influence of seismic cyclic loading history on small strain dr

8/13/2019 Influence of Seismic Cyclic Loading History on Small Strain Dr

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Inuence of seismic cyclic loading history on small strainshear modulus of saturated sands

Yan-guo Zhou, Yun-min Chen *

Department of Civil Engineering, Zhejiang University, Zheda Road 38, Hangzhou 310027, Peoples Republic of China

Accepted 2 March 2005

Abstract

Small strain shear modulus Gmax is a key parameter together with the state of stress and shear strain amplitude for predicting the dynamicbehavior of soils. Although the seismic cyclic loading on saturated soil deposits induces a decrease in effective stress and a rearrangement of the soil skeleton which may both lead to a degradation in undrained stiffness and strength of soils, only the contribution of effective stressreduction to Gmax degradation is considered in the Hardin and Richart equation which is widely used in seismic response analysis nowadays,and that of soil fabric change is neglected. In this paper, undrained cyclic triaxial tests were conducted on normally and isotropicallyconsolidated saturated sands with the shear wave velocity measured intermittently by bender element during cyclic liquefaction, to study theinuences of seismic cyclic loading history on small strain shear modulus Gmax during earthquake. And the Gmax values of samples withoutsuch inuences were investigated for comparison. The tests results indicate that G max of sand under high amplitude seismic cyclic loadinghistory inuences is moderately lower than the corresponding value of non-cyclic loading effects at the same effective stress. Hence it isnecessary to reinvestigate the determination of Gmax in seismic response analysis carefully to predict the ground responses more reasonably.q 2005 Elsevier Ltd. All rights reserved.

Keywords: Cyclic loading; Seismic response analysis; Undrained cyclic triaxial test; Sands; Small strain shear modulus; Effective stress; Soil fabric; Bender

element

1. Introduction

Adequate information on dynamic soil properties,especially dynamic shear modulus and damping ratio, isessential for accurate computations of ground response andsoilstructure interaction problems. Many experimentalinvestigations carried out on sandy soils through resonantcolumn test or improved cyclic triaxial test in early studies

(Hardin and Richart [1]; Hardin and Black [2]; Drnevichand Richart [3]; Seed and Idriss [4]; Kokusho [5]) showedthat the small strain shear modulus Gmax (g ! 10

K 5 ) wasbasically related to the mean effective principal stress s 0mand void ratio e of the soil, and even overconsolidation ratioOCR for cohesive soil, expressed by the well known Hardin

and Richart equations taking the general form:

Gmax Z AF es0m

nOCRk (1)

In which A is empirical constant reecting soil fabricformed through various stress and strain histories; n isempirically determined exponent, approximately equal to1/2; s 0m is mean effective conning pressure, s 0m Z (s 0v C2s 0h )/3, where s 0v is vertical effective consolidation stressand s 0h is horizontal effective consolidation stress; k isexponent of OCR that depends on plasticity index, whichmeans that for cohesionless soils OCR has no effect onGmax ; e is void ratio and F (e) is void ratio function, which isusually given by (for angular grain sand)

Fe Z 2:973 K e2 = 1 C e (2)

Although the Hardin and Richart equations have sinceundergone several adjustments (Hardin and Drnevich [6,7];Iwasaki and Tatsuoka [8]; Hardin [9]; Hardin and Blandford[10]; Hryciw and Thomann [11]), for cohesionless soilsthese various expressions could be readily reduced to almost

Soil Dynamics and Earthquake Engineering 25 (2005) 341353www.elsevier.com/locate/soildyn

0267-7261/$ - see front matter q 2005 Elsevier Ltd. All rights reserved.doi:10.1016/j.soildyn.2005.03.001

* Corresponding author. Tel.: C 86 571 8795 1340; fax: C 86 571 87952165.

E-mail address: [email protected] (Y.-m. Chen).
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the same form, with the most widely used one for Gmaxdetermination in the past decades being Eq. (1), especiallyin site-specic dynamic response analysis with total stressmethod (Idriss and Seed [12]) or effective stress method(Finn et al. [13,14] ; Martin and Seed [15]; Papadimitriouand Bouckovalas [16]).

It is generally known that in total stress analysis, Eq. (1)is used to estimate the small strain shear modulus variationin different layers with depth of soil proles as the initialmodulus for nonlinear analysis. Besides, in effective stressanalysis Eq. (1) will also account for the stiffnessdegradation caused by the gradual reduction of effectivestresses in a given layer during seismic shaking, by updatingthe initial modulus Gmax at various time intervals so as to beconsistent with the s 0m during the same interval. Thus thesmall strain shear modulus, G max , is the key parameter forpredicting the dynamic response and behavior of soils bothin total stress and effective stress analyses, since it degradeswith the reduction of s 0m and acts as the basis of secantshear modulus G evaluation corresponding to the dynamicshear strain amplitude at the existing constant connement(see Fig. 1).

However, it should be noted that Eq. (1) is summarizedfrom the small strain (generally less than about 10

K 5 )measurement with static connement in laboratory orin situ, while during seismic shaking the soils behavedynamically and undergo relatively large cyclic shearingstrain (about 10

K 4w 10

K 3 in general), when the effectivestress will decrease with the pore water pressures build updue to plastic deformations in the soil skeleton, andtherefore the loading effects on soils during earthquakeare not the same as those reected in Eq. (1).

