Abstract
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.
Data availability
Data is provided within the manuscript.
References
Yuan, L. et al. Construction of green,low-carbon and multi-energy complementary system for abandoned mines under global carbon neutrality[J]. J. China Coal Soc. 47 (06), 2131–2139 (2022).
Yuan, L. et al. Scientific problems and key technologies for safe and efficient mining of deep coal resources[J]. J. China Coal Soc. 50(01), 1–12 (2025).
Ling, B., Yang, W. & Liu, T. Typical characteristics of deep coal seams with high outburst risk, outburst inducing mechanism and prevention measures[J]. J. China Coal Soc. 50 (01), 311–325 (2025).
Lin, H. et al. Research progress on pressure released gas drainage technology of mining cracking zone in overburden strata of coal mine in China[J]. Coal Sci. Technol. 46 (01), 28–35 (2018).
Lin, H. et al. Overburden rock fracture evolution law and pressure relief gas extraction technology of gob-side entry retaining mining[J]. J. Min. Strata Control Eng. 6 (01), 52–64 (2024).
Zhai, C. et al. Strategic Conception and Research Progress of Methane in-situ Deflagration Fracturing Technology in Shale reservoirs[J]. Journal of China University of Mining & Technology. 53(03), 435–455 (2024).
Yuan, L. Theory and technology considerations on High-quality development of coal main energy security in China[J]. Bull. Chin. Acad. Sci. 38 (01), 11–22 (2023).
Lin, B. et al. Establishment and practices on distribution type energy system based on gas near zero emission in mining Area[J]. Coal Sci. Technol. 42 (06), 45–48 (2014).
Aruah, B. et al. Altering shale permeability by cold shock[J]. Gas Sci. Eng. 125, 205291 (2024).
Hao, H. et al. Effect of ultrasonic excitation time on pore and crack structure and permeability characteristics of coal[J]. China Saf. Sci. J. 34 (09), 155–164 (2024).
Wang, X. et al. Research progress and prospects of ultrasonic vibration in coal rock fracturing[J]. Coal Sci. Technol. 52 (01), 232–243 (2024).
Zuo, S. et al. Effect of acid fracturing fluid modifying coal microstructure stimulated by ultrasonic[J]. Int. J. Min. Sci. Technol. 35 (2), 275–293 (2025).
Zuo, S. et al. A study on the impact of ultrasonic-stimulated clean fracturing fluid on the pore structure of medium to high rank coal[J]. Sci. Rep. 14 (1), 21026 (2024).
Wang, L. et al. Effects of ultrasonic and surfactant coupling treatment on the wettability of coal[J]. Powder Technol. 427, 118767 (2023).
Liang, X. et al. Synergistic mechanism of Ultrasonic-Chemical effects on the CH4 Adsorption-Desorption and physicochemical properties of Jincheng Anthracite.[J]. ACS Omega. 8 (1), 1079–1087 (2023).
Myltykbayeva, Z. et al. Ultrasonic technology for hydrocarbon Raw recovery and Processing[J]. Processes 12 (10), 2162 (2024).
Zuo, S. et al. Mechanism of a novel ultrasonic promoting fracturing technology in stimulating permeability and gas extraction[J]. Energy Rep. 8, 12776–12786 (2022).
Zhang, L. et al. Controlled mechanism of dynamic behavior of water-based ultrasonic cavitation in coal pore microstructure[J]. Fuel. 2024,358(PB).
Liu, P. et al. Power ultrasound assisted coalbed methane enhancement recovery: field application and performance evaluation in underground coal mine[J]. Fuel. 2022,324(PA).
Fei, J. et al. Investigation of the ultrasonic stimulation performance on permeability enhancement in coal seam: field tests and in situ permeability Evaluation[J]. Geofluids, 2022, 2022.
Ding, X., Hou, J. & Xiao, X. Experimental study on ultrasonic irradiation for enhancing coalbed methane recovery[J]. Sci. Rep. 12 (1), 7768 (2022).
Yang, E. et al. Characteristic strength and energy evolution law of coal treated by ultrasonic wave with different power under uniaxial Compression[J]. Nat. Resour. Res. 31 (2), 1–16 (2022).
