SIMULATION OF THE RESPONSE OF A HYBRID …Base, or seismic isolation finds application in a large...

1

SIMULATION OF THE RESPONSE OF A HYBRID BASE-ISOLATED

BUILDING DURING PUSH AND QUICK-RELEASE TESTS

Giuseppe OLIVETO1 and Anastasia ATHANASIOU

2

ABSTRACT

In the early spring of 2013, in the town of Augusta in eastern Sicily, a newly built reinforced concrete

commercial building, equipped with a hybrid base isolation system, was subjected to several push and

quick-release tests. The objectives of the tests were the evaluation of the performance of the base

isolation system and the verification of the design expectations. In order to conduct the tests without

excessive risk, a blind simulation of the same was performed beforehand by Oliveto et al. (2013). In

this simulation, the response of the isolation system was evaluated first by considering the

superstructure rigid, and then the obtained base motion was imposed to the superstructure to estimate

the complete response. Later, Oliveto and Athanasiou (2013) extended the Mixed Lagrangian

Formulation used in the previous model to simultaneously account for the flexibility of the

superstructure and the non-linear behaviour of the base isolation system. This new model is used

herein to simulate the push and quick-release tests performed on the Augusta building and to compare

the results with the experimental ones. The properties for the isolation system considered in the

performed simulations are obtained from the identification of the release tests. The experimental

records obtained during the loading phase of the tests, are used for the identification of the properties

of the isolators under quasi-static conditions.

INTRODUCTION

Seismic risk is a real threat for the countries of the Southern and Eastern European zone. One of the

most popular passive vibration techniques implemented nowadays in Europe for the reduction of

earthquake risk is base isolation. Base, or seismic isolation finds application in a large class of

structures of major or minor importance, such as hospitals, bridges, residential buildings, artefacts etc.

Its concept is simple and lies in the decoupling of motion between the substructure and the

superstructure through the interposition of elements of low stiffness. Structures constructed on firm

soils, where far-fault motion events are expected to occur, are favourable for implementations of the

method. This study considers a residential building in the city of Augusta, Italy, designed to withstand

seismic action by means of a hybrid base isolation system. Before being put into use, the building was

subjected to a series of free vibration tests. The release tests were performed in low amplitudes to

ensure that no damage would occur in the building. A preliminary simulation of the system response

of the building under the tests can be found in (Oliveto et al., 2013). The experiments provided a huge

amount of information that give light to the nonlinear behaviour of the isolation system under real-

time motions. Herein the output of the tests is used for the assessment of the isolation system and the

validation of the existing models that are used to simulate the dynamic response of the structure.

1 Professor, University of Catania, Catania, [email protected]

2 Graduate student, University of Catania, Catania, [email protected]

2

THE AUGUSTA BUILDING

The Augusta building consists of a basement, two storeys above the ground level and a penthouse. The

foundation rests on site of class B according to the Italian technical regulations, that are in line with

Eurocode8 (D.M. 2008). The dimensions of the plan are 35.70 m x 16.00 m, the maximum height

above the ground level is 10.50 m and the basement storey height is 3.60 m. The isolation plane runs

along the top of the pillars of the basement storey slightly above the ground level and is composed by

16 High Damping Rubber Bearings (HDRB) and 20 Low Friction Sliding Bearings (LFSB).

According to the design the isolation period of the structure is Tis= 2.38s, while the displacement

demand for the isolation system at the collapse prevention limit state is ddc= 269 mm (Oliveto et al.,

2013). A picture of the building exterior and a plan view of the isolation system are shown in Fig.1.

The properties of the isolators shown in Fig.1(b) are given in Table 1.

Table 1. Technical requirements for the seismic isolators

High Damping Rubber Bearings (HDRB) Low Friction Sliding Bearings (LFSB)

Vertical load in seismic condition 1000 kN Load Displacement

Damping ratio at γ=1 ξ =15% 2000kN 300mm

Secant horizontal stiffness at γ =1 Ke = 1000 kN/m 1500kN 300mm

Vertical stiffness Kv > 800Ke 250kN 300mm

Horizontal displacement at γ =2 dc = 300 mm

a) b)

Figure 1. a) Exterior of the Augusta building and b) plan view of the hybrid isolation system

The HDRB isolators were produced by FIP Industriale S.p.A. with the following characteristics:

total bearing height 312 mm, external diameter 500 mm, bonded diameter 480 mm, total rubber

thickness 25×6 mm = 150 mm, steel height 24×3 mm= 72mm, end plates 2×20 mm = 40 mm. The

multidirectional VASOFLON bearings produced by the same industry (LFSB) are characterized by

maximum loading capacities that vary from 250 to 2000 kN, Table 1. The manufacturer provided also

a series of data obtained from static and dynamic laboratory tests performed on HDRB and LFSB

prototypes. These data were used earlier for the identification of the HDRB properties (Oliveto et al.,

2013).

