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International Conferences on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics

2010 - Fifth International Conference on Recent Advances in Geotechnical Earthquake

Engineering and Soil Dynamics

26 May 2010, 4:45 pm - 6:45 pm

Dynamic Properties of Sand in Constant-Volume and Constant-Dynamic Properties of Sand in Constant-Volume and Constant-

Load Tests Load Tests

F. Jafarzadeh Sharif University of Technology, Iran

H. Sadeghi Sharif University of Technology, Iran

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Recommended Citation Recommended Citation Jafarzadeh, F. and Sadeghi, H., "Dynamic Properties of Sand in Constant-Volume and Constant-Load Tests" (2010). International Conferences on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics. 11. https://scholarsmine.mst.edu/icrageesd/05icrageesd/session01/11

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Paper No. 1.11a 1

DYNAMIC PROPERTIES OF SAND IN CONSTANT-VOLUME AND CONSTANT-LOAD TESTS

Jafarzadeh, F. Sadeghi, H. Sharif University of Technology Sharif University of Technology Tehran, Iran 11365-9313 Tehran, Iran 11365-9313 ABSTRACT Constant-volume and constant-load tests were performed on Babolsar and Toyoura sands by using a modified SGI cyclic simple shear device which provides the capability of back pressure saturation. All tests were shear strain controlled and conducted under different values of relative density, vertical effective stress and shear strain amplitude. Results revealed that Dr, σ′v and γ affect shear modulus and damping ratio under both constant-volume and constant-load conditions in similar ways except the shear strain amplitude which has no important influence on damping of constant-volume tests. The effects of Dr, σ′v, γ and the number of cycles on variations of shear modulus and damping ratio of sand were found to be more pronounced under constant-load condition. It seems that the differences between the results may be due to the different fabric produced in two kinds of test samples rather than to the test method. However, further study is needed to clarify this issue. INTRODUCTION Wide application of dynamic properties of soil in geotechnical earthquake engineering problems (such as the analysis of soil-structure interactions, dynamic bearing capacity of machines foundations, soil structures subjected to cyclic loadings) has made researchers to investigate a variety of factors which affect shear modulus and damping ratio of soil (e.g. Hardin and Drnevich 1972a) and to develop various field and laboratory tests methods so far (Kramer 1996). A cyclic simple shear test is a convenient laboratory test method in evaluating G and D of soil, especially at large shear strains.

Results of truly undrained and conventional constant-volume tests by using a developed NGI direct simple shear device were compared by Dyvik et al. 1987. On the basis of static tests on clay, they concluded that the results obtained by two methods are equivalent for saturated soils. Theoretically, since there is no real pore pressure generation in the specimen under constant-volume condition, it is not necessary to saturate the specimen. However, poor saturation can modify soil resistance (Vanden Berghe et al. 2001).

The main objective of the present study is to investigate shear modulus and damping ratio of cyclically loaded sand under constant-volume and constant-load conditions. Additionally, the effects of some parameters on dynamic properties of sand under mentioned conditions will be presented and discussed.

LABORATORY PROCEDURE Test Materials Two poorly graded sands, Babolsar and the Japanese standard Toyoura sand were selected as test materials. The former is natural sand obtained from the South coast of Caspian Sea. Particle size distribution curves of sands are shown in Fig. 1.

Fig. 1. Gradation curves of test materials.

0102030405060708090

100

0.01 0.1 1 10

Fine

r by

wei

ght (

%)

Particle size (mm)

Babolsar sand

Toyoura sand

Silt GravelSandFine Medium Coarse

ASTM Babolsar ToyouraD422-63

D10 0.14 0.14D30 0.22 0.16D50 0.25 0.19Uc 1.79 1.56Cc 1.32 0.95

 

Paper No. 1.11a 2

Principal index tests were performed following the procedure of the ASTM standards. The physical properties of soils utilized in the all conducted tests are summarized in Table 1.

Table 1. Physical properties of test materials

Soil type Specific gravity emax eminBabolsar sand 2.753 0.777 0.549 Toyoura sand 2.645 0.973 0.609

Standard designation ASTM D854–02 ASTM

D4254–00 ASTM

D4253–00 Apparatus A servo-controlled pneumatic SGI cyclic simple shear, CSS; apparatus manufactured by Wykeham Farrance Co. was used in order to perform the cyclic loading of soil samples. This apparatus is capable of conducting stress and strain controlled tests in the both horizontal and vertical directions. Loading forces are applied through the pneumatic actuators mounted horizontally and vertically. A circular specimen is mounted between the base pedestal and piston top cap and surrounded by a number of circular rings to prevent lateral displacement during consolidation or shearing stages. Indeed, the specimen can be laterally restrained by rigid boundary plates (Cambridge-type device), a wire-reinforced membrane (NGI-type device), or a series of stacked rings (SGI-type device) according to the description of Kramer 1996.

Fig. 2. Schematic view of cyclic simple shear (SGI type)

apparatus and pressure test device.

