Seismic Response Analysis of a Six-Story Building in Sofia Using Accelerograms from the 2012 Mw5.6 Pernik Earthquake

Abstract

On 22 May 2012, a magnitude Mw 5.6 earthquake struck the Pernik region of western Bulgaria, causing structural damage in nearby cities, including Sofia. This study assesses the seismic response of a six-story reinforced concrete building in central Sofia, utilizing real accelerogram data recorded at the basement (SGL1) and sixth floor (SGL2) levels during the earthquake. Using the Kanai–Yoshizawa (KY) model, the study estimates inter-story motion and assesses amplification effects across the structure. Analysis of peak ground acceleration (PGA), velocity (PGV), displacement (PGD), and spectral ratios reveals significant dynamic amplification of peak ground acceleration and displacement on the sixth floor, indicating flexible and dynamic behavior, as well as potential resonance effects. The analysis combines three spectral techniques—Horizontal-to-Vertical Spectral Ratio (H/V), Floor Spectral Ratio (FSR), and the Random Decrement Method (RDM)—to determine the building’s dynamic characteristics, including natural frequency and damping ratio. The results indicate a dominant vibration frequency of approximately 2.2 Hz and damping ratios ranging from 3.6% to 6.5%, which is consistent with the typical damping ratios of mid-rise concrete buildings. The findings underscore the significance of soil–structure interaction (SSI), particularly in sedimentary basins like the Sofia Graben, where localized geological effects influence seismic amplification. By integrating accelerometric data with advanced spectral techniques, this research can enhance ongoing site-specific monitoring and seismic design practices, contributing to the refinement of earthquake engineering methodologies for mitigating seismic risk in earthquake-prone urban areas.

1. Introduction

Bulgaria is situated within the larger Balkan seismic belt, where active faulting and tectonic movements are common due to the convergence between the Eurasian and African tectonic plates. The country is among the European countries with the highest seismic hazard. The strongest earthquake in continental Europe occurred in southwestern Bulgaria in 1904, with a magnitude of M = 7.8. The capital city of Bulgaria, Sofia, is situated in one of the country’s most active seismic zones and has experienced strong earthquakes, including a M = 6.8 earthquake in 1858, which produced ground motions with an intensity of up to 9 on the MSK scale [1,2,3,4,5]. The city faces significant earthquake risks, so assessing structural response is critical. An earthquake with a magnitude of Mw = 5.6 (Ms = 5.8) struck Western Bulgaria on 22 May 2012, at 03:00:33 local time (00:00:33 UTC), 25 km southwest of Sofia (Figure 1). The earthquake hypocenter had a depth of 10 km, with epicenter coordinates of 42.66° N and 23.01° E. The maximum macroseismic effects in Pernik were classified as intensity VII–VIII on the MSK-64 scale [6,7,8,9]. The earthquake caused significant damage, including structural damage to buildings, and resulted in several injuries; fortunately, there were no reported fatalities. The event also triggered increased public awareness of seismic risks in the region, prompting discussions on better preparedness and monitoring of seismic activity in the future. This shallow earthquake was strongly felt and instrumentally recorded across the Balkan region, including Greece, North Macedonia, Turkey, and Romania [10].

Developing earthquake-resistant building codes requires seismic engineering studies based on real-world records of strong ground motions. To calculate seismic parameters needed for assessing the dynamic response of structures being built or designed, making realistic selections and processing input records of strong motions during an earthquake event is necessary. Researching large ground motions is crucial in seismic engineering and risk assessment [11,12]. The seismic risk in densely populated urban areas near seismic sources is very high [13,14,15,16]. Monitoring strong ground motions in such areas is crucial for obtaining accurate data on the actual response of buildings, which can be used to develop effective seismic design codes and informed prevention policies.

Local geological and tectonic settings can significantly influence the duration and intensity of strong ground motions, especially for shallow crustal earthquakes [17,18,19]. Factors such as the structure of stratigraphic soil layers, proximity to the seismic source, topographic effects, and the presence of sedimentary basins, such as the Sofia Graben, can, for example, amplify seismic responses [20]. These conditions underscore the importance of tailored monitoring and analysis in effectively addressing site-specific risks.

In the early 1970s, Kanai and Yoshizawa (KY) proposed a simple formula for computing the response of a building [21]. The developed model integrates stochastic processes and spectral analysis to evaluate the behavior of structures subjected to seismic forces using accelerometric data. The KY formula is based on the spectral representation of ground motion and structural response modeling, which links ground motion to the dynamic response of structures through transfer functions. Recent studies have revisited and expanded the KY formula, demonstrating its continued relevance in structural engineering. Ebrahimian et al. [22] revisit the KY formula for predicting responses based on recorded responses from 54 instrumented buildings at both the base and top floors (or roofs). Despite its simplifications, the KY formula is effective for many structures and motions, offering a helpful tool for earthquake engineering and post-event building response assessments. The prediction error increased for buildings with non-linear responses or irregularities but remained within practical margins. The error is attributed to foundation rocking, structural irregularities, and deviations from the 1D wave propagation assumption [22].

Many researchers have introduced and applied microtremor analysis to determine the dynamic characteristics of both soil and structures [23,24,25,26,27,28]. Nakamura’s technique, when applied to buildings—considered as wave propagation media (which differ substantially from soils)—models the structure as an equivalent system of virtual linear systems. In this approach, the horizontal components of the recorded signal are treated as outputs, while the vertical component serves as the input. This setup corresponds to a classic “black box” problem, in which the internal characteristics of a system are inferred from its input and output signals. The H/V spectral ratio yields the spectral features of the transfer function or the spectral response of this “black box.” Nakamura’s method [29] establishes a direct relationship between the transfer function’s characteristics and the amplitude of possible shear deformations within the building. Consequently, resonance peaks in the transfer function indicate the presence of resonant shear deformations at specific frequencies thereby marking frequency ranges with increased susceptibility to damage under external excitation.

The use of the Floor Spectral Ratio (FSR) method to identify the predominant (natural) frequency of a structure was proposed by Gosar [30]. It is a helpful tool in seismic engineering that provides insight into how different parts of a building amplify or attenuate earthquake energy, revealing crucial dynamic characteristics for safety, design, and monitoring. FSR employs the spectral ratio of the horizontal component (usually acceleration or velocity of one floor to another) of the structure’s microtremor data relative to that of the ground or free field. A peak in the FSR at a specific frequency indicates a resonance or mode shape, which is critical for assessing building vulnerability.

