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1 Structural Analysis of Historical Constructions Jerzy Jasieńko (ed) 2012 DWE, Wrocław, Poland, ISSN , ISBN NlN ifnbao SbfSMfC obsmlnsb lf Teobb-ibAF MASlNov STorCTrobS harapitta ik 1 I Mouzakis ChK 2 I Adami ChKJbK 3 I sintzileou bk 4 ABSToACT The seismic behavior of two buildings, two storeys high, made of three-leaf masonry is numerically investigated. The two structures are identical in geometry and materials; in one of them timber ties are arranged at intervals along the height. A detailed numerical finite element model of each building is developed, using shell elements and a free meshing technique. Special care is taken for the description of timber ties and timber floors. Masonry is considered as an equivalent composite material with non linear behaviour; the constitutive model is based on smeared crack approach and simulates the main failure modes of masonry under tension, compression and shear. Hysteretic rules for each type of failure are described. The mechanical properties of the masonry are identified from compression tests of single wallets, while non linear parameters are selected from literature. The numerical results of the analysis of each structure are verified with the experimental data obtained during shake table tests conducted at the Laboratory of Earthquake Engineering at NTUA, within the framework of NIKER project. The comparison of numerical and experimental data demonstrates that the numerical model successfully estimates the global response of three-leaf masonry structure with and without timber ties under seismic loads. heywords: bxplicit dynamic analysisi Constitutive lawi qhreejleaf masonry NK fntolarctfln In the last decades several efforts have been made in experimental and numerical investigation of heritage structures. This interest has arisen from the need for conservation and restoration of historical buildings, especially under earthquake actions. Within the framework of NIKER project, experimental investigation on sub-assemblies and scaled models is carried out at Laboratory of Earthquake Engineering (LEE), National Technical university of Athens (NTUA). Their response both at as-built state and after intervention is investigated. In parallel, the behaviour of the buildings is being modeled using Finite Element Method (FEM), with the aim to predict their pathology and the experimentally recorded response. For the analysis of historical masonry structures and traditional buildings, very sophisticated finite elements or simplified methods are commonly used [1, 4]. Although a large number of monotonic versions of constitutive models have been proposed for masonry in the past two decades, not many of them have been extended to include cyclic loading. In this paper, an efficient cyclic material model is presented. The obtained numerical results are compared with the experimental ones. 1 Dr. Civil Engineer, National Technical University of Athens, Faculty of Civil Engineering, Laboratory of Earthquake Engineering, klucia@central.ntua.gr 2 Assistant Professor, National Technical University of Athens, Faculty of Civil Engineering, Laboratory of Earthquake Engineering, harrismo@central.ntua.gr 3 Dr. Civil Engineer, National Technical University of Athens, Faculty of Civil Engineering, Laboratory of Reinforced Concrete, adamis@central.ntua.gr 4 Professor, National Technical University of Athens, Faculty of Civil Engineering, Laboratory of Reinforced Concrete, elvintz@central.ntua.gr 1590

2 OK ClNSTfTrTfsb Mlabi The uniaxial total strain smeared crack model used to simulate the nonlinear behavior of masonry in this study is recently described in [5]. It is based on smeared crack approach in conjunction with explicit dynamic procedure. The material system is assumed to be identical to the global x-y system, with the bed joints along the x-axis and the head joints along the y-axis. In this model, the three fundamental in-plane failure modes of unreinforced masonry are considered: cracking normal and parallel to bed joints, crushing normal and parallel to bed joints and shear under compressive vertical stress. Three separate total strain based criteria are used for failure initiation. Cracking and crushing are controlled through normal strains, while shear strain controls failure in shear. The equivalent strain [6] and fracture energy concepts [7] are also adopted. The latter is used in order to overcome the problem of mesh-dependent results. The monotonic shear, tensile and compressive behavior of model is shown in Figure 1. In tension, the material is initially linear elastic and when the maximum strain reaches the tensile strain, cracks initiate. After cracking, the tensile stress decays exponentially (mode-i fracture) as shown in Figure 1a. In