Effect of fines content and void ratio on the saturated hydraulic conductivity and undrained shear strength of sand–silt mixtures

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Environmental Earth Sciences ISSN 1866-6280 Environ Earth SciDOI 10.1007/s12665-013-2289-z

Effect of fines content and void ratio onthe saturated hydraulic conductivity andundrained shear strength of sand–siltmixtures

Mostefa Belkhatir, Tom Schanz &Ahmed Arab

1 23

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ORIGINAL ARTICLE

Effect of fines content and void ratio on the saturated hydraulicconductivity and undrained shear strength of sand–silt mixtures

Mostefa Belkhatir • Tom Schanz • Ahmed Arab

Received: 8 January 2012 / Accepted: 25 January 2013

� Springer-Verlag Berlin Heidelberg 2013

Abstract The hydraulic conductivity represents an

important indicator parameter in the generation and redis-

tribution of excess pore pressure of sand–silt mixture soil

deposits during earthquakes. This paper aims to determine

the relationship between the undrained shear strength

(liquefaction resistance) and the saturated hydraulic con-

ductivity of the sand–silt mixtures and how much they are

affected by the percentage of low plastic fines (finer than

0.074 mm) and void ratio of the soil. The results of flexible

wall permeameter and undrained monotonic triaxial tests

carried out on samples reconstituted from Chlef river sand

with 0, 10, 20, 30, 40, and 50 % non-plastic silt at an

effective confining pressure of 100 kPa and two initial

relative densities (Dr = 20, 91 %) are presented and dis-

cussed. It was found that the undrained shear strength

(liquefaction resistance) can be correlated to the fines

content, intergranular void ratio and saturated hydraulic

conductivity. The results obtained from this study reveal

that the saturated hydraulic conductivity (ksat) of the sand

mixed with 50 % low plastic fines can be, in average, four

orders of magnitude smaller than that of the clean sand.

The results show also that the global void ratio could not be

used as a pertinent parameter to explain the undrained

shear strength and saturated hydraulic conductivity

response of the sand–silt mixtures.

Keywords Undrained shear strength � Saturated

hydraulic conductivity � Fines content � sand–silt mixture �Void ratio

List of symbols

B Skempton’s pore pressure parameter

D10 Effective grain diameter

D50 Mean grain size

Dr Post consolidation relative density

e Post consolidation global void ratio

es Intergranular void ratio at the end of consolidation

emax Maximum global void ratio

emin Minimum global void ratio

Fc Fines content

Gs Specific gravity of the sand

Gf Specific gravity of the fines

G Specific gravity of the sand–silt mixture

Ip Plasticity index

ksat Saturated hydraulic conductivity

qpeak Undrained monotonic shear strength at the peak

c Total unit weight of soil

Introduction

The El Asnam (Algeria) earthquake of 1980 October 10

with an estimated wave magnitude of 7.3 (Ms = 7.3) is one

of the most destructive earthquake recorded in northern

Africa and more largely in the Western Mediterranean

Basin. This event occurred nearly at the same location as

the earthquake of 1954 (epicenter located at 36.285�N and

1.566�E in the locality of Beni-Rached). The earthquake

epicenter of the main shock was located 12 km in the east

M. Belkhatir (&) � A. Arab

Laboratory of Materials Sciences and Environment,

Hassiba Benbouali University of Chlef,

Route de Sendjes, BP 151, 02000 Chlef, Algeria

e-mail: [email protected]

T. Schanz

Laboratory of Foundation Engineering, Soil and Rock

Mechanics, Bochum Ruhr University, Bochum, Germany

123

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DOI 10.1007/s12665-013-2289-z

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region of Chlef City (210 km west of Algiers) at latitude

36.143�N and longitude 1.413�E with a focal depth of

about 10 km. The approximate duration of the quake was

between 35 and 40 s. The earthquake devastated the city of

El Asnam (actual Chlef), population estimated at 125,000,

and the nearby towns and villages. The large loss of life

(reportedly 5,000 to 20,000 casualties) and property was

attributed to the collapse of buildings. In several places of

the affected area, especially along Chlef river banks great

masses of sandy soils were ejected on to the ground surface

level. Belkhatir et al. (2010a) reported that a major damage

to certain civil and hydraulic structures (earthdams,

embankments, bridges, slopes and buildings) was caused

by this earthquake.