Jeary [31] was one of the first researchers to investigate damping in high-rise buildings using the Random Decrement Method (RDM). Subsequent studies by Davenport and Hill-Carol [32], Lagomarsino [33], Tamura et al. [34], Kareem and Gurley [35], and Arakawa and Yamamoto [36,37], as well as Satake et al. [38], applied RDM and other techniques to estimate structural damping ratios. Iiba et al. [39] demonstrated that the damping ratio of a structure can be calculated from microtremor data using the RDM technique. Herak [23,24] applied RDM, non-parametric, and spectral analyses to determine natural frequencies and damping ratios, showing that the parameters derived from ambient vibrations are stable. Farsi et al. [26] further confirmed that both the natural frequency and damping ratio obtained through the combined application of spectral and RDM analyses depend on the structural integrity of the building.

This study expands on previous analyses of earthquake recordings from the 22 May 2012 Pernik region earthquake, published by Hadjiyski et al. [7,8], Paskaleva and Ivanov [40,41], and Pashova et al. [20]. We analyzed two real accelerograms—three-component recordings of the 2012 Pernik earthquake at stations installed in the basement (SGL1) and on the sixth floor (SGL2) of a six-story building in the center of the Bulgarian capital, Sofia. These stations belong to the Strong Ground Motion Network of the National Institute of Geophysics, Geodesy, and Geography at the Bulgarian Academy of Sciences (NIGGG-BAS). The building is located at an epicentral distance of ~26 km from the seismic source (Figure 1). We processed accelerometric recordings using the KY, HV, FSR, and RDM approaches to assess the building’s response to the earthquake impact. Real accelerogram records from the 22 May 2012 earthquake were used to assess the dynamic response of a multi-story building. We apply three spectral methods: the Horizontal-to-Vertical Spectral Ratio (H/V) for identifying resonance frequencies, the Random Decrement Method (RDM) to determine the damping ratio (ζ), and the Floor Spectral Ratio (FSR) for calculating spectral amplitude variations between different levels. The rest of the paper is organized as follows: Section 2 describes data sets of strong ground motion and the methods used for data analysis. The results achieved are represented in Section 3 and discussed in Section 4. Finally, the main inferences and further recommendations are summarized in the last section, Section 5.

2. Materials and Methods

2.1. Site Location

On 22 May 2012, an earthquake occurred near the city of Pernik on the Meshtitsa normal fault (Figure 1) with a magnitude of Mw 5.6 and a hypocentral depth of ~10 km. It belongs to the group of slow earthquakes characterized by slower slip during rupture propagation compared to typical earthquakes [9,42,43]. Within a few hours after the main seismic event, several significant aftershocks occurred, including two notable ones with magnitudes of Mw = 4.7 and Mw = 4.2, recorded hours after the main shock (https://jaguar.emsc-csem.org/, accessed on 15 May, 2025) [9]. The duration of shaking caused by the earthquake recorded in Sofia is approximately 16 to 18 s, as referred to by Bommer and Martinez-Pereira [44]. The relatively long duration, compared to hard rock sites, is due to local site effects, such as sedimentary layers in the Sofia Graben, which cause wave amplification and resonance effects [45]. The duration is consistent with the earthquake magnitude (Mw 5.6), its depth of 10 km, and the epicentral distance of approximately 25 km. The primary damage from the 22 May 2012 earthquake and subsequent events was observed in buildings in the town of Pernik and the surrounding villages [8,10]. The main shock also affected the capital, Sofia. Immediately after the event, Radulov et al. [46] conducted a comprehensive field survey to analyze and assess the seismic source and its impact on construction sites in the area encompassing the city of Pernik, its surroundings, and the city of Sofia. Field surveys and analyses of seismic impacts on buildings revealed typical damage in massive buildings without columns and slabs, constructed in the late 1950s. Some buildings experienced partial collapses of external walls, corner collapses, separations of two adjacent walls converging at a corner, and extensive cracking in interior and exterior walls. Brick masonry houses with reinforced concrete vertical elements and/or concrete sixth-floor slabs built in recent years survived with less damage [10,41,47].

The main seismic event on 22 May 2012 and the subsequent stronger aftershocks were recorded by most National Strong Motion Network stations, which are maintained by the National Institute of Geophysics, Geodesy, and Geography at the Bulgarian Academy of Sciences (NIGGG-BAS). The location of the strong ground motion stations is, respectively, at an epicentral distance of R = 19 km for Vitosha station VTS (rock); 30 km for the NIGGG BAS station SGFI (Neogene sediments), R = 26 km for SGL1 (Neogene sediments) station, and R = 23 km for the station SBO (Neogene sediments) [9,42,43].

The building under research, the placement of the recording stations in the instrumented building, and the analytical model are shown in Figure 2.

2.2. Data

The placement of the instrumented building and the recording stations is shown in Figure 2c. From the available records in the Sofia area, we selected two three-component accelerograms: the SGL1 record was taken in the basement of the building, and the SGL2 record was taken on the sixth floor (Figure 3). The selection focused on the instrumental behavior of typical structures in the central area of Sofia. Afterward, we performed appropriate processing and analysis to determine the primary characteristics of ground motions suitable for engineering practice, which are presented below. The recordings used in this study were obtained using high-sensitivity digital accelerometers of ETNA type installed in the basement and on the top floor of the building. The duration of the strong-motion record varies depending on the station’s proximity to the epicenter and the sensitivity of the recording equipment. In general, more distant stations register shorter durations due to attenuation laws, while closer stations capture longer records that include P-wave arrival, the strong seismic shaking phase, and the coda. The signal windows used for analysis were carefully selected to exclude background noise and instrumental artifacts.

