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SHAKE-TABLE TESTING OF RESILIENT ROLLING SEISMIC
ISOLATORS BASED ON DEFORMABLE RUBBER SPHERES
Antonios A. KATSAMAKAS
1
& Michalis F. Vassiliou
2
Abstract: This study presents the results of a large-scale experimental investigation of
sustainable and low-cost seismic isolators based on deformable rubber spheres, rolling on
concrete surfaces. Different types of spheres, with or without a steel core were tested. Both flat
and spherical (concave) concrete plates were investigated. A potential application of the proposed
isolator could be in low-rise masonry structures in the developing world. The spheres were initially
subjected to monotonic uniaxial compression and sustained compression under vertical load to
examine their compressive behaviour. Subsequently, lateral cyclic tests under large
displacements were performed. Finally, a total of 1170 shake-table tests were performed in 1:2
scale, with various different isolators subjected to a large number of ground motion excitations.
Both in the lateral cyclic and in the shake-table tests, different vertical loads were investigated to
quantify the influence of the vertical load on the response. Results showed that the compressive
strength of the spheres was substantially higher than the estimated design load, whereas the
presence of the steel core made the spheres stiffer. The lateral cyclic response differs
substantially from the prediction of a rigid body model due to the non-negligible deformability of
the spheres. The rolling friction coefficient ranged between 3.7% and 7.1%, with these values
being suitable for seismic isolation applications. A higher vertical load leads to a slightly higher
value of the rolling friction coefficient and increased energy dissipation. The spherical concrete
plates increase the restoring force of the system. When tested in a shake table under 1170 ground
motions, the isolators substantially reduced the acceleration transmitted to the superstructure (to
approximately 0.15 g) while maintaining reasonable peak and zero residual displacements.
Notably, the shake table tests were repeatable, and the isolators did not deteriorate even after
subjected to 65 ground motion excitations.
Introduction
Numerous recent earthquakes prove that there is a pressing need to propose and implement
earthquake-resistant solutions applicable to lightweight residential structures both in the
developing and in the developed world.
Seismic isolation is an effective and mature method of seismic protection that is based on
uncoupling the building movement from the ground motion. Its conventional application includes
the creation of a layer with low lateral stiffness at the base of the structure. The seismic isolators
should have high bearing capacity under gravity loading to support the weight of the
superstructure and significant energy dissipation to limit displacements. Seismic isolation is
mainly used in projects of high significance in the developed world, due to the associated high
cost. Therefore, to make the method applicable to residential structures, the cost has to be
significantly reduced. Previous studies suggested reduced-cost isolators based on the following
three categories: flexible rubber bearings, sliding bearings, and rolling bearings.
Several studies proposed the replacement of steel shims that are used in conventional steel-
laminated bearings (Soleimani et al. 2022, Strauss et al. 2014, Kalfas et al. 2022, Forcellini and
Kalfas 2023) with flexible fibre reinforcement to reduce the cost and weight of the isolators,
leading to the “Fibre reinforced Elastomeric Isolator (FREI)” (De Domenico et al. 2023, Galano
and Calabrese 2023, Hadad et al. 2017, Osgooei et al. 2014, 2017, Ruano and Strauss 2018,
Russo et al. 2013, Sheikh et al. 2022, Losanno et al. 2022, Van Engelen et al. 2014, 2016).
However, FREIs remain too stiff to isolate lightweight residential buildings (Galano et al. 2022,
Tran et al. 2020).
1
Ph.D. candidate, ETH Zurich, Zurich, Switzerland, katsamakas@ibk.baug.ethz.ch
2
Assistant Professor, ETH Zurich, Zurich, Switzerland
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Conventional sliding-based seismic isolators (such as the Friction Pendulum System, FPS) (Fenz
and Constantinou 2006, Becker and Mahin 2012, Castaldo and Tubaldi 2015, Furinghetti et al.
2021) require stainless steel plates, and sliding surfaces of Teflon and polished metals. This
increases their cost and, therefore, limits their use in residential structures. Recent studies
suggested alternative materials of lower cost for the sliding surfaces. Jampole et al. (2014, 2016)
shake-table-tested bearings with high-density polyethylene sliders on galvanized steel. Brito et
al. (2019) used concrete-steel friction interfaces. In both previous systems the restoring force is
gravitational and provided through the use of concave surfaces, similar to the FPS. Messina and
Miranda (2022) characterized the frictional properties of steel-polymer interfaces. Tsiavos et al.
