TRACK QUALITY INDEX
AS TRACK QUALITY ASSESSMENT INDICATOR
Dian Setiawan M
Civil Engineering Department
Faculty of Engineering
Universitas Muhammadiyah Yogyakarta
Jl. Lingkar Selatan, Tamantirto, Kasihan, Bantul,
Yogyakarta, 55183
dian_setiawanm@yahoo.co.id
Sri Atmaja P. Rosyidi
Civil Engineering Department
Faculty of Engneering
Universitas Muhammadiyah Yogyakarta
Jl. Lingkar Selatan, Tamantirto, Kasihan, Bantul,
Yogyakarta, 55183
atmaja_sri@umy.ac.id
Abstract
Track Quality Index (TQI) is used in order to evaluate track quality. In this paper, TQI application for
Indonesian Railway (IR) has been reviewed and various methods to evaluate track quality have been
presented. IR have been used TQI-Geometry in infrastructure maintenance works and accident investigation.
UK SD Index, Netherlands Q Index, USA TRI, FRA TGI, Austrian TGI, Canadian TQI, SNCF’s MDI,
Chinese TQI, Polandia J Coefficient, Indian TGI, and European Standard are some methods to evaluate track
quality. However, their results rely only on a limited number of parameters and aspects of track deterioration.
Those methods cannot provide a thorough indication of all influencing parameters and their role in track
degradation. The author suggests that main track degradation should have 4 aspects: Track Super-Structural;
Track Sub-Structural; Track Geometrical; Traffic, and furthermore, a new TQI should be developed by
combining 3 index investigations: Track Irregularity, Track Settlement, and Track Geometry.
Keywords: Track Quality Index, Track Degradation, Track Structure, Track Geometry, Traffic Parameters
Abstrak
Track Quality Index (TQI) digunakan untuk mengevaluasi kualitas jalan rel. Penelitian ini membahas
penggunaan TQI dalam perkeretaapian Indonesia dan menyajikan berbagai metode yang digunakan untuk
mengevaluasi kualitas jalan rel. Perkeretaapian Indonesia menggunakan TQI-Geometrik pada pekerjaan
pemeliharaan infrastruktur dan investigasi kecelakaan. UK SD Index, Netherlands Q Index, USA TRI, FRA
TGI, Austrian TGI, Canadian TQI, SNCF’s MDI, Chinese TQI, Polandia J Coefficient, Indian TGI, dan
European Standard merupakan beberapa metode lainnya yang dapat digunakan untuk mengevaluasi kualitas
jalan rel. Namun, hasil dari metode-metode tersebut hanya terbatas pada beberapa parameter dan aspek
kerusakan jalan rel dan juga tidak dapat menyajikan indikasi terperinci dari semua parameter yang
berpengaruh dan perannya terhadap kerusakan jalan rel. Penulis menyarankan kerusakan jalan rel sebaiknya
terdiri dari 4 aspek: struktur atas jalan rel, struktur bawah jalan rel, geometrik jalan rel, dan lalulintas, serta
selanjutnya dikembangkan TQI terbaru yang merupakan kombinasi dari 3 investigasi index: Track
Irregularity, Track Settlement, and Track Geometry.
Keywords: Track Quality Index, Kerusakan Jalan Rel, Struktur Jalan Rel, Geometrik Jalan Rel, Parameter
Lalulintas
INTRODUCTION
The construction of railway networks involves a large amount of financial support
imposing, not only at the conception and design level, but also during the line operation, a
demanding, a complete, and a rigorous estimation of the total cost involved in the life cycle
of the system. Furthermore, due to the running of high-speed trains and heavy haul trains,
the track equipment is damaged more frequently, leading to a threat of running safety.
However, maintenance of railway tracks is both costly and difficult to manage effectively.
1
Simposium XIX FSTPT, Universitas Islam Indonesia, 11-13 Oktober 2016
It is due to the fact that there are a large number of parameters influencing the rate of track
degradation. Therefore, railway industries are trying to improve the productivity of their
maintenance teams through more effective control of track deterioration (Sadeghi and
Askarinejad, 2007). By using appropriate tools for estimating railway network life cycle
costs (LCC), it is possible to minimize the final cost and, at the same time, to identify the
most important aspects and parameters influencing the cost evaluation. Research is not
only required on the LCC modeling, but also on the estimation of major degradation
factors and the assessment of its impact on the maintenance needs (Berawi, et.al, 2010).
