ICAGE 2016

Evaporation, shrinkage and intrinsic permeability of unsaturated clayey

soil: analytical modelling versus experimental data

Houcem Trabelsi

1,2

& Bilel Hadrich

& Houda Guiras

1,4

Received: 13 April 2017 /Accepted: 27 March 2018

Saudi Society for Geosciences 2018

Abstract

This paper presents the experimental study conducted on a clayey soil originating from the region of Béja, north-west of Tunisia.

The evaporation, shrinkage and permeability behaviours were studied. The Soil Water Retention Curve (SWRC) was determined

from the slurry state to dry state, under the desiccation path (called initial drying curve). The Crack Intensity Factor (CIF),

settlement and void ratio were also studied to characterise the shrinkage phenomenon during desiccation. Moisture content (ω),

saturation degree (S

) and evaporation rate (R

) evolutions during desiccation path were also presented. This type of slurry clay

presents three stages during the desiccation process (pendular, funicular and capillary regimes). During desiccation process, the

evaporation rate presents a linear relationship as a saturation degree function. Furthermore, the evaporation rate versus suction

presents two phases: quasi-saturated and unsaturated states. This paper introduces a study of the hygroscopic and mechanical

parameters naturally modified during a desiccation process and proposes some analytical models to describe clay behaviour.

Using these parameters, we can determine the intrinsic permeability during the desiccation process.

Keywords Clay

Evaporation

Desiccation

Shrinkage

Suction

Analytical modelling

Introduction

Evaporation is an essenti al part of the water cycle. Water

evaporation is established from saturated soil surface, in con-

tact with air. In hydrology, evaporation is collectively termed

evapotranspiration. Water evaporation occurs when the soil

surface is exposed to a more or less dry environment, allowing

water molecules t o escape and form water vapour. In

geotechnical and environmental engineering, increasing atten-

tion has been paid to the coupled thermo-hydro-mechanical

problems of clayey soils. This is partially due to the increased

number of catastrophic landslide, induced by the degradation

of soil strength triggered by humidification/desiccation cycles

(Philip 1957;Or1996;Tangetal.2008; Trabelsi 2014). The

dryness phenomenon causes a considerable damage to struc-

tures built on initially quasi-saturated soils.

On one hand, the investigation of a water retention curve

and permeability as a function of cracked soil is crucial to the

soil stability study and long-term risk assessment for waste

disposal sites, recharge estimation for groundwater hydroge-

ology and petroleum engineering. Dams and clayey landfills

may create shrinkage with different intensities in relation with

the stress histories, initial hydraulic conditions, grain-size dis-

tributions of the used materials, permeability etc. (Trabelsi

2014, 2017; Trabelsi and Frikha 2017).

On the other hand, many hydrological and plant physiolog-

ical studies require soil hydraulic property measurements at

both lower and higher suctions with large samples. In this

study, the soil hydraulic properties were experimentally deter-

mined, using the natural evaporation method. Then, the exam-

ined soil, containing a double porosity (cracks or secondary

porosity) due to shrinkage effects, was studied. Our focus was

This article is par t o f the Topical Collecti on on Georesources and

Environmental Management

* Bilel Hadrich

bilel.hadrich@enis.tn

National Engineering School of Tunis, Civil Engineering laboratory,

University of Tunis EL Manar, B.P. 32, 1002-Le Belvédère,

Tunis, Tunisia

National Engineering School of Sfax, University of Sfax,

Sfax, Tunisia

National Engineering School of Sfax, Unité de Biotechnologie des

Algues, University of Sfax, Sfax, Tunisia

Higher Institute of Technological Studies of Nabeul-ISET,

Nabeul, Tunisia

Arabian Journal of Geosciences (2018) 11:184

https://doi.org/10.1007/s12517-018-3507-5

on explaining how the cracks evolution, and therefore the

volume change during the drying path, would result in the

intrinsic permeability change

Two principal processes govern the water flux exchange

between the soil and the atmosphere. Water enters the soil

surface as a liquid and goes out from the soil surface as vapour

through the evaporation process. Evaporation in porous media

is an important process in geotechnics and environment. In

fact, many physical effects are considered, such as water and

heat transfer in soil. Water flow on the soil surface, being in

contact with the atmosphere, is useful to predict the soil’s

behaviour during the evaporation process. Our investigation

here, was to describe how dry air flowing through saturated

soil, can partially change its volume (shrinkage phenomenon)

and its mechanical behaviou r (Konrad and Ayad 1997;

Mihoubi et al. 2002; Trabelsi et al. 2012).