(2022) used sand-timber or PVC-sand sliding interfaces and springs to provide restoring force.
Rolling bearings have been previously used, primarily to isolate building contents (Figure 1)
(Harvey et al. 2014, Harvey 2016, Menga et al. 2017). The majority of them uses steel spheres
rolling on steel surfaces. The extensive use of steel may make the bearings unaffordable for
isolating entire buildings, especially in the developed world. The use of rubber at the contact
interfaces is beneficial since it increases energy dissipation and reduces stress concentration at
the rolling interfaces (Zéhil and Gavin 2014, Katsamakas et al. 2021a, 2022a, Katsamakas and
Vassiliou 2022a).
Description and potential application of the isolator
Description of the isolator and rigid-body equations
A recently proposed isolator for the seismic protection of lightweight residential structures is the
Spherical Deformable Rolling Seismic Isolator (SDRSI) (Katsamakas and Vassiliou 2023),
proposed by Cilsalar and Constantinou (2019a, 2019b, 2020). Their work was based on the
isolator initially proposed by Cui et al. (2012). The isolator comprises a deformable elastomeric
sphere rolling on concrete surfaces (Figure 2). The deformability of the sphere is critical since it
makes the response deviate from a rigid-body model (Katsamakas et al. 2021b, 2022b,
Katsamakas and Vassiliou 2022b). This is due to residual “creep” deformation of the sphere under
sustained compressive load, that results in essentially rolling an oval-shaped object rather than a
perfect sphere (Figure 2). Equation (1) offers the lateral cyclic response predicted by the rigid-
body model (Katsamakas et al. 2022c):
4roll
eff
W
F u Wsign u
R
(1)
Where F is the horizontal (rolling) force applied to the isolator, W is the vertical force (weight) that
the sphere supports, u is the lateral displacement of the isolator, δ is the compressive
displacement under load W, R is the radius of curvature of the spherical concrete plate and r is
the radius of the rolling sphere (Figure 1). The first term of Eq. (1) is the gravitational restoring
force of the system. The translational displacement of the sphere (usphere) is equal to half of the
displacement of the isolator (u); hence, usphere = u/2. The isolation period of the system is equal
to
4
2eff
R
g
. The μroll term is the rolling friction coefficient of the system and is equal to the lateral-
to-vertical force ratio at zero lateral displacement. It is a macroscopic term that describes the
initiation of rolling motion and the energy dissipation of the isolator.
Figure 1: Rigid body model for rolling seismic isolators. Left, Isolator under compressive load
and zero lateral displacement; Middle, Isolator under compressive load and maximum lateral
displacement; Right, Bilinear force-displacement plot.
u = d0 - r
F(max)
W
D
Uplift
r
uball
uball = d0 /2 - r
d0
FW
D
u
R
r
Reff = R - r
F / W(-)
u (mm)
1/4Reff
2μW
u = d0 - r
F(max)
W
D
Uplift
r
usphere
usphere = d0 /2 - r
F / W
u
F / W
u
1/4Reff
2μW
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Figure 2: Left, Initial condition of the spherical isolator; Middle, Isolator under compressive load
with evident compressive displacement; Right, Isolator under compressive and lateral load, with
evident uplift.
The use of one concave concrete surface is proposed to guarantee restoring force to the system.
Configurations with two flat plates are also tested in the present study to characterize the behavior
of the rolling sphere without the curvature of the concrete surface influencing the response.
Configurations with two concrete plates are ignored since they do not offer increased
displacement capacity and are more expensive and complicated to manufacture (Cilsalar and
Constantinou 2019a).
Potential application of the isolator
A potential application of the proposed isolator could be in one- or two-story masonry houses in
the developing world. In these regions, the construction of seismically isolated masonry houses
could be a viable solution for earthquake-resistant structures. Communication with engineers from
Cuba and Peru has unveiled that, in many low-income countries, seismic isolation cannot be
financially viable for low-rise buildings because of the cost of the additional, heavily reinforced
slab (diaphragm) that is typically constructed at the isolation level. Unless the cost of this slab is
reduced, seismic isolation cannot be financially competitive. It is noted that the applications of the
isolator are not limited to the aforementioned cases. The isolator could also be applicable in the
developed world, in projects where conventional seismic isolation is too expensive to be applied.