How to evaluate the quality, and improve the maintenance of track equipment is
scientifically becoming an urgent issue to ensure the railway operation safety, reliability,
and rational allocation of resources. Track Quality Index (TQI) is figures of merit that
objectively quantify the condition of track. TQI can monitor track degradation and
maintenance operation, can summarize and display the condition of large sections of track,
and are correlated with both safety standards and values of ride quality (Hamid and Gross,
1981). This paper review TQI application for Indonesian Railway and present various
methods to evaluate the track quality from several recent literatures in order to understand
more about aspects and parameters that affects railway track deterioration and to propose
the main aspects and parameters to determine TQI analysis.
EXISTING TQI-Geometry APPLICATION FOR INDONESIAN RAILWAY
Railway Infrastructure Maintenance
Peraturan Menteri Perhubungan No PM 32 2011 about standard and procedure of
railway infrastructure maintenance, stated that the railway track maintenance is to fullfil
railway operation standard and TQI Value which has been assigned. On that regulation,
TQI for railway track is not mentioned and explained as detail as TQI for railway bridge
and tunnel which have been determined based on the classification of deterioration level
i.e. A, B, C, and S and completed with sheet of entry and rating index of degradation
assessment.
Railway Accident Investigation by The National Transportation Safety Committee
Track Condition
In this paper, author presents the example of TQI application on the train accident
analysis reporting. According to The National Transportation Safety Committee (2010), in
the location of train (KA) 80 derailment, wooden sleeper was obsolescent about 33,7% 43, 8%. The worst condition found where there were 5 obsolescent wooden sleeper
successively. Rail fastening on those broken wooden sleeper also would not work properly
in curvature. Rail fastening cannot withstand the centrifugal force appearing on train that
travel in curvature, and it result in the outer rail crumple up. Therefore, this condition will
endanger the train travel especially in curvature, sloping track, and bridge.
Sumber: The National Transportation Safety Committee, 2010
Gambar 1 Track Condition
2
Simposium XIX FSTPT, Universitas Islam Indonesia, 11-13 Oktober 2016
Track Recording Car
Track recording car is used to measure the geometry of railway track line. The
result of geometry measurement will depend on the track material condition. Bad material
condition will reduce the life of track counted from the date of the last measurement, while
the dynamic factor of track will affect the stability of a train travel. From the result of
geometry measurement by track recording car, geometry tolerant value is given to decide
the follow up of measurement, whether it needs to do track speed reduction, immediate
maintenance, or railway track line rehabilitation. There are various tolerant value given in
some countries, with consequence is that the smaller the tolerant value, the more
maintenance cost.
Currently, track recording car used by PT Kereta Api Indonesia (Persero) is EM120. Geometry measurement using track recording car will produce some parameters, such
as gauge, raising, listring, and superelevation. Four parameters are then summed to obtain
the value of TQI. TQI has no unit, because even the unit of the sum (mm) is same but it is
different in vector. Indonesian TQI is classified into 4 sections and converted as track
condition category I to IV. The classification of track condition category is intended as
suggestion of improvement and determination of the maximum speed on the related track.
