Damage constitutive model and damage evolution characteristics of gangue cemented backfill with different moisture contents based on energy dissipation

Abstract

To reveal the influence of moisture content on the mechanical properties and damage of gangue cemented backfill, uniaxial compression tests were carried out on gangue cemented backfill with four different moisture contents (dry, natural, immersed, and saturated). The influence of moisture content on the characteristic parameters, energy evolution, distribution characteristics and peak point energy index of gangue cemented backfill was considered. The unit characteristic change rate and unit energy change rate were proposed to describe the degree of variation in the characteristic parameters and peak point energy indicators with moisture content. From the perspective of energy dissipation, a damage constitutive model considering the initial compaction closure and post-peak failure stages was established, and the model was revised to compensate for the shortcomings of the current damage constitutive model research. The stress – strain curve of the gangue-cemented backfill before reaching the saturated state exhibited a typical four-stage characteristic, whereas the gangue-cemented backfill in the saturated state lost the initial compaction closure stage. The characteristic parameters of the cemented gangue backfill decreased in the form of a quadratic function with the increase of moisture content. The unit characteristic change rate gradually decreased with the increase of moisture content, and the decreased amplitude gradually increased, indicating that the order of the influence of moisture state on the unit characteristic change rate of gangue cemented backfill was: drying effect < immersion effect < saturation effect. The energy evolution law of gangue cemented backfill with different moisture contents was consistent with the stage characteristics of the stress – strain curve. Before the saturated state, the elastic energy ratio curves of the gangue-cemented backfill all showed a trend of first increasing and then decreasing, whereas the dissipation energy ratio curves showed a trend of first decreasing and then increasing. The order of influence of the moisture state on the unit energy change rate of the total strain energy and elastic energy of the gangue-cemented backfill was as follows: drying effect < immersion effect < saturation effect, while the order of influence on the unit energy change rate of the dissipated energy was as follows: saturation effect < immersion effect < drying effect. With the increase in the moisture content of the gangue-cemented backfill, the failure mode of the backfill mainly underwent a transformation from tensile failure to tensile-shear mixed failure and then to “V” -shaped shear failure. The modified damage constitutive model based on energy dissipation considering the initial compaction closure stage and the post-peak failure stage has a high consistency with the test curve, and the energy dissipation curve and damage evolution curve of the cemented gangue backfill with different moisture content were also consistent. When the dissipation energy curve reached the threshold, the damage evolution curve also reached the threshold. These results provide a theoretical basis for studying the long-term stability of gangue-cemented backfill with different moisture contents in the goaf.

Keywords

gangue cemented backfill / compressive strength / energy evolution / dissipation energy / damage constitutive model

References

[1] Yan H, Shi P-t, Zhang J-x, et al.. Mineralized carbon sequestration evaluation of coal-based solid waste consolidated backfill: A novel data-driven approach [J]. Fuel, 2024, 378: 132913

[2] Chen Q-s, Yuan X-y, Wu A-x, et al.. Enhancing CO₂ mitigation potential and mechanical properties of shotcrete in underground mining utilizing microbially induced calcium carbonate precipitation [J]. International Journal of Mining Science and Technology, 2024, 34(12): 1643-1653

[3] Yu X, Yang K, He X, et al.. Research progress on multi-source coal-based solid waste (MCSW) resource utilization and backfill mining basic theory: A systematic literature review [J]. Process Safety and Environmental Protection, 2025, 195: 106670

[4] Wang Y-m, Chen Q-s, Dai B-b, et al.. Guidance and review: Advancing mining technology for enhanced production and supply of strategic minerals in China [J]. Green and Smart Mining Engineering, 2024, 1(1): 2-11

[5] Zhang J-q, Yang K, He X, et al.. Study on mechanical properties and damage characteristics of coal-based solid waste cemented backfill [J]. Construction and Building Materials, 2023, 368: 130373

[6] Su L-j, Wu S-y, Yang J-b, et al.. Experimental study on the dynamic mechanical properties of polypropylene fibre-reinforced coal gangue-cemented backfill [J]. Construction and Building Materials, 2025, 459: 139843

[7] Huang P, Zhang J-x, Yan X-j, et al.. Deformation response of roof in solid backfilling coal mining based on viscoelastic properties of waste gangue [J]. International Journal of Mining Science and Technology, 2021, 31(2): 279-289

[8] Du X-j, Feng G-r, Zhang M, et al.. Influence of backfilling rate on the stability of the “backfilling body-immediate roof” cooperative bearing structure [J]. International Journal of Mining Science and Technology, 2022, 32(6): 1197-1206

[9] Long K, Li B-y, Ma J-y, et al.. Ecological risk analysis of leakage caused by coal-based solid waste backfill slurry bleeding: An experimental study [J]. Journal of Cleaner Production, 2025, 494: 144993

[10] Lu Y, Lu W, Wang C-x, et al.. Influences of water filling timing on the deformation mechanism of crushed gangue in goaf [J]. Case Studies in Construction Materials, 2024, 20: e03263

[11] Song H-q, Xu J-j, Fang J, et al.. Potential for mine water disposal in coal seam goaf: Investigation of storage coefficients in the Shendong mining area [J]. Journal of Cleaner Production, 2020, 244: 118646

