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Acta Geodyn. Geomater., Vol. 5, No. 2 (150), 137146, 2008

MODELING OF VIBRATION EFFECT WITHIN SMALL DISTANCES

Martin STOLRIK

VSB-Technical University of Ostrava, the Faculty of Civil Engineering, Ludvka Podt1875/17,

708 33 Ostrava Porubaalso: Institute of Geonics, Academy of Sciences of the Czech Republic, v. v. i., OstravaCorresponding authors e-mail: [email protected]

(ReceivedNovember 2007, acceptedFebruary 2008)

ABSTRACTThe growth in the field of construction of shallow underground structures has been associated with construction of new roads,collectors and other structures. This contribution deals with modeling of distribution pattern of the maximum velocityamplitude (blasting vibration field) on surface basement. This basement will be situated within small distance from source of

technical seismicity that is used as a part of technological processes. The model represents seismic effect of blasting operationin shallow tunnel. Plaxis 2D modeling system and its dynamic module based on finite element method are used for thispresentation.

KEYWORDS: technical seismicity, blasting operation, finite element method

dynamic model. Results of the mathematical modelwere evaluated statistically and also graphically in aform of vibration velocity waveforms and sectionalviews of spread footing. (Manual of the programPLAXIS 2D)

A REAL PATTERN FOR THE MODEL

As a pattern for the processing of themathematical model, a structure of motorwayKlimkovice tunnel was used, where during wholetunnel construction the seismic monitoring otechnical seismicity induced by blasting operationswas performed, and sensors were located also on the

building of a family house with the house number798. (internal materials of INSET company).

The Klimkovice tunnel is a part of structure oD47 motorway and belongs to the construction

stretch, Stavba 4707 Blovec Ostrava, Rudn. It iscomposed of two one-directional two-lane tunneltubes. The tunnel A is situated as a right tunnel tube inthe direction of stationing and is designed for the Brno

Ostrava direction of traffic; the tunnel B is designedfor the Ostrava Brno direction of traffic (Fig. 1). Thedriven part of tunnel A is 857.40 m long and thetrenched part at the Brno side is 158.90 m long and atthe Ostrava side 39.41 m; the driven part of tunnel Bis 867.90 m long and the trenched parts are 159.50 mand 39.60 m long at the Brno and at the Ostrava side,respectively. The heavy section of both the driventunnels is 116.4 m2 (with an emergency lay-by of up

to 155.3 m2

); the tunnel finished cross-section fortraffic is constant for the driven and the trenchedtunnel parts, namely 71.8 m2. An extraordinary

INTRODUCTION

In the Czech Republic, a tremendous expansionin the construction of tunnels and undergroundstructures in general occurs, which also brings certain

problems because a lot of structures already built or planned are there in built-up areas and at relativelysmall depths below the ground. The majority otunnels are constructed by using a New AustrianTunnelling Method, an integrated part of which isrock disintegration by blasting operations andcontinuous geotechnical monitoring including alsoseismic monitoring. Blasting operations are a sourceof technical seismicity that may cause surface damageto equipment in buildings or to the whole buildings.Seismic monitoring in the course of construction of anunderground structure should prevent all this. On the

basis of measured data, parameters of blasting

operations are modified so that the surface effects odriving a shallow underground structure may beminimized. (Holub, 2006; Kalb, 2007; Rozsypal,2001).

This work is to show, by means of amathematical model, a non-uniform distribution omaximal amplitude of vibration velocity along thelength of spread footing, which occurs at a smalldistance (i.e. one hundred meters) from the source otechnical seismicity. In the model, as a source otechnical seismicity a blasting operation executed inthe course of driving a tunnel tube shallowly belowthe ground was considered. Into the model, which was

created by the program PLAXIS 2D based on the principle of finite element method, this blastingoperation was implemented by means of a so-called

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M. Stolrik138

Fig. 1 Klimkovice tunnel situation plan.

alluvial and gravitational sediments of thecharacter of loamy sandy gravels, class G3 to G4,symbols GM GC

gravitational and glacial sediments of thecharacter of clay to clay-sandy loams with gravel

fragments of underlying solid rocks, classes F2and F4, symbols CG and CS

alluvial gravitational and glacial clay loams andloams with fragments in the amount less than15%, class F6, symbols CL, CI

glacial clays, class F8, symbol CV.