Acceleration time histories for the three orthogonal components of ground motion recorded in the basement of the building are shown in Figure 3. Significant ground accelerations occur between 6 and 15 s. Post-peak acceleration fluctuates, showing the dynamic ground response to seismic waves. These oscillations gradually decrease, indicating energy dissipation and damping. By the 40 s mark, the graph stabilizes with minor fluctuations, marking the end of major ground movement. EW (first graph) component acceleration remains relatively low initially but increases around the 5–10 s mark, where a clear seismic wave arrival is observed. The motion gradually diminishes after reaching peak amplitude, indicating energy dissipation over time. The response shows moderate intensity, with oscillations tapering off after approximately 15 s. Similarly to the EW component (upper graph) and the NS component (middle graph), the strongest motion occurs within the 5–12 s range. The amplitude is slightly different, indicating directional variation in ground shaking. The oscillation decay follows a pattern comparable to the EW component, suggesting consistent damping effects. The UD component (bottom graph) exhibits a more abrupt initial acceleration increase than the horizontal components. The peak acceleration occurs within the first 10 s, showing significant vertical shaking, which is crucial for evaluating structural response, especially for multi-story buildings. The vertical component generally has a lower amplitude than the horizontal components, but it still plays a significant role in seismic effects on structures.

The sixth-floor record of the EW component, starting around the 5 s mark (Figure 3b, first graph), exhibits significant oscillations with high amplitudes, indicating intense ground motion from primary seismic waves (P-waves). The NS component in Figure 4b exhibits a more intense and dynamic response compared to the NS component in Figure 4a, with higher acceleration peaks and larger displacements. The NS component in the basement suggests a stiffer or better-damped system, experiencing lower acceleration and smaller displacements. The NS component on the sixth floor indicates a more flexible or excitation-sensitive system with greater dynamic amplification and energy absorption. The energy input or excitation reflected in the NS component (sixth floor) is higher, while the NS component (basement) corresponds to a system with lower excitation levels or effective energy dissipation. The NS component (basement) represents a system with lower response amplitude, reduced deformation, and better damping. In comparison, the NS component (sixth floor) reflects a more dynamic, flexible system that experiences higher accelerations and displacements due to its greater sensitivity to input or lower damping efficiency.

2.3. Methods

2.3.1. Kanai–Yoshizawa Formula for Response Prediction

We follow the approach of Ebrahimian et al. [22] using the KY formula in the present study. The inter-story drifts and motion calculations for the two levels are carried out using records from the basement and six-story levels of the building located in the center of the Bulgarian capital, Sofia, during the 2012 Pernik earthquake (Figure 2a,b). The KY formula for predicting the response at any level of the building was derived by Ebrahimian et al. [22], representing the relationship between height H and the apparent velocity of vertically propagating waves V (Figure 2c). The z-axis is oriented upwards, so that at the basement z = 0, and the sixth-floor level is z = H. The incident motion at the base is assumed to be u₀ = F(t), and it is transmitted into the structure at the basement and the sixth floor, respectively [22],

$$u_{tr}\left(0^{+},t\right)=k_{tr}F\left(t\right)$$

(1)

$$u_{tr}\left(H,t\right)=k_{tr}F\left(t-{\displaystyle \frac{H}{V}}\right),$$

(2)

where k_tr is the transmission coefficient for the waves incident from the soil into the structure, and H/V is the time delay for the transmitted wave to reach the sixth floor. For the case of the studied building, depending on the soil conditions, category C is in the range V_s = 180–360 m/s, or the delay is 0.11–0.06 s [47]. Figure 2c shows a typical cantilever beam equivalent model of the analyzed building. This KY formula can be generalized to any intermediate level d (e.g., a building floor), using Equations (1) and (2).

Let d be the distance of that level from the sixth floor (0 ≤ d ≤ H). Then

$$u\left(H-d,t\right)={\displaystyle \frac{1}{2 }}[u(H,t-{\displaystyle \frac{d}{V}})+\mathrm{u}(H,t+{\displaystyle \frac{d}{V}})].$$

(3)

The derivation details can be found in Ebrahimian et al. [22].

Equation (3) shows that if the motion on the sixth floor and the apparent wave velocity V are known, the motion at any level can be computed simply as a superposition of two time shifts (one forward and one backward in time). For a cantilever uniform shear beam, V = 4 H/T₁, where T₁ is its fixed-basement fundamental period of vibration. Approximately T_sys ≥ T₁ if the soil is very stiff compared to the structure by the soil–structure system period T_sys, which we measured here from the Fourier spectrum of the sixth-floor record [22]. T_sys~T₁ can generally be estimated from the sixth-floor record only, e.g., from the zero crossings. A detailed analysis of how soil conditions in Sofia influence the seismic response of the building is outside the scope of this study. The amplification effects will be assessed by incorporating the recorded accelerogram data with soil modeling. Consequently, the motion at any level in the building can be computed approximately only from the sixth-floor record, even without the Fourier spectrum being computed.

The accelerograms were processed and analyzed using SeismoSignal v2025 and SeismoSignal 3D v2025, specialized software tools provided under a research license (https://seismosoft.com/, accessed on 24 January 2025). The programs are efficient and widely used for processing strong-motion data in earthquake engineering. Both tools are essential for refining strong-motion records, filtering noise, and improving seismic data analysis for structural assessments [48].

2.3.2. Spectral Methods

The Horizontal-to-Vertical Spectral Ratio (HVSR) method is a site response analysis technique used to estimate the fundamental resonance frequency of soil or site conditions, utilizing ambient vibrations (microtremors) or earthquake data [29]. It is beneficial for identifying site amplification effects without needing a borehole or detailed geotechnical data. For a given frequency f, the HVSR is defined as

$$HVSR\left(f\right)=\sqrt{{\displaystyle \frac{S_H\left(f\right)}{S_V\left(f\right)}}}$$

(4)

where $S_H\left(f\right)={\displaystyle \frac{1}{2}}[{\left|F_x\left(f\right)\right|}^2+{\left|F_y\left(f\right)\right|}^2$ is the average horizontal spectral amplitude (from two orthogonal components x and y), $S_H\left(f\right)={\left|F_z\left(f\right)\right|}^2$ is the vertical spectral amplitude, and F_x(f), F_y(f), and F_z(f) are Fourier amplitude spectra of ground motion in the x, y, and z directions. A clear peak in the HVSR curve corresponds to the site’s fundamental frequency, as the amplitude of the peak indicates relative amplification. The HVSR approach is useful for seismic microzonation and site classification (e.g., identifying soft vs. hard soil layers). As a non-invasive geotechnical method, it is applied for site resonance frequency identification, urban seismic hazard mapping, and input for 1D site response modeling.

