Assessment of the Soil-Structure- Interaction based on ... · 406 19 Assessment of the...

405

Chapter 19-x

Authors:Fritz KopfAdrian BekőDavid SchäferJohannes PistrolMichael PietschLudwig Rossbacher

19Assessment of the Soil-Structure- Interaction based on Dynamic Measurements

MotivationMany monitoring campaigns show large differences between the theoretical model

and the practical measurements. A major part of it can be attributed to soil-structure-interaction. It is therefore desirable to have methodologies available that enable quantify-ing these effects through monitoring campaigns.

Main ResultsIn an outstanding monitoring campaign a reliable approach has been demonstrated

to quantify soil-structure-interaction effects. The power of ambient vibration monitoring on soil has been demonstrated.

406

19 Assessment of the Soil-Structure-Interaction based on Dynamic Measurements

The Leitturm in Augarten, Vienna, built during World War II (left) and aperture in the 2.5 m concrete wall of the tower seen from inside (right)

F.19-1

19-1 IntroductionThe Leitturm in Augarten (Vienna) was built from 1943 till 1944 under the responsi-

bility of Prof. Dr. h.c. Dipl.-Ing. Friedrich Wilhelm August Tamms. It was created as one of three flak-positions, which were designed as a triangle around the centre of the city. At each position there are two towers, one for the radar (Leitturm) and one for the battle (Gefechtsturm). The platforms of the towers were constructed on the same height, so that collimation calculations could be handled more easily. The real purpose of the towers dur-ing World War II was as bunkers for the civil population.

The towers are now under monument protection. The Leitturm in the Augarten has been closed since the end of the war and was only inhabited by countless pigeons, which created a huge amount of waste. Nevertheless, historic documents, letters etc. can be still found there. The measurements were also a chance for historians to gain access to the structure, and they found some very interesting documents.

The rigidity of the structure and its tall shape make it the ideal test object. Apart from the special geometry and constitutive features, the location also plays an important part. Since the bunker is located in a quiet park, the data acquisitions were affected by very limited noise.

From the dynamic point of view, the main advantage of this structure is the possibility to distinguish between the vibration of the soil occurring at lower frequencies, and the vibration of the building and its members, which occurs at higher frequencies. Due to the high mass of the structure, the building behaves like a rigid body in the low frequency band, whereas the vibrations of the walls are in a much higher frequency band. Between

407

Introduction 19-1

N

200 metres

Triangular setups of sensors for measuring ambient soil vibrations F.19-2

high frequencies and low frequencies there is a significant gap. Most of the “normal” build-ings do not have such a gap. In that case the frequency bands are mixed and it is very dif-ficult to distinguish between them. In this case, the SSI phenomenon can be determined very conveniently, which is the reason why the Leitturm was instrumented.

The dynamic properties of the soil can be determined in two different ways. The first one is the common way, using the Rayleigh Waves dispersion on the soil surface, and the back calculation to shear wave profiles. The second approach is the back calculation of the soil stiffness, based on the soil-structure-interaction.

The simultaneous measurement of the dynamic movements of the building allows the determination of the kinematic behaviour of the SSI. The tilting oscillations of the tower occur in both directions with different frequencies. They are transmitted to the soil and they can be measured in the surroundings.

The measurements were carried out separately on the soil surface for the assessment of the soil parameters, and on the tower structure to record the building movements. The next steps were: the measurement of the influence of the tower oscillation on the soil; the determination of the decay of the influence with the distance, and the qualitative estima-tion of the influence on the H/V-method results.

The results of the dynamic measurements were compared to different numerical sim-ulations. Numerical models present the benefit to be tuned with the real dynamic proper-ties of the measured SSI-system. The methods were compared, highlighting benefits and disadvantages of each one. The calibration of these methods with the measured condi-tions led to scientific findings and the opportunity to evaluate the different methods.

