Ortuta J., Šimiček J., Brixová B., Putiška R. & Bednarik M., 2025: Modal analysis of subsoil using Fourier transformation under dynamic loading. Acta Geologica Slovaca, 17, 1, 27–38.

Modal analysis of subsoil using Fourier transformation under dynamic loading

Juraj Ortuta^1,2, Jozef Šimiček¹, Bibiana Brixová², René Putiška² & Martin Bednarik²

²Comenius University Bratislava, Department of Engineering Geology, Hydrogeology and Applied Geophysics, Faculty of Natural Sciences, Ilkovičova 6, 842 15 Bratislava, Slovakia

Abstract

When designing geotechnical constructions, it is important to know its behavior under dynamic loading, which is induced or natural seismicity. It is known from the solution of dynamically loaded structures that if the excited frequency of the load is equal to, or approximately equal to, the natural frequency, undesirable resonance phenomena occur. A reliable tool for investigating the dynamic properties of geotechnical engineering is the modal analysis, which uses its stiffness and mass properties to find the natural frequencies. The original “discrete” Fourier transformation (DFT) of the time function into the frequency domain found practical use only in 1965, when the American mathematicians James William Cooley and John Tukey substantially made it more efficient. It is thus possible to compare the solution of the differential equation of the natural oscillation of the tunnel lining structure with the experimental analysis based on the measurements, their subsequent processing and evaluation using the fast Fourier transformation (FFT). The article discusses the measurement of technical seismicity during real tunnel excavation and its use to control its dynamic effects on nearby structures. It also evaluates the effects of technical seismicity in different geological conditions and their connection with natural seismicity, which represents a major input to the design of geotechnical structures in seismically active areas.

Key words: Fourier transformation, induced seismicity, dynamic loading, earthquake, natural frequency

Manuskript doručený: 2025-06-05

Manuskript revidovaný: 2025-07-14