Repeated dynamic stress effects are of a different naturecompared with that of static stress, and repeated straining atrelatively high amplitude will cause the change of soildynamic properties in subsequent low amplitude vibrations(Drnevich et al. [17]). Vucetic [18] found empirically thatirreversible strains become increasingly signicant forcyclic shear strain amplitude g c larger than the cyclicthreshold shear strain g tv (between 6.5 ! 10

K 5 and2.5 ! 10K 4 for nonplastic sands and silts). And largeaccumulative strains could be expected to develop anonuniform structure in the sand leading to nonuniformdeformations in the sample during a cyclic loading test [19].Wichtmann and Triantafyllidis [20,21] also pointed out thatdue to its cyclic loading history the fabric of a soil

Nomenclature

A empirical constant reecting soil sample fabric;e void ratio of the soil;F (e) void ratio function;G secant shear modulus;Gmax small strain shear modulus;Gmax0 initial small strain shear modulus before the pore

water pressure generation;GImax small strain shear modulus without effects of

seismic cyclic loading history;GIImax small strain shear modulus under seismic cyclic

loading history inuences;K 0 coefcient of earth pressure at rest; L distance between the bender elements;n empirically determined exponent, approxi-

mately equal to 1/2; N cycles in undrained cyclic triaxial test corre-

sponding to T ; N 1 accumulative cycle number of liquefactionfailure;

OCR overconsolidation ratio;t shear wave travel time in soil specimen;T accumulative time of seismic loading on soil

deposits during earthquake;V s shear wave velocity of soil specimen;DT time interval of subsequent motion of in situ soil

deposits during earthquake;g shear strain amplitude;g c cyclic shear strain amplitude;g r residual strain during cyclic loading;g tv cyclic threshold shear strain amplitude;r mass density of soil;s

0m mean effective stress;

s0m0 initial mean effective stress due to the

connement;s

0v vertical effective consolidation stress;

s0h horizontal effective consolidation stress; and

t d cyclic shear stress amplitude.

1E-4 1E-3 0.01 0.1 1 100.0

0.2

0.4

0.6

0.8

1.0

0

10

20

30

40

50

maxG

G11

4

W

W

0

D a m p i n g r a

t i o ,

( % )

S h e a r m o d u l u s r e

d u c t

i o n ,

G / G

m a x

G / G

Shear strain amplitude, (%)

max

=

Fig. 1. Nonlinear characteristics of soils (after Martin and Seed, 1979).

Y.-g. Zhou, Y.-m. Chen / Soil Dynamics and Earthquake Engineering 25 (2005) 341353342


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(i.e. number, orientation and shape of particle contacts) aswell as the distribution of interparticle forces are changed,and the small strain shear modulus Gmax of dry sand wasreduced somewhat at high amplitude low-number of cyclicprestraining. Evidently sand fabric evolves duringundrained cyclic shearing, and the saturated sand may

acquire a cyclic loading history as the result of such fabricevolution besides the effective stress reduction. Andthis loading history is strongly characterized by itsinstantaneity because of the continuity and short durationof seismic shaking on soil deposits permitting no rest timefor soil to regain its original structure. Hence directlyassuming the small strain shear modulus Gmax using Eq. (1)equal to that of sands during earthquake is not appropriateand rigorous enough, and there is a necessity to examinemore carefully the Gmax of sands under high amplitudecyclic loading.

To study the problems mentioned above, a piezoelectricceramic bender element measuring system was establishedusing conventional cyclic triaxial apparatus, and a series of stress-controlled undrained cyclic triaxial tests were carriedout on saturated sands with measured of shear wave velocityduring cyclic liquefaction, to simulate the inuences of seismic cyclic loading history on soil stiffness, andinvestigate the mechanism of small strain shear modulusvariation under this inuence. For comparison, anotherseries of tests on Gmax without cyclic loading history effectswere conducted. These test results are presented in thispaper, which show that Gmax of sand under the inuences of relatively high amplitude and low-number cyclic loading ismoderately lower than that under no such inuences at the

same effective pressures.

2. Test fundamentals

The behavior of soil deposits subjected to seismicloading, is closely associated with the undrained cyclicshear deformation. Thus the examination of seismic cyclicloading history during earthquake can be simulated throughundrained cyclic triaxial tests in laboratory according to theprocedure suggested in Ref. [4], which allows the irregularstress sequences produced by an earthquake to be replacedby an equivalent series of uniform cyclic stress cycles. Fig. 2(a) and (b) show how the process will be simulated:

The seismic cyclic loading on soil deposits for a period of loading time T will induce both the excess pore waterpressure generation and the soil fabric evolution, and theireffects on Gmax can be simulated by evaluating the smallstrain stiffness of corresponding soil specimen subjected to N cycles in undrained cyclic triaxial test; then the loadinghistory effects on the subsequent motion of in situ soildeposits during following time interval DT may also beunderstood through investigating the specimen state duringthe ( N C 1)th cycle in tiraxial test, wherein the vital thing isto monitor correctly the development of the state variables

including the small strain shear modulus, residual porewater pressure and residual strain.

For it is hard to measure the shear wave velocity of specimens by bender element during continuous cyclicloading test, intermittences were adopted only long enoughto take reading during the whole cyclic liquefaction processin following tests.

3. Test apparatus

To measure Gmax of soils during undrained cyclicshearing, a piezoelectricceramic bender element systemwas established based on Model HX-100 multi-use triaxialapparatus (Zhou et al. [22]). The test system frame is shownin Fig. 3.

Fig. 3. Schematic of triaxial test system with bender elements.

Acceleration (g)

0

Time (s)

T T

0.5

1.0

-0.5

-1.0

-1.50 2 4 6 8 10

(a)

(b)

Fig. 2. Equivalent cycles simulation of seismic loading. (a) Acceleration

record during earthquake (Tangshan earthquake, M wZ

7.8, 1976);(b) Schematic of equivalent cycles simulation.

