Numerical simulations of tests masonry walls from ceramic block using a detailed finite element model

V. Salajka e alii, F a u a ed In eg i à S u u ale, 39 (2017) 88-99; DOI: 10.3221/IGF-ESIS.39.10 88 Focussed on Modelling in Mechanics Nume ical simula ions o es s mason y walls om ce amic block using a de ailed ini e elemen model V. Salajka B no Uni e si y o Technologye, Czech Republic salajka. @ ce. u b .cz, h p://www. u b .cz J. Klouda Technical and Tes Ins i u e o Cons uc ion P ague, Czech Republic klo[email p o ec ed], h p://www. zus.cz P. H adil B no Uni e si y o Technologye, Czech Republic [email p o ec ed], h p://www. u b .cz ABSTRACT. This a icle deals wi h an analysis o he beha iou o b ick ce amic walls. The beha iou o he walls was analysed expe imen ally in o de o ob ain hei bea ing capaci y unde s a ic loading and hei seismic esis ance. Simul aneously, nume ical simula ions o he expe imen s we e ca ied ou in o de o ob ain addi ional in o ma ion on he beha iou o mason y walls made o ce amic blocks. The esul s o he geome ically and ma e ially nonlinea compu a ions we e compa ed o he esul s o he pe o med es s. KEYWORDS. Ce amic blocks; Ma hema ical model o a wall; Fini e Elemen Me hod; Nonlinea compu a ions. Ci a ion: Salajka, V., Klouda, J., H adil, P., Nume ical simula ions o es s mason y walls om ce amic block using a de ailed ini e elemen model, F a u a ed In eg i à S u u ale, 39 (2017) 88-99. Recei ed: 11.07.2016 Accep ed: 22.09.2016 Published: 01.01.2017 Copy igh : © 2017 This is an open access a icle unde he e ms o he CC-BY 4.0, which pe mi s un es ic ed use, dis ibu ion, and ep oduc ion in any medium, p o ided he o iginal au ho and sou ce a e c edi ed. INTRODUCTION e o e i s in oduc ion o he ma ke , mason y made om inno a i e clay hollow blocks illed wi h mine al wool, had o be es ed o unc ionali y and eaching he con o mi y wi h calcula ion models acco ding o he Eu ocode 6 [1] and/o Eu ocode 8 [2], in mo e complex cases o load, be o e i was launched on he ma ke . Du ing he yea s 2011 – 2014, an ex ensi e p ojec [3-6] de o ed o he assessmen o he p oduc s a ic cha ac e is ics as well as he beha iou o he walls lined om hese blocks was ealized on Technical and Tes Ins i u e o Cons uc ion P ague, Czech Republic (TZÚS P aha). The basic as well as he ex ended es s we e ealized, including he e alua ion o i s esul s, B V. Salajka e alii, F a u a ed In eg i à S u u ale, 39 (2017) 88-99; DOI: 10.3221/IGF-ESIS.39.10 89 in TZÚS b unch o ice in B no. The clay block mason y walls we e es ed o a load capaci y unde he sho - e m and long- e m s a ic load on small mason y walls [3, 4], possibly on walls and pilla s o an ac ual size [5, 6]. Seismic esis ance es ing was ca ied ou acco ding o he ins uc ions o Klouda, J. K. and wi h his a endance in a es ing depa men o he Na ional Building and Ci il Enginee ing Ins i u e (ZAG) Ljubljana, Slo enia. Shea es s o he cyclic loading o ou (2+2) cons an ly e ically p eloaded walls we e conduc ed. The walls we e 2750 mm high and 440 mm hick. They di e ed in he leng h. Two o he walls we e 2500 mm long and he o he wo 1500 mm, he wall wid h and heigh a io was hen ca. 1 : 1 and 1 : 2. The e ical p eload was designed a wo le els, a a nominal amoun o app oxima ely 1/3 o 2/3 o he alue o he wall e ical design load capaci y. A he same ime, nume ical simula ions o he expe imen s o ob aining addi ional in o ma ion on he clay block mason y wall beha iou