FINITE ELEMENT ASSESSMENT OF THE SEISMIC PERFORMANCE OF THREE DIMENSIONAL BLOCKHAUS BUILDINGS

Transcription

1 FINITE ELEMENT ASSESSMENT OF THE SEISMIC PERFORMANCE OF THREE DIMENSIONAL BLOCKHAUS BUILDINGS Chiara Bedon 1, Giovanni Rinaldin 2, Massimo Fragiacomo 3, Salvatore Noè 4 ABSTRACT: The paper investigates the structural response and vulnerability of Blockhaus buildings under seismic loads. The typical Blockhaus systems consists of a series of linear timber members stacked horizontally one upon another and interacting by means of traditional timber joints based on the effectiveness of carvings and contacts of multiple surfaces. Native of forested areas, Blockhaus systems are widely used in daily practice for the construction of wooden houses or commercial buildings also in earthquake-prone regions. However, no design provisions are given in the Eurocode 8. In this work, a Finite-Element (FE) numerical investigation is performed on full three-dimensional Blockhaus timber buildings subjected to seismic loads. A computationally effective FE-model developed in a previous research is implemented in ABAQUS. In this model, a key role is played by nonlinear hysteretic springs used to schematize the cyclic behaviour of the joints between perpendicular linear members and validated on cyclic experiments of single joints. Nonlinear dynamic analyses are carried out for some building configurations of technical interest. Preliminary estimations of the corresponding q-behaviour factor are also presented. KEYWORDS: Blockhaus structural systems, nonlinear dynamic analysis, Finite Element investigation, seismic performance, q-behaviour factor 1 INTRODUCTION 123 AND STATE OF THE ART Despite the ancient origins, Blockhaus systems are used in daily practice for the construction of wooden houses and commercial buildings (Figure 1, [1]), and often located in urban regions characterized by high seismic hazard such as Japan, the Mediterranean, etc. These structural systems are commonly obtained by placing a series of timber logs, horizontally on the top of one another, so as to form the walls. The interaction between the basic timber components is generally provided by simple mechanisms such as simple joints and contact surfaces, and the use of metal fastener is reduced in them to a minimum. From a design point of view, the current available standards for timber structures (e.g. [2, 3]) do not provide analytical models and recommendations for an appropriate verification of these structural systems, especially under specific boundary and loading conditions. The actual seismic behaviour and vulnerability of timber log-wall structures under seismic events still requires detailed investigations to properly assess the effects deriving from the interaction of several 1 University of Trieste, Italy, bedon@dicar.units.it 2 University of Sassari, Italy, grinaldin@uniss.it 3 University of L Aquila, Italy, massimo.fragiacomo@univaq.it 4 University of Trieste, Italy, noe@units.it aspects, such as friction phenomena, nonlinear behaviour of the typical joints under cyclic loads, etc. Figure 1: Example of Blockhaus residential buildings (courtesy of Rubner Haus AG SpA [1]). For this purpose, some researchers investigated via experiments, analytical models and/or Finite Element (FE) studies the mechanical and seismic characterization of single Blockhaus structural components or single walls subjected to in-plane lateral loads (i.e. [4-7]). In [8], the FE study carried out in [7] was further extended and based on nonlinear dynamic simulations carried out by means of efficient FE models implemented in ABAQUS [9] some preliminary recommendations were provided for the estimation of the q-behaviour factor of Blockhaus walls under in-plane lateral loads. In this paper, the previously developed FE model [7, 8] is used to investigate full three-dimensional Blockhaus structural systems. The FE model, in particular, is first validated on experimental shake table results available in

