belkhatir et al._granular matter_2011

Granular Matter (2011) 13:599–609DOI 10.1007/s10035-011-0269-0

ORIGINAL PAPER

Laboratory study on the liquefaction resistance of sand-siltmixtures: effect of grading characteristics

M. Belkhatir · A. Arab · T. Schanz ·H. Missoum · N. Della

Received: 4 September 2010 / Published online: 4 May 2011© Springer-Verlag 2011

Abstract The liquefaction susceptibility of saturatedmedium sand-silt mixture samples is evaluated by monotonicand cyclic undrained triaxial laboratory tests that were car-ried out on reconstituted specimens at various relative densi-ties (Dr = 20, 53 and 91%) and a constant confining pressure(σ ′

3 = 100 kPa). The test results were used to conclude on theeffect of grading characteristics and other parameters on theliquefaction resistance of the sand-silt mixtures. The mono-tonic test results indicate that the undrained shear strength atthe peak and the undrained residual strength can be correlatedto the coefficient of uniformity (Cu) and the average diame-ter (D50). Indeed, they decrease linearly with the increase ofthe uniformity coefficient and decrease of the average diam-eter. It is found that a relationship between the liquefactionresistance and any of the diameters (D10 or D50) and thecoefficient of uniformity (Cu) would be more realistic thanto build a relation between the coefficient of gradation (Cc)and the liquefaction resistance. Undrained cyclic triaxial testsindicate that the cyclic liquefaction resistance of the sand-siltmixtures decreases linearly with the decrease of the effectivediameter (D10) and mean size (D50) and increase of the finescontent for the fines content range tested (Fc = 0–40%).

M. Belkhatir (B) · A. Arab · N. DellaLaboratory of Materials Sciences and Environment,University of Chlef, BP 151 Route de Sendjes,02000 Chlef, Algeriae-mail: [email protected]

T. SchanzLaboratory of Foundation Engineering, Soil and Rock Mechanics,Ruhr University of Bochum, Bochum, Germany

H. MissoumLaboratory of Construction, Transports and EnvironmentProtection, University of Mostaganem, Mostaganem, Algeria

Keywords Liquefaction resistance · Silty sand · Effectivediameter · Coefficient of uniformity · Void ratio

1 Introduction

Several earthquakes occurred in the region of Chlef located innorthern Algeria last century. The most disastrous earthquakewith Richter Magnitude, ML = 7.2, corresponding to a Sur-face Wave Magnitude, Ms = 7.3 hit Chlef City and surround-ing areas on October 10, 1980. This event inflicted importantdamages of varying extents to a large number of small tomoderate size civil and hydraulic structures in the vicinity ofthe earthquake epicenter. Some of the distress was due to theliquefaction of saturated alluvium in foundation. Liquefac-tion associated ground deformations such as lateral spread-ing, flow failures, ground fissures and subsidence, sand boils,and slope failures were observed. The earthquake epicenterof the main shock was located 12 km in the east region ofChlef City (210 km west of Algiers) at latitude 36.143◦ Nand longitude 1.413◦ E with a focal depth of about 10 km.The approximate duration of the quake was between 35 and40 s. The event, commonly referred to as the Chlef Earth-quake, was among the most disastrous earthquakes that haveaffected the northern region of Algeria. The earthquake dev-astated the city of Chlef, population estimated at 125,000, andthe nearby towns and villages. The large loss of life (report-edly 5,000 to 20,000 casualties) and property was attributedto the collapse of buildings. In several places of the affectedarea, especially along Chlef river banks great masses of sandysoils were ejected on to the ground surface level. A majordamage to certain civil and hydraulic structures (earthdams,embankments, bridges, slopes and buildings) was caused bythis earthquake.

123

600 M. Belkhatir et al.

The factors affecting the undrained shear (liquefactionresistance) strength of sands and silty sands under monotonicand cyclic loading conditions have been extensively stud-ied by Amini and Qi, Belkhatir et al., Lade and Yamamuro,Naeini, Naeini and Baziar, Sharafi and Baziar, Thevanaya-gam, Thevanayagam et al., Yamamuro and Lade, Zlatovicand Ishihara [1–3,8,10–12,14,15,20,21]. The influence ofseveral other parameters such as the confining pressure, therelative density, the degree of saturation, the sample prep-aration method, the overconsolidation ratio and the stressratio are well understood. However, the influence of otherparameters such as the fines content, the structure, size andshape of the grains is incomplete and requires further inves-tigation Moreover, limited studies in the literature have sub-stantially evaluated the influence of particle gradation alone[19]. Chang et al. [4] reported that cyclic liquefaction resis-tance (CLR) of a clean sand was strongly affected by themean size, D50, and the uniformity coefficient, Cu, providedthat D50 < 0.23 mm. However, the individual influences ofD50 and Cu were not isolated. Vaid et al. [17] examined theinfluence of Cu by testing three clean sands with the samegrain size characteristics. They concluded that the CLR ofclean sand increases with Cu at low relative density and thetendency was reversed at high relative density.

