Numerical and experimental analysis of grouted hollow block masonry under compression/Bloku su betonu uzpildytomis tustymemis gniuzdomojo muro itempiu buvio skaitine ir eksperimentine analize. (2024)

Introduction. Stress state analysis of grouted block masonry

Highly hollow concrete masonry units are the most common in masonryconstruction. They help accelerating the construction process andreducing labour-related costs. Hollow masonry units decrease the naturalweight of masonry constructions, improve physical properties of walls,such as noise and thermal insulation (Oan, Shive 2012). Occasionally,particular masonry construction elements, such as cavities betweenhatches and wall corner joints can be reinforced by filling in thehollowness, also, reinforced in-wall columns or ring beams can beinstalled. Hollow masonry units of a special construction solution canbe used as a residual mould (Fig. 1). In such cases, monolith concreteor reinforced concrete walls are set.

To improve strength and stiffness of such block constructions,their hollowness is filled with concrete (Fonseca, Siggard 2012). Blockconcrete and infill concrete have different properties. Blocks are madebeforehand and their concrete structure is formed, concrete shrinkagedeformations, which greatly influence concrete behaviour, have usuallytaken place. It is practically impossible to achieve such properties inhardened infill concrete poured into hollows. Acquired construction ofthe type consists of two layers, which have different properties andtheir internal stress state changes upon start of infill concretehardening (Fig. 2).

Assuming that infill concrete is not adhering to blocks, itsdeformations take place separately (Curve 4). Due to differentdeformation properties of the blocks and the infill concrete, the blocksare compressed and the infill concrete receives tensile stresses. If thesurface of the blocks is humidified, concrete shrinkage deformationsdiminish (Curve 2). After pouring infill concrete, both elements (blockand infill concrete) shrink in approximately the same way (Curves 3 and5). Therefore, the difference between shrinkage deformations issignificantly reduced, and adherence between the blocks and the infillconcrete is improved. This is one of the main conditions for ensuringjoint performance of both concrete layers.

Mechanical properties of the layers have a great influence onstress state in the initial and exploitation stages. Mechanicalproperties of hollow masonry units (1) (Fig. 1) and infill concrete (2)(Fig. 1), i.e. strength and deformational properties, are usuallydifferent. A few cases are possible: in the first case, the hollows canbe filled with a material weaker than the masonry units ([E.sub.infil]< [E.sub.b]), e.g. concrete with polystyrene granule infill or othermaterials, which possess good thermal insulation qualities. In anothercase, hollows can be filled with concrete, which has greater strengththan the strength of the masonry units ([E.sub.infil] > [E.sub.b]).This determines behaviour and mechanical properties, such as compressivestrength and deformations, of the compressed masonry. If layerdeformation properties are different, their strengths are usedunequally. Depending on mechanical properties of layers, severalbehaviour cases are possible.

If layers have the same deformational properties ([E.sub.fil] =[E.sub.b]), they deform in the same way under compression and performjointly until the moment of failure. In this case, strengths of layersare used to the maximum of their possibilities.

In other cases, the layers deform differently, depending on theirdeformational properties (modulus of elasticity). If greater stresses,which exceed elasticity limit of the layers, were involved, layerdeformations would be different, i.e. [e.sub.b] > [e.sub.infil](where [E.sub.b] > [E.sub.infil]) or [e.sub.b] < [e.sub.infil](where [E.sub.b] < [E.sub.infil] here [e.sub.b] and[e.sub.infil]--are longitudinal compressive deformations of masonryunits and the infill concrete respectively. Layer strengths duringfailure are employed to a different extent, depending on theirdeformational properties.

1. Theoretical background for assessment of layer contact zonebehaviour

Research shows (Bistrickaite et al. 2004) that effectiveexploitation of composite construction layer material propertiesrequires good bind between the layers, which ensures not only jointperformance of the layers, but also distribution of stresses betweenthem. If one of the layers is produced using the moulding method, therelation and bind between the components can be of two types: mechanicaland physicochemical. Mechanical bind is achieved due to the presence ofdifferent pores, capillaries, roughness of the block surface and etc.;the group of physicochemical binds encompasses adsorption, whichsubsequently covers adhesion and cohesion. Thickness of layersinfluences adhesive strength. Size of internal stresses depends on layerthickness of contacting materials. The internal stresses appear due todeformation of different layers, under the influence of forces,humidity, temperature and etc. This is further proved by the diagrams inFig. 2--if shrinkage deformations are more equal in the contact zone,the deformation difference as well as shear stresses are reduced.

