Dynamics of railway transition zones in soft soils

Dynamics of railway transition zones in soft soils

PROEFSCHRIFT

ter verkrijging van de graad van doctoraan de Technische Universiteit Delft,

op gezag van de Rector Magnificus Prof. ir. K.C.A.M. Luyben,voorzitter van het College voor Promoties,

in het openbaar te verdedigen op vrijdag 13 mei 2011 om 12.30 uur

door Bruno Emanuel ZUADA COELHO

Master of Science in Structures of Civil EngineeringUniversity of Porto, Portugalgeboren te Porto, Portugal

Dit proefschrift is goedgekeurd door de promotor:Prof. dr. ir. F.B.J. Barends

Samenstelling promotiecommissie:Rector Magnificus Technische Universiteit Delft, voorzitterProf. dr. ir. F.B.J. Barends Technische Universiteit Delft, promotorProf. dr. ir. C. Esveld Technische Universiteit DelftProf. dr. M.A. Hicks Technische Universiteit DelftProf. dr. G. Degrande Katholieke Universiteit LeuvenProf. dr. W. Powrie University of SouthamptonDr. L.M.M.S. Caldeira LNECDr. ir. P. Holscher DeltaresProf. ir. A.F. van Tol Technische Universiteit Delft, reservelid

ISBN 978-90-5335-402-5

Copyright c 2010 by B.E. Zuada Coelho

All rights reserved. No part of the material protected by this copyright notice maybe reproduced or utilized in any form or by any means, electronic or mechanical,including photocopying, recording or by any information storage and retrievalsystem, without the prior permission of the author.

Printed in the Netherlands

Abstract

Transition zones in railway tracks are locations of discontinuity in the support, suchas at bridges, culverts and tunnels. These zones are of main concern to railwayinframanagers, since often substantial additional maintenance is required to preserveline, level and ride quality. This extra maintenance increases the exploitation costs,and often causes delays. Despite the importance of transition zones, the fundamentalcauses of their poor performance are not fully understood.

This thesis aims to give new insight in the behaviour of transition zones. Thefirst step consists of the development of a monitoring plan of a real transition zone,located in The Netherlands, where the track on an embankment passes over a culvert.The underground consists of soft soil layers and sand. The measurements have twocomponents. The static behaviour of the structure is monitored during a periodof about ten months. The dynamic response of the track and surrounding soil isassessed during regular train services.

The main observation from the static measurements is that the settlement of thetrack is composed of two different stages. Initially, after maintenance has beenperformed, a significant densification of the ballast occurs, followed by a secondstage related to ongoing settlement of the embankment and peat layers. This causesa differential settlement of the track across the culvert, which has a stiff foundation.

The dynamic behaviour shows that a transition in stiffness between the free trackand the culvert, is not observed for the track, but only on the ballast bed. Thisresult at the track is related to the fact that the sleepers above the approach slabare hanging free, due to the settlement before and after the culvert. Since thehanging gap is significant, the majority of the displacement exhibited by the trackis due to this gap. At the same time, an increase in the axle load occurs within thehanging region, and a constant slapping of the free sleepers into the ballast occurs,which increases the degradation rate. The embankment is found to be moving as arigid body on top of the soft soil layer. The embankment response is quasistatic,and the attenuation of the displacement within the embankment is much smallerthan the expected from literature or analytical solutions.

The second step consists on the assessment of the behaviour by means of a numericalmodel, based on the finite element method. A fair agreement between the experimen-tal and numerical results is found. The numerical analysis showed that the presence

i

ii Abstract

of the slab combined with the fact that the sleepers are hanging causes a stressredistribution at the free end of the approach slab, that aggravates the longtermdeformation of the soil, and increases the differential settlement. The observationswere performed under normal train speed. The validated numerical analysis allowsanalysis of the behaviour at critical train speed, and special recommendations aresuggested.

The maintenance is found to play a key role on the longterm performance of thetransition zone. The standard maintenance procedure aggravates the ongoing settle-ment of the ground, particularly in the proximity of the approach slab. Applicationof slabs to smooth the transition is not recommended any longer, and the mainte-nance procedure at transition zones should be revised.

Contents

Abstract i

List of Figures vii

List of Tables xiii

List of Symbols xv

1 Introduction 1

1.1 Background problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Objective of this study . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Review on the experimental and numerical work in railways 5

2.1 Transition zone behaviour . . . . . . . . . . . . . . . . . . . . . . . . 52.2 Experimental work on railways . . . . . . . . . . . . . . . . . . . . . 6

2.2.1 Free track . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2.2 Transition zones . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.3 Numerical work on railways . . . . . . . . . . . . . . . . . . . . . . . 82.3.1 Free track . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82.3.2 Transition zones . . . . . . . . . . . . . . . . . . . . . . . . . 9

3 Problem description 11

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.2 Field survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.2.1 General outline . . . . . . . . . . . . . . . . . . . . . . . . . . 113.2.2 Results from field surveys . . . . . . . . . . . . . . . . . . . . 123.2.3 Discussion on site investigation . . . . . . . . . . . . . . . . . 14

3.3 Monitoring program . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.3.1 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.3.2 Test setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4 Processing of dynamic measurements 23

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.2 Background problem . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

iii

iv Contents

4.3 Spectral subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.3.1 Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.3.2 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . 29

4.4 Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.4.1 Synthetic case . . . . . . . . . . . . . . . . . . . . . . . . . . 294.4.2 Study on the phase influence . . . . . . . . . . . . . . . . . . 354.4.3 Real application . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

5 Static behaviour 41

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415.2 Results on the static longterm behaviour . . . . . . . . . . . . . . . 41

5.2.1 Track vertical movement . . . . . . . . . . . . . . . . . . . . . 415.2.2 Sleeper gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465.2.3 Horizontal movement of the embankment . . . . . . . . . . . 465.2.4 Pore water pressure variation . . . . . . . . . . . . . . . . . . 48

5.3 Discussion on the longterm behaviour . . . . . . . . . . . . . . . . . 485.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

6 Dynamic behaviour 51

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516.2 May 2008 measurements . . . . . . . . . . . . . . . . . . . . . . . . 51

6.2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526.2.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

6.3 May 2009 measurements . . . . . . . . . . . . . . . . . . . . . . . . . 636.3.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 636.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 636.3.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81

6.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

7 Numerical simulation 87

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 877.2 Analysis description . . . . . . . . . . . . . . . . . . . . . . . . . . . 877.3 Model parametrisation . . . . . . . . . . . . . . . . . . . . . . . . . . 897.4 Preliminary analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 917.5 Assessment of the structure behaviour . . . . . . . . . . . . . . . . . 96

7.5.1 Validation with experimental data . . . . . . . . . . . . . . . 967.5.2 Structure behaviour . . . . . . . . . . . . . . . . . . . . . . . 96

7.6 Parametric study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1067.6.1 Influence of hanging sleepers . . . . . . . . . . . . . . . . . . 1067.6.2 Effect of the approach slab . . . . . . . . . . . . . . . . . . . 1107.6.3 Effect of train configuration and travelling speed . . . . . . . 111

7.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1147.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

Contents v

8 Conclusions 117

Bibliography 121

A Train description 133

B Axle load measurement 135

C VSPT processing 137

C.1 Shear wave velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137C.2 Material damping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

D Infinite beam on inhomogeneous elastic foundation 141

D.1 Problem description . . . . . . . . . . . . . . . . . . . . . . . . . . . 141D.2 Governing equations . . . . . . . . . . . . . . . . . . . . . . . . . . . 141D.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142

Acknowledgements 145

Curriculum vitae 147

List of Figures

3.1 Culvert cross section. . . . . . . . . . . . . . . . . . . . . . . . . . . . 123.2 CPT results: (a) tip resistance (Tip) and pore water pressure (PWP)

for CPT3, (b) tip resistance (Tip) and pore water pressure (PWP)for CPT4, (c) tip resistance (Tip) and pore water pressure (PWP) forCPT7, (d) friction ratio for CPT3, (e) friction ratio for CPT4 and (f)friction ratio for CPT7. . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.3 VSPT results: (a) tip resistance, (b) friction number and (c) shearwave velocity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.4 Ballast thickness and approach slab location, from GPR and trial pitexcavations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.5 Comparison between the design (Holscher and Meijers 2009) and theavailable geometry at site. . . . . . . . . . . . . . . . . . . . . . . . . 15

3.6 Devices position during the dynamic measurements of May 2008: (a)along the track and (b) perpendicular to the track. . . . . . . . . . . 19

3.7 Overview of the monitored site during the dynamic measurements ofMay 2008. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.8 Devices position during the dynamic measurements of May 2009: (a)along the track and (b) perpendicular to the track. . . . . . . . . . . 21

3.9 Monitored site during the dynamic measurements of May 2009: (a)general view, and (b) detail of a sleeper that contains a geophone, anaccelerometer, strain gauges and a void indicator device. . . . . . . . 22

4.1 Transfer function of single and double integration procedure throughtrapezoidal rule. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4.2 Error induced by the presence of noise due to single and double inte-gration through trapezoidal rule. . . . . . . . . . . . . . . . . . . . . 27