Y.-g. Zhou, Y.-m. Chen / Soil Dynamics and Earthquake Engineering 25 (2005) 341353 343


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3.1. Brief introduction of bender element method

The bender element method was originally developed byShirley and Hampton [23] to obtain the very small strainshear modulus of a soil G max by measuring the velocity of shear wave propagating through a sample, which haveattracted intensive study since then (De Alba et al. [24];Dyvik and Madshus [25]; Thomann and Hryciw [26]). Abender element is a piece of piezoelectric ceramic platewhich bends if a voltage across it is changed or, if bent by anexternal force, the voltage across it changes. Benderelements are set into the top and bottom platens of a triaxialcell and penetrate about 3 mm into the sample (see Fig. 4).One element is vibrated by changing the voltage across it,and shear waves propagate through the sample and vibratethe other element. The input and output voltages arecontinuously recorded and the travel time determined. Theshear wave velocity V s in the specimen can be calculatedfrom the wave travel time t and the known separation L between the bender elements as

V s Z L = t (3)

For a known material density r , according elastic theory,the small strain shear modulus can thus be calculated as

Gmax Z r V 2s (4)

3.2. Preliminary test for determining the correct travel time

It is generally recognized that the principal thing withbender element method has always been the determinationof the travel time t used to calculate V s (Viggiani andAtkinson [27]; Jovicic et al. [28]; Arulnathan et al. [29]).The travel time of an impulse wave between two points inspecimen may be taken as the time between the rst directarrival of shear wave at each point. To reduce the degree of subjectivity in the interpretation of t , several types of inputsignal and different frequencies for each signal were tried inpreliminary tests, and the results with different travel time

denition (S-A or S-B in Fig. 5) were compared with thoseobtained from resonant column tests (see Table 1 ),improving the condence in the data. Resonant columntests were conducted by using Drnevich Long-TorApparatus.

As shown in Fig. 5 (a) and (b), the travel time values

remained almost the same despite the exciting frequen-cies in (a) where the travel time is dened from S to A;but were relatively scattered in (b) where the travel timeis dened as S-B. Further comparison in Table 1 showsthat the shear modulus measured by bender element wasa little higher than that obtained from resonant columntests for S-A travel time, but much lower for S-B traveltime. Since the vibration shear strain amplitude inresonant column test was about 10

K 6w 10

K 5 and a bithigher than that induced in bender element (generallyabout 10

K 6 or less), it is reasonable to accept the S-Atravel time as the correct travel time for about 10 kHzsine wave signal.

So in the subsequent tests sine pulse was selected as thetransmitted signal and the rst major reversal point A at thereceived trace was considered as the rst arrival of the shearwave at the receiver bend element. Exciting frequenciesselected were mainly about 1015 kHz, but adjusted tolower values for low connement such as s 0m Z 50 kPa orhigher values for higher connement such as s 0m Z 400 kPato obtain the most explicit traces of receiver bender element.And the effective length L through which the shear wavetravel time dened was taken as the distance between thetips of the elements.

4. Test procedures and contents

The mechanism of Gmax of saturated sand under theinuences of seismic cyclic loading was investigated, andthat of Gmax without such inuences was investigated forcomparison. Comparison between the two series of tests willshow the differences between them, and yield informationon the inuences of cyclic loading on small strain shearmodulus.

4.1. Tested sands and specimen preparation

Saturated specimens of 39.1 mm in diameter and 80 mmin height were sampled with the spooning method. Twotypes of sand (medium sand and ne sand, angular silicagrains) were tested here with physical properties as given inTable 2 , and the grain size distribution curves are shown inFig. 6.

The relative densities of the specimens were around60%. After a specimen was formed in a split mold, a15 kPa negative pressure was applied to support thespecimen. After the mold was removed and the pressurechamber and other components were installed, a 20 kPacell pressure was applied and the negative pressure was

Fig. 4. Triaxial apparatus equipped with bender elements.



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removed. Then the required full conning pressure wasapplied. As the minimum conning pressure in the testswas 50 kPa, this procedure prevented overconsolidationprior to testing.

4.2. Examination of G max without cyclic loading effects

To obtain the dependence of small strain shear modulusGmax on void ratio and conning pressure, a test series

Fig. 5. Typical bender element traces with different input frequencies ( s 0m Z 100 kPa). (a) Selected points (SP) for travel time: S-A (b) Selected points (SP) fortravel time: S-B.

Table 1Comparison between bender element tests and resonant column tests (medium sand)

s0m0 (kPa) Bender element tests Resonant column tests

Dr (%) SP F (kHz) Dt (ms) V s (m/s) Gmax / F (e)(MPa)

Dr (%) g (! 10K 6 ) V s (m/s) Gmax / F (e)

(MPa)

100 57.4 S-A 5 354 198.5 21.9 58.0 5.1 197.6 21.6S-A 10 352 199.6 22.1S-A 20 352 199.6 22.1S-B 5 400 175.4 17.1S-B 10 402 174.5 16.9S-B 20 394 178.1 17.6

200 62.8 S-A 10 296 236.1 30.3 61.2 7.4 234.6 30.1300 59.6 S-A 10 264 262.1 37.5 60.9 1.0 259.9 36.9



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without cyclic loading history effects was conducted. Twoways were adopted to change the effective conningpressure of specimens with different initial void ratios e0and relative densities D r0 : (1) Two specimens wereconsolidated isotropically with effective conning pressureincreasing gradually in steps of 50, 100, 200, 300, 400 kPafor medium sand (Specimen-M1) and ne sand (Specimen-F1) respectively; (2) The other two specimens wereconsolidated isotropically under high conning pressurerst, then subjected to multi-stage backpressure with the

effective stress decreasing gradually to zero. The back-pressure tests were conducted in steps of 100, 200, 300, 350,400 kPa for medium sand (Specimen-M2) and ne sand(Specimen-F2) respectively.

Shear wave velocity was measured 2 h after each of theloading stages being applied, which duration is usuallytaken as the required time period of primary consolidationcompletion for sands. Note that in way (1) specimens wereunder normal consolidation while in (2) they were in thestate of overconsolidation after back pressure being applied.Thus it is convenient to check out whether OCR will affectthe G max variation of sand indeed or not by comparing the

two ways of examination.Since the tests performed in the studies herein involvehours of connement duration, and the so called ageingeffect were found more pronounced for clay than for sand(A and Richart [30], Vucetic and Dobry [31]), it isnecessary to evaluate the connement duration effect onGmax . Thus two medium sand specimens were prepared andconned totally for about 30 h under constant conning

pressure 100 and 300 kPa, respectively. The shear wavevelocities of the specimens were measured in denite timeintervals during the whole conning duration, and thecorresponding Gmax variation were assessed.

