CIVIL AND ENVIRONMENTAL ENGINEERING REPORTS ISSN 2080-5187 CEER 2015; 18 (3): 055-063 DOI: 10.1515/ceer-2015-0036 STRENGTH PARAMETERS OF MASONRY WALLS IN MODELLING HISTORIC CONSTRUCTIONS Micał GOŁĘBIEWSKI 1, Izabela LUBOWIECKA, Marcin KUJAWA Gdańsk University of Tecnology, Faculty of Civil and Environmental Engineering, Gdańsk, Poland Abstract Te paper presents te determination of te basic material properties of a istoric brickwork. Experimental studies were used to identify te basic material properties of bricks. Te mecanical properties of te masonry, as an ortotropic omogenized material, were calculated. Ten, numerical simulations using te Finite Element Metod (FEM) were performed to verify te experimental outcomes. Macromodels wit element sizes of 40, 20, 10 and 5 mm, and a micromodel wit an element size of 5 mm were applied. Te results were compared wit experimental data and results available in literature. Keywords: istoric brick walls, masonry structures, omogenization, FEM modeling 1. INTRODUCTION Te aim of studies presented in te work is determining te basic material properties of te brick masonry walls of a Gotic curc located in Gnojewo near Malbork (Fig. 1). Tese parameters are used to assess te tecnical condition of te building, and especially te masonry part of te construction. Te analyzed building is a currently closed down evangelical curc, built in 1323 in alf timbered structure, was rebuilt numerous times over te years until te XIX century. 1 Corresponding autor: Gdańsk University of Tecnology, Faculty of Civil and Environmental Engineering, Gabriela Narutowicza st 11/12, 80-233 Gdańsk, Poland, e-mail: micgoleb@pg.gda.pl, tel.+48583486149 Unautenticated
56 Micał GOŁĘBIEWSKI, Izabela LUBOWIECKA, Marcin KUJAWA Fig. 1. Curc in Gnojewo 2. STRENGTH PARAMETERS OF WALL COMPONENTS Te structure under study was constructed of bricks measuring 8x15x30 cm. In order to determine te modulus of elasticity and compressive strengt of te material, uniaxial compression tests were done in accordance wit te PN EN 772-1 norm. Due to te bad tecnical condition of te bricks, 50 mm cubic samples were cut out from tem using abrasive waterjet cutting. Strengt tests were carried using a Zwick/Roell Z 400 strengt testing device. Fig. 2. Samples after testing Unautenticated
STRENGTH PARAMETERS OF MASONRY WALLS IN MODELLING HISTORIC CONSTRUCTIONS 57 Based on tests carried out on 6 samples (Fig. 2 and 3), te average value of te modulus of elasticity was determined for te bricks, E b = 2.104 GPa. Tis result falls into te range obtained in work [5], in wic values for te modulus of elasticity of bricks of a campanile from te turn of te XVI and XVII centuries fell in te range of E b = 2.050-5.300 GPa. Tese values differ significantly from te modulus of elasticity of modern-day bricks determined by Page [6] to be at te level of E b = 7.55 GPa or in work [7] at te level of E b = 12.50 GPa. N-EN 772-1, attacment A, table A1 provides coefficients accounting for te influence of te sape of te tested samples on te strengt of bricks determined on te basis of compression tests. For cubic samples wit sides measuring 50 mm, te normalized compressive strengt of te bricks was calculated applying te coefficient δ=0.85. were: f δ f = 0.85 5.338 = 4.537 MPa (1) b = B f b - normalized compressive strengt of bricks, δ - normative coefficient, f B - compressive strengt of bricks obtained in te tests. Fig. 3. Stress-strain curve (σ-ε) of te tested bricks: dased line - modern-day brick, solid line - bricks from te curc Taking samples of te mortar from te original construction witout damaging it proved impossible. Tus mortar strengt parameters provided in works [8] and [3] were taken into te analysis, i.e.: modulus of elasticity E m = 0.96 GPa, strengt f m = 0.8 MPa. An analysis of te influence of te material parameters of mortar on te parameters of omogenized masonry wall was carried out. Unautenticated