we e ca ied ou – he same as by eccen ic loaded pilla s [7]. The ma hema ical analyses we e ca ied ou using he ini e elemen me hod on he de ailed wall models. Block ma e ial p ope ies (modulus o elas ici y, ensile s eng h, comp ession s eng h, ensile s eng h in bending, e c.) we e de e mined expe imen ally be o e pe o ming he calcula ions. The models we e conside ed as geome ically and ma e ially nonlinea , including unila e al bonds. The calcula ion esul s a e u he compa ed wi h he esul s o he conduc ed es s. THE CLAY BLOCK MASONRY WALLS UNDER THE STATIC LOAD he load-bea ing capaci y o b ick walls ab ica ed om ce amic blocks (Fig. 1) unde s a ic loading was i s es ed on small specimens consis ing o h ee ows in he single block o ma , hen on medium-heigh pilla s consis ing o se en ows o blocks and inally on high wall pilla s consis ing o ele en ows o blocks. The es specimens we e loaded cen ically and eccen ically. Figu e 1: Mason y block used in expe imen al walls and FEM model o mason y block. De ails ega ding he execu ed es s a e shown in [5] and [6]. De ailed models we e c ea ed using he Fini e Elemen Me hod o use in he nume ical simula ion o s a ic es s. The b ick blocks we e modelled along wi h he mo a in he bed join s, he s eel pla es unde and abo e he pilla s, and he s eel appa a us o imposing load. Plana elemen s unde he bo om pla e simula e he possible lexibili y o he placemen o he s eel pla e. Con ac pai s (elemen s) o he modelling o in e ac ion be ween he blocks, mo a and s eel pla es a e inse ed be ween he blocks and he a eas adjacen o hem. These con ac elemen s ans e only comp essi e and shea o ces. Please see Fig. 2 a) o an example compu a ional model o a wall pilla . Fig. 1 and 2 b) illus a es he di ision o a block in o olume ic ini e elemen s. The loading ca ied ou in acco dance wi h he es was conside ed o be o ced displacemen load. De ails abou he calcula ions can be ound in [7]. Fig. 3 shows he dependence o ela i e ans o ma ion in he e ical di ec ion on load. The dashed lines show he measu ed esul s and he ull (FLX – lexible suppo ) and do ed (SLD – solid suppo ) cu es show he esul s o he calcula ions. Calcula ed alues o de o ma ion a e iden ical in a ious le els. I is appa en ha he suppo o he wall needs o be modelled ca e ully as he seemingly s i ness o suppo he es specimen can in luence he esul s o he measu emen s signi ican ly. T V. Salajka e alii, F a u a ed In eg i à S u u ale, 39 (2017) 88-99; DOI: 10.3221/IGF-ESIS.39.10 90 a) Model o a pilla , including de o me e s b) T h ee neighbou ing blocks Figu e 2: Compu a ional model o a high b ick pilla . a) T op a ea – alues om he de o me e . b) Bo om a ea – alues om he de o me e . Figu e 3: A sample o C 1-1 Specimen – load-dependen e ical s ain ε. ANALYSIS OF BEHAVIOR OF CYCLIC LOADED CLAY BLOCK WALLS es s o he s uc u e o he mason y walls buil om p ecise bu n mason y elemen s o he clay blocks POROTHERM 44 T P o i loaded by a cyclically o ced loading co espond o he shea es s o walls o he ac ual size. Fou walls o he di e en wid h we e es ed. The walls o he g ea e leng h a e ma ked “L” and he sho e walls a e ma ked “S”, (Fig. 4). The e ical walls we e buil on a igid ein o ced-conc e e beam ha was a ached i mly o he loo so ha he shea displacemen along he loo and beam il ing we e elimina ed. The ansmission o he e ical o ces was ca ied ou by s eel sec ions and ou independen hyd aulic cylinde s and one p og am-con