SCHUBERT, STEINDORFER AND BUTTON: DISPLACEMENT MONITORING IN TUNNELS – AN OVERVIEW

FELSBAU 20 (2002) NO. 2 7

TU

NN

EL

LIN

GDisplacement Monitoringin Tunnels – an Overview

By Wulf Schubert, Albert Steindorfer and Edward A. Button

Verschiebungsmessungen in Tunneln –Ein Überblick

Die Verschiebungsmessung im Tunnelbau hat eine langeTradition. Die Methoden haben sich über die Jahrzehnteverändert, was zu einer besseren Aussagekraft der Meßda-ten führen kann. Der Beitrag gibt einen kurzen Überblicküber die gängigen sowie neuere Methoden der Meßdaten-auswertung und Darstellung. Für einfache Verhältnissemag ein Blick auf die Zeit-Verschiebungskurven genügen,um das Verhalten des Tunnels beurteilen zu können. Beiheterogenen Baugrundverhältnissen oder nicht kontinu-ierlichem Vortrieb müssen hingegen weitere Analysen vor-genommen werden, um die „Normalität“ der gemessenenWerte überprüfen zu können. Die Arbeit zielt darauf ab,Personen, die auf der Baustelle mit Meßdaten zu tun ha-

ben, zu motivieren, den erzielbaren „Mehrwert“ durchneuere Meßdatenanalysen zu nützen.

Displacement monitoring in tunnels has a long tradition.Methods have changed over the decades, allowing extract-ing more information from the measured data. The paperprovides a brief overview of the methods to evaluate andplot the results of the measurements. For simple conditionsthe simple look on a displacement history plot may be suffi-cient to evaluate the tunnel performance. As soon as therock mass is heterogeneous or the progress discontinuous,additional tools have to be used to check the “normality” ofthe measured values. With the information given in the pa-per it is intended to motivate persons involved in the mon-itoring on site to make use of the “added value” of up todate measurement evaluation.

Observation and measurements have a longtradition in geotechnical engineering. The

reasons for measurements and the evaluationand interpretation of the acquired data are mul-tiple. Verification of design parameters, qualitycontrol, observation of the effectiveness of con-struction methods, observation of the rock massbehaviour, etc. may be the motivations to imple-ment a monitoring system.

Especially for tunnel projects in weak rockwith high overburden the observation of therock mass and system behaviour is an essentialbasis for the final design of the excavation andsupport. Due to the uncertainties in the geo-technical model, the heterogeneity of the rockmass, and the deficiencies in modelling of therock mass support interaction prior to con-struction, measurements are an important is-sue for optimisation of the construction whilesimultaneously observing the safety require-ments.

For shallow tunnels the monitoring plays animportant role in the stability assessment and tocontrol surface settlement requirements.

For the last 15 years in tunnelling, the meas-urement of absolute spatial displacements hasbecome very common, replacing the previouslyused convergence measurements. With the in-creased information inherent in the 3D data, ad-ditional methods of evaluation and displaywere developed. A vast number of projects havebeen successfully completed where these meth-ods have been used.

An enormous amount of data has been col-lected during this period. The question now is,

whether we use those data in a way that wouldallow for a considerable increase in understand-ing the rock mass behaviour, the rock-supportinteraction, and the degree of safety inherent inthe system. A literature review shows, that thereare not many institutions where site data arethoroughly analysed, and the results sufficientlyexplained and backed up by fundamental analy-ses. Considering the practice on many sites, itcan be stated, that in a few places there is a highstandard in evaluation of measurement dataand the application of the results for the controlof the construction, while on other sites notmuch progress in this respect can be seen. Inmany places displacement-time graphs are vis-ually inspected and no further evaluation fol-lows. How misleading this type of measurementdata evaluation can be is shown in this paperand in (1).

The gap between the state of knowledge andthe practice on many sites can easily lead to se-vere questions of responsibility and liability incase of accidents. The authors feel, that a shortsummary of the state of the art in evaluation andinterpretation of measurement data might bebeneficial.

