The hard rocks in the stratum can pose safety risks and hinder the progress of urban underground tunnel construction using shield and jacking methods, thereby reducing construction efficiency and increasing construction costs. This paper utilizes wavelet scale energy spectrum, wavelet packet theory and statistical methods to conduct research on the detection of special geological formations such as hard rocks and voids, as well as the analysis of their signal time-frequency characteristics based on the ground-penetrating radar (GPR) technique. On the basis of calibrating the permittivity of different types of rock blocks, we established a forward model for detecting hard rocks and voids, and the simulated signals were analyzed in the time and frequency domains. Subsequently, laboratory experiments were conducted to perform GPR tests on different types of hard rocks in natural and water-saturated states and voids, to explore the time-frequency characteristics, frequency band energy variations, and statistical patterns of typical single-trace signals. The results show that the granite detection signal contains more low-frequency components, the sandstone detection signal contains more medium-low frequency components, while the limestone detection signal contains more medium-high frequency components in their natural state; the signal from the karst cave has relatively more low-frequency components than the signal from the empty cavity. The geometric shape of the rock has no influence on the dominant frequency and time-frequency distribution of its reflection signal. Generally, rocks with higher rebound values (hardness) also exhibit larger variance and standard deviation in frequency band energy. The research has important theoretical significance and practical value for the measurement and assessment of special geological features such as hard rocks and voids in urban underground trenchless construction.