olled hyd aulic cylinde b inging in he la e al displacemen (along he wall) cyclically co esponding o he seismic loading. The con olled la e al displacemen was in oduced o he beam by he p edomina ing mason y wall. The indi idual blocks we e lined on hin join mo a o 1 mm hickness. The mo a is only in ho izon al join s, e ical inden ed join s a e d y. Idealized and eal la e al displacemen ime his o y is shown on he Fig. 5. Du ing he expe imen , he e ical and ho izon al o ces and he displacemen s a p ede e mined poin s we e measu ed (Fig. 6). An op ical came a measu emen sys em was used o de e mine he mo ion o he wall su aces. The la e al o ce ( esis ance) dependencies on he la e al displacemen we e he esul o he measu emen . The measu emen s p o ided da a ega ding dependencies o e ical o ce ( esis ance) on ans e se displacemen . The esul s o he expe imen s a e a anged in a abula o m. T V. Salajka e alii, F a u a ed In eg i à S u u ale, 39 (2017) 88-99; DOI: 10.3221/IGF-ESIS.39.10 91 Speci ica ion: L1 (L12112/4/3) Speci ica ion: S2 (L12112/4/4) L 4 L 3 L 1 L 2 L1 Fh 90 (208) 395 (245) 110 (210) 375 (245) 250 (19) L2 L1 770 Fh F 4 590 590 (50) 1380 2000 2506 (2561) 2507 (2560) E1 (baza 3125) E2 (baza 3122) 2745 2742 L 4 L 3 L 1 L 2 L1 Fh 108 (230) 194 (245) 88 (230) 183 (250) 276 (18) L2 L1 770 Fh F 4 590 590 (62) 900 2000 1505 (1568) 1505 (1555) E1 baza 2570 mm E2 baza 2570 mm 2746 2747 Figu e 4: Diag ams o walls “L” and “S”. Time [s] Time [s] Figu e 5: Idealized and eal imposed la e al displacemen ime his o y. Wall models In acco dance wi h he da a, nume ical models o he walls we e c ea ed using he ini e elemen me hod (FEM). Only he undamen al di e ence in he geome y, ha is he di e ence in he leng h o he walls, was aken in o conside a ion while modelling by he FEM model. On he basis o his conside a ion, wo compu a ional models we e only c ea ed: One o he analysis o he long “L” walls and he second one o analyze he sho “S” walls. The calcula ions also di e by e ical p eload and exci a ion unc ions. The e ical p eload alues (including he gi de and he conc e e block) a e conside ed o each model as ollows: L1 - 1/3 cd - e ical p eload 807 kN, L2 - 2/3 cd - e ical p eload 1613 kN, S1 - 1/3 cd - e ical p eload 484 kN, S2 - 2/3 cd - e ical p eload 968 kN. On he basis o he da a, see he diag ams in Fig. 4, models o long “L” on he le and sho “S” walls on he igh side including unde lay and deli e ing elemen s o e he walls we e c ea ed in he ANSYS so wa e. Conside ing he symme y o ealized complemen a y s uc u es and walls o he e ical plane in he longi udinal di ec ion and he manne o loading, he compu a ional models we e c ea ed using his symme y ( he x-z plane). The g aphic ep esen a ion is including he mi o ed pa o he model. The compu a ional models a e mainly c ea ed om he 3-D ini e elemen s o he SOLID45 ype, see ( ig. 7). They a e he blocks, he mo a , he conc e e base beam, he conc e e beam and he main s eel gi de s and wo addi ional beams di ec ly unde he p essu e cylinde s a he “S” ype walls (Fig. 8). The conc e e base beam o he dimensions V. Salajka e alii, F a u a ed In eg i à S u u ale, 39 (2017) 88-99; DOI: 10.3221/IGF-ESIS.39.10 92 3980x500x500 o he “L” model, o 2074x500x500 he “S” model, is conside ed as elas ically placed in he calcula ions, because he loo showed o be yielding. Rela i ely igid beam placing is modelled by he COMBIN14 and SHELL181 elemen s. The clay blocks a e bound