Desiccation cracking in dried soil is a common natural

phenomenon, which significantly affects the soil’smechanical

and hygroscopic behaviour (Louati et al. 2016; Trabelsi and

Jamei 2016). In this study, experimental desiccation tests were

conducted on a clayey soil. Several aspects of the soil behav-

iour, mainly water evaporation and volume shrinkage, were

investigated here. Engineers have traditionally used a term

defined as potential evaporation (PE) to estimate water evap-

oration or evapotranspiration rates (Ward Wilson et al. 1994)

and actual evaporation (AE) or evaporation rate (R

)toesti-

mate the actual evaporation in unsaturated soil.

The aim of this work is to determine the intrinsic perme-

ability of a characterised Tunisian soil under desiccation (dry-

ing path). Six analytical models were newly proposed, to de-

scribe many direct or/and indirect relationships between those

hygroscopic and mechanical behaviours and several other

physical soil proprieties, such as moisture content, saturation

degree, void ratio etc.

Soil properties, method and test procedure

Soil properties

Grain-size distribution curve

The soil used in this study is a clayey soil from Beja (North-

West of Tunisia) retrieved from an area close to the National

Tunisian Road RN 11, which was damaged after landslides

which were triggered by rainfall in November 2011.

Figure 1 shows the grain-size distribution curve (GSDC) of

the natural material, in which a dominant particle size of

55 μm was detected. The plasticity index (I

) = 32%, liquid

limit (ω

) = 62%, plastic limit (ω

) = 30%, and shrinkage limit

( ω

) = 15%, have been determined in a previous work

(Trabelsi 2014). Table 1 summarises the geotechnical proper-

ties of the clay, classified as high-plastic inorganic clay (CH).

Initial drying soil water retention curve

Two techniques were used to measure the soil suction at

the equilibrium state of humidity, namely the mid-range

tensiometer for suctions which was lower than 100 kPa

(T5x, UMS, Germany) and the Dew Point Mirror

Psychrometer (WP4, Decagon Devices Inc., USA) from

100 kPa to 200 MPa. As can be seen in Fig. 2, the different

techniques display consistent results. A consistent trend

was obtained through tensiometer and psychrometer

results.

The initial Soil Water Retention Curve (SWRC) for

slurry soil prepared at 1.5 ω

, illustrated in Fig. 2, shows

the capacity of gravity water to be dried at different suc-

tions and the water retention characteristics of the soil

exposed to drying. The SWRC was determined follow ing

a drying path, under unstressed conditions and starting

from remoulded state without considering the crack effect.

An air-entry value of around s

=0.45MPacouldbe

identified in Fig. 2.

The fitting of the experimental data by Van Genuchten’s

(1980) model (Eq. 1) was established via the least square

method by minimising the difference between the experimen-

tal data and the calculated data (Fig. 2).

¼ S

res

þ S

sat

−S

res

ðÞ1 þ

−P



1−λ

−λ

ð1Þ

where S

is soil saturation degree (%), s = P

− P

is suction

(MPa); P

and P

are gas and liquid pressure, respectively

(MPa), S

res

and S

sat

are the residual saturation and maximum

saturation degrees (%), respectively; P

(MPa) is a capillary

pressure parameter; and λ is an empirical constant affecting

the curve shape (Van Genuchten 1980).

The fitting quality was tested by two statistical coeffi-

cients: the coefficient of determination (R

)(Eq.2)andthe

root-mean-square error (RMSE) (Eq. 3). In fact, R

is the

proportion of the sum of squares in the dependent variable

20%

40%

60%

80%

100%

0.11101001000

Cumulative mass (%)

uivalent s

herical diameter (

Fig. 1 Grain-size distribution curve (GSDC) of natural material

184 Page 2 of 14 Arab J Geosci (2018) 11:184

that is predictable from the independent variables. The RMSE

is a frequently used measure of the differences between the

values predicted by a model and the observed ones.