State of the art

A number of reflectors (targets) are fixed to thelining. A freely positioned total station in regularintervals measures the co-ordinates of the tar-gets, commonly once each day. The targets usu-ally are arranged in measuring sections, whichare separated by 5 to 20 m. The number of tar-

8

TU

NN

EL

LIN

GSCHUBERT, STEINDORFER AND BUTTON: DISPLACEMENT MONITORING IN TUNNELS – AN OVERVIEW

FELSBAU 20 (2002) NO. 2

Fig. 3 Displacement histories and advance for both cases shown in Figure 1 andFigure 2.Bild 3 Zeit-Verschiebungskurven und Baufortschritt für beide oben gezeigten Fälle.

gets in one section depends on the size of the tun-nel and to a certain extent on the number of sub-sequent phases (heading-bench-invert). Theprocedure of measuring and data processing isdescribed in (2). The measurement accuracy isin the range of less than 1 mm, which in mostcases is sufficient.

Fig. 1 Displacement history and advance for a continuous excavation rate.Bild 1 Zeit-Verschiebungskurve und Baufortschritt bei gleichmäßiger Vortriebs-geschwindigkeit.

Fig. 2 Displacement history and advance for an unsteady excavation rate.Bild 2 Zeit-Verschiebungskurve und Baufortschritt für einen Vortrieb mit unterschied-lichen Vortriebsgeschwindigkeiten.

Evaluation methods andcommon displays

Displacement historyPlotting displacement versus time for one dis-placement component is the most common wayof displaying measurement data in tunnels. Theinterpretation of the curve is easy for homogene-ous rock mass conditions and continuous ad-vance rate. The condition for a satisfying stabili-sation, respectively the stress redistribution is asteadily decreasing displacement rate. Figure 1shows the development of the displacement forthe first couple of days for a steady advance rate.Sulem et al. (3) have formulated the relation-ships for time dependent closure of tunnels.Those formulations were used to produce Figure1, Figure 2 and Figure 3.

When the rock mass is heterogeneous and theadvance rate not constant, the interpretation of the“normality” of the measured values becomes moredifficult. Figure 2 shows a displacement history forthe same set of parameters as used for producingFigure 1 with an unsteady advance rate.

Without considering the progress one wouldnot interpret the displacement development as“normal”, but rather be concerned. With addition-al headings, heterogeneous rock mass conditions,or time dependent behaviour of the support it iseven more difficult to properly interpret the re-sults when using the displacement histories only.Figure 3 shows the total displacement histories forthe two different advance rates shown above.

Recently, a tool has been developed that isable to predict displacements even for complexsituations (4, 5). With this program it is possibleto model face advance effects, time dependentbehaviour and support effects, and thus checkthe measured displacements on their “normali-ty”. The use of this tool is shown with the help ofcase histories in this volume (5).

Deflection linesConnecting the measured values of one compo-nent (for example the vertical or horizontal com-ponent) at a certain time along the tunnel pro-duces deflection lines. By plotting these lines inregular intervals, the influence of the progress onthe sections behind the face can be easily seen.This is the reason why the deflection lines fre-quently are called influence lines. Details and ex-amples of application can be found in (6, 7, 8).Deflection lines are quite useful to get an over-view of the displacement development along asection of the tunnel. Producing trend lines fromthe deflection lines, a certain extrapolation be-yond the face is possible. Practice however showsthat the extrapolation in many cases does not re-veal much about the conditions ahead of the face.To be able to show comparable data from differ-ent monitoring sections on one plot, the determi-nation of the displacements occurring prior to thezero reading is important. Zero readings of the

SCHUBERT, STEINDORFER AND BUTTON: DISPLACEMENT MONITORING IN TUNNELS – AN OVERVIEW

FELSBAU 20 (2002) NO. 2 9

TU

NN

EL

LIN

G

Feinst-bindemittel-Injektionenund Soilfrac-VerfahrenSicherung undUnterfangung desBestandes beiNeubaumaßnahmen

Keller Grundbau GmbH

OffenbachKaiserleistraße 44Postfach 10 06 64

D-63006 OffenbachTelefon (069) 80 51- 0

Telefax (069) 80 51- 221

Internet: www.KellerGrundbau.comE-mail: Marketing@KellerGrundbau.com

®

Um den Neubau einerSchleuse in Berlin-Charlotten-burg zu ermöglichen, wird ein Pfeiler der Stadtautobahn mittels Feinstbindemittel-Injektionen unterfangen.

Unverträgliche Setzungeninfolge der Bauarbeiten werden begleitend imSoilfrac®-Verfahren reduziertund zurückgestellt.

