SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR …...SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES SERIES LNEC Training Course, Lisbon, 23 September 2012 Physical

S E R I E SSEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES

COMMISSION OF THE EUROPEAN COMMUNITIESFP7- INFRASTRUCTURES-2008-1SP4-Capacities

SERIES LNEC Training Course, Lisbon, 23 September 2012

Physical Modelling,

Instrumentation and Testing

Paulo Xavier CandeiasPost-PhD Grant Holder LNEC

SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES


Presentation outline

• Physical modelling

▫ Prototypes and models

▫ Similitude laws

• Instrumentation plan

▫ What to measure?

▫ Where to measure?

• Testing protocol

▫ Dynamic tests

▫ Seismic tests

• Shaking table operation



Physical modelling

• Seismic behaviour of real structures is complex;

• In order to study it on a controlled environment, prototypes of real structures have to be selected;

• Prototypes should include all the relevant elements that influence the seismic behaviour:

▫ Main structural elements (columns, beams, slabs, walls);

▫ Influencing nonstructural elements (e.g., partition walls, heavy equipments).



Physical modelling

• Construction of physical models in natural scale is frequently not possible due to several types of constraints :

▫ Geometrical

▫ Physical

• The construction of physical models can pose serious challenges:

▫ Materials

▫ Methods



Example

• Consider a reinforced concrete model built in a 1:1.5 reduced scale

Issue Prototype Model

Concrete maximumaggregate diameter

2.4cm 1.6cm

Concrete cover 2cm 1.33cm

8mm steel rebar 8mm 5.33mm

16mm steel rebar 16mm 10.67mm

22×11×7 bricks 22×11×7 14.67×7.33×4.67

30×20×15 bricks 30×20×15 20×13.33×10



Dimensional analysis

• Buckingham Pi Theorem:

▫ Any dimensionally homogeneous equation involving certain physical quantities can be reduced to an equivalent equation involving a complete set of dimensionless products.

• This theorem states that the solution equation for some physical quantity of interest, i.e.,

can equivalently be expressed in the form

( ) 0,,, 21 =nXXXF K

( ) 0,,, 21 =ΠΠΠ mG K




• The Pi terms are dimensionless products of the physical quantities X1, X2, ..., Xn.

• A complete set of dimensionless products are the m=n-r independent products that can be formed from the physical quantities X1, X2, ..., Xn.

• Generally, it can be stated that the number of dimensionless products (m) is equal to the difference between the number of physical variables (n) and the number of physical measures (r) that are involved.



Physical quantities of interest in

seismic tests

Quantity Dimension Quantity Dimension

Length, L L Mass, m ρL3

Mass density, ρ ρ Force, F F

Young’s modulus, E FL-2 Weight, W F

Area, A L2 Moment, M FL

Volume, V L3 Stress, σ E or FL-2

Time, t T Strain, ε -

Frequency, f T-1 Poisson’s ratio, ν -

Displacement, d L Pressure, q FL-2

Velocity, v LT-1 Energy FL

Acceleration, a LT-2 Gravitational acceleration, g

LT-2




• The main question met in applying the Buckingham Pi Theorem pertains to the formation of appropriate Pi terms;

• The following simple points are the only guidelines needed in the formation process:

▫ All variables must be included;

▫ The m terms must be independent;

▫ In general, there is no unique set of Pi terms for a given problem; alternate formulations are possible either by forming the Pi terms in several different ways or by suitable transformations of one set of Pi terms.



• Cauchy number:

• Froude number:

Dimensionless relations of interest

in seismic tests

ForceGravity

Force Inertial2

⇒=gl

vFr

Force Restoring Elastic

Force Inertial2

⇒=E

vCa

ρ



Models used in seismic tests

• Three types of structural models can be considered:

▫ The true model maintains complete similarity

▫ The adequate model maintains “first-order” similarity when it may be possible to reason that some of the stipulations set forth by proper dimensional analysis are of “second-order” importance;

▫ The distorted model fails to satisfy one or more of the first-order stipulations as set forth by proper dimensional analysis.