∑

i¼1

−y



∑

i¼1

−y



ð2Þ

RMSE ¼

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

∑

i¼1

−y



ð3Þ

where

and y

: are the calculated and experimental data; y:is

the arithmetic mean; and n is the total number of experimental

points.

The Van Genuchten model fitting quality was very good,

showing a very high R

= 98% and a very low RMSE = 0.036.

The identified parameters of the Van Genuchten model are S

res

=5%;S

sat

=98%;λ =0.3;andP

=1.03MPa.Forthestudied

soil, the suction of the air-entry value is around s

0.45 MPa.

Method and test procedure

In this research, the slurry soil was sieved through 400 μm.

The passing material was used in the tests at a slurry condition.

The tested material was saturated with distilled water. The

initial moisture content w as approximately 1.5 ω

,andit

was t hen poured into circular glass plates with 80 mm in

diameter at different heights (1, 8, 14 and 19 cm) correspond-

ing to four specimens (E1, E2, E3 and E4). All of them were

dried in the same testing climatic conditions (a relative humid-

ity HR = 60 ± 5% and a temperature T = 35 ± 1 °C). The rela-

tive humidity and temperature of the neighbouring air was

measured through a hygrometer (model: ETP110). A final

void ratio of e

min

= 0.73 was finally achieved after air drying

at an ambient relative humidity inside laboratory. To over-

come this climatic condition, we used a controlled temperature

climatic chamber. It was equipped with a box with water proof

walls, digital cameras and a balance with an accuracy of 0.1 g,

thermocouples and bulbs. The initial water content (ω

), void

ratio (e

) and thicknesses ( H

) are given in Table 2.The

grooves of the mould were intended to prevent the shrinkage

during drying. It can be observed that the corresponding effect

is negligible for thickness and that the shrinkage corresponds

to a crack on perimeter (lateral surface).

When the slurry sedimentation started, a thin water layer

appeared on the surface. This film of water was not considered

in the thickness measurement; however, it was considered in

the weight measurement. During drying, the specimens were

weighed, which allowed the recording of water loss at varying

intervals. Water content changes (ω) and water evaporation

rate (R

) (mm/day) during the drying time were then calculat-

ed. At the same measurement time, a digital camera was fixed

directly above the specimens and was used to monitor the

surface crack pattern evolution. Therefore, the crack heights

and surfaces were determined by the images’ analysis

technique.

The volume change of the material was continuously mon-

itored to correctly estimate the saturation degree during the

shrinkage phenomenon. The physical properties and initial

conditions are summarised in Tables 1 and 2.

Determination of intrinsic permeability via

an oedometric test

To measure the permeability saturated coefficient, a suitably

adapted oedometer was used in this investigation (Fig. 3). The

slurry clay with water content of 1.5 ω

was placed in a cell for

24 h. As a first step, the consolidation stress was increased

gradually. After 24 h (stabilisation of deformation), the poros-

ity and void ratios were determined, and then a hydraulic

gradient of 44 (dimensionless) was applied. The hydraulic

head was evaluated as a function of time through Darcy law

Table 1 Physical properties of the natural Beja clay

Soil properties Value

Solid density (ρ

)2.70g/cm

Liquid limit (ω

)62%

Plasticity index (I

)32%

Plastic limit (ω

)30%

Shrinkage limit (ω

)15%

Fraction of fines (< 80 μm) 97%

Clay-size fraction (< 2 μm) 18%

Water content under hygroscopic

conditions (relative humidity, 50%)

4.3%

Clay minerals (qualitative DRX) Illite, smectite

Specific surface (mercury intrusion porosimetry) 24 m

= 0.45 MPa

= 15 MPa

20%

40%

60%

80%

100%

0.1 1 10 100

Saturation degree (%)

Suction (MPa)

Beja clay, slurry

Van Genuchten model Ssat=98%,

Sres=5%,

Fig. 2 Soil water retention curve (SWRC) for initial drying curve of Beja

clay slurry soil

Arab J Geosci (2018) 11:184 Page 3 of 14 184

for a falling water head for an increment of time (Δt), and the

intrinsic permeability (K;m

) was determined.