A practical application could combine the isolator of Cilsalar and Constantinou (2019a) and the
sliding surface proposed by Tsiavos et al. (2022), for the isolation of 1-2 story masonry houses
(Figure 3). More specifically, the walls are supported on concrete beams that serve as the upper
rolling surface of the isolators. Two sheets of PVC (with sand in between) will continuously support
the ground floor slab. This continuous support allows for reducing the thickness and the
reinforcement of the slab. When the deformable rubber sphere rolls, the horizontal motion of the
isolator also causes a vertical one due to the deformed shale of the sphere (Figure 2). Therefore,
a PVC joint could be used to connect the slab to the beams. This would allow the vertical motion
of the beams while the slab only moves horizontally (Figure 3).
Experimental Setup
Testing equipment and instrumentation
The uniaxial shake table of ETH Zurich was used in both the lateral cyclic and the shake-table
tests. The setup comprised four isolators placed symmetrically on the shake table platen in a two-
by-two configuration (Figure 4). An isolator comprised a polyurethane (PU) sphere rolling between
two concrete plates. In all tested cases, the lower concrete plates were flat. The upper concrete
plates were either flat (“flat configurations”) or spherical/concave (“spherical configurations”). The
lower concrete plates were fixed to the shake table platen, whereas the upper ones were mounted
on a steel slab. During the lateral cyclic tests, the motion of the top slab parallel to the x-axis (and
the out-of-plane y axis) was restrained by two rigid struts fixed to a rigid column (Figure 4). The
shake table applied a sinusoidal motion by moving the bottom concrete plates, the top plates
were kept in place by the rods, and shearing of the isolators was achieved. Large steel beams
were placed on top of the steel slab to compress the isolators (emulating the weight of the isolated
superstructure). For the shake table tests, the steel rods were removed, and the steel slab was
free to move along the x-axis.
W
F
W
r
rinitial
δUplift
W = F = 0 W ≠ 0, F = 0 W ≠ 0, F ≠ 0
Initial condition Under compressive load Under compressive and lateral load
u
r >rinitial
Flat
surface
Flat
surface
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Figure 3: Representation of a potential application of deformable rolling isolators in low-rise
masonry buildings.
Three-dimensional accelerometers were placed on top of the steel slab and the shake table platen
(red triangles in Figure 4). The struts that hold the steel diaphragm in place were equipped with
load cells, measuring the reaction force of the isolators to the applied motion during the lateral
cyclic tests. Another load cell was placed at the actuator that drives the shake table. The
movement of the shake table and the superstructure was measured using an NDI Optotrak Certus
camera with an accuracy of 0.1 mm (displacement markers are shown as green circles in Figure
4).
Materials and geometry
Three types of spheres were tested: Solid spheres with a diameter of 100 mm, spheres with a
diameter of 100 mm and a 50 mm steel core inside (spheres 100/50 mm), and spheres with a
diameter of 80 mm and a 50 mm steel core inside (spheres 80/50 mm). All spheres were made
of polyurethane (PU) with a shore hardness of 95A. The steel core was made of Gcr15 steel. The
cost of 100 mm, 100/50 mm, and 80/50 mm spheres was $23, $30, and $25 per piece,
respectively. In an application in a residential structure, the price per piece is expected to be
significantly lower due to the increase in the total number of spheres ordered. A commercial M15
concrete mix was used for the construction of the concrete plates. Figure 5 shows the dimensions
of the spherical (concave) concrete plates. The mean compressive strength of the concrete mix
was 27.6 MPa. The plates were unreinforced. The material cost of each plate was $6. In plan
view, the diameter of the spherical concrete plate was 350 mm (Figure 5). The radius of curvature
of the spherical concrete plates (R) was R = 750 mm.
Similitude laws and tested configurations
All tests were performed in 1:2 scale. To ensure similitude of stresses, the geometric, force, and
time scaling factors were SL=0.5, SF = 0.25, and ST = 0.707, respectively. An unconfined masonry
house in Cuba was considered to calculate the expected vertical load, resulting in a gravity load
of 11 kN (i.e., 2.75 kN in the model scale) per isolator. Four compressive loads (2.08 kN, 3.23 kN,
4.74 kN, or 8 kN per sphere in model scale) under two rolling surface curvatures (flat and concave)
were planned for all three spheres.
Figure 4: Representation of the experimental setup. Green circles, red diamonds, and blue
squares show the location of the triaxial displacement sensors, the triaxial accelerometers, and
the uniaxial load cells, respectively.