Data processing to obtain the HVSR on the free field according to Equation (4) was performed as follows: the recorded time series were visually inspected to identify possible erroneous measurements and stronger transient noise. Each record was then split into 20–30 s long windows tapered with a 5% cosine function. Fast Fourier Transform (FFT) was calculated for each window in each seismometer component. The Fourier spectra were smoothed using the Konno and Ohmachi function [49] with 40 smoothing constants. HVSR was computed as the geometric average of both horizontal component spectra divided by the vertical spectrum for each window.

The floor spectra ratio (FSR) method is a technique for determining the natural and resonant frequencies of buildings, which describes the characteristics of buildings concerning earthquakes [50,51]. This ratio helps identify resonance frequencies, mode shapes, and amplification effects within the structure. For a given frequency f, the FSR is defined as

$$HFSR\left(f\right)={\displaystyle \frac{S_T\left(f\right)}{S_B\left(f\right)}},$$

(5)

where S_T(f) is the spectral amplitude (e.g., Fourier or response spectrum) at the top floor, S_B(f) is the spectral amplitude at the base (typically the ground or first floor), and f is the frequency [Hz]. The Fourier amplitude spectrum is computed for each floor using the acceleration time series

$$HFSR\left(f\right)={\displaystyle \frac{\left|F\left[a_T\right(t)\right|}{\left|F\left[a_B\right(t)\right|}},$$

(6)

where $\left|F[a_T(t)\right|$ is the Fourier transform of acceleration a(t) at time t, a_T(t), and a_B(t) are acceleration signals at the top and base floors. Peaks in FSR indicate natural frequencies or mode shapes, as a high FSR value implies strong amplification at that frequency. Any changes in FSR over time can indicate structural damage or degradation of the stiffness.

The RDM is a signal processing technique used to extract the damped natural frequency, damping ratio, and mode shape of a structure under random excitation, such as ambient vibrations or seismic events [39,52]. This method is advantageous in structural health monitoring and damage detection. It is applied to non-periodic (random) excitations, allowing for the analysis of structures without requiring knowledge of the exact forcing function. RDM analyzes a time series of response data and extracts the system’s natural frequencies and damping ratios by isolating the decaying oscillations of the system using the following equation:

$$x\left(t\right)=A.e^{-\xi {\omega }_{n}t}.\mathrm{s}\mathrm{i}\mathrm{n}({\omega }_{d}t+\varphi )$$

(7)

where A is the initial amplitude, ξ is the damping ratio (dimensionless), ω_n is the natural frequency, ω_d is the dumped angular frequency [rad/s], and ϕ is the phase angle. The method works by windowing the data around zero-crossings of the signal, then averaging the resulting signals to remove the random excitation and isolate the decaying oscillatory response. The RDM is applied for structural health monitoring to identify changes in damping or stiffness due to damage, to determine natural frequencies and mode shapes, and for damage detection.

For subsequent HVSR, FSR, and RDM analyses, the Geopsy software version 3.5.2 [53], widely used by the scientific community (www.geopsy.org, accessed on 17 March 2025), was employed.

3. Results

3.1. Parameters of Strong Ground Motion

In this study, a broad range of strong-motion parameters has been estimated and analyzed. The results from the main event records are presented in a tabulated form (see

Table 1. The main parameters of the records in the basement and on the sixth floor.

Location of the Record	Component	PGA cm/s2	PGV cm/s	PGD cm	PGV/PGA or PFV/PFA	PFA (Sixth Floor) vs. PGA (Basement)
SGL1 Basement	EW	42.62	2.97	0.96	0.07
	NS	30.26	−4.76	−1.35	0.16
	UD	21.94	1.42	−0.38	0.06
SGL2 Sixth floor	EW	87.15	−7.77	−1.57	0.09
	NS	−99.02	6.45	−1.57	0.07
	UD	46.21	1.98	0.55	0.04
SGL1 vs. SGL2	EW					2.04
	NS					3.27
	UD					2.11

). The results are discussed in light of their dependence upon the frequency content of the recorded accelerograms.

The comparison of the main parameters in the basement and on the sixth floor, as shown in Table 1, reveals that the PGA on the sixth floor exhibits significantly higher values in all components (EW, NS, and UD) compared to the basement. The PGV and Peak Floor Acceleration (PFV) values vary considerably between the basement and the sixth floor, with the sixth floor showing higher values for all components than the basement. The same tendencies are found for PGD and Peak Floor Displacement (PFD). The amplification of PFA SGL2 (sixth floor) versus PGA SGL1 (basement) shows significant value for the NS component [54]. This ratio is important for several reasons, as higher amplification ratios might indicate higher flexibility in the NS direction and more pronounced oscillations during the seismic event. The amplification ratio is a crucial parameter in earthquake engineering, enabling the assessment of a building’s seismic performance and ensuring its safety during earthquakes.

The PGV/PGA (PFV/PFA) ratio, shown in Table 1, is a measure used in earthquake engineering to describe the relationship between peak ground velocity (PGV or PFV) and peak ground acceleration (PGA or PFA). This ratio can provide insights into the frequency content of ground motion and is an essential characteristic for emergency preparedness and urban planning [55]. A higher PGV/PGA ratio indicates ground motion with more low-frequency content (SGL1), which can be more harmful to specific structures (skyscrapers, flexible bridges, masts, etc.). A high PGV/PGA ratio may lead to design strategies that mitigate the effects of low-frequency ground motion. Usually, the analysis of displacement distribution in the horizontal plane (Figure 4a,b) is neglected or underestimated, but this makes the picture more apparent regarding how different parts of the ground move during an earthquake.

