Numerical modeling of masonry wall under underground waves

Document Type : Article


1 Department of Civil Engineering, Faculty of Engineering, Razi University, Kermanshah, Iran

2 Department of Civil Engineering, Faculty of Engineering, Bu-Ali Sina University, Hamedan, Iran


The dynamic behavior of structures has always received considerable attention. The dynamic behavior of structures requires the suitable numerical modeling method in order for the behavior of structures under dynamic loads to be illustrated. In this study, the response of two identical unreinforced masonry walls to the underground blast was examined. The experimental variables were the horizontal distance from the explosion point and depth in which the explosives were located. After examining the behavior of the masonry walls under high-frequency dynamic loads, different numerical models were applied to simulate the dynamic behavior of these two walls against the underground blast experiments. Thus, a number of different factors, including yield criterion, types of meso and macro modeling for the masonry wall, and topography of the site were investigated. Finally, due to the degree of accuracy required, it was concluded that each of the methods can be used; however, the most appropriate and accurate modeling method for the unreinforced masonry wall is the frictional-cohesive zone material and modified Mohr-Coulomb model, which provided accurate and precise responses.


1.         Ali SS, Page AW. “Finite element model for masonry subjected to concentrated loads”. Journal of structural engineering. 114(8): pp. 1761-1784(1988).
2.         Dhanasekar M, Kleeman PW, Page AW. “Biaxial stress-strain relations for brick masonry”. Journal of structural Engineering. 111(5): pp. 1085-1100(1985).
3.         Andreaus, U., “Failure criteria for masonry panels under in-plane loading”. Journal of structural engineering. 122(1): pp. 37-46(1996).
4.         Ghiassi B, Soltani M, Tasnimi AA. “A simplified model for analysis of unreinforced masonry shear walls under combined axial, shear and flexural loading”. Engineering Structures. 42: pp. 396-409(2012).
5.         Grande E, Imbimbo M, Rasulo A, Sacco E. “A frame element model for the nonlinear analysis of FRP-strengthened masonry panels subjected to in-plane loads”. Advances in Materials Science and Engineering. 2013(2013).
6.         Berardi, V.P., “Initiation of failue for masonry subject to in-plane loads through micromechanics”. Modelling and Simulation in Engineering. 2016(2016).
7.         Pantò B, Caliò I, Lourenço PB. “A 3D discrete macro-element for modelling the out-of-plane behaviour of infilled frame structures”. Engineering Structures. 175: pp. 371-385(2018).
8.         Choudhury T, Milani G, Kaushik HB. “Experimental and numerical analyses of unreinforced masonry wall components and building”. Construction and Building Materials. 257: pp. 119599(2020).
9.         Giambanco G, Rizzo S, Spallino R. “Numerical analysis of masonry structures via interface models”. Computer methods in applied mechanics and engineering. 190(49-50): pp. 6493-6511(2001).
10.       Chaimoon K, Attard MM. “Experimental and numerical investigation of masonry under three-point bending (in-plane)”. Engineering Structures. 31(1): pp. 103-112(2009).
11.       Akhaveissy, AH. “The DSC model for the nonlinear analysis of in-plane loaded masonry structures”. The Open Civil Engineering Journal. 6(1)(2012).
12.       Akhaveissy, AH. “Lateral strength force of URM structures based on a constitutive model for interface element”. Latin American Journal of Solids and Structures. 8(4): pp. 445-461(2011).