4.3. Examination of G max under seismic cyclic loadinginuences

In cyclic loading tests, samples were consolidatedisotropically for 12 h at a given connement to obtain a

sufciently stablesoil fabric,and theshear wave velocity wasmeasured for Gmax , before applying cyclic loading. Thenthey were subjected to a few number of uniform highamplitude cyclic stresses at frequency of 1 Hz underundrained conditions; and when the cyclic loading ended,the shear velocity for Gmax , residual pore water pressure andresidual strain were recorded at the pause intervals only longenough to take reading (within 1 min). This process wasrepeated throughout one test series until the cyclic failureoccurred (see Fig. 7). The ve conning pressure levelsselected for the tests were 50, 100, 200, 300, 400 kPa, andspanned the range of soil pressure in situ for seismic response

analyses under normal circumstances. Meanwhile, differentstress amplitudes were tried at a given conning pressure tocheck out the diversity of test results between differentt d w N 1 combinations, in which t d is cyclic shear stressamplitude, N l is accumulative cycle number of liquefactionfailure. For simulating seismic cyclic loading more reason-ably, N l wascontrolledwithin several hundred cycles in tests.

Table 2Fundamental properties of tested sands

Sand Type Specicgravity (g/cm 3 )

Void ratio and Relative density Grain size distribution

emax emin Dr (%) D10 (mm) D50 (mm) D90 (mm) C u

Medium sand 2.65 0.788 0.432 52.3 w 65.0 0.13 0.34 0.80 3.1

Fine sand 2.69 1.096 0.593 59.6w

73.7 0.10 0.14 0.22 1.6

10 1 0.1 0.010

20

40

60

80

100

120

Medium sand Fine sand

F i n e r

b y w e i g h

t , %

Diameter, mm

SandCourse Medium Fine

Gravel Silt

Fig. 6. Grain distribution curves of tested sands.

Undrained cyclic loading

Fail or not?Cyclic

liquefactionfailure

Shear wave velocitymeasurement for G max

YES

NO

Shear wave velocitymeasurement for G

max0

Consolidation for 12 h

Fig. 7. Cyclic test procedure ow chart.



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In consideration of the inuence of pause interval lengthon reading, some other observations were carried out toexamine the change of Gmax during the pause interval underundrained conditions. The test procedure was similar to theabovementioned one, and the whole cyclic liquefactionprocess interrupted three times to study the G max variation

during each pause interval. Each pause interval was held forabout 120 min, and the shear velocities and residual porewater pressures of the specimen were measured after 0.5, 1,5, 10, 30, 60, 120 min from the beginning of the pause.These tests were performed on two medium sand specimensunder constant conning pressure 100 and 300 kPa,respectively.

5. Test results and analysis

5.1. Tests results without cyclic loading effects

The original test data of Gmax versus the effectiveconning pressure s 0m of the both sands are plotted in Fig. 8.To eliminate the effect of void ratio nonuniformity, Gmaxwas further divided by F (e) and the results are plotted inFig. 9, where e is the void ratio corresponding to the Gmax ata given loading stage.

As shown in Fig. 9, if divided by F (e), the data points of the two ways of tests are almost identical, and the smallstrain shear modulus is well correlated with the effectivestress s 0m regardless of the void ratio. And no evident OCReffect on Gmax was observed in back pressures applied testsof way (2). Then the following approximation for Gmax canbe tted:

Gmax Z AF es0m

n (5)

Where AZ 2.121, nZ 0.505 for medium sand and AZ 2.227,n Z 0.510 for ne sand. In Eq. (5), Gmax and s 0m areexpressed in MPa and kPa, respectively.

The test results of further study on the dependence of small strain shear modulus on connement duration are

presented in Fig. 10. A very slight increase of Gmax withtime could be determined about 3 w 4% after 30 h of connement, especially for the modulus values divided byF (e) this increase lay only between 1 w 2%.

This results tally with those presented in previous study(Petrakis and Dobry [32]) showing that for cohesionlesssoils, Gmax is ultimately a function of the number of intergranular contact points per soil grain and the effectiveconning pressure, and F (e) in Eq. (5) is a surrogate for theparticle contacts. In other words, in tests on sands understatic connement there was no signicant effect of previousstress history and no evident effect of loading time wasobserved, and the small strain stiffness variations were

mainly related to effective stress s0m and void ratio e

changes.

5.2. Undrained cyclic loading test results

As shown in Fig. 11 (ac), throughout the whole cyclicshearing process, interrupted frequently to measure

0 50 100 150 200 250 300 350 400 4500

25

50

75

100

125

150

175

200

225M1: D r0= 49.8%, e 0= 0.592

M2: D r0= 51.8%, e 0= 0.585

F1: D r0= 48.5%, e 0= 0.818

F2: D r0= 54.0%, e 0= 0.791

S m a l

l s t r a i n s h e a r m o d u l u s

G m a x , M

P a

Effective confining pressure ' m , kPa

Data in tests without

cyclic loading effects

Fig. 8. Dependence of Gmax on void ratio and conning pressure.

0

15

30

45

60M1: D r0= 49.8%, e 0= 0.592

M2: Dr0

= 51.8%, e0= 0.585

F1: Dr0

= 48.5%, e0= 0.818

F2: Dr0

= 54.0%, e0= 0.791

Fit curve equation : G max / F (e ) = A*( 'm)n

(medium sand) A = 2.121, n = 0.505 (fine sand) A = 2.227, n = 0.510

S m a l

l s t r a i n s h e a r m o d u

l u s

G m a x

/ F ( e ) , M P a

Effective confining pressure 'm , kPa

0 50 100 150 200 250 300 350 400 450

Fig. 9. Dependence of Gmax / F (e) on conning pressure.

1 10 100 10000

40

80

120

160

Gmax

Gmax / F (e ),

'm =100 kPa

Gmax G max / F (e ), 'm =300 kP a

S m a l

l s t r a i n s h e a r m o d u l u s G

m a x

, M P a

Time since confinement application, min

5000

Fig. 10. Effects of connement duration on Gmax .



