Seismic Response of Steel SMFs Subjected to Vertical Components of Far-and Near-Field Earthquakes with Forward Directivity Effects

TAAT Investment Group, Tehran 18717-13553, Iran Department of Civil Engineering, Birjand University of Technology, P.O. Box 97175-569, Birjand, Iran Department of Civil and Environmental Engineering, Incheon National University, Incheon 22012, Republic of Korea Incheon Disaster Prevention Research Center, Incheon National University, Incheon 22012, Republic of Korea Department of Civil Engineering, University of Science and Culture, Tehran, Iran Department of Civil, Environmental and Land Management Engineering, Politecnico di Milano, Milan 20133, Italy


Introduction
Near-fault (NF) ground motions are specified by longperiod velocity and displacement pulses [1] and high values of the ratio between the peak of vertical and horizontal ground accelerations [2].In near-fault earthquakes, the fault geometry position related to the considered place is significant besides the rupture mechanism and kind of faulting.
e amplitude of this pulse depends on the directivity of rupture distribution to the site.Since the rupture diffusion velocity is almost the same as the velocity of shear wave diffusion, if the fault rupture propagates to the considered place, the waves in a short-term period will reach to the place resulted in a pulse with high amplitude and short period that is called forward-effect directivity [3,4].
Over the past thirty years, there have been leading developments in the way that characteristics of vertical ground motion are interpreted and quantified [5][6][7][8][9].In comparison with other studies, these researches have determined that vertical response spectra are most susceptible to spectral period and source-to-site distance.Additionally, the vertical-to-horizontal (V/H) response spectral ratios are higher on soil than on rock, and at shorter periods than at longer periods, in general [10].
In engineering design, the vertical-to-horizontal acceleration (V/H) ratios of peak ground acceleration are usually recommended as 2/3.Moreover, the shape of the vertical response spectrum is similar to that of the horizontal response spectrum.During the recent years, it was understood that the areas near the epicenter and faults exert a strong vertical ground motion.
e vertical-to-horizontal V/H response spectral ratios are greater than 2/3.e ratios for long periods were smaller than the value of that for short periods.In the past studies, it has been found that the V/H response spectral ratios are potently related to the period and site-to-source distance during the 1994 Northridge earthquake [11].
In the seismic design of critical structures such as nuclear power plants and dams, vertical ground motions are frequently considered.However, some researches over the previous ten years recommend that the vertical ground motion component can have a great impact on the seismic response of common highway bridges especially for the sites placed in almost 15 km of major faults, as well [12][13][14].
Although, in recent years, nonlinear dynamic analysis has become standard practice to figure out the seismic performance of structures, applying the direct analysis to evaluate the critical demands is computationally expensive and difficult.As a result, the main goal of the present research is to perform extensive nonlinear dynamic analyses and obtain all important demands of structures for comparing the results of near-field and far-field ground motions.
In particular, the seismic response of steel moment frame with special ductility is investigated under the effect of panel zone modeling subjected to vertical components of nearfield earthquakes with the forward directivity effect and vertical components of far-field earthquakes.To this end, velocity, vertical acceleration, vertical displacement, column axial force, moment column, and the shear force of the stories under the impact of far-and near-field earthquakes have been compared in 3-, 5-, 8-, and 20-story structures.
In previous studies, the comparison of near-field and farfield earthquakes has been mentioned repetitively.However, near-field earthquakes are divided into two subdivisions: forward directivity and filling step. is research is the first to study the effect of the vertical component of near-field and far-field earthquake with forward directivity on the behavior of steel moment frames with special ductility.In order to obtain better results of this comparison, some of the major elements for the engineers and designers, e.g., axial force in the columns, generated a moment in the columns, maximum drift, and shear force, have been applied.

Characteristics of Modeled Buildings
In the present paper, 3-, 5-, 8-, and 20-story buildings were selected for the analysis.All modeled structures are shown in Figure 1.Also, the 20-story building is represented from reference [15].According to the classification of the HAZUS-MH MR5 [16] instruction, 3-, 5-, 8-, and 20-story buildings are categorized as low-, middle-, and high-rise buildings.
e lateral resisting systems are the special moment resisting frame in X and Y directions.ey were used in order to examine the seismic behavior of four models constructed in very high-risk zones on soil type III.ETABS software and Iranian national building code [17] were used for the seismic design of these four models.
According to the European standard profiles, different types of profiles were considered for beams and columns.As a result, profile we were used for the beams, and the box-shaped section was considered for columns (Table 1).
Different assumptions were made in the present study.In all stories, dead and live loads were 650 kg/m 2 and 200 kg/m 2 , respectively.However, different loads were applied for roofs, at 540 kg/m 2 and 150 kg/m 2 , respectively.e columns are assumed to be axially flexible.us, the beams should be simulated as flexible members in all directions [18].In a real structure, the vertical flexibility (bending) of very stiff beams is larger than the axial flexibility of the columns.Elastic elements were considered for all beams and columns in OpenSees, a software application employed for modeling these structures.Bilin Material was used to describe the behavioral properties of the elements.In addition, the Krawinkler Panel Zone Model [19] was used (Figure 2).e panel zone deforms primarily in shear due to the opposing moments in the columns and beams.e panel zone was explicitly modeled using the method of Gupta and Krawinkler [20] as a rectangle composed of eight very stiff elastic beam-column elements with one rotational spring to represent shear distortions in the panel zone [21] (Figure 2).e Bilin Material imitates the Modified Ibarra-Medina-Krawinkler Deterioration Model with a bilinear hysteretic response.Figure 3 shows the parameters of Bilin Material.
e relationships between variables were developed following Lignos and Krawinkler [22].
To represent the structure's nonlinear behavior, the studied structures were modeled with elastic beam-column elements connected by rotational springs.Based on the Modified Ibarra Krawinkler Deterioration Model, the springs follow a bilinear hysteretic response.
e plastic hinge was modeled by a rotational spring placed in the middle of the reduced beam sections (RBS).An elastic beam-column element was used to connect the spring and the panel zone.
Since an elastic element as a model of a frame member was connected in series with rotational springs at either end, the stiffness of these components had to be modified in order that the equivalent stiffness of this assembly was equivalent to the stiffness of the actual frame member [23].