Isolator
PU Sphere
Additional Weight
Actuator
Shake table/Fixed Part
Shake table/Moving Part
Restrainer
Rigid Column Rigid Beam
Restrainer
North South
Steel slab
Struts
Concrete Plates
(+)
Z
X
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Figure 5: (A) Shape and dimensions of the utilized spherical concrete plates (in mm); Elastic
response spectra of the applied ground motions and design spectrum of Santiago, Cuba (in
model scale). (B), Pseudo-accelerations; (C) Displacements.
Four compressive loads (2.08 kN, 3.23 kN, 4.74 kN, or 8 kN per sphere in model scale) under
two rolling surface curvatures (flat and concave) were planned for all three spheres. The actuator
of the shake table had a stroke of 230 mm. To test the isolators under larger lateral displacements,
two types of cyclic tests were performed: a) between -115 and +115 mm (“±115 mm”) and b)
between 0 and +230 mm and 0 and -230 mm (“±230 mm”).
The shake table tests were performed under an ensemble of 61 different ground motions,
selected from the three different categories of FEMA P695 (2009) (i.e., far-field, near-field pulse-
like, and near-field non-pulse-like). All ground motions were scaled in the frequency domain since
the tested model corresponds to a half-scale (SL=0.5) representation of a prototype structure.
Subsequently, all ground motions were acceleration-scaled to comply with the capacity of the
shake table, with the acceleration-scaling factor ranging from 0.7 to 1. Figure 5 (B,C) plots the
elastic response spectra of the pseudo-accelerations and displacements of the ground motions
used in the shake table tests, together with the design spectrum for a site in Santiago, Cuba
(model scale), assuming soil type C, 5% damping and a return period of 475 years. The example
of Santiago, Cuba is used since it is considered representative of regions of high seismicity and
low availability of construction materials. Similar (or higher) seismicity and analogous lack of
recourses can be found in many countries in Latin America, Asia, and Africa.
Compressive and lateral cyclic response
Compressive response
The maximum load that the spheres sustained under monotonic uniaxial compression was 105.2
kN, 118.8 kN, and 102.5 kN for the 100 mm, 100/50 mm, and 80/50 mm spheres, respectively
(Figure 6). These load levels are substantially higher than the ones that the spheres would have
to sustain in a practical application (2.75 kN/sphere in model scale). Therefore, the loss of vertical
load-bearing capacity of the spheres is not the critical design parameter. Under design loads, the
compressive displacement of the isolators is non-negligible, confirming the shape change of the
spheres. A comparison of the 100 and 100/50 spheres shows that the presence of a steel core
increases the stiffness of the sphere.
Lateral cyclic response
Before the lateral cyclic tests, the spheres were subjected to sustained compression for seven
days, so their “creep” displacement and shape change is concluded. The excitation frequency of
all cyclic tests was f = 0.2 Hz. Figure 7 collectively offers the force deformation loops for all lateral
cyclic tests. The first and most important observation is that the behavior of the system is clearly
not bilinear elastoplastic. In fact, since the sphere has deformed into an oval-shaped object, a
vertical motion of the top plate was recorded both in the tests presented in this study and in
(Katsamakas et al. 2022c). This vertical motion influences the restoring force, which is positive
for small displacements (up to 30 mm) but becomes negative for larger displacements due to the
rolling of the sphere. The use of concave concrete plates adds positive stiffness to the system.
The rolling friction coefficient (μroll), is defined as the lateral-to-vertical force ratio at zero lateral
displacement and describes the energy dissipation capacity of the isolator. In all following
sections, the rolling friction coefficient was obtained by the “±115 mm” cyclic tests and is noted in
Figure 7. It is observed that as the vertical load (W) increases, the rolling friction coefficient also
increases.
500
70 20
50
500
d0= 350
R = 750
T (sec) T (sec)
SA (g)
SD (mm)
(A) (B) (C)
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Figure 6: Compression testing results. Left: Force-displacement (overview); Right: Force-
displacement (detail).
Figure 7: Influence of the vertical load (W) on the cyclic lateral response of the spherical
isolator.
This is more pronounced in spheres without a steel core since they are more flexible. A detailed
explanation of this phenomenon appears in (Katsamakas and Vassiliou 2023).
Shake-table response
Figures 8 and 9 show scatter plots between the Peak Ground Acceleration (PGA) and a) the
acceleration of the top slab (Peak Superstructure Acceleration – PSA), b) the peak displacement
of the isolators. Different categories of ground motions appear with different marks.