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the shear wave velocity, the strain and pore water pressurebehaviors were similar to those in conventional cyclic

triaxial test (Seed and Lee [33]; Kokusho [5]), whichindicated that the test procedure adopted here wasreasonable enough for simulating the seismic cyclic loading.

The test conditions of all the cyclic tests are listed inTable 3 . And the small strain shear modulus Gmax obtained

at ve different conning pressures are plotted againsteffective stress s 0m in Fig. 12(a) and (b) for medium sand

and ne sand, respectively. There was similar trend of Gmaxvariations with reduction of effective stress regardless of theinitial connement. As shown in Fig. 13(a) and (b) withGmax divided by F (e), besides the rst point of each datagroup hitting almost the tting curve of test data without

0 20 40 60 80 100 120100

75

5025

0

25

50

75

100

A x i a l c y c l i c

l o a d

i n g d ,

k P a

Number of cycles, N

'm0= 300 kPa, D r= 62.1%

d= 49.8 kPa, N l= 115

0 25 50 75 100 1255

4

3

2

1

0

1

'm0= 300 kPa, D r= 62.1%

d= 49.8 kPa, N l= 115 A x i a l c y c l

i c s t r a

i n d ,

%

Number of cycles, N

0 25 50 75 100 1250

50

100

150

200

250

300 'm0= 300 kPa, D r= 62.1%

d= 49.8 kPa, N l= 115

P o r e w a t e r p r e s s u r e u , k

P a

Number of cycles, N

(c)

(a) (b)

Fig. 11. Time histories of undrained tiraxial cyclic loading tests ( s 0m0 Z 300 kPa). (a) Cyclic loading versus number of cycles (b) Cyclic strain versus number of cycles (c) Pore water pressure versus number of cycles.

Table 3Test conditions of cyclic triaxial tests

Sand type Specimen label Conning pressures

0m0 (kPa)

Relative density Dr (%)

Cyclic stressamplitude t d (kPa)

Cyclic strainamplitude g d

Failure cyclenumber N l

Medium sand MS-50 50 58.8 5.4 1.3 ! 10K 3 66

MS-400 400 64.5 27.2 0.8 ! 10K 4 188

MS-100A 100 54.9 9.5 2.1 ! 10K 3 15MS-100B 100 57.8 6.3 7.6 ! 10K 4 575MS-200A 200 59.9 16.8 1.1 ! 10

K 3 43MS-200B 200 62.8 13.2 8.8 ! 10

K 4 479MS-300A 300 62.1 24.9 1.0 ! 10

K 3 115MS-300B 300 59.6 18.0 6.2 ! 10K 4 713

Fine sand FS-50 50 61.0 8.3 1.7 ! 10K 3 39

FS-400 400 73.7 48.9 1.3 ! 10K 3 95

FS-100A 100 59.6 14.1 1.4 ! 10K 3 34

FS-100B 100 61.6 9.6 5.9 ! 10K 4 612

FS-200A 200 63.0 29.7 1.2 ! 10K 3 47

FS-200B 200 65.1 21.3 6.5 ! 10K 4 394FS-300A 300 68.5 37.2 1.8 ! 10

K 3 71FS-300B 300 72.0 26.3 5.6 ! 10

K 4 857



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cyclic loading effects, the other points are lower than thecurve at the same effective stress: the former showsthe variation of Gmax without cyclic loading effects whilethe latter reveals the characteristic of Gmax inuenced byseismic cyclic loading history. For explicitness, the smallstrain shear modulus and effective stress are normalized byinitial values Gmax0 and s 0m0 respectively, and the resultsare plotted in Fig. 14(a) and (b) for the two tested sands,where s 0m0 is the initial mean effective stress due to theconnement, and Gmax0 is the initial small strain shearmodulus before the pore water pressure generation.

If the small strain shear modulus without effects of cyclicloading is denoted as GI

max, and the one under the inuence

of seismic cyclic loading as GIImax , the modulus reductionGIImax K G

Imax = G

Imax under the same effective stress can be

computed from the data in Fig. 14(a) and (b), with theresults being plotted in Fig. 15(a) and (b). As shown inFig. 15, the modulus reduction G IImax K GImax appears at thebeginning of cyclic shearing, increases with the effective

stress degradation and reaches to a relatively stable valueround the midpoint of normalized effective stress; thenstabilizes or decreases slightly ultimately. In the case of theamplitude g e Z 5.6! 10

K 4w 2.1 ! 10

K 3 investigated herein,this stable value of modulus reduction was approximately6w 9% of GImaxfor medium sand and 3 w 5% for ne sandrespectively, which demonstrates that the further modulusreduction was larger for medium sand than for nesand. In the case of the dynamic prestraining amplitude g c Z5 ! 10K 3 for dry medium sand presented in Ref. [20],similar modulus reduction amounted 7% in average wasobserved. It should be noted that in Fig. 15 a tendency canbe gured out, that for a given sample at the same conningpressure, the higher the cyclic shear strain were applied, thelarger modulus reduction could be obtained.

Results of the two conducted tests on the inuence of pause interval length on data reading are shown in Fig. 16(a)(d). During pause interval, the pore water pressuredecreases a little, and small strain shear modulus will

450 400 350 300 250 200 150 100 50 00

30

60

90

120

150

180

Cyclic tests data of medium sand

MS-50 MS-400 MS-100A MS-100B MS-200A MS-200B MS-300A MS-300B S m

a l l s t r a i n s h e a r m o

d u l u s

G m a x , M

P a

Effective stress ' m, kPa

450 400 350 300 250 200 150 100 50 00

20

40

60

80

100

120

140

160

S m a l


G m a x , M

P a

Effective stress ' m, kPa

FS-50 FS-100A FS-100A FS-100B FS-200A FS-200B FS-300A FS-300B

Cyclic tests data of fine sand

(a) (b)

Fig. 12. Variation of Gmax against s 0m during cyclic loading tests. (a) Original data of Gmax versus s 0m (medium sand) (b) Original data of Gmax versus s 0m (nesand).