Liquefaction of sandy soil deposits during earthquakes

is one of the most important problems in the field of geo-

technical earthquake engineering. During earthquakes, the

undrained shear strength (liquefaction resistance) of satu-

rated sandy soil mass decreases due to a rapid build up of

excess pore water pressure within a short time. When the

excess pore pressure reaches the initial consolidation

pressure level, the effective stress becomes zero, inducing a

partial or a complete shear strength loss, called initial liq-

uefaction. At the state of initial liquefaction the soil mass

behaves as a liquid, causing tremendous damages to the

soil foundations and earth structures. Sand boils, settlement

or tilting of structures, failures of earth dams and slopes,

lateral spreading of bridge foundations, ground failures are

some examples of liquefaction damages. Numerous

researches have been reported on different factors influ-

encing the soil liquefaction phenomenon such as soil,

sample and testing parameters. However, most of the pre-

vious research has been concentrated on the liquefaction of

clean sands. But many natural soils contain a significant

amount of fines and many unstable phenomena occur in

soil layers with different amount of fines. Recent laboratory

research work carried out by Zlatovic and Ishihara (1995),

Lade and Yamamuro (1997), Thevanayagam et al (1997),

Thevanayagam (1998), Yamamuro and Lade (1998),

Amini and Qi (2000), Naeini (2001), Naeini and Baziar

(2004), Dash and Sitharam (2009), Sharafi and Baziar

(2010), Belkhatir et al. (2010a, b), Dash and Sitharam

(2011a, b) reveals that sand deposited with silt content can

be much more liquefiable than clean sand. Also, strain

properties and pore pressure generation in silty sand sam-

ples are quite different from clean sand. These new findings

emphasize the specific important features of deposits with

mixture of sand and silt. However, the conclusion forth-

coming from previous studies appears somewhat contra-

dictory and different.

The hydraulic conductivity influences in an important

manner the generation and redistribution of excess pore

pressure, thus, the undrained shear strength (liquefaction

resistance) of sandy soils subjected to earthquake loadings.

This soil parameter may be influenced by the type and

percentage of fines, sand gradation, void ratio, confining

pressure and density. The individual effects of these factors

cannot be practically determined from conventional field

tests. However, laboratory testing allows more control of

the different parameters that affect the hydraulic conduc-

tivity of soils.

Very limited laboratory results have been reported in the

published literature to assess the magnitude of the effects

of the percentage of fines, void ratio, confining pressure

and density on the saturated hydraulic conductivity of

sands mixed with fines. Thevanayagam (2000) observed

that the hydraulic conductivity, ksat was found to be one

order of magnitude smaller for silty sand compared to clean

sand for Ottawa sand mixed with low plastic fines. The-

vanayagam (2000) found values of k in the range of

0.6 9 10-3 to 1.3 9 10-3 cm/s for Ottawa sand,

9.0 9 10-5 cm/s for sand with 15 % fines, and 0.6 9 10-5

to 1.2 9 10-5 cm/s for sand with 25 % fines. Sathees

(2006) and Bandini and Sathiskumar (2009) also reported

mostly similar ranges of the hydraulic conductivity (ksat)

for two sands mixed with non-plastic fines.

This paper aims to evaluate the effects of fines content,

void ratio and relative density on the saturated hydraulic

conductivity and undrained shear strength characteristics of

sand–silt mixtures.

Experimental program

Description of materials

The soil samples used in this study was taken about 6.0 m

below ground surface from the bank of Chlef River where

severe liquefaction occurred during the El Asnam earth-

quake in 1980 (Fig. 1). Chlef sand has been used for all

tests presented in this laboratory investigation. Individual

sand particles are subrounded and predominant minerals

are feldspar and quartz. The tests were conducted on the

mixtures of Chlef sand and silt. Plasticity index (Ip) of the

silt is 5 %. Chlef sand was mixed with 0, 10, 20, 30, 40 and

50 % silt to get different fines contents. The index prop-

erties of the sand, sand–silt mixtures and silt used in this

laboratory research are presented in Table 1. The grain size

distribution curves of the tested materials are shown in

Fig. 2. The variation of emax (maximum void ratio corre-

sponding to the loosest state of the soil sample) and emin

(minimum void ratio corresponding to the densest state of

the soil sample) versus the fines content Fc (the ratio of the

weight of silt to the total weight of the sand–silt mixture) is

given in Fig. 3. We note that the two indices decrease with

the increase of the fines content until Fc = 30 %, then,

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they increase with further increase in the amount of fines.

Figure 4 illustrates the variation of emax versus emin. It is

clear from this Figure that the correlation between the

minimum and maximum void ratios of the sand–silt mix-

ture specimens is quite similar to that of Yilmaz and

Mollamahmutoglu (2009) and Cubrinovski and Ishihara

(2002).