compression, the material exhibits a linear elastic behavior, followed by a strain hardening and a strain softening behavior. ó xy ó x/y p (f cx/y p,ĺ cx/y ) ó x/y 0 (f s,ĺ 0 s ) G s (ó xy,ĺ xy ) f sr 0 (f cx/y,ĺ 0 cx/y ) (ó x/y,ĺ x/y ) (f tx/y 0 0,ĺ ) G t tx/y (ó x/y,ĺ x/y ) á sĺ xy ĺ xy á cĺ x/y u ĺ cx/y ~ ĺ x/y c) FigK N Monotonic stress-strain curve under: a) shear, b) compression, c) tension á t ĺ x/y ~ ĺ x/y The cyclic stress-strain relations of model incorporates the main feature of hysteretic response of masonry, such as energy dissipation, plastic strain at zero stress level, crack closing and reopening, strength and stiffness degradation, partial reloading and partial unloading rules. The unloading response from tension to compression and vice versa is shown shematically in Figure 2. This response is covered by two unloading parameters α t and α c as decribed in [5]. The shear cyclic stress strain relationship discribed in the present smeared crack model is shown in Figure 3, where an initial loading cycle and a subsequent one are shown. The cyclic shear response of the model is a typical shear stress-strain relation suitable for masonry consisted by normal strength solid units and poor quality mortar filling both head and bed joints [5]. ó x/y Reloading-Partial unloading- Partial reloading Transition curve from compression to tension Monotonic curve in tension ~ ĺ x/y Transition curve from tension to compression Monotonic curve in compression (Not in scale) Reloading-Partial unloading- Partial reloading FigK O Cyclic response from tension to compression and vise versa 1591

3 ó xy ~ ĺ xy 5 4 FigK P Cyclic response in shear OKNK Calibration of three-leaf masonry The complete definition of the constitutive model requires 18 parameters that account for the different tensile and compressive strength parallel and normal to the bed joints. In the case of three-leaf masonry which is examined in this study, the compressive/tensile strengths normal and parallel to the bed joints are assumed to be equal, since rubble masonry tends to behave as a homogenous material [8]. Consequently, the number of required parameters is reduced to 13 namely: Modulus of Elasticity, Poisson s ratio, tensile strength, mode-i fracture energy, compressive strength, compressive strain, crack closing strength, unloading parameters in tension and compression, shear strength, mode-ii fracture energy, residual shear strength and unloading parameter in shear. The elastic properties of the masonry (Modulus of Elasticity and Poisson s ratio) were based on the experimental data. However, the selection of post-elastic and unloading parameters is a rather complex task, since no relevant experimental data are usually available. Consequently, sensible assumptions were made, on the basis of the literature [5, 9-11]. It is noted that the value of the Shear Modulus G is obtained assuming the relationship with the Modulus of Elasticity G = 0.40E, as suggested by EC6 [12]. The masonry density is measures 1.90Mgr/m 3. In Table 1, the material parameters used in the analysis are presented. Table N Mechanical characteristics of masonry Properties Value Modulus of Elasticity 0.50 GPa Poisson s ratio 0.2 Tensile strength 0.50 MPa Mode-I fracture energy 05/05 MNm 1 Peak compressive strength MPa Peak compressive strain -25 Unloading from tension to compression parameter 0.85 Crack closing strength MPa Unloading from compression to tension parameter 0.85 Shear strength 0.10 MPa Mode-II fracture energy 01 MNm 1 Residual shear strength 0.05 MPa Unloading shear parameter 0.90 PK SeAhfNd TABib TbSTS A series of experiments have been performed in the framework of NIKER project with the purpose to investigate the dynamic behaviour of historical masonry structures under seismic excitations. In this study, plain and timber-laced three-leaf masonry models have been chosen for numerical analysis. The numerical results are compared to those obtained by the experimental investigation of two models. The tests have been performed at LEE/NTUA using the shaking table facility. The specimens were a 1:2 scale, 2-storey three-leaf masonry models with timber floors (Figure 4a-4c). Masonry walls consisted of three (approximately equal in thickness) leaves. The total thickness of walls was equal to 250 mm. The mean compressive strength of the limestone is approximately equal to 1592