The total thickness varies in a rather wide rangefrom about 0.90 to 11.40 m and more. In some places,a boundary between the Quaternary cover and theweathered bedrock is almost indistinctive.

BEDROCK

The whole locality of the tunnel is composed osedimentary rocks of unproductive Carboniferous culm. Clay sediments claystones and siltstones arethe most frequent petrographic type. They are usually

dark grey, thinly laminated, massive in places. Theoccurrence of flysch formations built of clayey andsandy rocks greywacke sandstones and greywackesis frequent. The colour of the rocks is grey, when thecolour of rather coarse-grained rocks is always lighter.Sandy sediments greywackes and greywackesandstones are the least abundant. Those are mostlyindistinctly bedded to massive. They contain veryoften thin laminae of clays that indicate the bedding ofthem.

MATHEMATICAL MODEL

The dynamic model of seismic effects of blasting

operation was implemented in the program systemPlaxis 2D as an axially-symmetric model. The general

procedure of dynamic model creation is analogous to

attention is paid to safety parameters of the tunnel.Both the tunnel tubes will be equipped, according tothe strictest European criteria, with a monitoringdevice, an adequate ventilation system, will beinterconnected with five tunnel connecting passagesfor the safety escape of persons and will haveregularly distributed tunnel alcoves with a necessarynumber of SOS boxes with the separate air supplies.In the place of central connecting passage, the cross-section of both the tunnel tubes is right-hand extended

by emergency lay-bys for the emergency parking o

vehicles. The central tunnel connecting passage is alsointerconnected with the surface via a vertical shaft inwhich connecting cables and feed water pipes for fire-fighting are placed. (Franczyk and Kotouek, 2006;Pechman, 2006).

ENGINEERING GEOLOGICAL CONDITIONS OFTHE LOCALITY

The whole tunnel structure, including parts of thestructure is situated in the cadastral area of the town oKlimkovice. Land immediately above the tunnel andin its vicinity has prevailingly the character of farmland. From the geomorphological point of view, the

locality of Klimkovice tunnel is there on the edge oVtkovsk vrchovina Uplands that are part of the

Nzk Jesenk Mts. Typologically, this is a case orough uplands in the area of fold-fault structures.

QUATERNARY COVER

In the locality of the tunnel, the Quaternary coveris formed mainly by gravitational (deluvial) sedimentsof clay-sandy loams with the admixture of fragmentsof parent material. The content and the size ofragments grow with depth, when the deepest layersof cover obtain even the character of loamy gravelswith angular fragments and debris. In the Quaternary

cover, four basic types of soils were defined(according to the norm SN 73 1001 Foundationostructures: Subsoil under shallow foundations):

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MODELING OF VIBRATION EFFECT WITHIN SMALL DISTANCES 139

Table 1 Propeties of rock environment.

into the model as horizontal layers of equal thickness.(Fig. 2). Physical properties of soils and thicknesses oindividual layers were implemented into the model onthe basis of results of engineering-geologicalexploration (internal materials of INSET company)and supplemented by tabular values (SN 73 1001)(Table 1). The influence of groundwater was not, forthe reason of simplification of mathematicalcalculation, considered.

In the model, a reference structure 50 metreslong replaces the building of a family house.

that of static analysis. It includes the setting of modelgeometry, the definition of boundary conditions, thegeneration of grid, the setting of initial conditions, thesetting of input geometric and material characteristicsof rock environment and constructional elements andthe determination of load characteristics. (Hrubeovand Aldorf, 2004).