Evaporation rate determination

The evaporation rate (R

; or actual evaporation, mm/day) is

defined using Eq. (4):

¼ 10

Δm

Δt  S  ρ

ð4Þ

where: Δt: is the time interval (day); Δm: is the mass variation

during the time interval (g); S: is the section of the specimen

(cm

); and ρ

: is the water density (g/cm

Results

Intrinsic permeability

The saturated permeability coefficient (K

sat

)formostsoilswas

considered a constant measured experimentally . This assumption

is valid with sands or silts, but for clay (i.e. deformable soil), it is

a current porosity evolution (ϕ) function and desiccation cycles

(Rodríguez et al. 2007; Louati et al. 2016; Chaduvula et al. 2017;

De Camillis et al. 2017; Mazzieri et al. 2017).

Two commonly used models were chosen from literature to fit

the experimental intrinsic permeability as a porosity function:

Rodríguez et al. (2007)model(Eq.5) (this model is like that

presentedbyTaylor1948) and Kozeny (1927) model (Eq. 6).

sat

ϕðÞ¼K

 exp b  ϕ−ϕ

ðÞðÞ ð5Þ

sat

ϕðÞ¼K



 1−ϕ

ðÞ

 1−ϕðÞ

ð6Þ

where b is a material parameter (soil characteristic) and K

the reference intrinsic permeability corresponding to the ref-

erence porosity of ϕ

The obtained fitting results are not very interesting for the

two models. In fact, the corresponding R

of the two models

do not exceed 31%. This result confirms that Rodríguez

et al.’s(2007) and Kozeny’s(1927) models are not suitable

for the obtained experimental data. Therefore, a new Power

function (Eq. 7) was proposed in this work (called model 1).

sat

ϕðÞ¼K



−ϕðÞ

ð7Þ

where ϕ

, m,andn are the fitting parameters. ϕ

is the porosity

corresponding to the moisture content equal to the ω

.Atthis

moisture content, going from the liquid phase to plastic phase,

permeability decreases significantly.

The identified parameters of the proposed law (model 1)

(Eq. 7), which are m = 12, n = 2 and K

= 7.85 × 10

−15

were determined for a porosity of ϕ

= 0.625. This newly

established model presents a very good relationship between

the intrinsic permeability and porosity in the measured range

from ϕ

min

=0.43toϕ

= 0.625. The calculated results from the

proposed law are shown in Fig. 4a. The proposed law matches

the experimental results with a higher R

= 81% and a lower

RMSE = 2.170 × 10

−15

. Thus, the first proposed law in this

work can be adopted for the experimental data, presenting

the intrinsic permeability as a porosity function.

Table 2 Specimens initial conditions

(%) H

(cm) e

(−)PE(mm/days)

E1 109 1 2.97 2.85

E2 78.6 8 2.09 2.49

E3 54.8 14 1.42 3.91

E4 98.6 19 2.60 4.71

Burette

LVDT Transducer

Fig. 3 Modified front loading

oedometer (consolidation

apparatus) with permeability

attachment connected to the End

Cap of the Hoek Cell (Burette

50 ml capacity and 0.1 ml div)

184 Page 4 of 14 Arab J Geosci (2018) 11:184

Figure 4b presents the variation of the intrinsic permeabil-

ity and void ratio as a function of effective stress, for loading

and unloading paths. The obtained results present standard

profiles for both values.

Global representation of drying curve under nil

external mechanical stress (desiccation)

As can be seen in Fig. 5, the global presentations of the drying

curves consist of:

& The moisture content variation throughout the drying time

(Fig. 5a).

& The saturation degree variation during desiccation (Fig. 5b).

To determine the saturation degree, we used the image anal-

ysis technique to determine the height and the crack intensity

factor (CIF). The crack volume and settlement are subtracted

from the total volume. In fact, Trabelsi (2014) proves that the

crack initiation and propagation is quickly established from

surface to bottom. In his research, the crack depth is

considered equal a long the sp ecimen depth. The mercury

immersion method, usually used to determine the exact

shrinkage volume, is destructive, and this is not suitable for

the entire desiccation path. However, the image analysis

technique was recently used by Tr abelsi and Frikha (2017)

for two types of soil and proved the accuracy of the results.

& The change in saturation degree as a moisture content

function is presented in Fig. 5c.