4 100 Mpa. The mortar was a lime-pozzolan one with a mixed aggregate matrix composed of siliceous river sand and limestone gravels. The compressive strength of mortar was equal to 4.60 MPa (at the age 90 days). The inner part of the walls consists of small stones and mortar in a proportion of 2/1. The floors consist of timber beams ( mm) placed every 340 mm and supported by masonry through a collector beam. A timber pavement, made of mm 2 timber planks was provided (nailed on the timber beams). Timber lintels are provided at the top of all openings. In the timber laced specimen, timber ties were positioned a): at floor levels and b) at top and bottom of openings. The timber laces consist of two longitudinal timber elements running along the perimeter of the building (Figure 4d) connected among them through transverse timber elements every 0.50 m approximately. The cross section of all timber elements were mm 2. The timber elements were made of coniferous wood (strength class C22). During testing, additional masses were placed on the two floors, namely, 4.5 Mgr and 3 Mgr on the floor of the 1 st and 2 nd level respectively. Thus, the total mass of each specimen was approximatly 22 Mgr. The instrumentation set-up was organised to measure acceleration and absolute displacement at various critical positions of each specimen. The specimens were subjected to step-wise increasing base motion in both horizontal directions (X-longitudinal direction, Y-transversal direction), using Kalamata records. Before the execution of shaking table tests, the dynamic properties of each specimen (initial frequency and relating damping) were measured through a sine logarithmic sweep signal of low amplitude. c) d) FigK 4 a) Typical plan, b) plain masonry building, c) timber-laced masonry building, d) in-thickness layout of longitudinal and transverse timber elements Both models were subjected to the Kalamata X- and Y- record; a sequence of tests was carried out with stepwise increasing acceleration of the input motion. The unreinforced masonry model was subjected to tests up to 90% of the original Kalamata earthquake, whereas tests up to 120% of the original records were imposed to the timber-laced model. The plain masonry model is characterized by pronounced vulnerability of longitudinal walls to out-of-plane bending. Thus, almost vertical cracks appear to all four corners of the building (Fig. 5a). Moreover, shear cracks appeared in the corners of several openings. The crack pattern of the timber-laced model is, in general, similar to that of the plain masonry model. However, the presence of timber ties has prevented the opening of cracks in the corners of openings, has postponed the occurrence and has limited the opening and the length of the cracks due to the out-of-plane bending of the perimeter walls. In Figure 5a and 5b, the damage pattern at the end of tests is shown for unreinforced and timber-laced masonry building respectively. FigK R Typical damages recorded at the long and short wall at the end of testing: a) plain masonry building (90% Kalamata earthquake), b) timber-laced masonry building (120% Kalamata earthquake) 1593

5 After the first series of tests, both models were strengthened and retested. A detailed description of the experimental campaign can be found in [13, 14]. 4K NrMbofCAi ANAivSfS The constitutive model, described in Section 2, is implemented in the general-purpose finite-element code Abaqus Explicit [15], using the Vumat user subroutine. The explicit procedure requires no iterations and no tangent stiffness matrix and is based on an explicit central difference integration rule together with the use of a diagonal lumped-mass matrix. The integration through time is performed by using many small increments. A detailed discussion of the explicit dynamic procedure in Abaqus is given in [13]. In this study, in all analyses, both physical and geometrical nonlinearities are considered. 4KNK Finite elements of models The numerical model of the two buildings is shown in Figure 6. For the simulation of walls, four node shell elements with reduced integration scheme were used, whereas for modeling of timber beams, collector beams and planks three dimensional beam elements were selected. The size of finite elements was approximately equal to 0.18m. It should be noted that the non linear material modeling refers to the composite material and not to the individual components of masonry (units, mortar). The behavior of the connection between floors and the walls is not known. For the purpose of these analyses, full wall-timber beams connections were assumed for the identification of the natural frequencies of each model as well as for dynamic analysis. The timber parts of each structure were modeled as elastic, since no visisble damage was observed during testing. The modulus of Elasticity of timber was taken equal to 10GPa; its shear modulus was taken eqaul to GPa. These values are typical for coniferous wood of strength class C22. The building models were assumed fixed to the base; the translation degrees of freedom in the base were restrained. The additional masses were taken into account by increasing the density of planks on which masses were fixed. 