4.3 Block diagram of the proposed method. . . . . . . . . . . . . . . . . 304.4 Signal x(n) = x(n) + (n). . . . . . . . . . . . . . . . . . . . . . . . . 324.5 Comparison between analytical and numerical integration for the first

integration step for: a) sample domain, and b) frequency domain. . . 334.6 Comparison between analytical and numerical integration for the sec-

ond integration step for: a) sample domain, and b) frequency domain. 344.7 Influence of the presence of noise in the phase for: a) first and b)

second integration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

vii

viii List of Figures

4.8 Vibrations due to the passage of a train at 114 km/h: a) velocitiesfrom geophone measurements and b) accelerations from accelerometermeasurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

4.9 Influence of the presence of noise in the phase for: a) first and b)second integration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5.1 Average rail level during one maintenance cycle (nine months). Thetrains are travelling from negative towards positive. . . . . . . . . . . 42

5.2 Vertical displacement of the rail during one maintenance cycle: (a)settlement and (b) settlement rate. The distances in between bracketsare defined in accordance with Figure 5.1. . . . . . . . . . . . . . . . 43

5.3 Vertical settlement of pylons located along the rail track during onemaintenance cycle. The distances in between brackets are measuredfrom the middle of the culvert towards the left/east side of the culvert. 44

5.4 Level difference between the left (inner) and right (outer) rail duringone maintenance cycle: (a) along the entire track, and (b) evolutionwith time in four different locations. The distances of the points aredefined in accordance with Figure 5.4a. . . . . . . . . . . . . . . . . 45

5.5 Deformation of the ballast slope towards a more stable configuration. 46

5.6 Estimation of hanging sleeper distance. . . . . . . . . . . . . . . . . 47

5.7 Typical inclinometer result. . . . . . . . . . . . . . . . . . . . . . . . 47

5.8 Changes of pore water pressure. . . . . . . . . . . . . . . . . . . . . . 48

6.1 Comparison of the vertical displacement obtained by a geophone andby the camera during the passage of a ILC train at 130 km/h: (a)without shift and (b) with shift of the geophone data. . . . . . . . . 53

6.2 Comparison of the vertical displacement obtained by a geophone andan accelerometer during the passage of a ILC train at 130 km/h. . . 54

6.3 Vertical sleeper displacement during passage of a IDD train at 114 km/hfor devices: (a) G7 (free track) (b) G3 (approach slab) and (c) G1(culvert). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

6.4 Average peak to peak displacement of the track recorded by geophonesfor different train passages at different speeds. . . . . . . . . . . . . . 56

6.5 Average peak to peak vertical sleeper displacement on the track forgeophones: (a) G7 (free track), (b) G3 (approach slab), (c) G2 (ap-proach slab) and (d) G1 (culvert). . . . . . . . . . . . . . . . . . . . 57

6.6 Average peak to peak vertical displacement for the geophones locatedon the track. The results for G1 are magnified by a factor of 5. . . . 58

6.7 Vertical displacement of the sleeper (G3) and of the approach slab(A16) during passage of a IDD train at 114 km/h. . . . . . . . . . . 59

6.8 Average peak to peak vertical displacement in the middle of the ap-proach slab (A16). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

6.9 Average peak to peak vertical displacement in the embankment onthe left/east side of the culvert at: (a) 1 m (T1) and (b) 3 m (T2)depth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

List of Figures ix

6.10 Average peak to peak vertical displacement in the embankment onthe right/west side of the culvert at: (a) 1 m (A12) and (b) 3 m (T4)depth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

6.11 Comparison of the vertical displacement obtained by a geophone andby the camera with shift for a sleeper located: (a) on the left side(G7) and (b) on the right side (G3) of the culvert. . . . . . . . . . . 64

6.12 Comparison of the Fourier transform (FFT) of the vertical displace-ment obtained for a sleeper located: (a) on the left side (G7) and (b)on the right side (G3) of the culvert. . . . . . . . . . . . . . . . . . . 65

6.13 Comparison of the vertical displacement obtained by a geophone (G9)and by an accelerometer (A7), for a train speed of 96 km/h: (a) inthe time domain and (b) in the frequency domain. . . . . . . . . . . 66

6.14 Comparison of the vertical displacement obtained by a geophone (G9)and by an accelerometer (A7), for a train speed of 66 km/h: (a) inthe time domain and (b) in the frequency domain. . . . . . . . . . . 67

6.15 Dynamic axle loads during passage of a Sprinter T1 train at 96 km/hfor: (a) free track (S1) and (b) approach slab (S2), positions accordingto Figure 3.8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

6.16 Dynamic axle loads and dynamic amplification for: (a), (c) free track(S1) and (b), (d) approach slab (S2), positions according to Figure 3.8. 69

6.17 Frequency response of the axle load during passage of a Sprinter T1train at 96 km/h for two sections, S1 located on the free track andS2 above the approach slab, positions according to Figure 3.8. . . . . 70

6.18 Comparison of the vertical displacement of the sleeper and ballast,during the passage of a Sprinter T1 train at 96 km/h for: (a) freetrack and (b) above the slab. . . . . . . . . . . . . . . . . . . . . . . 73

6.19 Average peak to peak displacement for train passages at 106 km/h:(a) along the track and (b) along the ballast. . . . . . . . . . . . . . 74

6.20 Vertical displacements for the geophones placed on the track duringthe passage of a Sprinter T1 at 96 km/h. . . . . . . . . . . . . . . . 76

6.21 Average dynamic stiffness: (a) on the free track (G8) and (b) abovethe approach slab (G5); and average displacement amplitude: (c) onthe free track (G8) and (d) above the approach slab (G5) for all trainpassages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

6.22 Average ratio between the axle load and the vertical displacement ofthe ballast: (a) on the free track (A10); and (b) above the approachslab (A8), and average displacement amplitude: (c) on the free track(A10) and (d) above the approach slab (A8) for all train passages. . 79

6.23 Vertical displacement within the embankment during the passage ofa Sprinter T1 at 96 km/h: (a) in depth and (b) in transversal direction. 81

6.24 Average dynamic displacement versus train speed for: (a) A1, (b) A2,(c) T3 and (d) T4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

6.25 Average dynamic displacement versus train speed for: (a) A4, (b) A5,(c) T1 and (d) T2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

x List of Figures

7.1 Threedimensional model overview. . . . . . . . . . . . . . . . . . . . 90

7.2 Twodimensional meshes: (a) longitudinal and (b) transversal models. 92

7.3 Effect of element size on: (a) vertical displacement (z) of point C1in the longitudinal model, (b) vertical stress (zz) of point C1 inthe longitudinal model, (c) vertical displacement (z) of point C2in the transversal model and (d) vertical stress (zz) of point C2 inthe transversal model. . . . . . . . . . . . . . . . . . . . . . . . . . . 93

7.4 Mesh and points of analysis for the threedimensional numerical anal-ysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

7.5 Points of analysis in the threedimensional model: (a) longitudinaland (b) transverse views. . . . . . . . . . . . . . . . . . . . . . . . . 95

7.6 Configuration of the Sprinter T1 train. . . . . . . . . . . . . . . . . . 96

7.7 Comparison of the vertical displacement for: a) P6 (A2) and b) P9(A9), according to Figure 7.5. . . . . . . . . . . . . . . . . . . . . . . 97

7.8 Comparison of the vertical displacement: (a) along ballast and (b) indepth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

7.9 Vertical strains (zz) for point P6, located in the ballast. . . . . . . 100

7.10 Ballast response for point P6: (a) displacement (x, y and z)and (b) stress (xx, yy and zz). . . . . . . . . . . . . . . . . 101

7.11 Distribution of: (a) average vertical displacement (z), and (b) av-erage vertical stress (zz), under the sleeper. . . . . . . . . . . . . 102

7.12 Behaviour under the sleeper for: (a) average displacement (x, yand z) and (b) average stress (xx, yy and zz), for analignment located on the embankment (L2). . . . . . . . . . . . . . . 103

7.13 Stress path p q for: (a) point P6 located on the ballast, and (b)point P1 located on the embankment, during the passage of a IDDtrain at 100 km/h. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

7.14 Average dynamic and static vertical displacement (z): (a) alongballast (alignment L4) and (b) in depth (alignment L5). . . . . . . . 105

7.15 Scheme of the hanging distance for the numerical simulation. . . . . 106

7.16 Effect of the hanging distance on the vertical displacement (z) of:(a) sleeper P22 and (b) ballast P7 during the numerical analysis ofan IDD train at 100 km/h. . . . . . . . . . . . . . . . . . . . . . . . 107

7.17 Effect of the hanging distance on the ballast (alignment L4) for: (a)average vertical displacement (z) and (b) average vertical stress(zz) during the numerical analysis of an IDD train at 100 km/h. 108

7.18 Vertical displacement (z) for sleepers P25, P27 and P30, duringthe numerical analysis of an IDD train at 100 km/h. . . . . . . . . . 109

7.19 Effect of hanging sleepers on the vertical displacement (z) of thesoil, during the numerical analysis of an IDD train at 100 km/h. . . 109

7.20 Effect of the presence of slab on the ballast (alignment L4) for: (a)average vertical displacement (z) and (b) average vertical stress(zz), during the numerical analysis of an IDD train at 100 km/h. 110

List of Figures xi

7.21 Effect of the presence of slab for the points located under the ap-proach slab: (a) average vertical displacement (z) and (b) averagevertical stress (zz), during the numerical analysis of an IDD trainat 100 km/h. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