2 Laboratory testing program

2.1 Materials properties

Silty sand samples were collected from liquefied layer ofthe deposit areas at a depth of 6.0 m (Fig. 1) close to theChlef earthquake epicenter (October 10th, 1980). The testswere conducted on the mixtures of Chlef sand and silt. Chlefsand was mixed with 0 to 50% silt to get different fines con-tents. The index properties of the sand, sand-silt mixturesand silt used in this laboratory research work are presentedin Table 1. The grain size distribution curves of the testedsand-silt mixtures are shown in Fig. 2. The variation of emax

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

(maximum void ratio corresponding to the loosest state ofthe soil sample) and emin (minimum void ratio correspond-ing to the densest state of the soil sample) versus the finescontent Fc (the ratio of the weight of silt to the total weightof the sand-silt mixture) is given in Fig. 3. According to thisFigure the different indices decrease with the increase of thefines content until Fc = 30%, then, they increase with furtherfines content increase. We note that the void ratios of sampleshave effectively changed after saturation and consolidationphases. The variation of emax versus emin is illustrated inFig. 4. It can be seen from this Figure that the correlationbetween the minimum and maximum void ratios of the sand-silt mixture samples is quite similar to that of [5] and [18].

2.2 Sample preparation

The dimensions of the samples were 70 mm in diameter and70 mm in height in order to avoid the appearance of shearbanding (sliding surfaces) and buckling. All samples wereprepared using seven layers. The resulting height to diame-ter ratio of 1 is kept constant. All samples were prepared byfirst estimating the dry weights of sand and silt needed for a

Table 1 Index properties of sand-silt mixtures

Material Fc (%) GS D10 ( mm) D50 ( mm) Cu Cc emin emax Ip (%)

Sand 0 2.680 0.22 0.68 3.36 1.36 0.535 0.876 −Silty Sand 10 2.682 0.08 0.50 7.75 2.76 0.472 0.787 −

20 2.684 0.038 0.43 15.26 1.31 0.431 0.729 −30 2.686 0.022 0.37 23.18 0.57 0.412 0.704 −40 2.688 0.015 0.29 27.33 0.64 0.478 0.796 −50 2.690 0.011 0.08 28.18 0.67 0.600 0.968 −60 2.692 − − − − 0.657 1.048 −

Silt 100 2.70 − − − − 0.72 1.137 5.0

123

Laboratory study on the liquefaction resistance of sand-silt mixtures 601

0.0010.0100.1001.00010.000

Grain Size (mm)

0

10

20

30

40

50

60

70

80

90

100P

erce

nt

Pas

sin

g b

y W

eig

ht

Sand-silt mixtures

Fc = 0%

Fc = 10%

Fc = 20%

Fc = 30%

Fc = 40%

Fc = 50%

Fig. 2 Grain size distribution curves of tested materials

Fines Content, Fc(%)

0.20

0.40

0.60

0.80

1.00

1.20

Void

Rat

ios

Ind

ex

emin

emax

e(Dr = 91%)

e(Dr = 20%)

0 10 20 30 40 50 60 70 80 90 100

Fig. 3 Void ratios index of the sand-silt mixtures versus fines content.(σ ′

3 = 100 kPa)

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 studyYilmaz and Mollamahmutoglu, (2009)Cubrinoski and Ishihara, (2002)

0.40 0.50 0.60 0.70 0.80

Fig. 4 Maximum void ratio versus minimum void ratio of the sand-siltmixtures

desired proportion into the loose, medium dense and densestate (Dr = 20, 53 and 91%) using undercompaction methodof sample preparation which simulates a relatively homoge-neous soil condition and is performed by compacted dry soilin layers to a selected percentage of the required dry unitweight of the specimen [7]. As each layer is placed, someof the compaction energy will be transmitted to the lowerlayers. Therefore, not only the layer being placed, but alsothe layers below it, is likely to be densified. To compensatefor this, the layers were at an increasing relative density fromthe bottom to top. For example, if an overall relative densityof 53% is desired, the seven layers would be placed from thebottom to the top at relative densities of 50, 51, 52, 53, 54, 55and 56% respectively. After the specimen has been formed,the specimen cap is placed and sealed with O-rings, and apartial vacuum of 15 to 25 kPa is applied to the specimen toreduce the disturbances.

2.3 Sample saturation

Saturation was performed by purging the dry specimen withcarbon dioxide for approximately 20 min. Deaired water wasthen introduced into the specimen from the bottom drain line.Water was allowed to flow through the specimen until anamount equal to the void volume of the specimen was col-lected in a beaker through the specimen’s upper drain line.A minimum Skempton coefficient-value greater than 0.96was obtained at back pressure of 100 kPa.