4KOK bigenvalue and time history analysis An eigenvalue analysis using the elastic properties of materials was first performed for each model. The results of this analysis are used for comparison with the experimental values of natural frequencies. Moreover, this procedure is nessecary to check the stiffness and the mass of the numerical model in the elastic state. For the plain specimen, the resonance frequency in transversal and longitudinal directions was calculated to be 4.87 Hz and 6.58 Hz respectively. Those values are quit close to 4.20 Hz and 6.22 Hz, values derived from sine- transversal and longitudinal sweep tests. For the timber-laced specimen, the values of frequncies derived from eigenvalue analysis were 6.67 Hz and 8.58 Hz along Y and X direction. Also in this case, the numerical values of frequencies are approximatly equal to the experimental ones (6.72 Hz and 8.18 Hz respectively). In Figure 7 the mode shapes corresponding to the calculated fundamental frequencies along the two main axes are presented for both examined models. FigK S Geometry and numerical model a) unreinforced masonry building, b) timber-laced masonry building Subsequently, a time history analysis was performed using the explicit dynamic technique. For each building model, a constant damping ratio of 4% and 10% for the first mode along X and Y direction respectively was used.these values were determined during the experimental procedure through sinesweep tests. Only mass proportional Rayleigh damping was used. 1594

6 It is well known that masonry buildings present nonlinear behaviour under acceleration with very low amplitude, or even under self weight and static loads, due to the low tensile strength of masonry. Thus the adopted procedure for the comparison between experimental and numerical response is to apply to the base of each model, the acceleration time histories (with increasing amplitude) imposed to the models during the experimental testing; both material and geometrical nonlinearities were taken into acount. As nonlinear dynamic analyses are time consuming, at present, only one numerical test is examined for each model building. To check the accurancy of the numerical simulation, for each model, the test at which the first damages were recorded was selected. Thus, for the plain masonry building, the Test No 6 (base motion scaled to 60% of kalamata rekord Fig. 8) was simulated. For the timber-laced model, the Test No 10 (base motion scaled to 120% of Kalamata rekord Fig. 9) was simulated. To further reduce the computing time, in both cases, only the first 10sec of the recorded signals were imposed. f y =4.87Hz f x =6.58Hz f x =6.67Hz f x =8.58Hz FigK T Calculated mode shapes in transversal (Y-direction) and longitudinal direction (X-direction) a) unreinforced masonry building, b) timber-laced masonry building Base Acceleration X (m/s 2 ) Base Acceleration X (m/s 2 ) Biaxial XY Test No. 6 pga (X / Y) = 0.14g / 0.12g Base Acceleration Y (m/s 2 ) Biaxial XY Test No. 6 pga (X / Y) = 0.14g / 0.12g FigK U Base acceleration for Test 6 for unreinforced specimen: a) X direction, b) Y direction Biaxial XY Test No. 10 pga (X / Y) = 0.35g / 0.33g Base Acceleration Y (m/s 2 ) Biaxial XY Test No. 10 pga (X / Y) = 0.35g / 0.33g FigK V Base acceleration for Test 10 for timber-laced specimen: a) X direction, b) Y direction The comparison between the acceleration time histories obtained by the FE model and the experiment is shown in Figure 10 for the plain masonry building. These time histories of Fig. 10 refer to the top acceleration at the cornens (A3X, A5X) and mid-length (A4X) of one of the short wall. In general, it is evident that the numerical results are in good agreement with the experimental response. In Figure 11, the acceleration time history at the middle of one long wall at point A7Y obtained by numerical

7 analysis is compared against the experimental one. As is shown in this figure numerical and experimental results compare quite well in the first part of the motion, However, significant deviation between experimental and numerical results is observed after 5 th second. This deviation is probably due to the fact that the numerical results are affected by the results of previous tests that were not analysed. In addition, during testing, long walls suffered significant out-of plane movements and separation of the external leaves. This mechanism is not simulated with the adopted constitutive model. results obtained for the timber-laced model and comparison against the experimental ones are depicted in Figure 12, in terms of top acceleration at points A3X and A7Y. The acceleration obtained by FE at point A3X is in good agreement with the recorded experimental reults. On the contrary, a deviation of experimental results occurs at point A7Y, after the 5 th second, as in the case of the plain masonry model. Acceleration A3X (m/s 2 ) Acceleration A4X (m/s 2 ) 4.00 Acceleration A5X (m/s 2 ) FigK NM Plain masonry specimen: comparison between experimental and numerical results at the corners and mid-length of one short wall Acceleration A7Y (m/s 2 ) FigK NN Plain masonry specimen: comparison between experimental and numerical results at the middle of one long wall (point A7Y) 1596