Tabel 1 TQI Classification and Determination of Track Maintenance Work
Parameter
Category 1
Category 2
Category 3
Category 4
Gauge
0 – 5 mm
6 – 10 mm
11 – 15 mm
> 15 mm
Tamping
0 – 5 mm
6 – 10 mm
11 – 15 mm
> 15 mm
Listring
0 – 5 mm
6 – 10 mm
11 – 15 mm
> 15 mm
Superelevation
0 – 5 mm
6 – 10 mm
11 – 15 mm
> 15 mm
Total (TQI)
0 – 20
21 – 40
41 – 60
> 60
Speed (Km/Hour)
100 < Vmax < 120
80 < Vmax < 100
60 < Vmax < 80
Max < 60
Condition
Comfort
Safe
Caution
Danger
Immediate
Very Immediate
Action
Maintain
Treat
Repairment
Repairment
Tabel 2 Measurement Result of Track Recording Car EM-120
Segmen
JR - KLT
JR - KLT
JR - KLT
JR - KLT
JR - KLT
JR - KLT
JR - KLT
JR - KLT
KM
From
To
Device
Type
Length
(m)
Cat
TQI
TQI
Total
Super
elevation
Tamping
Listring
Gauge
209.800
210.000
210.180
210.189
210.200
210.400
210.600
210.800
210.000
210.180
210.189
210.200
210.400
210.600
210.800
211.000
LRS
LRS
BH
LRS
LRS
LRS
LRS
LRS
200
181
9
11
200
200
200
200
3
2
2
2
2
2
2
2
43.3
35.8
37.4
39
35.7
22.5
28.5
26.6
16
14.5
18.8
8.7
13.8
8.7
9.9
9
17.1
10.1
12.6
19.4
16.1
11.4
12
12.1
7.8
9.2
2.7
8.9
3.4
0
4
3.2
2.4
2
3.3
2
2.4
2.4
2.7
2.3
On above table, it is concluded that track section where train derailment occur is
determined as category 2 that stating the track classification as “SAFE (aman)” condition
so that the suggestion of improvement is “treat”. The action of treat as improvement
suggestion means that the action needed is to repair minor damage with the aim of
improving the track condition. Lifting of listring at certain points must also be taken to
improve railway track construction dimension. Nevertheless, the result of measurement by
the track recording car, in fact, does not represent the whole condition of track, whereas
this measurement is very important to determine the maintenance works that should be
made and the maximum speed on the related track.
3
Simposium XIX FSTPT, Universitas Islam Indonesia, 11-13 Oktober 2016
VARIOUS METHODOLOGIES FOR EVALUATING TRACK QUALITY
For further evaluation, some methods from several literatures by which track
quality index can be obtained are discussed below:
UK SD Index
SD index consists of seven standard deviations {σi = 1, 2,…., 7}, each of which is
associated with a track quality parameter and is calculated from measurement values for
the parameter over a track segment, as formulated in (1). The larger the SD index is, the
worse the track segment is in some aspect represented with the quality parameter (Liu et
al., 2015).
……………………………………..(1)
where σi is the standard deviation of a quality parameter in mm, xij the measurement value
in mm for the parameter at the jth sampling point in the track segment, and n the number of
sampling points in the track segment. Track quality index of United Kingdom, Australia,
and so forth are like the SD index. Differently, they apply (1) to different lengths of track
segments.
Netherlands Q Index
ProRail of Netherlands converts the SD index into a more universal form across
different classes of tracks, as shown in (2) (where N denotes the Q index for a quality
parameter over a 200 m long track segment, σi is the standard deviation for the quality
parameter, and σi80 represents the 80th percentile of standard deviations for 200 m long
segments in a maintenance section ranging in length from 5 to 10 km). The Q index ranges
from 10 to 0. The larger the Q index, the better the track quality of a 200 m long track
segment (Liu et al., 2015).
………….…………….………(2)
USA Track Roughness Index
Track roughness index was proposed in 1998 by America Amtrak (Liu et al., 2015).
It is the average of squared measurement values for a quality parameter over a track
segment, as shown in below:
……………………...…..………………(3)
FRA Track Geometry Index
Track geometry index TGIi uses the measurement value space curve length Li for a
quality parameter over a track segment to quantify the quality of the track segment, as
shown in (4). A larger TGIi indicates that the track segment has a worse quality (Liu et al.,
2015).
4
Simposium XIX FSTPT, Universitas Islam Indonesia, 11-13 Oktober 2016
………………………………….(4)
where Li is the measurement value space curve length for a quality parameter over a track
segment, L0 the length of the track segment, and yj the milepoint of the jth sampling point
on the track segment.
Austrian Railway Track Geometry Index
Austrian Railway uses the five-parameter track defectiveness (w5) calculation for
data obtained from geometry recording cars. The defectiveness for each parameter in each
evaluated track section is the ratio of the length sum of subsections that have exceeded the
acceptable deviation to the total length of the section. In other words, defectiveness for
each measured track parameter is calculated from the following formula (Madejski and
Grabozyk, 2000 in Sadeghi, 2010):
………………………………………..…….(5)
where Li= length of subsections that have exceeded the acceptable deviation and L= total
length of the track section. Assuming that the geometry parameters have negligible effects
on each other, each geometry parameter is treated independently. Therefore, from the
probability theory, the five-parameter defectiveness is defined as follows:
……………..…….(6)
where wz and wy=arithmetic averages for the vertical and horizontal irregularities,
respectively, as determined from the defectiveness of the left and right rails;
wg=defectiveness of cross level; ww=defectiveness of twist; and we=defectiveness of the
track gauge. The amounts of deviations are calculated over a chord length of 18.9 m.
