriate method usually depends upon a number of fac-tors, such as accuracy, speed, and ease of measurement as wellas costs (Lee et al., 1985). Field methods are generally time-con-suming and costly (Wessolek et al., 1994; Iwanek, 2005). In turn,the collection and transport of samples may affect errors occurringduring laboratory measurements in an unspecified manner (Fodoret al., 2011).

Determination of the hydraulic properties of soil under labora-tory conditions requires the collection of undisturbed soil samples(Twardowski and Dro _zd _zak, 2007). The method of sampling is ofgreat importance due to the preservation of the natural pore sys-tem, rock fragments or roots. According to a study by Kucza(2007), disturbance of the natural structure of the samples

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obtained from the organic horizons of forest soil may have a largeimpact on the value of the hydraulic conductivity. In the litter hori-zon (Ol) these changes range from 3% to 15%, in the case of damageto the structure of the deeper horizons (Ofh, A), the changes in thehydraulic conductivity may reach up to 85%.

Mountain forest soils, most often containing rock fragments,numerous root systems and organic matter with varying degreesof decomposition, make it extremely difficult to examine hydraulicconductivity using both field and laboratory methods. In additionto a significant proportion of organic matter, forest soils containa large number of macropores, particularly in the surface layer,as a result of the activity of soil fauna, and a high content of rootsystems (Bonell, 1993). Although macropores may constitute a rel-atively small share of the total porosity of the soil, they may have adisproportionate effect on their infiltration properties (Buttle andHouse, 1997) and on the transport of nutrients in the soil(Bormann and Klaassen, 2008).

Difficult terrain, associated with a high slope and limited accessof water, often makes the in situ methods of testing the hydraulicconductivity of mountain forest soils difficult to apply(Hendrayanto et al., 1998). Under laboratory conditions, the largesterrors in the measurement of the hydraulic conductivity of forestsoils result from improper soil sampling techniques and small sizesof samples due to which the samples do not adequately representthe heterogeneity and macroporosity of soils. The most commonway of soil sampling is by driving a cylinder into the ground, whichin the case of forest soils may cause the displacement of root sys-tems and rock fragments or destruction and compaction of chan-nels present in the soil. The wrong sampling by uneven drivingthe cylinder into the ground creates gaps between the cylinderand the soil sample, thus leading to errors during measurements(Chappell and Lancaster, 2007).

The collection of samples for testing hydraulic conductivityunder laboratory conditions should ensure:

1. Preservation of continuity of the sample with the surroundingsoil.

2. Preservation of the natural residual system of the soil, i.e. theroot systems and soil channels within and on the boundary ofthe sample.

3. Preservation of the natural porosity of the soil medium.4. Preservation of main, vertical direction of infiltration of water

flowing through the sample during testing.5. Elimination of errors in the measurement of the hydraulic con-

ductivity due to leakage at the boundary.

Therefore, the aim of the present research was: (1) to developthe laboratory method of examination of the hydraulic conductiv-ity of mountain forest soils, in particular the method of collectingsoil samples with intact structure, that would fulfil the above crite-ria, (2) to determine the influence of the applied method of collect-ing samples on the thickening of their peripheral layer and onelimination of increased infiltration at the boundary between thesoil medium and the cylinder, (3) to determine the extent of theimpact of the irregular shape of a sample on its hydraulic conduc-tivity and (4) to develop an empirical method for determining theactual values of hydraulic conductivity, taking into account theerror associated with the flow of water through samples with dif-ferent shapes.

2. Materials and methods

2.1. The research area

In order to develop and test the method for testing the hydrau-lic conductivity of undisturbed soil samples, we selected 14

research plots located in the Beskid Makowski in south-centralPoland (Fig. 1). Samples were obtained at an altitude of 550–800 m above sea level, from the horizons of mountain forest soilsbelonging to brown acid soils (PTG, 2008), formed out of weath-ered Magura sandstone. The research covered bioaccumulationhorizons (A) developed under fir (Abies alba Mill.) and beech (Fagussylvatica L.) forest stands as well as mineral horizons (B) lyingdirectly below A horizons.

2.2. The method of collection of undisturbed soil samples

2.2.1. A container for collection of undisturbed soil samplesFig. 2 presents a container for collecting undisturbed soil sam-

ples, which essentially consists of three cylinders having the sameinner diameter, made of stainless steel, and two lids. Between thecylinders, there are angled spacers which preserve a gap betweenthem. The cylinders are connected with a strong adhesive tape,adhering closely to the cylinder walls.

The two cylinders – the top and bottom ones – with a height h0

of 30 mm, are used to protect the structure of the sample during itstransport to the laboratory while the middle cylinder is intendedfor the sample itself. The height of the central cylinder h dependson the thickness of the horizon of soil from which the sample isobtained and amounts to 20–90 mm in the case of sampling fromthe horizons of mountain soil. It may be larger in the case ofobtaining soil samples from non-stony soils.

During the development and testing of the method of collectingundisturbed soil samples, we used containers consisting of cylin-ders with a 150 mm internal diameter and the height of the centralcylinder of 30, 40 and 60 mm.