Sample preparation

The dimensions of the samples were 70 mm in diameter

and 70 mm in height (H/D = 1) to avoid the appearance of

shear banding (sliding surfaces) and buckling to get stable

and safe samples up to failure. Bottom and top face of the

samples were lubricated to overcome/minimize end fric-

tion. All samples were prepared using seven layers. The

resulting height to diameter ratio of 1 is kept constant. All

samples were prepared by first estimating the dry weights

of sand and silt needed for a desired proportion into the

loose and dense state (Dr = 20 and 91 %) using under

compaction method of sample preparation, which simulates

a relatively homogeneous soil condition and is performed

by compacted dry soil in layers to a selected percentage of

the required dry unit weight of the specimen Ladd (1978).

After the specimen has been formed, the specimen cap is

placed and sealed with O-rings, and a partial vacuum of

15–25 kPa was applied to the specimen to reduce the

disturbances.

Saturation and isotropic consolidation

Saturation was performed by purging the dry specimen

with carbon dioxide for approximately 20 min. Deaired

water was then introduced into the specimen from the

bottom drain line. Water was allowed to flow through the

specimen until an amount equal to the void volume of the

specimen was collected in a beaker through the specimen’s

upper drain line. A minimum Skempton coefficient-value

greater than 0.96 was obtained at back pressure of 100 kPa.

When samples were fully saturated, they were subjected to

consolidation. During consolidation the difference between

all-around pressure and back pressure was set so that for

each sample the effective consolidation pressure was fixed

as 100 kPa.

Shear loading

All undrained triaxial tests for this study were carried out at

a constant strain rate of 0.167 % per minute, which was

slow enough to allow pore pressure change to equalize

throughout the sample with the pore pressure measured at

the base of sample. All the tests were continued up to 24 %

axial strain.

Hydraulic conductivity tests

The hydraulic conductivity measurements were performed

using the triaxial device. A normally available triaxial set-

up in the laboratory was converted into a flexible wall

permeameter using two constant pressure systems. The

name ‘‘flexible wall’’ is given because the sand–silt soil

sample is confined in a latex rubber membrane which fits

tightly over the sample. A conventionally available triaxial

cell in the laboratory to test samples with 70 mm diameter

and 70 mm height was used for permeability measure-

ments. All the samples were tested at an initial confining

pressure of 100 kPa and initial relative densities (Dr = 20

and 91 %). The hydraulic conductivity was measured and

calculated according to the basic principles of constant

head permeameter using Darcy’s law.

When a granular soil contains fines, the global void ratio

of the soil, e, can no longer be used to describe the

behaviour of the soil. This is because, up to a certain fines

content, Fc (the ratio of the weight of silt to the total weight

of the sand–silt mixture), the fines only occupy the void

spaces, and do not significantly affect the mechanical

behaviour of the sand–silt mixture. For this reason, the use

of the intergranular void ratio has been suggested Kenny

(1977); Kuerbis et al. (1988); Mitchell (1993). Mitchell

(1993), and later Thevanayagam and Mohan (2000) pro-

posed to consider the matrix of sand with fines as a com-

bination of two sub-matrices: a coarse-grain matrix and a

fine-grain matrix. Thevanayagam and Mohan (2000) also

suggest that for fines content Fc (i.e. expressed as a per-

centage of the total weight of the soil specimen) below a

limit in the range of 20–30 %, the contribution of fines in

the force chain is minimal. In this idealization, a simpli-

fying assumption is proposed to consider the fine-grain

Fig. 1 Geotechnical profile of the soil deposit at the site

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matrix as part of the voids between the coarser grains. By

neglecting the difference in the specific gravity of coarser

and finer particles, Thevanayagam (1998) proposed Eq. (1)

to calculate the intergranular void ratio:

es ¼eþ ðFc=100Þ1� ðFc=100Þ ð1Þ

Monkul and Ozden (2007) studied the compressional

behaviour of clayey and transition fines content suggested

Eq. (2) for the intergranular void ratio. They conclude that

the intergranular void ratio es can be used as an alternative

parameter to study the compressional behaviour of sand–

clay mixtures. Later, Monkul and Yamamuro (2011)

investigated the influence of silt size and content on

liquefaction behaviour of sand mixed with three different

non-plastic silts proposed Eq. (3). They found that

commonly used comparison bases in the literature, such

as void ratio, intergranular void ratio and relative density

are not sufficient alone for assessing the influence of fines

on liquefaction resistance or dilatancy of silty sands:

es ¼eþ ðG=GfÞðFc=100ÞðG=GsÞ 1� Fc=100ð Þ ð2Þ

es ¼eþ ðG=GfÞðFc=100Þ1� ðG=GfÞðFc=100Þð Þ ð3Þ

Table 1 Index properties of sand–silt mixtures

Material Symbol Sand (%) Silt (%) GS D10 (mm) D50 (mm) emin emax Ip (%)