The stratified rock environment corresponds tothe geological conditions characteristic of the given

area and was simplified for the needs of the model.Individual layers of various dips and thicknesseschanging in the geological section were implemented

Fig. 2 The overall geometry of symmetric model.

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M. Stolrik140

To prevailing period of seismic vibration ofrockparticles (To = 0.5 s)Vp velocity of P-wave spread (Vp = 1018 m.s

-1)is given by relation (1) in which thefollowing items are considered:

E modulus of elasticity (E = 2 000 000 kPa) Poisson number ( = 0.25)g acceleration due to gravity (g = 9.80665 m.s-2) rock density ( = 2.314 g/m3)

The frequency of vibration was introduced intothe mathematical model from a real record ovibration velocity waveform obtained in the course o

monitoring of technical seismicity on the building of afamily house No. 798 due to blasting operationsperformed at the point of calotte on the tunnel tube Bwhen driving was carried out at the smallest distancefrom the building being monitored, i.e. at thestationing 141,576.65 (Fig. 4, Table 2).

In the geometry of the mathematical model, the proper load simulating the blasting operation waslocated in a form of uniform continuous load in the

place of calotte (Fig. 5). The duration of dynamic loadwas 0.01 s. This value followed from the prevailingfrequency measured on the building being monitored,i.e.:

Hz100f,][1

== sf

T (4)

In the course of modelling seismic influences, itis always necessary to insert into the calculation, inaddition to standard geometric boundary conditions,the conditions of model interface absorption, becausewithout introducing these absorption boundary

conditions, the unreal reflection of seismic wavesback into the model and their interaction would occur.Absorbed normal and tangential stresses depend onthe spread velocities of P waves Vp and S waves Vs,on the density of material and on relevantdetermined velocities of mass point vibration yx uu && , .

For the given type of dynamic task, the presentedabsorption boundary conditions are set for the rightand the lower model boundary.

In a case of modelling dynamic influences, it isnecessary to set, in addition to the basic characteristicsof rock environment (strain, strength, descriptive

parameters), the velocities of wave spread in the rockenvironment and the characteristics of materialattenuation. The velocities of wave spread can be seteither directly or these parameters can be calculatedon the basis of modulus of elasticityEorEoed, Poissonnumber and specific weight according to generalrelations (g is the normal acceleration of gravity being9.80665 m.s-2):

( )( ) ( ) g

EE

EV oed

oedp

=

+

== ,

211

1, (1)

( ) +==

12,E

GG

Vs (2)

To take into account material attenuation, so-called Rayleigh parameters of attenuation alpha andbeta must be set. For the axially symmetric model, itis often sufficient to consider merely so-calledgeometric attenuation following from the radial spreadof waves through the environment, and materialattenuation may be omitted in this case (Rayleighattenuation coefficients are null). (Hrubeov andAldorf, 2004)

The dynamic modulus, by means of which a

dynamic load is put into the mathematical model, ischaracterised by amplitude, vibration frequency andphase shift (Fig. 3).

The phase shift was not considered in this task,because the introduction of phase shift did not causeany changes. The load amplitude was calculated byusing a relation by Prof. Fotieva (Bulyev, 1988) fordynamic loadingpdyn:

][922

1kPaToVpKcpdyn =

(3)

where

Kc coefficient of seismicity (Kc = 0.05) average specific weight ( = 22.7 kN/m3)

Fig. 3 Dynamic load Plaxis 2D.

Table 2 Parameters of record of blasting operation.

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Fig. 4 A record of blasting operation tunnel tube B, stationing 141,576.65, calotte.

Fig. 5 Calotte load diagram.

OUTPUTS AND INTERPRETATION OF RESULTSOF MATHEMATICAL MODEL

The goal was to observe the distribution omaximum amplitude of vibration velocity along thefoundations of reference structure 50 m longrepresenting e.g. factory building or storage facility.Along the basement slab length, twenty sixmonitoring points were arranged (Fig. 6) in themathematical model before the beginning ocalculation. At the points, the maximum amplitudes ovibration velocity were subsequently evaluated.