2.2.2. Sampling the research materialThe essence of collection of soil samples with undisturbed

structure using the method proposed here involves gradual andprecise formation of a soil monolith in a cylindrical shape(Fig. 3a). The formation of the monolith must be carried out witha sharp knife, trimming the protruding root systems with shears,and removing portions of rock fragments from the side surfaces(Fig. 3b and c). The monolith diameter should be about 20 mmsmaller than the diameter of the container. After forming themonolith, its sides should be covered with a thin and flexible coat-ing (silicone spray) to provide reinforcement of its outer surface.The formed and secured monolith should be covered with a previ-ously prepared container in such a way that the lower and upperedge of the cylinder are located inside the soil horizon which willbe subjected to the tests of hydraulic conductivity (Fig. 3d). Then,the gap between the monolith and the container should be filledwith watertight filler in the form of low pressure assembly foam.The foam should be introduced using a four-nozzle, providing evenand simultaneous distribution of the foam. The container shouldcover the soil monolith in such a way that the expanding foamcan escape outside on both the upper and lower side of the con-tainer. This is particularly important for the collection of forest soilorganic horizons, since no escape of the excess foam beyond thecontainer may cause too much pressure of the filler onto the soil,and thus lead to its compaction. After drying of the filling material,the top surface of the monolith should be made even and the con-tainer should be closed with a steel cover. Then, the containershould be cut off together with the monolith, its bottom surfaceshould be made even and the bottom of the container should becovered with a lid.

This method also allows the collection of undisturbed soil sam-ples formed on mountain slopes of varying gradients. Sampling onthe slopes consists in the forming of the monolith in the mannerdescribed above except that the container should be placed onthe monolith in a vertical direction in such a way that the soil

Fig. 1. Location of the research area.

Fig. 2. The container for sampling of undisturbed soil. Explanations: 1 – top cover,2 – upper cylinder, 3 – angled spacers between adjacent cylinders, 4 – centralcylinder for the sample proper, 5 – adhesive tape, 6 – lower cylinder, 7 – bottomcover, h – central cylinder height, h0 – height of the upper and lower cylinder equalto 30 mm.

Fig. 3. A diagram of collection of undisturbed soil samples: a – the formed soil monolithsoil monolith with its soil skeleton removed and roots cut off, protected with a layer of scentral cylinder (5) located inside the soil horizon (6) intended for analysis, d – the soil mpressure foam (7).

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horizon located in the middle cylinder maintains its naturalarrangement, providing the main, vertical direction of waterinfiltration through the sample during tests (Fig. 4).

2.3. Preparation of samples for testing the hydraulic conductivity

Preparation of samples for testing the hydraulic conductivityconsists of several successive stages. The first involves cuttingthe soil monolith with a saw along the plane determined by thegap between the lower and the middle cylinder. After cutting offthe lower cylinder, the bottom surface of the sample should bealigned in relation to the edge of the central cylinder, and thenthe filler in the cross-section of the sample should be covered witha thin layer of silicone while the bottom of the sample should becovered with brass mesh and a perforated bottom filter positionedat the flange mounting the sample with the device. The boundarybetween the outer wall of the cylinder and the filter flange shouldthen be insulated with silicone. The next step is to cut off the uppercylinder along the plane determined by the gap between the upperand the middle cylinder. The upper surface of the sample should be

with protruding roots (1) and the soil skeleton (2) at the monolith boundary, b – theilicone spray (3), c – the soil monolith with the container placed on it (4), with the

onolith with the container placed on it, with the space between them filled with low

Fig. 4. A diagram of sample collection from a slope with a given gradient.Explanations: 1 – the soil horizon for testing the hydraulic conductivity, 2 – themiddle cylinder of the container, placed inside the tested soil horizon.

Fig. 5. A top view onto a soil sample prepared for testing, obtained from the horizonof biological accumulation, according to the method proposed by the presentauthors.

Fig. 6. A diagram showing the method for preparing test samples. Explanations: a – asample with its rock fragments protruding (1), b – a sample after removal of the rockfragments and filling the resulting cavity with waterproof filling medium (2).

Fig. 7. The apparatus for the study of hydraulic conductivity of undisturbed soilsamples. Explanations: 1 – round base, 2 – perforated base socket, 3 – lateral ventchannels, 4 – smooth ring to attach a sample in the socket, 5 – the pressure column,6 – the pressure column flange, 7 – the fixing screws, 8 – water level indicator,9 – outer scale, 10 – supply line, 11 –supply tank, 12 – outer cylinder, 13 – lateralmeasurement overflows, 14 – supports.

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aligned in relation to the edge of the central cylinder, and then thesurface of the filling medium should be covered with a thin layer ofsilicone. An example of a test sample with an irregular shape, pre-pared for tests, is shown in Fig. 5.

If in the course of cutting off the upper or bottom cylinder thepresence of rock fragments is noticed between the two cylinders,

the cutting off of the monolith with a saw should be performedonly to the point where the rock fragments have occurred. Thena thin sharp knife should be used to lever up the upper or bottomcylinder, thus separating it from the central cylinder. The protrud-ing rock fragments should be removed from the top or bottom sur-face of the sample (Fig. 6a), and the resulting cavity should be filledwith impermeable material in the form of molten plasticine, whichimitates the shape of the rock fragments when solidified (Fig. 6b).