The apparatus was equipped with a pressure test device made by ELE. The pressure test device which can introduce water pressure into the specimen was utilized in order to improve the apparatus so that it can be used in conducting undrained tests on fully saturated samples. On the other hand, the capability of saturating the specimen with back pressure has been possible using this ancillary device. A schematic illustration of the modified CSS apparatus is given in Fig. 2. Sample Preparation Constant-Volume Tests. Solid cylindrical samples with the nominal diameter of 70 mm and height of 22 mm were used in cyclic simple shear tests. Samples were prepared by using the moist placement method suggested by Ishihara 1996. The mixture of soil with 5% water content was poured in the mold with a spoon and the specimen was compacted until approaching the desired density. The relative density of the specimen was controlled by adjusting its height using a 0.01 mm digital caliper. This method of sample preparation was utilized in constant-volume and constant-load tests. Estimation of Pore Pressure Parameter. Use of Skempton’s pore pressure parameter, B value; in triaxial loading condition as a guide to achieve full saturation is conventional but, for the stress conditions other than triaxial condition e.g. where the specimen is consolidated under K0 condition (Fig. 3a), there is no criteria for assuring full saturation of the sample. It seems that a proper evaluation of pore pressure parameter under this special loading condition is inevitable. Figure 3a shows a saturated soil element subjected to an increase of total stress in which the intermediate and minor principal stresses are equal. The pore water pressure will grow by ∆u if drainage is not allowed from the soil. The change in the volume of pore water due to the increase of pore pressure by an amount of ∆u can be expressed as (Das 1983):

∆V nV C ∆u (1)

where n is porosity, V0 is the original volume of soil element and Cp is the compressibility of pore water.

On the other hand, the change in volume of the soil skeleton due to the effective stress increment indicated in Fig. 3b will be:

∆V C V ∆σ ∆σ ∆σ C V ∆σ 2∆σ (2a)

where ∆σ′1, ∆σ′2 and ∆σ′3 are principal effective stresses as shown in Fig. 3b corresponding to the total stresses in Fig. 3a and Cc is the compressibility of the soil skeleton. Figure 3c shows the determination of Cc from laboratory compression test results under uniaxial stress application with zero excess pore water pressure. By simplifying Equation 2a, we obtain:

∆V C V ∆σ 2K ∆σ C V ∆σ 1 2K (2b)

 

Paper No. 1.11a 3

(a)

(b)

1σ ′Δ

1σ ′Δ

102 K σσ ′Δ=′Δ102 K σσ ′Δ=′Δ

103 K σσ ′Δ=′Δ

103 K σσ ′Δ=′Δ

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σ ′ΔΔ

= 0VVCc

(c)

1σΔ

2σΔ

23 σσ Δ=Δ

1σΔ

2σΔ

23 σσ Δ=Δ

uΔ

Fig. 3. (a) Total stresses and (b) Effective stresses imposed on a saturated soil element consolidated under K0 condition and (c) Definition of compressibility of soil skeleton (Das 1983).

where K0 is the coefficient of at‒rest earth pressure. After substitute of ∆σ1‒ ∆u for ∆σ′1 in Equation 2b we have:

∆V C V ∆σ ∆u 1 2K (2c)

If the soil element is fully saturated with water, the change in the volume of both pore water and soil skeleton under the application of three principal total stresses plotted in Fig. 3a must be equal. So, a comparison of Equations 1 and 2c gives:

nV C ∆u C V ∆σ ∆u 1 2K (3) The pore pressure parameter, ∆u/∆σ1, is extracted from Equation 3 as:

∆u ∆σ⁄ 1 2K nC C 1 2K⁄⁄ (4a) Finally, by more simplification of Equation 4a, the pore pressure parameter can be estimated based on Equation 4b:

∆u ∆σ⁄ 1 1 nC C 1 2K⁄⁄ (4b) Since the compressibility of water is much smaller than compressibility of soil skeleton, the value of Cp/Cc converges to zero. So it would appear that, the value of ∆u/∆σ1 mainly depends on Cp/Cc than n/(1+2K0). Hence, the effect of K0 value on the estimation of pore pressure parameter can be neglected. However, the value of n/(1+2K0) is less than unity and makes the term, nCp/[Cc(1+2K0)] to decrease more. Subsequently, it can be inferred from the above expressions that, the upper limit of pore pressure parameter where the specimen is consolidated under the application of K0 condition, is equal to one.

Traditionally, the value of pore pressure parameter under triaxial stress conditions, B value, equals to 0.95 is accepted as representing virtually full saturation in laboratory reports. As an alternative, if several successive equal increments of confining pressure give identical values of B, full saturation of the specimen could be assured (Head 1998).