Conducted theoretical research (Marciukaitis 1999, 2001) indicatesthat if masonry units and infill concrete shrink in a different way,different stresses, which can reduce strength of adherence in thecontact zone, or even terminate it in some cases, are formed in thelayers. Stresses produced due to shrinkage deformations are not big andpractically do not exceed elasticity limit of the layer material.

Considering the fact that the contact zone of the layers isaffected by continuity of deformations into account, the deformations inthe contact zone are equal, i.e.:

[[epsilon].sub.1] (t) = [[epsilon].sub.2] (t). (1)

Balance condition in the stress contact will be:

[[epsilon].sub.1] (t) [E.sub.1]-[[[epsilon].sub.2](t)-[[epsilon].sub.1] (t)] [E.sub.2] [A.sub.2] = 0 , (2)

where: [[epsilon].sub.1] (t), [E.sub.1] and [A.sub.1] are lessshrinking layer shrinkage deformation, deformation module andcrosssection area accordingly; [[epsilon].sub.2] (t), [E.sub.2] and[A.sub.2] are more shrinking concrete shrinkage deformations, itsdeformation module and area accordingly.

Eq. (2) provides:

[[epsilon].sub.1] (t) = [[epsilon].sub.2] (t) [[E.sub.2] [A.sub.2]]/[[E.sub.1] [A.sub.1] + [E.sub.2][A.sub.2]]. (3)

Less shrinking layer average stresses can be estimated from Eq.(3):

[[sigma].sub.1] (t) = [[epsilon].sub.2] (t) [E.sub.1] [[E.sub.2][A.sub.2]] /[[E.sub.1] [A.sub.1] + [E.sub.2] [A.sub.2]]. (4)

Average tensile stresses in a more shrinking layer will be:

[[sigma].sub.2] (t) = [[epsilon].sub.2] (t) [E.sub.1][A.sub.1]/[A.sub.2] [[E.sub.2] [A.sub.2]] /[[E.sub.1] [A.sub.1] +[E.sub.2] [A.sub.2]]. (5)

When the [[sigma].sub.1] (t) and [[sigma].sub.2] (t) stresses thatform in layers, i.e. infill concrete and masonry units, are known, itenables estimating of shear (tangential) stresses in the layer contact:

[tau] = [[sigma].sub.1] (t)-[[sigma].sub.2] (t). (6)

If stress values of [[sigma].sub.1] (t) and [[sigma].sub.2] (t)(Eqs 3 and 4) are inserted into the formula (6) and some rearrangementsare introduced, tangential stress value in the contact is acquired:

[tau] = [[epsilon].sub.2] (t) [E.sub.1] [[E.sub.2] [A.sub.2]]/[[E.sub.1] [A.sub.1] + [E.sub.2] [A.sub.2]] (1- [A.sub.1]/[A.sub.2]).(7)

If tangential stresses formed due to different layer shrinkage[tau] exceed shear strength of the contact [[tau].sub.max] layeradhesion is eliminated and shear strength is ensured by frictional forceonly, binds between the layers are of partial stiffness.

Otherwise, i.e. if the following condition is met:

[tau] < [[tau].sub.max]. (8)

Binds between layers can be considered stiff, layers performedjointly and their behaviour under compression is fundamentally based ondeformational properties of the layers.

According to (Tschegg et al. 1995; Bistrickaite et al. 2004) shearstrength of contact can be estimated the following way:

[[tau].sub.max] = 0.35 [f.sup.0.195.sub.c], (9)

where: [f.sub.c]--concrete compressive strength of the weakerlayer.

As indicated in Figure 2, in order to reduce tangential stresses inthe contact it is necessary to meet certain technological requirements,i.e. before pouring infill concrete into the hollows, masonry units haveto be humidified. Upon humidification, masonry units expand, also, whenthe hollows are filled with concrete, masonry units are additionallyhumidified by the free water present in the infill concrete. On theother hand, humid masonry units "take" water from infillconcrete slower. Furthermore, the open surface, through which infillconcrete evaporates water, is small. Therefore, the difference inshrinkage deformations of infill concrete and masonry units is lower andreduces stresses in contact.

