EXPERIMENTAL AND NUMERICAL STUDIES OF FREESTANDING STRUCTURAL SYSTEMS Christine E. Wittich, Ph.D. Candidate, and Tara C. Hutchinson, Professor IGERT Award #DGE-0966375 MRI Award #CNS-1338192 ACKNOWLEDGEMENTS This 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. MOTIVATION Freestanding 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. REFERENCES Earthquake 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 METHODS Existing 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 m, I R R θ LiDAR GEOMETRIC SURVEY The 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: DEVELOPMENT A 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 arbitrary geometry and asymmetry. Interaction between individual bodies is modeled using a penalty-based contact algorithm which searches for nodal penetration at NUMERICAL MODEL: VALIDATION The 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).