2 literature [10-12] for a two-storey log-house building, and then used to investigate the seismic performance of three different case studies. Finally, some preliminary estimations of the q-factor for Blockhaus buildings are proposed and critically discussed. 2 NONLINEAR DYNAMIC FE INVESTIGATION 2.1 GENERAL FE APPROACH Full three-dimensional Blockhaus buildings are investigated by means of a computationally efficient FE modelling approach [13]. forces applied on one-half of each log. Once multiple shear walls are assembled together, configurations of real residential or commercial Blockhaus buildings can be investigated by properly taking into account the effects of possible geometrical irregularities, window and door openings, building asymmetries, etc FE modelling concept and calibration of the carpentry joints As also shown in [7, 8], the advantage of the adopted FE modelling approach is that structural systems of different mechanical and geometrical properties can be numerically described in an efficient way, once the hysteretic mechanical behaviour of the carpentry joints is known. In the current study, a single type of Standard carpentry joints was considered ( N01 type, based on [7]), see Figure 3) and Table 1. Figure 3: Standard and Tirolerschloss carpentry joints used for Blockhaus buildings [1]. Figure 2: Schematic view of the typical FE-model for Blockhaus log-walls; axial DOF and (c) shear DOFs. The single Blockhaus log-walls are described by a series of rigid beams representative of the main timber logs connected at their ends by nonlinear spring elements acting in their axial (Y direction) and transversal (shear X and Z directions) degrees of freedom (Figure 2). A single spring represents the mechanical cyclic behaviour of a carpentry joint, resisting shear (sliding in X and Z directions) and compressive (springs in Y direction) (c) The axial law represents the contact behaviour in compression between the overlapping timber logs in a lumped way (Figure 2), while the shear law is symmetric (Figure 2(c)). In the first case (branch #10, Figure (2)b), the compressive resistance was estimated by multiplying the characteristic compressive strength f c,90,k of timber in the direction perpendicular to grain by the top/bottom contact surface of a single orthogonal log. The tensile resistance of the same springs, on the other hand (branch #1, Figure 2), was characterized by means of an almost null stiffness in order to represent the uplift and possible separation of one beam from another. The shear hysteretic law (Figure 2(c)), applied for two in-plane shear directions, has a tri-linear backbone curve and specific unloading-reloading paths from the elastic (before F el in Figure 2(c), branches #1 and #10 on the backbone curve) and the inelastic phases (branches #2, #3, #20 and #30 on the backbone curve). The unloading paths in elastic phase, displayed in Figure 2(c) with dashed lines, are characterized by two branches: the first one (branch #11) leads to a null strength with a stiffness k sc times the elastic one (Table 1), whereas the latter one (branch #12) leads to a percentage of the maximum displacement reached on branch #10. The reloading path in Figure 2(c) in the elastic phase, finally, is symmetric compared to the unloading path (branches #110 and #120).

3 Table 1: Calibration of the input parameters for the simplified FE-model of full 3D Blockhaus buildings, according to [7, 8]. Figure 4: Constitutive relationship for friction in the shear DOF of each spring. The unloading and reloading paths are composed by four branches each (#4, #8, #6, #40 and the symmetric ones), which schematize the pinching effect in plastic phase, for unloading starting from branches #2 or #3 and #20 or #30. The branch #4 has a stiffness k sc times the elastic one, while the slope of branch #8 is a fraction of the elastic one. The branches #40 and #5 are characterized by a degrading elastic stiffness. The degradation is linear and starts once F el is attained; the ultimate value is used at the ultimate displacement and is equal to k deg times the elastic stiffness. The law implements also a strength degradation through an additional displacement at reloading ( E in Figure 2(c)), which is proportional to the dissipated energy in the last full reversed cycle and can be set through the parameters and (Table 1). Further details can be found in [7, 8, 13]. The effect of dynamic friction is also included in the FEmodel (Figure 4), since it provides an additional strength contribution to each shear spring given by: F f C f N, (1) where N signifies the resultant axial (vertical) force in the spring at the current analysis step, while C f and F f denote respectively the dynamic friction coefficient and the dynamic friction force applied in the shear direction of the spring. The stiffness k f (Figure 4), finally, was set to 10 times the shear stiffness of the connector (branch #1 in Figure 2(c)). Based on [7, 8], through the parametric study, C f was set to FE assembly of full 3D buildings Unlike in [7, 8], where the performance of single timber log-walls was investigated under in-plane seismic loads only, the same FE