Sand S100M0 100 0 2.680 0.22 0.68 0.535 0.876 –

Silty sand S90M10 90 10 2.682 0.08 0.50 0.472 0.787 –

S80M20 80 20 2.684 0.038 0.43 0.431 0.729 –

S70M30 70 30 2.686 0.022 0.37 0.412 0.704 –

S60M40 60 40 2.688 0.015 0.29 0.478 0.796 –

S50M50 50 50 2.690 0.011 0.08 0.600 0.968 –

Silt S0M100 0 100 2.70 – – 0.72 1.137 5.0

0.001 0.01 0.1 1 10

Soil Particle Diameter (mm)

0

10

20

30

40

50

60

70

80

90

100

Per

cen

t P

assi

ng

by

Wei

gh

t

Sand-silt mixtures

Fc = 0%

Fc = 10%

Fc = 20%

Fc = 30%

Fc = 40%

Fc = 50%

Fig. 2 Grain size distribution curves of the sand–silt mixtures used in

this experimental program

0 10 20 30 40 50

Fines Content, Fc (%)

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Void

Rat

io In

dex

Sand-silt mixtures

e (Dr = 20%)

e (Dr = 91%)

emin

emax

Fig. 3 Maximum and minimum void ratios sand–silt mixtures versus

fines content

0.40 0.50 0.60 0.70 0.80

Minimum Void Ratio, emin (.)

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

Max

imu

m V

oid

Rat

io, e

max

(.)

This study

Yilmaz and Mollamahmutoglu, (2009)

Cubrinoski and Ishihara, (2002)

Fig. 4 Maximum void ratio versus minimum void ratio of the sand–

silt mixtures

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where Gs and Gf are the specific gravity of coarser and finer

grains forming the soil respectively. G is the specific

gravity of the sand–silt mixture. Fc is the fines content and

e is the global void ratio. Note that in the Eqs. (2) and (3)

the difference in the specific gravity of coarser and finer

particles is not neglected.

Figure 5 shows the variation of the intergranular void

ratio versus the global void ratio and the fines content at a

relative density (Dr = 20, 91 %). As could be seen in this

Figure, the intergranular void ratio (es) increases with the

decrease of the initial global void ratio and increase of the

fines content until the value of 30 % beyond that it

increases almost linearly with the increase of the initial

global void ratio and fines content. This showed that the

global void ratio cannot represent the amount of particle

contacts in silty sands. As the void ratio and proportion of

the coarser of fine grains of soil change, the nature of their

microstructures also changes.

Monotonic test results

Undrained compression loading tests

Figures 6 and 7 show the results of the undrained mono-

tonic compression triaxial tests carried out for fines content

Fc = 10 and 40 % at 100 kPa mean confining pressure

within two separate density ranges (Dr = 20, 91 %). We

notice in general that the increase in the amount of fines

leads to an increase of the pore water pressure (Figs. 6b,

7b). This increase results from the role of the fines to

increase the contractancy phase of the sand–silt mixtures

leading to a reduction of the confining effective pressure

and consequently to a decrease of the peak shear strength

of the sand–silt mixture samples as it is illustrated by

(Figs. 6a, 7a). The stress path in the (p’, q) plane shows

clearly the role of the fines to decrease the average effec-

tive pressure and the maximum deviatoric stress (Figs. 6c,

7c). In this case, the effect of fines on the undrained

behaviour of the mixtures is clearly observed for the two

fines contents (10 and 40 %). These results of this labo-

ratory investigation confirmed similar tendencies observed

by Shen et al. (1977) and Troncoso and Verdugo (1985)

and Belkhatir et al. (2010a).

Table 2 presents the summary of the hydraulic conduc-

tivity and undrained monotonic compression triaxial tests.

Effect of the global void ratio on the peak strength

Figure 8 shows the peak strength versus the global void

ratio and fines content. It is clear from this that the peak

0.4 0.5 0.6 0.7 0.8 0.9 1.0 Global Void Ratio, e (.)

0.3

0.6

0.9

1.2

1.5

1.8

2.1

2.4

2.7

3.0

Inte

rgra

nu

lar V

oid

Rat

io, e

s (.

