IJR International Journal of Railway

Vol. 8, No. 2 / June 2015, pp. 50-54

Vol. 8, No. 2 / June 2015 − 50 −

The Korean Society for Railway

Stiffness Modulus Comparison in Trackbed Foundation Soil

Daesung Kim*, Hojin Cho**, Jaebeom Park**, and Yujin Lim†

Abstract

The primary function of the trackbed in a conventional railway track system is to decrease the stresses in the subgrade to

be in an acceptable level. A properly designed trackbed layer performs this task adequately. Many design procedures

have used assumed and/or are based on critical stiffness values of the layers obtained mostly in the field to calculate an

appropriate thickness of the sublayers of the trackbed foundation. However, those stiffness values do not consider strain

levels clearly and precisely in the layers. This study proposes a method of computation of stiffness that can handle with

strain level in the layers of the trackbed foundation in order to provide properly selected design values of the stiffness of

the layers. The shear modulus values are dependent on shear strain level so that the strain levels generated in

the subgrade in the trackbed under wheel loading and below plate of Repeated Plate Bearing Test (RPBT)

are investigated by finite element analysis program ABAQUS and PLAXIS programs. The strain levels generated in

the subgrade from RPBT are compared to those values from RC (Resonant Column) test after some consideration of

strain levels and stress consideration. For comparison of shear modulus G obtained from RC test and stiffness moduli Ev2

obtained from RPBT in the field, many numbers of mid-size RC tests in laboratory and RPBT in field were performed

extensively. It was found in this study that there is a big difference in stiffness modulus when the converted Ev2 values

were compared to those values of RC test. It is verified in this study that it is necessary to use precise and increased load-

ing steps to construct nonlinear curves from RPBT in order to get correct Ev2 values in proper strain levels.

Keywords: Trackbed, Repeated Plate Bearing Test, ABAQUS, Resonant Column test

1. Introduction

At present time, the so-called repeated plate load bear-

ing test (RPBT) is used to get Ev2 values in order to check

degree of compaction of subgrade in the field and to get

design value for determining thickness of trackbed founda-

tion [1]. However, strain levels below the plate have not

yet been investigated up to now, even though the strain

levels affect stiffness of the material very much. In usual,

triaxial compression (TC) test and Resonant Column (RC)

test can be used to get modulus of the compacted sub-

grade soil which is dependent on strain levels. Therefore,

it is necessary to investigate strain levels and to know real

range of modulus values of the subgrade soil below the

plate. The same subgrade soils from the construction sites

of high-speed rail line are compacted to the same degree

of compaction in the field. Medium size RC tests are per-

formed using the compacted soil to get shear modulus~

shear strain (G~γ) relation [2]. Modulus and strain levels

of the subgrade soils below the RPBT are investigated and

compared to those of test results from shear modulus~

shear strain (G~γ) range from the RC test in order to check

reliability of using the Ev2 values for checking DOC and to

use as design values for determining thickness of trackbed

foundation

2. Investigation of RPBT

The RPBT is in nature to verify stiffness at a specified

vertical deflection. Therefore, it is hard to determine non-

linear characteristics of stiffness of the soil based on strain

levels below the plate (Fig. 1). As can be seen in Fig. 1, it

is very difficult to consider strain levels since the test uses

†

*

**

Corresponding author: PaiChai University, Korea

E-mail : yujin@pcu.ac.kr

National Forestry Cooperatives Federation, Korea

PaiChai University, Korea

ⓒThe Korean Society for Railway 2015

http://dx.doi.org/10.7782/IJR.2015.8.2.050

− 51 −

Daesung Kim, Hojin Cho, Jaebeom Park and Yujin Lim / IJR, 8(2), 50-54, 2015

initial bearing pressure applied on the plate at a specific set-

tlement. The concept of vertical soil reaction represented

ask in Fig. 1, has been used as a parameter to check degree

of compaction of the trackbed soils in the field as the form

of Ev2 in German standard (DIN 18-134)[3]. In German

standard, test procedure is a bit more sophisticate rather

than usual methods adapted in road and geotechnical engi-

neering area. In German standard, Ev2 values are obtained

from RPBT. The Ev2 values are used for degree of compac-

tion (DOC) checking measures for high-speed rail line. Ev2

values are determined using Eq. (1) and Eq. (2). The maxi-

mum applied pressure (σo-max) on the plate is 500 kPa.

However, the incremental bearing pressure for increasing

loading step is too big to simulate nonlinear small strain

behavior of the subgrade soil. By comparing the RPBT test

results to the RC test results, it is possible to check draw-

backs and limitations of the RPBT. The comparison can

provide a way of improving reliability of the test data.

(1)

(2)

3. Modification and Correction of Modulus Considering Strain and Stress

Conditions

For comparison purpose, values of shear modulus G and

axial strains, εv, of the RC test must be converted to the

values logically compatible with Ev2 and axial strains, εv,

of the RPBT. Shear modulus and shear strain (G~γ) data

obtained from the RC test are converted to E modulus and

axial strain, εv using Eq. (3) and Eq. (4).

(3)

(4)

Using bearing pressures, q, and deflection, δ, measured

in the RPBT, E modulus and axial strains εv, are deter-

mined using the following equations:

(5)

(6)

For obtaining correct E modulus from the RPBT, the fol-

lowing equation can be used to consider stress condition

directly below the plate:

(7)

Fig. 3 demonstrates corrected E modulus of the RPBT

results by using Eq. (7) and E modulus values corrected by

using Eq. (3) and (4). The correction factor n is obtained

by applying different levels of confining pressures on the

RC test samples as shown in Table 1.