Examining Fig. 5, samples E3 and E4, for example have

twoclosethicknesses(14and19cm),buttheyhavetwo

very different initial moisture contents (ω

=54.8 and

98.6%, respectively). The moisture content decreases line-

arly, when the saturation degree is higher than 95% (phase

I corresponding to the constant drying rate, when ω

≥ 50%;

Fig. 5c) and reaches the hydraulic equilibrium when the

saturated degree reaches 21% (decreasing drying rate,

when ω

≤ 50%; Fig. 5c). W he n ω

≤ 50%, desiccation pro-

duces a shrinkage with unsaturated porous media. This

shrinkage tends to generate a radial tensile stress. When

this phenomenon reaches the tensile strength, crack networks

appear (Trabelsi et al. 2010; Trabelsi 2014;Latifaetal.2015;

Jommi et al. 2016). Jommi et al. (2016) proved that the tensile

strength depends on depth along the desiccation path. In ad-

dition, the shrinkage phenomenon tends to decrease the spec-

imen total volume. The sample mass is obviously constant.

Then, only the void volume decreases during desiccation. So,

the void ratio value decreases and affects especially the intrin-

sic permeability (Rodríguez et al. 2007).

Global representation of the evaporation curve

under fixed climatic conditions

The evaporation rate was determined for all the experiments.

The corresponding values are presented as a function of four

important parameters: drying time (Fig. 6a), saturation degree

(Fig. 6b), suction (Fig. 6c) and moisture content (Fig. 6d).

1.E-19

1.E-18

1.E-17

1.E-16

1.E-15

1.E-14

1.E-13

1.E-12

0.35 0.45 0.55 0.65

Saturated intrinsic permeability (m

)

Porosit

(-)

Exeprimental data

Proposed model (Model 1)

Rodríguez et al. model

Kozeny model

=0.625

0.2

0.4

0.6

0.8

1.2

1.4

1.6

1E-19

1E-18

1E-17

1E-16

1E-15

1E-14

1E-13

1E-12

0.001 0.01 0.1 1 10

Void ratio (-)

' (MPa)

Intrinsic permeability

Void ratio

Fig. 4 Change in permeability for

the slurry sample: a as a function

of porosity and b as a function of

the effective stress (σ′)

Arab J Geosci (2018) 11:184 Page 5 of 14 184

Three stages can also be observed for all the experiments:

& The first stage is characterised by a quasi-constant evapo-

ration (Fig. 6a–c) during the first 5 to 10 days, correspond-

ing to a quasi-saturated soil (95 < S

< 100%) (Fig. 6b) and

a moisture content less than 40% (Fig. 6d). This phase

period depends on the hydraulic conductivity as well as

the climatic conditions. This first stage is called the pen-

dular stage. The increase of fluctuation in the beginning of

all the experiments (in the first days), can be due to the

samples’ behaviour versus the experimental environment

(samples adaptation). Some peaks in Fig. 6a (during the

pendular regime) can be caused by the crack opening.

& In the second stage, this crack was characterised by

the CIF which is presented next. The evaporation rate

decreases linearly as function of saturation degree

(21 < S

< 95%) (Fig. 6b). This second stage is called

the funicular stage.

Sr=95%

Sr=21%

20%

40%

60%

80%

100%

120%

0 102030405060

Time (Days)

E1, Hi=1cm

E2, Hi=8cm

E3, Hi=14cm

E4, Hi=19cm

20%

40%

60%

80%

100%

10 20 30 40 50 60

Saturation degree S

(%)

Time (Days)

E1, Hi=1cm

E2, Hi=8cm

E3, Hi=14cm

E4, Hi=19cm

Sr=21%

20%

40%

60%

80%

100%

0% 20% 40% 60% 80% 100%

Saturation degree S

(%)

E1, Hi=1cm

E2, Hi=8cm

E3, Hi=14cm

E4, Hi=19cm

Fig. 5 Drying curves. a Moisture

content versus time, b saturation

degree versus time and c

saturation degree as function of

moisture content

184 Page 6 of 14 Arab J Geosci (2018) 11:184

& The last stage is the capillary regime stage (S

≈ 21%). In

this stage, the soil tends to an equilibrium.