)

Sand-silt mixtures

Dr = 20%

Dr = 91%

Fc = 50%

Fc = 40%

Fc = 30%

Fc = 20%

Fc = 10%Fc = 0%

Fig. 5 Variation of the intergranular void ratio with the global void

ratio and fines content (r3’ = 100 kPa)

Axial Strain (%)

0

50

100

150

200

250

Dev

iato

r S

tres

s, q

(kP

a)

Sand-silt mixtures (Fc = 0%)

Dr = 20%

Dr = 91%

Axial Strain (%)

0

10

20

30

40

50

60

70

80

Exc

ess

Po

re P

ress

ure

(kP

a)

Sand-silt mixtures (Fc = 0%)

Dr = 20%

Dr = 91%

0 5 10 15 20 25 30 0 5 10 15 20 25 30 0 50 100 150 200 250 300Effective Mean Pressure, p' (kPa)

0

50

100

150

200

250

Dev

iato

r S

tres

s, q

(kP

a)

Sand-silt mixtures (Fc = 0%)

Dr = 20%

Dr = 91%

(a) (b) (c)

Fig. 6 Undrained monotonic behaviour of the sand–silt mixtures (r3’ = 100 kPa, Fc = 0 %). a Deviator stress versus axial strain. b Excess

pore pressure versus axial strain. c Deviator stress versus effective mean pressure

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strength decreases as the global void ratio decreases and

fines content increases for the loose and dense state of the

specimen (Dr = 20 and 91 %) up to 30 % fines content. It

means that when decreasing the global void ratio and

increasing the fines content, the undrained shear strength

also decreases. In this case, we could say that the global

void ratio appears to be a parameter not as pertinent in

sand-fines mixtures as in clean sands for characterizing the

mechanical state of these materials in the range of 0–30 %

fines content. Beyond Fc = 30 % the peak strength con-

tinues to decrease with increasing of the global void ratio

and the fines content for the two relative densities (Dr = 20

and 91 %).

Effect of the fines content on the peak strength

Figure 9 illustrates the peak strength versus the fines con-

tent. It can be seen from this Figure that the undrained peak

shear strength of the sand–silt mixtures (qpeak) decreases

linearly with the increase of the fines content for the two

initial relative densities (Dr = 20 and 91 %). In this labo-

ratory investigation, for the range of 0–50 % fines content

in normally consolidated undrained triaxial compression

tests, the following expressions are suggested to evaluate

the undrained shear strength at the peak which is a function

of the fines content (Fc):

qpeak ¼ 96� 1:74 Fcð Þ for Dr ¼ 20 %

qpeak ¼ 230 � 3:65 Fcð Þ for Dr ¼ 91 %:

Effect of the intergranular void ratio on the peak

strength

Figure 10 shows the undrained shear strength at the peak

versus the intergranular void ratio. It is clear from this

figure that the peak strength decreases as the intergranular

Axial Strain (%)

0

10

20

30

40

50

60D

evia

tor

Str

ess,

q(k

Pa)

Sand-silt mixtures (Fc = 50%)

Dr = 20%

Dr = 91%

Axial Strain (%)

0

10

20

30

40

50

60

70

80

90

Exc

ess

Po

re P

ress

ure

(kP

a) Sand-silt mixtures (Fc = 50%)

Dr = 20%

Dr = 91%

0 5 10 15 20 25 30 0 5 10 15 20 25 30 20 40 60 80 100 120

Effective Mean Pressure, p' (kPa)

0

10

20

30

40

50

60

Dev

iato

r S

tres

s, q

(kP

a)

Sand-silt mixtures (Fc = 50%)

Dr = 20%

Dr = 91%

(a) (b) (c)

Fig. 7 Undrained monotonic behaviour of the sand–silt mixtures (r3’ = 100 kPa, Fc = 50 %). a Deviator stress versus axial strain. b Excess

pore pressure versus axial strain. c Deviator stress versus effective mean pressure

Table 2 Summary of monotonic compression triaxial and hydraulic conductivity test results

Test no. Sample USCS Symbols Fc (%) Dr (%) e es qpeak (kPa) ksat (m/s)

1 S100M0 SP 0 20 0.810 0.81 97.50 8.6 9 10-5

2 91 0.567 0.567 229.60 3.5 9 10-5

3 S90M10 SP 10 20 0.724 0.914 84.50 1.6 9 10-5

4 91 0.500 0.665 191.70 7.8 9 10-6

5 S80M20 SM 20 20 0.669 1.083 57.20 1.74 9 10-6

6 91 0.458 0.820 168.30 8.16 9 10-7

7 S70M30 SM 30 20 0.646 1.345 36.80 1.1 9 10-7

8 91 0.438 1.048 108.60 2.3 9 10-8

9 S60M40 SM 40 20 0.732 1.877 20.80 7.5 9 10-8

10 91 0.507 1.503 77.70 9.4 9 10-9

11 S50M50 SM 50 20 0.894 2.773 17.90 1.2 9 10-8

12 91 0.633 2.253 54.10 1.5 9 10-9

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void ratio increases. We notice that the variation of the