7.22 Effect of train speed and configuration on the average vertical dis-placement (z) for: (a) P6, (b) P7 and (c) P8. . . . . . . . . . . . . 113

7.23 Effect of train speed and configuration on the average vertical dis-placement (z) of P1, located in the embankment. . . . . . . . . . 114

7.24 Effect of train speed and configuration on the dynamic amplificationof the vertical displacement (z) of P6, located in the ballast. . . . 115

A.1 Train types measured during the dynamic measurements of 2008 and2009: a) IDD, b) ICM, c) ILC, d) Mat V and e) Sprinter. . . . . . . 134

B.1 Strain gauges: a) installation on the rail web and b) Wheatstonebridge circuit for each active strain gauge. . . . . . . . . . . . . . . . 136

C.1 Crosscorrelation method: a) signals x and y and b) xy . . . . . . . 138

D.1 Beam with stiffness difference. . . . . . . . . . . . . . . . . . . . . . . 141D.2 Vertical displacement when the load is moving from a soft to a stiff

spring when the load is located at: a) x = 20 m, b) x = 0 m, andc) x = 20 m from the discontinuity point. . . . . . . . . . . . . . . . 143

D.3 Vertical displacement when the load is moving from a stiff to a softspring when the load is located at: a) x = 20 m, b) x = 0 m, andc) x = 20 m from the discontinuity point. . . . . . . . . . . . . . . . 144

List of Tables

3.1 Maintenance during the period of interest. . . . . . . . . . . . . . . . 173.2 Train information during the dynamic measurement of May 2008.

The detailed characteristics of the train can be found in Appendix A. 183.3 Train information during the dynamic measurement of May 2009.

The detailed characteristics of the train can be found in Appendix A. 20

4.1 Normalized meansquare error due to the integration procedure. . . 334.2 Normalized meansquare error due to the integration procedure for

the displacement in the ground due to a train passage at 114 km/h. 39

6.1 Percentage of the average dynamic axle load that is transmitted tothe left (inner) and right (outer) rail. . . . . . . . . . . . . . . . . . . 71

6.2 Average peak to peak displacement during May 2008 and May 2009dynamic measurements. . . . . . . . . . . . . . . . . . . . . . . . . . 72

6.3 Estimative of the hanging sleeper distance. . . . . . . . . . . . . . . 75

7.1 Material parameters. . . . . . . . . . . . . . . . . . . . . . . . . . . . 907.2 Material damping. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 917.3 Influence of the boundary distance on the vertical displacement (z)

and vertical stress (zz), for points C1 and C2. . . . . . . . . . . . . 947.4 Influence of timestep on the results for point P6 . . . . . . . . . . . 967.5 Train load for a Sprinter T1 at 96 km/h derived from the strain gauge

data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 997.6 Train loads for numerical simulation. . . . . . . . . . . . . . . . . . . 111

A.1 Train description. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

xiii

List of Symbols

Latin

a Attenuation coefficient for dampingA Uniaxial accelerometer used during the measurements May 2008A0 Amplitude of the shear waveAx Horizontal displacement induced by shear wave propagationA Uniaxial accelerometer used during the measurements May 2009d DampingDijkl Constitutive tensorDs Material damping due to shear wavee ExponentialE Young modulusE{} Expectationf External/body forceF FrequencyFs Acquisition frequencyg Gravity forceG Uniaxial geophone used during the measurements May 2008G Uniaxial geophone used during the measurements May 2009G Shear modulusGA Amplification gainGF Gauge factorH(ej) Transfer functionj Imaginary numberk Hydraulic conductivityks Wave number of the shear wavel Distance between two accelerometers in the VSPT testL Alignment for the numerical analysism Indexn Soil porosity and indexN Normal distributionp Isotropic fluid pressureq Specific discharge

xv

xvi List of Symbols

S Strain gauge section during the measurements May 2009T Triaxial accelerometer used during the measurements May 2008T Triaxial accelerometer used during the measurements May 2009T Periodvi VelocityV Strain gauge voltagevs Shear wave velocityui Displacementt Timex(n) Pure signalx(n) Signal x(n) with phase contaminated by noisex(n) Signal x(n) contaminated with noisex(n) Estimation of signal x(n)x(n) Estimation of signal x(n) with correctionsX(ej) Frequency representation of the signal x(n)X(ej) Frequency representation of the signal x(n)

X(ej) Frequency representation of the signal x(n)

X(ej) Frequency representation of the signal x(n)y(n) Signaly Complex conjugated of yz Depthz(n) Signal

Greek

Imaginary part of the complex wave number Water compressibilityw Volumetric weight of the waterij Delta Kronecker Strain gauge extension(ej) Spectrum of the error introduced by noiseij Strain tensorvol Volume changeij Strain rate tensor Attenuation coefficient due to geometrical damping Lame constant Lame constant(ej) Average noise spectrum Poisson ratio Material density(n) Noise(ej) Noise spectrumij Total stress tensorij Effective stress tensor

xvii

ij Effective stress rate tensor Shift between two signalsxy Cross correlation between the random signals x and y Angular frequency

Abbreviations

BEM Boundary element methodCPT Cone penetration testFDM Finite difference methodFEM Finite element methodGPR Ground penetration radarICM Intercity single deck train set train typeIDD Intercity double deck train set train typeIEM Infinite element methodIIR Impulsive infinite response filterILC Intercity locomotive with carriages train typeMat V Local train typeNMSE Normalized meansquare errorPWP Pore water pressureSprinter Sprinter train typeVSPT Vertical seismic penetration test

Chapter 1

Introduction

1.1 Background problem

The train as an efficient mass transport system has been revitalized in the past twodecades all over the world. The reappraisal of the railway transport is related withhigher safety, reliability, low air pollution, and the high speeds that are achievablewith modern trains that allow the establishment of fast connections.

In Europe a highspeed network is available and being expanded. In China the rail-way network is expanding rapidly as more than 1000 km of new lines are constructedeach year (Okada 2007). In the United States, after a well received connection be-tween New York and Washington D.C., other lines were planned and are being built(Keer and Bathurst 2001).

After the initial effort to build a railway track, significant maintenance costs existduring the exploitation of the line. According to Zhai et al. (2004) and Schmitt(2006), maintenance represents between 40 to 75 % of the total operation costs.Within maintenance, a great share is spent to preserve safety and riding quality upto high standards. In the Netherlands it is estimated that 40 % of the maintenancecosts are associated with preserving track geometry (Holscher and Meijers 2007).Improvement of track maintenance will lead to a reduction of the total life costs,with major benefits for railway system owners, operators, and users.

One of the major sources of problems for the track geometry are transition zonesbetween the normal free track and stiff structures such as bridges, tunnels andculverts. According to Sasaoka and Davies (2005), about $200 millions are spentannually on US railways on track transition maintenance, while in Europe aboutAC85 millions are expended (Hyslip et al. 2009). In the Netherlands maintenanceof transition zones occurs up to two to four times more often than on the freetrack (Holscher and Meijers 2007). Due to the high traffic intensity of the Dutchrailway network, being one of the busiest in the world, the time available to performmaintenance is limited. Therefore a thorough maintenance scheme for the network

1

2 1 Introduction

is required, where all extra maintenance is performed at a high cost, by reducingthe capacity of the network or rearranging the upcoming maintenance schemes.Transition zones represent an area where significant improvements might be achievedby understanding the mechanics that are contributing for the acceleration of trackdegradation. This will lead to an improvement of the design of new structures anda more efficient maintenance of the existing ones.

1.2 Objective of this study

The aim of the present study is to increase the knowledge on the behaviour oftransition zones. From literature (Frohling et al. 1996, Esveld 2001, Keer andBathurst 2001, Li and Davis 2005, Lundqvist et al. 2006, Jenks 2006, Banimahdand Woodward 2007, Hyslip et al. 2009) the poor behaviour of transition zones isdue to two factors:

the difference in stiffness between the free track and the structure;

the differential settlement that occurs between the free track and the struc-ture.

However, these two factors are not independent. The stiffness difference causeshigher interaction forces between the train wheel and the rail, which leads to anincrease of the differential settlement. At the same time, this differential settlementmagnifies interaction force, which causes the differential settlement to become higherin a selfperpetuating mechanism. A solution suggested by several authors (Hunt1997, Esveld 2001, Keer and Bathurst 2001, Zarembski and Palese 2003, Lundqvistet al. 2006, Banimahd andWoodward 2007, Lei and Zhang 2010), consists of creatinga smooth transition in stiffness between the free track and the structure. This wouldminimize the increase of the interaction force, and hence the deterioration rate oftransition zones should be reduced.

On the other hand, experimental studies reveal that creating a stiffness transitionbetween the free track and the structure, does not lead to an improvement in thebehaviour of transition zones (Li and Davis 2005, Plotkin and Davis 2008, Li et al.2010). In the Netherlands, the standard solution for the construction of transitionzones consists on placing two approach slabs to perform a smooth increase of thestiffness. However, they remain problematic places on the network demanding asignificant amount of extra maintenance (Holscher and Meijers 2007).

In order to improve on the knowledge on this topic, a DelftCluster project startedin 2007 to study the performance of a typical Dutch transition zone. The projectinvolved the monitoring of a structure during a period of about one year, togetherwith the numerical analysis of it. The monitoring results provide a detailed insighton the true behaviour of the transition zone and allowed the calibration of thenumerical analysis. Simultaneously, the numerical part permits the extension of theanalyses of the transition zone into other scenarios.

