EXPERIMENTAL AND NUMERICAL STUDIES OF

FREESTANDING STRUCTURAL SYSTEMSChristine E. Wittich, Ph.D. Candidate, and Tara C. Hutchinson, Professor IGERT Award #DGE-0966375

MRI Award #CNS-1338192

ACKNOWLEDGEMENTSThis research was supported by the National Science Foundation under IGERT Award #DGE-

0966273, “Training, Research, and Education in Engineering for Cultural Heritage Diagnostics,” and

award #CNS-1338192, “MRI: Development of Advanced Visualization Instrumentation for the

Collaborative Exploration of Big Data,” as well as by the UC San Diego Academic Senate,

Achievement Rewards for College Scientists, the Qualcomm Institute at UC San Diego, the Friends of

CISA3, and the World Cultural Heritage Society. The assistance of support of the Charles Lee Powell

Laboratory staff and Professor Falko Kuester is greatly appreciated.

MOTIVATIONFreestanding structural systems encompass a wide variety of critical or significant components, such

as mechanical and electrical equipment, unreinforced masonry, classical multi-drum columns and

statue-pedestal systems. However, these unanchored structures have been observed to perform poorly

during earthquakes resulting in excessive translation, overturning, or collapse. Failure can result in

loss of cultural heritage, loss of functionality for a critical facility, or even loss of life.

Therefore, there is a critical need for accurate prediction of the

seismic response of freestanding structural systems.

REFERENCESEarthquake Engineering Research Institute (EERI). (2013). Earthquake Photo Galleries. Accessed 12/2013.

Housner GW. (1963). “The Behavior of Inverted Pendulum Structures During Earthquakes.” Bulletin of the Seismological Society of

America, 53(2), 403-417.

Livermore Software Technology Corporation (LSTC). (2006). LS-DYNA Theory Manual. LSTC: Livermore, CA.

Wittich, C.E. and Hutchinson, T.C. (2016). “Shake Table Tests of Unattached, Asymmetric Dual-Body Systems.” Earthquake

Engineering and Structural Dynamics. (Under Review).

Wittich, C.E. and Hutchinson, T.C. (2015). “Shake Table Tests of Stiff, Unattached, Asymmetric Structures.” Earthquake

Engineering and Structural Dynamics, 44(14): 2425-2443.

Wittich, C.E., Hutchinson, T.C., Lo, E., Meyer, D., and Kuester, F. (2014). “The South Napa Earthquake of August 24, 2014: Drone-

based Aerial and Ground-based LiDAR Imaging Survey.” Structural Systems Research Project Report No. SSRP 2014/09,

University of California, San Diego: La Jolla, CA.

Wittich, C.E., Hutchinson, T.C., Wood, R.L., Seracini, M., and Kuester, F. (2015). “Characterization of Full-Scale Human-Form

Culturally Important Statues.” Journal of Computing in Civil Engineering (ASCE). DOI: 10.1061/(ASCE)CP.1943-

5487.0000508.

Twisted and translated transformer

2014 South Napa Earthquake

(Wittich et al. 2014)

Collapsed unreinforced masonry wall

2011 Christchurch Earthquake

(EERI 2013)

Overturned and twisted (180°) statue

2014 South Napa Earthquake

(Wittich et al. 2014)

EXISTING ANALYSIS METHODSExisting analysis methods are quite limited and have not been validated against a broad range of

geometric configurations. Specifically, the analytical equations of motion for the two-dimensional,

symmetric rocking block are provided in the corresponding figure. These equations are:

• Nonlinear and piecewise with respect to geometry

• Derived assuming a highly simplified contact interface and geometry

• Not validated against broad range of geometric configurations

θ

R1

m, I

R2

Rnm, I

RR

θ

LiDAR GEOMETRIC SURVEYThe most complex example of freestanding structural systems is the

statue-on-pedestal. Therefore, an extensive field survey was

conducted in Florence, Italy, consisting of Light Detection and

Ranging (LiDAR) for 25 large statues. Subsequent tasks included:

1) Merging multiple scans into a unified point cloud

2) Poisson surface reconstruction to yield a surface mesh

3) Computation of geometric and mass properties.