2.4 Sample consolidation

When samples were fully saturated, they were subjected toconsolidation. During consolidation the difference betweentotal confining pressure and back pressure was set so that foreach sample the effective consolidation pressure was fixedas 100 kPa.

2.5 Shear loading

All undrained triaxial tests for this study were carried out ata constant strain rate of 0.167% per minute, which was slowenough to allow pore pressure change to equalize through-out the sample with the pore pressure measured at the baseof sample. All the tests were continued up to 24% axialstrain.

Figure 5 shows the variation of the intergranular void ratioversus the effective diameter and fines content at the relativedensities (Dr = 20 and 91%). As it can be seen from thisFigure, the intergranular void ratio (es) increases moderatelyin a linear manner with the decrease of the effective diame-ter and increase of the fines content until the value of 20%beyond that it increases significantly with the decrease of the

123


0.00 0.05 0.10 0.15 0.20 0.25

Effective Diameter, D10 (mm)

0.30

0.60

0.90

1.20

1.50

1.80

2.10

2.40

2.70

3.00In

terg

ran

ula

r Vo

id R

atio

, es

(.)

Sand-silt mixtures

Dr = 20%

Dr = 91%

Fc = 0%Fc = 10%

Fc = 20%

Fc = 30%

Fc = 40%

Fc = 50%

Fig. 5 Intergranular void ratio versus effective diameter and finescontent. (σ ′

3 = 100kPa)

Average Diameter, D50 (mm)

0.30

0.60

0.90

1.20

1.50

1.80

2.10

2.40

2.70

3.00

Inte

rgra

nu

lar V

oid

Rat

io, e

s (.

)

Sand-silt mixtures

Dr = 20%

Dr = 91%

Fc = 0%Fc = 10%

Fc = 20%

Fc = 30%

Fc = 40%

Fc = 50%

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80

Fig. 6 Intergranular void ratio versus average diameter and finescontent. (σ ′

3 = 100 kPa)

effective diameter and increase of the fines content for bothdensities.

Figure 6 shows the variation of the intergranular void ratioversus the average diameter and fines content at the rela-tive densities (Dr = 20, 91%). The results indicate that theintergranular void ratio (es) increases hyperbolically with thedecrease of the average diameter and increase of the finescontent for both densities.

Figure 7 shows the variation of the intergranular voidratio versus the coefficient of uniformity and fines contentat the relative densities (Dr = 20 and 91%). As can be seenfrom this Figure, the intergranular void ratio (es) increasesmoderately with the increase of the coefficient of unifor-mity and fines content until the value of 40% beyond thatit increases sharply from 40 to 50% fines content for bothdensities.

Uniformity Coefficient, Cu (.)

0.30

0.60

0.90

1.20

1.50

1.80

2.10

2.40

2.70

3.00

Inte

rgra

nu

lar V

oid

Rat

io, e

s (.

)

Sand-silt mixtures

Dr = 20%

Dr = 91%

Fc = 0%Fc = 10%

Fc = 20%

Fc = 30%

Fc = 40%

Fc = 50%

0 5 10 15 20 25 30

Fig. 7 Intergranular void ratio versus uniformity coefficient and finescontent. (σ ′

3 = 100 kPa)

3 Monotonic tests results

3.1 Undrained compression loading tests

Figures 8 and 9 illustrate the undrained monotonic compres-sion triaxial test results carried out under an initial confiningpressure of 100 kPa for different fines contents ranging from0 to 50% and two initial relative densities (Dr = 20, 91%). Ascan be seen from the Figures the increase of the amount offines induces a decrease of the sand-silt mixture liquefactionresistance. This decrease results from the role of the finesto increase the contractancy phase of the sand-silt mixturesleading to a reduction of the confining effective pressure andconsequently to a decrease of the peak resistance of the mix-tures as it is illustrated by Figs. 8a and 9a. The stress pathin the (p′, q) plane shows clearly the role of the fines in thedecrease of the average effective pressure and the maximumdeviatoric stress (Fig. 8b and 9b). In this case, the effect offines on the undrained behaviour of the mixtures is observedfor the lower fines contents (0% and 10%), and becomes verymarked beyond 20%. These results are in good agreementwith the observations of [13] and [16].

Table 2 presents the summary of the undrained monotoniccompression triaxial tests.

