Numerical Investigations on the Seismic Behavior of a Reinforced Concrete Frame Structure

Recent seismic events that took place during the past two decades and struck densely populated areas caused significant material losses and, sometimes, casualties. Taking into account the ageing of the building stock around the world coupled with unavoidable degradations, urgent measures need to be taken to either strengthen or retrofit such structures based on data obtained from analytical, experimental or numerical investigations. The present paper presents the results of numerical simulations, using time-history analyses, on a scaled-down reinforced concrete (RC) frame structure subjected to two multidirectional seismic scenarios. The obtained results are discussed from the point of view of maximum displacements, accelerations and equivalent stresses. Considering the dynamic characteristics of the model, neither considered seismic event were able to produce large lateral displacements or accelerations. Damages were localized at the beam-column joints in case of Turkey 2023 earthquake scenario.


Introduction
Recent moderate to severe seismic events that took place during the past two decades and struck densely populated areas caused significant material losses and, in some unfortunate cases, casualties.Investigations launched following the seismic event highlighted the fact that some of the totally or partially collapsed structures were either substandard or were not built according to the design plans.Substandard structures refer to the type of structures built in accordance to older code regulations (focusing on providing the elements with enough strength to resist lateral loads) that do not fulfil the requirements of modern design codes (to ensure a certain level of ductility in addition to strength requirements) [1].Taking into account the ageing of the building stock around the world coupled with unavoidable degradations [2], urgent measures need to be taken to either strengthen or retrofit such structures in order to prevent additional losses due to subsequent seismic events [3].Reinforced concrete structures are present in nearly all populated areas with a variety of structural typology and purpose, from individual houses to condominiums, schools, hospitals, a.s.o.Such diverse typology means different behaviour during a seismic event, a behaviour that should be correctly assessed and understood [1,4].Reinforced concrete frame structures provide both the required ductility and the strength necessary to resist lateral loads such as those induced by earthquakes.However, proper design of beams, column and joints should be applied in order to ensure the safety of occupants and to limit the damage of the structure [5].Numerical simulations have the advantage of being relatively simple to be applied from individual structural elements to complex, large-scale, structural systems.At the same time, they offer the possibility of changing a large number of parameters from geometrical dimensions, material behaviour, boundary conditions and/or input actions [6,7].In order for such simulations to provide trustworthy results, they should be based on accurate analytical models and should be validated by laboratory investigations on structural elements or scaled down models [8][9][10].While time-history analyses (THA) may not be significant from a practitioner's perspective, it may offer insightful information to researchers from the point of view of seismic behaviour of investigated component [11] or structure [12,13] subjected to different earthquake induced vibrations.This is because each component of the seismic motion may have a different frequency content that could produce damages to the structure to a lesser or greater extent depending on the dynamic properties of the structure itself coupled with local soil conditions.In view of the very recent disastrous earthquake that took place in Turkey, the present paper presents the results of numerical simulations on a scaled-down reinforced concrete (RC) frame structure subjected to two multidirectional seismic scenarios.The obtained results are discussed from the point of view of maximum displacements, accelerations and equivalent stresses.

RC frame geometry and materials
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 [14].The selected concrete strength class was C16/20 with the characteristics shown in Table 1.

Finite element model
The 3D numerical model was generate using ANSYS 2021R1.The model consisted of 6786 solid elements using SOLID186 option.The contact between the reinforcement and the concrete was modelled using CONTA174 and TARGET170 elements in ANSYS and Coulomb friction model was assumed.Taking into account the geometry of the model, Figure 1, and the fact that the maximum aggregate size was 16 mm, the SOLID186 brick element dimension was considered as 50 mm.This would result in a fine mesh to capture any local stress concentrations but coarse enough to include the concrete aggregate.The generated numerical model and mesh discretization are presented in Figure 2. The structure was considered to have fixed supports at the base of the columns.

Loading scenarios
Besides the self-weight, the model was loaded with a 0.03 MPa surface load, uniformly distributed over the entire surface of the slab, to simulate the live load.While Vrancea 1977 is a reference seismic event for Romania, the disastrous effects of Turkey 2023 [15] earthquake prompted for its use in the numerical simulation in order to assess its effects on the considered scaled-down model.The time histories of both Vrancea and Turkey earthquakes, with their components along East-West (EW), North-South (NS) and vertical (Z) directions, are presented in Figure 3 and Figure 4, respectively.The input data presented in Figures 3 and 4 was obtained from the Engineering Strong Motion Database, an European collection of accelerograms [15].In order to reduce the computational time, the acceleration data was sampled at 0.05 seconds time step from the original processed input file.The THA cases were run independently on the scaled down structural model.The considered scenarios are presented in Table 2.For both considered earthquake scenarios the E-W component was applied along the longitudinal direction of the model, X axis in Figure 2, whereas the N-S component was applied along the transversal direction of the model, Y axis in Figure 2. The numerical model will be improved during the subsequent stages of the research to account for different angles of incident seismic waves with respect to X and Y axes of the model.The load case combinations were generated in accordance to Romanian design code CR 0-2012 [16].