58 Micał GOŁĘBIEWSKI, Izabela LUBOWIECKA, Marcin KUJAWA However, considering te mortar stiffness range provided in literature (e.g., Augenti [1]), no considerable influence was observed. Tis can also result from te not significant variability of mortar properties and quite large size of gotic bricks. 3. HOMOGENIZATION Calculations of te modulus of elasticity of curc walls as a omogenous material were carried out accordingly to te algoritm of omogenization proposed in work [2]. In tis metod, an elementary cell is analyzed, were based on strain compatibility and stress balance equations of its components, te basic material properties of te entire element can be calculated. Fig. 4. Elementary cell and stress balance in individual states Te basic assumptions of tis metod are: Te widt and eigt of a elementary cell is greater tan its tickness, wic makes it possible to assume a plane stress state in te wall, A regular layout of bricks and joints in te wall, Small stress gradient in te construction, lack of stress concentrations. Horizontal stress balance equations σ x can be presented in te following form (2): σ σ x x x xb C = σ σ = σ σ = σ xb = σ xb xm1 B C xm1 B M 1 C + σ + σ xm 2 M 2 xm 2 + σ xm 2 M 2 C M 2 C = σ xm1 M 1 + σ xm 2 M 2 (2) Unautenticated
STRENGTH PARAMETERS OF MASONRY WALLS IN MODELLING HISTORIC CONSTRUCTIONS 59 were: σ ij - stresses in te i-t direction of te j-t component, j - eigt of j-t component. Te agreement of strains ε x in te orizontal direction can be represented by formula (3): were: xc LM 2 LB LM 1 xm 2 = ε xb ε xm1 LC LC LC ε = ε + (3) ε ij - strains in te i-t direction of te j-t component, L j - widt of j-t component. A precise description of te metod can be found in work [2] as well as in te works of oter autors, e.g.[8]. Te moduli of elasticity of te brick wall in two directions perpendicular to eac oter calculated accordingly to tis algoritm are E x = 2.374 GPa and E y = 2.120 GPa respectively. Matysek and Witkowski in teir work [3] obtained a modulus of elasticity of 1.0-2.4 GPa (average value of 1.6 GPa) in teir studies on XIX century walls, tus it can be observed tat te value obtained in te present work falls witin te range limits provided in literature. Based on empirical relationsips provided by Matysek in [4], te compressive strengt of a masonry wall was determined according to te following formula: were: 0,7 0,3 0,7 0,3 f χ 0.36 f f = 0,8 0.36 4.537 0.8 = 0.776 MPa (4) k = b m f k - compressive strengt of wall, χ - coefficient accounting for te caracteristics of a istoric wall, f b - compressive strengt of bricks, f m - compressive strengt of mortar. Strengt parameters calculated in suc a way were applied to calculations of te omogenized walls of te curc in Gnojewo, wic will be te subject of furter researc undertaken by te team. 4. VERIFCATION OF HOMOGENIZATION Te accuracy of used omogenization logaritms was verified performing numerical simulations of te static beavior of micro- and macromodels of te bent masonry deep beam (Fig. 5) given by Page and described in [6]. Tis deep beam was loaded midspan using a steel beam, applying a force of 20, 40, 60, 80 and 100 kn; te present work sows te results of loading wit a force of 20 kn. Unautenticated
60 Micał GOŁĘBIEWSKI, Izabela LUBOWIECKA, Marcin KUJAWA Te experimental data presented in [6] were repeatedly applied to verify te procedure of omogenization, among oters by Quinteros et al. [8]. In te study we followed te same procedure. Te models were created using te Abaqus 6.10 FEM software. Te studies of Page described in work [6] were preceded by detailed tests of te material. Values of strengt parameters of brick and mortar as well as teir dimensions were applied in our FEM model beavior simulations. Te parameters of te omogenized material of te masonry deep beam were obtained using te omogenization metod presented in Capter 3. A so-called micromodel was created, in wic bricks and mortar were modeled individually. A mes of finite elements based on solid exagonal elements wit a linear sape function marked as C3D8R was used; te finite element size was applied as equal to te tickness of te mortar, i.e. 5 mm. Fig. 5. Masonry deep beam studied by Page [6], measurements in [cm] A series of macromodels was carried out, in wic omogenized wall parameters were used. In tese models, a mes of solid exagonal finite elements wit a linear sape function marked as C3D8R was also built. Calculations were carried out assuming te following finite element size: 40 mm, 20 mm, 10 mm and 5 mm. Convergence of te solutions was assessed comparing te displacements of te central point on te lower surface of te panel. Graps of primary stresses along te line running troug te middle of te panel ave been sown in (Fig. 7). Te grap allows one to compare te values of stresses obtained by oter researcers and in experimental studies [6] wit results of te present work (macromodel). It also presents te results of stresses obtained in te analysis of te micromodel and macromodel wit te same mes Unautenticated