The EW PGV/PGA ratio indicates higher frequency content. Values < 0.1 suggest short-period ground motion, which can be potentially damaging for stiff structures. The NS component in the base shows a more intermediate period character, which is more demanding for mid-rise structures. The vertical content remains short-term; it has less influence on large deformations but is critical for detailing. Codes such as FEMA P-1050 [56] suggest that PGV/PGA < 0.2 aligns with pulse-type or stiff-soil profiles, while values greater than 0.3 reflect long-period ground motion that is more damaging to flexible structures. Seismic ground motions near a fault, as is the case with the 2012 Pernik earthquake, are often characterized by intense velocity and displacement pulses with relatively long periods, which clearly distinguish them from typical distant-source ground motions. High-velocity pulse motions can adversely affect the seismic response of physical systems [57].

Amplification greater than 1.5× suggests significant dynamic flexibility. Eurocode 8 [58] recommends conducting acceleration checks for non-structural elements on the sixth floor when the amplification factor exceeds 1.5. Substantial directional amplification may exceed limits for unrestrained façade or parapet elements. A vertical acceleration greater than 0.3 g (≈29.43 cm/s²) may require checks on vertical anchorage and diaphragms, as per ASCE 7-16 [59].

This analysis helps to understand the behavior of seismic waves as they interact with geological features, including faults and various rock types. Displacement patterns influence the response of buildings and infrastructure, informing the design of structures to withstand such movements. They also reveal ground anisotropy, essential for accurate modeling and engineering applications. Local site conditions influence ground motion, which facilitates more accurate seismic hazard assessments and informed urban planning. Understanding these patterns aids emergency response planning, identifying vulnerable infrastructure, and implementing targeted interventions to strengthen buildings and reduce risk.

The accelerogram records at both the basement and sixth floor stations were integrated over time, and corresponding orbit graphs were obtained, represented in 2-D seismograms (displacement in Figure 4) on the two horizontal components of ground motion. Key observations are given in

Table 2. Description of the ground motion orbit plots at the SLG1 and SLG2 locations.

Characteristic	Basement SLG1	Sixth Floor SLG2
Orbit Size	Larger elliptical spread	Smaller, more concentrated pattern
Displacement Range	Up to ±2.6 cm	Up to ±1.8 cm
Motion Type	Broader elliptical orbit, strong directivity	Complex path, more twisting and looping
Center Shift	Slightly shifted from origin	Slightly shifted, but less pronounced

.

The analysis of displacement configurations (basement vs. sixth floor) highlights significant differences between the two levels. Figure 4a (basement) displays higher displacement amplitudes and pronounced directional components, indicating stronger motion and lower damping. The dynamic trajectories and larger elliptical envelope indicate substantial energy release and directional anisotropy. In contrast, Figure 4b (sixth floor) shows more compact and confined displacement traces, indicative of weaker motion, higher damping, and isotropic behavior. The smaller, symmetric elliptical envelope and reduced oscillatory behavior imply more stabilized sixth-floor-level conditions. The basement exhibits stronger motion and a broader oscillatory range, while the sixth floor demonstrates more controlled and dampened motion.

The orbit at the base is larger, and it may seem counterintuitive, but here is why the base displacement orbit appears larger than that on the sixth floor. The displacement differences between the building’s base and sixth floor can be summarized as follows: (i) at the base, soil interaction and baseline drift can amplify low-frequency motion, leading to larger displacement readings; (ii) as motion travels upward, the structure filters and dissipates energy, reducing overall displacement on the sixth floor; (iii) measurement methods may also contribute to apparent differences, primarily due to processing artifacts. Briefly, the main applications of orbit analysis may be beneficial for structural monitoring to detect anomalies in building behavior during earthquakes, seismic design analysis to evaluate the transfer of energy through structures and verify the effectiveness of isolation systems, performance-based design for improved energy dissipation and tailored strengthening strategies, and experimental validation to verify simulation models. Regarding the seismic code improvement, there are requirements in design codes for complex or high-risk structures. However, this type of analysis not only influences the standards but also actively helps to rewrite them, which is beyond the scope of this study.

The pounding effect caused by insufficient separation distances during earthquakes [60] is not discussed in detail in this work. Seismic pounding occurs when adjacent buildings have insufficient separation during earthquakes, resulting in excessive vibration and potential damage. For a 20 m-tall building, the required separation distance is calculated based on the maximum lateral drift. With a drift ratio of 1.5%, the total drift is 29.7 cm. The 22 May 2012 earthquake did not cause non-elastic deformations, highlighting the importance of proper separation and mitigation measures to prevent structural damage.

The pulse identification module is used to classify seismic motions as either pulse-like (PL) or non-pulse-like (NPL), following the methodology of Kardoutsou et al. [61]. Beyond defining a new pulse indicator (PI) calculated as the cross-correlation factor between the dominant pulse and the original record, the method also identifies the predominant pulse within a seismic record, thereby aiding in the better classification and understanding of ground motion characteristics [62]. The analysis evaluates key parameters to determine whether the 22 May 2012 earthquake near Pernik exhibited a pulse-like or non-pulse-like nature. It also classifies the horizontal (EW, NS) and vertical (UD) components of seismic motion recorded at two instrumented stations: SGL1 (located in the basement) and SGL2 (located on the sixth floor). The processed velocity time histories for the horizontal components at both stations are presented in Figure 5. Seismic motions near fault zones are often characterized by intense velocity and displacement pulses with relatively long periods, distinguishing them from typical far-field ground motions. These high-velocity pulse-like movements can significantly amplify seismic responses in structural systems, potentially leading to adverse effects on physical structures [57].

Looking at the basement NS pulse indicator (Figure 5c), the velocity reaches a prominent peak around 6–8 s, indicating a strong seismic pulse. The oscillations decay gradually, stabilizing around 20–30 s. The oscillations appear relatively smoother, indicating a lower frequency component compared to the response on the sixth floor. The initial peak is sharp and well-defined, suggesting that the basement experiences a direct seismic input. On the sixth floor, the NS pulse indicator (Figure 5d) shows a peak at a similar timeframe (around 6–8 s), but with an overall amplitude higher than that of the basement. The oscillations persist for a longer time with noticeable amplitudes, which is typical for higher structural levels due to dynamic amplification. The sixth-floor response displays more high-frequency oscillations, suggesting greater structural resonance effects on the sixth-floor level. While the initial peak is comparable in timing to the basement, the subsequent oscillations are more pronounced, indicating amplified vibrations.

