Shake Table Testing of Stiff Model Statue Structures

Considering Mass Eccentricity Christine E. Wittich & Tara C. Hutchinson Department of Structural Engineering, University of California-San Diego

ABSTRACT

This work was supported by the National Science Foundation under IGERT Award #DGE-0966375,

“Training, Research, and Education in Engineering for Cultural Heritage Diagnostics.” Additional

support was provided by the World Cultural Heritage Society, Friends of CISA3, and the Italian

Community Center of San Diego. The authors thank Dr. Richard Wood for his assistance during the

field work conducted as part of this study, and Professor Falko Kuester for his input to the scope of

the work. Findings from this study are those of the authors and do not necessarily reflect the

opinions of the sponsoring agencies.

Berto, L., Favaretto, T. Saetta, A., Antonelli, F., and Lazzarini, L. (2012). “Assessment of the seismic vulnerability of art

objects: The ‘Galleria dei Prigioni’ sculptures at the Accademia Gallery in Florence.” J. Cult. Herit., 13(1), 7-21.

Nigbor, R.L. (1989). “Analytical/experimental evaluation of seismic mitigations measures for art objects.” Ph.D. thesis.,

University of Southern California.

Rosetto, T. et al. (2012). The 20th May 2012 Emilia Romagna Earthquake. EPICentre Field Observation Report EPI-FO-

200512, London, UK.

Thomas, H., Bowes, W., and Nelson, B.S. (1960). “Geologic report on the effects of the earthquake of 22 May 1960 in

the city of Puerto Varas.” Bull. Seismol. Soc. Am., 53(6), 1347-1352.

Wittich, C.E., Hutchinson, T.C., Wood, R.L., & Kuester, F. (2012). A Methodology for Integrative Documentation and

Characterization of Culturally Important Statues to Support Seismic Analysis. Progress in Cultural Heritage

Preservation: Proceedings of 4th International Conference, Euromed 2012 (pp. 825-832). Berlin: Springer.

Wittich, C.E. & Hutchinson, T.C. (2013). Computing Geometric and Mass Properties of Culturally Important Statues for

Rigid Body Rocking. Proceedings of the 2013 ASCE International Workshop on Computing in Civil Engineering.

Renton, VA: ASCE Press.

Figure 1: (left) Captain Scott Statue at Scott Reserve in Christchurch, NZ before the February 2011

Christchurch Earthquake. (right) Captain Scott Statue after the February 2011 Christchurch Earthquake.

Note that the statue was unrestrained with a stone-stone interface and that it overturned during the

earthquake. [“Fallen Captain Scott Statue.” (2011). Christchurch City Council.]

The response of eccentric rigid bodies to seismic loading is of paramount

importance for the protection of culturally important statues and can be

easily extended to building contents and mechanical equipment. The

analysis of cultural heritage artifacts, statues in particular, has been a

historically neglected area of structural and earthquake engineering with

advances only being made in the past decade or so (Nigbor, 1989). Yet,

their high cultural, national, and religious significance combined with

observations of toppling from recent earthquakes gives impetus to their

study (Thomas, 1960; Berto, 2012; Rosetto, 2012). Culturally important

statues have been observed to be typically constructed out of a single

piece of marble and to be resting unrestrained on a stone pedestal with a

high coefficient of static friction. As a result, they are expected to respond

to seismic loading in the predominant rigid body modes of rocking, sliding,

and slide-rocking. To date, few experiments have been conducted to

understand the dynamics of typical rigid bodies.

FIELD SURVEY A field survey was conducted in Italy

which included obtaining three-

dimensional reconstructions of 25

culturally important statues. These

reconstructions are used to obtain the

geometric parameters that theoretically

govern rocking and sliding responses.

Light detection and ranging (LiDAR)

and structure-from-motion (SfM) were

used in the field to obtain the point

clouds which were then triangulated

into the fully enclosed meshes. (Wittich

et al. 2012; Wittich & Hutchinson 2013)

An example is seen in the figure at

right.

ACKNOWLEDGEMENTS

REFERENCES

SPECIMEN DESIGN

Each configuration of the

specimen is subjected to a suite

of 12-15 input motions (Figure 4).

Two near-fault pulse-type ground

motions were selected along with

the corresponding transient and

extracted pulse motions. A

broadband motion was selected

for use in an experimental

incremental dynamic analysis. An

increasing sinusoidal protocol

was also developed in order to

induce many cycles of rocking

and sliding behavior.

Guided by the results of the field survey, the experimental specimen is

designed such that a consistent set of weight plates can be arranged to

shift the center of mass in three directions. This will vary the critical

geometric parameters for rocking: center of mass and slenderness. As

such, the specimen can represent 84% of statues surveyed. Furthermore,

the specimen is fixed to a marble base which rests unattached to another

piece of marble on the shake table. This maintains the in-situ frictional

interface and rebound properties. Figure 3 contains an image of this

experimental specimen and setup in the UCSD Powell Laboratory as well

as image of the specimen post-shaking with the catch system engaged.

0 1 2 3 40

1

2

3

4

Period, T [s]

Psuedo-S

pectr

al A

ccele

ration [

g]

1999Duzce,Bolu

1999Duzce transient

1999Duzce pulse

1989LP,Gavilon Col

1989LP transient

1989LP pulse

1994Northridge,UCLA

Figure 4: Pseudo-spectral acceleration (5% damped of critical)

of the selected ground motions including transient motions and

extracted pulses.

In order to record the observed three-dimensional rotation, sliding, slide-

rocking, accelerations due to impact, and angular accelerations, a large

network of sensors was used: (7) string potentiometers, (22)

accelerometers, (8) high definition cameras for motion tracking using grid

and circle patterns on specimen.

Figure 2: Three dimensional reconstructions of

a surveyed statue by LiDAR and SfM

GROUND MOTION SELECTION

INSTRUMENTATION

PRELIMINARY RESULTS

The following is a sequence of rotational time history responses of the

specimen in its tallest configuration with varying degrees of in-plane

eccentricity. The effect of the pulse-like ground motion is clearly seen with

comparison to the response of the transient motion. In addition, the

eccentricity, as expected, one-sidedly accentuates the response and leads

to overturning.

Symmetric

Eccentric 1

Eccentric 2

Figure 3: (left) Experimental setup in the UCSD Powell Laboratory uniaxial shake table with marble base

attached to shake table, steel specimen with marble base and attached weight plates, and safety catch

system to allow the specimen to rotate through 35°. The grid and circle patterns on the specimen are

used for camera motion tracking (see Instrumentation section). (right) Experimental specimen post-

shaking for a tall configuration with minor eccentricity in-plane of shaking (Eccentric 1 in Preliminary

Results section) in an overturned state with the safety system fully engaged.

Figure 5: Rotational time histories of the tall configuration with three levels of

eccentricity subjected to Duzce, Bolu ground motion as an original motion, transient

motion, and extracted pulse.