1.3 Outline of the thesis 3

1.3 Outline of the thesis

This thesis contains eight chapters. In Chapter 2 the existent work on monitoringand modelling of railways, and in particular of transition zones, are discussed. Chap-ter 3 presents a description of the conditions of the studied transition zone, togetherwith the description of the monitoring plan. Chapter 4 contains a description of themethodology developed for the processing of the dynamic measurements, based onspectral subtraction. The results of the static measurements are presented in Chap-ter 5. Chapter 6 presents the results of the dynamic measurements, comprisingregular train services. The numerical analysis is presented in Chapter 7. In Chapter8 the findings of the work are summarized and recommendations are suggested.

Chapter 2

Review on the experimental

and numerical work in

railways

2.1 Transition zone behaviour

Transition zones are intended to provide a smooth circulation of the train, minimiz-ing the impact of discontinuities that exist along the track. When a train is movingfrom an embankment towards a stiff structure, such as a bridge, tunnel or culvert, anabrupt change in the available stiffness occurs, which increases the dynamic wheelloads, and hence the rate at which the track is affected. At the same time a dif-ferential settlement between the track placed in the embankment and above thestructure starts to take place, generating differences in the track geometry, whichcauses an increase in the interaction forces between the train wheel and the rail(Frohling et al. 1996, Hunt 1997, Sasaoka and Davies 2005, Lundqvist et al. 2006,Jenks 2006, Banimahd and Woodward 2007, Hyslip et al. 2009, Lei and Zhang 2010,Li and Berggren 2010). This leads to a magnification of the differential settlement,that in turn causes an increase in the interaction force, on a mechanism that repeatsitself until maintenance is performed. At this point, the track initial geometry isrestored, and a new degradation cycle is initiated by the stiffness difference. In ad-dition to these two factors, Li and Davis (2005) and Jenks (2006) mention the poorperformance of transitions zones to geotechnical defects, such as bad compactionof the embankment, drainage issues, or poor consolidation of the ground where thetrack is laying. In reality, these factors are related. Geotechnical defects, such asconsolidation, might propel the initiation of the differential settlement, while thepoor compaction of the embankment leads to a reduction of the available stiffness,with the consequences mentioned before.

The direction of train circulation also plays a role. As the train moves from a lower to

5

6 2 Review on the experimental and numerical work in railways

a higher stiffness large dynamic loads develop on the rail located on the stiff side andwheel. When the train travels from the stiff towards a lower stiffness, the train wheelfalls off the stiff support, causing large dynamic loads on the track (Jenks 2006).According to Lundqvist et al. (2006) and Li and Wu (2007), higher interactionloads are generated as the train moves from a soft towards a stiffer structure thanthe opposite. The authors based their judgement on numerical simulations, withoutpointing at a reason.

Several procedures have been proposed to address the problem of transition zones,by creating a smooth stiffness transition between the free track and the stiff struc-ture (Hunt 1997, Esveld 2001, Zarembski and Palese 2003, Lundqvist et al. 2006,Banimahd and Woodward 2007, Lei and Zhang 2010), or by reducing the stiffnessof the track above the structure (Keer and Bathurst 2001, Sasaoka and Davies 2005,Hyslip et al. 2009). Though some authors suggest improvements by these solutions,experimental results from Li and Davis (2005), Li et al. (2010) and Plotkin andDavis (2008) show that by creating a smooth stiffness transition between the trackand the structure no real improvement in the longterm is obtained. The trackdegradation ratio at the transition zone is still higher than the observed for theregular track. Li and Davis (2005) and Li et al. (2010) show that, for four differentbridges in the U.S., the vertical settlement of the track located in the transition zoneis about 30 % higher than the one registered for the free track. In the Netherlands,for the past thirty years, the usage of approach slabs has been the standard solutionfor the construction of transition zones (Holscher and Meijers 2007). Again, signifi-cant amount of additional maintenance is required to mantain track quality at theseparticular spots.

2.2 Experimental work on railways

2.2.1 Free track

In recent years, the experimental studies in railways has increased. Most of thisgrowth consists of a reactive response to problems that arose during regular traintraffic, and measurements were the chosen tool to identify the causes. An exampleis the case of Ledsgard in Sweden, where significant displacement of the track owingto train traffic were encountered (Adolfsson et al. 1999, Madshus and Kaynia 1999,Madshus and Kaynia 2000, Holm et al. 2002). The main reason for the excessivevibrations was the presence of a very soft organic soil layer. In earlier time, in theNetherlands, Cuperus and de Nie (1948) and de Nie (1948), presented measurementsdue to static and dynamic effects of train passages. In this case, the authors concernregarded the stability of the track embankment.

Due to the development of train technology, the current trains can reach higherspeeds with higher axle loads. This demands an assessment of the suitability ofcurrent lines for the new loading cases. Therefore several authors (Kolisoja andMakela 2001, Picoux et al. 2003, Bowness et al. 2007, Priest and Powrie 2009,

2.2 Experimental work on railways 7

Kouroussis et al. 2011, Priest et al. 2010) report measurements on the behaviourof railway tracks under regular and heavy train traffic. At the same time, receptiontests have been performed on new highspeed lines before opening to regular trainservices (Degrande and Schillemans 2001, Auersch 2005, ADIF 2005, Lombaert andDegrande 2009, Galvn and Domnguez 2009). The upgrading of existing lines toafford the new types of traffic has also been tested by comparing the gain obtainedby reinforcement operations (SNCF 2005a, SNCF 2005b).

The effect of the train speed has been evaluated by several authors. de Nie (1948),Degrande and Schillemans (2001), ADIF (2005), SNCF (2005b) and Priest andPowrie (2009) report an increase of the vibration level with the train speed, forspeeds below the critical value. This critical value corresponds to the phase veloc-ity of the coupled tracksoil system (Madshus and Kaynia 2000). For the case ofa homogeneous halfspace, this critical velocity is the Rayleigh wave velocity of theentire subsoil (Krylov 1995, Frybra 1999). In the case of a track on top of an elastichalfspace, Dieterman and Metrikine (1997) show that there are two critical speeds,one corresponding to the Rayleigh wave velocity of the medium and a second slightlysmaller, function of the track stiffness. If the properties change within the soil, asin layered soils, the medium is dispersive and the critical speed becomes function ofthe frequency. The calculation of the critical speed requires solving the eingenvalueproblem of the system (Wolf 1985, Auersch 1994).

Kolisoja and Makela (2001) report the influence of the axle load on the magnitudeof the displacements. The attenuation in depth is shown in Picoux et al. (2003),SNCF (2005a) and Priest et al. (2010), while Degrande and Schillemans (2001),Galvn and Domnguez (2009) and Kouroussis et al. (2011) present the attenuationof vibrations with the distance to the track.

2.2.2 Transition zones

The experimental work in transition zones is rather scarce. So far, no real insightinto the long and shortterm effects has been made in a consistent manner. Previ-ous investigations into transition zone performance have concentrated on measuringstatic geometric changes in the track level. In a study based on results from fourdifferent types of transition zones, Li and Davis (2005) and Li et al. (2010) showedthat the track within the approach zones settled more than on the structure andon the free track. At the same time, the authors pointed that none of the mitiga-tion techniques improved the performance of the transition zones. Similar findingsabout the inefficiency of transition zone performance were found by Plotkin andDavis (2008). Kolisoja and Makela (2003) focused on the mechanical behaviour of areinforced concrete culvert, but very little information on the soil or track dynamicbehaviour was reported. Keer and Bathurst (2001) and Hyslip et al. (2009) sug-gested that an improvement on the behaviour of transition zones might be achievedby reducing the stiffness above the structure. Keer and Bathurst (2001) use pads tomatch the displacement obtained in the free track with the one above the structure,therefore no transition will be available. Hyslip et al. (2009) report a replacement

8 2 Review on the experimental and numerical work in railways

of an opendeck for a ballastdeck track on a bridge, where due to the reduction oftrack stiffness above the bridge, the problems at the transition zone were reduced.Though both authors present promising results, no real insight on the longtermbehaviour is available, and hence the cumulative degradation of the transition dueto regular train traffic is not addressed.

In Spain (CEDEX 2005, Adif-Cedex 2009), two transition zones were improved byinjecting stable mixtures of cement into the embankment. For both transitionsafter the operation a more gradual variation of the stiffness was achieved, and animprovement was found, but no evaluation on the longterm behaviour was reported.

2.3 Numerical work on railways

2.3.1 Free track

Numerical methods are the most used tool to evaluate the performance of railways.Often their development is made in parallel with experimental work, which allows foran evaluation and calibration of the numerical method. Significant work is availablein the semianalytical domain, where the rail is considered to be a beam, and thetrack and ground are considered by means of springs, in a Winkler type (Grassieand Cox 1985, Krylov 1995, Esveld 2001, Paolucci et al. 2003, Lei and Rose 2008,Li and Berggren 2010), or by an elastic or viscoelastic halfspace, or a multilayerhalfspace (Segil and Waters 1994, Suiker et al. 1998, Kaynia et al. 2000, Picoux andLe Houedec 2005, Lombaert et al. 2006, Cai et al. 2008a, Sun et al. 2009). Oftena close form solution of the system of equations is not possible, and a numericalprocedure is necessary for solving the system of equations. A recent review onmethods for simulation of moving loads on road and railway track is available inBeskou and Thedorakopoulos (2011). These models present some restrictions due tothe assumptions that are made. The soil layering is limited, and the properties needto be constant within the layer. With exception of the work of Kaynia et al. (2000)where nonlinear behaviour is accounted for by the equivalent linear method, allthe remaining references assume elastic or viscoelastic material behaviour, keepinggeometry and material properties invariant.