• True replica models: Cauchy-Froude similitude

▫ Duplication of inertial, gravitational and restoring forces

▫ Such models are practically impossible to build and test because of the severe restrictions imposed on the model material properties, especially the mass density




• Artificial mass simulation: Cauchy-Froude similitude

▫ Additional material of a nonstructural nature is added to simulate the required density of the model

• Gravity forces neglected: Cauchy-only similitude

▫ Applies in the case where gravity stresses can be neglected and where the same materials are used in both the model and the prototype to enable the testing to proceed to failure



Cauchy-Froude scaling factors

Quantity Scale factor Quantity Scale factor

Length, L Lp/Lm=λ Mass, m eλ2

Mass density, ρ ρp/ρm=e/λ Weight, w eλ2

Young’s modulus, E Ep/Em=e Force, F eλ2

Area, A λ2 Moment, M λ3

Volume, V λ3 Stress, σ e

Time, t λ1/2 Strain, ε 1

Frequency, f λ-1/2 Poisson’s ratio, ν 1

Displacement, d λ Pressure, q e

Velocity, v λ1/2 Energy λ3

Acceleration, a 1 Gravitational acceleration, g

1



Cauchy-only scaling factors

Quantity Scale factor Quantity Scale factor

Length, L Lp/Lm=λ Mass, m λ3

Mass density, ρ ρp/ρm=1 Weight, w λ3

Young’s modulus, E Ep/Em=1 Force, F λ2

Area, A λ2 Moment, M λ3

Volume, V λ3 Stress, σ 1

Time, t λ Strain, ε 1

Frequency, f λ-1 Poisson’s ratio, ν 1

Displacement, d λ Pressure, q 1

Velocity, v 1 Energy λ3

Acceleration, a λ-1 Gravitational acceleration, g

Neglected



Example

• Reinforced concrete 1:3 reduced scale model made of the same material as the prototype

Quantity Prototype Cauchy Cauchy-Froude

Length 3m 1m 1m

Mass density 2.5tonnes/m3 2.5tonnes/m3 7.5tonnes/m3

Young’s modulus 30.5GPa 30.5GPa 30.5GPa

Time 30s 10s ≈17.32s

Frequency 3Hz 9Hz ≈5.20Hz

Displacement 0.3m 0.1m 0.1m

Acceleration 0.3m/s2 0.9m/s2 0.3m/s2

Mass 27tonnes 1tonne 3tonnes

Force 9kN 1kN 1kN

Weight ≈264.8kN ≈9.8kN ≈29.4kN

Can be achieved through the use of additional masses

Higher than reinforced concrete



Instrumentation plan

• Measure the response of the physical model:

▫ Dynamic characteristics

▫ Seismic behaviour

• Adequate selection of measurement points;

• Must be adjusted to the dynamic/seismic behaviour of the physical model:

▫ Reinforced concrete

▫ Masonry (brick/block/stone)

▫ Steel




• Typical selection of measurements and measurement points in reinforced concrete structures (assuming rigid diaphragms):

▫ Three uniaxial accelerometers per floor

▫ Absolute floor displacements measured with optical transducers

▫ Relative displacements between floors measured with LVDT’s




• Typical selection of measurements and measurement points in masonry structures (assuming flexible diaphragms):

▫ Uniaxial accelerometers on the walls at the floor levels and at mid height

▫ Absolute wall displacements measured with optical transducers

▫ Relative displacements between floors measured with LVDT’s



Example

• Instrumentation plan of the hands-on application

Sensors Quantity

Accelerometers 16

Optical displacementtransducers

4



Testing protocol

• The testing protocol depends on the objectives of the test itself:

▫ Dynamic tests are carried out to identify the dynamic characteristics of the models;

▫ Seismic tests are carried out to assess the seismic vulnerability of the models.



Testing protocol

• Seismic tests are carried out with increasing intensity signals (low, medium, high);

• Seismic behaviour depends on the dynamic characteristics of the structure;

• Dynamic characteristics change with each test stage due to damage.