Austrian Railway uses this method to rate the track geometry condition using the tabulated
values presented in Table 3 (Madejski and Grabozyk, 2000 in Sadeghi, 2010).
Tabel 3 Track Condition Based on w5 Value
Canadian Track Quality Index
Canadian National Railway Company (CN) uses a 2nd order polynomial equation of
the standard deviation σi of measurement values for a quality parameter over a track
segment to assess its partial quality, as formulated in (7) (where C is a constant and takes
on the value of 700 for the main line tracks). The overall quality assessment is achieved by
averaging six partial quality indices for gauge, cross level, left (right) surface, and left
(right) alignment (Liu et al., 2015).
..........................................................(7)
5
Simposium XIX FSTPT, Universitas Islam Indonesia, 11-13 Oktober 2016
A larger track quality index implies the track segment has a better quality.
SNCF’s Mean Deviation Indices
SNCF’s indices are different from other indices. They are not based on standard
deviations but on weighted moving average over a track segment, as illustrated in:
……………………..…….(8)
where y0 is the maximum milepoint value in the track segment and ɳi(y) the measurement
data for a quality parameter at the milepoint y (Liu et al., 2015).
Chinese Track Quality Index
Like SD index, both national railroads and Nanjing Metro in China mainland use
the sum of standard deviations of seven quality parameters to assess the overall track
quality of a track segment, as formulated in (9). There are two lengths for the overall track
quality assessment, 200 m and 500 m. The track length of 500 m is applied to high-speed
railroads. Of course, the track length of 200 m is at the same time adopted for track
segment quality assessment. The larger the value of TQI, the worse the track segment in
the overall track quality (Liu et al., 2015).
...................................................................(9)
Polandia J Synthetic Coefficient
J synthetic coefficient is used as an indicator of the track quality based on the
standard deviation evolved by Polish Railways (Madejski & Grabczyk, 2002 in Berawi et
al., 2010). Four track geometry parameters are considered in this index: vertical
irregularities, horizontal irregularities, twist, and gauge. The equation for calculating J
synthetic coefficient is:
.....................................................(10)
where Sz, Sy, Sw and Se are the standard deviation of vertical irregularities, horizontal
irregularities, twist, and gauge, respectively. The standard deviation for each measured
parameter is calculated by the following equation:
.........................................................(11)
Based on the above equation, n is identified as the number of signals registered on
the track being analyzed, xi represents the value of geometry parameters at point i and x is
the average value of the measured signals. The J synthetic track quality coefficient also
specifies the allowable deviation of J, determining the track condition with respect to the
state defined by the track operating appropriately on one side and the track requiring
maintenance on the other.
6
Simposium XIX FSTPT, Universitas Islam Indonesia, 11-13 Oktober 2016
Table 4 Allowable deviations of J coefficient based on line speed (Madejski & Grabczyk, 2002 in Berawi et
al., 2010)
Indian Railways Track Geometry Index (TGI)
Indian Railways has developed a formula to represent the quality of track called TGI. This
model is based on the standard deviation of different geometry parameters over a stretch of
200 m segment. TGI is calculated for each segment and the average value of such
segments in every km gives the general TGI value (Talukdar et al., 2006 in Berawi et al.,
2010). With respect to the effect of each geometry parameter on the ride quality, TGI has
given different value for various geometry parameters as shown in the following formula:
..........................................................(12)
where UI, TI, GI, and AI are the index for unevenness, twist, gauge, and alignment
respectively. For each measured track parameters, the index is calculated from the relation:
..................................................(13)
where SDmes is the standard deviation of measured geometry parameters, SDn represents
the standard deviation prescribed for newly laid track and SDmaint is the prescribed standard
deviation for maintenance. The standard deviation values used in Equation 13 are specified
in Table 5. For the classification of track condition according to the required maintenance
is shown in Table 6.
