1.     Introduction

Earthquakes are among the most significant natural hazards humans have faced since their emergence on Earth. More than 5 million earthquake events occur each year, making it crucial to study every aspect of this phenomenon [1, 2]. A major characteristic of an earthquake that affects the induced damage and soil behavior is the distance to the quake-inducing fault. Based on the data on previous earthquakes, researchers have identified three types of quake events as near-field (within 20 km of the quake-inducing fault), mid-field (within 20–60 km of the quake-inducing fault), and far-field earthquake records (beyond 60 km of the quake-inducing fault) [3].

Near-field earthquake records are usually larger in magnitude than the far-field earthquake records. The near-field records exhibit intense pulse-like ground motions, which can be explained by the release of large amounts of energy in a short time upon faulting. This pulse-like ground motion imposes devastating amounts of energy on overlying structures at the start of the motions [4–6]. A near-field earthquake record generates higher frequencies than a far-field earthquake record because the closer distance to the source of the earthquake waves prevents the absorption of higher-frequency events, so that the resultant records contain higher frequencies than the records of far-fault areas [7–10].

Another characteristic of a near-field earthquake record is what is referred to as directivity. Pulse-like motions are particularly more pronounced in forward-directivity areas where the fault failure approaches at a velocity close to the shear-wave velocity. Another difference between the far- and near-field earthquake records is the peak vertical acceleration [11–15]. Typically, peak vertical acceleration is equal to two-thirds of the peak horizontal acceleration. However, studies on previous earthquakes have shown that the actual ratio is higher for near-fault areas and lower for the far-fault zones [16].

Very near-fault earthquake records (within 500 m of the fault) indicate substantial permanent ground displacement, which is a result of tectonic deformation of the ground in a process called the fling step. This deformation occurs during slippage along the fault plane and is therefore usually observed in the parallel component to the fault plane [17].

Considering the importance of the abovementioned topics, the present research was focused on evaluating the effect of the earthquake field on the site response with the help of equivalent linear and nonlinear methods. This evaluation included investigations of time histories of acceleration, velocity, displacement, as well as their peak values and response spectra. Records from the Bam earthquake, acquired at two different stations, were used for this purpose (Bam Station as near-field earthquake record and Ravar Station as far-field earthquake record). Despite extensive research on seismic site response and earthquake ground-motion characteristics, most previous studies have primarily focused on either near-fault ground motions, nonlinear soil behavior, equivalent linear analysis, or structural response independently. Limited attention has been given to a comprehensive comparative evaluation of near-fault and far-fault earthquakes using both nonlinear and equivalent linear approaches under identical soil conditions and real earthquake records. In particular, the combined investigation of acceleration, velocity, displacement, amplification behavior, and response spectra throughout soil depth has not been sufficiently addressed in earlier studies. Therefore, the present research aims to investigate the effects of near-fault and far-fault earthquakes on site response characteristics through nonlinear and equivalent linear analyses using real earthquake records. The study further evaluates how different seismic field conditions influence amplification behavior, spectral response, and depth-dependent ground-motion parameters, while also examining the role of soil nonlinearity in modifying seismic demand. Unlike previous investigations, this study provides an integrated assessment of seismic response characteristics together with their engineering implications for resonance behavior, structural vulnerability, and site-specific seismic design.

                                                                                                       2.     Methods

2.1.               Input Ground Motion (Bam Earthquake)

In the early morning (5:26:56 a.m. IRST) of Friday, December 26th, 2003, the city of Bam, Iran, was hit by a powerful earthquake. Fig. 1 shows the horizontal component of the studied earthquake for the Bam and Ravar Stations. As seen in the figure, the record at Bam Station (near-field) exhibits a peak horizontal acceleration of PHA = 0.777 while the corresponding figure to the Ravar Station (far-field) is PHA = 0.0126.

Figure 1. Horizontal acceleration records for the Bam earthquake at: a) Ravar Station; b) Bam Station.

