IJR International Journal of RailwayVol. 6, No. 3 / September 2013, pp. 112-119

Vol. 6, No. 3 / September 2013 112

The Korean Society for Railway

Evaluation of Dynamic Properties of Trackbed Foundation SoilUsing Mid-size Resonant Column Test

Yujin Lim†, Tien Hue Nguyen*, Seong Hyeok Lee** and Jin-Wook Lee**

Abstract

A mid-size RC test apparatus (MRCA) equipped with a program is developed that can test samples up to D=10 cmdiameter and H=20 cm height which are larger than usual samples used in practice. Using the developed RC test appa-ratus, two types of crushed trackbed foundation materials were tested in order to get the shear modulus reduction curvesof the materials with changing of shear strain levels. For comparison purpose, large repetitive triaxial compression tests(LRT) with samples of height H=60cm and diameter D=30 cm were performed also. Resilient modulus obtained fromthe LRT was converted to shear modulus by considering elastic theory and strain level conversion and were compared toshear modulus values from the MRCA. It is found from this study that the MRCA can be used to test the trackbed foun-dation materials properly. It is found also that strain levels of Ev2 mostly used in the field should be verified consideringthe shear modulus reduction curves and proper values of Ev2 of trackbed foundation must be used considering the strainlevel verified.

Keywords : Mid-size resonant column test, Shear modulus, Trackbed foundation materials, Large repetitive load test, Ev2

1. Introduction

It is a well known fact that vibration induced by run-ning trains causes deterioration of track foundation. Rail-way stiffness is a basic parameter of track design whichinfluences the bearing capacity, the dynamic behavior ofpassing vehicles, track geometry quality and the life oftrack components [1]. The usual method to obtain thetrack stiffness is to run track loading vehicle in order tomeasure deflection under a wheel load size since the trackstiffness is used as the parameter for calculating stresses inthe elements of track and track foundation. The track stiff-ness is, however, a composite value that represents vari-ous aspects of stiffness of different materials involved inmaking foundation layers below track. In this study, inorder to evaluate dynamic geotechnical properties of the

trackbed foundation, a mid-size RC test apparatusequipped with an analyzing program is developed that cantest samples up to D=10 cm diameter and H=20 cm heightwhich is larger than usual samples of D=5 cm andH=10 cm used mostly in practice. The obtained dynamicproperties such as shear modulus, G, of the sub-layersunder track can be utilized to calculate track stiffness k orcomposite equivalent modulus, , of the sub-layerscorrectly that can consider the influences of strain andstress levels in each sub-layers of the track and can beused to determine formation thickness of the track. Thelarger the samples used in resonant column test, the morecorrect test G values in each layers can be obtained. There-fore, it is helpful to use mid-size resonant column test toget reliable data for shear modulus of the trackbed founda-tion materials by scrutinizing various factors affecting theshear modulus which contribute in determining compositetrack modulus k and/or composite equivalent modulus,

values. In this study, a proper way of determiningcomposite equivalent modulus, by using shearmodulus of the sublayers. The composite equivalent mod-ulus, can be used as an input parameter for designof formation thickness

Eequiv

Eequiv

Eequiv

Eequiv

†

***

Corresponding author: Dept. of Civil, Environmental and Railroad Engineering,Paichai University, KoreaE-mail : yujin@pcu.ac.krPOSCO E&C at Hanoi, VietmanAdvanced Infrastructure Research Team, Korea Railway Research Institute, Korea

ⓒThe Korean Society for Railway 2013http://dx.doi.org/10.7782/IJR.2013.6.3.112

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Yujin Lim, Tien Hue Nguyen, Seong Hyeok Lee and Jin-Wook Lee / IJR, 6(3), 112-119, 2013

2. Determination of Dynamic Properties and Composite Equivalent Modulus

2.1 Shear properties G

In general, shear modulus, G of a geomaterial such astrackbed foundation is strain dependent ([2]) as shown inFig. 2.

In order to obtain correct design values of shear modu-lus, G, strain levels experienced by trackbed foundationmaterials in each layer must be known. The strain levels inthe sublayers can be calculated by finite element analysisof track structure.

Resonant column (RC) testing has some advantages overthe other techniques. A resonant column test apparatus(RCA) is capable of controlling shear strains induced in asoil specimen, and accurately measuring the resonant fre-quency of a specimen even at very small vibratory ampli-tude and allowing estimation of Gmax accurately withoutmeasuring applied torque. In addition, a RCA can widelyvary the shear strain from very small to medium range(e.g. from 10-5% to 10-2%). A shear strain range producedby RC testing is similar to that produced by in-situ seis-mic testing. Therefore, a shear modulus and damping ratio

measured using RC testing is comparable to that mea-sured using geophysics surveying. Furthermore, RC test-ing is a non-destructive technique, which allows a soilspecimen to be tested repeatedly at dierent eective stresslevels.