Fragen Sie danach.

10

TU

NN

EL

LIN

GSCHUBERT, STEINDORFER AND BUTTON: DISPLACEMENT MONITORING IN TUNNELS – AN OVERVIEW

FELSBAU 20 (2002) NO. 2

Fig. 5 Deflection lines with correct recording of the face position (top, red arrow) andwith mistake in face Position (bottom, red arrow).Bild 5 Einflußlinien bei richtiger Aufzeichnung des Ortsbruststands (oben, roter Pfeil)und bei fehlerhaftem Ortsbruststand (roter Pfeil, unten).

Fig. 6 Trend line of ratio of settlements of crown and sidewall points (9).Bild 6 Trendlinien der Verhältnisse der Setzungen zwischen den Ulmpunkten und derFirste (9).

Fig. 4 Deflection lines without consideration of pre-displacements (top) and withpre-displacements (bottom) .Bild 4 Einflußlinien ohne (oben) und mit Berücksichtigung der Vorverschiebungen(unten).

targets are not always done at the same distancebehind the face or time after excavation. Thisimplies, that besides the displacement occurringahead of the face, an additional part of the dis-placements are not recorded. To make displace-ment measurements comparable, normalizationis required. Commonly the displacements aheadof the face are neglected, and the value at theface taken to zero. Various methods to determinethe missing portion of the displacements betweenthe face and the measuring section are used. Themost appropriate method is to use time- and dis-tance dependent functions, as described in (4).

It is very important to accurately record thelocation of the face and the time of excavation toachieve comparable pre-displacement values fordifferent measuring sections.

Figure 4 shows the deflection lines without(top) and with consideration of the calculated pre-displacements (bottom). The blue lines representthe deflection lines, while the black line shows atrend 3 m behind the face. In this example thezero reading at measuring section 320 was donequite some time after the excavation. When thiscircumstance is not considered, and only themeasured values taken for the plot, one wouldassume, that the displacements are more or lessuniform. Using the calculated pre-displacements,an increase in displacement between station 310and 320 can be clearly seen. Additionally thetrend lines are considerably different.

Figure 5 shows the importance of precise re-cording of the face location for a proper use of theplots produced. In the upper plot the red arrowmarks the face location at a certain time. A mis-take in the face location of only one metre (redarrow, lower plot) produces a completely differ-ent plot.

Displacement differencePlotting differences of displacement components– for example the difference between crown andfooting settlement – in certain cases can help todetect abnormal system behaviour. With thisplot weak zones outside the excavated tunnelcan be identified, as local failure in the rockmass will show in an increase in the difference.For this purpose the authors prefer to use dis-placement vector plots or ratios of the singlecomponents, as the difference may also changewhen the behaviour is normal, but the quality ofthe rock mass gradually improves or decreases.

Displacement ratiosCalculating the ratio between displacement com-ponents and plotting them as a trend can helpdetecting weak zones outside the tunnel. An ex-ample shall demonstrate this: under normal con-ditions the settlement of the sidewall will be con-siderably smaller than the settlement of thecrown. Figure 6 shows this type of plot for a situ-ation, where the excavation crosses a steeplydipping fault. For a timely detection of such a sit-

SCHUBERT, STEINDORFER AND BUTTON: DISPLACEMENT MONITORING IN TUNNELS – AN OVERVIEW

FELSBAU 20 (2002) NO. 2 11

TU

NN

EL

LIN

GSTRECKE AMSTETTEN-TARVISBAULOS 12 UNTERWALD-KALWANG

Tunneldurchschlag auf Station 1052,6 am 21.02.2002

Bauausführung:

ARGE ÖBB – TUNNEL UNTERWALD

12

TU

NN

EL

LIN

GSCHUBERT, STEINDORFER AND BUTTON: DISPLACEMENT MONITORING IN TUNNELS – AN OVERVIEW

FELSBAU 20 (2002) NO. 2

Fig. 9 Combined plotof displacement vec-

tors in a cross sectionand in the longitudinal

section; note the re-latively pronounced

longitudinal displace-ment indicating a fault

zone ahead of theexcavation.

Bild 9 KombinierteDarstellung der Ver-schiebungsvektoren

im Quer- und Längs-schnitt. Bemerkens-

wert ist die relativ gro-ße Längsverschiebung,die auf eine Störungs-

zone hinweist.