4 Effect of grading characteristics on the peak strength

4.1 The effective diameter D10

Figure 10 illustrates the variation of the peak strength (qpeak)with the effective diameter (D10) and fines content. It is clearfrom this that the peak strength decreases almost linearly asthe effective diameter decreases and fines content increases

123


Axial Strain (%)

0

20

40

60

80

100

Dev

iato

r S

tres

s, q

(kP

a)

Sand-silt mixtures (Dr = 20%)

0% Fines

10% Fines

20% Fines

30% Fines

40% Fines50% Fines

0 5 10 15 20 25 30 35 0 25 50 75 100 125 150

Effective Mean Pressure, P' (kPa)

0

20

40

60

80

100

Dev

iato

r S

tres

s, q

(kP

a)


0% Fines10% Fines20% Fines30% Fines40% Fines50% Fines

(a) (b)

Fig. 8 Undrained monotonic response of the sand-silt mixtures. (σ ′3 = 100 kPa, Dr = 20%)

Axial Strain (%)

0

50

100

150

200

250

Dev

iato

r S

tres

s, q

(kP

a)


0% Fines

10% Fines

20% Fines

30% Fines

40% Fines

50% Fines

Effective Mean Pressure (kPa)

0

50

100

150

200

250

Dev

iato

r S

tres

s, q

(kP

a)


0% Fines

10% Fines

20% Fines

30% Fines

40% Fines

50% Fines

0 5 10 15 20 25 30 35 0 50 100 150 200 250 300

(a) (b)

Fig. 9 Undrained monotonic response of the sand-silt mixtures. (σ ′3 = 100 kPa, Dr = 91%)

Table 2 Summary of monotonic compression triaxial tests results

Test no Material FC(%) Dr(%) γd(g/cm3) e es Sus (kPa) qpeak(kPa)

1 20 1.48 0.810 0.81 16.79 97.50

2 Sand 0 91 1.71 0.567 0.567 18.37 229.60

3 20 1.56 0.724 0.916 13.57 84.50

4 10 91 1.79 0.500 0.667 17.37 191.70

5 20 1.61 0.669 1.086 11.69 57.20

6 20 91 1.84 0.458 0.823 13.94 168.30

7 20 1.63 0.646 1.351 09.69 36.80

8 Silty sand 30 91 1.87 0.438 1.054 12.78 108.60

9 20 1.55 0.732 1.887 08.14 20.80

10 40 91 1.78 0.507 1.512 11.04 77.70

11 20 1.42 0.894 2.788 07.07 17.90

12 50 91 1.65 0.633 2.266 10.84 54.10

e gross void ratio, es intergranular void ratio, Dr relative density, γd dry unit weight, Sus residual shear strength, qpeak peak strength

for the loose and dense state of the specimen (Dr = 20 and91%) up to 20% for the dense samples and 10% for the loosesamples followed by a significant decline of the sand-silt mix-ture strength. We notice that the undrained shear strength atthe peak converges towards the same values for smaller effec-tive diameter values for both relative densities.

4.2 The average diameter D50

Figure 11 shows the variation of the undrained shear strengthat the peak with the average diameter and fines content. It canbe seen from this Figure that the undrained shear strength(qpeak) of the sand-silt mixtures decreases linearly with the

123



0

50

100

150

200

250P

eak

Str

eng

th, q

p (

kPa)

Sand-silt mixtures

Dr = 20%

Dr = 91%

Fc = 0%

Fc = 10%

Fc = 20%

Fc = 30%

Fc = 40%Fc = 50%

0.00 0.05 0.10 0.15 0.20 0.25

Fig. 10 Peak strength versus effective diameter and fines content.(σ ′

3 = 100 kPa)

0.00 0.20 0.40 0.60 0.80


0

50

100

150

200

250

Pea

k S

tren

gth

, qp

(kP

a)

Fc = 0%

Fc = 10%

Fc = 20%

Fc = 30%

Fc = 40%

Fc = 50%

Sand-silt mixtures

Y = 152 x -7 (Dr = 20%)Y = 325 x + 11 (Dr = 91%)

Fig. 11 Peak strength versus average diameter and fines content.(σ ′

3 = 100 kPa)

decrease of the average diameter (D10) and increase of thefines content and converges towards a unique value of thepeak strength for higher fines content for the two initial rel-ative densities (Dr = 20 and 91%). In this laboratory inves-tigation, for the range of 0–50% fines content in normallyconsolidated undrained triaxial compression tests, the fol-lowing expressions are suggested to evaluate the undrainedshear strength at the peak which is a function of the averagediameter (D50):

qpeak = −7 + 152 (D50) for Dr = 20%

qpeak = 11 + 325 (D50) for Dr = 91%

4.3 The coefficient of uniformity Cu

Figure 12 shows the undrained shear strength at the peak(qpeak) versus the uniformity coefficient (Cu). It is clear from


0

50

100

150

200

250

Pea

k S

tren

gth

, qp

(kP

a)

Sand-silt mixtures

Y= -3.19 x + 108 (Dr = 20%)

Y = -6.53 x + 253 (Dr = 91%)