[12] Qian R-p, Liu X-l, Ma Q, et al.. Effect of water intrusion on mechanical behaviors and failure characteristics of backfill body and coal pillar composite specimens under uniaxial compression [J]. Journal of Cleaner Production, 2025, 502: 145388

[13] Yu X, Yang K, He X, et al.. Strength and damage characteristics of cemented gangue backfill during saturated immersion [J]. Coal Geology & Exploration, 2025, 53(2): 147-159

[14] Liu Z-y, Gan D-q, Sun H-k, et al.. Dynamic impact performance of cemented tailings backfill in a waterbearing environment: Coupling effects and damage characteristics [J]. Soil Dynamics and Earthquake Engineering, 2025, 191: 109249

[15] Wang J, Zhang C, Fu J-x, et al.. Effect of water saturation on mechanical characteristics and damage behavior of cemented paste backfill [J]. Journal of Materials Research and Technology, 2021, 15: 6624-6639

[16] Hu Y, Li Z, Su Y-w, et al.. Analyzing the energy and damage constitutive of cemented backfill with different water content under dynamic load [J]. Materials, 2023, 16(16): 5677

[17] Wu W-l, Xu W-bin. Experimental study on the effect of saturation on the triaxial mechanical properties of cemented tailings backfill [J]. Journal of Central South University (Science and Technology), 2023, 54(10): 4015-4029(in Chinese)

[18] Liu D, Xu J-c, Pu H. Experimental study on creep characteristics of gangue cemented fillers with different water content [J]. Journal of Mining & Safety Engineering, 2021, 38(5): 1055-1062(in Chinese)

[19] Zhao Y, Taheri A, Karakus M, et al.. Effects of water content, water type and temperature on the rheological behaviour of slag-cement and fly ash-cement paste backfill [J]. International Journal of Mining Science and Technology, 2020, 30(3): 271-278

[20] Zhou Y, Yu X, Guo Z-q, et al.. On acoustic emission characteristics, initiation crack intensity, and damage evolution of cement-paste backfill under uniaxial compression [J]. Construction and Building Materials, 2021, 269: 121261

[21] Zhan R, Zhang B, Liu L, et al.. Strength and damage constitutive model of backfill body after high temperature treatment [J]. Engineering Fracture Mechanics, 2025, 314: 110686

[22] Zhu T-y, Chen Z-h, Wang Z-y, et al.. Energy damage evolution and mesoscopic failure mechanism of cemented waste rock tailing backfill under axial compression [J]. Structures, 2025, 71: 108057

[23] Gan D-q, Lu Y-z, Sun H-k, et al.. Mechanical response and damage constitutive model of early-age cemented paste backfill after cyclic loading [J]. Journal of Building Engineering, 2024, 86: 108822

[24] Hou Y-q, Yin S-h, Chen X, et al.. Study on characteristic stress and energy damage evolution mechanism of cemented tailings backfill under uniaxial compression [J]. Construction and Building Materials, 2021, 301: 124333

[25] Gan D-q, Sun H-k, Xue Z-l, et al.. Damage evolution and strength prediction model of soda residue modified cemented tailings backfill under uniaxial compression [J]. Construction and Building Materials, 2023, 408: 133709

[26] Zhao Y-h, Ran H-y, Feng G-r, et al.. Damage evolution and failure characteristics of cemented gangue backfill body with different height-width ratios under uniaxial compression [J]. Journal of Mining & Safety Engineering, 2022, 39(04): 674-682(in Chinese)

[27] Liu W-z, Chen J-t, Guo Z-p, et al.. Mechanical properties and damage evolution of cemented coal gangue-fly ash backfill under uniaxial compression: Effects of different curing temperatures [J]. Construction and Building Materials, 2021, 305: 124820

[28] Fu J-x, Wang J, Song W-dong. Damage constitutive model and strength criterion of cemented paste backfill based on layered effect considerations [J]. Journal of Materials Research and Technology, 2020, 9(3): 6073-6084

[29] Hou Y-q, Yin S-h, Wang Y-l, et al.. Mechanical properties and damage evolution mechanisms of cemented backfill with tailored particle size range of coal gangue aggregates [J]. Process Safety and Environmental Protection, 2025, 198: 107123

[30] Nie Y-l, Wang X-j, Huang G-l, et al.. Strength and damage model analysis of pure tailings cemented filling body with different water content [J]. Bulletin of the Chinese Ceramic Society, 2018, 37(6): 2008-2013

[31] Yang K, Yu X, He X, et al.. Energy evolution and damage characteristics of gangue cemented backfill in different water content states [J]. Rock and Soil Mechanics, 2025, 46(1): 26-42(in Chinese)

[32] Song X-p, Hao Y-x, Wang S, et al.. Study on mechanical behavior and damage characteristics of cemented tailings backfill with different water content under different loading rates [J]. Materials Reports, 2022, 36(24): 103-112(in Chinese)

