Protection of Historical Buildings, PROHITECH 09 – Mazzolani (ed)© 2009 Taylor & Francis Group, London, ISBN 978-0-415-55803-7

Calibration of a numerical model for masonry with applicationto experimental results

E. Dumova-Jovanoska & S. ChurilovUniversity Ss. Cyril and Methodius, Faculty of Civil Engineering, Skopje, Macedonia

ABSTRACT: A calibration of a numerical model for analysis of masonry walls with application to experimentalresults is presented in this paper. The experimental results used for calibration are derived from the researchproject PROHITECH. This paper adopts micro-modeling strategy for analysis of masonry specimen by discreteelement method and application of different nonlinear material models both for blocks and mortar. In order todetermine the values and to calibrate the necessary material data for the used materials that were not obtainedexperimentally, several numerical investigations and simulations were performed. Numerical analysis of masonrywalls was performed by UDEC software. A comparison of numerical and experimental results as well as acomparison of the failure mechanisms is given. With the assumed modeling strategy and numerical method, asatisfactory agreement with the experimental results regarding limit state and developed failure mechanisms isobtained. With the results from this research and literature survey several recommendations regarding materialproperties necessary for numerical analysis are given in the end of this paper.

1 INTRODUCTION

This paper presents numerical simulation and identifi-cation of the dominant failure mechanisms of masonrywalls with different geometrical, load and boundaryconditions. Further on, a numerical model for calcula-tion of the ultimate bearing capacity by developmentof capacity curve of masonry walls by applicationof discrete element method is shown. Calculationspresented in this paper are obtained by perform-ing two-dimensional analysis with discrete elementmethod and the UDEC program (UDEC 2005).

2 MODELLING STRATEGY

In this research the main emphasis is given to thesimulation of the behavior of masonry walls basedon numerical models with the use of micro-modelingapproach and use of the discrete element method.Micro-modeling of masonry is probably the mostimportant approach to understand the behavior andperformance of masonry walls. In this paper a sim-plified micro-modeling strategy is adopted whereexpanded units are represented by continuum elementswhereas the behavior of the mortar joints and unit-mortar interface is lumped in discontinuous elements.

An accurate and precise micro-model shouldinclude all basic masonry failure mechanisms, i.e.(a) bed joint failure, (b) head and bead joint failureat low levels of the vertical stress, (c) block failureat direct tension, (d) block failure by overturning ofthe sample and (e) crushing of masonry by openingof gapping joints as a result of mortar dilatancy when

high levels of vertical stress are present, as shown inFigure 1 (Churilov 2007). With the previouslydescribed actions, several actions can be distinguishedas follows: occurrence of joint failure mechanisms (a,b), block failure mechanisms (c) and combined fail-ure mechanisms that include joint and block failure(d, e). But still, this approach yields one open ques-tion and that is how to investigate all those actions ina single model. The assumed approach suggests thatthe numerical model should concentrate on all jointfailure mechanisms when relatively weak joints arepresent and, if necessary, on potential cracks in theblocks due to tension stress in the blocks in the middlesection of each block, Figure 2.

3 DISCRETE ELEMENT METHOD

Discrete element method is a numerical method usedfor simulation of the mechanical behavior of struc-tures composed of particles or blocks and it is wellsuited for solving problems in which significant partof the deformation happens in the joints or in the con-tact points. This method treats the structures madefrom blocks that mutually interpenetrate each otherthrough contacts. This assumption eliminates the maintwo difficulties naturally connected to finite elementmethod, i.e. creation of compatible finite element meshbetween blocks and joints as well as the inability ofthe method for remeshing in order to update the con-tact size or to create new contacts if relatively largemovements are present. During the analysis with thediscrete element method, different contact types can

1139

Figure 1. Masonry failure mechanisms: Shear failure (a, b,c); Compression failure (d); Tension failure (e).

Figure 2. Adopted modeling strategy. Blocks (u) areexpanded in both directions by the thickness of the filledjoint and modeled by continuum elements. Filled joints (m)and potentional cracks are presented by zero thickness andinterface or contact elements.

be expected depending on the initial geometry anddisplacement history.

