Amplification effects of ground motion due to the local geology of the building site in the cities of Kyiv, Kryvyi Rih, Odesa

The results of the research presented in the article elucidate the importance of taking into account the amplitude-frequency characteristics of soil stratum models in the context of seismic safety of construction objects on the territory of Ukraine, in different regions. The presented results of the analysis of the calculated amplitude-frequency characteristics of models of soil environments for different regions of Ukraine reveal that the amplification of vibrations by soils has a complex nature that depends on many factors and can differ significantly for different construction sites. We have shown that during the earthquake-resistant design of buildings and structures, it is necessary to properly take into account the properties of soil complexes under the research site, which can significantly increase oscillations at “resonant” frequencies. The article examines in detail the features of amplitude-frequency characteristic models of soil strata for different geological conditions in Kyiv, Kryvyi Rih and Odesa. The purpose of this study is to compare these characteristics and develop recommendations for reducing risks associated with seismic hazards.


Introduction
Many studies of damages to buildings and structures caused by earthquakes have shown that the local soil conditions of the sites can affect the amplitude of seismic ground motions on the surface during an earthquake.The main reasons are: 1the occurrence of resonance phenomena caused by the natural frequency of buildings, similar to the dominant period of the territory; 2the local structure of the soil, which acts as a filter, selectively amplificates or attenuates the frequency components of the soil movement (when the soil movement is transferred from the bedrock to the surface, its frequency components and amplitude values change significantly).Thus, the influence of local soil conditions of the site on soil oscillations is a fundamental issue in seismology, as it has important theoretical and practical significance for the protection of people, buildings and structures from earthquakes [4].
For example, during the 1985 Mexico City earthquake (Ms=8.1),medium-rise buildings in Mexico City, 400 km from the epicenter, were severely damaged, while low-rise and high-rise buildings (more than 23 stories) remained undamaged [9].This example illustrates the need for research of resonant amplification of dominant frequencies by soils and their impact on safety and stability of buildings and structures during earthquakes.The obtained filtering properties of the soil stratum play a key role in preventing resonance phenomena during seismic impacts.Resonance can occur when the frequency of seismic oscillations coincides with the natural frequency of oscillations of the soil or engineering structures.As a result of resonance phenomena, the amplitudes of oscillations can increase significantly, which leads to damage or destruction of structures.Analysis of the filtering properties of the soil allows you to take this factor into account and develop construction solutions that minimize the likelihood of resonance effects.This will enhance infrastructure reliability and improve people's safety during seismic events.
Thus, the study of the impact of local soils on seismic fluctuations is an important and relevant area of research that contributes to the safety and sustainable development of cities and infrastructure in conditions of seismic activity.Understanding the influence of the soil stratum on seismic vibrations and taking into account resonance phenomena play an important role in modern earthquake-resistant construction, providing more effective and safer protection against earthquakes and reducing seismic risks.
III-IV category soils in terms of seismic properties have significant non-linear properties, which manifest themselves differently, depending on the intensity and frequency composition of the seismic impact.The nonlinear behavior of the soil leads to a change, sometimes very significant, in the forms and spectra of seismic waves in the soil stratums.Resonance frequencies of soils appear to be dependent on the intensity of impact and, in case of sufficiently intense earthquakes, may differ from the values determined by records of seismic noise or weak seismic events.
During intense seismic impacts, the geological properties of soils change, which may be associated, for example, with the movement of groundwater, the breaking of structural bonds between soil particles, and other phenomena.
The article examines the features of the amplitude-frequency characteristics (amplitude-frequency characteristic) of calculated models of soil strata for seismic fluctuations of local soil conditions in Kyiv, Kryvyi Rih and Odesa with the aim of comparing them and developing measures to reduce seismic risks.At the same time, greater attention is paid to the city of Kyiv, which has the largest concentration of construction sites within the territory of Ukraine.