Sun, Y. et al. Changes of coal molecular and pore structure under ultrasonic Stimulation[J]. Energy Fuels. 35 (12), 9847–9859 (2021).
Guo, X. et al. Mechanical damage to coal and increased coal permeability caused by Water-Based ultrasonic Cavitation[J]. Energies 17 (15), 3626 (2024).
Adelina, L. et al. The effects of sorbing and non-sorbing gases on ultrasonic wave propagation in fractured coal[J]. Int. J. Coal Geol. 249, 103906 (2022).
Chen, J. et al. Correlation mechanism between the law of ultrasonic propagation in coal samples and the migration of water[J]. Fuel. 2022,310(PA).
Liu, Y. et al. Prospects for the development of the theory and technology of non-hydration penetration enhancement in soft coal seams[J]. J. China Coal Soc. 50 (04), 2123–2146 (2024).
Cheng, Y. et al. Micro-cracking morphology and dynamic fracturing mechanism of natural brittle sandstone containing layer structure under compression[J]. Constr. Build. Mater. 26 (425), 136051 (2024).
Cheng, Y. et al. Failure mechanism and infrared radiation characteristic of hard siltstone induced by stratification effect[J]. J. Mt. Sci. 21 (3), 700–716 (2024).
Zhang, S. et al. Modelling Method of Heterogeneous Rock Mass and DEM Investigation of Seepage characteristics[J]. Geomechanics and Geophysics for Geo-Energy and Geo-Resources. 10(1), 46 (2024).
Lei, S., Hao, D. & Cao, S. Study on uniaxial compression deformation and fracture development characteristics of weak interlayer Coal–Rock Combination[J]. Fractal Fract. 7 (10), 731 (2023).
Gao, Z. et al. Mechanical behavior of a fissured clay subjected to impact loading under the plane strain condition[J]. Soil Dyn. Earthq. Eng. 183, 108764 (2024).
Nie, X. et al. Investigating mechanical properties of cemented gangue backfill materials subjected to static-dynamic combined loads[J]. Constr. Build. Mater. 400, 132674 (2023).
Ji, H. et al. Research on Stress State and Energy Evolution of Acoustic Emission Signal during Rock Materials Fracture process[J]. Journal of China University of Mining & Technology. 53(02), 211–223 (2024).
Paygozar, B. & Dizaji, S. Investigating energy absorption accessible by plastic deformation of a seismic damper using artificial neural Network[J]. Procedia Structural Integrity. 21138-1145 (2019).
Hu, S. B., Wang, E. Y. & Kong, X. G. Damage and deformation control equation for gas-bearing coal and its numerical calculation method[J]. J. Nat. Gas Sci. Eng. 25, 166–179 (2015).
Ding, W. Z. et al. Mechanical Properties and Energy Damage Evolution Characteristics of Coal Under Cyclic Loading and Unloading[J]. Rock Mechanics and Rock Engineering. 55(8), 4765–4781 (2022).
Jose, M. R. & Dutta, S. A phase-field regularized cohesive zone model to Bridge pore architecture and R-curve behavior in geopolymer composites[J]. Comput. Struct., 320, 108034 (2026).
Chen, S. et al. A new elastic-plastic constitutive model for the coupled thermo-mechanical damaged rock considering dilatancy equation[J]. Powder Technol., 466, 121415 (2025).
Khamidullin, R. et al. Comprehensive study of the structural integrity of a damaged turbine disk using FEM, DIC and phase field methods[J]. Int. J. Fatigue, 192, 108720 (2025).
Acknowledgements
This work was supported by the National Natural Science Foundation of China (NO. 52574265).
Author information
Authors and Affiliations
Contributions
**Ruoyu Bao: ** Methodology, data curation, theoretical modelling, writing, and Project management. **Fuyuan Zhang: ** Methodology, manuscript writing and revision. **Renhui Cheng: ** Methodology and manuscript revision.
Corresponding author
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
About this article
Cite this article
Bao, R., Zhang, Y. & Cheng, R. Study on energy evolution and damage constitutive model of coal fractured by dual-frequency ultrasonic cracking. Sci Rep (2026). https://doi.org/10.1038/s41598-026-38893-x
Received:
Accepted:
Published:
DOI: https://doi.org/10.1038/s41598-026-38893-x