Therefore, numerical methods present a branch for the exploration of more complexgeometries, or the usage of more advanced constitutive models. Several approachesmight be followed for the field discretization, namely Finite Element Method [FEM](Desai and Siriwawrdane 1982, Shahu et al. 1999, Lundqvist and Dahlberg 2005,Kettil et al. 2008, Yang et al. 2009, Priest et al. 2010), Boundary Element Methodcombined with FEM [BEM/FEM] (Auersch 2005, Lombaert et al. 2006, Sheng et al.2006, Galvn and Domnguez 2007, Chebli et al. 2008, Galvn and Domnguez 2009),Finite Difference Method [FDM] (Smith et al. 2007) or Infinite Element Methodcombined with FEM [IFM/FEM] (Costa et al. 2010, Kouroussis et al. 2011). Mostof the work assumes linear elasticity for soil behaviour. Exception is made by thework of Costa et al. (2010), in which the nonlinearity is assumed by the equivalent

2.3 Numerical work on railways 9

linear method, and Desai and Siriwawrdane (1982) where several constitutive nonlinear models can be selected. Additionally, all the models have been validated bycomparison with experimental results, with exception of the works of Lundqvistand Dahlberg (2005) and Kettil et al. (2008). In general a fair agreement betweennumerical and experimental results was found.

2.3.2 Transition zones

On transition zones, similar groups can be made as for the free track. Several authors(Frohling et al. 1996, Hunt 1997, Lei and Mao 2004, van Dalen 2006, Li and Wu2007, Lei and Zhang 2010, Li and Berggren 2010) used semianalytical methods tosolve a Winkler type supported beam where a difference in stiffness was available.This stiffness variation is made by changing the properties of the springs. Withexception of van Dalen (2006) all the other authors consider an interaction betweena train wheel and the rail. A general finding is that the interaction force increasesdue to the change of stiffness. van Dalen (2006) just considered a constant movingload travelling over a stiffness discontinuity. The author found that when a traincrosses a discontinuity in stiffness part of the energy is radiated backwards.

Numerical work with transition zones involving FEM (Kolisoja and Makela 2003,Lundqvist et al. 2006, Alves Ribeiro et al. 2007, Banimahd and Woodward 2007)and FDM (Smith et al. 2006). Lundqvist et al. (2006) and Alves Ribeiro et al. 2007showed that the interaction force increases with the stiffness variation. Lundqvistet al. (2006) and Banimahd and Woodward (2007) studied the effect of making angradual variation in the stiffness. The authors concluded that the interaction forcewould be reduced, and hence the problems caused by the transition zone would bemitigated. Smith et al. (2007) found that the displacement and stress increasewith the train speed, and that the embankment stiffness conditions the magnitudeof the vertical displacements of the track. Kolisoja and Makela (2003) focusedon the mechanical behaviour of a reinforced concrete substructure, but very littleinformation on the soil or track dynamic behaviour was reported.

From the analysis of the literature, it can be concluded that no real experimentalwork on transition zones comprising both dynamic and static response exists. Theavailable studies focused mainly on the immediate response of the structure afterapplication of mitigation techniques, and hence no real evaluation of the performanceon the long term is available. Additionally, no thorough experimental study onthe dynamic behaviour of transition zones, comprising several train passages andmeasurements on the embankment, track and structure, is available. Therefore, thiswork covering all aspects aims to improve the understanding of the mechanismsthat are governing the behaviour of transition zones and at the same time offers thepossibility of benchmarking numerical models developed by other authors.

Chapter 3

Problem description

3.1 Introduction

The transition zone that is studied during the present work is located in the centre ofthe Netherlands, in the railway connection between the cities of Gouda and Utrecht.It is a structure dated from 1995 that has been built as a widening of the old railwayline, built in 1855. The natural ground mainly consists of soft soil, typical for the areawhere the structure is inserted. The transition zone represents the link between asand embankment and a piled concrete culvert, consisting of two reinforced concreteslabs of 4 m each, with 0.30 cm thickness, hinged on either sides of the culvert. Onthe embankment side no special support is provided to the slabs. The culvert is a2 2 m reinforced concrete box, that allows the water flow between both sides ofthe track. The piles that support the culvert are extended until the pleistocene sandlayer. A schematic cross section is given in Figure 3.1.

3.2 Field survey

3.2.1 General outline

A field survey, comprising CPT (cone penetration test) and VSPT (vertical seismicpenetration test), was perform at the location. These tests were used as a firstoverview of the general condition at the site, and allowed to gather informationabout the soil layering, as well as information about the soil properties. Additionally,GPR (ground penetration radar) measurements were performed, in order to collectinformation on the location of the concrete elements, approach slabs and culvert,and an estimation of the ballast thickness.

11

12 3 Problem description

Figure 3.1: Culvert cross section.

3.2.2 Results from field surveys

CPT test

Figure 3.2 presents the results of three CPTs (CPT3, CPT4, CPT7) performed atthe site, at about 1 m from the track, where ballast is no longer available. Tests3 and 7 were performed on the right/west side of the culvert (according to Figure3.1), at about, respectively, 6 and 4 m from the centre of the culvert, while test 4was located at about 7 m from the centre towards the left/east side, as indicated inFigure 3.1.

The discrepancies within the tip resistance for the first meters indicate that theembankment is quite heterogeneous. The very low cone resistance together with theexcess of pore water generation and the high friction ratio confirm the existence ofa soft peat/clay layer with poor mechanical properties (between 4 and 11 m depth).Additionally, a thin sand layer at about 8 m depth is identified as well as the sandlayer for the pile foundation (11 12 m depth).

The phreatic level was found to be at 2 m depth from the reference level, whichcoincides with the water level inside the culvert.

VSPT test

The VSPT (Figure 3.3) was performed in the track, on the left/east side of theculvert, according to Figure 3.1, and shows velocities for the shear wave velocity of

3.2 Field survey 13

0 10 20 30 40

0

2

4

6

8

10

12

14

16

Tip resistance [kPa]

Dep

th fr

om th

e to

p of

the

balla

st [m

]

0 0.1 0.2 0.3 0.4Pore water pressure [kPa]

(a)

0 10 20 30 40

0

2

4

6

8

10

12

14

16

Tip resistance [kPa]

Dep

th fr

om th

e to

p of

the

balla

st [m

]

0 0.1 0.2 0.3 0.4Pore water pressure [kPa]

TipPWP

(b)

0 10 20 30 40

0

2

4

6

8

10

12

14

16

Tip resistance [kPa]

Dep

th fr

om th

e to

p of

the

balla

st [m

]

0 0.1 0.2 0.3 0.4Pore water pressure [kPa]

(c)

0 2 4 6 8 10 12

0

2

4

6

8

10

12

14

16

Friction ratio []

Dep

th fr

om th

e to

p of

the

balla

st [m

]

(d)

0 2 4 6 8 10 12

0

2

4

6

8

10

12

14

16

Friction ratio []

Dep

th fr

om th

e to

p of

the

balla

st [m

]

(e)

0 2 4 6 8 10 12

0

2

4

6

8

10

12

14

16

Friction ratio []

Dep

th fr

om th

e to

p of

the

balla

st [m

]

(f)

Figure 3.2: CPT results: (a) tip resistance (Tip) and pore water pressure (PWP) for CPT3,(b) tip resistance (Tip) and pore water pressure (PWP) for CPT4, (c) tipresistance (Tip) and pore water pressure (PWP) for CPT7, (d) friction ratiofor CPT3, (e) friction ratio for CPT4 and (f) friction ratio for CPT7.

14 3 Problem description

0 10 20 30 40

0

2

4

6

8

10

12

14

16

Tip resistance [MPa]

Dep

th fr

om th

e to

p of

the

balla

st [m

]

(a)

0 2 4 6 8 10 12

0

2

4

6

8

10

12

14

16

Friction ratio []

Dep

th fr

om th

e to

p of

the

balla

st [m

]

(b)

0 40 80 120 140 160

0

2

4

6

8

10

12

14

16

Shear wave velocity [m/s]

Dep

th fr

om th

e to

p of

the

balla

st [m

]

(c)

Figure 3.3: VSPT results: (a) tip resistance, (b) friction number and (c) shear wave veloc-ity.

about 60 to 80 m/s for the soft layer and about 140 m/s for the sand and embank-ment layers. Again the embankment evidences heterogeneity on the tip resistance,together with the presence of a sand layer in between the peat/clay formation. Themethodology for the processing of the signals is described in Appendix C.

GPR test

The ballast thickness was estimated by means of GPR together with trial pit ex-cavations (GPR was calibrated with the slab depths from the trial pits). Initially,according to the design drawings, the ballast was placed with 30 cm thickness, andthe slab at 3 % inclination. Nowadays, as shown in Figure 3.4, the ballast thicknesscan reach 80 cm on top of the approach slabs. There is some discrepancy betweenthe trial pits and the GPR results regarding the ballast thickness, which is due to thefact that there is no clear division between the ballast and the embankment. Afterseveral years of maintenance the ballast has penetrated into the sand layer, creatinga region where a mixture between the two materials exist. Figure 3.5 presents thecomparison between the designed and the existing geometry of the approach slab,showing a slab inclination reaching 13 %.

