High dimensional model representation for the probabilistic assessment of seismic pounding

High dimensional model representation for the probabilistic assessment of seismic pounding

R. Sinha, B.N. Rao

Abstract: The study presented herein aims to analyse the seismic performance of a two-dimensional eight-storey non-ductile reinforced concrete frame against structural pounding with an adjacent three-storey stiff frame having different storey heights. The examined case of pounding refers to the extremely critical floor-to-column structural pounding for three different initial separation gaps between the said structures. Seismic vulnerability analysis is usually performed by way of developing fragility curves for a set of damage and intensity measures using a suitable fragility curve generation technique. For this study, damage measures are characterized by the percentage maximum inter-storey drifts of the taller, flexible frame while the peak ground accelerations of the ground motion data are used as the corresponding intensity measures. Displacement-based fragility curves were generated for 9 sampling points using the High Dimensional Model Representation (HDMR) technique and the results were compared with actual probabilistic data obtained using Monte-Carlo Simulations (MCS). The results of this study imply that the proposed use of HDMR provides excellent fragility curves for the estimation of pounding risks with a significant reduction in the number of simulations required, thereby reducing the computational cost by huge margins. Results also indicate that fragility curves for target separation distances can also be obtained using HDMR without performing additional simulations. This can further be used for the mitigation of pounding risks and for the reliability-based design of buildings for target separation distances and damage measures.

Keywords
Fragility Curves, HDMR, MCS, Structural Pounding, Response Surface Method, Meta-Model

Published online 8/10/2023, 8 pages
Copyright © 2023 by the author(s)
Published under license by Materials Research Forum LLC., Millersville PA, USA

Citation: R. Sinha, B.N. Rao, High dimensional model representation for the probabilistic assessment of seismic pounding, Materials Research Proceedings, Vol. 31, pp 38-45, 2023

DOI: https://doi.org/10.21741/9781644902592-5

The article was published as article 5 of the book Advanced Topics in Mechanics of Materials, Structures and Construction

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 license. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