Fig. 7 Displacementvectors in a crosssection with fairly

“normal” orientation(first eight readings);

displacements magni-fied by a factor of 10.

Bild 7 Verschie-bungsvektoren im

Querschnitt mit an-nähernd „normaler“

Orientierung, dar-gestellt sind die ersten

acht Meßwerte;Verschiebungen um

Faktor 10 vergrößert.

Fig. 8 Displacementvectors in a cross

section, showing astrongly unsymme-

trical deformation dueto a fault zone outsidethe right sidewall (first

eight readings); dis-placements magnified

by a factor of 10.Bild 8 Verschie-bungsvektoren im

Querschnitt zeigeneine stark unsymme-trische Verformung,

die durch eine Störungaußerhalb des rechten

Kämpfers verursachtwird; dargestellt

sind die ersten achtMeßwerte in einer

Vergrößerung um denFaktor 10.

uation it is required to install measuring sectionsin rather small distances. As a rule of thumb thedistance between the measuring sections shouldnot exceed one tunnel diameter.

Displacement vectorsDue to the measurement technique it is possibleto plot the spatial displacement vectors. Someevaluation software plots the displacement vec-tors and their path over time in a cross sectionperpendicular to the tunnel axisby combiningthe vertical and horizontal components. Thisplot can be very useful to evaluate the influenceof the rock mass structure on the displacementof the tunnel. Similar to the ratios of displace-ment components, zones of weakness outside thetunnel profile can be detected in advance, pro-viding the measuring sections are in a reasona-ble distance (Figures 7 and 8). Figure 7 showsthe displacement vectors in a cross section witha fairly “normal” orientation, indicating a rela-tively homogeneous rock mass. The tunnel wasexcavated in a top heading-bench-invert se-quence. This is the reason why the displacementin the bench is rather minor, compared to the topheading.

The displacement vector plots are not onlyuseful for the early detection of weak materialoutside the tunnel profile, but also for the layoutof rock bolts.

It has been shown, that the ratio between thesettlement or horizontal displacement and thelongitudinal displacement can be a useful indica-tor for the quality of the rock mass ahead of theface (10, 11, 12). This especially applies to tun-nels with relatively high overburden and weak

SCHUBERT, STEINDORFER AND BUTTON: DISPLACEMENT MONITORING IN TUNNELS – AN OVERVIEW

FELSBAU 20 (2002) NO. 2 13

TU

NN

EL

LIN

G

ground. When the excavation approaches weak-er or stiffer material, the orientation of the dis-placement vector significantly changes wellahead of the change in rock mass stiffness. Thevector orientation can be shown in a longitudinalsection, as a trend line displaying the ratio be-tween the longitudinal displacement and settle-ment, or the spatial orientation in a stereo plot.

Figure 9 and Figure 10 show combined plotsof the displacement vectors in the cross sectionand in the longitudinal section. Note the pro-nounced longitudinal displacement in the plot inFigure 9, indicating a fault zone ahead of theface. The radial displacements are rather small.Figure 10 shows the situation after the excava-tion entered the fault zone, which was met withthe excavation at approximately station 2 700 m.The radial displacements dramatically increase,

Fig. 10 Combinedplot of displacementvectors in a cross sec-tion and in the longi-tudinal section rough-ly 90 m from stationshown in Figure 9,after entering the faultzone.Bild 10 KombinierteDarstellung der Ver-schiebungsvektoren imQuer- und Längsschnittetwa 90 m nach dem inBild 9 gezeigten Quer-schnitt nach Antreffender Störungszone.

while the displacement vector orientation in lon-gitudinal direction normalizes.

Figure 11 shows a trend line of the ratio be-tween the longitudinal displacement and the ver-tical displacement of the crown in the area thatwas shown in the previous figures. The strong rel-ative increase in longitudinal displacementaround station 2 600 m indicates the fault zone,which was encountered with the excavationaround station 2 700 m. The vector orientationreturns to the “normal” level within the fault zone.

The spatial vector orientations of the moni-tored points can also give a rough estimate on theprimary stress condition with respect to orienta-tion and ratio of the principal stresses (13, 14).The evaluation of the development of the displace-ment vector orientation is very useful for condi-tions, where the displacements are in the range of

Fig. 11 Trend of thedisplacement vector

orientation showing asignificant change wellahead of the fault zonemet by the excavationat approximately sta-

tion 2 700. The bluedashed line shows the“normal” vector orien-

tation in homogeneousrock mass conditions.