Constant-Load Tests. After preparation of samples on the basis of wet tamping method, CO2 was percolated through the specimens and de-aired water was then introduced into the soil sample, while the vertical stress was kept at 15 kPa to prevent the sample disturbance. After one stage of saturation using 25 kPa of vertical stress and 15 kPa of back pressure was taken, back pressure was raised following the vertical stress increase to the next step by 10 kPa and the procedure of raising the vertical stress and back pressure was then repeated. Considering the mentioned criteria for assuring full saturation, the saturation of the specimens by the application of back pressure was continued until two or three equal increments of vertical stress give identical values of pore pressure parameter, ∆u/∆σ1. The samples were then consolidated to a given vertical consolidation stress. The values of total vertical stress, effective consolidation stress and back pressure as well as the corresponding ratio of pore water pressure parameter, ∆u/∆σ1, at the last step of saturation for 16 undrained tests are summarized in Table 2.

 

Paper No. 1.11a 4

Table 2. Measured ∆u/∆σ1 in constant-load tests at the end of saturation stage

Test no. Dr (%)

σ v

(kPa) Back pressure

(kPa) σ′v

(kPa) ∆u/∆σ1

9 (B*) 31 175 125 50 0.90 10 (B) 35 175 125 50 0.88 11 (B) 71 205 155 50 0.88 12 (B) 67 205 155 50 0.88 13 (B) 32 275 125 150 0.89 14 (B) 30 275 125 150 0.87 15 (B) 74 305 155 150 0.90 16 (B) 71 305 155 150 0.89

25 (T**) 32 175 125 50 0.91 26 (T) 33 175 125 50 0.90 27 (T) 71 205 155 50 0.88 28 (T) 70 205 155 50 0.85 29 (T) 28 275 125 150 0.86 30 (T) 39 275 125 150 0.91 31 (T) 68 305 155 150 0.82 32 (T) 70 305 155 150 0.83

B*: Babolsar sand, T**: Toyoura sand Test Program Whereas the after consolidation relative density should be taken into account, a series of calibration consolidation tests were conducted to specify the initial relative density of the partially and fully saturated specimens. The values of initial Dr for different vertical σ′v and post consolidation relative densities as results of preliminary tests are reported in Table 3.

The main experimental program included tests with different

values of σ′v, Dr and γ which were performed under constant-volume and constant-load conditions. Unsaturated samples were sheared under equivalently undrained or constant-volume condition. On the other hand, truly undrained tests were carried out on fully saturated specimens under constant-load condition. Half of the specimens were consolidated to 50 kPa and the others to 150 kPa. Test samples had two different post-consolidation relative densities 30, 70% representing loose and medium dense conditions; respectively. All tests were shear strain-controlled with an approximately sinusoidal shape of cyclic straining at large shear strain amplitudes of 1.0 and 1.5%. The frequency of cyclic loading was 0.5 Hz and the number of loading cycles varied from 1 to 200 or to the cycle of initial liquefaction, which ever occurred first. General testing conditions at the beginning of cyclic shear stage are listed in Table 4 for 32 cyclic simple shear tests.

Table 4. Tests conditions at the beginning of cyclic stage

Test no. Sand type

Vertical load condition

Dr (%)

γ (%)

σ′v (kPa)

1, 2 B* Constant-volume 32, 29 1.0, 1.5 50 3, 4 B Constant-volume 69, 69 1.0, 1.5 50 5, 6 B Constant-volume 29, 30 1.0, 1.5 150 7, 8 B Constant-volume 70, 69 1.0, 1.5 150 9, 10 B Constant-load 31, 35 1.0, 1.5 50

11, 12 B Constant-load 71, 67 1.0, 1.5 50 13, 14 B Constant-load 32, 30 1.0, 1.5 150 15, 16 B Constant-load 74, 71 1.0, 1.5 150 17, 18 T** Constant-volume 31, 29 1.0, 1.5 50 19, 20 T Constant-volume 70, 69 1.0, 1.5 50 21, 22 T Constant-volume 29, 30 1.0, 1.5 150 23, 24 T Constant-volume 69, 69 1.0, 1.5 150 25, 26 T Constant-load 32, 33 1.0, 1.5 50 27, 28 T Constant-load 71, 70 1.0, 1.5 50 29, 30 T Constant-load 28, 39 1.0, 1.5 150 31, 32 T Constant-load 68, 70 1.0, 1.5 150

B*: Babolsar sand, T**: Toyoura sand Calculation of G and D Dynamic stiffness and damping ratio of each cycle can be determined from a graph of stress against strain, knowing as hysteresis loop. Figure 4 illustrates a schematic hysteresis loop and how secant modulus and damping can be determined based on data achieved from stress-strain curve. By using 50 data point per cycle which transferred through CDAS to PC, the area of hysteresis loop can be estimated precisely according to Equation 5. A 0.5

γ γτ τ

γ γτ τ

γ γτ τ (5)

in which Aloop is the area of hysteresis loop with vertices of (γ1, τ1), (γ2, τ2)…(γ50, τ50) and γi, τi are shear strain and shear stress at ith point; respectively. Jafarzadeh and Sadeghi 2009

Table 3. Preliminary tests results

Test no. Test condition Post

consolidation Dr (%)

σ′v (kPa)

Initial Dr(%)