concept was extended to full threedimensional buildings. In doing so, each log-wall was described in accordance with Figure 2. The interstorey floors and roofs were considered (in the hypothesis they ensure a fully rigid in-plane diaphragm) via kinematic constraints only. Beam elements (B31 type) with rectangular transversal section were used to describe the timber logs. Lumped masses representative of the building self-weight were then applied to the centre of gravity of each storey, while vertical loads acting on the building were uniformly distributed on the top logs only. Parameter symbol Calibrated value Units k el 3.34 kn/mm F el kn k p kn/mm F max kn k p kn/mm k sc R C S C d u 20 mm k deg gap 1 mm k PRELIMINARY VALIDATION OF THE 3D FE MODELLING APPROACH A preliminary assessment and validation of the FE modelling approach for full 3D timber log structures was carried out based on some experimental test results available in literature. The Rusticasa building was analysed, the dynamic and seismic performance of which has been experimentally investigated within the framework of the SERIES Timber building project ([12], see Figure 5). The Rusticasa building is a two-storey log-house, characterized by a m rectangular plan and a total height of 4.40m at the edge of the gable roof and 5.28m at the ridge. The building is almost symmetric along the longitudinal direction, and asymmetric in the transversal direction. The walls are obtained by assembling mm and mm logs composed of C24 class spruce. To ensure an in-plane rigid inter-storey floor, 22mm Oriented Strand Board (OSB) sheathing panels supported by timber joists were used. During the experiments, 398 additional steel plates (7.1 kg/each) were equally distributed on the roof. A full description of the Rusticasa building geometry and test methods can be found in [12] Modal analysis In accordance with Section 2.1, a 3D FE model of the Rusticasa building (Figures 5 and (c)) was implemented in ABAQUS [9]. The geometrical properties of the building were taken from [12]. The inplane rigid inter-storey floor was modelled via a kinematic constraint. The self-weight and the additional permanent loads were applied as nodal masses in the centre of gravity of the first floor and the roof, respectively. The 398 additional steel plates were also lumped in the centre of gravity of the roof. In terms of mechanical characterization of the joints, finally, the input parameters corresponding to the N01 carpentry joint calibrated in Table 1 were used.

4 Figure 6 shows the FE normalized vibration shapes of the first numerically predicted vibration modes, while Table 2 collects the corresponding vibration frequencies, together with the experimental values. FE mode #1 FE mode #2 (c) Figure 5: Rusticasa building. overview of the experimental full-scale specimen [12], with 3D view and (c) plan view of the FE model (ABAQUS [9]). A preliminary eigenvalue analysis was carried out, so that the predicted fundamental vibration modes could be compared with the corresponding experimental estimations, as obtained via dynamic identification techniques [12]. The experimental predictions calculated before the shaking table test were considered. FE mode #3 Table 2: Experimental [12] and numerical (ABAQUS [9]) vibration modes of the Rusticasa building. f= 100 ((exp num)/num). Vibration Mode # 1st 2nd 3rd 4th Frequency [Hz] Experimental FE f [%] FE mode #4 Figure 6: Numerically predicted fundamental vibration shapes for the Rusticasa building (ABAQUS [9]).

5 Despite the simplifications of the FE modelling approach, a fairly good correlation was found between numerical and experimental vibration frequencies, see Table 2. Larger discrepancies were obtained for the fourth vibration mode only, hence suggesting the general accuracy of the implemented FE model Seismic performance The same 3D model of the Rusticasa building was then numerically investigated by means of nonlinear dynamic analyses, in order to assess the seismic performance of the building. In accordance with [12], the 1979 Montenegro earthquake record was considered as seismic input. The dynamic simulations were carried out by taking into account several amplitudes for the same seismic record, i.e. by subjecting the FE-model to a low intensity earthquake (PGA= 0.07g), a moderate intensity (0.28g) and a high intensity earthquake (0.5g) respectively. The typical deformed shape is shown in Figure 7. The assessment of the FE predictions towards the full-scale shaking table tests was carried out by comparing the numerically obtained maximum displacements