408


Lennartz 3

Force-meter

Sampling rate1000 Hz

Spring

Mass 150 kg

appr

ox. 2

.3 m

15 mLennartz 2

17.5 mLennartz 1

10 m

Walesch 3 Walesch 2 Walesch 1

Dynamic loadplate tester

10 m12 m15 m

Surface-wave dispersion test setup with artificial harmonic excitation using a “shaker” as a mass-spring-system

Surface-wave dispersion test setup with artificial impulse excitation using a light falling weight device

F.19-4F.19-3

19-2 Measurements on the Soil SurfaceThe vibrations of the soil surface were measured for the documentation of the surface

wave propagation. The phase velocity of Rayleigh waves on the surface is not constant but it depends on the frequency of the wave. Usually the Rayleigh waves with low fre-quencies are faster than those with higher frequencies. This results in the fact that a vibra-tion signal containing a wide frequency spectrum changes shape with the propagation. This phenomenon is called “dispersion of the waves”. Low frequency waves, characterized by longer wave length, reach the measurement point distanced from the impact first. Contrarily, the high frequencies follow later.

To measure this effect, two artificial excitation types were applied: an impulse (for the high frequencies) and a harmonic excitation of the soil (for the low frequencies). The am-bient vibrations were recorded in several triangular setups with different dimensions. By analysing the measured vibrations the dispersion curve could be evaluated.

The interpretation of the dispersion curve of the surface waves by means of analytic models was affected by imperfections, arising from working outside of the method as-sumptions. The natural soil is indeed not a homogeneous infinite half-space but consists of different layers of soil types with diverse soil properties.

The evaluation of the dispersion curve was possible through the numerical simulation of differently layered soil profiles. By modelling each different soil profile it was possible to get an artificial dispersion curve as outcome. A special optimization algorithm was then useful to do the best fitting with the measured one. Even if this inverse analysis method does not yield a unique result, a most likely soil profile can be identified.

The results of these tests are the shear wave velocity profiles of the soil, the leading parameter for the assessment of the dynamic soil properties. It is a real material parameter because it is constant for all frequencies (shear waves do not disperse).

409

Measurements on the Soil Surface 19-2

0

20

40

60

80

100400 800 1200

vs [m/s]

Dep

th [m

]

0.001

0.005

0.004

0.003

0.002

2 4 6 8 10 20 40 60

Frequency [Hz]

Slow

ness

[s/m

]

0

20

40

60

80

100

400 600200 800 1000

vs [m/s]

Dep

th [m

]

0.001

0.005

0.004

0.003

0.002

21 4 6 810 20 40 60

Frequency [Hz]

Slow

ness

[s/m

]

F.19-5

F.19-6

Dispersion curve with misfit-values and corresponding shear wave velocity profile (Geopsy software)

Triangle setup: dispersion of best fitting profiles (left) and shear wave ve-locities of best fitting profiles (right)

410


z

y

x

GalleryOG 11

N

x2

y2

x3

y3R3

R2

R1x1

y1

x

y

α

2.50⋅10–7

Lennartz-x MW [m/s]Lennartz-y MW [m/s]Lennartz-z MW [m/s]Lennartz rot [m/s]

FFT

osci

llatio

n ve

loci

ty [m

/s]

2.00⋅10–7

1.50⋅10–7

1.00⋅10–7

5.00⋅10–8

100.00

2 3 4 5 6

Frequency [Hz]7 8 9 10

Rotatory waveform:R1 = +x1 ⋅ sinα + y1 ⋅ cosαR2 = −x2 ⋅ sinα + y2 ⋅ cosαR3 = −x3 ⋅ sinα − y3 ⋅ cosα