2.2 Midsize resonant column test apparatus

In this study, a mid-size RC test apparatus (MRCA)equipped with analyzing program is developed that cantest samples up to D=10 cm diameter and H=20 cm heightwhich is larger than usual samples of D=5 cm andH=10 cm used mostly in practice. Thus, crushed stoneswith larger grains up to 38 mm in diameter used mostly inKorea as trackbed foundation materials in track construc-tion could be considered effectively than conventionallyused RC apparatus for evaluation of the dynamic proper-ties of the materials by using the MRCA. The MRCA isdesigned and assembled based on the concept of fixed-freefixity conditions and driving mechanism proposed byStokoe. The one end of the specimen is fixed to the rigidtest base by the bottom pedestal while the other end isattached to drive plate (Fig. 3). Fig. 4 presents a sche-matic configuration of the MRCA used in this study.

A digital sinusoidal wave form is generated by Agilent33220A 20 MHz Function/Arbitrary Waveform Genera-tor, which is controlled by developed computer programvia a NI PCI-6014 multifunction DAQ card, then ampli-fied by an Eliezer EA100A power amplifier before goingto the coils. The electro-magnetic force generated betweenthe magnetic field of coils and the magnets mounted ondrive plate cross arm, excites the specimen with the driveplate harmonic oscillation.

The motion of the specimen is monitored by thePCB343B51 accelerometer mounted on drive plate. Accel-erometer signal goes through charge amplifier then con-

Fig. 1 Schematic of track structure

Fig. 2 General shear modulus-shear strain relation of geomaterials

Fig. 3 Fixity conditions of Stokoe type resonant column test:a) fixed free type with no mass, b) fixed free

type with added Mass

Evaluation of Dynamic Properties of Trackbed Foundation Soil Using Mid-size Resonant Column Test

114

verted into digital signals by NI PCI-6014 card beforebeing handled by the computer software in controlling PC.

Using the MRCA, three types of crushed stones used astrackbed foundation materials have been tested in order toobtain the dynamic properties of the trackbed foundationmaterials such as G/Gmax reduction curves and dampingratio D.

2.3 Calibration of the MRCA

The drive plate mass polar moment of inertia, Io, is animportant parameter in the analysis of RC test. In order tocalculate the shear modulus, G, Eq. 1 and 2 are used toobtain shear velocity, Vs.

(1)

(2)

Io can be calculated theoretically through geometrydimensions [3]. However, as shown in Fig. 4. drive sys-tem has complex shape with a magnet, an accelerometer,counterweight and threaded holes. Thus, it is difficult tocalculate Io. Theoretical Io was obtained as a referencevalue.

In experimental measurement of Io, three added massesand six calibration aluminum specimens are used. Thedrive plate calibration system can be modeled as a SDOFspring-mass system. The calibration specimen represents

the massless spring with torsional spring stiffness, Kq, andthe top plate of calibration specimen and the drive platerepresent the mass in the model. The natural resonant fre-quency, fr, can be expressed as:

(3)

where, fr = resonant frequency (Hz), Io = mass polarmoment of inertia of drive plate system, It = mass polarmoment of inertia of top plate of calibration specimen, Kq

= torsional stiffness of calibration specimen. Eq. 3 has twounknowns, the calibration specimen torsional stiffness, Kq,and mass polar moment of inertia of drive plate system, Io.

To obtain additional equations, the test was repeated onthe same calibration specimen with already known masspolar moment of inertia of added mass, ÄI. In this study,to increase the precision of test results, three added masseswere made for the calibration experiment. That meansthere are four equations (Eq. 3 to Eq. 6) with twounknowns:

(4)

(5)

(6)

In free vibration, the resonant frequency, fm is as fol-lows:

(7)

where D = damping ratio of calibration specimen.Substitution of Eq. 7 to Eq. 3 provides the following:

(8)

Therefore, there can be four equations to solve for Kq,and Io. Since D value for aluminum calibration bar is verysmall, the D value in Eq. 8 in this case of calibration using

Is

Io

---- tan=

nLVs

-----=

fn1

2------

KIo It+------------=

fn11

2------

KIo It I1+ +-------------------------=

fn21

2------

KIo It I2+ +-------------------------=

fn31

2------

KIo It I3+ +-------------------------=

fm fn 1 D2–=

fn1

2------

KIo It+------------ 1 D

2–=

Fig. 4 Schematic configuration of the MRCA

Fig. 5 Added masses and Calibration specimens

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Yujin Lim, Tien Hue Nguyen, Seong Hyeok Lee and Jin-Wook Lee / IJR, 6(3), 112-119, 2013

aluminum bar is neglected. Table 1 and 2 explain in detaildimensions of calibration bars and added masses used forcalibration process. The calibration procedure is explainedin detail by Nguyen ([3]).