P1–B* Constant-volume 30 50 23.2 P2–B Constant-volume 70 50 64.9 P3–B Constant-volume 30 150 16.6 P4–B Constant-volume 70 150 59.5 P5–B Constant-load 30 50 3.5 P6–B Constant-load 70 50 57.9 P7–B Constant-load 30 150 – 3.7 P8–B Constant-load 70 150 52.0

P9– T** Constant-volume 30 50 25.0 P10–T Constant-volume 70 50 65.7 P11–T Constant-volume 30 150 20.5 P12–T Constant-volume 70 150 62.1 P13–T Constant-load 30 50 4.5 P14–T Constant-load 70 50 62.7 P15–T Constant-load 30 150 – 1.7 P16–T Constant-load 70 150 58.3

B*: Babolsar sand, T**: Toyoura sand

 

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r No. 1.11a

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Paper

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1

Toyour

indicated thaportant influen

ping values arese to the cyclecific sample dicant decrease

decrease inial liquefactionorizontal load c

actuator cannore, the shag with the loopes damping raping values aftng at Nl.

the variationfor all constanFig. 9, dampinBy comparing he trends of d

under constanhose of constan, damping willnitial liquefac

ms that, the tesant-load condi

of damping rasts under const

10Numbe

sar

Number

ra

at, the developce on damping

e represented fe of initial liqudecreases signi

in shear mod shear modun, according tocell which direnot sense the

ape of hystep area and sheaatio unreliablefter a sample i

s of damping nt-volume testsng ratio decrethe results of F

damping variant-volume con

nt-load tests. Inl not increase bction under costs performed ition represent

tio with the nutant-load cond

100er of Cycles

10r of Cycles

7

ped pore wateg variations.

from cycle 1 touefaction, sheaificantly which

dulus. Dampingulus until tho Fig. 4. Afteectly connected

lateral forceresis loop iar modulus tha. So, it is juss liquefied, ar

ratio with ths. As shown ineases with thFigs. 8 and 9, iations with thndition are non contrast to thby approachingonstant-volumin the presen

t more reliabl

umber of cyclesdition.

1000

Test No.910111213141516

100

Test No.2526272829303132

7

er

o ar h g e

er d

es is at st e

e n e it e

ot e g e

nt e

s

 

Paper

trendsconst

The mnumbunderresistwith shear (Fig. dampSincedevelverticamoutruly strengliquefshearload until Effec The tand γ

Fig.

Dam

ping

Rat

io, D

(%)

(a)

Dam

ping

Rat

io, D

(%)

(b)

r No. 1.11a

s for damping tant-volume tes

main reason fober of cycles r truly undratance of specimthe shear mo

r modulus resu4). But, unde

ping variationse the specimloped pore watcal load was ount of shear m

undrained testgth to the latfaction due to r modulus prevtests and keepcycle 100.

cts of Dr, σ′v an

tests were condγ, while the oth

9. Variations ofor the tests

10

13

16

19

22

25

0 2

Bab

14

17

20

23

26

0 2

Toyo

variations witsts.

or rapid growtby getting cloained conditiomens to lateral dulus. Subseqult in the higher constant-vols with the numens were no

ter pressure is iomitted from

modulus which ts. It means thteral load evethe capillary e

vents damping ps it nearly co

nd γ

ducted under twher testing con

of damping rats under constan

0 40Number

Tesbolsar

0 40Number

Test No.oura

th the number

th in damping ose to the liquon was the forces which

quently, the loher values of ume condition

mber of cyclesot fully saturimaginary eventhe specimen,was more in

hat the specimen after the

effects. This refrom increase

onstant with a

wo different lenditions were k

tio with the numnt-volume cond

60of Cycles

st No. 1 25 6

60of Cycles

17 1821 22

of cycles than

ratio with theuefaction statelow shearingwas correlated

ower values ofdamping ratio

n the trends ofs are differentrated and then after the total there was ancontrast to the

mens had shearoccurrence ofsidual value ofas in constant-few scattering

evels of Dr, σ′vkept the same.

mber of cycles dition.

80 100

3 47 8

80 100

19 2023 24

n

e e g d f o f . e l n e r f f -g

v .

So, tshearcan bcondbasedcycle EffecrelatiThe Dr caload contacondratio and eThe relatitests condThis devedegraIn this geapplisampthe fidecrevalueundenumbbecau EffecmoduWiththe vconstcondFig. effecconstvolumconsttests.wereliqueare nFig. highewith of inresuldampincrementof oth

the effects of rr strain amplitbe investigated

ditions. Compad on the valuee 5.

ct of Relative ive density on increase in shean be seen in Ftests. Legends

ain the numbditions were sum

descends withequivalently urate of increaive density fro

conducted odition as well

is because ofloped during adation especiae other words,

enerated when ication of largeples to lose mofirst few cyclesease in shear me. But, as deser constant-vober of cycles use of the capi

ct of Vertical ulus and damp

h an increase invalues of dynatant-load and

ditions, based o11b, damping

ctive consolidatant-load condme tests. Trentant-load tests . These tests h

e sheared with efied until cyclnot so reliable8b, the valueser vertical effethe test # 26 u

nitial liquefactlts of constanping ratio atease in σ′v in tioned trend is her cases.

relative densitytude on shear d under constaarisons will bes of shear m

Density. Figushear modulu

ear modulus aFig. 10a for cos shown at thebers of indivmmarized in Th an increase iundrained condse in shear mom 30 to 70%

on saturated sas the rate of f the effect of

cyclic shearially for sample high amount oa specimen is

e shear strain. ost of their str, which subseq

modulus along scribed previouolume conditio

as much as llary effect.