8 Acceleration A3X (m/s 2 ) Acceleration A7Y (m/s 2 ) FigK NO Timber-laced specimen: comparison between experimental and numerical results at points A3X and A7Y Figures 13 and 14 illustrate the damage pattern (shear and tensile damage index) obtained in numerical simulations for plain and timber-laced masonry buildings respectively. The figures refer to the end of the load history and show the accumulated failure during the analysis. Compressive failures were not detected. As it can be observed, for both specimens, the damage pattern derived on the basis of the nonlinear material model is consistent with the experimental one (see Fig. 5). FigK NP Plain masonry specimen: damage index at the end of load history (damage areas in black color) a) tensile damage index, b) shear damage index FigK N4 Timber-laced masonry specimen: damage index at the end of load history (damage areas in black color) a) tensile damage index (long walls), b) shear damage index RK ClNCirSflNS In this paper, the capability of the uniaxial total strain smeared crack model to describe the hysteretic response of plain and timber-laced masonry structures is examined. In particular, two 1:2 scaled twostorey masonry structures which have been tested under seismic actions at LEE/NTUA are analysed. The comparison of numerical and experimental data demonstrates that the numerical model successfully estimates the global response of three-leaf masonry structure with and without timber ties under seismic loads. Further studies and parametric analyses will be performed to improve the applied model as well as to check its validity also in the case of buildings after the application of interventions. 1597

9 AChNltibadbMbNTS This research was carried out within the FP7 funded European Programme NIKER (Project Contract No ), obfbobncbs [1] Lourenco P B. (2001) Analysis of historical constructions: From thrust-lines to advanced simulations. In: mrock P rd fntk ConfK on eistorical Constructions Guimaraes, Portugal, University of Minho, [2] Giordano A., Mele E., De Luca A. (2002) Modelling of historical masonry structures: comparison of different approaches through a case study. bngineering ptructures 24: [3] Mallardo V.,Malvezzi R., Milani E. Milani G. (2008) Seismic vulnerability of historical masonry buildings: A case study in Ferrara. bngineering ptructures 30: [4] Mendes N., Lourensco P. B. (2010) Seismic Assessment of masonry Gaioleiro buildings in Lisbon, Portugal. gournal of barthquake bngineering 14: [5] Karapitta, L., Mouzakis, H., Carydis, P., (2011) Explicit finite-element analysis for the in-plane cyclic behavior of unreinforced masonry structures. gournal of barthquake bngineering and ptructural aynamics, 40(2): [6] Cope RJ, Rao PV, Clark LA, Noris P. (1980) Modelling of reinforced concrete behavior for finite element analysis of bridges slabs. In kumerical Methods for konjiinear mroblems, Swansea, UK, [7] Bazant ZP., Oh BH. (1983) Crack band theory for fracture of concrete Materials and ptructuresi ofibm 93 (16): [8] Calderini C., Cattari C., Lagomarsino S. (2009) In-plane strength of unreinforced masonry piers. barthquake bngineering and ptructural aynamics 38: [9] Gambarotta L., Lagomarsino S. (1997) Damage models for the seismic response of brick masonry shear wall. Part II: The continuum model and its applications. barthquake bngineering and ptructural aynamics 26: [10] Casolo S., Pena F. (2007) Rigid element model for in-plane dynamics of masonry walls considering hysteretic behavior and damage. barthquake bngineering and ptructural aynamics 36 (8): [11] Calderini C., Lagomarsino S. (2008) Continuum model for in-plane anisotropic inelastic behavior of masonry. ApCbI gournal of ptructural bngineering 134 (2): [12] Eurocode 6 (EC6) Design of masonry structure, EN [13] Mouzakis Ch., Vintzileou E., Adami Ch.-E., Karapitta L (2012) Dynamic tests on three leaf stone masonry building model without timber ties before and after interventions. Submitted to the 8 th fnternational Conference on ptructural Analysis of eistorical Constructions, Wroclaw, Poland. [14] Mouzakis Ch., Vintzileou E., Adami Ch.-E., Karapitta L (2012) Dynamic tests on timber-laced three-leaf stone masonry model. Submitted to the 8 th fnternational Conference on ptructural Analysis of eistorical Constructions, Wroclaw, Poland. [15] Abaqus Theory Manual. Dassault Systems. 1598