Comprehensive response analysis of stress wave propagation and energy dissipation of a cemented tailings backfill based on the relative dissipation factor

Abstract

The destruction of backfill under strong disturbances can be regarded as the result of stress waves propagating in the filling medium; however, accurately quantifying the stress wave attenuation and energy dissipation conversion process in backfill materials remains at an exploratory stage. The split Hopkinson pressure bar (SHPB) experimental system is employed in this study to conduct dynamic compression tests on backfill materials with different media, encompassing various strain rates. The relative dissipation factor, defined as the ratio of the wave attenuation coefficient to the energy dissipation coefficient, is utilized to establish dimensionless empirical formulas incorporating influencing factors such as the strain rate through a dimensional analysis method. Furthermore, the transformation process of stress wave propagation and energy dissipation within the backfill is thoroughly analyzed. The experimental results demonstrate that the strain rate and wave impedance affect the stress wave propagation and dynamic mechanical properties of the material. At a constant strain rate, a smaller sample wave impedance leads to a larger reflected wave and a smaller transmitted wave. Additionally, the backfill does not affect the normalized spectra of the incident and transmitted waves along the propagation path. When the wave impedance is constant, both the peak stress and peak strain increase with increasing strain rate. Samples subjected to strain rates of 34.51 and 68.34 s⁻¹ exhibit “double peaks” in their stress–strain curves, indicating prolonged plastic flow behavior. Furthermore, a negative correlation is observed between the model data and original data with respect to the peak stress and density, whereas positive correlations are observed for the wave impedance and strain rate. This study provides a new method for analyzing the stress wave propagation and energy dissipation of cemented tailings backfill (CTB) materials under strong disturbances, which can provide a comprehensive understanding of the failure mechanism of CTB materials under impact loads.

Keywords

Cemented tailings backfill / Strain rate / Wave impedance / Stress wave propagation / Energy dissipation / Relative dissipation factor

References

[1] R.V. Sagar, A parallel between earthquake sequences and acoustic emissions released during fracture process in reinforced concrete structures under flexural loading, Constr. Build. Mater. 114 (2016) 772-793.

[2] J. Zhou, M. Koopialipoor, E.M. Li, D.J. Armaghani, Prediction of rockburst risk in underground projects developing a neuro-bee intelligent system, Bull. Eng. Geol. Environ. 79 (8) (2020) 4265-4279.

[3] D.J. Armaghani, M. Hasanipanah, H.B. Amnieh, E.T. Mohamad, Feasibility of ICA in approximating ground vibration resulting from mine blasting, Neural Comput. Appl. 29 (9) (2018) 457-465.

[4] X.L. Li, Z.H. Tao, J.G. Wang, T. Zuo, J. Ma, Q. Li, Strain rate effect on mechanical properties of cemented backfill under dynamic and static combined loading, Shock. Vib. 2021 (1) (2021) 2196838.

[5] C.L. Wang, B.B. He, X.L. Hou, J.Y. Li, L. Liu, Stress−energy mechanism for rock failure evolution based on damage mechanics in hard rock, Rock Mech. Rock Eng. 53 (3) (2020) 1021-1037.

[6] Z.Q. Chen, C. He, G.Y. Ma, G.W. Xu, C.C. Ma, Energy damage evolution mechanism of rock and its application to brittleness evaluation, Rock Mech. Rock Eng. 52 (4) (2019) 1265-1274.

[7] L.M. Zhang, Y. Cong, F.Z. Meng, Z.Q. Wang, P. Zhang, S. Gao, Energy evolution analysis and failure criteria for rock under different stress paths, Acta Geotech. 16 (2) (2021) 569-580.

[8] H.S. Qu, L. Liu, Y.L. Suo, M.B. Zhu, P. Yang, C.X. Zhang, G. Xie, Anisotropic characteristics of layered backfill: mechanical properties and energy dissipation, J. Rock. Mech. Geotech. Eng. 15 (12) (2023) 3188-3208.

[9] H.P. Xie, J. Lu, C.B. Li, M.H. Li, M.Z. Gao, Experimental study on the mechanical and failure behaviors of deep rock subjected to true triaxial stress: a review, Int. J. Min. Sci. Technol. 32 (5) (2022) 915-950.

[10] R.S. Yang, W.Y. Li, Z.W. Yue, Comparative study on dynamic mechanical properties and energy dissipation of rocks under impact loads, Shock. Vib. 2020 (1) (2020) 8865099.

[11] J.F. Jin, W. Yuan, Y. Wu, Z.Q. Guo, Effects of axial static stress on stress wave propagation in rock considering porosity compaction and damage evolution, J. Cent. South Univ. 27 (2) (2020) 592-607.

[12] X.H. Liu, F. Dai, R. Zhang, J.F. Liu, Static and dynamic uniaxial compression tests on coal rock considering the bedding directivity, Environ. Earth Sci. 73 (10) (2015) 5933-5949.

[13] R.J. Wu, H.B. Li, X.F. Li, X. Xia, L.W. Liu, Experimental study and numerical simulation of the dynamic behavior of transversely isotropic phyllite, Int. J. Geomech. 20 (8) (2020) 04020105.

[14] D.H. Ai, Y.C. Zhao, Q.F. Wang, C.W. Li, Crack propagation and dynamic properties of coal under SHPB impact loading: experimental investigation and numerical simulation, Theor. Appl. Fract. Mech. 105 (2020) 102393.