450 400 350 300 250 200 150 100 50 00

10

20

30

40

50


MS-50 MS-400 MS-100A MS-100B MS-200A MS-200B MS-300A MS-300B

Medium sand data and fitting curve in tests without cyclic loading effects

S m a l


G m a x

/ F ( e ) , M P a

450 400 350 300 250 200 150 100 50 00

10

20

30

40

50


FS-50 FS-400 FS-100A FS-100B FS-200A FS-200B FS-300A FS-300B

Fine sand data and fitting curve in tests without cyclic loading effects

S m a l


G m

a x / F ( e ) , M P a

(a) (b)

Effective stress ' m, kPa Effective stress ' m, kPa

Fig. 13. Variation of Gmax / F (e) against s 0m during cyclic loading tests. (a) Data of Gmax / F (e) versus s 0m (medium sand) (b) Data of Gmax / F (e) versus s 0m (nesand).



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rapidly increase to a stable value within 5 w 10 min, butthis value is still moderately lower than GI

max at the

corresponding effective stress. Fig. 16 shows that furtherreduction of shear modulus compared to GImax is mostprobably attributed to the rearrangement of soilparticlestructure (including interparticle contact slippage andgrains connect crushing) under the cyclic shearing, andthis reduction could not recover at relatively short resttime. Fig. 16 (a) and (c) also implies that if the shearwave velocity could be measured at the exact beginningof the pause interval or even during continuous cyclicshaking, the small strain shear modulus calculatedconsequently would be smaller than that measured atpause time of 1 min adopted herein, since the unstablestate of soil fabric requires some time (5 w 10 min in tests)to stabilize primarily.

5.3. Reasons for further reduction of small strain stiffness

The variation of GIImax with effective stress reductioncould be understood based on G Imax , with further consider-ation of high amplitude dynamic stresses induced drastic

rearrangement of soilparticle structure effects (macro-scopically shown as the residual strain g r accumulation inFig. 17(a) and (b)). Finn et al. [19] studied the strain historyeffect on liquefaction of sand and concluded that a givennumber of cycles of a shear strain greater than 0.5% had aweakening effect on the resistance of sand samples toliquefaction under cyclic loads. And the reason for this lossof liquefaction resistance was postulated that the effect of any shear strain beyond a threshold value was to create anonuniform structure in the sand sample, which was moresensitive to liquefaction than the structure created byconsolidation. These statements are helpful to gain insightinto the seismic cyclic loading history effect on small strainmodulus of sand investigated herein, and indicate thatalthough the reduction of liquefaction resistance and Gmaxof sand under this loading history effects are phenomenallydifferent aspects of cyclic liquefaction process, they aresomewhat due to the same substantial mechanism: the soilfabric evolution at cyclic strain levels above the thresholdvalue. Cascante and Santamarina [34] and Santamarina [35]also concluded that the small strain stiffness of particulatematerials was strongly determined by the behavior of

1.0 0.8 0.6 0.4 0.2 0.020

15

10

5

0Cyclic tests data of medium sand

MS50 MS 400MS100A MS 100BMS200A MS 200BMS300A MS 300B

Normalized effective stress ' m / 'm0

1.0 0.8 0.6 0.4 0.2 0.020

15

10

5

0

FS50 FS 400 FS100A FS 100B FS200A FS 200B FS300A FS 300B S

h e a r m o d u l u s

d i f f e r e n c e

, %Cyclic tests data of fine sand

S h e a r m o d u l u s

d i f f e r e n c e

, %

(a) (b)


Fig. 15. Dependence of shear modulus reduction G IImax K G Imax = G Imax on effective stress. (a) Data of G IImax K G Imax = G Imax versus s 0m / s 0m0 (medium sand) (b)Data of G IImax K G Imax = G Imax versus s 0m / s 0m0 (ne sand).

1.0 0.8 0.6 0.4 0.2 0.00.0

0.2

0.4

0.6

0.8

1.0


Fitting curve of G I

max / G max0 ~( ' m / 'm0)

N o r m a l

i z e d s h e a r m o

d u l u s

G m a x

/ G m a x

0


1.0 0.8 0.6 0.4 0.2 0.00.0

0.2

0.4

0.6

0.8

1.0


Fitting curve of


N o r m a l

i z e d s h e a r m o d u l u s

G m a x

/ G m a x

0

(a) (b)

G Imax / G max0 ~( ' m / ' m0)

Normalized effective stress ' m / 'm0 Normalized effective stress ' m / 'm0

Fig. 14. Variation of Gmax / Gmax0 against s 0m / s 0m0 during cyclic loading tests. (a) Data of Gmax / Gmax0 versus s 0m / s 0m0 (medium sand) (b) Data of Gmax / Gmax0versus s 0m / s 0m0 (ne sand).



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contacts, and that compared with elastic contact, grainscontact crushing will result in more rapid change in sandstiffness. It seems reasonable to conclude, therefore, that thepossible cause of further small strain stiffness reduction isthe change of shape of particle contacts. Under a number of high amplitude cyclic shearing, the relatively stable contacts

formed under long time consolidation are replaced by softerand more unstable contacts due to particle re-orientation.And the observation on Gmax variation during pauseintervals is an additional evidence of this conclusion.

Objectively, there was also a little fabric change in soilsamples drained under static connement which was mainly

1.0 0.8 0.6 0.4 0.2 0.05

4

3

2

1

0

1


R e s

i d u a

l s h e a r s t r a

i n r ,

%

1.0 0.8 0.6 0.4 0.2 0.05

4

3

2

1

0

1

R e s

i d u a

l s h e a r s t r a

i n r ,

%


(a) (b)

Normalized effective stress ' m / 'm0 Normalized effective stress ' m / 'm0

Fig. 17. Residual shear strain development with effective stresses. (a) Data of g r versus s 0m / s 0m0 (medium sand) (b) Data of g r versus s 0m / s 0m0 (ne sand).