Fc = 0%Fc = 10%

Fc = 20% Fc = 30%

Fc = 40%

Fc = 50%

0 5 10 15 20 25 30

Fig. 12 Peak strength versus uniformity coefficient and fines content.(σ ′

3 = 100 kPa)

this Figure that the peak strength decreases in a linear manneras the coefficient of uniformity and fines content increase. Itseems that the decrease of the undrained strength at the peak(qpeak) due to the amount of fines is related to the contrac-tive behaviour of the sand-silt mixture samples. Moreover,the undrained shear strength range for both relative densitiesdecreases with the increase of the uniformity coefficient andfines content. In this laboratory investigation, for the rangeof 0–50% fines content in normally consolidated undrainedtriaxial compression tests, the following expressions are sug-gested to evaluate the undrained shear strength at the peakwhich is a function of the coefficient of uniformity (Cu):

qpeak = 108 − 3.19 (Cu) for Dr = 20%

qpeak = 253 − 6.53 (Cu) for Dr = 91%

4.4 The coefficient of gradation Cc

Figure 13 shows the undrained shear strength at the peak(qpeak) versus the coefficient of gradation (Cc). As it can beseen from this Figure, the peak shear strength decreases lin-early with the increase of the coefficient of gradation up to10% fines content, beyond that, it continues to decrease withthe decrease of the coefficient of gradation up to 30% finescontent, where it decreases sharply with slight increase ofthe coefficient of gradation.

5 Effect of grading characteristics on the residual shearstrength

When loose, medium dense and dense soil specimen is sub-jected to undrained shearing, the undrained shear strengthincreases rapidly until it reaches a strength point correspond-ing to a transitory state called contractancy-dilatancy phase

123


Coefficient of Gradation, Cc (.)

0

50

100

150

200

250P

eak

Str

eng

th, q

p (

kPa)

Sand-silt mixtures

Dr = 20%

Dr = 91%

Fc = 0%

Fc = 10%Fc = 20%

Fc = 30%

Fc = 40%

Fc = 50%

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Fig. 13 Peak strength versus coefficient of gradation and fines content.(σ ′

3 = 100 kPa)

change in the stress path curve (q, p′). Conventionally, thisshear strength is called the undrained shear strength at thephase transition state by Ishihara [6] and the characteristicsstate by Luong [9]. It is defined by Ishihara [6] as

Sus = (qs/2

)cos φs = (M/2) cos φs

(p′

s

)(1)

M = (6 sin φs)/(3 − sin φs) (2)

Where qs, p′s and φs indicate the deviator stress (σ ′

1 −σ ′3), the

effective mean principal stress (σ ′1+ 2σ ′

3)/3 and the mobilizedangle of inter-particle friction at the quasi-steady state (QSS)respectively. For the undrained tests conducted at the confin-ing pressure and various initial relative densities, the deviatorstress (qs) was estimated at phase transition point along withthe mobilized friction angle. Further the undrained residualshear strength at the phase transition point was calculatedusing Eq. 1.

5.1 The effective diameter D10

Figure 14 shows the variation of the undrained residual shearstrength (Sus) with the effective diameter (D10) and fines con-tent. It can be seen from this that the undrained residual shearstrength decreases almost linearly with the decrease of theeffective diameter and increase of the fines content for theloose and dense state of the specimen (Dr = 20 and 91%) upto 20% for the dense samples and 10% for the loose samplesfollowed by an important decline of the sand-silt mixturestrength.

5.2 The average diameter D50

Figure 15 illustrates the variation of the undrained residualshear strength with the average diameter and fines content.It can be seen from this Figure that the undrained residual

0.00 0.05 0.10 0.15 0.20 0.25


0

5

10

15

20

Res

idu

al S

hea

r S

tren

gth

, Su

s (k

Pa)

Sand-silt mixtures

Dr = 20%

Dr = 91%

Fc = 0%

Fc = 10%

Fc = 20%

Fc = 30%

Fc = 40%

Fc = 50%

Fig. 14 Residual shear strength versus effective diameter and finescontent. (σ ′

3 = 100 kPa)


0

5

10

15

20

Res

idu

al S

hea

r S

tren

gth

, Su

s (k

Pa)

Fc = 0%

Fc = 10%

Fc = 20%

Fc = 30%

Fc = 40%Fc = 50%

Sand-silt mixtures

Y = 17.22 x + 4.41 (Dr = 20%)Y = 14.37 x + 8.43 (Dr = 91%)

0.00 0.20 0.40 0.60 0.80

Fig. 15 Residual shear strength versus average diameter and fines con-tent. (σ ′

3 = 100 kPa)

shear strength (Sus) of the sand-silt mixtures decreases lin-early with the decrease of the average diameter (D10) andincrease of the fines content for the two relative densities(Dr = 20 and 91%). In this laboratory investigation, forthe range of 0–50% fines content in normally consolidatedundrained triaxial compression tests, the following expres-sions are suggested to evaluate the undrained residual shearstrength which is a function of the average diameter (D50):

Sus = 4.41 + 17.22 (D50) for Dr = 20%

Sus = 8.43 + 14.37 (D50) for Dr = 91%

5.3 The coefficient of uniformity Cu

Figure 16 shows the undrained residual shear strength (Sus)versus the uniformity coefficient (Cu). It is clear from this

123



5

10

15

20R

esid

ual

Sh

ear

Str

eng

th, S

us

(kP

a)