A bi-linear model is adopted for the description of the HDRB constitutive behaviour; this model

is used commonly in research and engineering practice for the description of the nonlinearity of the

rubber bearings (Kelly and Naeim, 1999). Three parameters are needed for the definition of the bi-

linear model: the elastic stiffness k0, the post-elastic stiffness k1 and the characteristic strength Q,

Fig.2(a). The properties of the rubber bearings, as identified from the acceptance tests provided by the

manufacturer, are shown in Table 2. It can be noticed how the values for k0, k1 and Q are significantly

larger when the tests are performed under dynamic conditions. All tests refer to a maximum shear

strain of 1. In the same table, the static and dynamic friction coefficients provided by FIP for the three

classes of LFSB are shown. The Constant Coulomb Friction Model (CCFM) is considered herein for

the description of the constitutive F-u behaviour of the friction sliders, Fig.2(b), where Ff0=μ·N, μ is

the friction coefficient and N the axial load acting on the bearing.

G.Oliveto and A.Athanasiou 3

Table 2. Mechanical properties of the isolators, as identified from the available laboratory tests

HDRB LFSB

at γ = 1 Static test 1 Static test 2 Dynamic test 1 Dynamic test 2 Axial load μst (%) μdyn (%)

k0 (kN/m) 3509 3521 5413 6199 0.50Vmax 0.30 0.15

k1 (kN/m) 658 708 802 847 0.75Vmax 0.175 0.10

Q (kN) 27 28 37 40 Vmax 0.15 0.09

Figure 2. F-u constitutive model for a) the rubber bearing and b) the friction slider

FREE VIBRATION TESTS

Ten free vibration tests were performed on the seismically isolated building of Augusta in late March

2013. During the tests the building was displaced statically from its initial position and then was left to

oscillate. The initial displacements varied in the range 50-100 mm (γ=0.40-0.80). The loading device

consisted of a reaction wall, a hydraulic jack, a sudden release device and a load cell and was the same

one used in a previous set of free vibration tests that took place in the city of Solarino, Italy, in 2004

(Oliveto et al., 2004). The loading velocity during the pushing phase was of the order of 6mm/min.

The experimental results include the histories of the loading force, displacements and

accelerations. The horizontal displacements were measured at various positions below and above the

isolation level through 15 channels, while the horizontal and vertical accelerations were measured at

the various floor levels using 16 channels. The displacement curves of Fig. 3 show the deformation

histories of the rubber bearings 8 and 25, Fig. 1(b), for the free vibration tests 4 and 10. During test 4,

the building was displaced statically by 68 mm applying a maximum load of 1305 kN. In the free

vibration phase, the system completed one full cycle of motion before coming to rest with a residual

displacement of the order of 8 mm (8.8 mm for rubber bearing 25 and 8.3 mm for rubber bearing 8),

Fig. 3 (a). The residual displacements were slightly larger in test 10, where an initial displacement of

a) b)

Figure 3. Deformation histories for HDRB 8 and 25, a) during test 4 (u0=68mm) and b) test 10 (u0=100mm)

460 470 480 490 500 510 520-10

0

10

20

30

40

50

60

70

80

t [s]

uR

B [

mm

]

Test 4 [ u0 = 68 mm, = 0.45 ]

RB-25

RB-8T=1.7 s

ur=8.8 mm

ur=8.3 mm

1040 1045 1050 1055 1060 1065 1070 1075-10

0

20

40

60

80

100

120

t [s]

uR

B [

mm

]

Test 10 [ u0 = 100 mm, = 0.67 ]

RB-25

RB-8T=1.9 s

ur=13.4 mm

ur=13.7 mm

4

a) b)

Figure 4. Longitudinal floor acceleration records, a) for test 4 (u0=68mm) and b) test 10 (u0=100mm)

a) b)

Figure 5. Fourier amplitude spectra of the longitudinal accelerations measured during tests 4 (black line)

and 10 (red line), a) at the various floors and b) the foundation

100 mm under a static load of 1597 kN was applied, Fig. 3(b). The residual displacements occur due to

the non-linearity of the isolation system. A simple re-centring mechanism was set up so that in the end

of each dynamic test the building was re-centred to the initial, zero displacement, equilibrium position.

