Proposal of a Numerical Simulation Method for Elastic, Failure and Collapse Behaviors of Structures and its Application to Seismic Response Analysis of Masonry Walls
Aiko Furukawa*, Junji Kiyono**, and Kenzo Toki***
*Department of Civil and Earth Resources Engineering, Kyoto University, Kyotodaigaku-katsura, Nishikyo-ku, Kyoto 615-8540, Japan
**Department of Urban Management, Kyoto University, Kyotodaigaku-katsura, Nishikyo-ku, Kyoto 615-8540, Japan
***Disaster Mitigation of Urban Cultural Heritage, Ritsumeikan University, 58 Komatsu-bara Kita-machi, Kitaku, Kyoto 603-8341, Japan
We propose a dynamic analysismethod – a refined version of the DEM- that can simulate three-dimensional elastic, failure and collapse behaviors of structures. A structure is modeled as an assembly of rigid elements. Interaction between elements is modeled using multiple springs and multiple dashpots attached to surfaces of the elements. The elements are assumed to be rigid, but the method allows the simulation of structural deformation by permitting penetration between elements. There are two types of springs: one is a restoring spring to simulate elastic behavior before failure and the other is a contact spring for simulating contact and recontact between elements. A contact dashpot is also used to dissipate the energy of contact. Structural failure is modeled by replacing restoring springs with contact springs and dashpots. A method for determining spring constants is also proposed. The validity of the method is confirmed by the numerical simulation of masonry wall models. First, the elastic behavior induced by an impact force is calculated. It is found that the elastic behavior determined using the proposed method is in good agreement with that determined using the finite element method. Second, the seismic behaviors of masonry wall models with different laying patterns and a wall model with reinforcement are analyzed. It is found that the proposed method allows expression of the difference in behavior due to different laying patterns and reinforcement. The validity of the proposed method is thus confirmed. The proposed method is suitable for simulating seismic behavior of masonry structures.
-  A. Coburn and R. Spence, “Earthquake protection,” 2nd edition, John Wiley and Sons, Chichester, 2002.
-  D. Giardini, G. Gruenthai, K. Shedlock, and P. Zhang, “The GSHAP global seismic hazard map,” in: W. HK. Lee, H. Kanamori, P.C. Jennings, C. Kisslinger (Eds.), International handbook of earthquake and engineering seismology, Vol.81B, Academic Press, London, U.K., pp. 1233-1239, 2003.
-  O. C. Zienkiewicz and R. L. Taylor, “The Finite Element Method,” 5th ed., Vol.1,2,3, Butterworth Heinemann, Oxford, U.K., 2000.
-  K. Oguni, M. Hori, and H. Sakaguchi, “Proposal of new FEM for analysis of failure phenomena,” J. of Japanese society for civil engineers, No.766, I-68, pp. 203-217, 2004.
-  P. A. Cundall and O. D. L. Strack, “A discrete numerical model for granular assemblies,” Geotechnique, 29, pp. 47-65, 1979.
-  G. H. Shi, “Block system modeling by discontinuous deformation analysis,” Computational mechanics publications, Southampton, U.K., 1993.
-  T. Kawai, “New element models in discrete structural analysis,” J. of the society of naval architects of Japan, 141, pp. 187-193, 1977.
-  K. Meguro and H. Tagel-Din, “Applied Element Method for structural analysis: Theory and application for linear materials,” Structural Eng./Earthquake Eng., Japan Society of Civil Engineers, Vol.17, No.1, 21s-35s, 2000.
-  P. B. Lourenco, “Analysis of masonry structures with interface elements, theory and applications,” Delft University of Technology, Faculty of Civil Engineering, TU-DELFT report no.03-21-22-0-01, 1994.
-  R. L. Courant, “Variational methods for the solution of problems of equilibrium and vibration,” Bulletin of the American mathematical society, 49, pp. 1-23, 1943.
-  M. A. Ghannad, A. Bakhshi, S. E. Mousavi Eshkiki, A. Khosravifar, Y. Bozorgnia, A. A. Taheri Behbahani, “A study on seismic vulnerability of rural houses in Iran,” The Proc. of the First European Conf. on Earthquake Engineering and Seismology, Paper No.680, 2006.
-  J. Kiyono and A. Kalantari, “Collapse mechanism of adobe and masonry structures during the 2003 Iran Bam earthquake,” Bulletin of earthquake research institute, University of Tokyo 79, pp. 157-161, 2004.
-  BHRC, The very urgent preliminary report on Bam earthquake of Dec 26-2003,