3.2.3 Discussion on site investigation

In the previous sections the results from the standard field survey were presented.It is found that the track is located on top of a heterogeneous embankment of about4 m thickness, on top of a clay/peat soft layer of about 7 m thick, which contains in

3.2 Field survey 15

25 20 15 10 5 0 5 10 15 20 250.2

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Distance to the middle of the culvert [m]

Dep

th fr

om th

e to

p of

the

balla

st [m

]

Approach slab GPRBallast GPRApproach slab trial pitBallast trial pit

Figure 3.4: Ballast thickness and approach slab location, from GPR and trial pit excava-tions.

Figure 3.5: Comparison between the design (Holscher and Meijers 2009) and the availablegeometry at site.

between a thin sand layer of variable thickness. The general mechanical propertiesof the soil are poor, especially regarding the soft layer. It is found that the stiffnessproperties of the sand layer in the soft layer formation are similar to the ones fromthe embankment (shear wave velocity of about 140 m/s).

Possible resonance effects, might occur when the train speed reaches a critical speed.This critical train speed for layered soils is frequency dependent, and hence, itsoccurrence is dependent on the loading conditions. However, in the case of a softhalfspace with a thin stiff layer on the top, which resembles a simplification of thesite, the first mode of the critical train speed will tend for high frequencies to theRayleigh wave velocity of the first layer, while for low frequencies, the deeper layersbecome more important, and the critical speed tends asymptotically to the Rayleighwave velocity of the halfspace (Strobbia 2002). For this case, the minimum shearwave velocity of the soft layer is 53 m/s 190 km/h, and the Rayleigh wavewill be about 95 % of this value, 50 m/s 181 km/h (Das and Ramana 2011).

16 3 Problem description

The maximum train speed allowed at site is 140 km/h 40 m/s, which seems torepresent a sufficient distance from the critical value. However, in reality the groundconditions do not correspond exactly to a halfspace with a thin layer at the top, soa careful analysis regarding the influence of the train speed is needed, in order toevaluate possible resonance phenomena.

A high thickness of ballast was found, reaching 80 cm, while originally it has beenplace with a thickness of 30 cm. This is the result of years of maintenance thatmainly comprises tamping and reballasting of the track. Moreover, the slab freeend shows a significant rotation over the fixed end on the culvert. This settlementmight be due to the consolidation of the soft layer, together with the localized effectof stress concentration on the free end of the slab.

3.3 Monitoring program

3.3.1 Objective

In order to gather more insight on the behaviour of the transition zone, a monitoringprogram was defined that comprised both long and shortterm measurements. Thelongterm measurements involved a period of about ten months (between September2008 and June 2009) and focused on the static behaviour of the track and surround-ing soil. The goal was to evaluate the influence of the cumulative loading on thedegradation of the structure, as well as the effect of the maintenance cycle. Theshortterm measurements concentrated on the dynamic response of the track andsoil, during the passage of several types of trains. The objective was to make anassessment of the structure response when submitted to standard loading conditions,and evaluate the influence of several parameters, such as train speed, configurationor load magnitude. The shortterm measurement took place during two differentdays of regular train services, the first in May 2008 and the second in May 2009.

Table 3.1 presents the period of measurements together with the maintenance times.Both dynamic measurements were performed at the end of the maintenance cycle,and the longterm measurements enclose a full maintenance cycle. In the nextsection both test setups will be defined.

3.3.2 Test setup

Static longterm measurement

The longterm measurements comprise the determination of both vertical and hori-zontal movement of the track and embankment, together with the determination ofthe pore water pressures on both sides of the culvert.

The vertical motion of the track was determined by means of levelling of the unloadedtrack. The levelling was performed during October 2008 and June 2009, on a monthlybasis, by means of an electronic theodolite.

3.3 Monitoring program 17

Table 3.1: Maintenance during the period of interest.

Dates Maintenance Staticmeasurements

Dynamicmeasurements

06Mar081 Performed04May08 First test08Jul08 Performed08Sep08 Inclinometer

starts07Oct08 Performed Levelling starts24Nov08 PWP starts24Jan09 Levelling starts21Apr09 Hanging

sleepers starts05May09 Hanging

sleepers stopsSecond test

08Jun09 PWP stops12Jun09 Levelling stops30Jun09 Performed

1 This date is not exact. Maintenance was performed between 06Mar08 and 03May08.

The horizontal movement of the embankment was monitored with an inclinometeron a monthly basis. The inclinometer was placed in eight different boreholes thatwere located on the ballast alongside the track.

The pore water pressure was monitored by two piezometers located within the em-bankment on both sides of the culvert (Figure 3.6). The results regarding the porewater pressure are available for the time enclosed between November 2009 and June2009, for every halfhour.

The likelyhood of a gap between the sleepers and the ballast was assessed by meansof a void indicator device Vortok International (2007). The devices were installedbefore the second dynamic test, being the measurements performed six times, inregular spaces, up to the end of the second dynamic test. The accuracy of thisdevice is poor, allowing only a qualitative rather than quantitative evaluation of thehanging distance between sleeper and ballast.

Dynamic shortterm measurement May 2008

The first dynamic measurements were performed in May 2008, during regular trainpassages. A setup involving eleven geophones (G), three triaxial (T) and six uni-axial (A) accelerometers and one highspeed video camera was defined, in order togather information on the dynamic behaviour of track, approach slabs and embank-ment. Most of the geophones were directly connected to the upper surfaces of thewooden sleepers, except for geophones G8 to G11 which were placed in the soil, G8

18 3 Problem description

Table 3.2: Train information during the dynamic measurement of May 2008. The detailedcharacteristics of the train can be found in Appendix A.

Train Type Number of trainpassages

Range ofvelocities[km/h]

Static axle load[kN]

Intercity doubledeck train set

(IDD)

3 114130 126192

Intercity singledeck train set

(ICM)

4 98129 97143

Intercitylocomotive withcarriages (ILC)

2 126130 160215

Local train(Mat V)

5 89114 95136

on top of the approach slab and G9G11 within the embankment. All geophoneswere orientated to measure vertical motion except for geophone G8, which mea-sured the horizontal longitudinal motion. The triaxial accelerometers T1, T2 andT3 were placed within the soil, at about 1 m (T1) and 3 m depth (T2 and T3).Thehigh speed video camera was used to record sleeper displacements directly as de-scribed by Bowness et al. (2007), and validate the displacements calculated fromthe measured geophone velocities, and indirectly from the accelerometers, by meansof comparing the displacements obtained through geophone G9 and accelerometerA16. A overview of device positioning is available in Figure 3.6.

In total fourteen trains passages of different types and configurations were monitoredas shown in Table 3.2. In Appendix A, a detailed description of train types ispresented.

Dynamic shortterm measurements May 2009

A second dynamic measurement campaign was performed in May 2009, during aday of standard train services. A new disposition of devices was applied in order toimprove and validate the conclusions found during the first dynamic measurement.Besides the use of ten geophones (G), ten uniaxial (A) and four triaxial (T) ac-celerometers, two locations on the rail were instrumented with strain gauges (S) tomeasure the dynamic axle load. The overbar is used to distinguish the device fromthe first dynamic measurement. All the geophones were placed on the top surfaceof the wooden sleepers, while all triaxial accelerometers were placed in the soil. Theuniaxial accelerometers were all placed in the ballast, several of them located underthe sleepers that contain geophones. Again, the use of a highspeed camera allowed

3.3 Monitoring program 19

(a)

(b)

Figure 3.6: Devices position during the dynamic measurements of May 2008: (a) along thetrack and (b) perpendicular to the track.

20 3 Problem description

Figure 3.7: Overview of the monitored site during the dynamic measurements of May 2008.

the validation of the results from the geophones and accelerometers, as defined inthe previous section. An overview of the positioning of the devices is available inFigure 3.8.

The strain gauges were placed on the rail web, at the neutral axis level, measuring thestrain in the vertical direction. In this way, the bending of the rail has no influence.Appendix B shows the description of the adopted scheme for mounting the straingauges. The static axle load was also measured by means of the Gotcha system(Lloyds Register 2010) which is the standard technique used in the Netherlandsto evaluate the train static load in a section placed nearby the culvert. Accordingto the manufacturer, this device has an accuracy within 5 %.

Thirteen train passages were recorded, but due to unexpected line restriction unfor-tunately only three types of trains crossed the monitored track (Table 3.3).

Table 3.3: Train information during the dynamic measurement of May 2009. The detailedcharacteristics of the train can be found in Appendix A.

Train Type Number of trainpassages

Range ofvelocities[km/h]

Static axle load[kN]

Sprinter T1 7 65105 76124Sprinter T2 4 67110 76124Mat V 3 85106 95136

3.3 Monitoring program 21

(a)

(b)

Figure 3.8: Devices position during the dynamic measurements of May 2009: (a) along thetrack and (b) perpendicular to the track.

22 3 Problem description

(a)

(b)

Figure 3.9: Monitored site during the dynamic measurements of May 2009: (a) generalview, and (b) detail of a sleeper that contains a geophone, an accelerometer,strain gauges and a void indicator device.