STRENGTH PARAMETERS OF MASONRY WALLS IN MODELLING HISTORIC CONSTRUCTIONS 61 density. In te micromodel, jumps in stress are noticeable in te layers of mortar. Fig. 6. Macromodels of masonry deep beam, mes and maximum stress on a deformed model at a mes density of a) 40, b)20, c)10 and d) 5 mm Fig. 7. Principal stress along te middle line of te masonry deep beam An analysis of te outlined model applying te extended finite element metod (XFEM) wic makes te analysis of cracks possible witout te necessity of applying remesing metods, was also carried out. 5. CONCLUSIONS Te strengt parameters of bricks from te original structure fall into te range obtained in oter works concerning istorical bricks (e.g. [5]), altoug tey differ significantly from te parameters of modern-day bricks. Unautenticated
62 Micał GOŁĘBIEWSKI, Izabela LUBOWIECKA, Marcin KUJAWA Te analysis of FEM numerical models using omogenized wall parameters indicates a strong similarity of tese results to te results of oter researcers. On te basis of graps (Fig. 7), it can be stated tat te metod of omogenization was applied properly, and gave results wic coincide wit te micromodel (Fig. 7b) and experimental outcomes, as well as te results of numerical simulations carried out by oter researcers (Fig. 7a). Tus it allows one to use te obtained results in modeling te brick walls of te curc in Gnojewo wile applying omogenized parameters, wic is to be te aim of te researc team s furter studies. ACKNOWLEDGMENTS Te autors gratefully acknowledge te tecnical support of te Emilia Malanowicz Foundation for te Preservation and Salvage of Monuments and Arteco Group. REFERENCES 1. Augenti N., Parisi F.: Constitutive models for tuff masonry under uniaxial compression, Journal of Materials in Civil Engineering, 22, 11 (2010) 1102-1111. 2. Lopez J., S. Oller S., Oñate E., Lubliner J.: A omogeneous constitutive model for masonry, International Journal for Numerical Metods in Engineering, 46, 10 (1999), 1651-1671. 3. Matysek P., Witkowski M.: Badania wytrzymałości i odkształcalności XIXwiecznyc murów ceglanyc, XXVI Konferencja Naukowo-Tecniczna Awarie Budowlane, Międzyzdroje 2013, 183-190. 4. Matysek P.: Uwagi o szacowaniu wytrzymałości murów zabytkowyc na podstawie wytrzymałości cegieł i zaprawy, Materiały budowlane, 457, 9 (2010), 44-51. 5. Modena C, Valluzzi MR, Tongini Folli R, Binda L. Design coices and intervention tecniques for repairing and strengtening of te Monza catedral bell-tower, Construction and Building Materials, 16, 7 (2002), 385-95. 6. Page A.: Finite element model for masonry. Journal of te Structural Division, 104, 8 (1978), 1267-1285. 7. Sieczkowski J., Szołomicki J.: Metody obliczeń statycznowytrzymałościowyc sklepień w budowlac gotyckic, Wrocław, Oficyna Wydawnicza Politecniki Wrocławskiej 1999 Unautenticated
STRENGTH PARAMETERS OF MASONRY WALLS IN MODELLING HISTORIC CONSTRUCTIONS 63 8. Quinteros R., Oller, S., Nallim, L.: Nonlinear omogenization tecniques to solve masonry structures problems. Composite Structures, 94, 2(2012), 724-730. PARAMETRY WYTRZYMAŁOŚCIOWE MURÓW CEGLANYCH W MODELOWANIU KONSTRUKCJI ZABYTKOWYCH S t r e s z c z e n i e W artykule przedstawiono metodę określania podstawowyc parametrów wytrzymałościowyc zabytkowego muru ceglanego. Zastosowano badania eksperymentalne, aby określić podstawowe parametry wytrzymałościowe cegieł. Uzyskane wyniki porównano z wartościami wymienianymi w literaturze. Tak uzyskane wartości wprowadzono do algorytmów omogenizacyjnyc umożliwiającyc obliczenie parametrów wytrzymałościowyc muru jako materiału jednorodnego (zomogenizowanego). Poprawność wykorzystanyc metod zweryfikowano opracowując modele numeryczne MES wykorzystujące uzyskane parametry zomogenizowanego materiału. Zbadano zbieżność modeli o rozmiarac elementów skończonyc 40, 20, 10, i 5 mm. Wyniki uzyskane z modeli zomogenizowanyc oraz mikromodelu porównano z wynikami uzyskanymi przez innyc badaczy oraz z wynikami eksperymentalnymi. Słowa kluczowe: mury ceglane, zabytki, omogenizacja, modelowanie MES Editor received te manuscript: 15.01.2015 Unautenticated
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