Effective Strping ratio with n vertical effectamic stiffness sd constant-volon the results ratio decreases

ation stress in dition except nd of damping(i.e. 26 and 3

had a nominal 1.5% shear stre 5 that means

e. However, bas of damping fective stress (tup to third cyclion for the tent-volume test cycle 5 intwo cases ofnot expected a

y, vertical effecmodulus and

ant-volume andbe presented odulus and da

ure 10 indicateus and dampingas a result of 4onstant-volumee right side ofvidual tests. Table 5. Conven relative dens

ditions as showodulus due to

% is more signsamples underf reduction in f excess pore ing and resules with 30% rof excess pores cyclically shThis mechanisrength to the laquently results

with an increausly, the valuon don’t redthose of cons

ess. The variaσ′v are illustra

tive stress fromsignificantly inlume tests foof Fig. 11a.

s with the incrall the tests peone, and mosg variation wi0) is different relative densi

rain amplitudes, the values ofased on the dafor the test cotest # 30) arele, which is equest # 26. Withsts illustrated ncreases slighf constant-voluand also differs

8

ctive stress anddamping ratio

d constant-loadand discussed

amping ratio a

es the effect og ratio of sand

40% increase ine and constantf each diagramComplete tes

ersely, dampingsity under trulywn in Fig. 10b the growth onificant for thr constant-loaddamping ratiowater pressur

lts in stiffnesrelative density water pressur

heared with thsm makes loosateral forces inin a substantiaase in damping

ues of moduluduce with thstant-load test

ations of sheaated in Fig. 11

m 50 to 150 kPncrease in bothfor all testingAs depicted in

rease in verticaerformed undest of constantith σ′v for twofrom the othe

ity of 30% ande. Both samplef damping at Nata depicted in

onsolidated to less compared

ual to the cyclh regard to th

in Fig. 11bhtly with thume tests. Ths from the trend

8

d o d d at

of d. n t-m st g y

b. of e d

o. e

ss y. e e e n al g

us e ts

ar 1. a h g n al er t-o

er d

es Nl n a d e e

b, he e d

 

Paper

Figdam

1122334

Shea

r Mod

ulus

, G5

(kPa

)

1

1

1

Shea

r Mod

ulus

, G5

(kPa

)

(a)

Dam

ping

Rat

io, D

5(%

)D

ampi

ng R

atio

, D5

(%)

(b)

r No. 1.11a

g. 10. Effect of mping ratio of c

0500

1000150020002500300035004000

10 3Re

Cons

0

200

400

600

800

1000

1200

1400

10 3Re

Consta

05

10152025303540

10 3Re

Cons

12

14

16

18

20

22

24

10 3Re

Consta

relative densityconstant-load a

30 50elative Density,

tant-load

30 50elative Density,

ant-volume

30 50elative Density,

stant-load

30 50elative Density,

ant-volume

y on (a) shear and constant-v

70 90Dr (%)

70 90Dr (%)

70 90Dr (%)

70 90Dr (%)

modulus, (b) volume tests .

Test No.9 & 1110 & 1213 & 1514 & 1625 & 2726 & 2829 & 3130 & 32

Test No.1 & 32 & 45 & 76 & 817 & 1918 & 2021 & 2322 & 24

Test No.9 & 1110 & 1213 & 1514 & 1625 & 2726 & 2829 & 3130 & 32

Test No.1 & 32 & 45 & 76 & 817 & 1918 & 2021 & 2322 & 24

Fig. (b) d

22

4

Shea

r Mod

ulus

, G5

(kPa

)Sh

ear M

odul

us, G

5(k

Pa)

(a)D

ampi

ng R

atio

, D5

(%)

Dam

ping

Rat

io, D

5(%

)

(b)

11. Effect of vedamping ratio o

0500

1000150020002500300035004000

25 50Vertic

Con

0

200

400

600

800

1000

1200

1400

25 50Vertic

Const

05

10152025303540

25 50Vertic

Cons

12

14

16

18

20

22

24

25 50Vertic

Consta

ertical effectiveof constant-loa

75 100 1cal Effective Stre

stant-load

75 100 1cal Effective Stre

ant-volume

75 100 1al Effective Stre

stant-load

75 100 1cal Effective Stre

ant-volume

e stress on (a) ad and constan

125 150 175ess, σ′v (kPa)

125 150 175ess, σ′v (kPa)

125 150 175ess, σ′v (kPa)

125 150 175ess, σ′v (kPa)

9

shear modulust-volume tests

5

Test No.9 & 1310 & 1411 & 1512 & 1625 & 2926 & 3027 & 3128 & 32

5

Test No.1 & 52 & 63 & 74 & 817 & 2118 & 2219 & 2320 & 24

5

Test No.9 & 1310 & 1411 & 1512 & 1625 & 2926 & 3027 & 3128 & 32

5

Test No.1 & 52 & 63 & 74 & 817 & 2118 & 2219 & 2320 & 24

9

s, .