Discrete element models use explicit solving algo-rithm, respectively dynamic and quasi-static analysesare conducted by dynamic relaxation. This methoduses large viscous damping for solving the differ-ential equations of movement in order to achieveconvergence to the static solution or steady failuremechanism. The method was introduced to model the

Figure 3. Walls geometry and load application: axial com-pression and shear compression test.

arrangement of free or unattached blocks when it isnot possible to compile the stiffness matrix. The mainadvantages of the discrete element method are: gen-eral and universal; nonlinear material behavior andlarge displacements (change in system interconnec-tions); low data storage requirements; simple program-ming; same algorithm for static and dynamic analysis;appropriate for parallel data processing.

4 CALIBRATION OF A NUMERICAL MODELWITH EXPERIMENTAL RESULTS

For the requirements of the research (Churilov 2007)validation and confirmation of the adopted strat-egy for micro-modeling of masonry walls was per-formed by comparison and calibration of the numer-ical model with the available experimental resultsfrom Jovanovski & Josifovski (2006) and Gramatikov(2006). In this paper special attention is given to exper-imental results performed by Institute of EarthquakeEngineering and Engineering Seismology (IZIIS),University Ss. Cyril and Methodius, Skopje, for theresearch project PROHITECH (Earthquake Protec-tion of Historical Buildings by Reversible MixedTechnologies).

In the numerical simulations, blocks were consid-ered as fully deformable, while the joints were pre-sented as point contacts which means that the blocksare connected by contact points between each other.Several parameters, as well as material models arevaried during the simulations.

Walls loaded with axial compression load as well aswalls loaded by diagonal shear compression load areconsidered during experimental testing. These experi-ments are conducted in order to determine the ultimatelimit force and modulus of elasticity of masonry as aprerequisite for numerical simulation of the model ofthe structure Mustapha Pasha Mosque, to be experi-mentally tested on a shaking table. The wall geometryand load application are presented in Figure 3.

Numerical simulations were performed by:

– Variation of mechanical properties of constituentcomponents due to limited data from experimentaltests on each component;

1140

Table 1. Characteristic material models.

Block Model 1 Model 2 Model 3

Stone Linearly elastic Elastic/PlasticMohr-Coulomb failure

Linearly elastic

Brick Linearly elastic Elastic/PlasticMohr-Coulomb failure

Linearly elastic

Mortar Elastic/Plastic with Coulombslip failure

Elastic/Plastic with Coulombslip failure, residual valuesfor friction, cohesion andtension

Elastic/Plastic with Coulombslip failure, residual valuesfor friction, cohesion andtension

Table 2. Material properties for Model 1-blocks.

Properties Unit Stone Brick Concrete

Unit weight t/m3 2.426 1.874 2.548Elastic modulus kN/m2 7 · 106 2 · 106 3.15 · 107Poisson’s ratio 0.2 0.2 0.2Bulk modulus kN/m2 3.89 · 106 1.11 · 106 1.75 · 107Shear modulus kN/m2 2.92 · 106 8.33 · 106 1.31 · 107

Table 3. Material properties for Model 1-joints.

Horizontal VerticalProperties Unit joints joints

Joint thickness m 0.0225 0.0225Elastic modulus kN/m2 1.3 · 105 1.3 · 105Poisson’s ratio 0.2 0.2Normal stiffness kN/m3 5.78 · 106 5.78 · 106Shear stiffness kN/m3 2.41 · 106 2.41 · 106Tensile strength kN/m2 0.4 · 103 0.1 · 103Cohesion kN/m2 0.22 · 103 0.12 · 103Friction angle deg 6.38 4.91Dilatancy angle deg 0 0

– Variation of numerical models and nonlinear mate-rial laws in order to determine the appropriate wallbehavior and failure during the experimental test.

– Variation of the numerical models regarding thesections of the walls in order to achieve bettercalibration with the experimental results due to2-dimensional software used.

4.1 Axial compression test – longitudinal section

First, several unreinforced masonry wall specimenswere constructed and experimentally tested on axialand shear compression, while in the end one wall wasexperimentally tested with applied FRP strengtheningin two bands.

Wall specimens were constructed by limestone andclay brick blocks and lime mortar filled joints. Theheight of the walls is 88 cm; length 94 cm and thickness33 cm, while the limestone blocks are 10×10×15 cmin dimension and clay blocks are 10 × 9 × 3.2 cm.