undrained strength qpeak due to the presence of the amount

of fines is related to the intergranular void ratio in the range

0–50 % fines content. In this case, the behaviour of sand–

silt mixture samples is influenced by the contacts of coarser

grains, which is solely quantified by the interparticle void

ratio. By increasing the fines content in the range of

0–50 %, the contact between sand grains decreases and

therefore, the granular void ratio increases and the

undrained shear strength at the peak decreases. Moreover,

the slope of the undrained shear strength line at the peak is

very pronounced for smaller fines contents comparing to

higher fines contents (Fig. 10). The following expressions

are proposed to assess the undrained shear strength at the

peak using the intergranular void ratio parameter (es) for

the range of 0–50 % fines content:

log qpeak

� �¼ 4:2� 1:48 log esð Þ for Dr ¼ 20 %

log qpeak

� �¼ 4:8� 1:08 log esð Þ for Dr ¼ 91 %:

Effect of the relative density on the peak strength

Figure 11 shows the variation of the undrained shear

strength at the peak (qpeak) with the relative density (Dr) at

various fines contents. It is clear from this Figure that an

increase in the relative density results in an increase in the

peak strength at a given fines content. Thevanayagam et al.

(1997) and Sitharam et al. (2004) report similar behaviour

of increasing undrained shear strength with increasing

relative density. The present laboratory study focuses on

the effect of the fines content and other parameters on the

undrained shear strength of sand–silt mixtures at various

initial relative densities (Dr = 20 and 91 %). It can be

noticed from the results of this study that there is a sig-

nificant decrease of the undrained shear strength at the peak

with the increase of the fines content for both relative

densities, but there is also a significant increase of the

undrained shear strength at the peak with the increase in the

relative density. Moreover, the slope of the peak strength

line is very pronounced for smaller fines contents (Fc = 0,

10 and 20 %) compared to higher fines contents (Fc = 30,

40 and 50 %). The aspect of the present study is in good

agreement with the experimental work reported by Ishihara

0.2 0.4 0.6 0.8 1.0

Global Void Ratio, e (.)

0

50

100

150

200

250P

eak

Dev

iato

r S

tres

s, q

p(k

Pa)

Sand-silt mixturesFc = 0%

Fc = 10%

Fc = 20%

Fc = 30%

Fc = 40%

Fc = 50%

Dr = 20%

Dr = 91%

Fig. 8 Variation of the peak deviator stress with the global void ratio

and fines content (r3’ = 100 kPa)

0 10 20 30 40 50 60

Fines Content, Fc (%)

0

50

100

150

200

250

Pea

k D

evia

tor

Str

ess,

qp

(kP

a)

Sand-silt mixtures

Dr = 20% (R-squared = 0.96)

Dr = 91% (R-squared = 0.98)

Dr = 20%

Dr = 91%

Fig. 9 Peak deviator stress versus fines content at various relative

densities (r3’ = 100 kPa)

0.5 1.0 1.5 2.0 2.5 3.0

Intergranular Void Ratio, es (.)

0

50

100

150

200

250

Pea

k D

evia

tor

Str

ess,

qp

(kP

a)

Fc = 0%

Fc = 10%

Fc = 20%

Fc = 30%

Fc = 40%

Fc = 50%

Sand-silt mixtures

Dr = 20% (R-squared = 0.95)

Dr = 91% (R-squared = 0.99)

Fig. 10 Variation of the peak deviator stress with the intergranular

void ratio and fines content (r3’ = 100 kPa)

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(1993) on Tia Juana silty sand, Baziar and Dobry (1995) on

silty sands retrieved from the Lower San Fernando Dam,

Naeini and Baziar (2004) on Adebil sand with different

fines contents and by Belkhatir et al. (2010a) on Chlef sand

mixed with low plastic fines.

Effect of the global void ratio on the hydraulic

conductivity

Figure 12 shows the hydraulic conductivity versus the

global void ratio and fines content. It is clear from this that

the hydraulic conductivity decreases as the global void

ratio decreases and fines content increases for the loose and

dense state of the specimen (Dr = 20 and 91 %) up to

30 % fines content. Beyond 30 % the hydraulic conduc-

tivity continues to decrease linearly with increasing of the

global void ratio and the fines content for the two relative

densities (Dr = 20 and 91 %). Moreover, the slope of the

hydraulic conductivity line is very pronounced in the case

of the higher fines contents (Fc = 40 and 50 %) compared

to lower fines contents (Fc = 0, 10, and 20 %) as it is

shown by Fig. 12b.