2. Numerical modelling of stress strain state

While investigating behaviour and manner of masonry as a materialfailure, micro-modelling can be applied. Two approaches of micromodelling are applicable--simplified and detailed (Lourenco 1996). Theconducted research (Lourenco 1996; Pina-Henrignes 2005; Haach 2009;Medeiros et al. 2013) shows that both methods produce reliable results.Micro modelling is often used when new masonry unit solutions areanalysed (Jaafar et al. 2006; Thanoon et al. 2008; Porto et al. 2010;Del Coz Diaz et al. 2007; Ghiassi et al. 2013).

More accurate results are obtained when 3D model of the researchedobject is used. While investigating a set of masonry units with infillconcrete hollows, provided masonry units are set in a "dry"way that is without filling bed joints with mortar, use of detailedmicro-modelling can be advised. In such instances, every masonry unit ismodelled as a separate body with its own geometry and materialproperties, and the contact zone between them is like a surface of aparticular stiffness.

In many cases, mechanical characteristics of materials, which areused in production of masonry units, are established by testingappropriately sized samples extracted from the units (Marzahn 2003;Ganzerli et al. 2003; Badarloo et al. 2009). There is no methodology toassess mortar properties of bed joints. Usually, generalisedcharacteristics are applied (Zavalis, Jonaitis 2011), which arespecified by performing specialised tests. While describing bed joints,contact zone with the masonry unit is modelled as binding surface,stiffness of which is presumed to be such that layer of masonry unitsand concrete would transfer compressive stresses appropriately.

The modelling task is even more complicated when masonry units aresupported in a "dry" way, i.e. without mortar in bed joints.In such case, it is typical for a contact of masonry units in the bedjoint to locally develop stress concentration due to roughness of thesurface. In such case, it is advisable to use an appropriately stiffsurface for modelling of the contact of masonry units in the bed joint.Stiffness of such surface can be described using stiffness of the bedjoint. Stiffness of the bed joint [k.sub.n] is described by the ratio ofcompressive stresses [s.sub.c] and shear Dc (absolute deformations ofthe bed joint):

[k.sub.n] = [[sigma].sub.c]/[DELTA]c (N/[mm.sup.3]). (10)

Yet another critical issue is description of infill concrete andcontact of a masonry unit. Shear stiffness of the contact depends onstrength of adherence and stresses induced by shrinkage deformations ofmasonry units and infill concrete. Considering the abovementioned facts,it can be deduced that since before the concrete is poured, when blocksare humidified, shrinkage deformations become close and tangentialstresses, which damage adherence, are not formed due to shrinkage in thecontact, also layers (walls) are bound by transverse edges, layersperform jointly and remain stiff when masonry fragment is compressed.

3. Experimental program

Masonry samples set from concrete blocks with concrete filledhollows were built for compressed composite masonry stress state test.Samples were set from P6-20 (hollowness--50%) and P6-30 (hollowness 68%)hollow concrete blocks (Fig. 3).

Compressive strength of masonry units (concrete blocks) wasestablished while testing it under brief static load in accordance withLST EN 772-1 (2011). Masonry unit and infill concrete properties areprovided in Table 1.

While constructing the samples (masonry fragments), blocks were setin a "dry" way, i.e. without mortar in bed joints, and blockswere humidified, hollows were filled with concrete, this way, complexmasonry samples were acquired.

In order to establish deformational properties of masonry units andstiffness of bed joints that have not been filled with concrete, samplesmade of the two masonry units were set in a "dry" way (Fig.4).

Mechanical properties of masonry units and infill concrete wereestablished by testing the blocks in accordance with LST EN 772-1(2011), and control samples--cylinders of infill concrete in accordancewith requirements of LST EN 12390-3.

Mechanical properties of masonry unit blocks P-20 and P6-30 and theinfill concrete are presented in Table 1.

Samples of hollow P6-20(30) blocks set in a "dry" way andmasonry samples with filled hollows were tested by applying brief staticcompressive load. While testing the samples, the block, masonry and bedjoint deformations were measured (Figs 4 and 5).

