Study on energy evolution and damage constitutive model of coal fractured by dual-frequency ultrasonic cracking

To address critical challenges in coal seam gas drainage—specifically low permeability and the inherent limitations of single-frequency ultrasonic fracturing, such as rapid energy attenuation and restricted effective range—this study investigates the potential of a novel dual-frequency approach. Using a custom-designed dual-frequency ultrasonic fracturing system, we investigated the impact of frequency coupling on meso-structural damage, macroscopic mechanical behavior, and energy evolution in coal. Uniaxial compression tests synchronized with acoustic emission (AE) monitoring were employed to analyze fracture network propagation, AE characteristics, strength degradation, and elastic energy dissipation under varying frequency coupling fields. Results demonstrate that the frequency coupling effect of dual-frequency ultrasound significantly surpasses single-frequency stimulation. Fracturing efficiency is intrinsically dependent on the frequency ratio (η), with optimal coupling performance observed within the range of η in (1.5, 2.0). Within this optimal interval, the total surface fracture length increased by 23.45% (from 67.8 mm in the control group to 83.7 mm in the dual-frequency group), driving a morphological transition from singular cracks to complex fractal network structures. Mechanical testing revealed a sharp deterioration in compressive strength as η increased, culminating in a maximum strength reduction of 87.2%. Furthermore, energy evolution analysis identified an “energy pre-dissipation” mechanism. Following dual-frequency treatment, the total input energy required for failure decreased by 82.99% (from 0.00876 MJ·m-3 to 0.00149 MJ·m -3), while the peak elastic strain energy dropped by 84.44% (from 0.00707 MJ·m-3 to 0.00110 MJ·m-3). This confirms that dual-frequency fractured coal undergoes brittle instability with minimal mechanical work input. Finally, a non-linear damage constitutive model incorporating frequency coupling effects was developed based on the Weibull distribution. Innovatively, this model integrates a fracture fractal dimension parameter to quantify initial damage and AE cumulative ring counts to characterize evolutionary damage. The model achieves high predictive accuracy, with a maximum error of only 6.06% compared to experimental data, effectively capturing the mechanical response of dual-frequency fractured coal.