Chapter 4

Processing of dynamic

measurements

4.1 Introduction

A major problem regarding monitoring concerns the measurement of dynamic dis-placements. Often, the displacements are calculated from measurements of veloc-ities, or accelerations, which demand a single or double integration, respectively.Besides errors related to acquisition, truncation and conversion from analogue todigital domain (Oppenheim et al. 1999, Boore 2003, Boore and Bommer 2005),significant errors in both low and high frequencies can arise when applying an inte-gration procedure (Hamming 1989, Worden 1990, Smyth and Wu 2007). Hysteresisof the sensor, temperature effects, tilting and presence of noise are main sources oferrors in the integration procedure (Boore et al. 2002, Thong et al. 2002, Graizer2005).

The problems related to integration of dynamic records, in the field of earthquakeengineering, have been addressed by several authors. Boore and Bommer (2005)presented a survey on the standard available tools for the processing of seismicdata, including both baseline corrections and low and highpass filtering. Baselinecorrections allow for adjustments in the low frequency range (Trifunac and Lee 1974,Yang et al. 2006), while filtering can be applied for both low and high frequencies(Boore and Bommer 2005). A general conclusion among the authors who studystrongmotion recordings due to earthquakes (Boore 2001, Trifunac and Todorovska2001, Graizer 2010) is that accurate determination of the permanent displacement istroublesome, often leading to miscellaneous results, especially due to the difficultiesin computing the low frequency response of the displacement.

One of the sources of low frequency errors in the double integration procedure isthe presence of noise in the signal. Though for most scenarios the noise errors can

This chapter is based on Coelho et al. (2011a).

23

24 4 Processing of dynamic measurements

be removed by methodologies comprising filtering or baseline corrections, as soonas the noise frequencies match the main components of the signal, the integrationprocedure tends to magnify the errors caused by the presence of noise. Since noiseand signal share the same frequencies, highpass filtering or baseline corrections cancorrect for the deviation of the signal, but cannot remove the noise from the signal.

Liu and Pang (2001) and Smyth and Wu (2007) presented a methodology basedon Kalman filtering (Brown and Hwang 1997) to overcome such problems. Thistechnique consists of a recursive method where results are corrected by a prediction,based on the state space equation of the problem. The main difficulty of this proce-dure concerns the estimation of the process covariance (Liu and Pang 2001, Welschand Bishop 2001), which often needs to be tuned to improve the results.

Jones and Levy (1987) and Lodono et al. (2005) presented a technique based on theKarhunenLoe`ve transform (Therrien 2002). This procedure involves the calcula-tion of the eigenvectors from the correlation matrix of the results. The eigenvectors,which exhibit the lowest eigenvalues corresponding to noise are removed. The limita-tion of the method is found when the signal and noise fall within the same frequencyrange. This leads to a high covariance, and hence prevents proper noise removal.

In this chapter, an alternative method based on spectral subtraction (Berouti et al.1979, Boll 1979, Lim and Oppenheim 1979) is presented. The method is based onthe application of a technique for enhancement of speech signal to the integrationproblem. It takes advantage of the noise record to improve the signal by means ofsubtraction of the noise spectrum from the original signal spectrum.

This method by itself does not solve the problem of the double integration procedure.Instead, it is a tool to support the predictions of the real displacement by interveningin one of the causes of errors in the integration procedure, which is the presence ofnoise during signal acquisition.

4.2 Background problem

The integration problem of a discretized signal can be addressed by considering thetrapezoidal rule as the integration scheme

y(n) = y(n 1) +t

2[x(n) + x(n 1)]

z(n) = z(n 1) +t

2[y(n) + y(n 1)] ,

(4.1)

in which y(n) and z(n) are, respectively, the first and second integration of the signalx(n). This can be written as

y(n) = H1(ej)x(n)

z(n) = H2(ej)x(n),

(4.2)

4.2 Background problem 25

where H1(ej) and H2(e

j) represent the transfer functions between the inputx(n), and the output y(n), and z(n), respectively, and follow:

H1(ej) =

t

2

(1 + ej

1 ej

)

H2(ej) =

t2

4

(1 + ej

1 ej

)2.

(4.3)

This means that a general input x(n), multiplied in the frequency domain by thetransfer function H1(e

j) or H2(ej), yields a single or double integration output,

following the trapezoidal rule as the integration scheme. Considering the signalx(n) = ejn as input, the exact integrals are:

yexact(n) =ejn

j

zexact(n) =ejn

2.

(4.4)

Figure 4.1 presents the ratio between Equations (4.2) and (4.4), and gives the errorinduced by the integration scheme, for the case where t = 1, which makes pito be coincident with the Nyquist frequency, which corresponds to the maximumfrequency that can be sampled without aliasing error (Hamming 1989, Oppenheimet al. 1999).

It follows from Figure 4.1, that for frequencies up to pi/2 (which corresponds to half ofNyquists frequency), the error induced by the integration procedure is insignificant.

0 pi/4 pi/2 3pi/4 pi108

106

104

102

1+00

1+02

1+04

Frequency [rad]

Accu

racy

ratio

First integrationSecond integration

Figure 4.1: Transfer function of single and double integration procedure through trape-zoidal rule.

26 4 Processing of dynamic measurements

However, for frequencies higher than pi/2, significant errors arise for both integrationsteps, where the error induced by the second integration step corresponds to thesquare power of the error caused by the first integration. Though this error can beminimized by selection of a more suitable integration scheme, such as Simpson orTicks rule, it is not completely removable (Hamming 1989).

The presence of noise induces errors in both low and high frequencies. Assuming ameasured signal x(n), composed by a signal x(n), with noise (n),

x(n) = x(n) + (n), (4.5)

the error induced by the presence of noise can be evaluated by making use of Equa-tion (4.2), and comparing the results obtained with both x(n) and x(n) by:

1(ej) = y(n) y(n)

2(ej) = z(n) z(n),

(4.6)

which is equivalent to

1(ej) = H1(e

j)x(n)H1(ej)x(n)

2(ej) = H2(e

j)x(n)H2(ej)x(n),

(4.7)

and leads to:

1(ej) = H1(e

j)(n)

2(ej) = H2(e

j)(n).(4.8)

Figure 4.2 presents the error for both integration steps. It follows that the additionof noise (n) leads to an error in both low and high frequencies, with the shape ofthe transfer function of the integration scheme. The error in the low frequenciesis independent of the adopted integration method (Hamming 1989, Smyth and Wu2007), being related to the recursive character of the cumulative summation. Thedenominator of the transfer function will always be (1 ej), independent of themethod, which tends towards infinity as the frequency tends to zero, and hence itcontrols the solution in the low frequency range. Again, the second integration stepcauses an increase by a power two of both low and high frequency errors.

4.3 Spectral subtraction 27

0 pi/4 pi/2 3pi/4 pi108

106

104

102

1+00

1+02

1+04

Frequency [rad]

(e

j )/

(n)

First integrationSecond integration

Figure 4.2: Error induced by the presence of noise due to single and double integrationthrough trapezoidal rule.

4.3 Spectral subtraction

4.3.1 Concept

This section presents the proposed method to overcome the problem related to theintegration procedure. It is based on the method proposed by Boll (1979) for theimprovement of the intelligibility of speech reproduction. The method takes advan-tage of the noise record to correct the measured signal by means of the subtractionof the average noise spectrum. Two main assumptions are made during the develop-ment of the method: the noise and signal are uncorrelated variables; and the noiseis stationary (Berouti et al. 1979, Boll 1979, Wojcicki et al. 2006). As pointed outin Thong et al. (2002) and Stiros (2008), though in reality noise and signal are notstatistically independent variables, the covariance between both for modern devicesis close to zero, which makes it a reasonable assumption. The fact that the durationof the dynamic measurements is usually small, it is reasonable to accept that theproperties of the background noise do not change significantly, and therefore mightbe considered stationary (Kyoya and Arakawa 2009).

The measured signal, x(n), is composed by the addition of the exact signal x(n) andthe noise (n),

x(n) = x(n) + (n), (4.9)

being the exact signal estimated by means of:

x(n) x(n) = x(n) (n), (4.10)

28 4 Processing of dynamic measurements

where x(n) is used to designate the estimation of the exact signal x(n). In thefrequency domain Equation (4.10) is written as:

X(ej) = X(ej) (ej). (4.11)

The noise spectrum (ej) is replaced by the average noise value, (ej) , recordedduring silence periods, in order to improve the consistency and accuracy (Boll 1979,Espy and Lim 1982), according to:

(ej) = E{|(ej)|}. (4.12)

The silent periods can be pre or post events, or a combination of both, since thenoise is assumed stationary. The choise of the silent period mainly depends on thesetup used for the dynamic measurements (use of trigger and length of the measuringwindow).

The amplitude of the estimated signal is obtained by the subtraction of the measuredsignal amplitude with the average noise amplitude, while the phase is kept equal tothe one from the measured signal,

|X(ej)|= |X(ej)||(ej)|

^X(ej) = ^X(ej).(4.13)

A correction is needed to prevent the amplitude of the signal producing negativevalues due to the subtraction. Additionally, as suggested in Boll (1979), betterresults are achieved if the results from the correct estimate that are higher than theaverage noise spectrum magnitude are set to zero, as follows,

|X(ej)|= 0, if |X(ej)|< 0

|X(ej)|= 0, if |X(ej)|< |(ej)|

|X(ej)|= |X(ej)|, otherwise,

(4.14)

where X(ej) is used to designate the corrected estimation of the amplitude ofthe signal x(n). This means that, if the spectrum of the signal has an amplitudesmaller than the mean level of the noise spectrum or it has a negative amplitude,the amplitude is set to zero.

