Experimental study on stress wave attenuation and energy dissipation of sandstone under full deformation condition

  • Yun ChengEmail author
  • Zhanping SongEmail author
  • Jiefang Jin
  • Junbao Wang
  • Tong Wang
Original Paper


Excavation behaviours not only destroy the balance of original stress in rock mass but lead to the redistribution of initial stress, resulting in rock mass in a new stress environment. The static stress in rock mass has the characteristics of dynamic change. For the purpose of investigating the effect of increasing static stress on attenuation mechanism and energy dissipation of stress wave in sandstone under the overall deformation condition, small disturbance experiments on sandstone bar are carried out with a modified split-Hopkinson pressure bar test system. The stress waveform, p wave velocity, temporal and spatial attenuation of amplitude, and energy dissipation are studied under various static stresses. Results show that stress waveforms at different locations are approximately the same, those at the same locations vary greatly, and the tensile waves that appeared at the tails of stress waves are larger with increasing static stress. With increasing static stress, p wave velocity experiences a dramatic increase, then develops gently, and finally a sharp decrease; the stress demarcation points are σs/σc = 30% and σs/σc = 55%, respectively. P wave velocity can be predicted by a quadratic equation when σs/σc > 63.69%. The relation between longitudinal wave velocity and static stress can be described by a quadratic function. Stress wave amplitudes decrease exponentially with increasing distance and time. Values of temporal spatial response intensity (RI) and spatial RI are approximately equal and present the same development tendency of nonlinear and linear stages due to the same dimensions. Values of temporal attenuation characteristic (AC) and spatial AC are differed by 2 or 3 orders of magnitude although they present the same development tendencies. Ratios of RI and AC can indicate the sensitivity of temporal and spatial attenuation to different static stresses. Full-wave energy declines in an exponential function with increasing static stress and decays as a logarithmic function with increasing distance. Widespread attenuation characteristics like these should provide a theoretical basis for rock mass stability analysis.


Sandstone Stress wave P wave velocity Attenuation characteristics Energy dissipation 



The authors thank the National Natural Science Foundation of China and fund of housing urban and rural construction technology research and development project foundation of China. And we thank Liwen Bianji, Edanz Editing China (, for editing the English text of a draft of this manuscript.

Funding information

This study received support from the National Natural Science Foundation of China (Grant No. 51578447) and fund of housing urban and rural construction technology research and development project foundation of China (Grant No. 2017-K4-032).

Compliance with ethical standards

Competing interests

The authors declare that they have no competing interests.


