Time-History Analyses on the Effect of Partial Infill Walls on the Seismic Response of a Reinforced Concrete Frame Structure

Time-history analysis (THA) is based on direct step-by-step integration of the equation of motion in time domain considering as input either the recorded accelerograms of real or artificially generated earthquakes. Numerical simulations are sensitive in terms of material properties, geometry, boundary conditions and applied loading scenarios correct definition. Therefore, additional care is required in the pre-processing stage of the analysis when the numerical model is defined. Infill walls play an important role on the seismic behaviour of structures during earthquakes. The response of the structure to seismic action changes due to the presence of the infill walls. The paper presents the results obtained by means of THA on the effect of partial infill walls on the seismic response of a scaled-down RC frame structure subjected to four consecutive uniaxial seismic motions. The parameters of the research were the presence of the partial infill wall and the thickness of the wall. The obtained results are discussed from the point of view of maximum lateral displacements and response spectra expressed in terms of accelerations. The results contribute towards the setting up of the subsequent shake table tests of scaled-down RC frame models with different configurations that would validate and help calibrate the numerical model.


Introduction
The significant advances made in the microarchitecture of computer processors increasing their computational power and efficiency reflected in every aspect of modern life.Research in the field of civil engineering, in terms of numerical simulations, has seen a huge development due to the afore mentioned advances.Improved mathematical models of physical phenomena, coupled with more and more complex numerical models of civil engineering structures, resulted in accurate assessments of their behaviour under various loading conditions.Numerical simulations are now at the heart of every major research project, from reliability analyses [1,2], to assessing the behaviour of different structures in difficult site conditions [3][4][5], to optimizing the design process and increase the safety of newly built or strengthened buildings [6][7][8][9][10], to creating intervention strategies and relief plans in case of occurring natural disasters [11].Time-history analysis (THA) is based on direct step-by-step integration of the equation of motion in time domain considering as input either the recorded accelerograms of real earthquakes or synthetically / artificially generated ones to fit design elastic response-spectra of different design codes.Although this type of analysis is used mainly by researchers, as it requires a vast amount of knowledge on how to properly define de input motion, it successfully overcomes the drawbacks of other often employed methods such as: modal analysis used together with the behaviour factor q to account for the effect of energy dissipation, non-linear static (pushover) analysis which, although quite widespread, fails to account for the effect of load reversals on the capacity of a structure [12].Numerical simulations, on the other hand, albeit being very useful, are sensitive in terms of material properties, geometry, boundary / support conditions and applied loading scenarios correct definition.Therefore, additional care is required in the pre-processing stage of the analysis when the numerical model is defined, especially in case of complex structures with geometries that require attention, various materials being used and loading scenarios that have to be applied in a certain order [13].Although numerical simulations offer the advantage of varying a large number of parameters [14], they do, however, need experimental validation [15][16][17].Still, numerical simulations could be used as a tool to predict the behaviour of the investigated structure during the laboratory experiments, in order to avoid damages to equipment.Infill walls play an important role on the seismic behaviour of structures during earthquakes [18].The response of the structure to seismic action changes due to the presence of the infill walls, although their effect is still disregarded in many countries [19].They significantly reduce the deformation capacity of the structure, increasing its stiffness and, consequently, the intensity of the seismic force taken over by the structure.This may result in damages either at the level of the load bearing structure, e.g. the reinforced concrete (RC) frame, or at the level of the infill wall.Either way, the overall behaviour changes significantly from what was initially considered during the design stage [19].The paper presents the results obtained by means of THA on the effect of partial infill walls on the seismic response of a scaled-down RC frame structure.The parameters of the research were the presence of the partial infill wall and the thickness of the wall.The model was subjected to four consecutive uniaxial seismic motions.The obtained results are discussed from the point of view of maximum lateral displacements and response spectra expressed in terms of accelerations.The results contribute towards the setting up of the subsequent shake table tests of scaled-down RC frame models with different configurations that would validate and help calibrate the numerical model.