Figure 4. Axial compression wall and the failure mecha-nisms.

Figure 5. Real wall layout in longitudinal section.

Mortar joints have thickness of 2.0–2.25 cm. Thevertical load is slowly applied until failure.

Three different numerical models are simulated; allof them with the same geometric properties, but dif-ferent material models were used. The following tablepresents the model properties and material parametersused.

The following tables present the calibrated materialproperties for Model 1 that were taken into account fornumerical simulations.

Figures 5 and 6 present a comparison betweenthe real wall geometry and the geometry used in thenumerical model in UDEC program. One can noticethe difference in the joints presented in the numeri-cal model, where the block height has been increasedfor half of the thickness of the neighboring joints, and

1141

Figure 6. UDEC wall layout in longitudinal section.

Figure 7. Comparison of experimental and numericalforce-displacement diagrams for longitudinal section ofthe wall.

the joint thickness is introduced directly as a materialparameter when calculating joint stiffness.

During the experimental test as well as in the numer-ical simulation, vertical displacement of a point in theupper middle section of the wall was monitored.

Figure 7 presents comparison between experimen-tal curve and numerical capacity curve. The experi-mental behavior of the wall is simulated numerically insatisfactory manner and it can be concluded that curvescorrespond very well. Obviously the best results areobtained by using models 1 and 3 which assumelinearly elastic behavior of blocks and nonlinear elas-tic/plastic relationships for joints. The results frommodels 1 and 3 are identical. As expected, model 2yields smaller values for forces at the same displace-ments as for models 1 and 3, as a result of nonlinearmaterial model used for the blocks and taking into con-sideration block tensile strength, cohesion, friction anddilatancy angle.

4.2 Axial compression test – transversal section

Due to the two-dimensional software used for numer-ical simulations, a change in the numerical modelin regards of the wall cross-section was performed.Namely, a transversal section model of the wall wasconstructed by using the same material and geome-try properties as in the longitudinal section. As in the

Figure 8. Real vs. UDEC wall layout in transversal section.

Figure 9. Comparison of experimental and numericalforce-displacement diagrams for transversal section of thewall.

previous analyses, several material models were usedand calibrated.

Wall specimens were constructed by limestone andclay brick blocks and lime mortar filled joints. Thegeometry and block size of the walls is the same asfor longitudinal section. The vertical load is slowlyapplied until failure.

The material, geometry and boundary conditionsremain the same, without changes and the only differ-ence between them are the values of the joint modulusof elasticity which was varied between 50, 80 and130 MPa. Figure 8 presents a comparison between realwall layout and the layout of the blocks used in thenumerical model.

Figure 9 presents a comparison of the force-displacement diagrams between numerical simula-tions and experimental results where the joints wereconsidered with modulus of elasticity of 130 MPa.Again good agreement between experimental andnumerical results has been achieved.

4.3 Shear compression test – unstrengthenedspecimen

In addition to experimental testing of masonrywalls with vertical load, several specimens weretested in shear compression. It must be noted thatthese experiments are not fully compatible with therequirements for experimental determination of the

1142

Figure 10. Wall layout and failure in shear compression.

Figure 11. Wall layout and failure in shear compression(back side).

shear resistance of masonry walls usually performed.A modification of the procedure for testing was mademostly because of lack of suitable testing set-up andequipment. That’s the reason why masonry specimenwalls were rotated for 45◦ in relation to the horizontalplane and the load is gradually applied on the trimmedcorner edge of the wall until failure.

Figures 10 and 11 presents the layout of the spec-imen and the failure after reaching the ultimate limitstate, while Figure 12 shows the magnified deformedblock structure in DE simulation, for an imposedforce of 12.5 kN. The predicted failure mechanisms bynumerical simulation for block and joint failure corre-spond well with the crack distribution found throughthe experiment.

4.4 Shear compression test – strengthened specimen

The experimental investigations on a shaking tableof the Mustapha Pasha Mosque model structure con-sisted of acquiring structure behavior with and without

Figure 12. Numerical wall failure and deformed shape, foran imposed force of 12.5 kN.