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 are in agreement with previously reported data but for a different concrete strength class [14].It can be observed the scaled down model is very rigid with a fundamental frequency of vibration nearing the value corresponding to a rigid body.The first two modes of vibration were purely translational.The fundamental mode of vibration resulted in translation along X axis, the longitudinal axis of the model, Figure 5, whereas the second mode of vibration resulted in translation along the Y axis of the model, the transversal axis, Figure 5.
Taking into account the response spectra presented in Figure 3 and Figure 4 as well as the fundamental period of vibration of the model, it can be anticipated that the Turkey 2023 earthquake scenario will have a stronger influence on the model in terms of accelerations, displacements and even induced stresses in the material.

Maximum 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.This would give valuable information in terms of the seismic performance of a structure.The combined effect of all three components of the seismic motion for both considered earthquake scenarios is presented in Figure 6.It can be observed that the maximum lateral displacement was almost four times larger for Turkey 2023 earthquake compared to Vrancea 1977.At the same time, the maximum displacement for Turkey 2023 earthquake took place along Y axis of the model corresponding to the N-S component, Figure 4, with larger amplitudes of the seismic motion in terms of input acceleration.Similarly, the maximum displacement for Vrancea 1977 earthquake was also obtained along the Y axis of the model.While both E-W and N-S components had similar amplitudes for the input acceleration the decreased stiffness of the model along Y axis resulted in the maximum lateral displacement being obtained along this axis.

Maximum accelerations
Considering the inertia forces that develop in a structure during a seismic event, the acceleration levels may offer insightful information on the overall seismic behaviour of the structure.The obtained results, shown in Figure 7, indicate an almost 10-fold increase in the values of acceleration recorded at the level of slab for the Turkey 2023 earthquake compared to Vrancea 1977 event.Considering the spectral accelerations of the two earthquakes (Figures 4 and 3

Equivalent von Misses stress
Since the input seismic motion was a complex one, with components along all three axes of the model, the strength check could be performed only in terms of equivalent stress.Equivalent von Misses stress was chosen to express the magnitude of the obtained results, Figure 8.The stress levels for the two earthquake scenarios indicate that Turkey 2023 even would produce equivalent stresses that would exceed the tensile strength of concrete and, therefore, cracks would be expected in the structure.The localization of these cracks were obtained at the base of the columns and at the top part of the columns, near the connection point with the beam elements.A similar localization was obtained for the Vrancea 1977 scenario.It would be interesting to point out the fact that the maximum displacement, maximum acceleration and maximum equivalent stress values were all obtained at the time stamp 5.05 seconds for Turkey 2023 earthquake.Taking into account the acceleration records presented in Figure 4, the obtained results are in accordance to the input data.For Vrancea 1977 seismic event, both maximum displacements and accelerations were obtained at the time stamp 16.5 seconds whereas the maximum value of the equivalent stress showed a little delay corresponding to a time stamp of 17.2 seconds.

Compliance with Romanian seismic design code specifications
Figure 9 presents a comparative analysis in terms of maximum relative displacements and the allowable displacement specified in the Romanian seismic design code, P100-2013 [17].It can be observed that neither seismic events would generate relative lateral displacements that would exceed the allowable value for serviceability limit state (SLS).The structure being rigid, it would try to dissipate the input energy by means of internal friction mechanisms instead of lateral vibrations.This is why, in case of Turkey 2023 seismic even, the tensile strength of C16/20 concrete was exceeded and damages would be expected at the base of the columns and at the beam-column joints.

Conclusions
The paper presents some preliminary results on the numerical investigations of the seismic behaviour of a reinforced concrete frame structure subjected to different earthquake scenarios by means of time history analysis.The earthquakes are chosen based on their relevance for Romania, Vrancea 1977, and in view of the recent disastrous seismic even in Turkey 2023.The numerical model of a scaled-down ground-floor RC frame building is generated in ANSYS 2021R1 environment.Based on the obtained results, the following conclusions can be drawn: Neither seismic events produce large lateral displacements of the model that would exceed the allowable values corresponding to serviceability limit state specified in the Romanian seismic design code.The total maximum displacement is obtained for along the direction on the strong motion component with the highest intensity.In case of Vrancea 1977 earthquake, taking into account that both horizontal components have similar intensities, the maximum displacement is obtained along the weaker axis of the model.Similar results are obtained for the maximum acceleration.The results obtained from the TH analysis of Turkey 2023 earthquake indicate that the tensile strength of concrete is exceeded during the early stage of seismic motion.The localization of the damage is obtained at the base of the columns and near the beam-column connection joints.

Figure 6 .
Maximum displacements for the selected seismic scenarios.

7 .
, respectively) the obtained results follow the pattern of the input motions taking into account the fact that the model was very rigid.a) Vrancea 1977 earthquake b) Turkey 2013 earthquake Figure Maximum acceleration for the selected seismic scenarios.

Figure 8 .
Maximum equivalent stresses for the selected seismic scenarios.

Table 1 .
Material properties of concrete