A model has been set for numerical analysis of compressive masonrysample P6-30, which was realised using DIANA software package. Numericalmodel has been developed by applying detailed micro modelling method,modelling exact masonry unit and infill concrete geometry withvolumetric finite elements. A stiff steel beam, which transferscompressive load onto the fragment, is modelled applying the sameprinciple. Upon evaluating symmetry, a V fragment model is set (Fig. 6).The model is analysed using arch length method with Newton-RapsonIteration considering that displacement and energy convergenceconditions are equal to 10-3.

Behaviour of masonry units and infill concrete is describedapplying the total strain crack model based on the fixed crack concept.Behaviour of tensile concrete is described by assessing tensile strengthand tensile fracture energy of concrete by exponential dependence (TNODiana 2005). Tensile strength of masonry units and infill concrete iscalculated in accordance with tension and compressive strengthdependences provided in LST EN 1992-1-1 (EC2). Tensile fracture energyof concrete Gf is estimated in accordance with CEP FIP recommendations(CEP 1990):

[G.sub.f] = [G.sub.F0] [([f.sub.c]/[f.sub.cm0]).sup.0,7], (11)

where: [G.sub.F0]--the base value of fracture energy;[f.sub.c]--compressive strength, [f.sub.cm0]--constant considered to beequal to 10 N/[mm.sup.2] .

Behaviour of compressed concrete is described by parabolicdependence provided in DIANA software package, taking into considerationcompressive strength of concrete established while testing controlsamples and estimated fracture energy of compressed concrete [G.sub.Fc](Sandoval el al. 2012):

[G.sub.Fc] = 15 + 0,43 [f.sub.c]-0,0036 [f.sup.2.sub.c] , (12)

Contact between masonry units (concrete blocks) is modelled usingplane elements as a surface capable of transferring only compressivestresses. Contact between infill concrete and masonry units isconsidered to be stiff. Contact zone of bed joints of blocks that wasnot filled with mortar (dry) is described using compressive (normal) andshear stiffness.

Stiffness of the contact of masonry units (bed joint) was estimatedperforming special experiments, i.e. samples consisting of two groutedblocks set in a "dry" way was tested applying brief staticcompressive load (Fig. 4). During the experiment, block and contactdeformations were measured, and block material compressive strength andelasticity modulus and contact stiffness were estimated. Compressivestiffness of bed joint contact zone was estimated using Eq. (10) fromthe results of the experiment, shear stiffness of contact [k.sub.[tau]]was estimated in accordance with dependence:

[k.sub.[tau]] = [k.sub.n]/[2(1+v)], (13)

where: [k.sub.n]--normal (compressive) bed joint stiffness,v--Poisson's ratio.

Parameters of numerical model are presented in Table 2.

3. Experiment results and its analysis

Experiment and numerical modelling results of P6-20(30) hollowblocks with concrete filled hollows masonry samples are presented inTable 3 and Figs 7-11.

Character of the failure of masonry samples is similar to that ofthe concrete prism failure (Fig. 7). Cracks were formed under the loadof 90-100% of failure load, i.e. before the failure of the sample,sudden (crumbling) failure took place. Until the moment of failure,blocks and infill concrete performed mutually, no layer scaling wasobserved (Fig. 8).

Longitudinal (vertical) sample deformations before stresses 50-60%of compressive strength are similar to longitudinal deformations ofcontrol samples (cylinder) (Fig. 9). Longitudinal deformations ofmasonry sample blocks and bed joints revealed sufficiently good jointperformance of the blocks and infill concrete.

Distribution of compressive stresses obtained by numericalmodelling is presented in Figs 10 and 11.

Numerical modelling results of compressed masonry revealed thatcompressive stresses in both, grouted blocks and infill concrete aredistributed unevenly. This is determined by different elasticity modulusof hollow block concrete and infill concrete ([E.sub.b] <[E.sub.infil]), also, contact stiffness of the bed joint issignificantly smaller than stiffness of concrete blocks. A significantincrease of compressive stresses can be observed in the bed joint zoneof infill concrete (Fig. 10). Compressive stresses are also distributedunevenly in the blocks (Figs 10a and 11). Web assumes greatercompressive stresses than shells (Fig. 11a). Distribution of stresses ininfill concrete and hollow block indicates that both elements mentionedabove are involved in joint performance; stresses are distributeddepending on deformational properties of infill concrete and hollowblock concrete. Diagrams of numerical modelling and[[sigma].sub.c]-[[epsilon].sub.c] obtained during the experiments arepresented in Fig. 11.