Modelling the evaporation rate versus saturation

degree and suction

res

and S

sat

are the residual saturation and maximum satura-

tion degrees.

Figure 6b shows a linear relationship between the

evaporation rates as a saturation degree function, within

the range of 20–100% only. In this case, we can define a

res

of 20% and an initial saturation degree S

of 100%.

An average evaporation PE potential, for the saturated

stage (S

= 100%), is calculated f rom all the experiments.

A given value of around PE = 4 mm/day was chosen. PE

represents the evaporation capacity of the soil under a

complete saturated condition.

The proposed evaporation rate and saturation degree rela-

tionship was defined by Eq. (8) (called model 2). The corre-

sponding result is shown in Fig. 6b:

¼ PE

−S

res

−S

res



ð8Þ

The fitting quality of Model 2 was measured by the coeffi-

cient of determination R

equalto77.6%andanRMSEequal

to 0.750. These statistical parameters prove that Model 2 can be

considered acceptable for the experiments range (Fig. 6b).

The experimental observation of soil water evaporation

from the saturated state generally indicates two main phases

in relation to suction (Fig. 6c). The first phase corresponds to a

constant evaporation rate over time (95 < S

<100%and 3<

< 5), in which suction develops slowly and the soil remains

in a saturated state. In the second phase, the evaporation rate

decreases rapidly, and the soil suction increases significantly

(21 < S

< 95% and 1 < R

< 3). At the end of this phase, the

= 95%

= 21%

0 204060

Re (mm/day)

Time (Days)

E1, Hi=1cm E2, Hi=8cm

E3, Hi=14cm E4, Hi=19cm

0% 20% 40% 60% 80% 100%

Re (mm/day)

Saturation degree S

(%)

E1, Hi=1cm E2, Hi=8cm

E3, Hi=14cm E4, Hi=19cm

Model 2

0.1 1 10 100

Re (mm/day)

Suction (MPa)

E1, Hi=1cm E2, Hi=8cm

E3, Hi=14cm E4, Hi=19cm

Model 3

0% 20% 40% 60% 80% 100%

Re (mm/day)

Moisture water content (%)

E1, Hi=1cm E2, Hi=8cm

E3, Hi=14cm E4, Hi=19cm

Fig. 6 Evaporation rate during

desiccation process and

relationship between evaporation

rates versus a time, b saturation

degree, c suction and d moisture

water content

Arab J Geosci (2018) 11:184 Page 7 of 14 184

evaporation rate reaches the residual value, which depends on

the soil characteristics and climatic conditions. Combining

this finding with the water retention curve (Fig. 2), the rela-

tionship between the evaporation rate and the soil suction was

determined. The evaporation rate was calculated based on the

soil suction. The third proposed model (model 3) is defined as

follows (Eq. 9):

sðÞ¼max PE

−β Ln



þ Ln







; 0



ð9Þ

where s is the suction, s

is suction of air-entry value

(0.45 MPa) and β is a curve coefficient. The parameters were

obtained by minimising the error between the calculated

values using model 3 and the evaporation rate evolution ex-

perimental points, via the least square method. The obtained

results were β =0.4 mm/day and PE′ = R

= 90%) =

3.5 mm/day. PE′ corresponds to the evaporation rate, exactly

at the time corresponding to the air-entry. When s is less than

, this quantity Ln



þ Ln







becomes equal to

zero and then R

(s) = PE

′

The fitting has a very good quality with a higher R

=83%

and a lower value of RMSE = 0.722.

These modelling investigation results can be considered

important, since models 2 and 3 allow determining the evap-

oration rate value (and obviously, the corresponding drying

time) for any saturation degree and/or suction determined ex-

perimentally from any sample of this soil type.

Crack network

The crack pattern characteristics were quantified using the

commonly used image analysis technique (Vogel et al. 2005;

Costa et al. 2008;Tangetal.2008; Trabelsi and Jamei 2016).

To this end, computer-operated digital cameras were posi-

tioned directly above the upper and lateral surfaces of each

mould. These cameras were programmed to take the samples

snapshots, which were automatically saved throughout the

tests. Since the crack network involves segments and nodes

formation (Liu et al. 2013), and aiming to quantify the crack-

ing intensity and distribution, several parameters should be

defined (Nahlawi and Kodikara 2006). In this work, the CIF

evolution (calculated according to Eq. 10) was presented. The

CIF was described as an indicator of surface cracking (Vogel

et al. 2005; Costa et al. 2008;Tangetal.2008; Trabelsi and

Jamei 2016; Trabelsi and Frikha 2017).