2.4. An apparatus for the testing of the hydraulic conductivity inundisturbed soil samples

The basic element of the apparatus to study the hydraulic con-ductivity (Fig. 7) is a circular base with three props made of stain-less steel. The base comprises a socket with a perforated bottomwith a diameter slightly larger than the diameter of the flange ofthe bottom filter of the sample. Around the perforated socket, thereis smooth ring having a width of about 8 mm, where the sample ismounted. In the walls of the base of the apparatus, there are threehorizontal vent channels, reaching radially into the socket centre.The channels are connected by tubes to a vacuum pump andensure the removal of air from under the sample. The apparatusis equipped with perforated plates (reducers) put onto the basesocket, allowing the testing of the hydraulic conductivity of homo-geneous samples, collected into the cylinders with smallerdiameters.

The proposed method of testing the hydraulic conductivitybelongs to the group of fixed- and variable-gradient methods andis based on Darcy’s law (PKN-CEN ISO/TS 17892-11, 2009). Thehydraulic conductivity is calculated using the following formula:

kt ¼Q � L

A � T � Dhð1Þ

where kt is the hydraulic conductivity, determined at temperature t(m�h�1); Q is the volume of water flowing through the soil sample(m3); L is the height of the sample (m); A is the cross-sectional areaof the sample (m2); T is the time (h); Dh is the difference in levels of

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the water table in the column and in the outer cylinder of the appa-ratus (m).

The hydraulic conductivity calculated according to Eq. (1) con-verted to the temperature of 10 �C, according to the Poiseuille for-mula (PKN-CEN ISO/TS 17892-11, 2009):

K ¼ kt �1:359

1þ 0:0337 � t þ 0:00022 � t2

� �ð2Þ

where K is the hydraulic conductivity at 10 �C (m�h�1); kt is thehydraulic conductivity (m�h�1), as determined at the temperaturet (�C).

2.5. Testing the method of soil sampling

Due to the use of filler during soil sampling, it was necessary toconduct test studies, allowing answers to the following questions:

1. To what extent does the foam filler eliminate the phenomenonof increased infiltration occurring at the boundary between thesoil medium and the cylinder, typical of traditional methods ofsampling?

2. To what extent does the expanding and drying foam affect thecompaction of the peripheral layer of the obtained samples?

2.5.1. Research on the impact of foam on the elimination of peripheralflow

Increased infiltration at the boundary between the soil mediumand the cylinder is a factor that significantly affects the value of theobtained hydraulic conductivity. Therefore, studies were con-ducted to test the impact of the foam on the elimination of periph-eral leakage. Tests was performed on a homogeneous soil medium,i.e. sharp-edged quartz sand with grains with a diameter of 0.3–0.5 mm. Tests consisted of three series of experiments which dif-fered in the way of forming the samples and the connection ofthe soil medium with the cylinder walls.

In the first series of experiments, sand with a moisture contentensuring its integrity was placed in batches in a cylinder with aheight of 120 mm and a diameter of 125 mm. Sand was graduallycompacted in order to form a sample in the shape of a regular cyl-inder. Then, the upper surface of sand in the forming cylinder wasloaded (0.10 kPa�cm�2), and it was removed from the formed sam-ple. After removal of the forming cylinder, the side surface of thesand cylinder became covered with a thin layer of silicone spray.Onto the so prepared undisturbed soil sample a sampling containerwas placed with the diameter of 150 mm (Fig. 2) and the height ofthe central cylinder of 60 mm. The empty space between the sandand the container was filled with low pressure foam. The propersand sample, located in the central cylinder, was obtained asdescribed in Section 2.3, by cutting off the two external cylindersof the container.

In the second series of experiments, the sand was placed inbatches in a stainless steel cylinder with 125 mm diameter and60 mm height. Sand was gradually compacted and after levellingthe upper surface of the sand, the sample was tested for its hydrau-lic conductivity.

In the third series of experiments, the samples were prepared asin the second series, with the difference that before inserting thesand, the inner surface of the cylinder was covered with a thinlayer of silicone.

In each of the three series of experiments, tests were performedon 8 samples of quartz sand, varying in terms of the porosity of theexamined medium. Tests of the hydraulic conductivity of the sandsamples were performed in an apparatus adapted to samples withundisturbed structure (Fig. 7), and a strainer was applied to theapparatus socket for the samples in the second and third series

of experiments, which allowed examination of samples with diam-eters smaller than 150 mm.

The hydraulic conductivity for each sample was calculatedaccording to Eqs. (1) and (2). In the first series of experiments, inspite of forming the samples in the cylinders with the diameterof 125 mm, the expansion of the foam could result in slight com-paction of the peripheral layer of sand. For that reason, the cross-sectional surface areas A, necessary to calculate the hydraulic con-ductivity, were determined for each sample after completion of thetests, by measuring the inner diameters in the two end sections ofthe foam form created after the removal of sand from the cylinder.In each section, 4 diameters were measured, and their averagevalue was used to calculate the radius and the surface area A.

After completion of the research, the dry sand masses placed inthe cylinders with known volume were the basis for determiningthe total porosity of the examined samples, calculated accordingto the formula:

TP ¼ qs � qdð Þ=qs ð3Þ

where qs is the specific density of quartz sand equal to2.650 Mg�m�3, determined with the pycnometer method (PKN-CEN ISO 17892-3, 2009); qd is the bulk density of a given sample(Mg�m�3).

2.5.2. Determination of the impact of foam on the compaction of thesoil medium

Testing the impact of the expanding and drying foam on thecompaction of the peripheral layer of the soil medium involvedcomparing the diameter of the samples before using the filler withthe diameter of the samples after its application. Tests were carriedout on 8 samples of calibrated quartz sand, used in the first seriesof experiments, as described in Section 2.5.1. and 8 samples ofquartz sand with the addition of silt (7%) and clay (3%), preparedin the same manner as the samples of pure quartz sand. The sam-ples differed in the total porosity of the tested soil medium, definedby Eq. (3); for the sand samples with the addition of silt and claythe obtained specific density qs amounted to 2.656 Mg�m�3.