Figure 13. Shear compression test on a strengthenedspecimen.

strengthening method applied when the structure issubjected on a real earthquake movement and seis-mic forces. In order to obtain some knowledge aboutthe strengthening method to be used, one wall speci-men was experimentally tested in shear compressionstrengthened with two FRP bars which were embed-ded on the same position where the cracks appeared inthe unstrengthened specimen.

The wall was build with the same blocks and mor-tar properties as in the previous test. The geometry,load and boundary conditions were kept exactly thesame as in the unstrengthened model in order to obtainthe real contribution of the strengthening method.The wall layout and strengthening is presented inFigure 13. During the experiment it was found that thestrengthened model showed almost the same strengthproperties as the unstrengthened model without signif-icant change in the modulus of elasticity, but the failuremechanism was changed. While the unstrengthenedwall showed diagonal crack opening after de-bonding

1143

Figure 14. Force-displacement diagram of the strengthenedwall.

Figure 15. Failure mechanism of the strengthened wall.

between block and mortar layers and the typical headand bed joint failure in shear as in Figure 1b, thestrengthened model demonstrated bed joint failure inshear as in Figure 1a in the layers beneath the FRPbars.

Moreover, the strengthened wall failed after reach-ing the ultimate limit force of 10 kN as presentedin Figure 14. This is less then the ultimate limitforce obtained at the unstrengthened wall of 12.5 kN.The failure mechanism of the strengthened wall ispresented in Figure 15.

Numerical simulation for the strengthened wall wasnot performed because of the inability of the soft-ware to introduce strengthening elements over blocksor joints.

5 CONCLUSIONS

This paper presents calibration of a numerical modeland calculation of capacity curves of masonry walls byusing discrete element method implemented in UDEC.For the sake of controlling the possibilities of the usedsoftware and interpretation of results, a verificationof the software in regards to experimental test was

Table 4. Suggested material properties for clay bricks.

Properties Unit Clay bricks

Tensile strength kN/m2 (0.03–0.1) · compressionstrength

Cohesion kN/m2 (0.0–2.0) · tensile strengthFriction angle deg 35–51Dilatancy angle deg 0–12

Table 5. Suggested material properties for mortar.

Properties Unit General purpose mortar

Tensile strength kN/m2 (0.0–0.1) · compressionstrength

Cohesion kN/m2 (0.1–0.4) · tensile strengthFriction angle deg 13–40Dilatancy angle deg 0

performed.Also, a calibration of some material param-eters included in the numerical model is completed.According to the numerical simulation data one canmake conclusion that UDEC software as well as thediscrete element method is capable to simulate thebehavior of masonry walls under monotonous loadingconditions. In addition, failure mechanism of masonryspecimen walls is achieved very precisely.

In this work only monotonous loading has been con-sidered. Due to simplification reasons in the input datamonotonous loading in several steps was applied asa vertical load. This method is good enough whenloading values are close to the ultimate load whichgenerates structure failure. Numerical analysis involv-ing cyclic loading on a masonry wall specimen shouldpresent more accurate results for masonry behaviorand should be able to present softening behavior orstiffness degradation in more detail. In order to load thespecimen in cycles, one has to create numerical modelthat is able to include stiffness degradation explicitly.Also, it is recommended to generate a model whichwill be able to predict unit failure more precisely aswell.

It has to be emphasized here that in order to deter-mine the behavior of masonry walls more preciselyby using discrete element method it is necessary toknow all material properties of the components. Rec-ommended values for some material parameters arehard to obtain through literature survey and it is pro-posed to acquire them experimentally.According to theresults from the numerical simulations, several sug-gestions for masonry clay bricks and general purposemortar are given in Tables 4 and 5.

ACKNOWLEDGMENTS

We wish to express our gratitude to Prof. Dr. KirilGramatikov, national coordinator of PROHITECH

1144

project for the opportunity to participate in the project,and to Prof. Dr. Christoph Butenweg (RWTH Aachen)for making UDEC available and his kind remarks.

REFERENCES

Bićanić, N. et al. 2002. Discontinuous Modelling of Struc-tural Masonry. Mang H.A. et al (eds),WCCMV, FifthWorldCongress on Computational Mechanics, Vienna, Austria,July 7–12.

Butenweg, C. & Mistler, M. 2006. Seismic Resistance ofUnreinforced Masonry Buildings. The Fifth InternationalConference on Engineering Computational Technology,Las Palmas de Gran Canaria, 12–15 September.