The estimated exact signal is obtained combining the estimated amplitude of thesignal, with the measured phase signal,

x(n) = |X(ej)|e^X(ej). (4.15)

4.4 Application 29

During the previous exposition, it is assumed that phase is of little importance forthe improvement of the signal, being all the attention paid to the correction of theamplitude. Though the phase contains a significant amount of information (Hayeset al. 1980, Oppenheim and Lim 1981), the correct estimation of phase does notlead to a noticeable improvement during signal enhancement (Wang and Lim 1982,Shannon and Paliwal 2006).

4.3.2 Implementation

In Section 4.2, it is shown that the presence of noise leads to errors, in low andhigh frequencies, when performing a numerical integration. Section 4.3.1 presents aprocedure to reduce the noise in measured signals. Combining this last techniquewith the numerical integration, a procedure that reduces the error in the integratedresult is developed. The proposed approach consists of splitting signal and noise intotwo distinct signals. The two signals are integrated and processed independently,and at the end a spectral subtraction is performed. As a result, the error that isgenerated in the signal due to the presence of noise is removed afterwards by theindependent processing of the noise. Figure 4.3 presents an overview of the proposedprocedure.

While for the standard low and highpass filtering the signal components that areoutside the range of cutoff frequencies are removed, the signal components are keptover the entire frequency range with the proposed method. Additionally, the cutofffrequency must be defined by the user, which due to its signal dependency (Trifunacand Lee 1974) represents a possible source of mistakes, since the present techniqueis signal independent. Therefore, the proposed technique is a suitable alternative fordealing with problems where the low frequencies are dominant and the presence ofnoise is the main issue leading to inaccurate integration steps.

A remark is due regarding the low and high frequency errors. As presented in Section4.2, there are two distinct errors that occur during integration: errors induced bythe adopted method, which lead to high frequency errors, and errors induced by thepresence of noise, which contaminate the signal in both low and high frequencies.However, in the present thesis, the problems related with the high frequency are ofminor importance due to the high acquisition frequencies adopted which cause theproblem to be low frequency dominated.

4.4 Application

4.4.1 Synthetic case

In this section the features of the proposed method are highlighted through a syn-thetic application. Consider x(n) to be:

30 4 Processing of dynamic measurements

Figure 4.3: Block diagram of the proposed method.

4.4 Application 31

x(n) =pi

2

[cos

(npi2

)sin

(npi80

)], (4.16)

the exact first and second integration follow:

y(n) = 20

[1

39sin

(39

80npi

)

1

41sin

(41

80npi

)]

z(n) =402

pi

[

1

1521cos

(39

80npi

)+

1

1681sin

(41

80npi

)].

(4.17)

Consider the added noise (n) composed by the addition of random noise followingthe normal distribution with a signal which has the same frequency as the mainsignal but a different phase:

(n) = N(0, 0.04) +1

4sin

(npi2pi

8

), (4.18)

the signal x(n) follows Figure 4.4. The signal x(n) is defined for 80 000 samples,starting at sample 5 000, while the noise is defined for the entire domain (100 000samples). The last 10 000 samples are used to compute the noise estimation, i.e.silence period.

The comparison between the standard numerical integration, by means of a trape-zoidal rule, and the proposed method are in Figures 4.5 and 4.6, for the first andsecond integration, respectively. The standard procedure involves the applicationof a highpass filter after the integration step, which is used to correct the low fre-quency error induced by the integration, as suggested in Trifunac (1971) and Booreand Bommer (2005). The high pass filter consists of a causal Impulse Infinite Re-sponse (IIR) elliptic filter, of the 6th degree, with a passband ripple and stopbandattenuation of 0.01 and 80 dB, respectively. The data is filtered twice, the first inforward time and the second in reverse time, in order to remove the phase distortion(Kormylo and Jain 1974). Two cutoff frequencies are used, 0.20 and 0.25 Hz, inorder to highlight its influence on the results.

For the spectral subtraction, a 256 points Hanning window (Oppenheim et al. 1999)is used with 50 % of overlap. Both methodologies are implemented in Matlab (TheMathworks 2008).

The results for both integrations show that the proposed method is the closest to theexact results (Figures 4.5a and 4.6a). The reasons for this difference become clearwhen considering the response in the frequency domain (Figures 4.5b and 4.6b). Theproposed method matches perfectly the exact response, while both standard methodsoverestimate due to the fact that the error has a frequency component that coincideswith the main frequency of the signal. By the application of a highpass filter,

32 4 Processing of dynamic measurements

0 20 40 60 80 1002

1

0

1

2

Sample 1000

Sign

al x

(n)

Figure 4.4: Signal x(n) = x(n) + (n).

it is not possible to distinguish between the two, and hence the error componentcannot be removed from the signal. The proposed method can be considered anenhancement on the integration of low frequency signals, since it accounts for allnoise components. Standard methodologies cannot decouple the noise that matchesthe frequency of the signal.

The cutoff frequency of the standard procedure is found to have influence on theresults, which is in agreement with Trifunac and Lee (1974). For both integrationsteps, differences are shown in the amplitude spectrum for 0.20 and 0.25 Hz, inFigures 4.5b and 4.6b.

From Figures 4.5 and 4.6 the second integration step leads to higher differencesbetween the standard methodology and the proposed method. Table 4.1 presentsthe normalized meansquare error (NMSE) defined as:

NMSE =

Nn=1

[x(n) x(n)]2

Nn=1

x(n)2

. (4.19)

The bigger difference occurs for the second integration step, which is in agreementwith the theoretical background presented in Section 4.2, where the second integra-tion step is found to be more severe than the first. For this particular application,it is found that the spectral subtraction leads to errors four and eight times smallerthan the standard procedure for the first and second integration steps, respectively.

4.4 Application 33

0 5 10 15 20 25 301.5

1

0.5

0

0.5

1

Sample 1000

Firs

t int

egra

tion

Exactfc=0.20Hzfc=0.25HzSpectral sub

(a)

0.20 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.300

0.1

0.2

0.3

0.4

Frequency [Hz]

Ampl

itude

[Hz 1

]

Exactfc=0.20Hzfc=0.25HzSpectral sub

(b)

Figure 4.5: Comparison between analytical and numerical integration for the first integra-tion step for: a) sample domain, and b) frequency domain.

Table 4.1: Normalized meansquare error due to the integration procedure.

Method Firstintegration

Secondintegration

Spectralsubtraction

0.0119 0.0059

Standardprocedure

(fc = 0.20 Hz)

0.0505 0.0505

Standardprocedure

(fc = 0.25 Hz)

0.0465 0.0431

34 4 Processing of dynamic measurements

0 5 10 15 20 25 300.8

0.6

0.4

0.2

0

0.2

0.4

0.6

Sample 1000

Seco

nd in

tegr

atio

n

Exactfc=0.20Hzfc=0.25HzSpectral sub

(a)

0.20 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.300

0.05

0.1

0.15

0.2

0.25

Frequency [Hz]

Ampl

itude

[Hz 1

]

Exactfc=0.20Hzfc=0.25HzSpectral sub

(b)

Figure 4.6: Comparison between analytical and numerical integration for the second inte-gration step for: a) sample domain, and b) frequency domain.

4.4 Application 35

4.4.2 Study on the phase influence

In the present method, it is assumed that the noise in the phase is of less importancefor the enhancement of the signal. In order to highlight this fact, the pure signalx(n) is compared with x(n) defined as follows:

x(n) = |X(ej)|e^X(ej), (4.20)

in which the amplitude of the pure signal is combined with the phase contaminatedwith noise. In the same way the signal referring to the first y(n) and second z(n)integration can be obtained. Making use of the signals x(n) and (n) as defined inEquations (4.16) and (4.18), the two integrated signals y(n) and z(n) are found, andthe resulting phase is combined with the amplitude of the pure integrated signals.Figure 4.7 presents the results for both integration steps.

It follows that the contamination of the phase with noise has no significant influenceon the quality of the results. The only visible differences occur for the initial samples(up to 5 000), in which there is just noise in the signal x(n) silence period. As soonas the signal x(n) is added, the phase containing noise causes no difference betweenthe exact integration and the proposed method. These results are in agreement withexperimental findings in speech enhancement (Wang and Lim 1982, Shannon andPaliwal 2006).

4.4.3 Real application

Having highlighted the proposed methodology by processing a synthetic application,in this section results concerning real data will be presented. These results concernone train passage recorded during the dynamic measurements of 2008. The detailsand interpretation of the results will be performed in Chapter 6. One geophoneand one accelerometer were placed together in the ground at about 1 m depth (seeFigure 3.6), and the vibrations induced by the train passage were recorded. Figure4.8 presents the measured velocity and acceleration during the passage of a train at114 km/h.

The geophone data was processed following the approach of Bowness et al. (2007).Moreover the displacements resulting from the geophones were compared with theresults from a highspeed camera, which allowed the validation of the geophonesresults (see Chapter 6). The data from the accelerometer was double integrated bythe meth