R = (R1 + R3) / 2

1.99

1.62

3.87 3.84

3.903.181.643.482.93

2.662.02 5.8

FFT-analysis of combined values from measurements in the corner of the gallery

Sensor setup for the measurement on the gallery level inside the tower

F.19-8

F.19-7

19-3 Measurements on the TowerThe ambient vibrations of the Leitturm-structure were measured with three very sen-

sitive geophones (Lennartz LE-3D-5s) on different levels. The Fast Fourier Transformation (FFT) analysis of the measured data of vibrations on the 11th floor shows the eigenfre-quency of 1.6 Hz for the tilting motion in the “weak”, y-direction and 2.0 Hz in the “stiffer”, x-direction. The peak of the vertical oscillation is not as significant but can be found at 3.9 Hz. Because of the tower’s rigid structure, the soil-structure interaction behaviour is governed by the mass of the tower and the stiffness of the soil. By use of the Random Decrement Technique (RDT), the damping ratio of the vibrations can be separately evalu-ated for each frequency. The algorithm analyses ambient vibrations and looks for “events”

411

Measurements on the Tower 19-3

Damping: 7.6%

RDT-evaluation with BRIMOS

Random Decrement Techniquez-vertical oscillation 3.9 Hz

5μm43210

–3–4

–1–2

0 0.4 1.0 s0.50.1 0.2 0.3 0.90.6 0.7 0.8

xn

xn+1

……

from RDT-algorithm:

Lehr's damping ratio:krit

cD

c=

1ln

2nx

Dπ

= ⋅⋅

xn+m

xn+mm

Eigenfrequ.[Hz]

Intensity[μm]

Zone RDT[%]

0.257 1 1033.772 I1.627 2 104.011 I2.000 3 133.753 I1.621 4 0.0001.984 5 0.000

I2.000 6 133.7533.937 7 133.753 I 7.643

18⋅10–6 45⋅10–9

Internal oscillations of the structure

Building-subsurfaceinteraction

40⋅10–9

35⋅10–9

30⋅10–9

25⋅10–9

20⋅10–9

15⋅10–9

10⋅10–9

5⋅10–9

0

FFT-

ampl

itude

[m/s

2]

[m/s]

10⋅10–6

14⋅10–6

6⋅10–6

8⋅10–6

2⋅10–6

12⋅10–6

16⋅10–6

4⋅10–6

00 20 40 60 80 200180160140100 120

Frequency [Hz]

Epi x [m/s2]Epi y [m/s2]Epi z [m/s2]Walesch x [m/s]Walesch y [m/s]Walesch z [m/s]

FFT- analysis of signals (acceleration, oscillation velocity) for impulse-excitation of the Leitturm at gallery level

RDT-analysis of signals in z-direction, corner points in gallery level

F.19-10

F.19-9

in the signal. All the detected events can be averaged to an artificial event which contains information about the vibrations’ decay. The damping ratio of the relating vibration mode can be then determined.

The artificial excitation with impulses of a medicine ball (5 kg) on the gallery of the Leitturm (mass about 40000000 kg) could be detected inside the tower with its 2.5 m thick walls and a ceiling with more than 3.5 m concrete slab. Each individual impact could be clearly detected. From the analysis it was possible to get the natural frequencies caused by the SSI in the low frequency domain, and after a gap without any significant peaks, the internal vibrations of the building in the high frequency domain. In this special case of the Leitturm the metrological evidence of separation between internal vibrations of the building and global movements caused by the soil-structure interaction (F.19-10) subsists. In usual buildings the effects are overlapping and it leads to mixed effects in the measurement signals and difficulties in the interpretation.

412


y1

z1

y2

z2

x2

z2

x3

z3

”translatory amplitude“”rotatory

amplitude“

1 2 1 2( ) ( )2y

y y

z z y yd t

ψ − += =

⋅

1 2

1 2

( )2 ( )y y

y yt d

z z+

= ⋅⋅ −

3 2 2 3( ) ( )2x

x x

z z x xd t

ψ− +

= =⋅

2 3

3 2

( )2 ( )x x

x xt d

z z+

= ⋅⋅ −

xy z

dx

tx

Axis ofrotation

yxz

dy

ty

yψ xψ

50

Leve

l of r

otat

ion

axis

ov

er fo

unda

tion

leve

l [m

]

40

20

30

10

–30

–20

–10

–40

–501.0 1.2 1.4 1.6 1.8 2.4 2.62.0 2.2 2.8 3.0

Frequency [Hz]

Eigenfrequency2.0 Hz

Rotation axis

0

In a first approximation the soil structure interaction of the Leitturm can be under-stood as a rigid body motion of a concrete block socketing in an elastic half space of soil.