In Figures 7 to 9 the areal distribution o

vibration velocity along the length of foundationsobtained from outputs of the mathematical model isprocessed graphically. To each of twenty six observedpoints, maximum amplitudes of vibration velocities inthe horizontal and the vertical direction and in thevertical plane (in the model area) correspond(Stolrik, 2007).

Furthermore, a change in the maximumamplitude of vibration velocity in relation to thedistance from the source of dynamic load wasobserved as well. The distance ranged from 42.36 m(shortest distance between the calotte and point 1) to84.26 m (shortest distance between the calotte and

point 26). Correlations of maximum amplitude ovibration velocity with the distance from the source o

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M. Stolrik142

Fig. 6 The layout of points observed.

Fig. 7 Distribution of velocity amplitude on surface basement in horizontal direction.

Fig. 8 Distribution of velocity amplitude on surface basement in vertical direction.

1.252

1.681

0.6050.6134

0.55150.575

0.6551

0.696

0.6036

0.87

0.9712

1.01

0.7391

0.9036

0.9384

0.6588

0.8495

0.9296

0.7036

0.6367 0.4832

0.4460.4317

0.6688

0.4601

1.077

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

0 5 10 15 20 25 30 35 40 45 50

size of surface basement [m]

velocityamplitude[mm.s-1]

1.5971.412

1.975

1.495

1.052

1.293

1.6

1.594

2.039

1.7811.761

1.669

1.415

1.194

1.1461.251

1.013

1.089

0.9021 0.8694

0.9048

0.8029

0.885

0.85

0.9181

0.8120.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

0 5 10 15 20 25 30 35 40 45 50


velociytyamplitude[mm.s-1]

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Fig. 9 Distribution of velocity amplitude on surface basement in vertical plane.

dynamic load were done and adequate correlationcoefficients were calculated. The correlations weresubsequently graphed again for the maximumamplitudes of vibration velocities in the horizontaldirection, the vertical direction and in the verticalplane. (Graphs 1, 2, 3).

A general overview of the calculated maximalamplitudes of vibration velocities in the horizontal

1.602

1.508

1.992

1.501

1.076

1.749

1.597

2.073

1.334

1.8381.761 1.736

1.197

1.415

1.1471.252

1.055

0.9115

1.093

0.9644

0.85110.9225

0.9007

0.85

0.9459

0.8380.7

0.9

1.1

1.3

1.5

1.7

1.9

2.1

2.3

0 5 10 15 20 25 30 35 40 45 50



0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.82

2.2

30.00 50.00 70.00 90.00

distance [m]


Graph 1 Correlation of maximum velocity amplitudeson distances of surface basement fromsource of dynamic load horizontaldirection of velocity amplitudeCorrelation coefficient: - 0.8556369

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

30.00 50.00 70.00 90.00

distance [m ]


Graph 2 Correlation of maximum velocity amplitudeson distances of surface basement from sourceof dynamic load vertical direction of velocityamplitudeCorrelation coefficient: - 0.8711178

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

22.2

30.00 50.00 70.00 90.00

distance [m ]


Grahp 3 Correlation of maximum velocityamplitudes on distances of surface

basement from source of dynamic load velocity amplitude in vertical planeCorrelation coefficient: - 0.8851067

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M. Stolrik144

Table 3 A comprehensive overview of maximum amplitudes of vibration velocities.

vibration velocity at point 1 again in the horizontaldirection, the vertical direction and the vertical plane.

direction, the vertical direction and in the vertical planr at single points with adequate locations of thepoints on the foundations and relevant distances fromthe source of dynamic load is given in Table 3. InTable 4 the calculated maximum amplitudes ovibration velocities calculated by using the finite

element method at point 1 and the maximumamplitudes of vibration velocities measured on the building of the family house in the course omonitoring technical seismicity are presented forcomparison. The location of these points in thevertical section in reality corresponds to that in themathematical model. Small differences between thecalculated and the measured amplitudes of vibrationvelocities can be imputed to a considerably simplifiedmodel of very complicated situation, values, whichwere obtained partly from engineering-geologicalexploration and partly from tables, used in the model,and the implementation of dynamic load that wasgenerated in the model by using a real record andcalculation. In Figures 10 to 12, there is the programsystem Plaxis 2D graphical output of waveforms o

Table 4 A comparison of results of mathematicalmodel and IN-SITU measurements.