Effect of the fines content on the hydraulic conductivity

Figure 13 shows the variation of the saturated hydraulic

conductivity with the fines content. As it can be seen from

this Figure, the saturated hydraulic conductivity (ksat) of

the sand–silt mixtures decreases linearly with the increase

of the fines content for the two initial relative densities

(Dr = 20 and 91 %). The laboratory results reveal that the

saturated hydraulic conductivity (ksat) of saturated sand

containing 50 % silt is approximately four orders of mag-

nitude smaller than the saturated hydraulic conductivity of

clean sand (Fig. 13). There is a relatively high degree of

correlation between the fines content (Fc) and the logarithm

of the saturated hydraulic conductivity (ksat) for both rel-

ative density tests (coefficient of determination R2 = 0.97

for Dr = 20 % and R2 = 0.98 for Dr = 91 %). The fol-

lowing expressions are suggested to evaluate the saturated

hydraulic conductivity (ksat):

log ksatð Þ ¼ �0:18 Fcð Þ � 9:54 for Dr ¼ 20 %

log ksatð Þ ¼ �0:21 Fcð Þ � 10:11 for Dr ¼ 91 %:

0 10 20 30 40 50 60 70 80 90 100

Relative Density, Dr (%)

0

50

100

150

200

250P

eak

Dev

iato

r S

tres

s, q

p(k

Pa)

Sand-silt mixtures

Fc = 0%

Fc = 10%

Fc = 20%

Fc = 30%

Fc = 40%

Fc = 50%

Fig. 11 Peak deviator stress versus relative density at various fines

contents (r3’ = 100 kPa)

0.4 0.5 0.6 0.7 0.8 0.9 1.0

Global Void Ratio, e (.)

1E-9

1E-8

1E-7

1E-6

1E-5

1E-4

1E-3

Hyd

rau

lic C

on

du

ctiv

ity,

k(m

/s)

Sand-silt mixtures

Dr = 20%

Dr = 91%Fc = 0%

Fc = 10%

Fc = 20%

Fc = 30%Fc = 40%

Fc = 50%

Fig. 12 Hydraulic conductivity versus global void ratio at various

fines contents (r3’ = 100 kPa)

0 10 20 30 40 50 60

Fines Content, Fc (%)

1E-9

1E-8

1E-7

1E-6

1E-5

1E-4

1E-3H

ydra

ulic

Co

nd

uct

ivit

y, k

(m/s

)Sand-silt mixtures

Dr = 20% (R-squared = 0.97)

Dr = 91% (R-squared = 0.98)

Fig. 13 Hydraulic conductivity versus fines content (r3’ = 100 kPa)

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Effect of the intergranular void ratio on the hydraulic

conductivity

Figure 14 presents the saturated hydraulic conductivity

(ksat) versus the intergranular void ratio. It is clear from this

Figure that the saturated hydraulic conductivity decreases

linearly in a significant manner until 30 % fines content

with the increase of the intergranular void ratio. After that

it continues to decrease moderately for both densities

(Dr = 20 and 91 %). Moreover, the slope of the saturated

hydraulic conductivity line is very pronounced for higher

fines contents (intergranular void ratio) comparing to lower

fines contents (Fig. 14).

Effect of the relative density on the hydraulic

conductivity

Figure 15 shows the variation of the saturated hydraulic

conductivity (ksat) with the initial relative density (Dr) at

various fines contents. It is clear from this Figure that an

increase in the relative density results in a decrease in the

saturated hydraulic conductivity (ksat) at a given fines

content. However, the hydraulic conductivity decreases

with the increase of the fines content at a given relative

density. It can be noticed from the results of this study that

there is a significant decrease in the hydraulic conductivity

with the increase in the fines content for both relative

densities. Moreover, the slope of the saturated hydraulic

conductivity line is very pronounced for higher fines con-

tents (Fc = 30, 40 and 50 %) compared to smaller fines

contents (Fc = 0, 10 and 20 %).

Effect of the hydraulic conductivity on the undrained

shear strength

Figure 16 shows the variation of the undrained shear

strength at the peak with the saturated hydraulic conduc-

tivity (ksat) at various fines contents. It is clear from this

Figure that the undrained shear strength at the peak

decreases with the decrease of the logarithm of the satu-

rated hydraulic conductivity and increase of the fines

content for both densities. However, the undrained shear

strength slope line is very pronounced for the dense

0.5 1.0 1.5 2.0 2.5 3.0

Intergranular Void Ratio, es (.)