To prove the existence of a centre of rotation for both tilting modes and to find its po-sition, vibration measurements were performed in the cellar of the tower and the signals were processed with the following procedure. In a first approximation, the tilting of the tower can be divided into a rigid translational component and into an independent rigid rotatory one. Combining the signals of two sensors is possible to identify the position of the centre of rotation, in relation to the measurement level. A fixed rotation centre exists only if both the translational and the rotatory oscillation components are oscillating either exactly in phase or exactly out of phase. The outcomes of the evaluation of the level of

Level of the rotatory centre for tilting oscillations in x-direction depending on the frequency. Only the oscillations in phase or out of phase are considered

Determining the rotatory centre of the rigid body by analysing signals from two sensors on one level

F.19-12

F.19-11

413

Measurements on the Tower 19-3

4⋅10–8 FFT ((y1 + y2)/2)FFT (z1 − z2)FFT ((x2 + x3)/2)FFT (z3 − z2)

FFT

osci

llatio

n ve

loci

ty [m

/s]

3⋅10–8

2⋅10–8

1⋅10–8

0.00

1.0 4.03.02.0 3.5

Frequency [Hz]2.51.50.5

1.95 Hz1.63 Hz

2.02 Hz

1.61 Hz

Frequency

Rotation

Translation = rotation × distance from level of measurementsDistance

between levelof measurements and centre

FFT

- am

plitu

de

0

1

2

3

4Displacementof maximum

the centre of rotation are represented in F.19-12 as a cloud of blue dots. Every dot cor-responds to the centre of rotation for the tilting movement in x-direction for each sample of the FFT analysis in correct phasing. The position of the rotation centre at the eigen-frequency of the tower (2.0 Hz) is well identified. It is the highest density within the red dotted cloud in this domain. It can be seen that a fixed centre of rotation does exist but the position depends on the frequency. This fact that the centre of rotation depends on the frequency is the reason why the frequency at the maximum of the translational com-ponent (turquoise, blue) is lower than the related rotatory components (green) in F.19-13. It is not trivial because both of the peaks indicate the frequency of the same oscillation mode and should be exactly the same. But since there are also frequencies besides the eigenfrequency and the translational component is also influenced by the distance to the rotation centre, the peak of this component is shifted according to the sketch in F.19-14.

Sketch of coherence between rotatory oscillation component (green), transla-tional component (turquoise) and distance to rotation centre (blue)

Translational and rotatory oscillation components of tilting oscillation whose maxima have different positions

F.19-14

F.19-13

414


Console ZSensor 5 m ZSensor 10 m ZSensor 15 m ZSensor 20 m ZSensor 30 m ZSensor 40 m Z

Console ZSensor 10 m ZSensor 15 m ZSensor 20 m ZSensor 30 m ZSensor 40 m Z

1

2.5⋅10–6

2.0⋅10–6

1.5⋅10–6

1.0⋅10–6

0.5⋅10–6

01.5 2 2.5 3

Frequency [Hz]3.5 4 4.5 5 5.50.5

Sign

al [V

]

2 Hz

1

16⋅10–6

12⋅10–6

14⋅10–6

10⋅10–6

6⋅10–6

2⋅10–6

4⋅10–6

8⋅10–6

01.5 2 2.5 3

Frequency [Hz]3.5 4 4.5 5 5.50.5

Sign

al [V

]

2 Hz1.63 Hz

z

y

x

GalleryOG 11

N

Acceleration measurements for x- (left) and y-direction (right)array: z-component of the sensors

Sketch of the ambient vibration measurement setup on the surface in x- and y-direction

F.19-16

F.19-15

19-4 Measurements of Soil-Structure Interaction

According to the soil-structure interaction mechanism the soil stiffness influences the movements of the building just as the building affects the soil. To measure the effect of the movement in the interaction, the tower oscillation and the vibration on the soil sur-face were measured simultaneously. One sensor was fixed on the tower and the others were placed in a line on the soil in both axis directions.