Bild 11 Trend derOrientierung des Ver-schiebungsvektors imLängsschnitt. Deutlichzu sehen ist die starkeÄnderung bereits weit

vor der bei etwa Station2 700 mit dem Vortriebangefahrenen Störung.

Die strichlierte blaueLinie zeigt die „norma-le“ Vektororientierung

bei gleichmäßigenGebirgsverhältnissen.

14

TU

NN

EL

LIN

GSCHUBERT, STEINDORFER AND BUTTON: DISPLACEMENT MONITORING IN TUNNELS – AN OVERVIEW

FELSBAU 20 (2002) NO. 2

several centimetres. In shallow tunnels due to thesmall stress level and the usually relatively stifflining, the vector orientation is not a reliable indi-cator for changing rock mass conditions.

As has been discussed in the previous sec-tions, an efficient use of the information provid-ed by the evaluation of the measurement data ispossible only, when the quality of the data isgood. Poor quality in surveying or data process-ing severely reduces the potential for furtherevaluations and may lead to misinterpretation.

Additional evaluationsOnce data are recorded and stored, one shouldmake the maximum use of the information con-tained in the data. One of the methods to increasethe level of information is to analyse stresses inthe lining and compare them to the strength.Rokahr (1, 15) has done pioneering work in thisfield and the model is practically applied. Anoth-er model, simulating the complex behaviour ofshotcrete is currently under development (16),but has not proved its practical applicability yet.Especially for tunnels with low overburden,where the shotcrete lining is the predominantsupport and the rock mass plays a minor role inthe stress redistribution, the knowledge of thedevelopment in the stress intensity index is animportant decision aid. With higher overburdenthe integrity of the shotcrete lining usually loosesimportance, because in most cases the natural“rock arch” can compensate the loss in lining ca-pacity, under the condition that is has still re-serves or is properly reinforced by rock bolts.

Value of the differentevaluation methods

It has been shown, that methods of data evalua-tion have to be chosen according to the problemon hand. The Table shows a brief and preliminaryoverview of the applicability of the single evalua-tion and display methods for specific targets.

It is pointed out, that usually a combination ofevaluation methods is required to obtain a clear

understanding of the geotechnical situation andthe rock mass and tunnel behaviour. In additionthe continuous updating of the geological modeland its prediction into the volume of interest is ofessential importance for the reliability of themeasurement data interpretation.

Conclusion

Displacement monitoring for tunnels hasreached a high standard. Many sites run moni-toring programs in order to control displace-ments and to finalize the design during construc-tion. The extent of use of the data acquired how-ever differs very much from site to site. Visualinspection of time- displacement histories is stillstandard on many sites. With a few simple exam-ples it has been shown, that a simple visual im-pression of those plots in many cases is not suffi-cient to be able to assess the stability of the tun-nel, or even the “normality” of the stress redistri-bution process. This especially applies with un-steady advance, multiple drifts, and variation insupport. During the last years considerable re-search has been undertaken to improve the dataevaluation methods, and to maximize the infor-mation inherent in the monitored data. Practicehowever shows, that those methods are adoptedon site rather slowly and reluctantly out of vari-ous reasons.

Neglecting state of the art methods in dataevaluation may not only cause financial losses,but also may lead to serious consequences for thepersons involved on site in case of accidents. Eve-rybody involved in the process of data acquisitionand evaluation must be aware of the fact that thevalue of the information that can be obtainedstrongly depends on the quality of the data.

Much has been achieved during the last dec-ades, but there is still ample room for improve-ment.