Near-Field Earthquakes
Near-field ground motions are more complex than the farfield records, and this difference can change the response 2 Advances in Civil Engineering characteristics of the structure significantly.e main characteristics of near-field ground motions are as follows: (1) permanent displacement (fling) effect induced by the permanent tectonic offset of a rupturing fault; (2) severe impulsive velocity effect observed in the velocity time histories of various strong-motion earthquakes (e.g., 2015 Nepal earthquake); and (3) hanging-wall by which earthquakes at sites placed on the hanging wall of a dip-slip fault are larger than at sites placed on the footwall at the same distance [24].
In earthquakes occurring near the fault, diverse key factors, including geometry position, failure mechanism, and faulting, appear to be important.As in most cases with a high period describing a kind of excitation like a strike, ground velocity can result in pulse [25].In addition, one of the features of near-field earthquake records including forward directivity is the existence of long-period pulses in their velocity time history.ese pulses can be observed in the velocity time history of the vertical and horizontal components of these records (Figure 4).

Selection of Ground Motions
In the evaluation of structures in time history analyses, various factors seem to play a major role.e selection of ground motions has been made so that they all represent the Mw � 6.5 template scenario as the result of the risk segmentation in Iran's with very high seismic zones.Furthermore, as the conditions of a site have a significant effect on the characteristics and frequency content of the strong ground motion records, the ground motions were selected to ensure that the average of the spectrum resultant closely matches the design spectrum at all periods (Figures 5 and 6).Based on this, 15 earthquake records for both near-and far-field subjected to forward directivity have been considered for the evaluation of nonlinear timehistory.Near-and far-field earthquakes which were calculated on type 3 soil have been recorded in the maximum from 10 to 100 km away from the fault, respectively.e magnitudes of near-and far-field earthquakes ranged from 6.53 to 6.93 moment magnitude scale and 6.4 to 7.5 moment magnitude scale, respectively.Tables 2 and 3 demonstrate the seismographs and their related characteristics.

Evaluation of Seismic Response of Structures
e ground motions were scaled so that the average value of their square root of the sum of the squares (SRSS) Advances in Civil Engineering spectra did not fall below 1.4 times the Standard Design-Spectra for periods of 0.2T second to 1.5T seconds, where T is the fundamental period of vibration [17].Figure 7 shows the elastic response spectra for 5% damping of these selected near-eld ground motions, as well as the process of scaling for the 8-story building.In OpenSees, three types of sti ness matrix can be considered for the Rayleigh damping command: current sti ness matrix, initial stiness matrix, and committed sti ness matrix.In the inelastic analysis, the "committed sti ness matrix" should be employed.
Totally, in the present research, 120 nonlinear time history analyses were performed according to the 30 selected records and the number of considered buildings.
Basic strength det.