of the 3D model and the corresponding experimental measurements [12], for some selected points only. No structural damage was noticed under the assigned seismic records, either in the full-scale specimen or in the simplified FE model. In terms of FE predictions, an average maximum deformation in the carpentry joint (PGA= 0.028g) was found to be about 0.5mm, hence comprised within the assigned gap (see Table 1). In terms of FE and experimental comparisons, a close agreement was found also for the maximum drifts of the Rusticasa building. For the seismic record corresponding to the deformed shape displayed in Figure 7, for example, the maximum experimental drift at the ground floor was found to be 0.005%, while the corresponding FE estimation was 0.004%. At the first inter-storey level, the maximum drift was 0.003% and 0.002% for the fullscale experimental tests and the simplified 3D FE model, respectively EXPLORATORY FE PARAMETRIC STUDY Based on the preliminary validation of the 3D modelling approach, an exploratory FE study was carried out by taking into account several building configurations SELECTED CASE STUDIES All the 3D models were assembled and calibrated as described in Section 2.1. Figure 8 shows the undeformed geometrical configuration for the examined 3D buildings. Figure 7: Typical deformed configuration of the Rusticasa building FE-model under the 1979 Montenegro seismic record (0.28g), red-to-blue contour plot (scale factor: 500). 3D and top view (ABAQUS [9]). Figure 8: 3D models of the Blockhaus buildings investigated through the parametric study (ABAQUS [9]). B01, B02 and (c) B03 buildings. The first case study (labelled B01, see Figure 8) represents a single storey Blockhaus building, with m regular plan and 2.50m height (4.60m at the (c)

6 ridge). The walls are made of mm, C24 class resistance spruce logs. The second example (B02, Figure 8) is a single storey Blockhaus building characterized by a symmetric configuration along both the longitudinal and transversal directions. The plan has almost a square shape, with m dimensions and 2.66m the height of the building at the edge of the roof (4.10mm at the ridge). In this case, the log-walls consist of mm, C24 spruce elements. The third examined building (B03, Figure 8(c)), finally, is a single storey system characterized by a markedly asymmetrical geometrical configuration. The plan has overall dimensions of m, while the building height is 2.48m (4.10m at the roof edge). The walls are composed of mm, C24 class, spruce logs. Each 3D building was investigated via nonlinear dynamic simulations, under the effects of a set of seven natural seismic accelerograms obtained from REXEL v.3.5 software ( [14]) DYNAMIC AND SEISMIC PERFORMANCE ASSESSMENT The B01 to B03 buildings were preliminary analysed via eigenvalue analyses, to explore their dynamic performance. Figure 9 shows the so predicted fundamental vibration modes. The corresponding vibration frequencies were found to be equal to 9.95Hz, 9.92Hz and 11.12Hz respectively. Figure 10: Typical deformed configuration of the B03 building under seismic events (0.35g), red-to-blue contour plot (scale factor: 5000). 3D and top view (ABAQUS [9]). All the earthquake records were derived, specifically, by considering a PGA of 0.35g, with type A soil (e.g. rock soil), topographic category T1 and nominal life of 50 years. A maximum lower and upper tolerance of 10% was considered in the derivation of the seven natural seismic records. The assessment of the seismic performance of the B01 to B03 systems was carried out by monitoring the maximum inter-storey drifts and the response of each carpentry joint. A qualitative assessment was also carried out in terms of global deformed shape and possible local mechanisms, especially near the openings and the intersections of the log-walls. In general, in accordance with [7, 8], the investigated buildings demonstrated a marked flexibility under the assigned seismic records. Table 3 collects some comparative results, as obtained for the tested Blockhaus systems. Table 3: FE comparative study (ABAQUS [9]) on the dynamic performance of Blockhaus buildings under seismic events (0.35g) Figure 9: Fundamental vibration modes for the B01, B02 and (c) B03 buildings (ABAQUS [9]). (c) Model # Max. drift [%] Max. joint sliding [mm] x-dir. z-dir. B B B

