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A NEW SEISMIC ISOLATION DEVICE BASED ON TRIBOLOGICAL
SMOOTH ROCKING (TROCKSISD)
Maurizio Froli1, Linda Giresini2, and Francesco Laccone3
1 Department of Energy, Systems, Territory and Construction Engineering, University of Pisa,
Largo L. Lazzarino, 56122, Pisa (Italy)
m.froli@ing.unipi.it
2 Department of Energy, Systems, Territory and Construction Engineering, University of Pisa
Largo L. Lazzarino, 56122, Pisa (Italy)
linda.giresini@unipi.it
3 Institute of Information Science and Technologies (ISTI) “A. Faedo”
National Research Council of Italy (CNR),
via G. Moruzzi 1, 56124, Pisa (Italy);
Department of Energy, Systems, Territory and Construction Engineering, University of Pisa,
Largo L. Lazzarino, 56122, Pisa (Italy)
francesco.laccone@isti.cnr.it
Abstract
In the field of seismic risk mitigation of art objects, an innovative isolation device is here il-
lustrated. The device, called TROCKSISD (Tribological ROCKing Seismic ISolation Device),
couples multiple components to dissipate energy and control smooth rocking: spherical con-
tact surfaces with frictional layers, elastic springs ensuring re-centering and viscous elastic
dampers. The conceptual idea is described and the equations of motions of the two degrees of
freedom system presented, discussing the performance-based structural behaviour and the
mechanical/geometric parameters involved. Moreover, dynamic analyses are performed to
understand the role of the frictional layers with respect to the peripheral dampers in the miti-
gation of motion under spectrum compatible seismic records. The results in terms of rocking
spectra are presented and comparisons with the equivalent single degree of freedom system
without the isolation device are made.
Keywords: Damage Avoidance Design, Rocking, Seismic protection, Seismic isolation, Vi-
bration control, Friction.
750
COMPDYN 2019
7th ECCOMAS Thematic Conference on
Computational Methods in Structural Dynamics and Earthquake Engineering
M. Papadrakakis, M. Fragiadakis (eds.)
Crete, Greece, 24–26 June 2019
Available online at www.eccomasproceedia.org
Eccomas Proceedia COMPDYN (2019) 750-760
ISSN:2623-3347 © 2019 The Authors. Published by Eccomas Proceedia.
Peer-review under responsibility of the organizing committee of COMPDYN 2019.
doi: 10.7712/120119.6954.19893
Maurizio Froli, Linda Giresini and Francesco Laccone
1 INTRODUCTION
A classical approach in earthquake engineering invokes the performance-based Capacity
Design for which the formation of plastic hinges is necessary to dissipate energy provided by
the ground motion. Despite human lives and goods are preserved with this approach, high and
medium-high return period events cause damages not only on secondary components but also
on primary structural members. Moreover, repair costs are usually as high as rebuilding costs
and, in the immediate post-event time, the reconstruction can be unsafe and sometimes useless.
Damage Avoidance Design (DAD) and other isolation techniques were therefore proposed as
alternative design paradigms in earthquake engineering. DAD design philosophy was set out
by Mander and Cheng [1] and later applied for practical cases of braced frame structures [2],
among others. However, this concept was not completely new at that time, neither in the theo-
retical research nor into building practice. Following the early Housner’s work [3], related to
a non-smooth contact problem, efforts were spent on studying the rocking motion of rigid
blocks; Meek [4] introduced the coupled effect of flexibility of the bracing with rocking of
foundation, and Aslam et al. [5] the effect of pre-stressing. On the other hand, frictional prob-
lems were treated in rigid block limit analysis of masonry structures [6,7], based on specific
formulations of 3D yield conditions for contact interfaces [8]. Friction sliding connections
and rocking resisting systems may be found in ancient Greek and Roman temples or in Japa-
nese Pagodas [9], and this is probably why some of these buildings survived so long, not sen-
sitively damaged by earthquakes. More recent examples of DAD structures are the 315 m
span South Rangitikei Bridge [10] and the 35 m high tower of Christchurch [11]. Other ex-
amples are the Alan Macdiarmid Building at Victoria University in Wellington and Southern
Cross Endoscopy Building in Christchurch [12], both located in New Zealand. DAD struc-
tures follow the principles of isolation, with absence of damage and energy dissipation, and
give the possibility of controlling displacements, to respect specific limit states. These charac-
teristics are based on the rocking behavior, whose analytical framework was extensively in-
vestigated in the past. When discussing about rocking, it is necessary to distinguish between
rigid contact problems - where the base of the rocking element can be considered rigid - and
elastic contact models - where the base exhibits elasticity. For the first typology, rocking is
able to describe the seismic behavior of rigid structural elements such as, for instance, mason-