[33] Li Z-f, Zhang C, Zhang J, et al.. Mechanical properties and damage mechanism of backfill with different water saturation [J]. Journal of Mining and Safety Engineering, 2021, 38(5): 1063-1070(in Chinese)

[34] Zhao Y-h, Guo Y-x, Feng G-r, et al.. Study on strength and deformation characteristics of cemented gangue backfill body under the coupling action of load and salt erosion [J]. Construction and Building Materials, 2022, 342: 128003

[35] Yang J, Yang X-b, Yin S-h, et al.. Damage characteristics and constitutive model of magnesium slag-based cemented backfill based on energy dissipation [J]. Construction and Building Materials, 2024, 449: 138443

[36] Liu L, Ding X, Tu B-b, et al.. Energy evolution and mechanical properties of modified magnesium slag-based backfill materials at different curing temperatures [J]. Construction and Building Materials, 2024, 411: 134555

[37] Qu H-s, Liu L, Suo Y-l, et al.. Anisotropic characteristics of layered backfill: Mechanical properties and energy dissipation [J]. Journal of Rock Mechanics and Geotechnical Engineering, 2023, 15(12): 3188-3208

[38] Yang Y-b, Lai X-p, Zhang Y, et al.. Strength deterioration and energy dissipation characteristics of cemented backfill with different gangue particle size distributions [J]. Journal of Materials Research and Technology, 2023, 25: 5122-5135

[39] Gao H, Xie H-p, Zhang Z-t, et al.. True triaxial energy evolution characteristics and failure mechanism of deep rock subjected to mining-induced stress [J]. International Journal of Rock Mechanics and Mining Sciences, 2024, 176: 105724

[40] Zhao K, Lai Y-m, He Z-w, et al.. Study on energy dissipation and acoustic emission characteristics of fiber tailings cemented backfill with different ash-sand ratios [J]. Process Safety and Environmental Protection, 2023, 174: 983-996

[41] Xia Z, Yao Q-l, Li X-h, et al.. Acoustic emission characteristics and energy mechanism of CFRP-jacketed coal specimens under uniaxial compression [J]. Construction and Building Materials, 2022, 342: 127936

[42] Liu W-z, Niu S-wei. Energy evolution properties and strength failure criterion of coal-fired slag concrete based on energy dissipation [J]. Case Studies in Construction Materials, 2022, 17: e01369

[43] Ou X-d, Chen F-g, Jiang J, et al.. Characteristics of energy and cracks evolution of foam concrete under different bauxite tailing contents and dry and wet cycling environments [J]. Journal of Building Engineering, 2025, 101: 111847

[44] Xu Y-j, Yao Z-s, Wang J-q, et al.. Mechanical properties and energy evolution of drilling shaft lining concrete under hydro-mechanical coupling [J]. Construction and Building Materials, 2024, 419: 135548

[45] Zhang C, Wang J, Song W-d, et al.. Pore structure, mechanical behavior and damage evolution of cemented paste backfill [J]. Journal of Materials Research and Technology, 2022, 17: 2864-2874

[46] Hou Y-q, Yin S-h, Yang S-x, et al.. Mechanical properties, damage evolution and energy dissipation of cemented tailings backfill under impact loading [J]. Journal of Building Engineering, 2023, 66: 105912

[47] Yin S-h, Zeng J-l, Yan Z-p, et al.. Damage constitutive models and damage evolution of cemented tailings and waste-rock backfill under impact loading [J]. Construction and Building Materials, 2025, 460: 139838

[48] Wang J, Fu J-x, Song W-d, et al.. Mechanical properties, damage evolution, and constitutive model of rock-encased backfill under uniaxial compression [J]. Construction and Building Materials, 2021, 285: 122898

[49] Wang J, Fu J-x, Song W-d, et al.. Acoustic emission characteristics and damage evolution process of layered cemented tailings backfill under uniaxial compression [J]. Construction and Building Materials, 2021, 295: 123663

[50] Zhang P-l, Gong F-q, Luo S, et al.. Damage constitutive model of uniaxially compressed coal material considering energy dissipation [J]. Journal of Materials Research and Technology, 2023, 27: 920-931

[51] Yin S-h, Hou Y-q, Chen X, et al.. Mechanical behavior, failure pattern and damage evolution of fiber-reinforced cemented sulfur tailings backfill under uniaxial loading [J]. Construction and Building Materials, 2022, 332: 127248

[52] Han P-h, Zhao Y-x, Gao S, et al.. Progressive damage characteristics and damage constitutive model of coal samples under long-term immersion [J]. Chinese Journal of Rock Mechanics and Engineering, 2024, 43(4): 918-933(in Chinese)

[53] Yang L, Wang B-w, Liu C-y, et al.. Energy dissipation characteristics and constitutive model of structural backfill under uniaxial compression [J]. The Chinese Journal of Nonferrous Metals, 2024, 34(10): 3532-3546(in Chinese)

[54] Yin S-h, Hou Y-q, Yang S-x, et al.. Analysis of deformation failure and energy dissipation of mixed aggregate cemented backfill during uniaxial compression [J]. Journal of Central South University (Science and Technology), 2021, 52(3): 936-947(in Chinese)

RIGHTS & PERMISSIONS

Central South University