The damped period of vibration for the system can be estimated from the displacement response

histories; that would be T = 1.7 s for test 4 and T = 1.9 s for test 10.

The longitudinal acceleration histories, measured during tests 4 and 10 at the basement and the

superstructure, are shown in Fig. 4. The beneficial effect of base isolation is straightforward; de-

amplification of motion is observed along the superstructure height. The record at the roof seems to be

somewhat important, including some low frequency content, probably due to the irregularity of the

structure in height and to the low stiffness of the last storey, Fig. 1. Comparing the signals obtained

from the two tests it becomes clear that the higher is the initial displacement, the higher are the

acceleration amplitudes and the longer is the period of vibration. The Fourier amplitude spectra of the

acceleration signals shown in Fig. 4, are given in Fig. 5(a). The Fourier spectrum amplitudes of the

accelerations recorded on the ground floor (just above the isolation plane) and on the upper floors are

very similar in the neighbourhood of the fundamental isolation frequency; that is approximately equal

to fis = 0.60 Hz for test 4. The following peaks, located in the higher frequency range, correspond to

the superstructure’s modes. The dominant frequencies and corresponding Fourier spectrum

amplitudes, obtained from the Fourier analysis of the acceleration signals of test 4 are shown in Table

3. It is interesting to notice that the ground floor and the first floor spectra have a relatively sharp peak

at the frequency of 32 Hz. This high frequency is less important for the second floor acceleration

response and absent in the roof signal. A comparison between the spectra of tests 4 and 10, confirms

the previous observations that larger initial displacements result to larger amplitudes and shift of the

463 464 465 466 467-0.3

0

0.4

a (

g) roof0.21 g

463 464 465 466 467-0.3

0

0.4

a (

g) 2

nd floor0.16 g

463 464 465 466 467-0.3

0

0.4

a (

g) 1

st floor0.20 g

463 464 465 466 467-0.3

0

0.4

a (

g) ground floor0.34 g

463 464 465 466 467-0.3

0

0.4

t (s)

a (

g) basement0.07 g

1052 1053 1.054 1055 1056 1057-0.3

0

0.4

a (

g) roof0.26 g

1052 1053 1054 1055 1056 1057-0.3

0

0.4

a (

g) 2

nd floor0.18 g

1052 1053 1054 1055 1056 1057-0.3

0

0.4

a (

g) 1

st floor0.26 g

1052 1053 1054 1055 1056 1057-0.3

0

0.4

a (

g) ground floor0.37 g

1052 1053 1054 1055 1056 1057-0.3

0

0.4

t (s)

a (

g) basement0.08 g

1 10 100 2500

2

4

f (Hz)

[cm

/s]

basement

1 10 100 2500

10

20

[cm

/s]

ground floor

1 10 100 2500

10

20

[cm

/s]

1st

floor

1 10 100 2500

10

20

[cm

/s]

2nd

floor

1 10 100 2500

10

20roof

[cm

/s]

f (Hz)

1 10 100 2500

0.5

1

1.5

2

2.5

3

3.5

4

f (Hz)

[cm

/s]

test 4 (u

0=68 mm)

test 10 (u0=100 mm)


Table 3. Dominant frequencies and corresponding Fourier spectrum amplitudes,

obtained from the Fourier analysis of the acceleration signals of test 4

Ground floor 1st floor 2nd floor Roof

fmax (Hz) Smax (cm/s) fmax (Hz) Smax (cm/s) fmax (Hz) Smax (cm/s) fmax (Hz) Smax (cm/s)

0.61 10.19 0.61 10.39 0.61 10.55 0.61 10.55

6.59 6.48 6.71 1.40 6.47 4.07 6.59 8.00

13.79 2.06 13.67 2.36 13.79 2.42 13.67 3.22

- - 19.41 2.86 19.53 1.67 19.04 1.49

31.98 6.96 32.23 3.68 32.23 2.52 - -

fundamental frequency to the left. Fig. 5(b) is an enlargement of the Fourier spectrum of the

longitudinal acceleration recorded at the foundation, shown in the last subplot of Fig. 5(a). The Fourier

spectrum of the foundation response has a sharp peak in the proximity of 7 Hz, significantly above the

isolation frequency, justifying why there was no amplification of motion at the basement during the

tests.