Statistical analysis of the results emphasized aspect ratios, AR,

(height-to-width) ranging from 1.5 – 10 and very high levels of

asymmetry (min AR/max AR ≥ 0.3). (Wittich et al. 2015).

Therefore, shake table testing must account for a very wide

range of asymmetric geometric configurations.

SHAKE TABLE TESTING: DESIGN

A stiff, steel tower specimen was designed to account for over 85% of the geometry encountered in

the field survey. Reconfigurable weight plates generated 15 unique configurations for single-body

tests varying the size and asymmetry. A subset of four configurations were tested atop two

geometrically-unique pedestals in dual-body tests. Each configuration was subjected to at least 5

earthquake motions (near-fault and far-fault) as well as free rocking and variable-velocity slip tests.

SHAKE TABLE TESTING: RESULTS

Three primary modes of response were observed (i.e.

rocking, sliding, twisting). In addition, multiple modes of

response were observed in over 30% of all single-body

tests and in nearly all of dual-body tests.

The top figure emphasizes the significant difference in

response for symmetric and eccentric configurations,

particularly for squatter/smaller structures. Specifically, the

squat eccentric configuration is highly vulnerable to

overturning while its symmetric counterpart is dominated

by sliding.

Counter-intuitively, this squat eccentric configuration is

more stable within a dual-body system, as shown in the

schematic at right. This can be attributed to the complex

interactions between multiple bodies at impact, which

occurs between two moving bodies and can result in

significant energy dissipation. (see figure at right).

NUMERICAL MODEL: DEVELOPMENTA numerical model was developed in the three-dimensional, explicit multi-physics solver, LS-DYNA. Individual bodies (e.g. tower, pedestal, foundation)are modeled as three-dimensional discrete, rigid entities accounting for arbitrarygeometry and asymmetry. Interaction between individual bodies is modeledusing a penalty-based contact algorithm which searches for nodal penetration at

NUMERICAL MODEL: VALIDATIONThe developed numerical model

with average contact parameters

was compared to the dynamic

response of the multiple

geometric configurations of

single- and dual-body tests. The

model was found to capture:

1. Multi-modal behavior of

individual bodies (top fig.)

2. Complex multi-body

interaction (bottom fig.)

The numerical (approximate)

model was further validated

against the fundamental rocking

equations of motion. In this

context, the numerical model is

able to sufficiently represent the

amplitude and decay associated

with the fundamental rocking

dynamics.

RESEARCH OBJECTIVES

1. Quantify the range of geometries for the extreme cases of

freestanding structural systems

2. Generate a comprehensive database of the response of these

systems to extreme loads via shake table testing

3. Develop and validate a numerical model which can predict the

seismic response of these systems with high fidelity

Primary Experimental Conclusions Impact on Numerical Modeling

Eccentric bodies may respond with varying

magnitude and in different modes than

symmetric counterparts

Three-dimensional model capable of

representing asymmetric geometries

Systems tend to respond with multi-modal

behavior

Modeling scheme must allow primary and

interactive response modes within a single

simulation

Single bodies can be less stable than dual-body

counterparts

Multi-body systems must be solved

simultaneously and account for distinct motion

of each body

each time step and generates spring and

dashpot elements at the location of the

penetrating node. Utilizing the free rocking

and slip tests, an average model was

developed with calibrated spring stiffness,

damping ratio, and friction coefficients.

(left) Schematic of the penalty-

based contact algorithm, and

(above) Numerical scheme for the

developed multi-physics model

Tall, Symmetric Tower – Tall Pedestal

Validation of the developed numerical model in terms of the multi-modal behavior including

modal transitions and modal interaction.

Validation of the developed numerical model in terms of the multi-body interaction including

primary and interactive modes of both tower and pedestal, as well as the large rotation response

of the tower which would be markedly different as a single-body.

Summary of single-body tests: Maximum rocking or sliding response of an eccentric configuration normalized by that of

the corresponding symmetric configuration as a function of the configuration’s size (height of the center of mass). (Wittich

and Hutchinson 2015).

Comparison of a squat, eccentric configuration as a

single-body to that of a corresponding dual-body

system evidencing an increase in stability due to the

complex multi-body interactions. (Wittich and

Hutchinson 2016).