Experiments consisted of measuring the internal diameters ofthe foam forms created by the removal of the sand samples fromthe cylinders. Calipers were used to measure four inner diametersin the upper and lower section of the cylinder with foam. The meandiameter of the measurements was compared with the diameter of125 mm, i.e. one that a sample should have after it is formed in acylinder with this diameter, before filling the space between thesample and the container with the filling material. The differencebetween these diameters was the basis for determining the effectof the expanding and hardening foam on the compaction of theperipheral layer of the samples.

2.6. Methodological assumptions for determining the hydraulicconductivity of soil samples with an irregular shape

Due to the presence of filler which filled the space between thecylinder and the side surface of the sample, determination of thehydraulic conductivity values required an assumption that the vol-ume of water flow Q0 through an irregular lump of soil will undercertain conditions be smaller than the volume of water flow Qthrough a lump of soil in the shape of a regular cylinder of the sameheight, volume, average cross-sectional areas and the same physi-cal properties of the soil medium (Fig. 8). The difference betweenthe values of Q and Q0 will be the result of variation of the cross-sectional sizes along the filtration path and the enlarged side sur-face of the sample with an irregular shape.

Accordingly, the actual value of the hydraulic conductivity ofsoil samples with an irregular shape was to be determined fromthe formula:

Fig. 8. A diagram showing the differences in the values of the volume of water flow Q and Q0 and hydraulic conductivity K and K0 for samples having a regular shape (a) and anirregular shape (b) with the same characteristics of the soil medium, sample volume V and V0 , the average cross-sectional area A and A0 , the height of samples L and L0 and thetotal porosity of soil media TP and TP0 .

Fig. 9. An example of the surface of a foam form, for a sample with an irregularshape, remaining after removal of the soil from the cylinder.

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K ¼ K 0 �Wk ð4Þ

where K is the actual value of hydraulic conductivity (m�h�1), corre-sponding to the hydraulic conductivity which would be obtained ifthe test sample had the shape of a regular cylinder; K0 is the approx-imate value of hydraulic conductivity (m�h�1), obtained from directmeasurements of samples with an irregular shape; Wk is the con-version coefficient, taking into account the effect of the shape ofthe sample on the volume of water flowing through it.

2.7. Measurement of the approximate values of hydraulic conductivityK0

A soil sample was placed in a socket of the apparatus base(Fig. 7), on a thin layer of silicone that provides a tight connectionbetween the cylinder and the socket. On the upper surface of thesample was applied a mesh filter with a perforated plate, providingprotection against leakage from the sample during testing. Thehydraulic conductivity test required the maximum load of samples,corresponding to the natural load resulting from the weight of wetsoil lying directly above the examined soil horizon. Before theactual measurement of hydraulic conductivity, a soil sample wasslowly filled with distilled water starting from the bottom by grad-ually raising the water level in the external cylinder of the appara-tus. Since the proposed research methodology was adapted tomeasure the dynamics of hydraulic conductivity, individual sam-ples remained in the apparatus until the value of hydraulic conduc-tivity underwent significant changes, i.e. until a given samplereached the state of the maximum filling with water.

The approximate value of hydraulic conductivity K0 for irregularsoil samples was determined from Eqs. (1) and (2). In order toobtain the average cross-sectional area of an irregularly shapedsample, it was first necessary to determine its volume V0. For thatpurpose, after the hydraulic conductivity tests, a soil sample wasremoved from the cylinder, with attention not to damage the foamcover. After removal of the sample, what remained in the cylinderwas the filling medium in an ideal shape of an impression of thesample (Fig. 9). Then, the bottom surface of the cylinder coveredwith foam was covered with a thin layer of silicone and appliedto the flat surface of the container cover, after which the wholeset was weighed. In the next step, the inside of the cylinder wasfilled with distilled water and, after measuring its temperature,the entire cylinder was reweighed. The volume of the samplewas determined from the formula:

V 0 ¼ MH2O=qt ð5Þ

where V0 is the volume of an irregular soil sample (cm3); MH2O is themass of water occupying the free space in the cylinder (g); qt iswater density in temperature t (g�cm�3).

The average cross-sectional area of a sample was determinedfrom the formula:

A0 ¼ V 0=L ð6Þ

where A0 is the average cross-sectional area of an irregular sample(cm2); V0 is the volume of an irregular sample, calculated accordingto Eq. (5) (cm3); L is the height of the sample (cm).

2.8. The conversion coefficient Wk

Separating the impact of individual parameters of the shape ofan irregular soil sample on the value of hydraulic conductivity K0 is,at this stage of research, virtually impossible. Therefore, it was nec-essary to develop an empirical method for determining the conver-sion coefficient Wk, which would take into account all factorsdisturbing the water flow through the soil medium and associatedwith an irregular shape and enlarged side surface of a sample.Experiments designed to determine the value of the conversioncoefficient Wk required the assumption that its value would beconstant for a particular shape of the sample, regardless of the typeof soil medium (sand, clay, loam) forming that shape, provided thatthe contact of the medium with the filling material was identical.Therefore, each sample in the shape of an irregular lump will haveits own conversion coefficient Wk.