Stress and relative deformation values estimated by numericalmodelling were assumed during the experiments in the deformationmeasuring zones. As shown in Fig. 12, [[sigma].sub.c]-[[epsilon].sub.c]dependences in the masonry and the bed joint zones estimated applyingnumerical modelling match fine with the ones estimated during theexperiments. Masonry samples modulus of elasticity that was calculated(numerical modelling [E.sub.cal] = 25 GPa) and determined during theexperiments ([E.sub.obs] = 28.8 GPa) differs in up to 15%. Estimated andexperimental average compressive strength of P6-30 masonry fragment isequal to [f.sub.cal] = 26.72 N/[mm.sup.2] and [f.sub.obs] = 26.5N/[mm.sup.2] , accordingly. The performed analysis revealed thatdetailed micro modelling of masonry stress deformations produces ratheraccurate results.

Conclusions

Experimental and numerical stress state research of hollow blockswith infill concrete proved the assumption that the difference betweenshrinkage deformations of grouted blocks and infill concrete is reducedby humidifying masonry units. The difference of shrinkage deformationsof infill concrete and block does not damage the contact, and reliablejoint performance of infill concrete and blocks is ensured until thevery moment of compressed masonry failure. In such case, stiff bind oflayers can be used while modelling.

Detailed numerical micro-model of the compressed masonry providessufficiently accurate computing results.[[sigma].sub.c]-[[epsilon].sub.c] dependences in masonry and bed jointzones acquired through the means of numerical modelling correspond tothose estimated during the experiments. Modulus of elasticity of masonrysamples was estimated by calculations (numerical modelling [E.sub.cal] =25 GPa) and experiments ([E.sub.obs] = 28.8 GPa) differs up to 15%.Estimated and experimental average compressive strength of a masonrysamples is equal respectively to [f.sub.cal] = 26.72 N/[mm.sup.2] and[f.sub.obs] = 26.5 N/[mm.sup.2]. Detailed numerical micro modelling canbe applied while conducting research of compressed masonry stress strainanalysis.

Caption: Fig. 1. Masonry unit with concrete filled hollownessmasonry solution: 1--hollow masonry unit; 2--infill concrete.

Caption: Fig. 2. Changes in concrete block and infill concreteshrinkage deformation development: 1--blocks before use; 2--blockexpansion due to external humidity; 3--recursive deformations of theblock along with infill concrete deformations; 4--infill concretedeformations when the block is not humid; 5--infill concretedeformations, which take place together with humid block deformations.

Caption: Fig. 3. Hollow concrete masonry blocks used inexperimental program.

Caption: Fig. 4. Sample of a hollow block set in a "dry"manner, scheme of testing and measuring tool deployment

Caption: Fig. 5. Experimental scheme of masonry with filled hollowsand tool deployment

Caption: Fig. 6. Numerical masonry fragment model

Caption: Fig. 7. Failure of P6-20 (a) and P6-30 (b) concrete blockswith concrete infill specimen of masonry

Caption: Fig. 8. Contact zone of a masonry unit and concrete infill

Caption: Fig. 9. Deformations of masonry set with concrete infill(a) P6-20 and (b) P6-30 blocks: 1--longitudinal deformation of aspecimen; 2--longitudinal deformation of the bed joint, 3--longitudinaldeformation of a block; G1 and G2--longitudinal deformation of theinfill concrete control sample

Caption: Fig. 10. Distribution of P-30 masonry fragmentscompressive stresses

Caption: Fig. 11. Distribution of compressive stresses of concreteblocks within the P6-30 masonry fragment

Caption: Fig. 12. Diagram of [[sigma].sub.c] stresses and[[epsilon].sub.c] relative deformations: 1 and 1NM--of the masonryestimated by experiments and numerical modelling respectively; 2 and2NM--of the bed joint zone estimated by experiments and numericalmodelling respectively

doi: 10.3846/2029882X.2013.811784

References

Badarloo, B.; Tasnimi, A. A.; Mohammadi, M. S. 2009. Failurecriteria of unreinforced grouted brick masonry based on a biaxialcompression test, Scientia Iranica Transaction A: Civil Engineering16(6): 502-511.