Testing protocol

• Typical seismic test sequence:

▫ Dynamic identification of the model

▫ Test signal (low intensity)


▫ Test signal (medium intensity)


▫ Test signal (high intensity)




Shaking table operation

• LNEC large 3D shaking table characteristics:

▫ Maximum payload of 40tonnes

▫ Three independent axes (Transverse, Vertical, Longitudinal)

� Displacements controlled actively (actuators)

� Rotations passively restrained (torque tubes)

▫ Nominal stroke of 200mm

▫ Nominal peak velocity of 70cm/s

▫ Nominal peak acceleration depends on the mass of the model and the type of signal




• The operation of the shaking table results from a combination of:

▫ Mechanical components

▫ Hydraulic components

▫ Electrical components

▫ Control algorithms




• Mechanical components:

▫ Actuators

▫ Struts

▫ Swivels

▫ Torque tubes




• Hydraulic components:

▫ Pipe lines

▫ Accumulator banks

• Electrical components

▫ Power supply

▫ Switch gear

▫ Pumps

▫ Substations




• Control algorithms:

▫ Proportional–Integral–Derivative controller (PID controller) in the inner loop

▫ Shaking table tuning process on the outer loop

• The outer loop has been developed in LabVIEW and runs in a standard PC system;

• The inner loop (PID controller) runs in three dedicated FPGA boards connected to a LabVIEW Real Time PXI system





Shaking table control

• The PID controller calculation involves three separate constants:

▫ The Proportional value (P) depends on the present error

▫ The Integral value (I) depends on the accumulation of past errors

▫ The Derivative value (D) is a prediction of future errors based on current rate of change

• The weighted sum of these three actions is used to adjust the process via a control element.




• The control loop feedback mechanism (controller):

▫ Calculates an “error” value as the difference between a measured process (y) and a desired setpoint (u)

▫ The controller attempts to minimize the error by adjusting the process control inputs.



Shaking table control

• PID real time servo controller carried in FPGA boards:

)(teK p ×

∫×t

i deK0

)( ττ

dt

tdeKd

)(×

Σ Σ)(tu

+

Shaking table

)(ty

-

+

++

Feedback signal

)(te



Shaking table tuning

• Before conducting a test the shaking table has to be tuned following a sequence of steps:

▫ Dynamic identification of the whole system (ST+model) using a low amplitude “pink” noise in acceleration to obtain a frequency response function (FRF)

▫ Start with a low amplitude displacement signal input

▫ Measure displacements and accelerations as output



Shaking table tuning

• LNEC 3D shaking table tuning procedure (continued):

▫ Obtain a feedback synthesized displacement signal using a selected cross over frequency between measured displacements and accelerations

▫ Deconvolution of the feedback signal through the system FRF

▫ Obtain the new “error” signal to use as input signal to the shaking table

▫ Iterate until input signal is tuned for shaking table

▫ Increase the input signal and repeat the process for the next stage



Example

• Shaking table tuning process for the hands on application

▫ Definition of the parameters to compute the system (ST+model) FRF

Input signal (displacement)

Output signals (displacement and acceleration)



Example


▫ System (ST+model) FRF obtained with the “pink” noise excitation

ST-model interaction

Oil column ressonance

Delay between input and output



Example


▫ Signal tuning iterative process

Previous drive

Next drive

Target signal

Inverse FRF deconvolution

Error correction factors

Error signal

Acquired signal



Example

• Consider a target signal with a PGA of 0.2g and a correction factor of 65% in each iteration and 100% in the last one:

Drive Target Error Correction Acquired

0 0.2 0.2 0.65 0.13

1 0.2 0.07 0.65 0.1755

2 0.2 0.0245 0.65 0.191425

3 0.2 0.008575 1.00 0.2



ST+model interaction

• ST with foundation mass

• Model on a stiff foundation

CST

KST

MST

M1

K1

C1

Drive motionsu(t), v(t), a(t) Mfoundation



ST+model interaction

• Coupled (ST with model)

Drive motionsu(t), v(t), a(t)

CST

KST

MST

M1

K1

C1Mfoundation



Example

• Numerical simulation in the longitudinal direction of the LNEC ST

▫ fST = 5.00Hz

▫ fmodel = 3.00 Hz

▫ Model foundation mass = 11.80 tonnes

▫ Model story mass = 15.71 tonnes

Frequency Uncoupled(ST with foundation mass)

Coupled(ST with model)

f1 (structural mode) 3.00 Hz 2.71 Hz

f2 (ST mode) 4.39 Hz 4.87 Hz



References

• Harry G. Harris, Gajanan Sabnis, “Structural Modeling and Experimental Techniques”, Second Edition

• E. C. Carvalho, “Invited lecture: Seismic testing of structures”, 11ECEE



Thank you for your attention!

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SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR …...SEISMIC ENGINEERING RESEARCH INFRASTRUCTURES FOR EUROPEAN SYNERGIES SERIES LNEC Training Course, Lisbon, 23 September 2012 Physical