by he mo a a he ho izon al di ec ion and hey a e wi hou illing in he e ical join s. Figu e 6: Scheme o loca ions o indica o s – walls L and a angemen o de ice o e ical loading. a) “L” ype model b) “S” ype model Figu e 7: Axonome ic iew on models – ini e elemen s mesh. The in e ac ion be ween he blocks, possibly he mo a is modelled using con ac pai s – he elemen s o CONTA173 and TARG170 ype (Fig. 8). Simila ly, hese elemen s a e pu be ween he mo a and he conc e e beams. The wall heigh including he mo a is 2,749 mm. The uppe conc e e beam is 2,928 mm long (1,789 mm “S” ype), 150 mm high and 500 mm wide. The s eel gi de is bound wi h he conc e e beam i mly. The ex e nal con ou o he gi de ha is 3,500 mm long is 300x250 mm. Down p essu e ( he cons an e ical load) is b ough in o he s uc u e using special PRETS179 elemen s in connec ion wi h BEAM44 elemen s ha allow a ho izon al slip a he leaning poin on he gi de and a deli e ing a ea o SHELL63 elemen s. The se ing depends on he comp essi e o ce and igidi y in he e ical di ec ion. Thus, he down p essu e is implemen ed a ou loca ions a he “L” ype walls (Fig. 6). This me hod o he p essu e o ces se ing did no p o e success ul wi h he sho wall models. The uppe gi de ended o il du ing he mo emen because o he eccen ic ac ion o he e ical o ces. The models we e supplemen ed wi h wo sliding beams on he main load dis ibu ion beam. Thanks o his, he gi de guiding a he o ced ho izon al displacemen was ensu ed. These beams o he leng h o 1,000 mm, he heigh and he wid h o 250 mm a e modelled in a simpli ied manne . The comp essi e o ce is applied by he special PRETS179 elemen s in he connec ion wi h he LINK8 elemen s and again a ou poin s. The modi ied V. Salajka e alii, F a u a ed In eg i à S u u ale, 39 (2017) 88-99; DOI: 10.3221/IGF-ESIS.39.10 93 model e lec s he eal beha iou o he comp essi e de ice in a be e way. The eal e sion o he comp essi e de ice is in he Fig. 6. Figu e 8: Con ac ini e elemen s (on le ) and he beams and he conc e e blocks (on igh ) o “S” ype model. B ick body and mo a p ope ies a e de i ed om he measu emen [3]. The ma e ial model o he s eel gi de s and conc e e beams is conside ed as iso opic and linea ly elas ic. On he con a y, he ma e ial model o he b ick body and mo a is conside ed as nonlinea wi h di e en ensile and comp ession s eng h. A summa y o he p ope ies o he indi idual pa s o he model ha e been used in calcula ions as i is men ioned in Tab. 1. B ick body Mo a Conc e e S eel Modulus o Elas ici y E [GPa] 14.0 7.9 30 210.0 La e al Con ac ion Coe icien ν [-] 0.1 0.2 0.2 0.3 Speci ic Weigh ρ [kg.m-3] 1390 1400 2300 7850 Comp ession S eng h c [MPa] 19.2 17.3 - - Tensile S eng h [MPa] 3.7 4.6 - - Table 1: Ma e ial p ope ies. The o al compu a ional model o al e na i e solu ions wi h he “L” ype wall consis s o 113,337 ini e elemen s localized by 134,550 nodes and has 399,477 deg ees o eedom. The o al compu a ional model o al e na i e solu ions wi h he “S” ype wall consis s o 68,799 ini e elemen s localized by 83,177 nodes and has 246,013 deg ees o eedom. The imposed unc ions a e modi ied unc ions aken om esponse a he expe imen s. The majo adjus men consis s o he co ec ion o he exci a ion poin loca ion. The esponse unc ions a e moni o ed a he heigh o 2,824 mm (“L” ype) abo e he wall bed join , while he exci a ion poin by he o ced mo ion o he gi de is a he di e en place, a highe le el om he cen e o he bo om o he wall du ing