Fig. 2 exhibits velocity records for the Bam and Ravar Stations. As observed, the record for the Bam Station is clearly pulse-like at the start of the ground motion, while the record for Ravar Station does not exhibit such pulses.

Figure 2. Horizontal velocity records for the Bam earthquake at: a) Ravar Station; b) Bam Station.

As explained in the Introduction, near-field earthquake records exhibit directivity. Fig. 3 indicates this fact. As seen in this figure, the component  of the horizontal record at Bam Station exhibits some pulses that are almost attenuated in the component

Figure 3. Horizontal acceleration records for the Bam earthquake: a) component L; b) component T.

Fig. 4 shows the vertical acceleration of the studied earthquake for the Bam and Ravar Stations. As seen in the figure, the record at Bam Station exhibits a peak vertical acceleration of PVA = 0.994, while the corresponding figure to the Ravar Station is PVA = 0.006088 Moreover, the ratio of the peak vertical-to-horizontal acceleration was seen to be 1.28 (> 2/3 = 0.666) at Bam Station and 0.48 (< 2/3 = 0.666) at Ravar Station.

Figure 4. Vertical acceleration records for the Bam earthquake at: a) Ravar Station; b) Bam Station.

Fig. 5 indicates the displacement records at Bam and Ravar Stations for the component  According to this figure, permanent displacements recorded at Bam and Ravar Stations were 2.8 and 0.0002 (~ 0) cm, respectively.

Figure 5. Horizontal displacement records for the Bam earthquake at: a) Ravar Station; b) Bam Station.

Fig. 6 depicts the response spectrum for the records at Bam and Ravar Stations for a damping ratio of 5 %. For shorter periods (i.e., higher frequencies), the response spectra of the Bam Station exhibits higher values than those for the record at Ravar Station. The opposite was observed for longer periods. In general, far-field and near-field earthquake records are the controlling factors for the structures of long and short periods, respectively.

Figure 6. Response spectrum for a damping ratio of 5 %.

2.2.               Modeling

In order to evaluate the site effect, Fig. 7 was considered as the base model for the soil layers. Four reference points (A, B, C, and D) were considered at the interfaces of successive layers, and the results were studied at these reference points.

Figure 7. Characteristics of soil layers.

In this research, the effects of the earthquake and the soil were evaluated via two approaches, namely equivalent linear and nonlinear methods. The equivalent linear method uses linear properties for the elements. Obtained as average values over dynamic motion, these properties then remain constant during the ground motions. Accordingly, the phenomena that are driven by interactions among multi-frequency components encountered in a nonlinear material are actually omitted in an equivalent linear analysis. The equivalent linear method provides no information on irreversible deformation and permanent changes, as it barely models the vibrational motions. The so-called plastic flow is inappropriately modeled in the equivalent linear method [18–21].

In contrast, the nonlinear method can follow any predetermined nonlinear behavior of the material. Applying nonlinear rules for the material, mixing of different multi-frequency components can be naturally captured, and irreversible deformations and other permanent changes can be automatically modeled. Although this methodology can follow any stress-strain relation, its results are highly sensitive to the details of the constitutive models used [18–22].

Different steps of modeling by the nonlinear method in the PLAXIS software include general setting, geometry design, application of boundary conditions, definition of material properties, generation of element grids, establishment of initial conditions, and processing the computations. In this research, the Mohr–Coulomb constitutive model was implemented, with material damping approximated by the Rayleigh damping model, which assumes proportionality between damping and material mass and stiffness. Given that calculating the Rayleigh damping ratio requires the angular frequency in two vibration modes, the angular frequencies were calculated by modal analysis in the Abaqus software.

Modeling by the equivalent linear method in the Deepsoil software goes through 5 steps: (1) configuring the analysis, (2) applying the properties of the soil layers and bedrock, (3) determining the input ground motion, (4) analyzing the model, and (5) producing the results.

The most important part of an equivalent linear analysis is the proper choice of the diagrams of shear modulus and damping ratio, which shall be based on the studied soil layering.