However, strain influence factor used in Eq.(6) to get

converted E modulus and representative strain levels was

assumed here 0.4 as recommended by Schmertman et al

δ ao a1σo a2σo

2+ +=

Ev 1.5r1

a1 a2σo max+------------------------------=

Es 2G 1 v+( )=

εv1

3------γ=

Es

q

δ---B 1 μ

2–( )=

εvδ

B 1 μ2

–( )---------------------Iz=

Ecorrecled ERPBT

σ′m reference,

σ′m RPBT,

---------------------------⎝ ⎠⎛ ⎞

n

=

Fig. 1 Schematics of RPBT

Fig. 2 A typical RPBT test results based on German standard

(DIN 18-134)

Stiffness Modulus Comparison in Trackbed Foundation Soil

− 52 −

[4]. This representative value of strain influence factor Iz

affects much on the strain range. Thus, a full size 3D finite

element analysis with ABAQUS program and axisymmet-

ric static loading analysis with PLAXIS program were per-

formed to get correct strain levels below sleepers and plate

respectively [5].

For ABAQUS and PLAXIS FE analyses, wheel load is

assumed as 153 kN with consideration of DAF (Dynamic

Amplification Factor) that was calculated based on maxi-

mum design speed (350 km/h) of KTX (Korean Express

Railway). Under the model loading, strain levels on the

top of subgrade were investigated from ABAQUS FE

analysis. In ABAQUS simulation, modulus of the sub-

grade was assumed to be 50, 80 and 120 MPa in order to

see strain level variation by different values of modulus of

the subgrade.

Using newly computed strain influence factor Iz, modu-

lus of the RC test are compared again with converted Ev2

values obtained from the RPBT. The precise strain levels

Fig. 3 Comparison of modulus obtained from RPBT and RC

Test (Site A, Subgrade, σ’m,reference=30 kPa)

Table 1. Correction factor for confining pressure

Site A Site B

correction factor, n 0.174 0.032

Fig. 4 Comparison of modulus obtained from RPBT and RC

Test (Site B, Subgrade, σ’m,reference=30 kPa)

Fig. 5 3D finite element mesh used for static loading analysis

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Daesung Kim, Hojin Cho, Jaebeom Park and Yujin Lim / IJR, 8(2), 50-54, 2015

calculated from ABAQUS 3D analysis of the track are

compared together in Fig. 6. It is easy to see the strain lev-

els under wheel load below sleeper are in small strain

range of 0.000289~0.000395 depending on modulus of the

subgrade. However, the strain range encountered below

the plate in the field sites is much bigger than this range

and is showing big difference dependent on taking values

of strain influence factor Iz as shown in Fig. 6. Whatever

values of subgrade modulus are encountered in the sub-

grade soil, strain levels are always exiting in the range of

small strain under the wheel load expected in KTX high-

speed rail line. Since the measured Ev2 values are bigger

than specified critical design value of 80 MPa in the sub-

grade soil, it can be confirmed that the converted modulus

of the measured Ev2 values are always providing and mis-

guiding highly overestimated values. This fault in obtain-

ing stiffness or DOC by adapting Ev2 can cause settlement

in the subgrade after completion of construction of track.

Therefore, it is required to develop new procedure for per-

forming RPBT by introducing very small steps of loading

intervals and increasing steps as many as possible to

obtain precise values of stiffness modulus of the subgrade

with nonlinear characterizing of the test under proper

strain levels.

4. Conclusion

Stiffness values obtained in the RPBT do not consider

strain levels clearly and precisely in the sublayers of track.

The strain levels generated in the layers from RPBT are

compared to those values from RC (Resonant Column)

test. To develop a correlation between shear modulus G

obtained from RC test and stiffness moduli Ev2 obtained

from RPBT in the field, many numbers of mid-size RC

tests in laboratory and RPBT in field were performed

extensively. Finite element analyses using PLAXIS and

ABQUS programs are performed in order to investigate

influence of strain influence coefficient by getting newly

computed Iz and to get precise strain level predicted on the

surface of subgrade in the full track structure under wheel

loading, respectively. It was found in this study that there

is a big difference in stiffness modulus when the con-

verted Ev2 values were compared to those values of RC

test. It is verified in this study that it is necessary to use

precise and increased loading steps to construct nonlinear

load-settlement curves from RPBT in order to get correct

Ev2 values in proper strain levels.

Acknowledgement

This research was supported by a grant(15RTRP-

B067919-03) from Railroad Technology Research Pro-

gram funded by Ministry of Land, Infrastructure and

Transport of Korean government

References

1. Korea Rail Network Authority. (2013). Design Specification

for Railroad: Road bed.

2. Pezo, R. F., Kim, D. S., Stoke, K. H., Hudson, W. R (1991).

“Developing a Reliable Resilient Modulus Testing System”,

Table 2 Input values for ABAQUS FE analysis

Young’s Modulus, E

(MPa)

Poisson’s ratio

(ν)

Mass density

(kN/m3)

Rail 210,000 0.3 76.4

Sleeper 29,100 0.2 22.5

Ballast 100 0.2 19.6

Sub-ballast 180 0.2 20.58

Subgrade 50, 80, 120 0.3 18.6

Fig. 6 Axial strain(εv) and Young’s modulus(E) changes due to

strain influence coefficient (Iz) difference

Stiffness Modulus Comparison in Trackbed Foundation Soil

− 54 −

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