[15] J.H. Wu, H.B. Wang, Q. Zong, Y. Xu, Experimental investigation of dynamic compression mechanical properties of frozen fine sandstone, Adv. Civ. Eng. 2020 (1) (2020) 8824914.

[16] Z.Y. Han, D.Y. Li, T. Zhou, Q.Q. Zhu, P.G. Ranjith, Experimental study of stress wave propagation and energy characteristics across rock specimens containing cemented mortar joint with various thicknesses, Int. J. Rock. Mech. Min. Sci. 131 (2020) 104352.

[17] W. Sun, S.Y. Zhang, J.X. Li, Z.Y. Li, Experimental study on energy dissipation of layered backfill under impact load, Constr. Build. Mater. 347 (2022) 128478.

[18] X. Chen, X.Z. Shi, J. Zhou, E.M. Li, P.Y. Qiu, Y.G. Gou, High strain rate compressive strength behavior of cemented paste backfill using split Hopkinson pressure bar, Int. J. Min. Sci. Technol. 31 (3) (2021) 387-399.

[19] Z.X. Zhang, D.F. Hou, A. Aladejare, Empirical equations between characteristic impedance and mechanical properties of rocks, J. Rock. Mech. Geotech. Eng. 12 (5) (2020) 975-983.

[20] Y.Y. Tan, X. Yu, D. Elmo, L.H. Xu, W.D. Song, Experimental study on dynamic mechanical property of cemented tailings backfill under SHPB impact loading, Int. J. Miner. Metall. Mater. 26 (4) (2019) 404-416.

[21] Y.Q. Hou, S.H. Yin, S.X. Yang, X. Chen, H.H. Du, Mechanical properties, damage evolution and energy dissipation of cemented tailings backfill under impact loading, J. Build. Eng. 66 (2023) 105912.

[22] Z.L. Zhou, X.B. Li, Z.Y. Ye, K.W. Liu, Obtaining constitutive relationship for rate-dependent rock in SHPB tests, Rock Mech. Rock Eng. 43 (6) (2010) 697-706.

[23] Y.J. Xie, Q. Fu, K.R. Zheng, Q. Yuan, H. Song, Dynamic mechanical properties of cement and asphalt mortar based on SHPB test, Constr. Build. Mater. 70 (2014) 217-225.

[24] L.L. Wang, Foundations of Stress Waves, Elsevier, 2007, pp. 77-85.

[25] Z.X. Zhang, Rock Fracture and Blasting: Theory and Applications, Butterworth-Heinemann, 2016, pp. 50-66.

[26] H. Liao, W.W. Chen, Specimen-bar impedance mismatch effects on equilibrium and rate constancy for Kolsky bar experiments, Exp. Mech. 58 (9) (2018) 1439-1449.

[27] D. Alleyne, P. Cawley, A two-dimensional Fourier transform method for the measurement of propagating multimode signals, J. Acoust. Soc. Am. 89 (3) (1991) 1159-1168.

[28] A.M. Abdelalim, Y. Shalaby, M. Salem, M. Al-Adwani, G.A. Ebrahim, M. Badawy, Automated vision-based crack detection for reinforced concrete bridges using Matlab algorithms, Preprints (2024) 2024110078.

[29] J.C. Li, L.F. Rong, H.B. Li, S.N. Hong, An SHPB test study on stress wave energy attenuation in jointed rock masses, Rock Mech. Rock Eng. 52 (2) (2019) 403-420.

[30] X.L. Huang, S.W. Qi, K.W. Xia, H. Zheng, B.W. Zheng, Propagation of high amplitude stress waves through a filled artificial joint: an experimental study, J. Appl. Geophys. 130 (2016) 1-7.

[31] L. Gaul, The influence of damping on waves and vibrations, Mech. Syst. Signal Process. 13 (1) (1999) 1-30.

[32] Y. Sogabe, K. Kishida, K. Nakagawa, Wave propagation analysis for determining the dynamic properties of high damping alloys, Bull. JSME 25 (201) (1982) 321-327.

[33] J. Kimberley, K.T. Ramesh, The dynamic strength of an ordinary chondrite, Meteorit. Planet. Sci. 46 (11) (2011) 1653-1669.

[34] M. Li, X.B. Mao, L.L. Cao, H. Pu, A.H. Lu, Influence of heating rate on the dynamic mechanical performance of coal measure rocks, Int. J. Geomech. 17 (8) (2017) 04017020.

[35] S. Aziznejad, K. Esmaieli, J. Hadjigeorgiou, D. Labrie, Responses of jointed rock masses subjected to impact loading, J. Rock Mech. Geotech. Eng. 10 (4) (2018) 624-634.

[36] L.J. Su, S.Y. Wu, J.B. Yang, M.Q. Zhang, W.C. Zhu, X.T. Fu, Experimental study on the dynamic mechanical properties of polypropylene fibre-reinforced coal gangue-cemented backfill, Constr. Build. Mater. 459 (2025) 139843.

[37] B. Pichler, C. Hellmich, Upscaling quasi-brittle strength of cement paste and mortar: a multi-scale engineering mechanics model, Cem. Concr. Res. 41 (5) (2011) 467-476.