For the SGL2 sixth-floor horizontal component shown in the figure, the computed PI value is 0.50447, which classifies it as non-pulse-like according to established thresholds. Nevertheless, the velocity time history exhibits moderate velocity transients around 7–10 s, which may still influence dynamic amplification at upper floors.

Referencing ASCE 7-16 and Eurocode 8, even when motions are classified as non-pulse-like, near-threshold PI values (e.g., ~0.5) can still demand increased deformation capacity, underscoring the importance of robust detailing and energy dissipation measures in mid-rise reinforced concrete (RC) frames.

Comparative observations reveal that the sixth floor experienced more significant oscillations and higher amplitudes than the basement, indicating the influence of dynamic amplification resulting from the structure’s height and flexibility. The basement exhibits smoother oscillations, whereas the sixth floor displays more complex, higher-frequency vibrations, likely due to resonance. The sixth-floor decay in velocity is slower, which could indicate reduced damping efficiency at higher structural levels.

Figure 6 shows amplification in the Fourier spectrum (FS_{sixth floor} vs. FS_basement) as a function of the period for different directional components. The highest amplification occurs in the FS_NS (purple) component at a period of 0.36 s, as derived from the Fourier spectrum. This period represents a dominant vibration frequency in the building’s dynamic response. At this period, the building absorbs more energy, making it more vulnerable to seismic damage. The mean amplification (red) also shows significant values around this period. The dominant amplification period is 0.36 s, with noticeable peaks in FS_NS, FS_EW, and the mean. FS_EW (blue) shows smaller peaks around 0.3–0.4 s, while FS_UD (green) remains primarily flat. Beyond 0.5 s, amplification stabilizes, indicating a reduced dynamic response. The results highlight a strong response and potential vulnerabilities at shorter periods, particularly in the NS direction, suggesting the need for targeted mitigation measures.

3.2. Evaluation of Amplification Effects Between Basement and Sixth-Floor Accelerations

Understanding how buildings respond to seismic events is essential for minimizing damage and ensuring public safety. The real-time seismic monitoring data enable an accurate assessment of building behavior, support the refinement of building codes, and enhance design practices, ultimately improving urban seismic resilience in cities like Sofia. The analysis focuses on key aspects of seismic performance, including peak accelerations, velocities, and displacements at various levels within the building. A frequency response analysis is conducted to identify the building’s natural frequencies and their correlation with the dominant frequencies of earthquakes. Amplification effects are evaluated by comparing acceleration responses at the basement and sixth floor.

The graphs of the orientation-independent response spectra for the horizontal components of the motion, RotD100max and RotD00min (https://seismosoft.com/products/seismosignal/, accessed on 24 January 2025) [48,63], which are independent of the site orientation relative to the epicenter and provide the maximum spectral amplitude for different rotation angles, are shown in Figure 7a,b.

Figure 7a–d represents Response Spectra Acceleration (RSA). The RSA_SGL1 (Figure 7a) exhibits lower acceleration amplitudes, peaking at a maximum of 0.12 g for a duration of 0.25 s. In contrast, the RSA_SGL2 (Figure 7b) exhibits amplified accelerations of approximately 0.35 g for a period of around 0.4 s, corresponding to the building’s natural frequencies. This amplification is caused by resonance in the building, which can be rated as a flexible structure. The sixth-floor RSA spectrum shifts slightly to longer periods, showing a 3–4 times increase in maximum acceleration compared to the basement. Understanding these differences is essential for structural retrofitting and seismic design, particularly in mitigating dynamic amplification effects on non-structural components and equipment on the sixth floor, especially if it is costly. Basement isolation or energy dissipation systems can help reduce amplifications on the sixth-floor level.

The analysis examines the RSA for the UD component at two levels of the building: the base (Figure 7c) and the sixth floor (Figure 7d). The maximum RSA_SGL2 on the sixth floor is significantly higher (0.21 g) than at the base (0.062 g), indicating strong amplification of vertical accelerations as seismic waves propagate upward. The base RSA is concentrated in shorter periods (~0–1 s) and decays rapidly, demonstrating effective energy dissipation. In contrast, the sixth-floor RSA exhibits higher amplitudes over a broader period range, with slower decay, reflecting dynamic effects such as resonance and vibration amplification. This result highlights the importance of considering vertical acceleration impacts in multi-story building designs to mitigate the damage and stress caused by amplified vibrations.

The vertical PGA amplification on the sixth floor (2.11) and RSA-UD values (0.21 g) could contribute to column axial shortening, shear failures, or beam compression buckling. We now reference ASCE 7-16 §13.5 and Eurocode 8 Part 1 §4.3.3.5, emphasizing the need to explicitly account for vertical excitation in multi-story building design and retrofitting—especially for older RC frames lacking confinement and redundancy. The Spectral Acceleration–Spectral Displacement diagram (Figure 7e,f) highlights the structural responses to seismic waves, identifying the natural frequencies at which acceleration and displacement peak, thereby aiding in the detection of vulnerabilities and prioritization of improvements. In Figure 7e, the structure shows low acceleration (0.02 g to 0.12 g) and limited displacement (up to 4.0 cm), reflecting minimal deformation, low dynamic excitation, and effective damping. This result indicates a stiffer, well-damped system with efficient energy dissipation. In Figure 7f, the acceleration rises sharply to 0.3 g before stabilizing, while displacement increases to about 4.0 cm. This reflects a more flexible, excitation-sensitive system with higher energy absorption and reduced damping efficiency. Overall, the sixth floor experiences greater dynamic amplification, while the basement demonstrates lower response amplitudes and better damping. This analysis underscores the contrasting behaviors of the “soil–structure” (basement) and “structure” (sixth floor) systems under seismic loads, providing insights for structural engineering.

3.3. Results from Spectral Analysis

The graph of H/V spectral ratio analysis shows two distinct peaks, visible in Figure 8:

• For SGL1 (basement), the fundamental frequency is at f₀ ≈ 0.35–0.41 Hz and the amplification is A₀ ≈ 6.1;
• For SGL2 (sixth floor), the fundamental frequency is f₀ ≈ 2.2 Hz and the amplification is A₀ ≈ 6.6.

