Authors:Adil Rafiq,Muhammad Fahad,Mohammad Adil,
Keywords:Macro-Scale,Masonry,Numerical Model,Squat Pier,Tension Stiffening,
AbstractNumerical modeling of brick masonry behaviour under different performance conditions has always remained a challenging task. Several modeling strategies have been developed for masonry, in general, through the course of time that have been simplified to speed up modeling and analysis duration. This ranges from a simplified strut model to a highly discontinuous micro-scale nonlinear model. With the current advent of high-speed computing and modeling tools, more realistic numerical modeling of masonry is now possible. In this paper, the strategy adopted is based on macro-scale modeling, where isotropic material properties are considered for the homogenous continuum. ABAQUS is used as a state-of-the-art finite element-based analysis and modeling tool. The Concrete Damage Plasticity (CDP) model is used for simulating inelastic material behaviour of brick and mortar, which is available in the ABAQUS library. This material model can be used in both implicit and explicit schemes of integration but the explicit procedure is highly preferred as it overcomes the convergence issues. Various parameters required for CDP modeling of brick and mortar are adapted from literature. The model is assembled in two parts, first part is modeled for masonry with both elastic and plastic properties, while the other part simulates a rigid beam at the top of the masonry part to create a uniform in-plane shear loading effect. The masonry part has been fixed at the bottom with free vertical ends, while horizontal in-plane displacement was applied to the top rigid beam. The load-displacement curves were generated from these models for monotonic push, to compare them with the envelopes of experimental results, loaded similarly. Since brick masonry is a highly disjointed material, it is a complicated procedure to develop an exact model and predict its exact behaviour. However, the overall representative load-displacement curve developed numerically was in good agreement with the ones produced experimentally.
I. ABAQUS, (2016). “Analysis User’s Guide”, Version 6.8, Hibbitt, Karls-son & Sorensen, Inc., Pawtucket, Rhode Island, USA.
II. ABAQUS, (2016). “Analysis Theory Guide, Version 6.8, Hibbitt, Karls-son & Sorensen, Inc., Pawtucket, Rhode Island, USA.
III. ABAQUS, (2016). Analysis Example Manual, Version 6.8, Hibbitt, Karls-son & Sorensen, Inc., Pawtucket, Rhode Island, USA.
IV. Aref A.J., Dolatshahi K.M., (2013) “A three-dimensional cyclic meso-scale numerical procedure for simulation of unreinforced masonry structures”, Computers and Structures 120: 9-27.
V. Brencich A., Lagomarsino S., (1998) “A macro element dynamic model for masonry shear walls” in Pande G. et al. (ed), Computer methods in structural masonry 4. London: E&FN Span; 67-75.
VI. Backes, H. P. (1985), “Behaviour of Masonry Under Tension in the Direction of the Bed Joints”, Ph.D. thesis, Aachen University of Technology, Aachen, Germany.
VII. Belardi, A. Zhang, L. and Thomas, T.C. (1996), “Constitutive Laws of Reinforced Concrete Membrane Elements”. The 11th World Conference on Earthquake Engineering, paper No. 1208.
VIII. Calderon B., Marone P., Pagano M., (1987) “Modelli perrla verifica static degli edifici in Murature in Zona sismica”, Ingegneria sismica, n.3, pp. 19-27.
IX. Dolatshahi K.M., Aref A.J., (2011) “Two-Dimensional computational framework of meso-scale rigid and line interface elements for masonry structures”, Engineering Structures 33: 3657-67.
X. Grecchi G., (2010) “Material and structural behaviour of masonry: Simulation with a commercial code”, Master’s Dessertation, Alme Ticinensis Universitas, Universita di Pavia.
XI. Gambarotta L., Lagomarsino S., (1997) “Dynamic response of masonry panels” in Gambarotta L. (ed), Proc. of the National Conferenche “La meccanica delle murature tra teoria e progetto”, Messina (in Itallian).
XII. Ghiassi, B. Soltani, M. and Tasnimi, A.A. (2012), “A Simplified Model for Analysis of Unreinforced Masonry Shear Walls Under Combined Axial, Shear and Flexural Loading”, The International Journal of Engineering Structures, Elsevier, Volume 42, September 2012, Pages 396–409
XIII. Hemant B, Kaushik, Rai D.C., and Jain S.K., (2007), “Uniaxial Compressive Stress-Strain Model for Clay Brick Masonry”, Current Science, 92(4), Indian Academy of Sciences, Bangalore, India, 25 February 2007, pp. 497-501.
XIV. Javed M., (2006), “Seismic Risk Assessment of Unreinforced Brick Masonry Buildings System of Northern Pakistan”, Ph.D. Thesis, University of Engineering and Technology, Peshawar, Khyber Pakhtunkhwa, Pakistan
XV. Lourenco P., (1996) “Computational strategies for masonry structures”, Ph.D. Dissertation, Netherlands: Delft University.
XVI. Masood Fawwad , Asad-ur-Rehman Khan, : Behaviour of Full Scale Reinforced Concrete Beams Strengthened with Textile Reinforced Mortar (TRM), J. Mech. Cont. & Math. Sci., Vol.-14, No.-3, May-June (2019) pp 65-82.
XVII. Mohammad Khaki, : Effect of Infilled Frame on Seismic Performance of Concrete Moment-Resisting Frame Buildings, J. Mech. Cont. & Math. Sci., Vol.-14, No.-4, July-August (2019) pp 466-480.
XVIII. Page A.W., (1978) “Finite element model for masonry”, J. Structure Div ASCE; 104(8): 1267-85.
XIX. Penna A., (2002) “A macro-element procedure for the non-linear dynamic analysis of masonry building”, Ph.D. Dissertation, Politecnico di Milano, Italy.
XX. Senthivel R., Lourenco P.B., (2009) “Finite element modeling of deformation characteristics of historical stone masonry shear walls”, Engineering Structures 31: 1930-43.
XXI. Toumazevic, M., (1978) “The computer program POR”, Report ZRMK.
XXII. Tomazevic M., (1999), “Earthquake-Resistant Design of Masonry Buildings, Series on Innovation in Structures and Construction”, Volume I, Chapter 3, Masonry Materials and Construction Systems, Imperial College Press.
XXIII. Tomazevic M., (2000), “Some aspects of experimental testing of seismic behaviour of masonry walls and models of masonry buildings”, ISET Journal of Earthquake Technology, Vol. 37, No. 4, pp. 101-117.
XXIV. van Noort J.R., (2012), “Computational Modeling of Masonry Structures”, Master thesis, Delft University of Technology, Delft, The Netherlands.
XXV. Van der Mersch, W. A. (2015), “Modeling the seismic response of an unreinforced masonry structure”, M.Sc. thesis, Delft University of Technology.