RC frame geometry without infill walls
The geometry of the considered scaled-down RC frame ground floor structure is presented in Figure 1.While the material properties of the reinforcement are similar to the ones presented in [20], the selected concrete strength class was C20/25.The considered partial infill-wall had a height of 80 cm and was assumed to be located along axes A and B (Figure 1, left).While previous shake table tests conducted on similar configurations [16] considered an infinite, in plane, rigidity of the partial infill wall, the present study accounts for the influence of the partial infill wall on the lateral stiffness of the model depending on the wall thickness.

Finite element model
The 3D numerical model was generate using SAP2000.Standard material properties were considered for the C20/25 concrete that was applied to all elements: slab, beams, columns and infill walls.The beams and the columns were defined as linear frame elements and the slab and the infill walls as thinshell 2D-surface elements.For this stage of the research, a full bond was assumed between the infill walls and the columns.Fixed supports were considered at the base of the columns and linear simple supports at the bottom edge of the infill walls.The slab was 6 cm thick and was reinforced with 4 mm bars spaced at 100 mm in both directions.The columns were reinforced with four 14 mm bars as longitudinal reinforcement and 4 mm stirrups spaced at 100 mm.The longitudinal reinforcement was defined as 1D Reinforcement type element.The beams in both in-plane directions (Figure 1 left) were reinforced with four 12 mm and four 10 mm bars respectively as longitudinal reinforcement and 6 mm stirrups spaced at 100 mm in the shear spans and at 200 mm in the middle for both beams.The reinforcement in the columns was assumed to be fully bonded to concrete, whereas the reinforcement in the beams was defined only as equivalent crosssectional area of steel.The material properties for the three typologies are presented in Table 1.The models were named in accordance with the presence or absence of the partial infill walls.Hence, RCF stands for reinforced concrete frame, whereas W followed by a number indicates that a partial infill wall was considered with a thickness (in cm) corresponding to the number following letter W. The material properties of C20/25 concrete were considered in accordance with Eurocode 2 [21], where fcd and fctd are the design compressive and tensile strength, respectively, and E is the longitudinal modulus of elasticity.The characteristics of the selected earthquakes are presented in Table 2.The analysis codes tried to include the earthquake year and the recording station code.Hence 901IAS1 stands for the Vrancea earthquake that took place in 1990 (the one on May 30 th ), 901, and IAS1 represents the station code where the strong motion was recorded.

Modal analysis
The dynamic characteristics of the model were determined prior to running the time-history analyses.The obtained data is summarized in Table 3.The results for RCF analysis case are in agreement with previously reported data but for a different concrete strength class [20].It can be observed the scaled down model is very rigid.The addition of the partial infill wall leads to a further increase in the stiffness of the model, lowering its fundamental period of vibration.Increasing the partial infill wall thickness results in a further decrease in the value of the fundamental period of vibration.Figure 4 presents the deformed shape of the considered models obtained from the modal analysis.It can be observed that adding the infill wall results in a change of direction for the fundamental mode of vibrations.While for RCF case the first mode was a translational one along the longitudinal direction (Figure 1), for both RCF-W6 and RCF-W12 case the first mode of vibration took place along the transversal direction (Y in-plane axis of the model).Moreover, in case of RCF-W6 case the second and thirds modes were local ones, involving the deformation of the partial infill wall.Mode 4, on the other hand, was a global torsional one.For the RCF-W12, however, case the second mode of vibration was a torsional one.It can, therefore, be concluded that not only the presence of the partial infill wall changes the dynamic characteristics of the model, but the vibrational modes themselves and their order are changed, too.The thickness of the partial infill wall has also a significant influence on the presented aspects.

Maximum lateral displacements
The maximum lateral displacements recorded in a building subjected to seismic motions is an important parameter because it helps assessing the inter-storey drift.The obtained results, for each model, are summarized in Table 4.It can be observed that in case of RCF the maximum lateral displacement increases with each applied seismic load case.It could be concluded that there might be an accumulation of damage inside the structure.This assumption could be validated by the analysis of the input and response spectra.For both cases when the partial infill wall was considered the obtained values of the maximum lateral displacements were 3-8 times smaller, depending on the considered scenario, compared to the more flexible RCF case.The obtained results indicate that the thickness of the partial infill wall did not play any role on the values of the maximum lateral displacements.