2.3 The Composite Equivalent Modulus

If the modulus of each sublayers of the trackbed founda-tion is known by using the MRCA and/or large repeatedload test (LRT), the composite equivalent modulus,

, of trackbed foundation including ballast can becomputed using the modulus and can be used as inputdesign parameter for deciding of formation thickness.

In this study, the composite equivalent modulus, ,of trackbed foundation is defined as the follows:

(9)

where EB = modulus of a ballast layer, tB = thickness of bal-last layer, ESB =modulus of trackbed foundation layer, tSB =thickness of trackbed foundation layer, ESG =modulus ofsubgrade, DESG = thickness or top influencing depth part ofsubgrade. The composite equivalent modulus, , oftrackbed foundation can be developed as an alternativedesign parameter instead of tack stiffness, k. In order to dothis purpose, each modulus of the sublayers below the trackmust be evaluated using proper test procedure.

3. Test

3.1 Properties of testing materials

Prior to the RC test, the typical trackbed foundation

granular materials used in Korea were tested for obtainingbasic physical properties. Grain size distribution and thetest results are summarized in Table 1 and Table 2, respec-tively . Compaction test results are shown in Table 3. Allmaterials tested are non-plastic (NP).

3.2 Large Repetitive Triaxial Compression

Test

Concept of shear stress ratio has been proposed ([4], [5])because the trackbed materials, mostly composed of gran-ular soil, are highly affected by shear strength of the mate-rial. In this study a large repetitive triaxial load test (LRT)has been adapted for performing test to get resilient modu-lus of the trackbed foundation materials. The test proce-dure which includes concept of shear stress ratio has beennewly designed.

Permanent deformation of the granular material isdependent on strength since a limiting value of shear stressratio is believed to control the permanent defor-mation. It is well known that the permanent deformation ishighly dependent on the resilient modulus.

The shear strength of the granular material is governedby Mohr-Coulomb failure criteria. Therefore, decreasedshear strength as a result of a lower friction anglewould result in a higher shear stress ratio for the samestress level. Hence, the shear stress ratio becomes an indi-cator of the aggregate performance under various stresslevel. A combination of stress states was adapted in thisstudy for the LRT procedure. Axial deviator stress calcula-tion was performed by the following equations consideringthe stresses activated on the Mohr-Coulomb failure planeand by considering the Mohr-Coulomb failure criteria:

(10)

(11)

Using the same LRT apparatus, static triaxial compres-sion tests were performed in order to get strength parame-

Eequiv

Eequiv

Eequiv

EBtB ESBtSB ESGDESG+ +

tB tSB DESG+ +---------------------------------------------------------=

Eequiv

f max

max

f

f

---d 2 2 f 3 d 2+– 2–

c f tan+-------------------------------------------------------------------=

f

23 2 3 d d2 d

24tan+

2tan–

2

tan+2

tan+

2 1 2tan+ -----------------------------------------------------------------------------------------------------------------=

Table 1 Grain size distribution of trackbed foundation material

Percentage Passing (%)

75 mm 50 mm 40 mm 20 mm 5 mm 2.0 mm 425 m 75 m

- 100 80-100 55-100 30-70 20-55 5-30 0-10

Table 2 Basic physical test results

Trackbed Foundation Materials No.1 No.2

Testresults

D10 (mm) 0.2 0.2

D30 (mm) 1.35 1.35

D60 (mm) 10 10

Coefficient of Curvature (Cc) 0.91 0.91

Coefficient of uniformity (Cu) 50 50

P200 (%) 4 4

P4 (%) 47.5 47.5

Soil classification

Uniform Classification GW GW

Table 3. Compaction test results

Trackbed Foundation Materials No.1 No.2

Compactiontest results

Optimum Moisturecontent (%)

4.3 5.9

Maximum dry unitweight (kN/m3)

23.53 22.84

Evaluation of Dynamic Properties of Trackbed Foundation Soil Using Mid-size Resonant Column Test

116

ters as shown in Table 4. Test procedure was scheduledbased on the calculated deviator stress using the aboveequations at each level of confining stress and shear stressratio as explained in Table 5 and Table 6.