Churilov S. 2007. Expert System for Seismic VulnerabilityAssessment of Masonry Structures. MSc thesis, Uni-versity “Sts. Cyril and Methodius”, Faculty of CivilEngineering, Skopje, Macedonia.

Dumova-Jovanoska E. & Denkovska L. 1995. Classifi-cation of Individual Unreinforced Masonry BuildingsConsidering Their Seismic Vulnerability. Developmentsin Computer Aided Design and Modelling for Struc-tural Engineering, Civil-Comp Press, Edinburgh, UK,pp. 279–284.

Giordano A. et al. 2002. Modelling of Historical MasonryStructures: Comparison of Different Approaches Througha Case Study. Engineering Structures 24, pp. 1057–1069.

Gramatikov K. 2006. WP7: Experimental Analysis, Reporton Testing of Bricks and Lime Mortar for Mustafa PashaMosque Model, PROHITECH Project, Sixth FrameworkProgramme, INCO-CT-2004-509119.

Guggisberg, R. & Thürlimann, B. 1987. Experimentaldetermination of masonry strength parameters. ReportNo. 7502–5, Institute of Structural Engineering, Zürich.

Jovanovski M. & Josifovski J. 2006.WP 7: LaboratoryTestingon the Intact Parts of Stone Used in Construction of LargeScale Model For “Mustafa Pasha Mosque” in Skopje,Testing Report, PROHITECH Project, Sixth FrameworkProgramme, INCO-CT-2004-509119.

Lemos, J.V. 2004. Modelling Stone Masonry Dynamics with3DEC. Konietzky (eds): 1st International UDEC/3DEC

Symposium: Numerical modelling of Discrete Materials inGeotechnical Engineering, Civil Engineering and EarthSciences, Bochum, Germany, 29 September – 1 October,pp. 7–13.

Lourenço, P.B. 1996. Computational Strategies for MasonryStructures, Ph.D. Dissertation, Delft University of Tech-nology, Delft, Netherlands.

Lourenço, P.B. Experimental and Numerical Issues in theModelling Of the Mechanical Behaviour of Masonry.In P. Roca et al. (eds), Structural Analysis of HistoricalConstructions II. CIMNE, Barcelona, pp. 57–91.

Meskouris, K. et al. 2004. Seismic Behaviour of HistoricMasonry Buildings. 7th National Congress on Mechanicsof HSTAM, Chania, Crete, Greece.

Oliveira, D.V.C. 2003. Experimental and numerical analysisof blocky masonry structures under cyclic loading. Escolade Engenharia, Universidade do Minho, Portugal.

Orduña A. 2003. Seismic Assessment of Ancient MasonryStructures by Rigid Blocks Limit Analysis. Ph.D.Dissertation, University of Minho, Department of CivilEngineering, Guimarães, Portugal, November.

Priya et al. 2007. Some Case Studies on Probabilistic Fail-ureAnalysis of Unreinforced Brick Masonry Structures inIndia against Earthquake. Journal of the British MasonrySociety, Masonry International vol. 20. No. 1, pp. 35–54.

Ramos, L.F. 2002. Análise experimental e numérica de estru-turas históricas de alvenaria. MSc Thesis, Universidadedo Minho, Guimarães, Portugal.

Roca, P. et al. 2001. Mechanical response of dry jointmasonry. G. Arun and N. Seçkin (eds): 2nd Interna-tional Congress on Studies in Ancient Structures, YildizTechnical University, Istanbul, pp. 571–579.

Schlegel R. et al. 2004. Comparative Computations ofMasonry Arch Bridges Using Continuum and Dis-continuum Mechanics. Konietzky (eds): 1st Interna-tional UDEC/3DEC Symposium: Numerical modellingof Discrete Materials in Geotechnical Engineering, CivilEngineering and Earth Sciences, Bochum, Germany,29 September – 1 October, pp. 3–6.

UDEC – Universal Distinct Element Code 2005. User’sGuide, Itasca Consulting Group, Inc., Minnesota, USA.

1145

Welcome pageTable of contentsAuthor indexSearchHelpShortcut keysPage upPage downFirst pageLast pagePrevious paperNext paperZoom InZoom OutPrint