 

Paper

Effecmodudemoin damplicondisignifbe seDamptests. the shversahas nvolum

A staDr, σtestedconstdiagra2nd, 5increaconstdiagradampthe dealso sfor cy

Basedfrom constdecrecondireducconst29% damp13% load can bparammater

Of pvoluminflueof tecondithe coDr, σvariatcondiσ′v almagnratio volum

r No. 1.11a

ct of Shear Straulus and dampionstrated in Figescending orditude, under itions. With 0ficant increase een from the reping doesn’t fIn the other w

hear strain ampa in the other cno important efme condition.

atistical study hσ′v and γ on shd in the curtant-load condams in Fig. 13

5th and 10th cycase in γ is showtant-volume tesam of Fig. 13

ping ratio becauecrease in γ foshown in uppeycles 2, 5 and 1

d on the results150 to 50 kP

tant-volume aneases by 45% itions. Accordction in Dr (i.etant-volume anon average; re

ping ratio at cyand 42%; resptests. Thereforbe used to m

meter affects shrials under diff

articular intereme and constaences of Dr, σ′vested sands uitions were coolumn charts o′v and γ have tions under bitions, but the lso affect dam

nitudes under bis not affected

me compared w

ain Amplitude.ing ratio of Babg. 12. The varder with the

constant-vo.5% increase in damping ra

esults of truly follow a specifwords, dampingplitude in somcases. It seemsffect on dampi

has done in ordhear modulus rrent study u

ditions. Results. The average cles due to thewn in Fig. 13a.sts are pasted in3a; respectiveluse of the incror truly and eqer and lower h10.

s of Fig. 13a, fa causes 55%

nd constant-loaand 65% on ading to the e. 70 to 30%),nd constant-loadespectively. Aycle 5 due to tectively, for core, the columnmoderately sphear modulus ferent loading c

est was a comant-load condiv and γ on sheaunder constantompletely the of Fig. 13 woulsimilar effectsboth constantquantities are

mping ratio inboth conditiond by shear straiwith constant-lo

. The influencebolsar and Toyriations of sheae increase in olume and in shear strainatio of saturateundrained tes

fic trend in cog ratio increase

me cases and ths that, shear sting variation u

der to compareand damping

under constans are shown idecrease in shee decrease in D Results of conn the upper anly. The averagrease in Dr andquivalently undalf of Fig. 13b

for example, a and 60% dec

ad tests; respecaverage under results of Fi, decreases damd tests at cycle

Also, the averagthe reduction ionstant-volumen charts indicaecify how mand damping rconditions.

mparison betwitions on test ar modulus andt-volume and same, the horild act like a mis on trends of -volume and somewhat dif

similar way s but, it seemsin amplitude uoad condition.

e of γ on shearyoura sands arear modulus are

shear strainconstant-load

n amplitude, aed samples cants in Fig. 12b

onstant-volumees slightly withhe trend is vicetrain amplitudeunder constant-

e the effects ofratio of sands

nt-volume andin the columnear modulus ofDr and σ′v andnstant-load andd lower half ofge decrease ind σ′v as well asdrained tests isb; respectively

decrease in σ′vcrease in G2 ofctively. G5 alsothe mentioned

ig. 13b, 40%mping ratio ofe 2 by 11% andge decrease inin Dr grows toe and constant-ated in Fig. 13

much a certainratio of similar

ween constant-results. If the

d damping ratioconstant-load

izontal axis inirror. Actuallyshear modulus

constant-loadfferent. Dr andwith different

s that dampingunder constant-

r e e n d a n . e h e e -

f s d n f d d f n s s ,

v f o d

% f d n o -3 n r

-e o d n , s d d t g -

Fig. (b) d

22

4

Shea

r Mod

ulus

, G5

(kPa

)Sh

ear M

odul

us, G

5(k

Pa)

(a)D

ampi

ng R

atio

, D5

(%)

Dam

ping

Rat

io, D

5(%

)

(b)

12. Effect of shdamping ratio o

0500

1000150020002500300035004000

0.75 1She

0

200

400

600

800

1000

1200

1400

0.75 1She

05

10152025303540

0.75 1She

12

14

16

18

20

22

24

0.75 1She

hear strain ampof constant-loa

.00 1.25ar Strain Amplit

Con

.00 1.25ear Strain Amplit

Cons

.00 1.25ear Strain Ampli

Con

.00 1.25ear Strain Amplit

Cons

plitude on (a) sad and constan

1.50 1.75tude, γ (%)

nstant-load

1.50 1.75tude, γ (%)

tant-volume

1.50 1.75itude, γ (%)

nstant-load

1.50 1.75tude, γ (%)

tant-volume

10

shear modulust-volume tests

5

Test No.9 & 1011 & 1213 & 1415 & 1625 & 2627 & 2829 & 3031 & 32

5

Test No.1 & 23 & 45 & 67 & 817 & 1819 & 2021 & 2223 & 24

5

Test No.9 & 1011 & 1213 & 1415 & 1625 & 2627 & 2829 & 3031 & 32

5

Test No.1 & 23 & 45 & 67 & 817 & 1819 & 2021 & 2223 & 24

0

s, .