                                                                                   3.     Results and Discussion

3.1.               Acceleration

Figs. 8 and 9 illustrate the time histories of acceleration produced by the nonlinear and equivalent linear methods, respectively, at the reference points under the influence of near-field and far-field earthquake records. As can be seen, the magnitude of the acceleration time history increases as one moves toward the surface. In general, it can be inferred that, given the lower shear-wave velocity and density of the material on the surface compared to the underlying materials and ignoring the damping and propagation decay effects, the principle of the conservation of elastic energy implies that the flow of energy shall remain unchanged, and this explains that the reduction in the shear-wave velocity and density of the soil tends to increase the magnitude of the associated ground motions. Moreover, when the earthquake waves reach the surface, a significant portion of their energy is reflected back to the crust, so that parts of the ground surface are simultaneously affected by the upward- and downward-propagating waves [23]. These two reasons can explain the increase in the ground motion from the bedrock to the ground surface. Of course, one should further consider the fundamental frequencies of the site and the ground motion with a focus on possible resonance.

As can be seen from the results, the predicted increase by the equivalent linear method exceeds that by the nonlinear analysis. Indeed, the linear nature of the equivalent linear method leads to unreal resonance. It is further clear that the acceleration at the ground surface is higher in a near-field earthquake record than in a far-field earthquake record. This can be attributed to the attenuation of ground motion waves as one moves farther from the earthquake source. Another observation is that the time history of acceleration for a near-field earthquake record contains higher frequencies than a far-field earthquake record because the distance from the source of earthquake energy is insufficient to damp high-frequency events.

Figure 8. Time history of acceleration at reference points under the influence of a near-field earthquake record (Bam Station): a) nonlinear analysis; b) equivalent linear analysis.

Figure 9. Time history of acceleration at reference points under the influence of a far-field earthquake record (Ravar Station): a) nonlinear analysis; b) equivalent linear analysis.

Fig. 10 shows the Peak Horizontal Acceleration (PHA) as a function of depth for the near-field and far-field earthquake records using the equivalent linear and nonlinear analyses. As is evident from the figure, the peak acceleration from the equivalent linear analysis is higher than that from the nonlinear method. Indeed, with the equivalent linear methodology, the linear nature of the problem tends to exaggerate the result. Additionally, the deviation of the obtained PHAs from the nonlinear and equivalent linear methods was greater for the near-field earthquake record than for the far-field earthquake record. This is linked to the fact that the bedrock motion amplitude is larger in a near-field earthquake record (because of a shorter offset to the source of the earthquake) than in a far-field earthquake record. In fact, the motion of the bedrock dampens as one moves farther from the earthquake source, due to the effect of damping. As the bedrock acceleration increases, deformation of the soil layers increases, thereby intensifying the damping phenomenon and reinforcing the nonlinear behavior of the soil. Accordingly, the deviation of the estimated PHAs by the nonlinear and equivalent linear methods is minimized in far-field earthquake records where the bedrock acceleration is small.

Figure 10. PHA as a function of depth for: a) far-field analysis; b) near-field analysis.

Fig. 11 indicates the amplification factor as a function of depth for near-field and far-field earthquake records, as approximated by the equivalent linear and nonlinear analyses. The difference in the results of the two methods is even clearer than that for the PHA. In particular, for the near-field earthquake records, the amplification at the ground surface was approximated at 3.7 and 1.8 by the equivalent linear and nonlinear methods, respectively. The corresponding figures for the far-field earthquake records were 3.8 and 3.1, respectively. That is, the deviation was as wide as 51 % for the near-field earthquake record but as low as 22 % for the far-field earthquake record.

Figure 11. Amplification factor as a function of depth.

3.2.               Velocity

Velocity time histories provide an alternative insight into an earthquake event. Figs. 12 and 13 show velocity time histories for the reference points using the nonlinear and equivalent analyses under the influence of near-field and far-field earthquake records. The velocity time history is typically obtained by integrating the acceleration time history. The integration, however, tends to produce smooth and filtered outputs. This is why you can see that the velocity time history exhibits fewer high-frequency events than the acceleration time history [23].