Method
The nature of the passage of seismic vibrations through the sedimentary layers of the soil stratum during distant earthquakes depends on the angle of incidence of seismic waves on the bottom of the sedimentary cover, the directional diagram of energy radiation from the hearth, the strength of the sedimentary layers on construction (exploitation) sites, the geological and geophysical properties of the layers, the geomorphological structure of the location area of the studied area.Large ground accelerations can cause liquefaction and nonlinear effects in soils that, in turn, can cause damage to structures depending on the geometry of the layers, physical-mechanical and seismic properties.The soil can amplify the intensity of seismic vibrations at some frequencies, and weaken it at others.Consider how the soil stratum changes the amplitude and frequency composition of seismic vibrations propagating through it [8].
At the first stages of building models of the soil environment, geological sections were analyzed, built according to the data of well researches within the studied construction sites.Soil stratum models include both physical (speed of elastic waves, density, absorption decrements, etc.) and geometric (thickness of layers, shape of boundaries) characteristics.The boundaries of the interface between the soils with a different composition and physical and mechanical properties, which make up the engineering geological sections, have a characteristic horizontal or close to it lying.
The use in calculations of the dependences of the shear modulus and the absorption coefficient on the shear deformation allows to take into account the nonlinear reaction of the soil stratum to seismic influences [4].
Calculations of the amplitude-frequency characteristic of the model of the soil stratum under the construction site were carried out using the ProShake software complex [7; 10], developed for onedimensional modeling of the response of upper part of the section of the geological environment to seismic influences.Amplitude-frequency characteristic was built for models built based on the data of wells drilled within construction sites.The initial data for the construction of models of the soil environment were taken from the technical reports of engineering and geological surveys for the research site.The parameters of the deeper layers, up to the crystalline foundation, are taken from literary and stock sources.
When constructing the amplitude-frequency characteristic model of the geological environment, the method of equivalent linear modeling of the response of the soil stratum to seismic influences was used.The behavior of each layer of the soil model during calculations was determined by the Kelvin-Voight (viscoelastic) model.Each layer of the soil model was characterized by such parameters as: layer capacity, velocities of longitudinal and transverse waves, density, nonlinear dependencies of shear modulus and absorption coefficient on shear deformation.The boundaries of the interface between soils with a different composition and physico-mechanical properties, which make up engineering-geological sections, have a characteristic horizontal, or close to it, lying [2; 12].
The use in calculations of the dependences of the shear modulus and the absorption coefficient on the shear deformation allows you to take into account the possible nonlinear behavior of soils during an earthquake.The obtained data on the filtering properties of the soil stratum at the studied sites provide an opportunity to develop more effective and safer construction solutions, as well as to reduce the cost of earthquake-resistant construction by avoiding resonant amplification by the sedimentary layer of seismic oscillations in the natural periods of the designed buildings and structures [4; 12].This allows you to take into account the features of each specific geological environment and create optimal conditions for protecting infrastructure and people's lives from seismic threats.

Results and discussion
Consider the calculated amplitude-frequency characteristic models of soil strata under some construction sites of high-rise construction in Kyiv (figure 1).

Figure 1.
Amplification ratio curve for soil of construction sites in the city of Kyiv.
Figure 1 illustrates the amplitude-frequency characteristic of soil stratum models beneath construction sites in Kyiv, showcasing one or two peaks within the frequency range of 0.2 to 2.0 Hz.The observed amplification at these low frequencies (0.2 -2.0 Hz) is crucial to consider during the design of earthquake-resistant high-rise structures in Kyiv.This is particularly significant due to the elevated risk posed to tall buildings by low-frequency vibrations originating from subcrustal seismic events, notably those occurring in the Eastern Carpathians, such as the Vrancea area in Romania.
Figure 2 presents a constructed map illustrating the distribution of calculated Peak Ground Accelerations (PGA) on the free surface of the soil stratum for the city of Kyiv, depicting maximum predicted seismic impacts of up to 0.06 g. Figure 2. Map depicting the distribution of estimated PGA on the free surface in the territory of Kyiv with maximum seismic impacts up to 0.06 g [12].
Figure 2 illustrates that during seismic impacts with a maximum amplitude of input oscillations at 0.06 g, the PGA on the free surface within Kyiv's territory varies from 0.038 g to 0.062 g.Generally, ground motions with higher PGA values are deemed more destructive than those with lower peak accelerations.However, extremely high PGA values, characterized by short durations and high frequencies, may not cause significant damage to certain elongated structures with low natural frequencies of oscillation.
It is essential to consider that, from an engineering perspective, a high PGA value might not be relevant in the case of a singular high-amplitude event or when the oscillation frequency with a high PGA value falls outside the natural oscillation frequencies of the building.Therefore, when interpreting research results, it is crucial to account for the spectral composition of seismic oscillations.
Next, we delve into specific models of the geological environment in the cities of Kyiv, Kryvyi Rih, and Odesa.