BEHAVIOUR OF ISOLATORS UNDER THE STATIC PHASE OF TESTS

The quasi-static force-displacement curves obtained during the loading phase of the free field tests are

used herein for the identification of the mechanical properties of the isolators. The constitutive

behaviour of the HDRB is described by the bi-linear model shown in Fig. 2(a). For the LFSB, an

elastic-perfectly plastic model is considered; the initial stiffness k0f of the elastic branch accounts for

the fact that the friction force doesn’t reach instantaneously its breakaway value ff0. Although there are

three classes of sliders, all sliders are assigned the same coefficient of friction. The axial load N acting

on the three groups of LFSB is considered equal to N= 750 kN, 900 kN, 25 kN resulting to an overall

vertical load Ntotal =13900 kN=0.58W=0.52Nmax, where W=24000 kN is the weight of the superstructure

as evaluated for the building design and Nmax is the maximum axial load that could act on the sliding

bearings accordingly to their load capacities. These N values were evaluated by the designer

considering the building conditions under the experiments.

The identification process is performed using the Covariance Matrix Adaptation Evolution

Strategy (CMA-ES). The CMA-ES is an non-elitist continuous domain evolutionary algorithm used

for difficult non-linear, non-convex optimization problems in continuous domain (Hansen, 2011). In

each generation the algorithm generates λ candidate solutions xi, which are then evaluated according to

the objective function e2, i.e. the function to be minimized. The sampled solutions are re-ordered

according to their value (fitness). At the end of each generation the (λ-μ) worst solutions are discarded,

while the μ best ones are used for the update of the internal state variables and the sampling of the new

population. Over the generations the search is oriented towards solutions of minimum fitness. The

optimization is terminated when there is no more improvement in the fitness function.

In the present case the candidate solution vectors xi include the properties (k0, k1, Q, k0f, μ) of the

isolators. For each set of feasible solutions the static force-displacement curves (F-u)sim are produced

according to the constitutive laws of the bi-linear and the elastic-perfectly plastic model. The

simulated curves are then compared to the experimental curves (F-u)exp. The static experimental

curves are fitted using a 10th order polynomial in order to remove the noisy content (function polyfit,

MATLAB 2013). The fitness or error function is defined as the normalized distance between

simulated (Fsim) and experimental data (Fexp):

2

2

2

exp

exp

sime

F F

F

.

The identification process was performed 10 times on each set of static F-u data available,

Fig. 6(a). The results for the most successful run, in terms of fitness, per set of data (release test) are

given in Table 4. The tests are ordered according to increasing maximum imposed shear strain γ. The

mean value and coefficient of variation (c.o.v.) for the ten identified system parameters are given in

the last two columns of Table 4. The average of the identified static laboratory values for k0, k1, Q,

6

Table 4. Mechanical properties of the isolators,

as identified from the static loading force–displacement Augusta records

test 1 test 3 test 4 test 2 test 10 test 8 test 9 test 5 test 6 test 7 lab mean c.o.v.

γ 0.40 0.44 0.45 0.61 0.67 0.68 0.68 0.73 0.78 0.79 1.0

k0 (kN/m) 1396.1 4292.5 1253.3 1298.6 1140.1 3053.4 1127.6 2445.6 1227.5 1228.3 3515 1846.3 0.58

k1 (kN/m) 945.2 966.9 857.6 896.1 773.9 852.3 757.1 879.3 806.9 810.8 683 854.6 0.08

Q (kN) 7.4 20.0 11.9 11.4 12.8 21.9 13.2 18.1 12.5 12.9 27.5 14.2 0.31

k0f (kN/m) 8808.5 61916.7 3398.9 4874.0 1707.4 3891.6 2377.7 36891.6 2008.6 1867.9 - 12774.3 1.59

μ (%) 1.46 0.60 1.51 2.00 1.20 0.27 1.50 0.42 1.50 1.24 - 1.17 0.48

e2 (E-04) 1.4 8.0 1.4 2.8 1.4 3.0 2.0 2.7 1.4 0.91 -

a) b)

Figure 6. a) Static loading force – displacement curves for the tests of Augusta and

b) comparison between fitted experimental and identified F-u curves for test 8 (Fmax=1792 kN, u0=103 mm)

Figure 7. Comparison of the 3rd

cycle static laboratory data and the identified F-u curves

a) for tests 1-5 and b) tests 6-10

shown in Table 2, are provided herein to facilitate the comparison between identified laboratory and

field data.