3.3 Test results

3.3.1 The normalized modulus reduction curveShear modulus reduction curves of trackbed foundation

materials were obtained using the raw data from MRCAand small resonant column test apparatus (SRCA) and areshown in Fig. 6 through 9.

Normalized shear modulus (G/Gmax) curves wereobtained using the raw data from RC tests and are shownin Fig. 10 through Fig. 11. The normalized shear modulus(G/Gmax) curves are compared with those offered by Seedet al. [6,7]. Three tested crushed stones all provide similartrend of the normalized shear modulus (G/Gmax) values tothe band suggested. All the normalized shear modulus (G/Gmax) values are dependent on confining stress. Thethreshold strain increases with confining stress. Three

tested crushed trackbed foundation materials were made asspecimens by compaction with degree of compaction over95% of maximum dry unit weight at optimum moisturecontent, OMC.

It is found that the shear modulus is highly dependent onlevels of confining pressure and shear strain. Higher the

Table 4. Large static triaxial compression test results

C (kPa) (Degree)

Trackbed fdn. Mat’l No.1 67 45.35

Trackbed fdn. Mat’l No.2 46 47.68

Table 5 Test conditions for large repeated load test (trackbed fdn. Mat’l No. 1)

Confiningstress

Shear stress ratio(/f)

Deviatoric stress(kPa)

Number of repetition(N)

35 kPa

0.3/0.7 86.25/249.96 5,000 10,000 total

0.5/0.7 159.26/249.96 5,000 10,000 total

0.7/0.7 249.96 10,000

69 kPa

0.3/0.7 124.39/360.49 5,000 10,000 total

0.5/0.7 229.69/360.49 5,000 10,000 total

0.7/0.7 360.49 10,000

Table 6 Test conditions for large repetead load test(trackbed fdn. Mat’l No. 2)

Confiningstress

Shear stress ratio(/f)

Deviatoric stress(kPa)

Number of repetition(N)

35 kPa

0.3/0.7 99.91/287.79 5,000 10,000 total

0.5/0.7 183.99/287.79 5,000 10,000 total

0.7/0.7 287.79 10,000 회

69 kPa

0.3/0.7 133.48/384.49 5,000 10,000 total

0.5/0.7 245.81/384.49 5,000 10,000 total

0.7/0.7 384.49 10,000 total

Fig. 6 Shear modulus reduction curves of No. 1 trackbed foundation material (MRCA, D=10 cm)

Fig. 7 Shear modulus reduction curves of No. 2 trackbed foundation material (MRCA, D=10 cm)

Fig. 8 Shear modulus reduction curves of No. 1 trackbed foundation material (SRCA, D=5 cm)

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Yujin Lim, Tien Hue Nguyen, Seong Hyeok Lee and Jin-Wook Lee / IJR, 6(3), 112-119, 2013

confining pressure is, the greater the shear modulus is atthe same shear strain level.

It is found that the shear modulus decreases nonlinearlyfrom threshold strain of 10-3%. The shear modulus obtainedfrom mid-size specimen is bigger than that of small sizespecimen at the same shear strain level. Therefore, it is found

that there is sample size effect on the shear modulus.

3.3.2 Resilient modulusIn this study large repetitive triaxial load tests (LRT)

were performed using the same crushed stones which werecompacted to 95% of maximum dry density(D=30 cm,H=60 cm) as the trackbed foundation materials used forthe MRCA tests in order to compare the magnitude ofmaximum modulus quantitatively. Fig. 12 shows a typi-cal test results from the LRT. All test results obtained fromthe LRT are summarized in Table 7 and Table 8.

Poisson’s ratio of trackbed foundation materials used inthe MRCA and LRT tests can be assumed to be 0.3. All

Fig. 9 Shear modulus reduction curves of No. 2 trackbed foundation material (SRCA, D=5 cm)

Fig. 10 Normalized shear modulus reduction curves of trackbed foundation material No. 1 (MRCA, D=10 cm)

Fig. 11 Normalized shear modulus reduction curves of trackbed foundation material No. 2 (MRCA, D=10 cm)

Fig. 12 Deviator stress-axial strain relation (confining stress: 35 kPa)- trackbed foundation material No.1

Table 7 Resilient modulus obtained for trackbed foundation material No.1

Shear stress ratio (/f)

0.3 0.7 0.5 0.7 0.7

No. load repetition

1st half 5,000

2nd half5,000

1st half 5,000

2nd half 5,000

10,000

ER (MPa)(3=35 kPa)