13.       Akhaveissy AH, Milani G. “Pushover analysis of large scale unreinforced masonry structures by means of a fully 2D non-linear model”. Construction and Building Materials. 41: pp. 276-295(2013).
14.       Deng M, Yang S. “Experimental and numerical evaluation of confined masonry walls retrofitted with engineered cementitious composites”. Engineering Structures. 207: pp. 110249(2020).
15.       Khan HA, Nanda RP, Das D. “Numerical Analysis of Geosynthetic Strengthened Brick Masonry Panels, in Advances in Structural Vibration”. 2020, Springer. p. 35-41.
16.       KARATON M, ÇANAKÇI K. “INVESTIGATION OF HEAD AND BED MORTAR REGION EFFECT IN MICRO SCALE MODELLING OF MASONRY WALLS”. Sigma: Journal of Engineering & Natural Sciences/Mühendislik ve Fen Bilimleri Dergisi. 38(2)(2020).
17.       Komurcu S, Gedikli A. “Macro and Micro Modeling of the Unreinforced Masonry Shear Walls”. European Journal of Engineering and Natural Sciences. 3(2): pp. 116-123(2017).
18.       Hao H, Wu C. “Numerical study of characteristics of underground blast induced surface ground motion and their effect on above-ground structures. Part II. Effects on structural responses”. Soil Dynamics and Earthquake Engineering. 25(1): pp. 39-53(2005).
19.       Soheyli MR, Akhaveissy AH, Mirhosseini SM. “Large-scale experimental and numerical study of blast acceleration created by close-in buried explosion on underground tunnel lining”. Shock and Vibration. 2016(2016).
20.       Wu C, Hao H., “Numerical study of characteristics of underground blast induced surface ground motion and their effect on above-ground structures. Part I. Ground motion characteristics”. Soil Dynamics and Earthquake Engineering. 25(1): pp. 27-38(2005).
21.       Ma HJ, Quek ST, Ang KK. “Soil–structure interaction effect from blast-induced horizontal and vertical ground vibration”. Engineering structures. 26(12): pp. 1661-1675(2004).
22.       Ma G, Hao H, Zhou. “Assessment of structure damage to blasting induced ground motions”. Engineering Structures. 22(10): pp. 1378-1389(2000).
23.       Shi Y, Xiong W, Li ZX, Xu Q. “Experimental studies on the local damage and fragments of unreinforced masonry walls under close-in explosions”. International Journal of Impact Engineering. 90: pp. 122-131(2016).
24.       Wang J, Ren H, Wu X, Cai C. “Blast response of polymer-retrofitted masonry unit walls”. Composites Part B: Engineering. 128: pp. 174-181(2017).
25.       Li Z, Chen L, Fang Q, Chen W, Hao H, Zhu R, Zheng K. “Experimental and numerical study on CFRP strip strengthened clay brick masonry walls subjected to vented gas explosions”. International Journal of Impact Engineering. 129: pp. 66-79(2019).
26.       Hu XD, Zhao GF, Deng XF, Hao YF, Fan LF, Ma GW, Zhao J. “Application of the four-dimensional lattice spring model for blasting wave propagation around the underground rock cavern”. Tunnelling and Underground Space Technology. 82: pp. 135-147(2018).
27.       Ma GW, Hao H, Zhou YX. “Modeling of wave propagation induced by underground explosion”. Computers and Geotechnics. 22(3-4): pp. 283-303(1998).
28.       ASTM C. 109., Standard test method for compressive strength of hydraulic cement mortars (Using 2-in. or [50-mm] cube specimens). 2013: ASTM International.
29.       Committee, M.S.J., “Building code requirements for masonry structures (TMS 402-11/ACI 530-11/ASCE 5-11)”. The Masonry Society, Boulder, CO, (2011).
30.       ASTM Committee D-18. Standard test method for consolidated undrained triaxial compression test for cohesive soils. 2011: ASTM International.
31.       ASTM. D. 3080. 2011. Standard test method for direct shear test of soils under consolidated drained conditions”. ASTM West Conshohocken,