Amplitude-Frequency Characteristics of the Geological Environment for the city of Kyiv, specifically at the construction site located at 210 Kharkivske Highway.
The soil stratum model includes both physical (elastic wave velocities, densities, absorption decrements, etc.) and geometric (layer thicknesses, shape of boundaries) characteristics.
One engineering-geological district was allocated within the construction site during seismic microzoning works.Therefore, the averaged model of the geological environment under the construction site was built alone.The groundwater level (GW) is 6.0 m.
The model of the geological environment was built as horizontally layered and vertically heterogeneous.The initial data for building the model were taken from the technical report on the engineering and geological investigations of the research site.Its parameters are shown in table 1.According to the data of engineering and geological searches (up to 33 meters), the sections of the environment within the entire area of the planned construction are composed of alternating sands with different physical and mechanical properties.The boundaries of the interface between the soils with a different composition and physical and mechanical properties, which make up the engineering geological sections, have a characteristic horizontal or close to it lying.
Up to the explored depth of 33 m, a certain number of horizontal layers were conditionally selected (according to the results of the comparison of seismic and geological rock boundaries).Some of these layers included several interlayers similar in lithology.When combining several layers into one seismological soil stratum, the models (such physical parameters as densities and speeds of elastic waves) were calculated as weighted averages for each layer according to the formulas recommended by the current SBC B.1.1-12:2014"Construction in Seismic Areas" [3]: where Hk -thickness of the k-layer, Vs av -average shear velocity.
Values of decrements of absorption of longitudinal and transverse waves in layers were estimated according to literature data [1; 2], in accordance with dependencies: Data for building a model of the environment from a depth of 33 meters to the crystalline foundation was supplemented from literary sources and stock materials.
Thus, the averaged model of the soil stratum under the construction site of the planned construction at the address: 210, Kharkivske Highway has 10 horizontal-parallel soil stratums with different physical parameters, separated from each other by seismological boundaries.
Calculations of the amplitude-frequency characteristic (frequency characteristic) of the model of soil stratum under the construction site were carried out using the ProShake software complex [7; 10], developed for one-dimensional modeling of the response of the upper part of the section of the geological environment to seismic influences.Amplitude-frequency characteristic was built for a model built based on the data of wells drilled within the construction site.The initial data for the construction of amplitude-frequency characteristic were taken from table 1 and the technical report on the engineering and geological investigations of the research site.The parameters of the deeper layers to the crystalline foundation are taken from literary and stock sources.
Figure 3 shows the amplitude-frequency characteristic for the model of the soil stratum under the investigated construction site on the 210, Kharkivske Highway.
Amplitude-frequency characteristic of the soil environment under the site at the address of 210, Kharkivske Highway in the Darnytskyi District of Kyiv is characterized by a frequency range of resonant amplification of oscillations by local soil conditions from 0.3 to 0.98 Hz with a maximum amplification factor of 10.8.In the specified frequency range, one clear maximum is observed at a frequency of 0.48 Hz.