Advances in Civil Engineering
In this study, the total acceleration response has been evaluated.By comparing the peak oor ampli cations under the in uence of near-eld (NF) and far-eld (FF) earthquakes, it was determined that, in the NF shocks with forward directivity in the 3-story building, peak oor ampli cations was 0.106 g, under the #Record11 record; in the   Advances in Civil Engineering 5-story building, it was 0.067 g, which is the location on the fifth floor under the #Record10 record; for the 8-story building, it was 0.506 g, which is located on the seventh floor under the #Record11 record; finally, in the 20-story building, it was 1.818, which is located on the third floor under the #Record10.On the other hand, in each of the four structures under the influence of FF earthquakes, the peak floor amplification values of the floors amounted to 0.067 g, 0.068 g, 0.669 g, and 0.557 g.For a more accurate evaluation, a comparison of the average value of the peak floor amplifications of stories was made (Table 4).
By investigating the maximum roof displacement subjected to far-and near-field earthquakes, we found that nearfield earthquakes including forward directivity in the 3-story building resulted in the maximum displacement in the roof (0.74 mm).In the 5-story building, near-field earthquakes caused a 0.80 mm displacement, which is 1.73 times greater than the displacement subjected to the vertical component of far-field earthquakes.is parameter can also be seen in 8story building with the corresponding values of 0.96 mm for near-field and 0.62 mm for far-field earthquakes.At the end, the maximum roof displacement in the 20-story building with the corresponding values of 0.817 mm for near-field and 0.556 mm for far-field earthquakes.
Table 4 shows a comparison of the maximum roof displacements by the influence of far-and near-field earthquakes.Figure 8 shows the graphs related to the maximum displacement of the stories under the effect of near-and far-field earthquakes.Furthermore, for a more accurate investigation, the results of a comparison of the average roof displacements are given in Table 4.
From the results of the analysis shown in Table 5, the maximum axial forces in the 3-story structure subjected to near-field earthquakes were by 13% greater than those same forces subjected to far-field earthquakes.In the 5-story structure, the axial forces in the columns in both records of far-and near-field earthquakes were almost equal.In addition, the maximum axial force produced in the 8-story structure under the effect of near-field earthquakes was by 22% lower than that subjected to far-field earthquakes.Furthermore, in the 20-story structure, the maximum axial force subjected to near-field earthquakes was by 26% higher than that subjected to far-field earthquakes.
As can be seen from the results shown in Table 6, the ratio of the maximum moment subjected to vertical component of near-field earthquakes to the maximum moment generated under the effect of vertical component of far-field earthquakes in all four structures (3-, 5-, 8-, and 20-story) was 1.07, 0.96, 0.77, and 1.08, respectively.
From the results shown in Figure 9 and Table 7, it can be clearly observed that the maximum shear force generated in 3-and 8-story buildings subjected to the vertical component of near-field earthquakes was by 6% and 24% lower than farfield earthquakes, respectively, and in 5-and 20-story buildings subjected to the vertical component of near-field earthquakes was by 7% and 31% higher than far-field earthquakes, respectively.In the end, the moment of beams has investigated, and the result is shown in Table 8.
Finally, the results of this paper are summarized based on the comparison methodology in references [26,27].Tables 9 and 10 show that the peak vertical floor acceleration (named as PFAv) may exceed the peak vertical ground acceleration (named as PGAv).e results demonstrate that the ratio of PFAv/PGAv in 3-, 5-, 8-, and 20-story buildings under near-field records is 1.79, 1.27, 3.17, and 24.68, respectively.Moreover, this ratio for those buildings subjected to far-field records is 3.30, 4.69, 25.88, and 25.26.

Conclusions
e present study has evaluated the seismic behavior of special steel moment frames of 3-, 5-, 8-, and 20-story buildings subjected to the vertical components of far-and near-field earthquakes.According to the classification of the HAZUS-MH MR5 [16] instruction, 3-, 5-, 8-, and 20-story buildings are categorized as low-, middle-, and high-rise buildings.From the results of the nonlinear time history analysis for the models studied, the following conclusions can be drawn: (i) One of the major elements in evaluating the seismic behavior of structures is known as displacement.
is study shows that the amount of forced displacement to the structure under the effect of the    Advances in Civil Engineering     12 Advances in Civil Engineering near-field earthquake is greater than the amount if that under the effect of the far-field earthquake.(ii) By investigating the structures analysis results, it can be observed that the average value of the maximum axial force in the columns of 3-, 8-, and 20-story structures under the effect of the near-field earthquake is 5%, 4%, and 38% greater than their values under the effect of the far-field earthquake, respectively.However, this value for the 5-story structure is almost the same in both situations.(iii) e ratios of the average value of the maximum moments in the columns subjected to near-and farfield earthquakes in 3-, 5-, 8-, and 20-story structures were 1.03, 0.98, 1.03, and 1.33 respectively.(iv) Regarding the assessment of the generated shear force on the buildings, it would be valid to claim that Advances in Civil Engineering the average of maximum created shear force in all structures (3-, 5-, 8-, and 20-story) subjected to the near-field earthquake was higher than the far-field one with the results of 10%, 5%, 14%, and 38%, respectively.

Figure 4 :Figure 5 :
Figure 4: Velocity-time history of vertical and horizontal components of near-eld earthquake with the e ect of forward directivity.

Table 1 :
Sections of 3-, 5-, and 8-story structures.belowsyntax is used for the position of columns and beams in the result of analysis (Table8).C * ij is the code for location of columns results.i number of stories.B * ik is the code for location of beams results.j number of columns from the left of structures.k number of spans from the left of structures. e

Table 4 :
Comparison of the average value of the peak floor amplification of stories and roof displacement subjected to near-and far-field earthquakes.

Table 5 :
Comparison of the maximum axial force of columns in 3-, 5-, 8-, and 20-story buildings subjected to near-and far-field earthquakes.

Table 6 :
Comparison of the maximum moment of columns in 3-, 5-, 8-, and 20-story buildings subjected to near-and far-field earthquakes.

Table 9 :
Ratios of PFAv/PGAv for the near-field earthquakes.

Table 10 :
Ratios of PFAv/PGAv for the far-field earthquakes.