The FSR calculation between SGL2 and SGL1 using Equation (6) in the 0.1–20 Hz range, as shown in Figure 9, reveals a distinct peak at approximately 2.2 Hz, with typical damping of around 5%, indicating good structural resilience, which corresponds to the fundamental frequency of the structure.

The results of applying the RDM (Equation (7)) are visualized in Figure 10. The frequency f is measured in Hz, while the damping coefficient ζ is expressed as a percentage. Based on the analysis of earthquake accelerograms for SGL1 (basement), we obtained f₀ ≈ 0.44–0.46 Hz and ζ = 3.6–5.3%. For SGL2 on the sixth floor, these values are, respectively, f₀ ≈ 2.3–2.7 Hz, and ζ = 4.3–6.5%.

Although the ambient vibration data before the earthquake are unavailable, the lower damping observed at the basement level (3.6–5.3%) is interpreted as potentially reflecting foundation flexibility or measurement artifacts due to lower motion amplitudes.

4. Discussion and Study Implications

The building, typical of mid-20th-century residential or mixed-use structures in Sofia, features a reinforced concrete frame and slabs. While designed to resist lateral forces, such as wind and earthquakes, its age is approximately 70–80 years, and the design may not align with modern seismic codes. As such, this building can represent many similar regional structures that lack retrofitting for contemporary earthquake standards. Assessing the response of such buildings during seismic events highlights vulnerabilities and informs future retrofitting strategies to enhance resilience. The comparison of response spectra shows that the vertical acceleration on the sixth floor of the building is significantly amplified compared to that at the base. These findings underscore the importance of considering vertical acceleration effects in structural design to prevent potential damage, particularly in multi-story buildings.

In this study, we apply the KY approach [22] to compare accelerometric data from the basement and the sixth floor of a six-story building located in the central part of Sofia, Bulgaria. Analyses were performed based on the comparison, evaluating the differences in seismic response between the basement and the structure’s sixth floor. The sixth floor experienced more significant oscillations and higher amplitudes than the basement due to dynamic amplification. The basement primarily reflects the direct seismic input, while the sixth floor exhibits amplified and prolonged oscillations due to structural dynamics. This highlights the importance of evaluating resonance and damping mechanisms in tall structures to effectively mitigate seismic effects.

The KY formula provides a simplified method for estimating a building’s seismic response using sixth-floor-level acceleration data; however, it has notable limitations. It assumes a linearly elastic, one-dimensional shear beam model, which overlooks non-linear behaviors like cracking or plastic deformations that occur during strong earthquakes. The model does not account for irregularities in mass or stiffness, nor does it consider soil–structure interaction (SSI), which can significantly affect a building’s response, especially in areas with soft soil, such as the Sofia Graben. It also assumes uniform material properties and vertical shear wave propagation, ignoring torsion, asymmetry, and other complex dynamics present in real structures. These simplifications can lead to inaccurate predictions of inter-story drifts and acceleration amplifications. Future enhancements to the KY model should aim to incorporate non-stationary ground motion characteristics, site-specific geotechnical profiles, and multidirectional dynamic inputs to better reflect the actual seismic demand on buildings in complex urban environments.

The PI analysis of accelerogram data from the basement (SGL1) and sixth floor (SGL2) provides valuable insights into seismic ground motion characteristics and their impact on structural behavior. It classifies seismic events as pulse-like (PL) or non-pulse-like (NPL) based on the presence of velocity pulses, which are typical in near-fault earthquakes. For the 22 May 2012 Pernik earthquake, pulse-like features were notably present in the horizontal (NS) components, exhibiting strong velocity peaks around 6–8 s and a gradual decay, particularly at the sixth-floor level. These concentrated energy bursts can significantly affect the performance of flexible, mid- to high-rise buildings.

Classifying ground motions as pulse-like has significant implications for seismic design and building codes. Current codes, such as Eurocode 8, generally do not differentiate between pulse-like and non-pulse-like motions in their design spectra, despite research showing that pulse-like motions can be more damaging. To address this, design provisions should include specific modifications or spectral shapes for pulse-type motions. Buildings near active faults or in regions prone to pulse amplification should be designed with greater ductility, energy dissipation systems, and sufficient separation to avoid pounding. Identifying pulse-like features early can also guide retrofitting and performance-based assessments, especially for older structures. Overall, PI analysis underscores the significance of pulse-sensitive design approaches, particularly in urban areas like Sofia, which are vulnerable to near-source seismic events.

Although soil–structure interaction (SSI) is mentioned in the study, its effects have not been quantitatively evaluated. SSI can significantly influence the seismic response of buildings, particularly mid-rise reinforced concrete structures such as the one examined in this paper. The additional flexibility introduced by SSI reduces the system’s natural frequency, potentially bringing it closer to resonance with the long-period components of seismic waves, leading to accelerations at upper floors being increased by as much as 20–40%.

Given the geotechnical conditions typical of Sofia, future analyses should incorporate at least a simplified SSI model (e.g., an impedance-based approach) to enhance the reliability of response predictions and prevent overestimating structural safety.

Amplification of the maximum accelerometric parameters reached values given in Table 1, indicating significant dynamic effects toward upper levels. The FSR method, which compares the amplitude spectra between the sixth floor (SGL2) and the basement (SGL1), revealed a dominant amplification peak at approximately 2.2 Hz, consistent across the horizontal components (EW and NS), and moderately visible in the vertical (UD). This dominant frequency corresponds to the natural mode of the structure identified through other analyses, such as H/V and response spectra. The amplitude of the FSR reached values that indicate significant dynamic amplification towards the upper floors. This observation is consistent with the findings based on PGAs and confirms the building’s resonant behavior under seismic excitation. RDM analysis determined damping ratios ranging from 3.6% to 6.5%, showing frequency shifts across floors. This technique utilizes the decay of oscillatory segments of the response signal to estimate the damping ratio (ζ) and dominant frequencies. The results indicated, for the basement level (SGL1) f₀ ≈ 0.44–0.46 Hz and ζ ≈ 3.6–5.3%, and for the sixth-floor level (SGL2) f₀ ≈ 2.3–2.7 Hz and ζ ≈ 4.3–6.5%. These values illustrate the frequency shift and increased damping as a function of height and match well with the building’s flexible dynamic response as assessed in the Fourier and KY model interpretations.