Fig. 12 suggests that the velocity time history resulting from the near-field earthquake record exhibits sharply pulse-like motions. In contrast, Fig. 13 demonstrates that the velocity time history resulting from the far-field earthquake record lacks such pulses. This can be explained by the release of large amounts of energy in a short time upon faulting. That is, the short time of release is less than enough for such a vast amount of energy to spread over the entire time history. A comparison between the results of the nonlinear and equivalent linear analyses demonstrates that the amplitude of the velocity time history obtained from the nonlinear analysis is smaller than that from the equivalent linear analysis.

Figure 12. Velocity time histories at different reference points under the influence of the near-field earthquake record (Bam Station) from: a) nonlinear analysis; b) equivalent linear analysis.

Figure 13. Velocity time histories at different reference points under the influence of the far-field earthquake record (Ravar Station) from: a) nonlinear analysis; b) equivalent linear analysis.

Peak horizontal ground velocity (PHGV) is another parameter used to describe the amplitude of ground motions. The fact that the velocity is less sensitive to high-frequency components of the ground motions makes the PHGV at moderate frequencies a more accurate measure of ground motion amplitude than the peak horizontal ground acceleration (PHGA). For the structures or facilities that are sensitive to moderate frequencies (e.g., mid-rise or flexible structures, mid-span bridges, etc.), the PHGV is a more appropriate parameter for damage assessment, as compared to the PHGA.

Fig. 14 depicts PHGV as a function of depth for the near-field and far-field earthquake records from the equivalent linear and nonlinear analyses. As seen, the equivalent linear method generally approximates higher PHGVs than the nonlinear method, with both equivalent linear and nonlinear methods producing higher PHGVs for the near-field earthquake record compared to the far-field earthquake record. This can be explained by the fact that, in a near-field earthquake record, the shorter offset to the epicenter implies that the bedrock motions are of larger amplitudes than in the far-field earthquake record. With increasing bedrock acceleration, soil layer deformations increase, thereby contributing to the nonlinear behavior of the soil. Therefore, in far-field earthquake records, the bedrock acceleration is usually low, the resulting strains at the soil level are small, and the PHGVs produced from the equivalent linear and nonlinear methods are very close to one another.

Figure 14. PHGV as a function of depth for; a) far-field earthquake record; b) near-field earthquake record.

3.3.               Displacement

The application of displacement time histories for characterizing earthquake-induced ground motions is less common than the acceleration and velocity time histories [23]. Figs. 15 and 16 show displacement time histories for the reference points, as obtained from the nonlinear and equivalent linear analyses on the near-field and far-field earthquake records. A common practice for obtaining the displacement time history is to integrate the velocity time history. The integration has some smoothing and filtering effects. Therefore, as can be seen in the figures, the displacement time history exhibits fewer high-frequency events than the acceleration and velocity time histories.

Another point to note is that the nonlinear analysis produces some permanent displacement, while the equivalent linear analysis does not predict such a permanent displacement and ends up with zero displacement at the end of the motion. This is linked to the elastic nature of the equivalent linear method that ignores the generation, redistribution, and elimination of pore water pressure, thereby producing zero permanent deformation. A comparison of the nonlinear and equivalent linear methods indicates that the displacement time history approximated by the nonlinear analysis exhibits smaller amplitudes than the equivalent linear analysis.

Figure 15. Displacement time histories for the reference points under the influence of near-field earthquake record (Bam Station) using: a) nonlinear analysis; b) equivalent linear analysis.

Figure 16. Displacement time histories for the reference points under the influence of far-field earthquake record (Ravar Station) using using: a) nonlinear analysis; b) equivalent linear analysis.

Peak horizontal ground displacement (PHGD) is a measure of characterizing ground motion amplitudes. The PHGD is associated with motion components of an earthquake at lower frequencies. As far as ground motion evaluation is concerned, the PHGD is a less common measure than the PHGV and PHGA. Nevertheless, the damage induced to highly soft structures is directly proportional to this parameter.