ry walls in out-of-plane modes. Diverse contributions were provided for analyzing the rocking
response of walls in free configuration [13,14] or for horizontally [15–18] or vertically [19]
restrained walls. For masonry structures the assumption of rigid blocks is generally acceptable,
but for other materials, several authors included the elasticity of the superstructure in the for-
mulation [20–23]. In addition, the dynamics of an elastic structure coupled with a rocking
wall was analyzed by [19]. In the context of elastic contact models, Psycharis and Jenning [24]
firstly proposed the rocking rigid block on an elastic foundation realized through coupled
springs and dampers. These models were recently used, properly updated, for new isolation
techniques for instance to protect marble structures [25], showing that these devices are high-
ly performant to sustain seismic actions. However, still only few contributions are available to
quantify the base isolation properties allowed by free rocking [26,27], which is the core of the
DAD philosophy. In this framework of elastic contact models, the present paper proposes an
innovative device, conceived by M. Froli, able to protect from damages different types of su-
perstructures by following the DAD principles. In general, the device allows a favorable dy-
namic behavior since:
(i) in case of low-intensity excitation, the superstructure remains undamaged, so that the
post-event serviceability is preserved;
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Maurizio Froli, Linda Giresini and Francesco Laccone
(ii) in case of a strong excitation, the motion of the superstructure is mitigated by a fric-
tional contact and the effect of dampers, enabling the structure to smoothly rock.
The use of this device aims at limiting the damage of slender structures and valuable ob-
jects under seismic actions and vibrations. The acronym of this device has been inspired by its
mechanics: TROCKSISD (Tribological ROCKing Seismic ISolation Device). The concept
and the equations of motions are obtained for the corresponding two degrees of freedom
(2DOF) system (Section 2), whereas the main design steps are discussed in Section 3 to size
geometrically and mechanically the device in a performance-based perspective. Afterwards, a
quantitative estimation of the response of the system is obtained by performing nonlinear dy-
namic analyses (Section 4), and finally a parametric analysis is carried out to estimate the in-
fluence of friction on the global behavior of the dynamic system (Section 5).
2 TRIBOLOGICAL ROCKING SEISMIC ISOLATION DEVICE - TROCKSISD
2.1 Inspiring idea
For structures or historic assets that are slender and vulnerable to impacts, tensile stresses
and vibrations, bending, induced by dynamic motion, is a relevant problem. The present con-
cept introduces, as an alternative to common shear or pendulum devices, a novel isolation and
dissipation system based on smooth rocking of the structure. This idea brought to a jointed
connection that is installed between the structure and the foundation and works as an articu-
lated mechanism. The TROCKSISD is made of two ribbed plates: the upper one that is inte-
gral with the superstructure, the lower with the foundation. Two homothetic and frictionally
connected spherical cups are included between these ribbed plates and respectively jointed to
them. The two surfaces can reciprocally slide once the static friction is overcome, allowing a
smooth rocking of the structure. Aiming at conferring additional damping and stiffness as
well as re-centering capability, the outer perimeters of the ribbed plates are equipped with vis-
cous-elastic dampers. A mock up showing the conceptual idea is shown in Figure 1.
(a)
(b)
Figure 1 TROCKSISD mock-up: (a) rocking prevented in stick phase, (b) rocking admitted in sliding phase.
2.2 Performance-based structural behavior
The presence of friction at the interface of the two spherical cups allowing to distinguish
and appropriate design two mechanic regimes. A fist one identifies the stick phase, in which
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Maurizio Froli, Linda Giresini and Francesco Laccone
the jointed mechanism is blocked because the external excitation is not able to exceed the stat-
ic friction. In this stage the structure reacts elastically. A second regimes identifies the slip
phase, in which the rocking is activated with smooth oscillations.
This double regime well fits a performance-based design. The geometric and mechanic pa-
rameters of the device can be sized to have the stick phase at the SLS (Serviceability Limit
State), while the sliding phase at ULS (Ultimate Limit State). In this latter case, attention
should be paid to design the components not to be accidentally in contact. Moreover, dis-
placement demands should be guaranteed as well as equilibrium and stability to the structure.
A beneficial energy dissipation occurs at the ULS thanks to friction and viscosity of dampers.