Sand-silt mixtures

Y= -0.34 x + 17.16 (Dr = 20%)

Y = -0.3 x + 19.35 (Dr = 91%)

Fc = 0%

Fc = 10%

Fc = 20%Fc = 30%

Fc = 40%

Fc = 50%

0 5 10 15 20 25 30

Fig. 16 Residual shear strength versus uniformity coefficient and finescontent. (σ ′

3 = 100 kPa)

Figure that the undrained residual shear strength decreasesin a linear manner as the coefficient of uniformity and finescontent increase. It seems that the decrease of the undrainedresidual shear strength (Sus) due to the amount of finesis related to contracting behaviour of the sand-silt mixturesamples. In this laboratory investigation, for the range of0–50% fines content in normally consolidated undrained tri-axial compression tests, the following expressions are sug-gested to evaluate the undrained residual shear strength whichis a function of the coefficient of uniformity (Cu):

Sus = 17.16 − 0.34 (Cu) for Dr = 20%

Sus = 19.35 − 0.30 (Cu) for Dr = 91%

5.4 The coefficient of gradation Cc

Figure 17 shows the undrained residual shear strength (Sus)versus the coefficient of gradation (Cc). As it can be seenfrom this Figure, the residual shear strength decreases lin-early with the increase of the coefficient of gradation up to10% fines content, beyond that, it continues to decrease withthe decrease of the coefficient of gradation up to 30% finescontent, where it decreases sharply with slight increase ofthe coefficient of gradation.

6 Undrained cyclic tests results

6.1 Compression-extension loading tests

Three series of stress-controlled cyclic triaxial tests werecarried out on isotropically consolidated soil specimenswith three different fines content (Fc = 0, 10 and 40%)and alternated symmetric deviator stress under undrained

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Coefficient of Gradation, Cc (.)

5

10

15

20

Res

idu

al S

hea

r S

tren

gth

, Su

s (k

Pa)

Sand-silt mixtures

Dr = 20%

Dr = 91% Fc = 0%

Fc = 10%

Fc = 30%

Fc = 20%

FC = 40%

Fc = 50%

Fig. 17 Residual shear strength versus coefficient of gradation andfines content. (σ ′

3 = 100 kPa)

conditions simulating essentially undrained field conditionsduring earthquakes in order to derive liquefaction potentialcurves of the sand-silt mixtures. A frequency of 0.3 Hz wasused all along the testing program. The first series includedthree alternated cyclic tests was realized on clean sand sam-ples (Fc = 0%) with an initial relative density of 53% and aconfining initial pressure of 100 kPa. The loading amplitudesof the cycles (qm) used were respectively 30, 50 and 70 kPa.The tests of the second series were realized on the mixturesand-silt samples with a fines content of 10% and loadingamplitudes of 30, 40 and 60 kPa; while the third series of testsconcerned samples with a fines content of 40% and loadingamplitudes of 20, 30 and 50 kPa. It is noted that the presenceof fines affects considerably the liquefaction of the sand-silt mixture samples. Figure 18 illustrates the results of thetest carried out on clean sand samples (Fc = 0%) with cyclicstress ratio of CSR = 0.15 (CSR = qmax/2σ ′

3). It is clearfrom the Figure that the pore water pressure increases duringthe cycles resulting in a reduction of the average effectivepressure. The rate of increase in the pore pressure remainslow, because liquefaction is obtained only after 158 cycles(Fig. 18); for the test with CSR = 0.15 and a Fines content of10%, we notice an important increase in the pore water pres-sure during 27th cycle with a significant development of theaxial strain (2.9%) leading to the sand-silt mixture specimenliquefaction (Fig. 19).

While for the test with CSR = 0.15 and a fines content of40%, we notice an important increase in the pore water pres-sure during the 3rd cycle with a significant development ofan axial strain of 8.0% leading to the liquefaction of the spec-imen at the 4th cycle (Fig. 20).This shows that the increaseof the amount of fines in the range of 0–40% accelerates thepotential of liquefaction of the sand-silt mixture samples.

123


Axial strain, ε: %

-50

-40

-30

-20

-10

0

10

20

30

40

50D

evia

tor

stre

ss, q

: kP

a

Axial strain, ε: %

0

20

40

60

80

100

Exc

ess

po

re p

ress

ure

, Δ

u: k

Pa

-8 -6 -4 -2 0 2 4 6 -8 -6 -4 -2 0 2 4 6 0 10 20 30 40 50 60 70 80 90 100

Effective mean pressure, P': kPa

-50

-40

-30

-20

-10

0

10

20

30

40

50

Dev

iato

r st

ress

, q: k

Pa

Fc = 0%

Fc = 0%

Fc = 0% (a) (b) (c)

Fig. 18 Undrained cyclic response of clean sand. (ef = 0.685, es = 0.685, CSR = 0.15, Dr = 53%, σ ′3 = 100 kPa)