Fig. 17 shows PHGD versus depth for near-field and far-field earthquake records, as obtained from equivalent linear and nonlinear analyses. The figure suggests that the equivalent linear method generally ends up with higher PHGD than the nonlinear method. Moreover, the deviation of PHGD between the equivalent linear and nonlinear methods is wider for the near-field earthquake records compared to the far-field earthquake records. This can be attributed to the fact that, in a near-field earthquake record, the shorter offset to the epicenter implies that the bedrock motions are of larger amplitudes than in the far-field earthquake record. With increasing bedrock acceleration, soil layer deformations increase, thereby contributing to the nonlinear behavior of the soil. Therefore, in far-field earthquake records, the bedrock acceleration is usually low, the resulting strains at the soil level are small, and the PHGDs produced by the equivalent linear and nonlinear methods are very close to one another.

Figure 17. PHGD as a function of depth for: a) far-field earthquake record; b) near-field earthquake record.

For a better comparison of the results, PHGA, PHGV, and PHGD, together with their corresponding times at reference points, are listed in Table 1. These results imply that the soil layers can change the earthquake amplitude characteristics. The equivalent linear produces higher peak values of the amplitude parameters than the nonlinear method. Moreover, the deviation between the results of the two methods is greater for the near-field earthquake than for the far-field earthquake, which can be explained by the larger amplitude of the bedrock motion and the resultant nonlinear behavior of the soil.

Table 1. Motion amplitude characteristics at reference points.

Displacement

Velocity

Acceleration

Depth

(s)

(cm)

(s)

(cm/s2)

(s)

(g)

(m)

2.70

28.87

3.11

88.47

2.65

0.79

35

A

Equivalent linear

Near-field

2.71

33.45

3.30

147.99

5.60

1.80

25

B

3.57

61.30

3.25

280.86

3.58

2.13

10

C

3.60

74.26

3.32

316.71

2.95

2.94

0

D

2.70

28.87

3.11

88.47

2.65

0.79

35

A

Nonlinear

2.75

27.34

3.16

88.98

5.66

1.08

25

B

2.85

20.89

3.26

90.11

8.62

1.25

10

C

3.00

22.52

3.21

111.68

9.02

1.49

0

D

30.69

1.28

21.19

6.33

23.01

0.050

35

A

Equivalent linear

Far-field

30.65

1.01

23.31

4.31

24.11

0.033

25

B

30.50

0.59

23.37

1.65

18.46

0.017

10

C

30.39

0.53

30.00

1.71

15.38

0.013

0

D

32.78

0.58

27.91

3.85

17.70

0.040

35

A

Nonlinear

30.52

0.50

30.21

2.00

18.27

0.022

25

B

30.40

0.53

17.35

1.80

17.43

0.021

10

C

30.39

0.53

30.00

1.71

15.38

0.013

0

D

3.4.               Response Spectrum

The response spectrum describes the maximum response of a one-degree-of-freedom (1-DoF) system to a specific input motion as a function of natural frequency or natural period and damping ratio of the system. The response spectrum is an appropriate instrument for evaluating the maximum response of a 1-DoF system to an earthquake. The equation of motion for a 1-DoF structure under an earthquake stimulation is expressed as follows:

                                                    (1)

In which  is the natural angular velocity of the structure    is the ground acceleration,  is the damping ratio, and  is the displacement of a 1-DoF system. In order to plot the response spectrum, the equation of motion was solved for different natural frequencies, followed by obtaining the maximum of the response spectrum. In general, the response spectra include acceleration, velocity, displacement, pseudo-velocity, pseudo-acceleration, and pseudo-displacement, each of which describes the structural behavior in a particular way. For instance, the displacement spectrum provides information for calculating peak internal forces and deformation, the pseudo-velocity response spectrum is, however, associated with the maximum strain energy, and the pseudo-acceleration response spectrum is related to the lateral forces applied to the structure. The relationships among the displacement, pseudo-acceleration, and pseudo-velocity response spectra are expressed in the following:

                                                                          (2)

                                                                          (3)

where  is the natural angular velocity of the structure,  is the displacement response spectrum,  is the pseudo-velocity response spectrum, and  is the pseudo-acceleration response spectrum [24–29].