2.3 Conceptual design and parameters
The design of TROCKSISD should contemporarily meet several geometric and structural
requirements: it should be resistant to vertical and shear forces, while it should allow the dy-
namics of the jointed mechanism for bending moments. The device is consequently made of
four main components, with reference to Figure 2: the upper ribbed plate, the convex spheri-
cal cup, the concave spherical cup and the dampers.
The upper ribbed plate is integral with the structure to protect and is connected to the con-
vex spherical cup, which is bolted to the ribs of the upper plate. The latter transfers both verti-
cal and horizontal loading to the lower components, while allowing the rotation around the
pole O. The friction develops by contact of the two spherical cups onto a surface with radius
R, cut at a latitude angle of φ0. To guarantee a constant surface in contact the convex cup is
larger and is cut at a latitude angle of . The concave spherical cup is integral with the lower
plate, which represents the component in contact with the foundation.
Viscous-elastic link the perimeter of the upper plate and the perimeter of the lower plate,
and add stiffness (k), damping (c), and re-centering capacity to the system. Dampers that re-
sult polar-arrayed and each couple of them is arranged as a V bracing to help the system to
self-center and to oppose torsional effects. The hexagon is a convenient shape for the plates,
where for each edge a couple of dampers can be installed. A 3D view of the device is reported
in Figure 3.
Figure 2 Section of TROCKSISD: geometric and mechanical parameters.
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Maurizio Froli, Linda Giresini and Francesco Laccone
(a) (b)
Figure 3 TROCKSISD 3D view: (a) axonometric view; (b) exploded view.
The material for TROCKSISD is common steel for all its component parts. Moreover, the
interface of the two spherical cups can be equipped with stainless steel, anodized aluminum or
PTFE on the basis of the desired friction coefficient.
3 ANALYTICAL MODEL
An analytical model of the planar behavior of the TROCKSISD is developed by adopting a
2DOF simplification, in which the structure is a translational mass and the device is a rota-
tional mass with reference to Figure 4.
Figure 4 Schematic view of the 2DOF model.
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Maurizio Froli, Linda Giresini and Francesco Laccone
The friction contribution in the dynamics of the system is expressed by means of the tribo-
logical moment that is generated by rotations α of the device. This frictional reaction depends
on the friction coefficient μ and the radial pressures on the spherical cup.
The tribological moment expresses the dependency on and as per Eq. (1)
(1)
If all parameters are considered lumped the equation of the dynamic equilibrium can be ex-
pressed as:
(2)
The structure is described by the stiffness k and the damping c, while the device is described
by the friction coefficient μ the stiffness and the damping . In the dynamic motion, the
three phases may occur:
- A static phase characterized by absence of motion, so where both the velocity and the angular
acceleration equal zero:
- The incipient motion phase, where the velocity is still null, but the static friction is exceeded;
- The dynamic phase, with nonzero velocity.
The geometric and mechanical parameters can be selected based on target displacement and
action as per the Eurocodes Limit States.
4 DYNAMIC ANALYSIS AND RESULTS
The To highlight the performances of the TROCKSISD, an ideal case study is selected and
analysed. Seismic loading is expressed by means of response spectrum compatible accelero-
grams obtained from the site specifications. Natural response spectrum compatible accelero-
grams are generated by the software REXEL v3.5 [30] on the basis of two target spectra, one
for the SLS and one for the ULS. Seven accelerograms that provide a mean spectrum close to
the code design response spectrum (within the upper limit of +30% and lower limit of -10%)
are selected for both cases.
The site is in Castelnuovo di Garfagnana, Italy (44°07′19″N 10°24′20″E). The site class is B.
The structure parameters are: height ; the mass , the period is
, while mechanical parameters and . The spherical cup is
sized to have the rocking mechanism locked at the SLS, so when the mass m is submitted to
the plateau acceleration the structure should mechanism should behave as stick. The resulting
parameters are and .
The mechanical parameters of dampers can be derived from the ULS spectra, using as target
maximum rotation the value of and supposing to have steel/steel frictional con-
tact. The values of and are obtained. Thus, from the modal analysis
the first period of the system results , so that the seismic force demand is lowered,
while at the meantime the displacement demand can be met by the components.
The role friction is to regulate the rocking mechanism and to provide for energy dissipation.
The effect of limiting the rotations can be visualized by means of the results of a parametric
analysis, in which the friction is suppressed (on ) while is varied to match the
curve with steel/steel friction ( ) and . The displacement spectra
of absolute maximum rotations is reported in Figure 4.