The sixth floor-to-basement PGA ratios for the EW, NS, and UD components—2.04, 3.27, and 2.11, respectively—are essential for assessing flexibility and torsional response. EC8 does not explicitly define acceptable amplification thresholds between floors but emphasizes modal analysis to capture floor-level responses. Ratios greater than 2 typically indicate a flexible structure with the potential for high inter-story acceleration differentials, which is relevant for equipment anchorage and non-structural performance checks.

Eurocode 8 [58] recommends evaluating floor acceleration amplification and inter-story drift when the PGA amplification exceeds 1.5, as observed in the NS and EW directions in this case. For non-structural elements, ASCE 7-16 specifies that amplified floor accelerations must be considered when the sixth floor PGA > 0.4 g (~392 cm/s²). Though the values here are below that, the relative amplification (up to 3.3×) signals a potential for dynamic resonance and local failure. The displacement (PGD) values, although modest (<2 cm), show a doubling from the basement to the sixth floor. In flexible buildings, amplified displacement can affect drift-sensitive components, like curtain walls or piping systems. The EW and NS sixth-floor amplifications (2.04 and 3.27) are well above unity, indicating that upper-story components may require additional detailing, bracing, or isolation measures. The amplification factor (sixth floor/basement) of ~3.27 aligns with EC8 soil amplification expectations and highlights the building’s dynamic response contribution, not solely due to soil amplification. While the absolute PGA values remain below standard design thresholds, the amplification at the upper levels suggests higher internal force demands, particularly for non-structural elements. Even for moderate ground shaking (~0.1 g base-level PGA), localized dynamic effects justify the use of response modification factors (R-factors) and non-linear time history analysis for critical or irregular structures. Although often neglected, the vertical PGA on the sixth floor (0.046 g) warrants evaluation of vertical load paths, especially in areas with high axial loads or slender columns. Additionally, the lower PGV/PGA on the sixth floor indicates a more abrupt acceleration profile, reflecting resonant amplification at higher modes. The basement’s higher ratio suggests softer, broader waveform input, typical of soil-filtered ground motions. Although these values may not generate high structural forces, they could significantly impact inter-story drift, especially when resonance periods align.

Structural response comparisons reveal stronger oscillations on the sixth floor, underscoring the importance of assessing resonance and damping. While the KY formula remains a valuable tool, further research is needed to refine its integration of non-linear dynamics and SSI effects. The findings reinforce the necessity of seismic retrofitting for older buildings and contribute to improving earthquake early warning systems, structural monitoring, and resilience strategies.

Simplified structural models used in modeling may overlook complex non-linear behaviors in structures. The accuracy of predictions relies heavily on the availability and precision of accelerometric data. The KY formula does not explicitly account for SSI effects, which can significantly influence the seismic response. Despite these limitations, it remains a valuable tool in earthquake engineering for analyzing structural responses to seismic events. Its ability to integrate stochastic processes with accelerometric data offers a robust framework for seismic analysis. However, advancements in computational methods and a deeper understanding of non-linear dynamics and SSI effects are needed to address its limitations. Future research should enhance the formula to incorporate non-stationary ground motion and complex structural behaviors, ensuring greater accuracy and applicability in modern engineering practices.

5. Conclusions

This study highlights the significance of examining a building’s dynamic behavior under actual seismic loading, utilizing real accelerometric data from the Mw 5.6 Pernik earthquake (22 May 2012). The selected recordings, from the basement and sixth floor of a mid-rise RC building in Sofia, reveal significant vertical and horizontal amplification phenomena. The resulting data form a basis for understanding site-specific seismic performance and informing both retrofit strategies and instrumentation planning.

The findings show that the structure remained largely within elastic limits; however, amplified responses at the top floor (e.g., PGA ratio up to 3.27) highlight critical demands on non-structural components and the necessity for careful attention to seismic detailing. Natural period estimates derived from RSA (0.25 s in the basement and 0.42 s on the sixth floor) confirm an increasing flexibility and deformation with building height, consistent with the modal behavior observed in similar structures.

The applied methodology—combining recorded motions, spectral analysis, and the Kanai-Yoshizawa (KY) linear modal estimation—demonstrated suitability for rapid seismic vulnerability assessment in reinforced concrete buildings. Significantly, this framework may also be adapted to other construction typologies, such as unreinforced masonry, steel-frame, or hybrid systems, provided the following conditions are met:

• Sufficient sensor deployment for meaningful modal extraction.
• Reasonable knowledge or estimation of structural properties.
• Consideration of soil–structure interaction effects where applicable.

Regarding methodological refinement, we acknowledge that incorporating non-linear constitutive models—such as the Kent model for concrete and the Kent–Park model for reinforcement, as illustrated by Longarini et al. [64] in their study on RC chimneys with tuned mass dampers—could offer improved realism in capturing post-yield behavior and damage evolution. While this would introduce computational complexity, particularly in finite element or fiber-based frameworks, it may lead to significantly different results regarding residual drifts and localized damage.

Although this study focuses on system-level metrics and employs linear elastic assumptions due to data limitations, future work should explore non-linear extensions to enhance risk characterization and support informed retrofit decision-making.

The Mw 5.6 earthquake in the Pernik region serves as a critical case study for assessing seismic risk in Sofia, a region prone to earthquakes. The seismic response analysis of a six-story building highlights the importance of utilizing real accelerogram data to comprehend structural behavior under earthquake loading. Using records from the basement and sixth floor during the 2012 Pernik earthquake, the study evaluated key parameters, including PGA, PGV, PGD, PFA, PFV, PFD, and displacement distributions. The results emphasize the increasing flexibility and deformation of the structure with height, reflected in the natural periods of the RSA: 0.25 s in the basement and 0.42 s on the sixth floor. These findings align with the typical dynamic responses of multi-story buildings, where displacements on the top floor are amplified. The findings support the use of simple predictive models, such as KY, combined with spectral analysis to assess seismic building vulnerability [15,16]. These insights inform design codes, retrofitting strategies, and urban seismic risk management approaches.

In summary, the conclusions affirm the value of strong-motion monitoring, the effectiveness of simplified spectral models for vulnerability analysis, and encourage broader methodological application with future integration of non-linear structural response modeling.