Table 5 Standard deviation (SD) values (Sadeghi, 2010)
Table 6 TGI Classification for maintenance (Talukdar et al., 2006 in Berawi et el., 2010)
European Standard EN 13848-5
The rail track geometry can also evaluated in accordance with European Standard
EN 13848-5 (CEN, 2005, in Berawi et al., 2010). Three track geometry parameters are
7
Simposium XIX FSTPT, Universitas Islam Indonesia, 11-13 Oktober 2016
considered: longitudinal level, alignment, and gauge. The measurement of longitudinal
level and alignment are conducted based on the standard deviation of irregularities on a
200 m long segment, while the irregularities on the gauge is measured based on a mean
value of 100 m long segment. Apart from that, specification of geometry irregularities with
wavelength domain in the range of 3 m < λ ≤ 25 m is another required parameters to be
calculated in the standard deviation. The allowable thresholds for geometry parameters
based on the European Standards are given in Tables 7-8.
Table 7 SD Threshold values for profile and alignment (CEN, 2005, in Berawi et al., 2010)
Table 8 Distance limit between specified gauge and mean over 100 m segment (CEN, 2005, in Berawi et al.,
2010)
ASPECTS AND PARAMETERS TO TRACK DEGRADATION
According to Sadeghi and Askarinejad (2007), some recent studies have been
intended to investigate the rate of track degradation which have led to the development of
several track degradation models. They have mostly concentrated on one particular aspect
of the railway track system. Their results rely only on a limited number of parameters and
in each study they considered only one of many aspects of the track deterioration and in
turn, took into account those parameters directly related to this aspect. This method cannot
provide a thorough indication of all influencing parameters and their role in the track
degradation. To provide a cost effective and efficient railway track maintenance, a
thorough appreciation of all the parameters is needed even if they are seen from different
aspects.
In this research, author suggests that main track degradation should have 4 (four)
aspects: Track Super-Structural Aspect; Track Sub-Structural Aspect; Track Geometrical
Aspect; and Traffic Aspect, and furthermore, track quality index assessment is therefore
conducted as combination of 3 (three) index investigation: Track’s Irregularity Index
(Track Super-Structure aspect; Sleeper and Rail), Track Settlement Index (Track SubStructure aspect; Ballast and Track Sub-Layers), and Track Geometry Index (Track
Geometrical aspect).
Based on the various literatures review and analysis, the track deterioration
parameters from the four aspects of track super-structure, sub-structure, geometry and
traffic parameters are investigated. Track structural parameters include rail-pad stiffness
and rail type, fastening condition-fastening type, sleeper condition-sleeper type, ballast
conditions-ballast type, and subgrade compaction (Sadeghi and Askarinejad, 2012;
Sadeghi and Askarinejad, 2007). Track geometrical parameters are gauge (trackplane),
8
Simposium XIX FSTPT, Universitas Islam Indonesia, 11-13 Oktober 2016
profile (longitudinal vertical plane), alignment (horizontal plane), cross-level and twist
(transverse vertical plane), sleeper spacing, listring-tamping works, drainage condition and
initial track geometry index (Sadeghi and Askarinejad, 2012; Sadeghi and Akbari, 2006 in
Sadeghi, 2010; Sadeghi and Askarinejad, 2007). Traffic parameters consist of tonnage,
train speed, axle loads and load cycles (Sadeghi and Askarinejad, 2007). New track quality
index should be developed and established by combining these 3 index investigation
including the more complete track deterioration parameters from the four aspects of track
super-structure, track sub-structure, track geometry and traffic parameters.
CONCLUSION
In this paper, TQI application for Indonesian Railway has been reviewed and
various methods to evaluate the track quality have been presented. From the results
obtained in this research, the following conclusions are given.
TQI-Geometry was applicated not only in Indonesian Railway Infrastructure
Maintenance works as stated in PM 32 2011, but also in Indonesian Railway Accident
Investigation by The National Transportation Safety Committee. However, in PM 32 2011,
TQI for railway track is not mentioned and explained as detail as TQI for railway bridge
and tunnel which have been determined based on the classification of deterioration level
i.e. A, B, C, and S and completed with sheet of entry and rating index of degradation
assessment. On the other hands, The National Transportation Safety Committee used 4
parameters (gauge, raising, listring, and superelevation) to obtain the value of TQI and it
classified TQI into 4 sections and converted as track condition category I to IV. The
classification of track condition category is intended as suggestion of improvement and
determination of the maximum speed on the related track. Nevertheless, the result of track
condition classification, in fact, does not represent the whole condition of track. So it is
clearly seen that there is a distinction between TQI application in Indonesian Railway
maintenance regulation and in Indonesian Railway accident investigation.