It can be seen how the CMA-ES yielded solutions of minimum fitness of the order of 10-4

,

resulting to a very good matching between experimental and identified data, Fig. 6(b). However, as

seen from Table 4, the identified properties of the isolators vary significantly from test to test. The

initial stiffness of the friction model k0f is the variable with the largest scatter (c.o.v.=1.59), while the

post-elastic stiffness of the bi-linear spring k1 is the one with the smallest one (c.o.v.=0.08).

Comparing the obtained results with the available static laboratory data, it can be seen how the

identified parameters k0 and Q are significantly lower than the corresponding laboratory ones with

differences reaching -73%. k1 results generally greater than its static laboratory value, the maximum

difference being 42%; however this could be due to the smaller shear strains experienced during the

0 25 50 75 100 125 1500

500

1000

1500

2000

u [mm]

F [

kN

]

test 1

test 2

test 3

test 4

test 5

test 6

test 7

test 8

test 9

test 10

[ ]0 0.330.17 0.50 0.67 0.83 1

0 25 50 75 100 125 1500

500

1000

1500

2000

u [mm]

F [

kN

]

fitted record, test 8

identified record

[ ]0 0.330.17 0.50 0.67 0.83 1


field tests (γ =0.40-0.80). In fact, the identified values for k1 show a decreasing trend with increasing

shear strain γ. All static and dynamic laboratory tests were performed at γ=1. The 10 identified bi-

linear models for the HDRB are compared against the 3rd

cycle static laboratory data in Figs 7(a) and

(b). Tests 6 and 7 and tests 9 and 10 yielded similar results, therefore the corresponding curves cannot

be distinguishable in the scale of Fig. 7(b).

The coefficient of friction μ takes a minimum value of 0.27% for test 8 and a maximum value of

2 % for test 2, Table 4. Under a similar axial load of 0.50Nmax, the static and dynamic coefficients of

friction provided by the manufacturer are significantly smaller, 0.30% and 0.15% respectively, Table

2.The majority of data (tests 1, 4, 6, 7, 9, 10) provided values of μ coherent with the ones found from

the Solarino experiments (Oliveto et al., 2010). μ tends to take lower values when k0 and Q are higher

and vice versa; see for instance tests 8, 9 and 10.

The identification was repeated in a narrow domain to ensure that the isolator properties would

not vary more than 10% from the laboratory data. That operation resulted to worse results in terms of

fitness function and curve matching; hence those results are not shown herein. It should be mentioned

that the identification procedure provides the parameters that minimize the considered fitness function.

Those parameters, while satisfying the mathematical problem, do not necessarily match the physics of

the problem.

IDENTIFICATION OF THE 1D ISOLATION SYSTEM

In the following the deformation histories of the rubber bearings 25 and 8 obtained from tests 4 and

10, Figs 3(a) and (b), are used for the identification of the isolation system properties. For the purposes

of the identification a simple 1D model is adopted for the structure. The superstructure is considered a

rigid block; this assumption is reasonable given the similarity of the Fourier amplitude spectra of the

superstructure’s floor acceleration records, Fig. 5(a). The Augusta HBIS is symmetrical with respect to

the short (y) axis, while not symmetrical with respect to the long (x) axis due to the presence of the

four sliding bearings under the elevator. However during the tests no significant transverse records

were observed and hence the response to a 1D excitation along the x direction is expected to be

unidirectional and can be adequately predicted by the 1D model. The mechanical system considered

herein is shown in Fig. 8. The bi-linear spring and the viscous damper together account for the HDRB,

while the plastic slider accounts for friction in the LFSB. The friction law is described by the CCFM,

shown in Fig. 2(b). All HDRB are of one class, and hence have the same properties. The same

coefficient of friction is assigned to all the LFSB. Hence, the system parameter vector to be identified

includes the mass m of the structure, the 3 properties (k0, k1, Q) of the bi-linear spring, the coefficient

of friction of the sliders μ and the damping ratio ζ describing the linear viscous damper.