1E-9

1E-8

1E-7

1E-6

1E-5

1E-4

1E-3

Hyd

rau

lic C

on

du

ctiv

ity,

k(m

/s)

Sand-silt mixtures

Dr = 20%

Dr = 91%

Fc = 0%

Fc = 10%

Fc = 20%

Fc = 30%Fc = 40%

Fc = 50%

Fig. 14 Hydraulic conductivity versus intergranular void ratio at

various fines contents (r3’ = 100 kPa)

0 10 20 30 40 50 60 70 80 90 100

Initial Relative Density, Dr (%)

1E-9

1E-8

1E-7

1E-6

1E-5

1E-4

1E-3

Hyd

rau

lic C

on

du

ctiv

ity,

k (

m/s

)

Sand-silt mixtures

Fc = 0%

Fc = 10%

Fc = 20%

Fc = 30%

Fc = 40%

Fc = 50%

Fig. 15 Hydraulic conductivity versus initial relative density at

various fines contents (r3’ = 100 kPa)

1E-9 1E-8 1E-7 1E-6 1E-5 1E-4 1E-3

Hydraulic Conductivity , ksat (m /s)

0

50

100

150

200

250

Pea

k D

evia

tor

Str

ess,

qp

(kP

a)

Fc = 0%

Fc = 10%

Fc = 20%

Fc = 30%

Fc = 40%Fc = 50%

Sand-silt mixtures

Dr = 20% (R-squared = 0.97)

Dr = 91% (R-squared = 0.99)

Fig. 16 Peak deviator stress versus hydraulic conductivity at various

fines contents (r3’ = 100 kPa)

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samples (Dr = 91 %) compared to loose samples

(Dr = 20 %). There is a relatively high degree of correla-

tion between the peak shear strength (qpeak) and the loga-

rithm of the saturated hydraulic conductivity (ksat) for both

relative densities (coefficient of determination R2 = 0.97

for Dr = 20 % and R2 = 0.99 for Dr = 91 %).

qpeak ¼ 9:6 log ksatð Þ þ 187 for Dr ¼ 20 %

qpeak ¼ 17:2 log ksatð Þ þ 402 for Dr ¼ 91 %:

Conclusion

A series of hydraulic conductivity and undrained mono-

tonic triaxial tests were carried out on sand–silt mixture

samples collected from liquefied sites at Chlef River

(Algeria). The effects of fines content and void ratio were

studied. In the light of the experimental evidence, the

following conclusions can be drawn:

• Undrained monotonic triaxial compression tests per-

formed with two relative densities (Dr = 20 and 91 %)

showed a contractive behaviour of the sand–silt mix-

tures samples at the initial confining pressure in the

global void ratio range tested.

• The undrained shear strength at the peak decreases as

the global void ratio decreases and the fines content

increases up to 30 %. Beyond that it decreases with

increasing the global void ratio and the fines content.

• The global void ratio does not appear as a pertinent

parameter to explain the mechanical response of sandy

soils mixed with low plastic fines.

• The peak shear strength correlates very well with the

fines content up to 50 %. Indeed, it decreases linearly

with the increase of the fines content.

• The intergranular void ratio appears as a suitable

parameter to explain the behaviour of sand–silt mix-

tures. However, the peak shear strength decreases

hyperbolically with the intergranular void ratio. The

slope of the undrained shear strength at the peak is very

pronounced for smaller fines contents compared to

higher fines contents.

• The initial relative density influences significantly the

undrained shear strength at the peak. There is an

important decrease of the undrained shear strength at

the peak with the increase of fines content for particular

initial relative density; however, there is a significant

increase of the undrained shear strength at the peak

with the increase of the initial relative density for

particular fines content. The slope of the peak strength

line is very marked for smaller fines contents (Fc = 0,

10 and 20 %) compared to higher fines contents

(Fc = 30, 40 and 50 %).

• The saturated hydraulic conductivity (ksat) of sand with

low plastic fines lesser than 50 % can be, in average,

four orders of magnitude smaller than that of clean

sand. For a given fines content, the saturated hydraulic

conductivity (ksat) varies mostly half (1/2) magnitude

for lower fines contents (Fc = 0, 10 and 20 %), and one

magnitude for higher fines contents (Fc = 30, 40 and

50 %) for the two initial relative densities under

consideration (Dr = 20 and 91 %).

• The global void ratio is not a pertinent parameter to

explain the saturated hydraulic conductivity response of

the sand–silt mixtures.

• The saturated hydraulic conductivity (ksat) correlates

very well with the fines content up to 50 %. Indeed,

there is a relatively high degree of correlation between

the fines content (Fc) and the logarithm of the saturated

hydraulic conductivity [log (ksat)] for both initial

relative densities.

• The saturated hydraulic conductivity (ksat) decreases

either with the increase of fines content and initial

relative density.

• The undrained shear strength at the peak can be

correlated to the saturated hydraulic conductivity up to

50 % fines content. Indeed, it decreases linearly with

decrease of the saturated hydraulic conductivity [log

(ksat)] and increase of the fines content (Fc).

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