Axial strain, ε :%

-50

-40

-30

-20

-10

0

10

20

30

40

50

Dev

iato

r st

ress

, q: k

Pa

Axial strain, ε :%

0

20

40

60

80

100

Exc

ess

pore

pre

ssur

e, Δ

u: k

Pa

-4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 0 10 20 30 40 50 60 70 80 90 100

Effective mean pressure, P': kPa

-50

-40

-30

-20

-10

0

10

20

30

40

50

Dev

iato

r st

ress

, q: k

PaFc = 10%

Fc = 10%

Fc = 10% (a)

(b) (c)

Fig. 19 Undrained cyclic response of sand-silt mixture. (ef = 0.625, es = 0.806, CSR = 0.15, Dr = 53%, σ ′3 = 100 kPa)

Axial strain, ε:%

-50

-40

-30

-20

-10

0

10

20

30

40

50

Dev

iato

r st

ress

, q: k

Pa

Axial strain, ε : %

0

10

20

30

40

50

60

70

80

90

100

Exc

ess

pore

pre

ssur

e, Δ

u: k

Pa

-10 -8 -6 -4 -2 0 2 4 6 8 10 -10 -8 -6 -4 -2 0 2 4 6 8 10 0 10 20 30 40 50 60 70 80 90 100

Effective mean pressure, P' : kPa

-50

-40

-30

-20

-10

0

10

20

30

40

50

Dev

iato

r st

ress

, q: k

Pa

Fc = 40%

Fc = 40% Fc = 40%

(a) (b) (c)

Fig. 20 Undrained cyclic response of sand-silt mixture. (ef = 0.597, es = 1.662, CSR = 0.15, Dr = 53%, σ ′3 = 100 kPa)

6.2 Effect of the effective diameter on the liquefactionresistance

Figure 21 shows the variation of the CLR which is definedas the cyclic stress ratio (CSR = qmax/2σ ′

3) leading to thesand-silt mixture sample liquefaction for 15 cycles according

to Ishihara [6] with the effective diameter D10. It can beobserved from this Figure that the CLR can be correlated tothe effective diameter D10. Indeed, it increases linearly withthe increase of the effective diameter D10 and decrease of thefines content for the tested samples. In this laboratory inves-tigation, for the range of 0–40% fines content in normally

123



0.05

0.10

0.15

0.20

0.25

0.30C

yclic

Liq

uef

acti

on

Res

ista

nce

, CL

R (

.)

Fc = 0%

Fc = 10%

Fc = 40%

Sand silt mixtures (Dr = 53%)

Y = 0.57 x + 0.11

R-squared = 0.99

0.00 0.05 0.10 0.15 0.20 0.25 0.30

Fig. 21 Cyclic liquefaction resistance versus effective diameter andfines content. (σ ′

3 = 100 kPa, Dr = 53%)

consolidated undrained triaxial compression-extension tests,the following expression is suggested to evaluate the CLRwhich is a function of the effective diameter (D10):

CLR = 0.11 + 0.57 (D10) for Dr = 53%

6.3 Effect of the average diameter on the liquefactionresistance

Figure 22 illustrates the variation of the CLR with the aver-age diameter D50. As it can be seen from this Figure, the CLRdecreases linearly with the decrease of the average diameterD50 and increase of the fines content for the tested sand-siltmixture samples. In this laboratory investigation, the follow-ing expression is proposed to assess the CLR depending on

0.20 0.30 0.40 0.50 0.60 0.70 0.80


0.05

0.10

0.15

0.20

0.25

0.30

Cyc

lic L

iqu

efac

tio

n R

esis

tan

ce, C

LR

(.)

Fc = 0%

Fc = 10%

Fc = 40%

Sand silt mixtures (Dr = 53%)

Y = 0.31 x + 0.017

R-squared = 0.98

Fig. 22 Cyclic liquefaction resistance versus average diameter andfines content. (σ ′

3 = 100 kPa, Dr = 53%)

the average diameter (D50) for the range of 0–40% fines con-tent in normally consolidated undrained triaxial compres-sion-extension tests:

CLR = 0.017 + 0.31 (D50) for Dr = 53%

7 Conclusion

A series of undrained monotonic triaxial tests were carriedout on sand-silt mixture samples retrieved from liquefied sitesat Chlef River banks (Algeria). The effect of grading char-acteristics and other parameters was studied. In the light ofthe experimental evidence, the following concluding remarkscan be drawn:

Undrained monotonic triaxial compression tests per-formed with two relative densities (Dr = 20 and 91%) showeda contractive behaviour of the sand-silt mixture samples sub-jected to the initial confining pressure in the gross void ratiorange tested. The undrained shear strength at the peak andundrained residual shear strength decrease as the coefficientof uniformity increases and the average diameter decreasesand fines content increases up to 50%. The peak strength andresidual strength decrease linearly with the increase of thecoefficient of uniformity and decrease of the average diam-eter. Moreover, the undrained monotonic test results dem-onstrate clearly that a relationship between the liquefactionresistance and any of the diameters (D10 or D50) and thecoefficient of uniformity (Cu) would be more realistic thanto build a relation between the coefficient of gradation (Cc)and the liquefaction resistance.