7 The maximum obtained drifts were found to be about %, hence in the same order of the Rusticasa building FE model and the corresponding full-scale specimen. Regarding the carpentry joints, a total maximum sliding of around 0.7mm was also obtained. The effect of such deformations is an almost fully frictional performance of the same carpentry joints, being the sliding amplitudes slightly higher than the assigned gap of 1mm (see Table 1). In terms of overall performance and deformation, finally, an almost stable global behaviour was generally observed, even in the B03 building characterized by a markedly irregular geometry and by a large number of door and window openings (Figure 10). The presence of internal log-walls, in this sense, typically resulted in an increase of stability for the examined systems, hence in an improved seismic performance. 3. PRELIMINARY q-factor ESTIMATION A final exploratory investigation was carried out, in order to derive a preliminary assessment of the actual dissipative capacity and seismic resistance of timber logwall structural systems. While in [8] single log-walls under in-plane seismic loads only were considered, in this paper full 3D buildings were analysed. Although a proper estimation of the q-factor is essential in the force-based design of structural systems, the current generation of design standards (e.g. [2, 3]) does not provide exhaustive recommendations, especially for Blockhaus structural systems METHODOLOGY Nonlinear dynamic analyses (NLDA) were first carried out on the B01 case study (Figure 8) for the previous set of seven natural seismic accelerograms obtained from REXEL v.3.5 software, see Section Through the NLDA investigations, however, the magnitude of these accelerograms was incrementally increased until a certain limit state was attained, i.e. so that for the B01 building under the i-scaled accelerogram the values PGA u,i and PGA y,i could be separately collected. In accordance with the past exploratory FE study carried out on single walls only [8], specifically, these reference limit values were defined as: PGA u,i (Near Collapse Limit State, NCLS): peak ground acceleration leading to a pre-fixed maximum level of inter-storey drift; and PGA y,i (Damage Limit State, DLS): design peak ground acceleration leading to yielding of a single corner joint. For each i-scaled accelerogram, the q 0 value was then estimated as the average ratio of the so collected PGA u,i and PGA y,i peak ground accelerations, so that the corresponding q-behaviour factor value is given by: q q 0 (2) M with M the partial safety coefficient for timber [3], assumed 1 and 1.3 for dissipative and non dissipative systems, respectively [3]. The ultimate limit for the CLS was preliminary assumed at the attainment of a pre-fixed maximum inter-storey drift max derived from standards. In [15], for example, the CLS damage configuration for wooden walls is associated to a 3% transient or permanent inter-storey drift, with severe damage of the primary timber components ( Connection loose, nails partially withdrawn; some splitting of members and panels; veneers dislodged ). Based on the observed structural response of single logwalls under in-plane seismic loads (see [8] for a detailed discussion of results), as well as on the shake table test results presented in [12], a largest ultimate drift was also considered ( max= 5%). The latter CLS configuration, although recommended in [15] for steel frames only, was in fact rationally applied in this work to Blockhaus buildings, due to their intrinsic high flexibility RESULTS As expected, the B01 building generally showed high flexibility under the assigned seismic records, and almost a stable global behaviour (Figure 11). Figure 11: Typical deformed configuration for the B01 building under seismic events, red-to-blue contour plot (scale factor: 50), 3D view (ABAQUS [9]). In terms of q-factor estimation, the main results of this exploratory study are proposed in Figure 12, in the form of PGA u (Figure 12) and q 0 values (Figure 12) calculated for each i-scaled accelerogram. The average values are also proposed as straight lines. The so collected FE data are shown for two different CLS scenarios ( max= 3% and 5%). The obtained FE results confirm the recent findings proposed in [8] for single log-walls subjected to in-plane seismic loads. The NLDA simulations highlighted, in particular, that the assumption of a reference CLS drift max= 3% as conventionally done for wood structures would generally result in fully neglecting the postyielding behaviour of the adopted carpentry joints. Consequently, this assumption would result in a q 0-factor equal to 1 (see Figure 12), i.e. in a final q-factor 1.3 (Eq.(2)). For the B01 case study, an average q value of 1.28 at a maximum drift of 3% was in fact obtained.