Excitations with relatively small PGAs (smaller than 0.10-0.15) are not strong enough to start
rolling the system (activate the isolators). Hence, the superstructure acceleration is roughly equal
to the PGA (Figure 8). However, for larger PGAs, the superstructure acceleration is capped at
0.15-0.2 g (Figure 8). These values are slightly higher than the peak of the force-displacement
loops of the cyclic loops (Figure 7).
μroll = 4.4 %
μroll = 5.4 %
μroll = 7.1 %
μroll = 4 %
μroll = 4.7 %
μroll = 6.1 %
μroll = 5.3 %
μroll = 6 %
μroll = 7.1 %
μroll = 4.9 %
μroll = 4.7 %
μroll = 4.9 %
μroll = 4.1 %
μroll = 4 %
μroll = 4.6 %
μroll = 3.8 %
μroll = 5.4 %
μroll = 4.9 %
μroll = 4.1 % μroll = 3.7 %
μroll = 6 %
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Figure 8: Correlation between the acceleration transmitted to the superstructure (PSA) and PGA
for all tested configurations. Top, Flat concrete plates; Bottom, Spherical concrete plates.
Figure 9: Correlation between the maximum displacement of the isolators and PGA for all tested
configurations. Top, Flat concrete plates; Bottom, Spherical concrete plates.
The isolators maintained moderate peak displacements during testing, which were below 120 mm
and 100 mm for the flat and the spherical plates, respectively. No systematic trend that could
correlate the category of the ground motion to the response is observed (Figure 9). After the
shake table tests, another set of lateral cyclic tests was performed to evaluate the deterioration
of the spheres.
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Figure 10: (Left) Lateral cyclic response of the isolators before and after subjected to 65 ground
motions. No deterioration was observed. (Right) Repeatability of the shake table tests when
using the same excitation in 3 sequential tests. Use of the 1989 Loma Prieta, USA, ground
motion, component 0, as recorded at Capitola station.
The lateral cyclic response of the isolators was practically the same as before the shake table
tests (Figure 10, Left). Hence, even after 65 ground motions, the spheres did not deteriorate.
Some shake table tests were performed three times (using the same ground motion input) to
examine the repeatability of the results. The response of the isolators was practically identical,
both in terms of accelerations and displacements, confirming the repeatability of the tests (Figure
10, Right).
Conclusions
The present study investigated the compressive, lateral cyclic, and shake-table response of an
isolator based on polyurethane spheres (with and without steel core) rolling on concrete plates.
Different levels of supported weight and curvatures of concrete plates were considered. A total of
21 different combinations of vertical load, sphere dimensions, and concrete plate curvature were
tested under lateral cyclic loading. In the shake-table tests, 18 combinations were tested with 65
ground motions each, leading to a total of 1170 shake-table tests. According to the experimental
results, the following conclusions are drawn:
The compressive strength of the spheres is substantially higher than the estimated design
vertical load applied to the spheres, considering an application in a low-rise residential
masonry structure.
The lateral cyclic response differs substantially from the one that a rigid body model would
suggest. This is due to the non-negligible deformability of the spheres that leads to both
positive and negative stiffness branches.
The curvature of the concrete surface affects the lateral cyclic response. When spherical
(concave) plates are used, the stiffness of the system increases. The final stiffness of the
isolators is affected by the deformed shape of the isolators (source of negative stiffness)
and the curvature of the concrete plate (source of positive stiffness).
During the shake-table tests with excitations at the order of the seismicity of Santiago,
Cuba, the isolators significantly reduced the accelerations transmitted to the superstructure
(in the range of 0.15g), while maintaining displacements below 120 mm in the model scale
(240 mm in the prototype scale). This means that the proposed isolators cap the
accelerations transmitted to the superstructure to less than 0.2 g, while they maintain
reasonable displacements.
When the same isolators were subjected to 3 identical sequential shake table excitations,
the measured response, both in terms of accelerations and displacements, was practically
the same. Therefore, the shake-table tests were repeatable.
Even after subjected to 65 ground motion excitations, the isolators do not deteriorate, and
their cyclic lateral response remains unaffected by the loading history.
Acknowledgements
Financial support to the authors was provided by the European Research Council (ERC) under
Starting Grant 803908. The methods, results, opinions, findings, and conclusions presented in
this report are those of the authors and do not necessarily reflect the views of the funding agency.
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