Undrained cyclic triaxial tests indicate that the CLR of thesand-silt mixtures decreases linearly with the decrease of theeffective diameter (D10) and mean size (D50) and increase ofthe fines content for the fines content range tested (Fc = 0–40%).

References

1. Amini, F., Qi, G.Z.: Liquefaction testing of stratified silty sands.J. Geotech. Geoenviron. Eng. Proc. ASCE 126(3), 208–217 (2000)

2. Belkhatir, M., Arab, A., Della, N., Missoum, H., Schanz, T.:Influence of inter-granular void ratio on monotonic and cyclicundrained shear response of sandy soils. C. R. Mecanique 338,290–303 (2010)

3. Belkhatir, M., Arab, A., Della, N., Missoum, H., Schanz, T.:Liquefaction resistance of Chlef river silty sand: effect of lowplastic fines and other parameters. Acta Polytechnica Hungari-ca 7(2), 119–137 (2010)

4. Chang, N.Y., Yey, S.T., Kaufman, L.P.: Liquefaction potential ofclean and silty sand. In: Proceedings of 3rd International Earth-quake Microzonation Conference, pp. 1018–1032 (1982)

5. Cubrinovski, M., Ishihara, K.: Maximum and minimum void ratiocharacteristics of sands. Soil Found. 42(6), 65–78 (2002)

123


6. Ishihara, K.: Liquefaction and flow failure during earthquakes.Geotechnique 43(3), 351–415 (1993)

7. Ladd, R.S.: Preparing test specimen using under compaction. Geo-tech. Test. J. GTJODJ 1, 16–23 (1978)

8. Lade, P.V., Yamamuro, J.A.: Effects of non-plastic fines on staticliquefaction of sands. Can. Geotech. J. 34, 918–928 (1997)

9. Luong, M.P.: Etat caractéristique du sol. C.R. Académie Des Sci-ences, Paris 287(série B), 305–307 (1978)

10. Naeini, S.A.: The influence of silt presence and sample prepara-tion on liquefaction potential of silty sands. PhD Dissertation, IranUniversity of Science and Technology, Tehran, Iran (2001)

11. Naeini, S.A., Baziar, M.H.: Effect of fines content on steady-statestrength of mixed and layered samples of a sand. Soil Dyn. Earthq.Eng. 24, 181–187 (2004)

12. Sharafi, H., Baziar, M.H.: A laboratory study on the liquefactionresistance of Firouzkooh silty sands using hollow torsional system.EJGE 15, 973–982 (2010)

13. Shen, C.K., Vrymoed, J.L., Uyeno, C.K.: The effects of fines onliquefaction of sands. In: Proceedings of 9th International Confer-ence Soil Mechanics and Foundation Engineering, Tokyo, vol. 2,pp. 381–385 (1977)

14. Thevanayagam, S.: Effect of fines and confining stress on undrainedshear strength of silty sands. J. Geotech. Geoenviron. Eng. Div.ASCE 124(6), 479–491 (1998)

15. Thevanayagam, S., Ravishankar, K., Mohan, S.: Effects of fines onmonotonic undrained shear strength of sandy soils. ASTM Geo-tech. Test. J. 20(1), 394–406 (1997)

16. Troncoso, J.H., Verdugo, R.: Silt content and dynamic behaviourof tailing sands. In: Proceedings of 12th International Conferenceon Soil Mechanics and Foundation Engineering, San Francisco,pp. 1311–1314 (1985)

17. Vaid, Y.P., Fisher, J.M., Kuerbis, R.H.: Particle gradation andliquefaction. J. Geotech. Eng. 116(4), 698–703 (1991)

18. Yilmaz, Y., Mollamahmutoglu, M.: Characterization of liquefac-tion Susceptibility of sands by means of extreme void ratios and/orvoid ratio range. J. Geotech. Geoenviron. Eng. 135, 1986–1990(2009)

19. Yilmaz, Y., Mollamahmutoglu, M., Ozaydin, V., Kayabali, K.:Experimental investigation of the effect of grading characteristicson the liquefaction resistance of various graded sands. Eng. Geol.J. 100, 91–100 (2008)

20. Yamamuro, J.A., Lade, P.V.: Steady-state concepts and staticliquefaction of silty sands. J. Geotech. Geoenviron. Eng.ASCE 124(9), 868–877 (1998)

21. Zlatovic, S., Ishihara, K.: On the influence of non-plastic fines onresidual strength. In: Proceedings of the First International Confer-ence on Earthquake Geotechnical Engineering. Tokyo, pp. 14–16(1995)

123

belkhatir et al._granular matter_2011

Documents