Experiments aimed at the determination of the conversioncoefficients Wk for the tested soil samples, eliminating errorsdue to their irregular shape, first consisted in determining the

Fig. 10. The dependence of hydraulic conductivity (K) on total porosity (TP) ofcalibrated quartz sand samples with various ways of contact of the peripheralsample layers with the cylinder walls.

Fig. 11. The percentage error (E) of determination of hydraulic conductivityresulting from increased infiltration at the boundary between the soil mediumand the cylinder, determined for silicone secured samples and samples directlyadjacent to the cylinder walls, in relation to the hydraulic conductivity valuesobtained for samples with foam.

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approximate values of hydraulic conductivity K0sq for calibratedsand with the grain diameter of 0.3–0.5 mm, placed in the foamforms remaining after the removal of soil samples from thecylinders (Fig. 9). Before filling the forms with the sand, the outersurface of the foam was covered with a thin layer of silicone spray,which was covered with a thin layer of sand that provided the rightconnection between the medium and its side surface. Compactionof the sand in the forms was performed from inside the cylinderwith the use of a compactor with the diameter of 70 mm in sucha way as not to damage the foam surface. For particular sandsamples, the values of the coefficients K0sq were determined takinginto account the error associated with the irregular shape of thetested medium. The weight of dry sand in the foam form of knownvolume V0 was the basis for calculating the total porosity of thetested soil medium TP, according to Eq. (3).

The next stage of experiments consisted in determining theactual value of hydraulic conductivity Ksq, for a given sample of cal-ibrated sand with the same volume, height and porosity but with aregular cylindrical shape. This was done using the empirical rela-tionship between the hydraulic conductivity of calibrated quartzsand and its porosity TP (Section 3.1, Fig. 10), for samples with theirside surface protected with foam and used to study the effect of fil-ler on elimination of lateral leakage (Section 2.5.1). The value of Ksq

(m�h�1) for a given porosity TP of quartz sand, filling a given formremaining after an irregular soil sample, was calculated using theformula:

Ksq ¼ 22:212� 124:313 � TP þ 184:748 � TP2 ð7Þ

The coefficient Wk for each soil sample was calculated from theformula:

Wk ¼ Ksq=K 0sq ð8Þ

where Wk is the conversion coefficient taking into account theimpact of the irregular shape of a sample on the value of hydraulicconductivity; K0sq is the approximate value of the hydraulic conduc-tivity of a calibrated sand sample with an irregular shape, with agiven porosity (m�h�1); Ksq is the actual value of the hydraulic con-ductivity of a calibrated sand sample with a regular cylindricalshape, with the same porosity (m�h�1).

2.9. The effect of sand compaction on the deformation of the foam form

During preparation of quartz sand samples, necessary to deter-mine the conversion coefficient Wk (Section 2.8), there appeared a

question whether sand compaction in the foam forms distorted theside surface of the foam (Fig. 9). Any deformation of the foammight affect the enlargement of the average cross-sectional areaof a given form, and thus lead to errors in calculating the approx-imate values of the coefficient K0sq.

Verification tests were carried out on the foam forms from thefirst series of experiments, testing the impact of the foam on elim-ination of increased infiltration at the boundary between theground medium and the cylinder (Section 2.5.1). The experimentsconsisted in gradual filling with quartz sand the foam forms inwhich it was compacted with the use of a compactor with thediameter of 70 mm. After forming a sample, the sand was removedand then the inner diameters of the foam forms in their two outersections were measured using calipers. The average diameter of aform after sand compaction was compared to the diameter priorto placing the sand in the cylinder. For each form, three experi-ments were performed with a varying intensity of ground mediumcompaction as well as sand moisture content and porosity.

3. Results

3.1. The impact of foam on elimination of peripheral leakage

The results of the experiments indicate that the method of con-nection of the cylinder with a homogeneous soil medium sampleaffects the obtained hydraulic conductivity values (Fig. 10). Theuse of the foam on the side walls of the cylinder results in obtain-ing the minimum value of coefficient K while the direct contact ofsand with the walls of the steel cylinder results in obtaining themaximum hydraulic conductivity values for such samples. A sili-cone layer on the inner walls of the cylinders also significantlyeliminates the phenomenon of increased infiltration at the bound-aries of the samples.

By means of the functions describing the dependence of thehydraulic conductivity on the porosity of the soil medium for allthree methods of connection of the sample with the cylinder(Fig. 10), the hydraulic conductivity values were calculated forthe porosity equal to 0.360, 0.370, 0.380, 0.390, 0.400 and 0.410.On the basis of these factors, we calculated the percentage errorE resulting from increased infiltration in samples secured with sil-icone and samples directly adjacent to the walls of the steel cylin-ders. This error was determined in relation to the hydraulicconductivity values obtained for the samples with foam, which

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were the lowest. Hydraulic conductivity values for the samplesprotected with silicone are about 5% higher than for thesamples with foam while the hydraulic conductivity values forthe samples immediately adjacent to the cylinder walls assumehigher values averaging about 30% higher (Fig. 11).

3.2. The impact of foam on the compaction of the soil medium

Measurements of the internal diameters of the foam forms cre-ated after removal of the samples from the cylinders are shown inTable 1. Results indicate that the smallest diameter, and thus thehighest degree of distortion of the peripheral layer of the soil med-ium, was obtained for the samples with the highest porosity, bothfor the quartz sand and the sand mixed with silt and clay.