Figure 8. Mechanical model for the isolation system

20 runs of CMA-ES were performed. In runs 1-10 the input for the identification were the

displacement records of test 4, while in runs 11-20 input were the displacement records of test 10. The

system response was simulated using the 1D Mixed Lagrangian Formulation (Oliveto et al., 2014).

The Mixed Lagrangian Formulation (MLF) is an algorithm developed for the simulation of the

dynamical response of base isolated buildings. The MLF is an energy formulation of the dynamic

problem; the governing equations are derived by setting the first variation of an appropriate Hamilton's

action integral to zero introducing suitable Lagrangian and dissipation functionals. The time step

solution is provided in the form of a constrained non-linear optimization problem. The reliability and

8

Table 5. Identified properties for the isolation system for tests 4 and 10

m (tons) k0 (kN/m) k1 (kN/m) Q (kN) μ (%) ζ e2

Runs 1-10, test 4 (γ = 0.45) 2942.4 3289.5 782.2 36.3 0.91 0 1.38 E-03

Runs 11-20, test 10 (γ = 0.67) 2824.5 2395.8 616.3 42.2 1.09 0 1.75 E-03

robustness of the method is demonstrated through a series of numerical applications that can be found

in (Oliveto et al., 2014).

Once the system response was simulated for each candidate solution the fitness function was

evaluated as the normalized quadratic distance between simulated and experimental response. The

experimental response is evaluated as the average of the two displacement records available for the

two monitored isolators. A search space, established on the basis of the dynamic laboratory data

provided by the manufacturer was considered for the search. The search space was enlarged after the

first run to account for larger variations in the friction coefficients. Τhe identified system properties for

tests 4 and 10, obtained from the best run performed, are given in Table 5. Runs 1-10 yielded similar

properties for the isolation system, the identified parameters varying from run to run not more than

6%. The same observation holds for runs 11-20.

The identification of the two tests yielded two different systems. However, it is true that test 4

was performed at a smaller shear strain level with respect to test 10 and hence it is reasonable that k1

was identified with a larger value. Comparing the identified parameters of Table 5 with the dynamic

laboratory data shown in Table 2, it can be seen how the elastic stiffness k0 of the rubber bearings is

approximately 50% lower than the corresponding laboratory one. The differences between the

identified Q and the corresponding laboratory parameters are less than 10%. The post-elastic stiffness

results are always slightly smaller than the laboratory ones. The coefficient of friction is 6-7 times

greater than the dynamic coefficient provided by the manufacturer under similar axial load (0.50Nmax),

Table 2, however the identified friction value is in line with the results of the Solarino experiments

(Oliveto et al. 2010).

a) b)

Figure 9. Recorded and identified displacements for tests 4 and 10, a) and b)

a) b)

Figure 10. Recorded and simulated ground floor and first floor accelerations for test 4, a) and b)

0 1 2 3 4 5-10

0

10

20

30

40

50

60

70

Test 4

t (s)

u (

mm

)

recorded displacement

identified displacement

ur = 13.4 mm

0 1 2 3 4 5-10

0

20

40

60

80

100

Test 10

t (s)

u (

mm

)

recorded displacement

identified displacement

ur = 17.5 mm

0 1 2 3 4 5-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25Test 4 - ground floor

t (s)

a (g

)

recorded acceleration

identified acceleration

0 1 2 3 4 5-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25Test 4 - 1

st floor

t (s)

a (g

)




a) b)

Figure 11. Recorded and simulated second floor and roof accelerations for test 4, a) and b)

The identified displacement and acceleration histories are plotted against the experimental ones

in Figs 9-11. The good matching between experimental and identified displacements demonstrates that

the unidirectional system response can be successfully identified using a simple 1D model. The

matching between experimental and identified accelerations is good but less satisfactory. The isolation

frequency is identified correctly, however the rigid superstructure model cannot account for the high

frequency content induced from the superstructure flexibility. A more refined model is expected to

provide better results. Nevertheless, the identification of a complex NDOF model would increase

significantly the problem dimension and consequently the computational time.