The FFT-analysis shows how the tower with its significant eigenfrequencies of 1.6 Hz and 2.0 Hz affects the soil. The movement of the building produces a vibration in the soil, detected with the geophones. This influence (velocity V ) decreases with the distance r to the tower (F.19-17). According to the influence depth of the different modes (see F.19-19)

415

Measurements of Soil-Structure Interaction 19-4

7 0.641.4 10xV r− −= ⋅ ⋅ 7 0.993.6 10yV r− −= ⋅ ⋅

1.6⋅10–7

1.4⋅10–7

1.2⋅10–7

1.0⋅10–7

2.0⋅10–8

4.0⋅10–8

6.0⋅10–8

8.0⋅10–8

010 20

Distance from source [m]30 40

InterpolationSample points

InterpolationSample points

500Max

imum

osc

illat

ion

velo

city

[m/s

]

4.0⋅10–7

3.5⋅10–7

3.0⋅10–7

2.5⋅10–7

5.0⋅10–8

1.0⋅10–7

1.5⋅10–7

2.0⋅10–7

010 20

Distance from source [m]30 40 500M

axim

um o

scill

atio

n ve

loci

ty [m

/s]

3

H/V 5 m 20 m

30 m

40 m

2

1

0

3H/V

2

1

0

0.4 0.6

3H/V

2

1

00.8 1.0 2.0

Frequency [Hz]4.0 6.0 8.0 10.0

10 m

15 m

3

H/V

2

1

0

3H/V

2

1

0.4 0.6

4

3

H/V

2

1

00.8 1.0 2.0

Frequency [Hz]4.0 6.0 8.0 10.0

H/V – evaluation of measurements in x-direction, distances 5, 10, 15, 20, 30 and 40 m (evaluation with Geopsy)

Propagation of tower vibrations in the soil. Damping function in x-direction

F.19-18

F.19-17

there is more damping in the propagation function in y-direction. The deeper the influ-ence, the less is the decay. This effect can be seen in the value of the damping exponent in this function. Due to the eccentricity of the sensor setup in y-direction, the peak of the x-direction movement (2.0 Hz) can be also detected in F.19-16 (right). Due to the different damping exponents in the formula of propagation, the effect of y-movement becomes dominant with increasing distance from the tower.

The H/V-method evaluates the relationship between the horizontal and the vertical vibrations. This “ellipticity” of the ambient vibrations is an indicator for site effects in case

416


Modulus of subgrade reaction

Dynamic soil parameter? Dynamic soil parameter: vs , G, ρ, ν, E

Analytical with FEM Analytical for rigidcircular foundation

on half space

Finite elementmethod (FEM)

ks kr

kν

ks

Es, G, ν

Stiffnessmethod

Es

rigidbody

rigidbody

flexiblebody

flexiblebody

flexiblebody

k k= = ⋅

2

3

3

2

4 8

23 12

12

s

s

s

r s

bk

b l bF l F k

l bM b F k

M l b

ψσ

ψσ

ψ

ψ

⋅= ⋅

⋅ ⋅= ⋅ ⋅ = ⋅

⋅= ⋅ ⋅ = ⋅

⋅

rr

kI

ω =

v s s= ⋅ ⋅ = ⋅k l b k A k

kmν

νω =

/ 2bψ

ψ

⋅F

F2/3 b

l

F

bb

Mass

Area

Mass moment of inertia

Moment of inertia

Modulus ofsubgrade reaction

Modulus ofsubgrade reaction

σσ

l

Eigenfrequencies with dynamical modulus of subgrade reaction method: tilting motion and vertical motion

Different methods of numerical modelling

F.19-20

F.19-19

of earthquakes and the eigenfrequency of the soil (peak at 0.9 Hz, 40 m-line) can be evalu-ated in case of special soil conditions. The soil structure interaction causes a magnifica-tion of the vertical vibration component at the eigenfrequency of the tower (2.0 Hz in x-direction) causing a depression of the curves of F.19-18 in the near-field of the tower. Within the first 30 m the vibrations of the tower influence the H/V values.