Response spectra of seismic motions
The response spectra on the considered seismic motions, expressed in terms of spectral acceleration, are presented in Figure 5. Taking a look at the SA for the Vrancea 1977 earthquake it can be observed the peak values would correspond to longer period structures, longer than 1 second, for the NS component.
On the other hand, the EW component seems to affect structures with a fundamental period of vibration lower than 1 second.Moreover, the amplitude of the SA for the EW component was lower than for the NS component.
The SA spectra of the Vrancea 1990 earthquake indicate that both components would affect lower period structures.The amplitude of SA is almost similar for both EW and NS components, at around 0.25 seconds.Hence, taking into account the dynamic characteristics of the RCF model, Table 3, the results presented in Table 4 in terms of maximum lateral displacements could be explained by a closer match between the large amplitude of SA of the Vrancea 1990 earthquake and the fundamental period of vibration of the model, coupled with a higher flexibility of the RCF model compared to the RCF-W models.
The amplitude of the spectral acceleration corresponding to the fundamental period of vibration for each analysis case are summarized in Table 5.

Response spectra of the considered analysis models
The response spectra of the considered analysis models, for a 5% structural damping, are presented in Figure 6.The amplitudes of the SA determined from the response spectra are summarized in Table 6.By comparing the values presented in Table 6 with the data summarized in Table 5, it can be concluded that there are amplifications of the input SA amplitude for each considered model.Considering the large in plane stiffness of the slab and its inertia coupled with the high stiffness of each model, these amplifications of the amplitude of input SA were expected.

Conclusions
The paper presents the results obtained by means of time-history analyses on the seismic behaviour of a reinforced concrete frame structure subjected to different earthquake scenarios considering the presence and the thickness of the partial infill walls.The infill walls were positioned along the longitudinal direction of the model and the selected strong motion components were applied sequentially along the same direction.The presence of partial infill walls change the fundamental mode of vibration as well as the order of subsequent modes of vibration.In both cases where infill walls were considered, the second mode of vibration is a torsional one and not a translational one.Thinner walls lead to the occurrence of local modes of vibration, meaning additional support conditions are required in the numerical model.None of the selected seismic events produce large lateral displacements of the model in both configurations -with and without partial infill walls.This may be due to the high stiffness of the model, taking into account the dynamic properties of each investigated geometry.All models exhibited amplification in the magnitude of the spectral acceleration.Taking into account the high in-plane stiffness of the slab, present in all models, and the overall stiffness of the structure, derived from the dynamic characteristics, the higher amplitudes of the response spectral accelerations are expected.
The obtained results will be used to prepare subsequent shake table tests of scaled down models of reinforced concrete structures having similar geometry.

2. 3 .Figure 2 .Figure 3 .
Time history loading scenariosBesides the self-weight, the model was subjected to ground motion accelerograms recorded for the Vrancea 1977 and Vrancea 1990 earthquakes.All seismic scenarios were applied uniaxially, along the longitudinal direction of the model in order to assess the influence of the partial infill walls on the seismic response of the structure.The EW and NS components of both earthquakes were applied in sequence for a total of 4 time-history analyses for each considered model.The accelerograms of Vrancea 1977 and 1990 earthquakes are presented in Figure2and Figure3, respectively.The two earthquakes were considered representative for Romania based on their magnitude and peak ground acceleration (PGA) values.EW ComponentNS Component Acceleration time histories and response spectrum for Vrancea 1977 earthquake.Acceleration time histories and response spectrum for Vrancea 1990 earthquake.

RCFFigure 4 .
Modes of vibration for the considered analysis cases.

Table 1 .
Model typology and concrete characteristics

Table 2 .
Characteristics of selected earthquakes

Table 3 .
Modal analysis results

Table 4 .
Maximum lateral displacement and storey drift 6

Table 6 .
Amplitude of spectral acceleration from the response spectra [m/s 2 ]