The curves exhibit some peaks due to resonance phenomena, which flatten whether damping
increases. With respect to the reference curve ( ; ), the absolute maximum
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Maurizio Froli, Linda Giresini and Francesco Laccone
rotations are magnified along the entire monitored spectrum if the friction is suppressed and
dampers with same characteristics are adopted. Increasing the damping ratio, for values of
periods smaller than 10 s the curves tend to approach the reference curve. For larger periods
the curves diverge, and, while the reference curve tends to be constant, the frictionless curves
are monotonically growing. To guarantee performances which are similar to those of a tribo-
logical device at least for lower periods, the viscous damping capacity should increase sub-
stantially, bringing to larger devices that may also impair the feasibility of the device.
Consequently, the contribution of friction is fundamental both in the dynamic behaviour to
minimize the displacement and to increase the economy of the device.
In Figure 6 and Figure 5 are reported the results of the dynamic analyses respectively at the
SLS and at the ULS for some significant natural accelerogram the displacement time history.
Both DOFs are reported.
At the SLS, friction substantially prevents the sliding of the base surfaces, namely the sec-
ond DOF of the system is blocked. However, sometimes the rocking mechanism is activat-
ed because of localized peaks in the accelerograms (as in the case of S1). The possible
residual rotation is even small (maximum value ; mean value ). Also, from
the S1 output the re-centering capability of the system is evident. Concerning the first DOF,
the horizontal displacement does not exceed the value of for which the superstructure
is designed to behave elastically.
Figure 6 SLS dynamic response for S1 and S3 seismic records (in blue the horizontal displacement time-history, in
red the rotation time-history).
Figure 4 Displacement spectra of the absolute maximum rotation for several values of the rotational damping
ratio in the period range with and without friction.
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Maurizio Froli, Linda Giresini and Francesco Laccone
Figure 7 ULS dynamic response for S4 and S6 seismic inputs.
The dynamic response at the ULS for S4 and S6 seismic record is shown in Figure 7. To
effectively evaluate the response of the present system, the results concerning the first DOF
are compared with the results of the reference SDOF oscillator (OSR).
In the first plot, the absolute horizontal displacement of both systems is shown. As expected
for any isolated system, the structure equipped with TROCKSISD exhibits larger displace-
ment than the reference SDOF oscillator.
The second plot concerns the oscillations of the rotational DOF, where slip-stick motions with
incipient motion phases included occur. Moreover, there are residual rotations at the end of
each acceleration story. Their magnitudes, as in the SLS case, are relatively reduced, if com-
pared with the maximum rotations.
In the third plot the SDOF oscillator curve is compared with the relative displacement of the
superstructure mass , where the horizontal displacement due to rotations at the second
DOF is deducted from the absolute value.
In all cases, the rotation values are close to the limitation imposed in the design phase of
for the absolute maximum. Concerning the translation of the first DOF, values are mean-
ly three times larger than these of the reference SDOF oscillator in terms of absolute values,
or at least more than two times larger for the mean value ( vs. ). This result is a
consequence of shifting the period towards higher values in order to obtain reduced level of
accelerations but paying with increased displacement. Nevertheless, it is interesting to observe
that the relative displacement is about the 30% of the SDOF oscillator. This result means that
using TROCKSISD produces displacement that are smaller than those for the SDOF os-
cillator. Consequently, the structure is less stressed.
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Maurizio Froli, Linda Giresini and Francesco Laccone
5 CONCLUSIONS AND FUTURE DEVELOPMENTS
The Tribological ROCKing Seismic ISolation Device (TROCKSISD) can provide seismic
protection of slender structures and valuable objects such as artistic or historic assets (altars,
statues, art objects, etc.). It is based on the development of friction at the interface of a jointed
mechanism that allows smooth rocking of the superstructure in a frictional model. Viscous-
elastic dampers provide for additional stiffness and damping as well as re-centering capability.
Two main regimes in the dynamic behavior occur: a prevalent stick phase (at SLS) and of
mixed slip-stick phase (at ULS).
The behavior of a system equipped with such a device has been described by means of a
simple 2DOFs analytical model with all lumped parameters. From the analyses results, it can
be stated that TROCKSISD follows DAD principles because the structure substantially re-
mains in the elastic phase in both the SLS and the ULS. Moreover, the residual rotations at
ULS are very small and shall be reversed once the excitation stops, providing for post-event
serviceability.
ACKNOWLEDGEMENTS
The authors would like to acknowledge Ing. Enrique Vagelli Saldana Vila for the develop-
ment of the MATLAB codes and the drawing of figures.
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