Bistrickaite, R.; Marciukaitis, G.; Zilinskas, R. 2004. Precast andcast in-situ concrete slabs with residual mould. Kaunas: Technologija.229 p. (in Lithuanian).

Comite Euro-International Du Buton (CEB). 1990. CEB-FIP model codefor concrete structures. Lausanne, Switzerland.

Del Coz Diaz, J. J.; Garcia Nieto, P. J.; Betegon Biempica, C.;Prendes Gero, M. B. 2007. Analysis and optimization of theheat-insulating light concrete hollow brick walls design by the finiteelement method, Applied Thermal Engineering 27(8-9): 1445-1456.http://dx.doi.org/10.1016/j.applthermaleng.2006.10.010

Fonseca, F.; S.; Siggard, K. 2012. Replacement of portland cementwith supplemental cementitious materials in masonry grout, inProceedings of the 15th International Brick and Block MasonryConference, 2012, Florianopolis, Brazil.

Ganzerli, S.; Rosslow, J.; Young, T.; Kres, K.; Mujumdar. V. 2003.Compression strength testing for nonstandard concrete masonry units, inProceedings of The 9th North American Masonry Conference, 2003, Clemson,South Carolina, USA, 60-71.

Ghiassi, B.; Oliveira, D. V.; Lourenco, P. B.; Marcari, G. 2013.Numerical study of the role of mortar joints in the bond behavior ofFRP-strengthened masonry, Composites Part B: Engineering 46: 21-30.http://dx.doi.org/10.1016/j.compositesb.2012.10.017

Haach, V. 2009. Development of a design method for reinforcedmasonry subjected to in-plane loading based on experimental andnumerical analysis: PhD thesis summary. University of Minho.

Jaafar, M. S.; Alwathaf, A. H.; Thanoon, W. A.; Noorzaei, J.;Abdulkadir, M. R. 2006. Behaviour of interlocking mortarless blockmasonry, Construction Materials 159(August): 111-117.http://dx.doi.org/10.1680/coma.2006.1593.111

LST EN 1992-1-1. 2007. Eurokodas 2. Gelzbetoniniu konstrukcijuprojektavimas. 1-1 dalis. Bendrosios ir pastatu taisykles.

LST EN 772-1. 2011. Muro gaminiu bandymo metodai. 1 dalis.Gniuzdymo stiprio nustatymas.

LST EN 12390-3. 2003. Betono bandymas. 3 dalis. Bandiniu stiprisgniuzdant (in Lithuanian).

Lourenco, P. B. 1996. Computational strategies for masonrystructures: PhD thesis summary. Delft University of Technology.

Marciukaitis, G. 1999. Estimation of redistribution of stressesbetween layers of composite masonry walls, in Proceedings of The 6thInternational conference "Modern Building Materials, Structures andTechniques", 19-22 May 1999, Vilnius: Technika, 104-109 (inLithuanian).

Marciukaitis, G. 2001. Shrinkage influence on stress-strain stateof composite masonry members, Civil Engineering 7(3): 177-183 (inLithuanian).

Marzahn, G. 2003. Extended investigation of mechanical propertiesof masonry units, in Proceedings of the 9th North American MasonryConference, 2003, Clemson, South Carolina, USA, 813-824.

Medeiros, P.; Vasconcelos, G.; Lourenco, P. B.; Gouveia, J. 2013.Numerical modelling of non-confined and confined masonry walls,Construction and Building Materials 41: 968-976.http://dx.doi.org/10.1016/j.conbuildmat.2012.07.013

Oan, A. F.; Shrive, N. 2012. Effect of construction method on shearresistance of concrete masonry walls, in Proceedings of the 15thInternational Brick and Block Masonry Conference, 2012, Florianopolis,Brazil.

Pina-Henriques, J. 2005. Masonry under compression: failureanalysis and long-term effects: PhD thesis summary. University of Minho.