The percentage of distortion S of the samples by the expandingand drying foam, depending on their porosity relative to the diam-eter of 125 mm, is shown in Fig. 12. For the quartz sand sampleswith porosity up to 0.380, the degree of distortion of their periph-eral layer may be regarded as negligible (up to 0.87%). For sampleswith porosity above 0.380, the degree of distortion increases to2.68% at a porosity of about 0.402. Similarly, for the samples ofsand mixed with silt and clay, the degree of distortion of thesamples with porosity below 0.380 is low (0.48%), increasing to2.05% at a porosity of 0.406.

The average value of the degree of distortion S of the samples ofsand with the addition of silt and clay is almost half the average

Table 1The results of measurements of internal diameters of foam forms created after theremoval of quartz sand samples and sand samples with the admixture of silt and claywith different porosities.

No. Quartz sand Sand with silt and clay

TP da (mm) TP da (mm)

1 0.402 121.65 0.406 122.442 0.395 121.95 0.392 123.783 0.389 123.22 0.388 124.284 0.381 123.81 0.379 124.405 0.379 124.08 0.374 124.516 0.368 124.26 0.365 124.507 0.362 124.40 0.360 124.548 0.359 124.34 0.356 124.61

Where TP – total porosity, da – the average value of the internal diameter for a givensample.

Fig. 12. The effect of the expanding and hardening foam on the degree of distortion(S) of quartz sand samples (Type I) sand samples with the admixture of silt and clay(Type II), depending on their total porosity (TP), expressed as the percentage changein the diameter of the sample before and after use of the filler.

obtained for the samples of pure quartz sand (Table 2). This sug-gests that sandy soils will be the most susceptible to deformationby the expanding foam when collecting soil samples using themethod proposed here. Conversely, any admixture of silt and clay,the aggregate structure of soil, the presence of rock fragments androot systems should effectively counteract the pressure during theexpansion of the foam, without causing significant compaction ofthe outer layer of the sample, which might affect the obtainedhydraulic conductivity values.

3.3. The effect of the irregular shape of a sample on hydraulicconductivity

The proposed method was tested and the impact of the irregu-lar shape of the sample on hydraulic conductivity was analysed on27 soil samples, 15 of which came from the humus horizons and 12from the mineral horizons of mountain forest soils. The approxi-mate K0 and actual K values of hydraulic conductivity, as deter-mined for particular samples with an irregular shape, and theircharacteristics are provided in Table 3.

Fig. 13 presents the study results of the approximate values ofhydraulic conductivity K0sq for calibrated sand with the total poros-ity TP, placed in different foam forms remaining after the removalof soil samples, against the background of the actual values of coef-ficients Ksq, determined by means of Eq. (7). Lower values of coef-ficients K0sq, as compared to coefficients Ksq, suggest that they arethe result of factors which disturb water flow through a given sam-ple and which are related to its irregular shape. The results wereused to calculate the percentage error ER, made during the deter-mination of hydraulic conductivity K0sq, associated with the shapethat was specific for a particular foam form. Error ER was deter-mined in relation to the values of coefficient Ksq and ranged from7.84% to 15.12% (Table 4).

Given the relatively small value of error ER, the values of K0 mayhave a practical use when dealing with problems in hydrology andenvironmental engineering, without the need to calculate conver-sion coefficients Wk. However, for scientific purposes, aimed todevelop mathematical formulas describing relationships betweenthe infiltration capacity of the soil medium and its physical proper-ties, hydraulic conductivity should be determined as accurately aspossible. Therefore, in this type of study using the method pro-posed by the present authors, errors in the calculation of hydraulicconductivity due to the shape of the sample should be nullified bythe application of conversion coefficients Wk, which make it possi-ble to obtain the actual value of hydraulic conductivity K. The val-ues of the conversion coefficient Wk, calculated according to Eq. (8)for particular foam forms of soil samples, are given in Table 3 whileits statistical characteristics are shown in Table 5.

The research results indicate that coefficient Wk, calculated forall foam forms, had a relatively small range (from 1.085 to1.178), assuming the mean value of 1.131.

3.4. The effect of sand compaction on foam deformation

For each of the eight foam forms, experiments were performedin three repetitions which differed in the intensity of sand compac-tion. The average diameters obtained from the triplicate measure-ments, as compared with the average diameters of the foam formsbefore the experiments, are shown in Table 6.

The results indicate that these diameters are not significantlydifferent from one another, which proves the correctness of theassumptions made and the good resilience of the foam, allowingit to maintain its original shape after the release of the stresscaused during compaction. The small difference between thesediameters may be attributed to errors resulting from inaccuratemeasurement.

Table 2Statistics of the degree of distortion S of quartz sand samples and sand samples with the admixture of silt and clay by expanding and hardening foam.

Type of samples N Mean Std error Median Min Max SD CV (%)

Sand 8 1.23 0.31 0.85 0.48 2.68 0.88 71.37Sand with silt and clay 8 0.69 0.21 0.44 0.31 2.05 0.59 84.95

Where SD – standard deviation, CV – coefficient of variation.

Table 3Results of the infiltration capacity of soil samples with an irregular shape and their characteristics.