 

Paper

Basedof Drratio Someboth saturaprepapressumenti Shear Data were sand. for dToyocurrenToyoDampBabo

Figurand dcurveon the

Fig.dam

9

6

3

3

6

9A

vera

ge D

ecre

ase

in G

by

Perc

ent

(a)

54321

12345

Ave

rage

Dec

reas

e in

D b

y Pe

rcen

t

(b)

r No. 1.11a

d on the resultr, σ′v and γ on

are more proe of possible exconditions are

ated testing sared for constaure developeioned reasons w

r modulus and

of shear modcompared wiHigher values

damping were ura sand durinnt study. Accura sand is apping ratio of Tlsar sand by ne

re 14 comparedamping ratio ies of other inve basis of Equa

13. Effects of mping ratio in

90

60

30

0

30

60

90

Cycle 2Cycle 5Cycle 1

Decrease

(70 to 30

50403020100

1020304050

Cycle 2Cycle 5Cycle 1

Increase (70 to 30

ts of Fig. 13, ivariations of

onounced undxplanations foe the differenamples, the cant-volume ted under conwere discussed

damping ratio

dulus and damith the corresps of shear modobserved for

ng cyclic simplecording to thepproximately 3Toyoura sand isearly 20% on a

s the measuredin this study w

vestigators. Vaation 6 suggest

f Dr, σ′v and γ on

constant-load

0

in Dr Decre

%) (150

0

in Dr Incre0 %) (150

t is revealed thshear modulus

der constant-lor differences o

nt fabric of uncapillary effecsts and the renstant-load cod previously in

of two tested s

mping ratio of ponding valuedulus as well aBabolsar sand

e shear tests pee results, shea0% less than Bs also more th

average.

d normalized with the previoalues of Gmax wted by Kokusho

n (a) shear moand constant-v

ease in σ′v I

to 50 kPa) (

Co

Con

ease in σ′v Dto 50 kPa) (

Co

Con

hat, the effectss and dampingoad conditionobserved undernsaturated andcts in sampleseal pore waterondition. Thedetail.

sands

Babolsar sands for Toyoura

as lower valuesd compared toerformed in thear modulus ofBabolsar sand

han damping of

shear modulusously publishedwere estimatedo 1980.

odulus and (b) volume tests.

ncrease in γ

(1.0 to 1.5 %)

onstant-load tests

nstant-volume tests

Decrease in γ(1.0 to 1.5 %)

onstant-load tests

nstant-volume tests

s g . r d s r e

d a s o e f . f

s d d

G wherratio;throuand D1986constcurvetherestudyfor dalso tin the1986effec CON A SGpressdevicspeciperfoconstsatur

Figwit

Nor

m. S

hear

Mod

ulus

, G/G

max

(a)

Dam

ping

Rat

io, D

(%)

(b)

8400 2.17

re σ′m and e ar; respectivelyugh cyclic simpDrnevich 1972

6 for sands. Ctant-volume aes by other rese is not a goody, but the diffdamping ratio tremendous. He current study

6 and curve of ctive stress equ

NCLUSIONS

GI cyclic simpsure test device, so it can beimens. This meorming real untant-volume anrated specimen

g. 14. Comparith the previous

0.00.10.20.30.40.50.60.70.80.91.0

0.01

0

10

20

30

40

50

0.0001 0

31--31293131

σ

7 e σ

re mean princi. As shown

mple shear tests2b as well as thComparison of and constant-losearchers in Fid agreement bferences betweof sand at larg

However, somey fall between tf Tatsuoka et auals to 24.5 kPa

le shear apparice in order te used in conduethod of satura

ndrained tests. nd constant-loans; respectively

ison of measursly published cu

0.1Cyclic Sh

0.001 0.0Cyclic She

33.3100----

33.310024.598.133.310033.3100

σ'm (kPa)

Hardin & Drnevic

Seed et al. (1986)

Ishibashi & Zhang

Tatsuoka et al. (19

Constant-volume t

Constant-load test

. 1 e⁄

ipal effective in Fig. 14a,

s follow the cuhe lower boundf damping ratioad tests withig. 14b reveals

between data oeen reported cuge shear strain

e of damping vthe lower bounal. 1978 for a a.

atus was instruto modify theucting tests onation yields relTesting prograad tests on pary, under differ

red (a) G/Gmax-urves of other i

1hear strain, γ (%)

33.3100------33.310033.310033.3100

σ'm (kPa)

Hardin

Seed e

Ishiba

Consta

Consta

1 0.1ear strain, γ (%)

ch (1972)

- Range

g (1993)

978)

tests

ts

1

kPa (6

stress and voiddata obtained

urves of Hardind of Seed et alio measured inh the proposeds that, althoughobtained in thiurves of othern amplitude aralues measured

nd of Seed et almean principa

umented with e conventiona

n fully saturatedliable results byam included 32rtially and fullyrent conditions

-γ and (b) D-γ investigators.