References1. Rokahr, R. ; Stärk, A. ; Zachow, R.: On the art of interpretingmeasurement results. In: Felsbau 20 (2002), No. 2, this issue.2. Rabensteiner, K.: Advanced tunnel surveying and monitor-ing. In: Felsbau 14 (1996), No. 2, pp. 98-102.3. Sulem, J. ; Panet, M. ; Guenot, A.). Closure analysis indeep tunnels. In: Int. Journal of Rock Mechanics and MiningScience 24 (1987), pp. 145-154.4. Sellner, P.: Prediction of displacements in tunnelling.Riedmüller, Schubert & Semprich (eds), Gruppe GeotechnikGraz, Heft 9, 2000.5. Sellner, P. ; Grossauer, K.: Prediction of displacements fortunnels. In: Felsbau 20 (2002), No. 2, this issue.6. Vavrovsky, G.M. ; Ayaydin, N. (1988). Bedeutung der vor-triebsorientierten Auswertung geotechnischer Messungenim oberflächennahen Tunnelbau. Forschung und Praxis,Band 32, pp. 125-131.7. Vavrovsky, G.M. (1988). Die räumliche Setzungskontrolle –ein neuer Weg in der Einschätzung der Standsicherheit ober-flächennaher Tunnelvortriebe. In: Mayreder Zeitschrift 33.8. Vavrovsky, G.M. ; Schubert, P.: Advanced analysis ofmonitored displacements opens a new field to continuouslyunderstand and control the geomechanical behaviour of tun-nels. Proc. 8th ISRM Congress Tokio, pp. 1415-1419. Rotter-dam: Balkema, 1995.

Table Overview of the value of evaluation methods for specific questions;: + = good,o = limited value, - = no value.Tabelle Überblick über den Wert der einzelnen Darstellungsmethoden für unterschied-liche Fragestellungen; + = gute Aussage, o = beschränkte Aussagekraft, - keine Aussagemöglich.

Displacement history + + - o - +Deflection lines, trends o - + o o -Trends of relativedisplacement values - - - + - -Vectors in cross section - - - + - +Vectors in longitudinalsection - - - o + -Spatial vector orientation - - + + + -

Eva

luat

ion

of s

tabi

li-za

tion

proc

ess

Pre

dict

ion

final

dis

-pl

acem

ents

Str

ess

redi

strib

utio

nlo

ngitu

dina

l

Det

ectio

n w

eak

zone

s ou

tsid

e pr

o-fil

e, k

inem

atic

s

Pre

dict

ion

ahea

d

Est

imat

e of

str

ess

inte

nsity

in li

ning

SCHUBERT, STEINDORFER AND BUTTON: DISPLACEMENT MONITORING IN TUNNELS – AN OVERVIEW

FELSBAU 20 (2002) NO. 2 15

TU

NN

EL

LIN

G

9. Schubert, W., Steindorfer, A.: Selective displacementmonitoring during tunnel excavation. In: Felsbau 14 (1996),No. 2, pp. 93-97.10. Schubert, W. (1993). Erfahrungen bei der Durchörterungeiner Großstörung im Inntaltunnel. In: Felsbau 11, No 6, 443-447.11. Schubert, W., Budil, A. (1995) The Importance of Longi-tudinal Deformation in Tunnel Excavation. Proceedings 8thInt. Congress on Rock Mechanics (ISRM), Vol.3, BalkemaRotterdam, 1411-1414.12. Steindorfer, A.: Short term prediction of rock mass be-haviour in tunnelling using advanced analysis of displace-ment monitoring data. Riedmüller, Schubert & Semprich(eds), Gruppe Geotechnik Graz, Heft 1, 1997.13. Golser, H. ; Steindorfer, A.: Displacement Vector Orienta-tions in Tunnelling - What do they tell? In: Felsbau 18 (2000),No. 2, pp. 16-21.

14. Schubert, W. (1996). Dealing with squeezing conditionsin alpine tunnels. In: Rock Mechanics and Rock Engineering29 (1996), No. 3, pp. 145-153.15. Rokahr, R. ; Zachow, R.: Ein neues Verfahren zur tägli-chen Kontrolle der Auslastung einer Spritzbetonschale. In:Felsbau 15 (1997), No. 6, pp. 430-434.16. Hellmich, Ch. ; Macht, J. ; Mang, H.: Ein hybrides Ver-fahren zur Bestimmung der Auslastung von Spritzbetonscha-len. In: Felsbau 17 (1999), No.5, pp. 422-425.

AuthorsWulf Schubert, Institute of Rock Mechanics and Tunnelling,Univ. of Technology Graz, E-Mail Schubert@fmt.tu-graz.ac.at, Albert Steindorfer, 3G-Gruppe Geotechnik Graz ZTGmbH, steindorfer@3-G.at, Edward A. Button, Institute ofRock Mechanics and Tunnelling, Univ. of Technology Graz,E-Mail button@fmt.tu-graz.ac.at