No. Stand Horizon L0 (cm) V0 (cm3) A0 (cm2) qd (Mg�m�3) K0 (m�h�1) Wk K (m�h�1)

1 Fir A 4 527.52 131.88 0.699 0.0276 1.111 0.03072 Fir B 4 455.92 113.98 1.113 0.0224 1.120 0.02513 Fir B 6 794.00 132.33 0.968 0.2918 1.170 0.34144 Fir A 3 348.39 116.13 0.861 0.0777 1.101 0.08555 Fir B 6 760.80 126.80 1.236 0.0726 1.130 0.08206 Fir A 4 491.12 122.78 0.790 0.2674 1.094 0.29257 Fir B 6 775.02 129.17 1.089 0.0900 1.085 0.09778 Fir A 3 375.69 125.23 0.437 0.1318 1.098 0.14479 Fir A 3 333.99 111.33 0.904 0.4016 1.150 0.4618

10 Fir A 3 320.01 106.67 0.944 0.5296 1.165 0.617011 Fir A 3 324.99 108.33 0.848 1.1666 1.143 1.333412 Fir A 3 354.33 118.11 0.259 1.4927 1.139 1.700213 Fir A 3 348.69 116.23 0.490 0.3456 1.143 0.395014 Fir B 4 487.00 121.75 1.137 0.1123 1.113 0.125015 Fir B 6 771.42 128.57 1.175 0.0572 1.110 0.063516 Fir B 6 757.74 126.29 0.944 1.2571 1.176 1.478317 Beech B 4 550.32 137.58 1.210 0.0993 1.097 0.108918 Beech B 6 792.90 132.15 1.332 0.1784 1.124 0.200519 Beech B 4 506.16 126.54 1.038 0.3239 1.124 0.364120 Beech B 4 532.24 133.06 1.120 0.5684 1.142 0.649121 Beech A 3 345.09 115.03 0.859 0.3814 1.140 0.434822 Beech B 4 537.12 134.28 1.394 0.1021 1.117 0.114023 Beech A 3 396.99 132.33 0.922 0.5193 1.139 0.591524 Beech A 3 324.09 108.03 0.591 0.7200 1.129 0.812925 Beech A 3 383.01 127.67 0.802 0.5094 1.177 0.599626 Beech A 3 393.51 131.17 0.726 0.2979 1.132 0.337227 Beech B 4 478.00 119.50 1.235 0.1523 1.178 0.1794

Where L0 – the height of the sample; V0 – sample volume determined by Eq. (5); A0 – the average cross-sectional area of an irregular sample, determined according to Eq. (6);qd – bulk density of a sample; K0 – the approximate value of hydraulic conductivity obtained from direct measurements; Wk – conversion coefficient; K – the actual value ofhydraulic conductivity calculated according to Eq. (4).

Fig. 13. Approximate values of the hydraulic conductivity K0sq of irregular samplesof calibrated sand as compared with the actual values of the hydraulic conductivityKsq of the same sand, as determined in Eq. (7), in relation to its total porosity TP.

Table 4Statistics of error ER (%) for determining water permeability, resulting from anirregular shape of samples.

Variable N Mean Std error Median Min Max SD CV (%)

ER 27 11.57 0.40 11.48 7.84 15.12 2.06 17.34

Where SD – standard deviation, CV – coefficient of variation.

Table 5Statistics of the conversion coefficient Wk.

Variable N Mean Std. error Median Min Max SD CV (%)

Wk 27 1.131 0.01 1.130 1.085 1.178 0.026 2.34

Where SD – standard deviation, CV – coefficient of variation.

A. Ilek, J. Kucza / Journal of Hydrology 519 (2014) 1649–1659 1657

4. Discussion

The techniques of collecting soil samples with an intact struc-ture are being developed and improved. For example, Barahonaand Iriarte (1999) developed a method for the collection of soil

monoliths from stony soils. Similarly, Vrbek (2013) proposed away of monolith sampling by means of epoxy resin. Ponder andAlley (1997) developed a portable hand-operated sampler andextractor for extracting undisturbed soil cores from stony soils.Caldwell et al. (2005) also constructed a sampler for collectingsamples from organic soils. Bouma and Dekker (1981) developeda method for the collection of peat samples in order to study thehydraulic conductivity known as the ‘cube method’. The methodwas later modified by Beckwith et al. (2003), Surridge et al.(2005) and Kruse et al. (2008). The modifications consisted mainlyin sinking the peat cubes in plaster or wax.

Table 6Results of the experiments concerning the impact of sand compaction on foam formdeformation.

No. da1 (mm) da2 (mm)

1 121.65 121.782 121.95 121.983 123.22 123.194 123.81 123.915 124.08 124.066 124.26 124.357 124.40 124.368 124.34 124.41

Where da1 – the average diameter of the form before the commencement of theexperiments, da2 – the average diameter of the form after completion of theexperiments.

1658 A. Ilek, J. Kucza / Journal of Hydrology 519 (2014) 1649–1659

The sampling method proposed here allows the testing ofhydraulic conductivity according to the main, vertical direction ofthe infiltration of rainwater into the soil profile, while preservationof the natural structure of the samples makes it possible toprecisely determine some of the physical properties of the samples,such as bulk density and total porosity, which have a direct impacton the obtained hydraulic conductivity values.

The construction of containers for undisturbed soil samplingallows appropriate transport and storage of the samples for alonger period of time. The sample proper, contained in the centralcylinder, is secured not only by the soil contained in the upper andlower cylinder, but also by two steel lids, which reduces excessiveevaporation and drying of the sample designed for analysis.