32.       Goel RK, Chopra AK. “Evaluation of modal and FEMA pushover analyses: SAC buildings”. Earthquake spectra. 20(1): pp. 225-254(2004).
33.       Lysmer J, Kuhlemeyer RL. “Finite dynamic model for infinite media”. Journal of the Engineering Mechanics Division. 95(4): pp. 859-878(1969).
34.       Liu GR, Achenbach JD. “A strip element method for stress analysis of anisotropic linearly elastic solids”. (1994).
35.       Gratkowski S, Pichon L, Razek A. “INFINITE ELEMENTS FOR 2D UNBOUNDED WAVE PROBLEMS”. COMPEL - The international journal for computation and mathematics in electrical and electronic engineering. 14(4): pp. 65-69(1995).
36.       Chen SG, Cai JG, Zhao J, Zhou YX. “Discrete element modelling of an underground explosion in a jointed rock mass”. Geotechnical & Geological Engineering. 18(2): pp. 59-78(2000).
37.       Jiao YY, Zhang XL, Zhao J, Liu QS., “Viscous boundary of DDA for modeling stress wave propagation in jointed rock”. International journal of rock mechanics and mining sciences (1997). 44(7): pp. 1070-1076(2007).
38.       Army, U.S., Structures to resist the effects of accidental explosions. 1969: US Government Printing Office.
39.       Station UA. TM5-855-1. Fundamentals of protective design for conventional weapons”. US Army, (1986).
40.       Murrell DW, Joachim CE. 1996 Singapore ground shock test. ENGINEER RESEARCH AND DEVELOPMENT CENTER VICKSBURG MS STRUCTURES LAB.
41.       Fan SC, Jiao YY, Zhao J. “On modelling of incident boundary for wave propagation in jointed rock masses using discrete element method”. Computers and Geotechnics. 31(1): pp. 57-66(2004).
42.       Willam KJ. “Constitutive model for the triaxial behavior of concrete”. International association for bridge and structural engineering proceedings. 19: pp. 1-30(1975).
43.       ANSYS, A.W., 18.2.2 help documentation [db]. Mechanical APDL ANSYS Parametric Design Language Guide.
44.       Asteris PG, Antoniou ST. “Mathematical Macromodeling of Infilled Frames: State of the Art”. Journal of Structural Engineering. 137(12): pp. 1508-1517(2011).
45.       Madan A, Reinhorn AM, Mander JB, Valles RE. “Modeling of masonry infill panels for structural analysis”. Journal of Structural Engineering. 123(10): pp. 1295-1302(1997).
46.       Milani G, Tralli A. “A simple meso-macro model based on SQP for the non-linear analysis of masonry double curvature structures”. International Journal of Solids and Structures. 49(5): pp. 808-834(2012).
47.       Wood, D.M., “Soil behaviour and critical state soil mechanics”. 1990: Cambridge university press.
48.       Bićanić N, “Detection of multiple active yield conditions for Mohr-Coulomb elasto-plasticity”. Computers & Structures. 62(1): pp. 51-61(1997).
49.       Menetrey P, Willam KJ. “Triaxial failure criterion for concrete and its generalization”. Structural Journal. 92(3): pp. 311-318(1995).
50.       Alfano G, Sacco E. “Combining interface damage and friction in a cohesive‐zone model”. International Journal for Numerical Methods in Engineering. 68(5): pp. 542-582(2006).
51.       Giambanco G, Rizzo S, Spallino R. “Numerical analysis of masonry structures via interface models”. Computer Methods in Applied Mechanics and Engineering. 190(49): pp. 6493-6511(2001).
52.       Parrinello F, Failla B, Borino G. “Cohesive–frictional interface constitutive model”. International Journal of Solids and Structures. 46(13): pp. 2680-2692(2009).
53.       Vandoren B, De Proft K, Simone A, Sluys LJ. “Mesoscopic modelling of masonry using weak and strong discontinuities”. Computer Methods in Applied Mechanics and Engineering. 255: pp. 167-182(2013).
54.       Boussabah L, Bruneau M. “Review of the seismic performance of unreinforced masonry walls”. in Proc. of the 10th World Conf on Eq. Eng. 1992.