Figure 3.
Amplification ratio curve sample for the T-component of surface oscillations of models of the soil stratum under the research site at the address: 210, Kharkivske Highway in the Darnytskyi district of Kyiv, for the case of a transverse wave falling from below on the sole of the half-space (table 1).
Calculated accelerograms for simulating earthquakes in the Vrancha zone at the research site were synthesized using a regularized inverse Fourier transform algorithm [4].During their generation, various combinations of theoretical contour amplitude spectra of calculated accelerograms, normalized frequency characteristics of the environment and phase spectra obtained from various records of real subcortical earthquakes from the Vrancha zone were used.
The obtained data were transferred to designers and builders for further assessment of the impact of Frequency, Hz seismic vibrations on building structures and engineering systems, as well as for modeling the behavior of the structure under a specific seismic load, presented in the form of sets of calculated accelerograms and response spectra.

Amplitude-frequency characteristics of the geological environment for the city of Kryvyi Rih
(seismological station "Kryvyi Rih") Amplitude-frequency characteristic was calculated for the location of the Kryvyi Rih seismological station, where the geological section is represented by a sedimentary cover with a thickness of up to 30 m, which overlaps the crystalline rocks of the Precambrian basement [5; 6].
Accelerograms (records on bedrock) on the free surface of the soil were calculated for the Myroliubivka district of the city of Kryvyi Rih, where the seismic station "Kryvyi Rih" is located, in order to assess the influence of the soil stratum on the seismic hazard parameters on its free surface.To solve the problem, two records of earthquakes on bedrock with PGA=0.06g(where g is the acceleration of gravity, 1g = 9.81 m/s 2 ) and PGA=0.1g were chosen.The equivalent-linear method of modeling soil response to seismic loads and the ProShake software package [7] were used.
The model of the soil stratum of the Myroliubivka district of the city of Kryvyi Rih is given in table 2.
Figure 4 shows the calculated accelerograms on the free surface of Myroliubivka district.The obtained results indicate an increase of PGA on the free surface relative to PGA on bedrock (in both cases) by approximately 4 times.Figure 5 shows the variation of PGA with depth, in the direction from bedrock to the free surface.
The Fourier amplitude spectrum plot reveals that the highest PGAs occur within the frequency range of 1.2 Hz to 1.75 Hz, as depicted in figure 6.
Thus, the soil stratum in the Myroliubivka area, composed mainly of loams and clays, exhibits Input earthquake (PGA=0.06g)Input earthquake (PGA=0.10g)resonant properties in the frequency range from 1.2 Hz to 1.75 Hz.Theoretical modeling showed an increase in the amplitude of seismic oscillations in the indicated range by approximately 4 times.Since civil buildings have their own resonance frequencies in the same range (1 -2 Hz), during construction, it is necessary to conduct detailed studies on the prevention of resonance effects and ensuring the seismic resistance of buildings.

Amplitude-frequency characteristics of the geological environment for the city of Odesa
Figures 7 -9 present amplitude-frequency characteristics (frequency characteristics) constructed for models of soil strata under the construction sites of high-rise buildings in the city of Odesa and in the Odesa region [11; 12].
Analyzing the amplitude-frequency characteristic of the soils under the construction sites of the Odesa region, it can be seen that they have a large number of well-defined maxima and a wide frequency range of possible resonant amplification of seismic vibrations.According to amplitude-frequency characteristic of models of soil strata presented in figure 8, the frequency ranges of possible resonant amplification of seismic vibrations by local soil conditions for each construction site were determined.For all construction sites of the Odesa region, the first maximum of the frequency characteristic is observed in the low-frequency range from 0.15 Hz to 0.35 Hz, which is obviously a manifestation of the large (from 1400 to 1600 m) power of sedimentary deposits.The following maxima of the frequency characteristics of the soil strata under the construction sites of the Odesa region are observed in the frequency range from 0.5 Hz to 10 Hz.Thus, it can be concluded that in earthquake-resistant construction design, it is necessary to carry out detailed studies of the resonant properties of the soils construction, regardless of the number of floors of the buildings and the complexity of the structure, since the natural frequencies of oscillations of both single-story and high-rise buildings usually lie in this frequency range.
For all studied sites, the influence of the physical and mechanical properties of the sediment layer on the seismic effect on the surface within the territory of the studied construction site was analyzed under possible seismic impacts with different maximum peak accelerations, which with a 90% probability will not be exceeded in the next 50 years.
Based on the obtained results, recommendations were formulated to prevent the occurrence of resonance effects in the designed objects due to the coincidence of the frequencies of the maximum oscillations in incident seismic oscillations with the maxima of the frequency characteristics of the soil and the frequencies of the natural oscillations of buildings and structures.