10

n & Drnevich (1972)

et al. (1986) - Range

shi & Zhang (1993)

ant-Volume tests

ant-Load tests

1

1

6)

d d n l. n d h is rs e d l. al

a al d y 2 y s.

0

 

Paper No. 1.11a 12

The following can be drawn on the basis of the current experimental study.

An increase in Dr and σ′v as well as a decrease in γ, result in a growth in shear modulus along with a reduction in damping ratio under constant-load condition. These parameters have similar effects on shear modulus and damping ratio under constant-volume condition except the shear strain amplitude which has no significant effect on damping ratio. Trends of shear modulus variations with the number of cycles are in descending order under both conditions. Damping didn’t widely vary with the number of cycles until 10 cycles to Nl under constant-load condition and afterward a significant growth in damping values were observed. Conversely, damping ratio of constant-volume tests decreases with the number of cycles and the trend is complicated to be judged.

Comparisons between the results of constant-volume and constant-load tests reveal that, shear modulus and damping ratio are much affected by Dr, σ′v, γ and the number of cycles under constant-load condition. It is found that some differences exist between two kinds of samples prepared for tests which should be taken into account. First, saturated samples are more homogenous than unsaturated samples. Second, capillary forces affect the response of constant-volume test samples during the whole cyclic stage whereas such effects do not exist in saturated specimens. So, it would appear that observed differences between the results of constant-volume and constant-load tests may be because of the different fabric produced in saturated and unsaturated samples rather than of the vertical load controlling mode. However, further work is needed to compare the results of constant-volume tests on completely dry and saturated sand with constant-load test results on saturated sand. REFERENCES Das, B.M. [1983]. “Advanced Soil Mechanics”. Chapter 4. Hemisphere Publishing, New York.

Dyvik, R., T. Berre, S. Lacasse and B. Raadim [1978], “Comparison of Truly and Constant Volume Direct Simple Shear Tests”, Geotechnique., Vol. 37(1), pp. 3-10.

Hardin, B.O., V.P. Drnervich [1972a], “Shear Modulus and Damping in Soils: measurement and parameter effects”, J Soil Mech Found Div, ASCE Vol. 98(6), pp. 603-624.

Hardin, B.O., V.P. Drnervich [1972b], “Shear Modulus and Damping in Soils: Design Equations and Curves”, J Soil Mech Found Div, ASCE Vol. 98(7), pp. 667-692.

Head K.H. [1998]. “Manual of Soil Laboratory Testing”. 2nd Edition, Vol. 3, Chapter 15. John Wiley & Sons, New York.

Ishibashi, I. and X. Zhang [1993], “Unified Dynamic Shear Moduli and Damping Ratios of Sand and Clay”, Soils Found Vol. 33(1), pp. 182-191.

Ishihara K. [1996]. “Soil Behavior in Earthquake Geotechnics”. Oxford University Press, Great Britain.

Jafarzadeh, F., and H. Sadeghi [2009], “Effect of Water Content on Dynamic Properties of Sand in Cyclic Simple Shear Tests”, Proc. Intern. Conf. on Performance-Based Design in Erthq. Geotech Engrg. (IS-Tokyo 2009), pp. 1483-1490.

Kokusho, T. [1980], “Cyclic Triaxial Test of Dynamic Soil Properties for Wide Strain Range”, Soils Found Vol. 20(2), pp. 45-60.

Kramer SL. [1996]. “Geotechnical Earthquake Engineering”. Chapter 6. Prentice Hall, Upper Saddle River.

Seed, H.B., R.T. Wong, I.M. Idriss and K. Tokimatsu [1986], “Moduli and Damping Factors for Dynamic Analysis of Cohesionless Soils”, J Geotech Eng Vol. 112(11), pp. 1016-1032.

Tatsuoka, F., T. Iwasaki and Y. Takagi [1978], “Hysteretic Damping of Sands under Cyclic Loading and Its Relation to Shear Modulus”, Soils Found Vol. 18(2), pp. 25-40.

Vanden Berghe, J.F., A. Holeyman and R. Dyvik [2001], “Comparison and Modeling of Sand Behavior under Cyclic Direct Simple Shear and Cyclic Triaxial Testing”, Proc. Fourth Intern. Conf. on Recent adv. in Geo. Erthq. Engrg. and Soil Dyn., Paper No. 1.52.