CIF ¼

ð10Þ

with A

as the crack area and A as the sample total area.

The calculated areas used above were determined using

recorded images during drying. These images were converted

to binary images, where the set of white pixels represented

clayey aggregates and the black ones the crack network.

Figure 7 shows the sample E1 before (Fig. 7a) and after

(Fig. 7b) the test. The image analysis was performed in two

basic steps. The first involved the preparation of the image, in

which the original digital image colour was processed in

various stages, including conversion of the image colour

(Fig. 7b) to a grey-scale image and then to a binary (black-

and-white) image (Fig. 7c) by thresholding the grey-scale

image (Fig. 7d). The second step consisted in analysing the

processed image to obtain the parameters that characterise

the cra ck pattern. This was achieved by per form in g several

types of binary operati ons depending on the desired mag-

nitude. The public domain program ImageJ, with plug-ins

and additions, w as used to carry out these operations.

The main objective of the image analysis was the study of

the crack intensity factor evolution through time, for which

sequences of images representing the initiation, formation and

evolution of cracks during the experiment were used.

Figure 8a shows the evolution of the CIF samples during

the drying time. The lower the depth is, the faster the initiation

of cracks will be. In addition, the cracks start at a moisture

content around ω = 44% (Fig. 8b) and remain constant when

the moisture content reaches the shrinkage limit ω

=15%.

As observed previously (Tang et al. 2010, 2011), when the

actual suction is smaller than the s

(0.45 MPa) no cracks

appear. This observation is still valid for E4 with an initial

depth of 19 cm and an initial moisture content higher than

1.5 ω

. However, for sample E1 corresponding to an initial

depth of 1 cm and an initial moisture content also higher than

1.5 ω

, the crack networks appear before reaching air-entry

value. This can probably be induced by the friction effect. For

E2 and E3, the initial moisture content is less than 1.5 ω

and

the cracks appear before reaching the air-entry value. For each

sample, cracks appear when the soil saturation degree reaches

95% (Fig. 8c). The crack increases until a saturation degree of

60% and stabilises at the residual state.

Settlement and shrinkage

The volume change during shrinkage is associated with cracks

and vertical strain (ε

). By determining the CIF and consid-

ering the crack thickness in depth as constant and continuing

to the bottom, we can determine the crack volume (v

.).The

solid volume (v

) was considered constant. The settlement (h

× ε

, with h

is the initial high) was quantified by the image

analysis technique using a lateral picture, taken automatically

at the same time with a surface picture. Figure 9apresentsthe

vertical strain (ε

) during desiccation. It can be observed that

in the beginning, the water loss was accompanied by a volume

change induced only by settlements, until a moisture content

close to 44% corresponding to the air-entry value. The vertical

strain presents two linear phases: before and after the air-entry

184 Page 8 of 14 Arab J Geosci (2018) 11:184

value (with a higher R

of 79–99.5% and a very low RMSE of

0.90–2.76). Indeed, in the saturated phase, the slopes of all the

curves vary as a function of the ω

and they are expressed as

1.3–0.63 ω

. The equation was determined by the least square

method. However, for the unsaturated phase, the slopes are

constant and are equal to 0.25.

At a given time, the total volume associated with the soil

sample is the sum of three volume components: v

, v

and v

volumes. In fact, the solid volume corresponds to the solid mass

) divided by the solid density (ρ

. ). The pores volume

corresponds to voids in the soil mass. By quantifying the three

differen t components of soil shrinkage, we can determine the

net dry density (ρ

. ). This is one of the main advantages of the

practice used in this research and previously (Sanchez et al.

2013). The advantage of quantification of the volume changes

associated with each component after the crack network gener-

ation is the clay medium characterisation. The dry density var-

iation (and the void ratio), that ef fectivel y takes plac e during

shrinkage (Eqs. 11 and 12), is corrected by subtracting the crack

volume from the void volume (Eqs. 13 and 14).