Figs. 18 and 19 present response spectra of acceleration, velocity, and displacement, as obtained from the nonlinear and equivalent linear analyses for the near-field and far-field earthquake records, respectively. As can be seen in the figures, the spectra produced by the equivalent linear method exhibit larger values than those by the nonlinear method. This can be attributed to the elastic nature of the equivalent linear method, which results in higher amplification.

Compared to the velocity and displacement response spectra, the acceleration response spectrum exhibits peak values in shorter periods. This finding indicates that the low-rise rigid structures (with short natural periods) are sensitive to acceleration, while moderate- and long-period structures are more sensitive to velocity and displacement, respectively.

Comparing the spectra obtained from the near-field and far-field earthquake records, it was found that the maximum spectral amplitude for the near-field earthquake occurred in relatively shorter periods than that in the far-field earthquake. Indeed, near-field earthquake records exhibit higher frequency contents thanks to their shorter distance to the source of energy (no damping), while far-field earthquake records lack high-frequency contents due to the damping effect. This suggests that the near-field earthquakes impose further damage to highly stiff and low-rise (short-period) structures, while far-field earthquakes can induce more damage to less stiff high-rise (long-period) structures.

Figure 18. Response spectra for the near-field earthquake record (Bam Station): a) acceleration; b) velocity; c) displacement.

Figure 19. Response spectra for the far-field earthquake record (Ravar Station): a) acceleration; b) velocity; c) displacement.

Different response spectra (displacement, pseudo-velocity, and pseudo-acceleration) provide valuable information on the impact of earthquakes on structures. Given one of the mentioned response spectra, the other two can be derived. According to Equations (2) and (3), one can compile the spectra to come up with a mixed spectrum. Such a triple spectrum contains information about all of the three mentioned spectra. The horizontal axis of this spectrum indicates the period on a logarithmic scale, while the vertical axis refers to the pseudo-velocity values on a logarithmic scale. The bisectors of the first and second quarters indicate the axes of the displacement and pseudo-acceleration on logarithmic scales, respectively. In terms of the period, the triple response spectrum can be divided into three segments: short-period segment (0–0.5 sec) that is sensitive to the acceleration, moderate-period segment (0.5–3 sec) that is sensitive to velocity, and long-period segment (>3 sec) that is sensitive to displacement. Fig. 20 shows the triple response spectrum. As can be seen in this figure, the equivalent linear method produces higher results than the nonlinear method in almost all segments of the period. Moreover, the deviation of the results of the two methods is smaller for the far-field earthquake records.

Figure 20. Triple response spectrum.

3.5.               Natural Frequency

The standard spectral ratio (SSR) is used to obtain the dominant frequency of the site. This parameter is calculated as the ratio of the Fourier amplitude spectrum of the time history of the soil to the time history of nearby bedrock subjected to the same earthquake and motion component [24–29]. The frequencies corresponding to the first and second peaks along the SSR graph indicate the first-mode (dominant) and second-mode frequencies, respectively [23]. Fig. 21 shows the amplification factor versus frequency. As is evident from this figure, the first-mode and second-mode frequencies of the studied site were approximated at 0.823 and 2.18 Hz, respectively.

Figure 21. Amplification factor versus frequency.

3.6.               Engineering Implications for Seismic Design

The results of this study highlight the critical importance of considering the characteristics of earthquake field conditions in seismic design, particularly for structures located near active faults. The analyses demonstrated that near-fault ground motions generate significantly higher seismic demands due to their pulse-like behavior, high-frequency content, and larger acceleration amplitudes. Consequently, conventional design approaches based solely on equivalent linear assumptions or generalized design spectra may not accurately capture the actual seismic demand imposed on structures in near-fault regions.