SIMULATION OF THE SUPERSTRUCTURE RESPONSE

The 1D Mixed Lagrangian Formulation algorithm, initially presented in (Oliveto et al., 2011) was

extended to account for 2D horizontal earthquake motions (Oliveto et al., 2012). The superstructure

was still considered as a rigid block, however 3 DOFs were accounted for the isolation system: 2

horizontal displacements and a rotation about the vertical axis. In the ultimate extension of the MLF,

the method is updated to account for the flexibility of the building (Oliveto and Athanasiou, 2013).

Each floor is considered as a rigid diaphragm, hence 3 DOFs are considered per floor. A complete

description of the method can be found in (Oliveto and Athanasiou, 2013).

Several efforts were made for the simulation of the flexible superstructure response under test 4

using the MLF for NDOF systems. The system properties obtained from the identification of test 4

were used for the simulation of the isolation system. A diagonal mass matrix was constructed using

the mass data provided by the designer. The mass matrix was scaled so that the total mass equaled the

one identified by the experiment. The stiffness matrix for the superstructure was also provided by the

designer. The mass and stiffness matrix coefficients for the superstructure can be found in (Oliveto

and Athanasiou, 2013). The performed simulations showed that the superstructure was more rigid than

expected. In order to match the frequency content present in the signal the stiffness matrix available

for the superstructure, Kinitial , had to be amplified; a good compromise was found to be K=4.5Kinitial.

Simulations with K=4.5Kinitial provided a better matching between recorded and simulated data at the

ground floor and the top two floors, Figs 12(a), 15(a) and 16(a). The matching is fair for the

accelerations of the ground and first floor, Figs 13(a) and 14(a). The comparison of recorded and

simulated accelerations confirms that there is a high frequency content present in the signals of the two

bottom floors of the order of 32 Hz, see Table 3, that cannot be accounted for by the present model.

The presence of high acceleration spikes in the simulated signal during the last cycle of motion, absent

in the original signal, stresses the need for the introduction of a supplementary damping mechanism in

the model. The existent damping mechanisms seem unable to damp properly the acceleration

response. The rubber bearings undergo pure elastic behavior in the last cycle of motion while the

viscous damper is inactive; the corresponding damping ratio was found to be 0 from the identification

of test 4, Table 5. Hence there is only friction to account for energy dissipation.

In a further attempt to tune the simulated response, a damping matrix was introduced for the

superstructure. The damping matrix was constructed using superposition of modal damping matrices

0 1 2 3 4 5-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25Test 4 - 2

nd floor

t (s)

a (g

)



0 1 2 3 4 5-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25Test 4 - roof

t (s)

a (g

)



10

(Chopra, 2007). The superstructure mode 5, i.e. the mode describing unidirectional deflections along

the x axis, was assigned a light damping ratio of 1%. No damping was assigned to the rest of the

modes. The obtained simulated displacement and acceleration histories for the damped superstructure

model are shown in Figs 12(b)-16(b). Close observation of Figs 12(a)-16(a) and Figs 12(b)-16(b)

shows that the introduction of classical damping had a slight beneficial effect in damping the response

at all floors but floor 1. That could be justified by the fact that mode 5 has a node at floor 1.

Introduction of larger damping ratios for mode 5 improved the system response, though not as

satisfactorily as expected.

a) b)

Figure 12. Recorded and simulated ground floor displacements for test 4,

a) when no and b) light damping is assigned to the superstructure

a) b)

Figure 13. Recorded and simulated ground floor accelerations for test 4,


a) b)

Figure 14. Recorded and simulated first floor accelerations for test 4,


0 1 2 3 4 5-10

0

10

20

30

40

50

60

70Displacement at GFL, no damping in the superstructure

t (s)

u (

mm

)

signal

simulation

0 1 2 3 4 5-10

0

10

20

30

40

50

60

70Displacement at GFL, damping in the superstructure

t (s)

u (

mm

)

signal

simulation

0 1 2 3 4 5-0.2

-0.1

0

0.1

0.2

0.3Acceleration at GFL, no damping in the superstructure

t (s)

a (g

)

signal

simulation

0 1 2 3 4 5-0.2

-0.1

0

0.1

0.2

0.3Acceleration at GFL, damping in the superstructure

t (s)

a (g

)

signal

simulation

0 1 2 3 4 5-0.2

-0.1

0

0.1

0.2

0.3Acceleration at 1FL, no damping in the superstructure

t (s)

a (g

)

signal

simulation

0 1 2 3 4 5-0.2

-0.1

0

0.1

0.2

0.3Acceleration at 1FL, damping in the superstructure

t (s)

a (g

)

signal

simulation


a) b)