167 180 176 154 148

ER (MPa)(3=69 kPa)

178 260 192 296 268

Table 8 Resilient modulus obtained for trackbed foundation material No.2

Shear stress ratio (/f)

0.3 0.7 0.5 0.7 0.7

No. load repetition

1st half 5,000

2nd half5,000

1st half 5,000

2nd half 5,000

10,000

ER (MPa)(3=35 kPa)

246 297 260 324 260

ER (MPa)(3=69 kPa)

310 410 327 390 331

Evaluation of Dynamic Properties of Trackbed Foundation Soil Using Mid-size Resonant Column Test

118

resilient modulus obtained from the LRT are recalculatedto get shear modulus, G, since shear modulus, G, can beconverted to elastic modulus, E, easily by using the fol-lowing equation:

(12)

The following correlation equation can be affirmedusing elasticity theory:

(13)

Therefore, vertical compressive strain obtained from theLRT can be easily converted to shear strain using theabove equation so that the converted shear modulus, G, -the converted shear strain, , relation graphs are to be rep-resented as shown in Fig. 13 and Fig. 14. The newly recal-culated shear modulus values obtained from the LRT arecompared to those values obtained from MRCA. Averagevalues of the newly calculated shear modulus obtained

from the LRT are shown also. As shown in Fig. 13, allshear modulus values obtained from the LRT are locatedin the range of medium to large strain (>0.01%). How-ever, it is found the averaged values of shear modulus ateach confining stress levels obtained from the LRT areclose to maximum shear modulus, in the MRCA.This big difference in shear strain levels between LRT andMRCA is believed to be generated due to different mea-suring system. In order to get precise strain levels in LRT,it is required to use very accurate LVDT to measure strainsin the range of small strain.

For design purposes, in order to determine correct val-ues of modulus to be used in deciding the formation thick-ness, strain levels must be known from site fieldinstrumentations and full 3-D finite element analysis con-sidering dynamic amplification effects induced by runningtrain on the track. In addition, it should be pointed out thatthe use of which is defined as stiffness modulusobtained from unloading-reloading part of pressure-settle-ment curves from repeated plate bearing test (RPBT)mostly used in the field of track construction site to checkdegree of compaction and adapted as the design criteriavalue of trackbed foundation layer must be compared tothose values as shown in Fig. 13 and Fig. 14 tested fromthe MRCA and the LRT since it is important to know therange of stain levels generated in the RPBT. Up to now,range of strain levels of repeated plate load test performedon the surface of compacted trackbed foundation layer and

test values accounted at these strain levels are not ver-ified yet. This is going to be next task of this study.

4. Conclusion

In this study, a mid-size RC test apparatus (MRCA)equipped with program is developed that can test samplesup to D=10 cm diameter and H=20 cm height which arelarger than usual samples used mostly in practice. Usingthe developed RC test apparatus, two types of crushedtrackbed foundation materials were tested in order to getthe shear modulus reduction curves of the materials withchanging of shear strain levels. For comparison purpose,large repetitive triaxial compression tests (LRT) with sam-ple of height H=60 cm and diameter D=30 cm were per-formed also. Resilient modulus obtained from the LRTwas converted to shear modulus by considering elastic the-ory and strain level conversion procedure and were com-pared to shear modulus values from the MRCA.

The following conclusions are made from this study:(1) The MRCA can be used to test the trackbed founda-

tion materials properly. It is believed that even though theLRT can provide relatively larger values of shear modulus

GE

2 1 v+ ------------------=

xy 1 3– 1 – v= =

Gmax

Ev2

Ev2

Fig. 13 Comparison of shear modulus reduction curves with shear modulus values from the LRT using trackbed foundation

material No. 1

Fig. 14 Comparison of shear modulus reduction curves with shear modulus values from the LRT using trackbed foundation

material No. 2

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Yujin Lim, Tien Hue Nguyen, Seong Hyeok Lee and Jin-Wook Lee / IJR, 6(3), 112-119, 2013

close to Gmax at shorter band of strain range and atmedium to large strain levels, the MRCA can simulatesgeneration of shear modulus with changing strain levelsproperly and relatively wider band of strain range.

(2) It is found that strain levels of Ev2 mostly used in thefield should be verified considering the shear modulusreduction curves obtained from MRCA and/or the LRTand proper values of Ev2 of trackbed foundation. Fordesign purposes, in order to determine correct values ofmodulus to be used in deciding the formation thickness,strain levels must be known from site field instrumenta-tions and full 3-D finite element analysis consideringdynamic amplification effects induced by running train onthe track.

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