The findings indicate that short-period and stiff structures are especially vulnerable to near-fault earthquakes because the peak spectral responses of these motions occur at relatively higher frequencies. In contrast, far-fault earthquakes tend to impose greater demands on flexible and long-period structures. Therefore, the compatibility between the dominant frequency of the site, the frequency content of the earthquake motion, and the natural period of the structure should be explicitly evaluated during the design stage to avoid resonance-induced amplification.

Another important implication of this research is the significant discrepancy observed between nonlinear and equivalent linear site response analyses under strong near-fault motions. Equivalent linear analysis generally overestimates amplification factors and peak response parameters because it cannot fully represent strain-dependent soil nonlinearity, stiffness degradation, hysteretic damping, and irreversible deformation mechanisms. As the intensity of ground motion increases, soil nonlinearity becomes more pronounced, particularly in shallow soft deposits, making nonlinear analysis more reliable for estimating realistic seismic demand.

From a practical engineering perspective, the results suggest that nonlinear site response analysis should be considered mandatory for critical facilities and essential infrastructures located in near-fault seismic zones, including hospitals, bridges, tunnels, dams, nuclear facilities, transportation networks, and high-importance buildings. For ordinary structures located in moderate seismic regions, equivalent linear analysis may still provide acceptable preliminary estimations when soil strains remain relatively small.

The obtained results also emphasize the necessity of incorporating site-specific seismic response analysis into performance-based seismic design frameworks. Since local soil conditions substantially modify acceleration, velocity, displacement, and spectral characteristics of ground motions, relying exclusively on code-based generalized spectra may lead to either unsafe or overly conservative designs. Site-specific analyses can improve the estimation of structural demand, story drift, foundation response, and seismic energy transfer mechanisms.

Furthermore, the observed amplification patterns suggest that seismic codes may require additional modification factors for near-fault regions to account for pulse-type motions and strong nonlinear soil behavior. The results also indicate that evaluating only peak ground acceleration (PGA) is insufficient for seismic damage assessment. Parameters such as peak ground velocity (PGV), peak ground displacement (PGD), frequency content, and spectral characteristics should also be considered because different structural systems exhibit different sensitivities to acceleration-, velocity-, and displacement-dominated motions.

Finally, this study demonstrates that accurate seismic hazard assessment requires simultaneous consideration of earthquake source characteristics, wave propagation effects, local soil conditions, and structural dynamic properties. Neglecting any of these interacting mechanisms may lead to inaccurate prediction of seismic demand and structural vulnerability, especially in near-fault environments where nonlinear soil behavior and pulse-like ground motions govern the seismic response.

                                                                                                  4.     Conclusions

In this research, the impacts of near-field and far-field earthquake records on the site response were evaluated by nonlinear and equivalent linear methods utilizing the PLAXIS and Deepsoil software tools. The analyses included the time histories of acceleration, velocity, and displacement, as well as their peak values and response spectra. A summary of the findings is presented in the following:

1.    Near-fault earthquakes produce stronger nonlinear soil behavior than far-fault motions.

2.    Near-fault motions shift peak response spectra toward higher frequencies, making short-period structures more vulnerable, whereas the opposite trend is generally observed for far-fault earthquakes, which tend to impose greater seismic demand on long-period and flexible structures due to their relatively lower-frequency content.

3.    The results demonstrate that equivalent linear analysis may significantly overestimate seismic amplification under strong near-fault motions due to its inability to fully capture nonlinear soil behavior. Therefore, nonlinear analysis provides a more reliable estimation for seismic assessment in near-fault regions. For ordinary structures located in moderate seismic regions, equivalent linear analysis may still provide acceptable preliminary estimations when soil strains remain relatively small.

4.    The discrepancy between equivalent linear and nonlinear analyses is substantially greater for near-fault records. This can be explained by the larger amplitude of ground motions in near-field earthquake records, which leads to extended damping and nonlinearity of the soil behavior.

5.    From an engineering perspective, the findings of this study emphasize the necessity of site-specific seismic analysis during the design stage of structures located in seismic zones. Furthermore, nonlinear site response analysis is strongly recommended for important structures and infrastructures in near-fault regions to achieve a more realistic estimation of seismic demand and potential structural damage.