19-5 Numerical SimulationTo show the potential achievement of the different dynamic calculation methods, sev-

eral numerical analyses have been carried out as shown in F.19-19.

417

Numerical Simulation 19-5

12

sv

l b kf

mπ⋅ ⋅

=

sk

3

1 122

s

rxy

b lk

fIπ

⋅

=

3

1 122

s

ryx

l bk

fIπ

⋅

=

6

Nat

ural

freq

uenc

y [H

z]

3

5

1

2

4

00 50 100 300250150 200

Modulus of subgrade reaction [MN/m3]

z-verticalx-longitudinaly-lateralz-measured 3.9 Hzx-measured 2.0 Hzy-measured 1.6 Hz

rigid

38 MN/m3

145 MN/m3 180 MN/m3

z x yVertical

38 MN/m3

Tilting longitudinal

145 MN/m3

Tilting lateral

180 MN/m3

Coherence between modulus of subgrade reaction and eigenfrequency for different oscillation modes, comparison with measured values

F.19-21

Effect of missing scale effect on the results of the dynamic modulus of sub-grade reaction method

F.19-22

19-5-1 Method of Modulus of Subgrade Reaction

The method of “modulus of subgrade reaction” is the most common method. The ef-fect of the soil is simulated by linear elastic springs distributed on the horizontal projec-tion. The modulus of subgrade reaction ks is meant as a spring stiffness per square metre. It is not a real soil parameter because it may depend on the geometry, shape, and scale of the building as well as on the influence depth for layered soil profiles.

In F.19-21 the results of the calculation with the modulus of subgrade reaction meth-od are reported beside the “reality” case. The results of the measurements are represented with dotted lines. The modulus of subgrade reaction is plotted versus the eigenfrequency of the interaction system.

The problem of the method of modulus of subgrade reaction is evident in F.19-21. There is no value for the modulus of subgrade reaction to fulfil all the oscillation mode fre-quencies measured in the field on the same soil conditions. This effect can be explained by F.19-22 where the different soil loading and the influence depth of the modes are shown.

418


Es

flexiblebody

5

6

7

Nat

ural

freq

uenc

y [H

z]

3

1

2

4

00 500 1000 300025001500 2000

282 398 690630488 563

Shear wave velocity [m/s](ρ = 1800 kg/m3, ν = 0.3)

Oedometric modulus Es [MN/m2]

vertical [Hz]x-longitudinaly-lateralmeasured vertical 3.9 Hzmeasured x-direction 2.0 Hzmeasured y-direction 1.6 Hz

1140 MN/m3

1900 MN/m3 2000 MN/m3

Results of back-calculation of eigenfrequencies with the stiffness method F.19-23

The method is theoretically and practically not able to describe the real physical situation. It can only be used for simple estimations within the frame of existing experiences.

19-5-2 Stiffness Method

While the method of modulus of subgrade reaction is limited to normal stresses in the subgrade, the stiffness method allows to take shear stresses into account as well. Therefore the deformation of a single point in the area of contact between soil and tower depends on the loading of the point itself as well as the loading of the surrounding area. Moreover it is possible to take the flexibility of the tower structure into consideration. The method is based on the oedometric modulus, a real physical soil parameter. The oedometric modu-lus is assumed to be constant for the whole soil domain influenced by the foundation. A stress-dependency of the oedometric modulus and a layered soil structure were not taken into account. For the stiffness method the geometry of the tower is segmented into n single, finite elements. To determine the deformation characteristics of the interacting soil – tower system, a single element i is loaded with the single load p = 1, which causes a settlement trough with its maximum c0 under the loaded element i . The settlement under the adjacent elements (i−1) and (i+1) is c1 et cetera.