References
[1] Anagnostopoulos, S. A. 1988. “Pounding of buildings in series during earthquakes.” Earthq. Eng. Struct. Dyn., 16 (3): 443–456. https://doi.org/10.1002/eqe.4290160311.
[2] Maison, B. F., and K. Kasai. 1990. “Analysis for a Type of Structural Pounding.” J. Struct. Eng., 116 (4): 957–977. https://doi.org/10.1061/(asce)0733-9445(1990)116:4(957).
[3] Polycarpou, P. C., and P. Komodromos. 2010. “Earthquake-induced poundings of a seismically isolated building with adjacent structures.” Eng. Struct., 32 (7): 1937–1951. Elsevier Ltd. https://doi.org/10.1016/j.engstruct.2010.03.011.
[4] Skrekas, P., A. Sextos, and A. Giaralis. 2014. “Influence of bi-directional seismic pounding on the inelastic demand distribution of three adjacent multi-storey R/C buildings.” Earthq. Struct., 6 (1): 71–87. https://doi.org/10.12989/eas.2014.6.1.071.
[5] Wolf, J. P., and P. E. Skrikerud. 1980. “Mutual pounding of adjacent structures during earthquakes.” Nucl. Eng. Des., 57 (2): 253–275. https://doi.org/10.1016/0029-5493(80)90106-5.
[6] Hideo Takabatake and Masaaki Yasui and Yoshihisa Nakagawa and Akiko, K. 2007. “Relaxation method for pounding action between adjacent buildings at expansion joint.” Pacific Conf. Earthq. Eng., (056): 1–6. https://doi.org/10.1002/eqe.2402.
[7] Tubaldi, E. 2011. “Dynamic behavior of adjacent buildings connected by linear viscous/viscoelastic dampers.” Struct. Control Heal. Monit., (May 2011). https://doi.org/10.1002/stc.1734.
[8] Tubaldi, E. and Freddi, F. and Barbato, M. 2007. “Probabilistic seismic demand model for pounding risk assessment.” Pacific Conf. Earthq. Eng., (056): 1–6. https://doi.org/10.1002/eqe.2725.
[9] Whitman, R. V, J. M. Biggs, J. E. Brennan, C. A. Cornell, R. L. de Neufville, and E. H. Vanmarcke. 1975. “Seismic Design Decision Analysis.” J. Struct. Div., 101 (5): 1067–1084. https://doi.org/10.1061/JSDEAG.0004049.
[10] Porter, K. A. 2003. “An Overview of PEER’s Performance-Based Earthquake Engineering Methodology.” 9th Int. Conf. Appl. Stat. Probab. Civ. Eng., 273 (1995): 973–980.
[11] Gardoni, P., K. M. Mosalam, and A. Der Kiureghian. 2003. “Probabilistic seismic demand models and fragility estimates for RC bridges.” J. Earthq. Eng., 7: 79–106. https://doi.org/10.1080/13632460309350474.
[12] Ramamoorthy, S. K., P. Gardoni, and J. M. Bracci. 2006. “Probabilistic Demand Models and Fragility Curves for Reinforced Concrete Frames.” J. Struct. Eng., 132 (10): 1563–1572. https://doi.org/10.1061/(asce)0733-9445(2006)132:10(1563).
[13] Flenga, M. G., and M. J. Favvata. 2021. “Probabilistic seismic assessment of the pounding risk based on the local demands of a multistory RC frame structure.” Eng. Struct., 245 (July). https://doi.org/10.1016/j.engstruct.2021.112789.
[14] Box, G. E. P., and K. B. Wilson. 1951. “On the Experimental Attainment of Optimum Conditions.” J. R. Stat. Soc. Ser. B, 13 (1): 1–38. https://doi.org/10.1111/j.2517-6161.1951.tb00067.x.
[15] Bhasker, R., and A. Menon. 2022. “A seismic fragility model accounting for torsional irregularity in low-rise non-ductile RC moment-resisting frames.” Earthq. Eng. Struct. Dyn., 51 (4): 912–934. https://doi.org/10.1002/eqe.3597.
[16] Chowdhury, R., B. N. Rao, and A. M. Prasad. 2009. “High-dimensional model representation for structural reliability analysis.” (April 2008): 301–337. https://doi.org/10.1002/cnm.1118.
[17] Rabitz, H., and Ö. F. Aliş. 1999. “General foundations of high-dimensional model representations.” J. Math. Chem., 25 (2–3): 197–233. https://doi.org/10.1023/a:1019188517934.
[18] Rabitz, H., Ö. F. Aliş, J. Shorter, and K. Shim. 1999. “Efficient input-output model representations.” Comput. Phys. Commun., 117 (1): 11–20. https://doi.org/10.1016/S0010-4655(98)00152-0.
[19] Li, G., C. Rosenthal, and H. Rabitz. 2001a. “High dimensional model representations.” J. Phys. Chem. A, 105 (33): 1–26. https://doi.org/10.1021/jp010450t.
[20] Li, G., S. W. Wang, C. Rosenthal, and H. Rabitz. 2001b. “High dimensional model representations generated from low dimensional data samples. I. mp-Cut-HDMR.” J. Math. Chem., 30 (1): 1–30. https://doi.org/10.1023/A:1013172329778.
[21] V. U. Unnikrishnan, A. M. Prasad, and B. N. Rao. 2007. “Development of fragility curves using high-dimensional model representation.” Pacific Conf. Earthq. Eng., (056): 1–6. https://doi.org/10.1002/eqe.2214.
[22] Mander, J. B., M. J. N. Priestley, and R. Park. 1988. “Theoretical Strss-Strain Model for Confined Concrete.” J. Struct. Eng, 114 (8): 1804–1826.
[23] Bureau of Indian Standards New Delhi. 2000. “IS 456 – Plain and Reinforced Concrete – Code of Practice.” 1–114.
[24] PEER Ground Motion Database. 2011.
[25] Bureau of Indian Standards New Delhi. 2002. “IS 1893 Part 1 – Criteria for Earthquake Resistant Design of Structures – General Provisions and Buildings Part-1.” Bur. Indian Stand. New Delhi, Part 1 (1): 1–39.
[26] Ghobarah, A. 2004. “On drift limits associated with different damage levels.” Int. Work. performance-based Seism. Des. concepts Implement., (February): 321–332.