0 30 60 90 120 15020

40

60

80

Gmax0 = 76.2 MPa

Group1, u = 8.9~8.83 kPaGroup2, u = 26.8~26.5 kPaGroup3, u = 53.0~54.95kPa

S m a l

l s t r a i n s h e a r m o

d u l u s

G m a x , M

P a

Pause time, min

1.0 0.8 0.6 0.4 0.2 0.00.0

0.2

0.4

0.6

0.8

1.0

Fitting curve

N o r m a l


G m a x

/ G m a x

0


'm0=100 kPa, D r= 54.4%, G max0 =76.2 MPa

Measured at puase time 1 min Group1, u = 8.9~8.83 kPaGroup2, u = 26.8~26.5 kPaGroup3, u = 53.0~54.95 kPa

(a) (b)

0 30 60 90 120 15060

80

100

120

140

'm0= 300kPa, D r= 67.2%G

max0 = 144.9 MPa

Group1, u =52.4~49.2 kPaGroup2, u =94.8~93.2 kPa

Group3, u =201.3~199.1 kPa

S m a l


G m a x , M

P a

Pause time, min

1.0 0.8 0.6 0.4 0.2 0.00.0

0.2

0.4

0.6

0.8

1.0 Fitting curve

N o r m a l


G m a x

/ G m a x

0

'm0=300 kPa, D r= 67.2%, G max0 =144.9 MPa

Measured at puase time 1 min Group1, u = 52.4~49.2 kPaGroup2, u = 94.8~93.2 kPaGroup3, u = 201.3~199.1 kPa

(c) (d)

'm0= 100 kPa, D r= 54.4%

G Imax / G max0 = ( ' m / 'm0 )

0.505

G Imax / G max0 = ( ' m / 'm0 )

0.505


Fig. 16. Time-dependent regain in small strain shear modulus during pause interval. (a) G max versus pause time ( s 0m0 Z 100 kPa) (b) G max / G max0 versuss

0m / s 0m0 (s 0m0 Z 100 kPa) (c) Gmax versus pause time ( s 0m0 Z 300 kPa) (d) Gmax / Gmax0 versus s 0m / s 0m0 (s 0m0 Z 300 kPa).



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associated with the minimal void ratios reduction, whichwas reported by Richart [36] and also observed in testsherein, but differs from the relatively more drasticinterparticle contact slippage and grains crushing inducedby high amplitude undrained cyclic shearing, and the lattercauses further stiffness degradation with constant void ratio.

It is interesting that similar degradation was observed on theimmediate postcyclic undrained secant modulus of cohesivesoils (Yasuhara and Hyde [37]), which may imply somecorrelation between the small strain shear modulus andsecant modulus under undrained cyclic loading.

It should be noted that, although the tests conductedherein were just under isotropic stress states, the test resultsevidently revealed the particular phenomena of Gmaxinuenced by seismic cyclic loading history. In furtherstudy, other factors such as K 0 conditions, grain character-istics, and cyclic frequencies will be taken into consider-ation to gain more general and profound understanding of the Gmax variation mechanism under the inuence of seismic cyclic loading.

6. Summary and conclusions

In the present study, the small strain shear moduli of saturated sands consolidated normally under isotropicconnement were investigated throughout the undrainedcyclic triaxial tests where cyclic shear strain amplitude of about 5.6 ! 10

K 4w 2.1! 10

K 3 , and further reduction of Gmax different from Eq. (1) were observed at almostconstant void ratio. The modulus difference GIImax K GImax

appeared at the beginning of cyclic shearing, increased withthe effective stress reduction and reached to a relativelystable value around the midpoint of cyclic liquefactionprocess; then stabilized or decreased slightly ultimately.This stable value of modulus reduction amounted approxi-mately 6 w 9% of GImaxfor medium sand and 3 w 5% for nesand, which indicates that this reduction is soil typedependent. And for a given sample at the same conningpressure, the higher the cyclic shear strain was applied, thelarger modulus reduction could be obtained. These obser-vations are consistent with part of the ndings reported inthose literatures, which were based on intensive investi-gation on the dry sand dynamic properties subjected to highamplitude and low-number previbration.

The Gmax difference of sands between the two types of test (namely, with or without cyclic loading effects) at thesame effective stress is due to the inuence of relativelyhigh amplitude cyclic loading, which results in not onlyreduction of effective stress, but also the change of shape of particle contacts, namely, the interparticle contact slippageand grains connect crushing. Under high amplitude cyclicshearing, the relatively stable contacts formed under longconnement duration are replaced by softer and unstablecontacts due to particle re-orientation, which contributes tofurther reduction of Gmax .

During earthquake, the ground deposit shakes continu-ously, so the determination of small strain shear modulus inseismic response analyses should take into account thecyclic loading history effects, including both the inducedeffective stress reduction and rearrangement of the soilparticle structure. The test results presented herein indicate

that present seismic response analyses may overestimate thevalue of small strain shear modulus, which overestimationwill increase with the development of earthquake process,thus the variety of response analysis results will beinuenced to some extent. Therefore, it is necessary tocarefully reinvestigate the determination of small strainshear modulus in present seismic response analyses andeven to make some modication based on it.

Acknowledgements

This study was supported by the National NaturalScience Foundation of China (No.10372089). The writerswould like to acknowledge Prof. Charles W. W. Ng andDr Bo Huang for their valuable suggestions on this study,and express the gratitude to Yan-Hong Ma, Wei-An Lin andZhi Yang for their kind help in conducting part of thelaboratory tests. The writers also wish to thank Prof. W. D.Liam Finn and the SDEE anonymous reviewers whosecomments led to substantial improvement of this paper.

References

[1] Hardin BO, Richart Jr FE. Elastic wave velocities in granular soils.J Soil Mech Foundations Div, ASCE 1963;89(1):3365.

[2] Hardin BO, Black WL. Vibration modulus of normally consolidatedclay. J Soil Mech Foundations Div, ASCE 1968;94(2):35369.