Figure 15. Recorded and simulated second floor accelerations for test 4,


a) b)

Figure 16. Recorded and simulated roof accelerations for test 4,


The simulation output stress the inability of the present model to account for frequencies higher

than 30Hz and to damp properly the superstructure response. This model inadequacy could be

attributed to possible inconsistencies in the considered superstructure mass and stiffness matrices, but

this is something yet to be investigated. Future research shall be towards identifying the mass and

stiffness matrices for the superstructure and implementing appropriate damping mechanisms. A

modification of the isolation system model, where the viscous damper acts in parallel with the elastic

spring ke instead of in parallel to the bi-linear spring, Fig. 8, is believed to describe more effectively

the response of the isolation system, observed during the experiments.

CONCLUSIONS

This paper presents recent research on the response of base isolated structures under real-time strong

motion. The case study considers a newly constructed RC base isolated building, that was subjected to

a set of free vibration tests. The effectiveness of the seismic isolation to reduce the dynamic demand

for the superstructure was demonstrated throughout the tests. The displacement demands input during

the release tests were accommodated mainly by the isolators; the energy input was dissipated by the

isolation system through nonlinear mechanisms, while the superstructure remained elastic. The static

phase of the experiments was used herein for the assessment of the static nonlinear behaviour of the

bearings. The identified static properties of the isolators provided a good matching between recorded

and simulated curves; however they were significantly different from the corresponding laboratory

parameters. It may be assumed that the laboratory tests provide more reliable results, since they are

performed independently on the isolators under controlled conditions. Nevertheless, the attempts to

0 1 2 3 4 5-0.2

-0.1

0

0.1

0.2

0.3Acceleration at 2FL, no damping in the superstructure

t (s)

a (g

)

signal

simulation

0 1 2 3 4 5-0.2

-0.1

0

0.1

0.2

0.3Acceleration at 2FL, damping in the superstructure

t (s)

a (g

)

signal

simulation

0 1 2 3 4 5-0.2

-0.1

0

0.1

0.2

0.3Acceleration at roof, no damping in the superstructure

t (s)

a (g

)

signal

simulation

0 1 2 3 4 5-0.2

-0.1

0

0.1

0.2

0.3Acceleration at roof, damping in the superstructure

t (s)

a (g

)

signal

simulation

12

restrict the identification towards solutions close to the laboratory parameters resulted to bad matching

between recorded and simulated data. That shows that the laboratory properties do not necessarily

predict sufficiently well the system response under real ground motions. The displacements histories

of two monitored isolators during two release tests were used for the dynamic identification of a

simple 1D model describing the isolation system. Although the flexibility of the superstructure was

not accounted for by the model adopted, the results were satisfactory. Consequently, the identified

dynamic properties of the isolators were used in combination with the available mass and stiffness

matrices of the superstructure for the simulation of the dynamic response of a more refined model. The

flexible superstructure model provided promising results; meanwhile pointing out the inefficiencies of

the present simulations. The model considered was unable to account for the high frequency content

present in the recorded signals. Furthermore, the attempts for the implementation of a suitable

damping mechanism that accounted for energy dissipation in the high frequency cycles of motion,

proved unsuccessful. The problems arisen with the performed simulations set the basis for future

developments. Future research will be focused on the improvement of the flexible superstructure

model so that the latter can simulate adequately the observed dynamic behaviour of the considered

system.

ACKNOWLEDGEMENTS

This work was performed with the financial support of ReLUIS (Italian National Network of

University Earthquake Engineering Laboratories), “Project D.P.C - ReLUIS 2014-2016, WP1”.

REFERENCES

Chopra A (2007) Dynamics of Structures : Theory and Applications to Earthquake Engineering, 3rd

edition,

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Hansen N (2011) “The CMA Evolution Strategy: A Tutorial”, available online at:

http://www.lri.fr/~hansen/cmatutorial.pdf

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