Differences in the maximum amplitude ovibration velocity at observed points along the lengthof foundations (very small distance between the points, about 3 metres) are up to 100%. These vastdifferences over small distances may cause a

considerably non-uniform distribution of load on abasement slab and may lead to its possible vibrationand subsequent possible damage to the basement slab

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Fig. 10 Velocigram Horizontal direction of velocity amplitude.

Fig. 11 Velocigram Horizontal direction of velocity amplitude.

Fig. 12 Velocigram Velocity amplitude in vertical plane.

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M. Stolrik146

0.5

1.75

1.53

-0.77

-1.15

-0.11

1.57

0.65

-0.77

-0.61

-0.38

0.8

0.65

0.08

-0.04

0.34 0.31

spot 1

50 m

Fig. 13 A section through the basement slab.

Holub, K.: 2006, Analysis of blasting vibration effects tounderground workings, urban structures andinhabitants, Transactions of the VB-TechnicalUniversity of Ostrava, Civil Engineering Series, 2,113123.

Hrubeov, E. and Aldorf, J.: 2004, Analysis of ramming ofa steel pile on the underground structures in itssurrounding, Geotechnika the conferenceproceeding, 5762.

Kalb, Z.: 2007, Shallow underground construction andvibrations, Tunel, 2, 12-20. Program manual PLAXIS2D.

Pechman, J.: 2006, The Klimkovice tunnel, D47 highway,Tunel, 1, 3234.

Rozsypal, A.: 2001, Monitoring and risks in geotechnic,Jaga group, Bratislava, (in Czech).

Stolrik, M.: 2007, Modelling of the seismic effects of blasting in shallow tunnel, text-book on CD, II.meeting of the students of doctoral studies ofgeotechnics departments, (in Czech).

avek, P.: 2006, Diploma thesis: Effect of the progres ofdriving the Klimkovice's tunnel on development of thesubsidence curve, VSB-Technical University ofOstrava, (in Czech).

and the building. As an example Figure 13, whichrepresents a section through the foundations oreference building at the time when at point 1 the totalmaximum amplitude of vibration velocity in area o1.749 mm.s-1 was recorded, may be given. It isnecessary to realize that in this contribution themathematical model is merely two-dimensional, andthus considerably simplified.

CONCLUSION

In this work, the applicability of program systemPlaxis 2D to the modelling of seismic effects o

blasting operations carried out in a shallowlyconstructed underground structure situated at a smalldistance from a built-up area was verified.

At a small distance (i.e. the first hundred meters)from the source of dynamic load (specifically blastingoperation), the existence of indirect dependence odistance from the source of dynamic load on themaximum amplitude of vibration velocity wasconfirmed by means of a mathematical model This is proved by favourable values of correlationcoefficients.

ACKNOWLEDGEMENT

This contribution was prepared in the frame odealing with the project GAR 103/05/H036.

REFERENCES

Bulyev, N.S.: 1988, Mechanika podzemnych sooruenij, Nedra, Moskva, UDK (622.012.2:69.035.4)(075.8),(in Russian).

SN 73 1001 Foundation of structures: Subsoil undershallow foundations, (Zakldn staveb: Zkladovpda pod plonmi zklady), (in Czech).

Franczyk, K. and Kotouek, S.: 2006, The Klimkovicehighway tunnel excavation completed, Tunel, 2, 5456.

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