he expe imen . The displacemen co ec ion co esponds o app oxima ely 5 o 6 pe cen . Tha means ha he imposed la e al displacemen unc ion used as he exci a ion we e inc eased by 6 pe cen . Calcula ion Fou calcula ions we e ca ied ou on models L1, L2, S1 and S2. The calcula ions a e nonlinea , ime-consuming and equi ed la ge disc space. The solu ion is conside ed as quasi-s a ic due o he slow loading p ocess. The ime s ep is conside ed as a iable wi h he la ges s ep o 15 s. In each ime s ep an i e a i e s a e o equilib ium is sea ched. In case ha he ime s ep canno be al eady dec eased and he calcula ion does no con e ge, he calcula ion p ocess is e mina ed. V. Salajka e alii, F a u a ed In eg i à S u u ale, 39 (2017) 88-99; DOI: 10.3221/IGF-ESIS.39.10 94 The displacemen , s ain and s ess ields a he disc e e poin s o he models we e ob ained by he calcula ions on he L1, L2, S1 and S2 models. Conside ing he scope o he da a, he esul s we e mainly p ocessed in a o m o g aphs and igu es. L1 Wall The cyclic esponse solu ion on he L1 model wi h he p eload 807 kN (including he gi de and he conc e e block) was compa ed wi h he alues ob ained om he es . Exci a ion unc ion o ime his o y la e al displacemen is shown on he Fig. 9. The esponses o he la e al displacemen on he su ace in he cen e o he conc e e beam ob ained om he measu emen and by he calcula ion a e p esen ed in Fig. 9. The la e al displacemen ob ained om he measu emen is ep esen ed by a ed dashed line and he la e al displacemen o he same a iable ob ained by he calcula ion is shown by a blue line. In Fig. 10, he e is a ep esen a ion o he eac ion o ce dependence on he la e al displacemen o he bo h cases o he expe imen and he calcula ion. Figu e 9: Imposed unc ion – la e al displacemen ux (on le side) and la e al displacemen ux om measu emen and calcula ion a cen al poin o he beam (on igh side).  expe imen ── calcula ion Figu e 10: Reac ion o ce dependence on displacemen . L2 Wall Du ing he solu ion o he L2 wall he p eload was 1,613 kN (including he gi de and he conc e e block). The esul s o he compa ison a e in Figs. 11 and 12. The mode o “s ep-by-s ep” des uc ion and ele an s ages o he walls a e es ing a e shown in Fig. 13. V. Salajka e alii, F a u a ed In eg i à S u u ale, 39 (2017) 88-99; DOI: 10.3221/IGF-ESIS.39.10 95 Figu e 11: Imposed unc ion – la e al displacemen ux (on le side) and la e al displacemen ux om measu emen and calcula ion a cen al poin o he beam (on igh side)  expe imen ── calcula ion Figu e 12: Reac ion o ce dependence on displacemen . Figu e 13: Typical iew on he walls a e es ing. S1 Wall and S2 Wall The cyclic esponse solu ion on he S1 model and S2 model wi h he p eload 484 kN, esp. 968 kN (including he gi de and he conc e e block) was compa ed wi h he alues ob ained om he es . Exci a ion unc ion o ime his o y la e al displacemen is shown on he Fig. 14, esp. Fig. 16. The esul s o he compa ison a e in Figs. om 14 o 17. V. Salajka e alii, F a u a ed In eg i à S u u ale, 39 (2017) 88-99; DOI: 10.3221/IGF-ESIS.39.10 96 Figu e 14: Imposed unc ion – la e al displacemen ux (on le side) and la e al displacemen ux om measu emen and calcula ion a cen al poin o he beam (on igh side).  expe imen ── calcula ion Figu e 15: Reac ion o ce dependence on displacemen . Figu e 16: Imposed unc ion – la e al displacemen ux (on le side) and la e al displacemen ux om measu emen and calcula ion a cen al poin o he beam (on igh side).