UK SD Index, Netherlands Q Index, USA Track Roughness Index, FRA Track
Geometry Index, Austrian Railway Track Geometry Index, Canadian Track Quality Index,
SNCF’s Mean Deviation Indices, Chinese Track Quality Index, Polandia J Synthetic
Coefficient, Indian Railways Track Geometry Index, and European Standard EN 13848-5
are some methods to evaluate the track quality. Those methods have mostly concentrated
on one particular aspect of the railway track system. Their results rely only on a limited
number of parameters and in each study they considered only one of many aspects of the
track deterioration. Those methods cannot provide a thorough indication of all influencing
parameters and their role in the track degradation. A thorough appreciation of all the
parameters is needed even if they are seen from different aspects to provide a cost effective
and efficient railway track maintenance.
The author suggests that there are 4 (four) main track degradation aspects: Track
Super-Structural Aspect; Track Sub-Structural Aspect; Track Geometrical Aspect; and
Traffic Aspect, and a new track quality index should be developed and established by
combining 3 (three) index investigation: Track’s Irregularity Index, Track Settlement
Index, and Track Geometry Index. Track structural parameters include rail-pad stiffness
and rail type, fastening condition-fastening type, sleeper condition-sleeper type, ballast
conditions-ballast type, and subgrade compaction. Track geometrical parameters are gauge
9
Simposium XIX FSTPT, Universitas Islam Indonesia, 11-13 Oktober 2016
(trackplane), profile (longitudinal vertical plane), alignment (horizontal plane), cross-level
and twist (transverse vertical plane), sleeper spacing, listring-tamping works, drainage
condition and initial track geometry index. Traffic parameters consist of tonnage, train
speed, axle loads and load cycles.
DAFTAR PUSTAKA
Berawi, et al. 2010. Evaluating Track Geometrical Quality Through Different
Methodologies. International Journal of Technology (2010) 1: 38‐47, ISSN
2086‐9614.
CEN, 2005. Railway Applications –Track – Track Geometry Quality – Part 5: Geometric
Quality Assessment. German version prEN 13848-5:2005.
Hamid, A. and Gross, A. 1981. Track-Quality Indices And Track-Degradation Models For
Maintenance-Of-Way Planning. 60th Annual Meeting of the Transportation Research
Board. Washington District of Columbia, United States.
KNKT (The National Transportation Safety Committee). 2010. Laporan Hasil Investigasi
Kecelakaan Kereta Api Anjlokan Ka 80 Mutiara Timur Km 210+100/200 Petak Jalan
antara Stasiun Kalisat – Stasiun Kotok, Jawa Timur Daop IX Jember. Ministry of
Transportation, Indonesia.
Liu, et al. 2015. Establishment of Track Quality Index Standard Recommendations for
Beijing Metro. Hindawi Publishing Corporation, Discrete Dynamics in Nature and
Society, Volume 2015, Article ID 473830, 9 pages.
Sadeghi, J and Askarinejad, H. 2007. Influences Of Track Structure, Geometry And Traffic
Parameters On Railway Deterioration. IJE Transactions B: Applications, Vol. 20, No.
3, December 2007.
Sadeghi, J and Askarinejad, H. 2012. Application of Neural Networks in Evaluation of
Railway Track Quality Condition. IJE Transactions B: Applications, Vol. 20, No. 3,
December 2012.
Sadeghi, J. 2010. Development of Railway Track Geometry Indexes Based on Statistical
Distribution of Geometry Data. Journal Of Transportation Engineering, ASCE-August
2010.
Sadeghi, J., and Akbari, B. 2006. “Field Investigation on Effect of Railway Track
Geometry Parameters on Rail Wear.” International Journal of Zhejiang University,
Science A, 711, 1846–1855.
Sekretariat Negara. (2011). Peraturan Menteri Perhubungan Nomor PM 32 Tahun 2011
tentang Standar dan Tata Cara Perawatan Prasarana Perkeretaapian. Jakarta,
Indonesia.
Talukdar, K., Arulmozhi, U., Prabhakar, K. & Satyanarayan, 2006. Project Presentation
Improvement of TGI Value by Computer Analysis. Ministry of Railways Indian
Railways Institute of Civil Engineering, India.
10
View publication stats