[3] Drnevich VP, Richart Jr FE. Dynamic prestraining of dry sand. J SoilMech Foundations Div, ASCE 1970;96(2):45369.

[4] Seed HB, Idriss IM. Simplied procedure for evaluating soilliquefaction potential. J Soil Mech Foundation Div, ASCE 1971;97(9):124973.

[5] Kokusho T. Cyclic triaxial test of dynamic soil properties for widestrain range. Soils Foundations 1980;20(2):4560.

[6] Hardin BO, Drnervich VP. Shear modulus and damping in soils:measurement and parameter effects. J Soil Mech Foundations Div,

ASCE 1972;98(6):60324.[7] Hardin BO, Drnervich VP. Shear modulus and damping in soils:

design equations and curves. J Soil Mech Foundations Div, ASCE1972;98(7):66792.

[8] Iwasaki T, Tatsuoka F. Effects of grain size and grading on dynamicshear moduli of sands. Soils Foundations 1977;17(3):1935.

[9] Hardin BO. The nature of stress-strain behavior for soils. In:Conference on Earthquake Engineering and Soil Dynamics, ASCE1978: 390.

[10] Hardin BO, Blandford GE. Elasticity of particulate materials.J Geotech Eng, ASCE 1989;115(6):788805.

[11] Hryciw RD, Thomann TG. Stress-history-based model for G e of cohesionless soils. J Geotech Eng, ASCE 1993;119(7):107393.

[12] Idriss IM, Seed HB. Seismic response of horizontal soil layers. SoilMech Foundations Div, ASCE 1968;94(4):100331.



13/13

[13] Finn WDL, Byrne PM, Martin GR. Seismic response and liquefactionof sands. J Geotech Eng Div, ASCE 1976;102(8):84156.

[14] Finn WDL, Lee KW, Martin GR. An effectivestress model forliquefaction. J Geotech Eng Div, ASCE 1977;103(6):51733.

[15] Martin PP, Seed HB. Simplied procedure for effective stress analysisof ground response. J Geotech Eng Div, ASCE 1979;105(6):73958.

[16] Papadimitriou AG, Bouckovalas GD. Plasticity model for sand undersmall and large cyclic strains: a multiaxial formulation. Soil DynEarthquake Eng 2002;22:191204.

[17] Drnevich VP, Hall Jr JR, Richart Jr FE. Effects of amplitude of vibration of the shear modulus of sand. In: Proceedings of international symposium on wave propagation and dynamic proper-ties of earth materials, Albuquerque, NM, 1967.

[18] Vucetic M. Cyclic threshold shear strains in soils. J Geotech EngASCE 1994;120(12):220828.

[19] Finn WDL, Bransby PL, Pickering DJ. Effect of strain history onliquefaction of sand. J Soil Mech Foundations Div, ASCE 1970;96(6):191734.

[20] Wichtmann T, Triantafyllidis Th. Inuence of a cyclic and dynamicloading history on dynamic properties of dry sand, part I: cyclic anddynamic torsional prestraining. Soil Dyn Earthquake Eng 2004;24:12747.

[21] Wichtmann T, Triantafyllidis Th. Inuence of a cyclic and dynamicloading history on dynamic properties of dry sand, part II: cyclic axialpreloading. Soil Dyn Earthquake Eng 2004;24:789803.

[22] Zhou YG, Chen YM, Ke H. Improvement on simplied procedure forliquefaction potential evaluation of sands by shear wave velocity (inChinese). Chinese J Rock Mech Eng 2005;24(13).

[23] Shirley DJ, Hampton LD. Shear wave measurements in laboratorysediments. J Acoustical Soc Am 1978;63(2):60713.

[24] De Alba P, Baldwin K, Janoo V, Roe G, Celikkol B. Elastic-wavevelocities and liquefaction potential. Geotech Testing J ASTM 1984;7(2):7787.

[25] Dyvik R, Madshus C. Lab measurement of G max using benderelements. In: Advances in the art of testing soils under cyclicconditions. Detroit, MI. Geotechnical Engineering Division, ASCE;1985, 18696.

[26] Thomann TG, Hryciw RD. Laboratory measurement of small strainshear modulus under K 0 conditions. Geotech Testing J ASTM 1990;13(2):97105.

[27] Viggiani G, Atkinson JH. The interpretation of the bender elementtests. Geotechnique 1995;45(1):14954.

[28] Jovicic V, Coop MR, Simic M. Objective criteria for determing G maxfrom bender element. Geotechnique 1996;46(2):35762.

[29] Arulnathan R, Boulanger RW, Riemer MF. Analysis of benderelement tests. Geotech Testing J ASTM 1998;21(2):12031.

[30] A SS, Richart Jr FE. Stress-history effects on shear modulus of soils. Soils Foundations 1973;13(1):7795.

[31] Vucetic M, Dobry R. Effect of soil plasticity on cyclic response.J Geotech Eng, ASCE 1991;117(1):89107.

[32] Petrakis E, Dobry R. A self consistent estimated of the elasticconstants of a random array of equal spheres with application togranular soil under isotropic conditions. NY: Rensselaer PolytechnicInst., Troy; 1986 (Rep. No. CE-86-04).

[33] Seed HB, Lee KL. Liquefaction of saturated sands during cyclicloading. J Soil Mech Foundation Div, ASCE 1966;92(6):10534.

[34] Cascante G, Santamarina JC. Interparticle contact behavior and wavepropagation. J Geotech Eng 1996;122(10):8319.

[35] Santamarina JC. Soil behavior at the microscale: particle forces.Geotechnical Special Publication, ASCE 2003;119:2556.

[36] Richart Jr FE. Some effects of dynamic soil properties on soilstructure interaction. J Geotech Eng Division, ASCE 1975;101(12):447.

[37] Yasuhara K, Hyde AFL. Method for estimating postcyclic undrainedmodulus of clays. J Geotech Geoenviron Eng, ASCE 1997;204(3):20411.


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