The settlement c0 is evaluated for the characteristic point. The actual settlements can be calculated with these lines of influence and the real loads for each element.

For the natural frequency of the vertical motion the settlements under the dead load of the tower are calculated. An equivalent stiffness per square metre ks can be derived from the mean settlement wm. The total equivalent stiffness can be written as

419

Numerical Simulation 19-5

5

Nat

ural

freq

uenc

y [H

z]

3

1

2

4

00 235 333 408 667624471 527 5770 100 200 300 800700400 500 600

Dynamic shear module [MN/m2] Shear wave velocity [m/s]

vertical [Hz]x-direction [Hz]y-direction [Hz]measured vertical 3.9 Hzmeasured x-direction 2.0 Hzmeasured y-direction 1.6 Hz

Results of numerical estimation of eigenfrequencies with dynamic parameters for a rigid circular foundation on elastic isotropic half-space

F.19-24

v sk k A= ⋅

where A is the ground area of the building. With the buildings mass m, the natural fre-quency of the vertical motion is defined as

vv

kmω = .

The angle ψ of rotation is calculated for a tilting moment of M = 1 to evaluate the natural frequency for the tilting motions, which can be written as

rr

kIω = .

with /rk m ψ= and the mass moment of inertia I of the building.

19-5-3 Analytic Formulas for Circular Rigid Body on Linear Elastic Half-Space

It is possible to use the analytic formulas for circular rigid bodies on linear elastic half-space to get reliable results if the foundation of the building is rigid and can be described by a circular shape. The method is based on real physical soil parameters (shear modulus) [Flesch, 1993; Wolf, 1985]. F.19-24 shows that the results are very well corresponding to the measured tilting modes from the field test. The relationship between the damping ratios fits with the test results, but not in absolute values, because of the small amplitudes.

420


6

3

5

1

2

4

00 50 100 300250150 200

Modulus of subgrade reaction [MN/m3]

Flexible tower, x-directionFlexible tower, y-directionFlexible tower, z-directionRigid tower, x-directionRigid tower, y-directionRigid tower, z-direction

33.5 MN/m3

3.9 Hz verticalz-direction

2.0 Hz longitudinalx-direction

Flexible tower, rigid soillimit for x-direction

Flexible tower, rigid soillimit for y-direction

1.6 Hzlateraly-direction

175 MN/m3 255 MN/m3

Nat

ural

freq

uenc

y [H

z]

41v

G rk

ν⋅ ⋅

=−

0.425

B

0.27 mB⋅

383(1 )r

G rk

ν⋅ ⋅

=−

5

3 (1 )8

Irν

ρ⋅ ⋅ −⋅ ⋅

3

(1 )4

mrν

ρ⋅ −⋅ ⋅

0.15

(1 )B B+ 0.24 I

B⋅

Stiffness

x

z

y

2.0 HzD = 0.06 %

1.6 HzD = 1.9 %

3.9 HzD = 7.6 %

Circular foundation

Vertical

Tilting

Mass ratio Damping ratioD

AdditionalmassB

Damping

x-direction: longitudinal 1.915 % 7.686 % 0.25

y-direction: lateral 0.959 % 4.186 % 0.23

z-direction: vertical 7.643 % 36.859 % 0.21

MeasuredRDT

Analytical circular foundation

RelationshipRDT/analyt.

Coherency between modulus of subgrade reaction and eigenfrequency for different modes of vibration in case of rigid body movement and elastic build-ing characteristic; comparison of FE computations with measured results

F.19-26

Results with dynamic substitute parameters for a rigid circular foundation on elastic isotropic half-space [Studer, 2007]

F.19-25

19-5-4 Finite Element Method (FEM)

The Finite Element Method (FEM) was used for two separate analyses. First, the meth-od of the modulus of subgrade reaction was applied to investigate the flexibility of the tower structure. The resulting consideration was that as shown in F.19-26, a modulus ful-filling the real dynamic soil conditions for all modes at the same time cannot be found. The reason is described in 19-5-1 and pictured in F.19-22.