Porto, F.; Mosele, F.; Modena, C. 2010. Compressive behaviour of anew reinforced masonry system, Materials and Structures 44(3): 565-581.http://dx.doi.org/10.1617/s11527-010-9649-x

Sandoval, C.; Roca, P. 2012. Study of the influence of differentparameters on the buckling behaviour of masonry walls, Construction andBuilding Materials 35: 888-899.http://dx.doi.org/10.1016/j.conbuildmat.2012.04.053

Thanoon, W. A.; Alwathaf, A. H.; Noorzaei, J.; Jaafar, M. S.;Abdulkadir, M. R. 2008. Nonlinear finite element analysis of grouted andungrouted hollow interlocking mortarless block masonry system,Engineering Structures 30(6): 1560-1572.http://dx.doi.org/10.1016/j.engstruct.2007.10.014

TNO Diana 2005. DIANA finite element analysis. The Netherlands.Tschegg, E. K.; Rotter, H. H.; Bourgund, H.; Jussel, P. 1995. Fracturemechanical behaviour of aggregate cement matrix interfaces, Journal ofMaterials in Civil Engineering 7(4): 199-203.http://dx.doi.org/10.1061/(ASCE)0899-1561(1995)7:4(199)

Zavalis, R.; Jonaitis, B. 2011. The analysis of stress deformationstate peculiarities of masonry units and bed joints, EngineeringStructures and Technologies 3(3): 105-111 (in Lithuanian).http://dx.doi.org/10.3846/skt.2011.12

Robertas Zavalis, Bronius Jonaitis, Gediminas Marciukaitis

Vilnius Gediminas Technical University, Sauletekio al. 11, LT-10223Vilnius, Lithuania

Received 10 March 2013; accepted 31 May 2013

Corresponding author: R. Zavalis E-Mail: [emailprotected]

Robertas ZAVALIS. PhD student at the Department of ReinforcedConcrete and Masonry Structures, Vilnius Gediminas Technical University(VGTU). Research interests: masonry and masonry structures.

Bronius JONAITIS. Dr, Associate Professor at the Department ofReinforced Concrete and Masonry Structures, Vilnius Gediminas TechnicalUniversity (VGTU). Research interests: theory of reinforced concretebehaviour, masonry and masonry structures, strengthening of structures.

Gediminas MARCIUKAITIS. Dr Habil, Professor at the Department ofReinforced Concrete Structures, Vilnius Gediminas Technical University(VGTU). Research interests: mechanics of reinforced concrete, masonryand layered structures, new composite materials, investigation andrenovation of buildings.

Table 1. Masonry unit and infill concrete propertiesSeries Code of Type of Compressive strength specimens units of units, N/[mm.sup.2] Normalised Mean of units [f.sub.b] concrete P6-20-1 P6-20(M) 10.53P6-20 P6-20-2 P6-20(K) 10.78 28.23 P6-20-3 P6-30-1P6-30 P6-30-2 P6-30 6.78 29.49 P6-30-3Series Mean modulus of Infill concrete elasticity of units concrete, [E.sub.cm], Mean cylinder GPa compressive strength, N/[mm.sup.2]P6-20 2.92 * 22.7P6-30 3.2 * 30.9Series Infill concrete Mean modulus of elasticity E, GPaP6-20 2.2P6-30 2.92* determined from experimental tests (Fig. 4)Table 2. Material properties of the numerical modelParameter Units Infill Masonry concrete unitCompressivestrength, [f.sub.c] N/[mm.sup.2] 25.27 24.55Tensile strength, N/[mm.sup.2] 3.09 2.9 [f.sub.ct]Tensile fractureenergy, [G.sub.F] Nmm/[mm.sup.2] 0.069 0.053Compressive fractureenergy, [G.sub.Fc] Nmm/[mm.sup.2] 25.27 24.55Poison's ratio, v -- 0.2 0.22Normal stiffness of N/[mm.sup.3] 44.5 the joint, [k.sub.t]Shear stiffness of the N/[mm.sup.3] 18.2 joint, [k.sub.[tau]]Table 3. Experimental resultsSeries Code of Compressive strength specimens of masonry, N/[mm.sub.2] Specimens MeanP6-20 P6-20-1 21.5 P6-20-2 23.3 22.9 P6-20-3 23.9P6-30 P6-30-1 27.4 P6-30-2 24.5 26.5 P6-30-3 27.5Series Code of Modulus of masonry specimens elasticity, E, GPa Specimens MeanP6-20 P6-20-1 26.0 P6-20-2 23.6 25.2 P6-20-3 25.9P6-30 P6-30-1 30.7 P6-30-2 24.7 28.8 P6-30-3 31.2

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