The use of foam as a means of filling the gap between the quartzsand sample and the cylinder results in the lowest values ofhydraulic conductivity when compared to conventional samplingmethods (Fig. 10). This leads to the conclusion that the foameffectively eliminates increased infiltration at the boundarybetween the soil medium and the cylinder. The most commonmethod of sampling soil for testing the hydraulic conductivity isdriving a cylinder into the ground, which causes not only distur-bance of the internal structure of samples, but also a significantoverestimation of hydraulic conductivity by increasing the flowof water at the boundary between the soil medium and the cylin-der (Fig. 11). According to Fodor et al. (2011), the use of silicone onthe inner walls of the cylinders should be an obligatory step in themethodology of soil sampling for the testing of hydraulic conduc-tivity. This observation is confirmed by the results presented in thisstudy, according to which the use of silicone on the inner walls ofthe cylinders substantially reduces the effect of increased infiltra-tion (Figs. 10 and 11). However, it must be considered that thesamples were prepared for examination in an artificial way, dueto which the obtained results do not reflect the actual influenceof silicone on the elimination of increased infiltration at the borderbetween the soil medium and the cylinder. In the course ofintroducing the cylinder into the soil, silicone may becomeremoved from its sides, by which the influence of silicone on theelimination of side leakage may be considerably lower.

The expanding and drying foam does not significantly affect thecompaction of peripheral layers of soil samples. In the case of cohe-sive soils, which additionally contain rock fragments and root sys-tems, the impact of foam on the collected sample appears to be ofmarginal significance. The possible influence of the filler on thecompaction of peripheral layers of soil samples can be avoidedby ensuring the escape of excess expanding foam both upwardsand downwards.

The apparatus for testing hydraulic conductivity in undisturbedsoil samples can be modified depending on the type of the test soil,i.e. depending on the size of samples. The apparatus can be adapted

to the cylinder diameters of 250, 200, 150 mm or less by producinga socket with a larger diameter or by using special reductioninserts.

When testing hydraulic conductivity using the method pro-posed by the authors, the average error for the determination ofhydraulic conductivity was 11.57% (Table 4). This error is causedboth by the variability of successive cross-sections and by theenlarged side surface of a sample. These factors cause the processesof water obstruction and increase the friction of water on the sur-face of the side walls of a sample. Taking into account the samplingmethod, which eliminate errors associated with the occurrence oflateral leakage, soil sample compaction and destruction of theinternal structure of the samples by shifting root systems and rockfragments, it may be concluded that the error is relatively small. Itshould be noted that traditional methods of sampling by driving acylinder into the ground result not only in the disturbance of thetested soil medium structure but also in errors due to increasedlateral water flow. In the case of samples immediately adjacentto the walls of the steel cylinder, the error associated only withincreased infiltration at the boundary may amount to about 30%(Fig. 11).

The laboratory method proposed here to test the hydraulic con-ductivity of undisturbed soil samples has been created for the pur-pose of forest hydrology in order to examine the infiltrationabilities of mountain forest soils. However, it can be successfullyapplied to other, more homogeneous types of soil.

5. Summary and conclusions

1. The presented method of sampling soil for testing hydraulicconductivity, consisting of gradual formation of a soil monolithin the shape of a cylinder and filling the free space between themonolith and the container with low pressure foam, ensuresthe preservation of the natural structure of the samples, thearrangement of root systems and rock fragments, and allowsexamination of hydraulic conductivity in accordance with thenatural direction of water infiltration into the soil profile.

2. Maintaining the natural structure makes it possible to preciselydetermine some of the physical properties of the samples, suchas bulk density and total porosity, which have a direct effect onthe infiltration properties of soils.

3. The filling medium effectively eliminates the increased flow atthe boundary between the soil medium and the cylinder, thusincreasing the credibility of the obtained hydraulic conductivityvalues.

4. The expanding and drying foam does not significantly affect thecompaction of peripheral layers of soil samples.

5. Due to the irregular shape of soil samples, the obtained hydrau-lic conductivity values reveal an error due to factors that inter-fere with the flow of water through the soil medium, whichinclude an enlarged side surface and a variable area of subse-quent cross-sections of the samples.

6. Given the complexity of mountain forest soils, and thus the dif-ficulty in testing their infiltration abilities, the average error indetermining the hydraulic conductivity, amounting to 11.57%,may be regarded as negligible, especially that the samplingmethod proposed by the authors effectively eliminates othererrors associated with increased infiltration at the boundarybetween the soil medium and the cylinder and with violationof the internal structure of the samples.

7. The conversion coefficient Wk nullifies the error in determininghydraulic conductivity, associated with the irregular shape ofthe samples. Because of its low variability, research of the infil-tration capacity of soils may assume the average value of thecoefficient Wk, amounting to 1.131.

A. Ilek, J. Kucza / Journal of Hydrology 519 (2014) 1649–1659 1659

Acknowledgements

The authors would like to thank five anonymous reviewers forthe thorough assessment of the present paper and for their manyvaluable and helpful suggestions.

The present research was conducted under a grant for youngscientists, funded by the Polish Ministry of Science and HigherEducation (No. BM4406/KIL/11).

The proposed research method has been subject to patent pro-tection in the Polish Patent Office: (1) No. P.398167 – application;(2) No. P.398168 – application; (3) No. W.120781 – the appliedpattern. The method has also been submitted for internationalpatent protection: No. PCT/PL2013/000001 – application.

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