In the second analysis with FEM, the soil was modelled with linear elastic elements. This is acceptable because the ambient measurements focus on waves with limited am-plitude. By updating the model according to the measured dynamic soil profile and by

421

Conclusions 19-6

FE calculation result: deformation in z-direction, 1st harmonic mode F.19-27

adjusting the soil stiffness, the determination of a solution fulfilling the tilting mode fre-quencies, the position of the rotation centre and the damping exponent for vibration de-cay with distance was possible. The fact that the soil of the updated model is stiffer, leads to get higher shear wave velocities than measured, but in this case the fitting relationship between the layers is known.

19-6 ConclusionsThe target of the research work was to find a method to determine dynamic soil pa-

rameters using dynamic surface measurements, to find calculation parameters for differ-ent numeric simulations and to compare the results with the dynamic measurements of the soil-structure interaction, performed on a simple test object.

It is possible to formulate two main reasons to explain the demonstrated differences between the measured soil properties in the adjacent domain and the stiffer soil behav-iour from the back calculation: The water content of the soil has no relevant effect on the shear wave velocity (just the mass difference) but it is important for the dynamic compres-sion stiffness of the soil because of the pore water pressure. The considered modes are dominated by the compression stiffness of the soil.

The second reason for the stiffer soil properties beneath the Leitturm building is the soil consolidation. The average soil pressure of 610 kN/m² of the foundation slab of 31 m × 21 m has been loading the soil for the last 66 years. The measurements of the shear wave profiles were carried out on unaffected soil conditions in the adjacent park.

Summarizing the experiments in and around the Leitturm in Augarten in Vienna led to two different metrological approaches for determination of the dynamic soil properties connected with numerical inverse analysis. The benefits and the disadvantages of several

422


400 800

vs [m/s]

Dep

th [m

]

0

4

8

12

16

20

2.90

0.80

4.30

(-9.95) 14.60

(-10.35) 15.00

(-14.65) 19.30(-15.45) 20.10

(-18.35) 23.00

0.40

11.00

0.10

0.10

0.502.90

Modulus of subgrade-reaction method:

ks x = 145−175 MN/m3 ks y = 180−255 MN/m3 ks z = 30−38 MN/m3

analytic FEM

(1.55) 3.10

(4.55) 0.10(4.45) 0.20

WN +4,65 m

(1.05) 3.60

vs x = 568 m/s vs y = 568 m/svs z = 477 m/s

Analytical formulas for rigid circular foundation on elastic isotropic half-space:

Gdyn x = 580 MN/m2 Gdyn y = 580 MN/m2 Gdyn z = 410 MN/m2

Assumption: ρ = 1800 kg/m3, ν = 0.3

ρ = 1800 kg/m3

Neogene clays G = 908 MN/m2 vs = 710 m/s ν = 0.35

20 m

Finite element method (linear elastic):

G = 317 MN/m2 vs = 420 m/sQuarternary gravels ν = 0.3

290 m/s

480 m/s

Comparison of the obtained soil-parameters: results from measuring the Rayleigh-waves and from inverse analysis of the soil-structure interaction

F.19-28

numerical methods which are used in engineering practice could be pointed out. There is a difference between the dynamic soil structure interaction for the usual load cases (live loads, ambient excitation) and for the extraordinary conditions of earthquakes; the shear wave velocity profile and the H/V-method are developed for these conditions.

ReferencesSeismid. Boden-Gebäude Interaktion. Internal report in the project SEISMID. www.seismid.comStuder, J., Laue, J. and Koller, M., 2007. Bodendynamik. 3rd edition, Springer Verlag.Flesch, R., 1993. Baudynamik. Bauverlag, Issue 1.Achs, G. et al., 2011. Erdbeben im Wiener Becken.Wolf, J. P., 1985. Dynamic Soil-Structure Interaction. Prentice-Hall, Inc., Englewood Cliffs,

New Jersey.

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