In fact, the soil mechanics classical formulas are:

þ v

ð11Þ

e ¼

þ v

ð12Þ

To calculate the dry density (ρ

) and the void ratio (e), we

propose, in this work, to consider only the v

without v

follows:

þ v

ð13Þ

e ¼

ð14Þ

From Eqs. 13 and 14, the dry density can be calculated by

Eq. (15):

1 þ e

ð15Þ

where ρ

= 2.7 g/cm

is the solid density.

Figure 9b shows the change in dry density versus moisture

content in the compaction diagram presented with three types

of tests: the first one was applied on slurry and dried samples,

the second was applied for the consolidated specimen (at the

end of oedometric test) and submitted to desiccation at the

same hygrothermal condition applied in the first test (main

drying curve), and the third test was performed on compacted

states (Standard Proctor test energy). The soil volumetric

shrinkage takes place during desiccation for the first and the

second tests. The third test corresponding result (Standard

Proctor test), is presented in the same diagram. The dry

Fig. 7 Crack networks: a

saturated soil at the beginning of

test and b dried soil at the end of

the test. c, d an example of

performed image analysis

technique

Arab J Geosci (2018) 11:184 Page 9 of 14 184

density increases for all samples, when the moisture content

decreases from slurry (S

= 100%) to residual state (S

=20%),

under the desiccation (drying path). The modelling of this

relationship was carried out with a newly proposed model 4

(‘Correlation of porosity with suction and moisture’)inthe

following section (Fig. 9b). For the proctor test, the dry den-

sity is above the desiccation path experiments for a first do-

main (60 < S

< 85%). Otherwise, when the soil saturation de-

gree is lower than 60%, the dry density becomes lower than

the desiccation path. Therefore, the corresponding mechanical

energy has a significant influence on the first domain only. For

the main drying curve, the specimens consolidated inside the

oedometer cell under σ′ = 1 MPa (Fig. 4b), the mechanical

deformation increases the dry density a little bit. The dry den-

sity at the residual state tends approximately to the same

values of the natural shrinkage curve. The main curve is al-

ways higher than the natural shrinkage and standard proctor.

To show the similarity between the two used methods (ef-

fect of suction and that of mechanical stress) within the inter-

val 0.1 to 1 MPa, an oedometric test was performed. The

oedometric curve was compared with the drying path curves

in the same diagram (e, s)(Fig.10). The results show that the

experimental drying curves are close to the oedometric one

(consolidation). When the oedometric test was finished, the

consolidated sample was dried. The consolidate-drying varia-

tion (main drying curve; Pham et al. 2005) curve is negligible

compared with the initial slurry with a nil initial stress. In the

engineering application, this clay can be stabilised by consol-

idation under mechanical stress in the order of 1 MPa, before

building. In fact, during desiccation (main drying curve), the

consolidated clay has a little shrinkage.

The proctor energy increases the dry density only when

saturation is in the range of 60–80%. In addition, the soil final

dry density is higher than the optimum dry density (Standard

Proctor). On the contrary, for the consolidated soil with a

stress around 1.2 MPa, the final dry density is a little higher

than the dried soil. The global representation highlights the

difference in the soil shrinkage and saturation behaviour, with

respect to moisture. In the (ω, e)plan(Fig.11), the different

heights of the different samples having different initial mois-

ture contents approximately coincide with each other.

Unsaturated soil behaviour modelling

To study the behaviour of drying soil based on image analysis

technique, a novel method was presented in this paper. The

results presented above are used in this section to predict the

intrinsic permeability variation with the respective volume

change. To understand the soil drying process by modelling

its behaviour, some correlations were presented.

E1, Hi=1cm E2, Hi=8cm E3, Hi=14cm E4, Hi=19cm

10%

15%

010203040

CIF (%)

Time (Days)

= 15%

10%

15%

20% 40%

60%

CIF (%)

10%

15%

0% 20% 40% 60% 80% 100%

CIF (%)

Saturation degree S

(%)

= 0.45 MPa

= 15 MPa

10%

15%

0.1 1 10 100

CIF (%)

Suction s (MPa)

Fig. 8 Va riation o f C IF v ers us a

time, b water content, c saturation

degree and d suction

184 Page 10 of 14 Arab J Geosci (2018) 11:184