8 When the ultimate allowable drift is increased and set to 5%, the carpentry joints activate, hence the high flexibility and dissipative capacity of Blockhaus buildings is further exploited. For the examined B01 system, a direct effect of this latter assumption is that an average q 0-factor in the order of 1.15 was obtained, hence leading to an average q-factor of 1.49 (Eq.(2)). Due to the high deformation capacity of the Blockhaus structural typology, however, even the assumption of a 5% maximum drift does not fully exploits the potentiality of the adopted carpentry joints, with maximum slidings up to 11mm for the reference case study. REFERENCES [1] Rubner Haus AG SpA, [2] EN :2009. Eurocode 5 - Design of timber structures - Part 1-1: General-common rules and rules for buildings. European Committee for Standardisation, CEN, Brussels, Belgium, [3] EN :2004. Eurocode 8 - Design of Structures for Earthquake Resistance - Part 1: General rules, seismic actions and rules for buildings. European Committee for Standardisation, CEN, Brussels, Belgium, [4] J.M. Branco, and J.P. Araújo. Structural behaviour of log timber walls under lateral in-plane loads. Engineering Structures, 40(3), , [5] P. Grossi, T. Sartori, I. Giongo, and R. Tomasi. Analysis of timber log-house construction system via experimental testingand analytical modelling. Construction and Building Materials, 102(2): , [6] C. Bedon, M. Fragiacomo, C. Amadio, and C. Sadoch. Experimental study and numerical investigation of Blockhaus shear walls subjected to in-plane seismic loads. Journal of Structural Engineering, 141(4), article number , doi: /(ASCE)ST X , [7] C. Bedon, G. Rinaldin, and M. Fragiacomo. Nonlinear modelling of the in-plane seismic behaviour of timber Blockhaus log-walls. Engineering Structures, 91: , [8] C. Bedon, G. Rinaldin, M. Fragiacomo, and C. Amadio. Exploratory cyclic and dynamic numerical investigation for the assessment of the seismic vulnerability of Blockhaus shear walls under inq 0 Figure 12: PGAu and q0-factor values numerically derived for the B01 building (ABAQUS [9]). 4. CONCLUSIONS In this paper, an exploratory nonlinear dynamic FEinvestigation was proposed for full three-dimensional Blockhaus timber buildings. Compared to past research projects available in literature, typically focused on the mechanical and seismic characterization of small Blockhaus components only or single shear walls under in-plane lateral loads, the novelty of presented study was in fact represented by the application of a simplified but accurate FE-modelling approach to geometrically complex buildings. At a preliminary stage, the FE-modelling approach was assessed and validated towards the experimental results of full-scale shaking table tests and modal identification measurements carried out on the Rusticasa building (SERIES Project). In general, a good agreement was found between the experimental measurements and the corresponding FE data, both in terms of vibration modes and seismic performance for the same log-wall building. The nonlinear dynamic investigation was then extended to some selected case studies. The so obtained results were critically discussed for some geometrical configurations of technical interest, in order to investigate the seismic performance and provide a rational estimation of the corresponding q-behaviour factor. In general, the examined geometrical configurations proved to be stable and markedly flexible under the assigned seismic records. The results of this investigation provide a useful background for the implementation of q-factor rules and recommendations in the next generation of seismic design standards for Blockhaus buildings. ACKNOWLEDGEMENTS Rubner Haus AG SpA is gratefully acknowledged for the financial and technical support during the experimental investigations on full-scale Blockhaus timber walls and small carpentry joints. DPC-ReLUIS is also gratefully acknowledged for partially funding the research activity within the framework of the PR4-Timber structures project. Prof. Maurizio Piazza and Dr. Jorge Branco are finally acknowledged for providing technical details on the SERIES Project experiments carried out on the Rusticasa building.

9 plane lateral loads. Proceedings of XVI ANIDIS Conference, September 2015, L Aquila, Italy. [9] Simulia. ABAQUS v.6.12 [Computer Software], Dassault Systems, Providence, RI, USA, [10] J.M. Branco, P.B. Lourenço, and C.A. Aranha. Seismic analysis of a 2-storey log house. Advanced Materials Research, 778: , [11] M. Piazza, and R. Tomasi. Investigation of seismic performance of multi-storey timber buildings within the framework of the SERIES Project. Proceedings of the 2nd International Conference on Structures amd Architecture ICSA 2013, Portugal, pp [12] M. Piazza. Seismic performance of multi-storey timber buildings Rusticasa building Final Report, SERIES Timber Buildings Project, [13] G. Rinaldin, C. Amadio, and M. Fragiacomo. A Component approach for the hysteretic behaviour of connections in cross-laminated wooden structures, Earthquake Engineering and Structural Dynamics, 42(13): Wiley Online Library, doi: /eqe.2310, [14] I. Iervolino, C. Galasso, and E. Cosenza. REXEL: computer aided record selection for code-based seismic structural analysis. Bulletin of Earthquake Engineering, 8(2): doi: /s , [15] FEMA 356 Prestandard and commentary for the seismic rehabilitation of buildings, Federal Emergency Management Agency.