Conclusions
Based on the analysis of amplitude-frequency characteristics of soil models across various construction sites in different cities of Ukraine, it is evident that vibration amplification by soils exhibits a complex pattern.This phenomenon depends on numerous factors and can vary significantly between different construction locations.Therefore, a crucial inference to draw is that earthquake-resistant design for buildings and structures must appropriately consider the filtering properties of soil complexes.This entails acknowledging the potential substantial increase in vibrations at "resonant" frequencies.
When calculating frequency characteristics, it is essential to factor in the influence of rheological properties of soil strata and employ nonlinear methods to determine their frequency characteristics.Calculated accelerograms should also consider the vibrations originating from earthquake epicenters and the filtering properties of the site's soil complexes.
The inclusion of frequency characteristics that fully reflect the influence of the soil stratum beneath the future building allows for cost reduction in construction while simultaneously enhancing the seismic resistance of structures.This can be achieved by developing design solutions that prevent the alignment of the natural frequencies of the intended building with the maxima of the frequency characteristic of the soil stratum.
A comparison of the resonant properties of soils in Kyiv, Kryvyi Rih, and Odesa reveals valuable insights into their seismic potential.Our research indicates that, from a seismicity standpoint, the local A key indicator of this is the wide frequency range of resonant amplification in Odesa compared to Kyiv and Kryvyi Rih.This suggests that Odesa's soils possess characteristics such as catacombs, landslides, and a high groundwater level, contributing to seismic vibration amplification across a broader frequency spectrum compared to other cities.The substantial sedimentary layer in Odesa, in contrast to Kyiv and Kryvyi Rih, significantly influences resonance amplification results.
Consequently, our research underscores that Odesa faces hazardous local ground conditions in a seismic context, characterized by a wide frequency range of resonant amplification of seismic oscillations spanning from 0.1 Hz to 10 Hz.This information is vital for consideration during construction and seismic protection planning in the region.
The data obtained on the filtering properties of the soil stratum at the studied sites, determining quantitative seismic hazard characteristics, concurrently ensure the stability of designed structures and substantially reduce earthquake-resistant construction costs by averting resonant amplification by the sedimentary layer of seismic oscillations at their own periods in designed buildings and structures.
and δs -decrements of absorption of longitudinal and transverse waves, respectively.

Figure 4 .
Figure 4. Recalculated accelelograms from PGA=0.06g and PGA=0.1g to the free surface of the Miroliubivka area.

Figure 5 .
Figure 5. Change of PGA with depth, in the direction from bedrock to the free surface of the Myroliubivka area.

Figure 6 .
Figure 6.Amplitude Fourier spectrum of seismic oscillations on the free surface of Myroliubivka district.

Figure 7 .
Figure 7. Amplification ratio curve for soils of different sites in Odesa [11].

Figure 8 .
Figure 8. Amplification ratio curve sample for the T-component of surface oscillations of models of the soil stratum of engineering-geological districts I, II and III at the site at the address: Odesa, 30, Academic street, for the case of a transverse wave falling from below on the sole of the half-space.Conventions: 1districts I; 2districts II; 3districts III.

10 Figure 9 .
Figure 9. Amplification ratio curve for soil of the construction site of the complex of berths No. 5, 6, 7, 8 in the Port of Pivdenyi.
soil conditions in Odesa are the most perilous.

Table 1 .
Averaged Model of the Geological Environment at the Site on Kharkivske Highway, 210, Darnytskyi District, Kyiv.

Table 2 .
Model of the soil stratum of the Myroliubivka district of the city of Kryvyi Rih.