  1. Aydan Ö, Kumsar H (2010) An experimental and theoretical approach on the modeling of sliding response of rock wedges under dynamic loading. Rock Mech Rock Eng 43(6):821–830CrossRefGoogle Scholar
  2. Cao A, Dou L, Cai W, Gong S, Liu S, Zhao Y (2016) Tomographic imaging of high seismic activities in underground island longwall face. Arab J Geosci 9(3):1–10CrossRefGoogle Scholar
  3. Cheng Y, Chang XX, He C, Yuan W (2016) Analysis of stress wave characteristics of concrete pile based on analytic equation. J Jiangxi U Sci Techno 37(5):41–46Google Scholar
  4. Cheng Y, Song ZP, Jin JF, Yang TT (2019) Attenuation characteristics of stress wave peak in sandstone subjected to different axial stresses. Adv Mater Sci Eng 1–11. Google Scholar
  5. Cichowicz A, Milev AM, Durrheim RJ (1999) Transfer function for the seismic signal recorded in solid and fractured rock surrounding deep level mining excavations. J S Afr I Min Metall 99(4):201–206Google Scholar
  6. Davies EDH, Hunter SC (1963) The dynamic compression testing of solids by the method of the split Hopkinson pressure bar. J Mech Phys Solids 11(3):155–179CrossRefGoogle Scholar
  7. Domnesteanu P, Mccann C, Sothcott J (2010) Velocity anisotropy and attenuation of shale in under-and overpressured conditions. Geophys Prospect 50(5):487–503CrossRefGoogle Scholar
  8. Fan LF, Sun HY (2015) Seismic wave propagation through an in-situ stressed rock mass. J Appl Geophys 121(13):13–20CrossRefGoogle Scholar
  9. Gong SY, Dou LM, Xu XJ, Jiang H, Lu CP, He H (2012) Experimental study on the correlation between stress and P-wave velocity for burst tendency coal-rock samples. J Min Safe Eng 29(1):67–71Google Scholar
  10. Gratchev IB, Towhata I (2011) Analysis of the mechanisms of slope failures triggered by the 2007 chuetsu oki earthquake. Geotech Geol Eng 29(5):695–708CrossRefGoogle Scholar
  11. Guo X, Wei P (2014) Effects of initial stress on the reflection and transmission waves at the interface between two piezoelectric half spaces. Int J Solids Struct 51(21–22):3735–3751CrossRefGoogle Scholar
  12. Hartman W, Handley MF (2002) The application of the Q-Tunnelling Quality Index to rock mass assessment at Impala Platinum Mine. J S Afr I Min Metall 102:155–166Google Scholar
  13. Hosseini N, Oraee K, Shahriar K, Goshtasbi K (2013) Studying the stress redistribution around the longwall mining panel using passive seismic velocity tomography and geostatistical estimation. Arab J Geosci 6(5):1407–1416CrossRefGoogle Scholar
  14. Hudyma N, Avar BB, Karakouzian M (2004) Compressive strength and failure modes of lithophysae-rich topopah spring tuff specimens and analog models containing cavities. Eng Geol 73(1):179–190CrossRefGoogle Scholar
  15. Jin JF, Li XB, Zhong HB (2013a) Study of dynamic mechanical characteristic of sandstone subjected to three-dimensional coupled static-cyclic impact loadings. Chin J Rock Mech Eng 32(7):1358–1372Google Scholar
  16. Jin JF, Li XB, Yin TB, Zhou XJ (2013b) Effect of axial static stress of elastic bar on incident stress wave under axial impact loading. Eng Mech 30(11):21–27Google Scholar
  17. Ju Y, Sudak L, Xie HP (2007) Study on stress wave propagation in fractured rocks with fractal joint surfaces. Int J Solids Struct 44(3):4256–4271CrossRefGoogle Scholar
  18. Khaksar, Griffiths, Mccann (2010) Compressional-and shear-wave velocities as a function of confining stress in dry sandstones. Geophys Prospect 47(4):487–508CrossRefGoogle Scholar
  19. Li XB, Lok TS, Zhao J (2005) Dynamic characteristics of granite subjected to intermediate loading rate. Rock Mech Rock Eng 38(1):21–39CrossRefGoogle Scholar
  20. Li D, Zhao F, Zheng M (2014) Fractal characteristics of cracks and fragments generated in unloading rock burst tests. Int J Min Sci Tech 24(4):819–823CrossRefGoogle Scholar
  21. Li XP, Zhao H, Luo Y, Cheng ZG, Sun CZ, Dong Q, Yang YP (2015) Experimental study of propagation and attenuation of elastic wave in deep rock mass with joints. Chin J Rock Mech Eng 34(11):2319–2326Google Scholar
  22. Liu SH, Mao DB, Qi QX, Li FM (2014) Under static loading stress wave propagation mechanism and energy dissipation in compound coal-rock. J China Coal Soc 39(s1):15–22Google Scholar
  23. Ma GW, Fan LF, Li JC (2013) Evaluation of equivalent medium methods for stress wave propagation in jointed rock mass. Int J Numer Anal Met 37(7):701–715CrossRefGoogle Scholar
  24. Ömer A, Kumsar H (2010) An experimental and theoretical approach on the modeling of sliding response of rock wedges under dynamic loading. Rock Mech Rock Eng 43(6):821–830CrossRefGoogle Scholar
  25. Peng FH, Li SL, Cheng JY, Jia BS (2014) Experimental study on characteristics of stress wave propagation in mesoscale and complex rock mass by microseismic monitoring. Chin J Geotech Eng 36(2):312–319Google Scholar
  26. Qian J, Sun LM, Jiang Y (2013) Experimental study on wave velocity and energy attenuation in cables. J Tong Ji U (Natural Science) 41(11):1618–1731Google Scholar
  27. Resende R, Lamas L, Lemos J, Calcada R (2014) Stress wave propagation test and numerical modelling of an underground complex. Int J Rock Mech Min 72:26–36CrossRefGoogle Scholar
  28. Sainoki A, Mitri HS (2014) Numerical simulation of rock mass vibrations induced by nearby product blast. Can Geotech J 51(11):1–10CrossRefGoogle Scholar
  29. Shang JL, Hu JH, Zhou KP, Luo XW, Aliyu MM (2015) Porosity increment and strength degradation of low-porosity sedimentary rocks under different loading conditions. Int J Rock Mech Min 75:216–223CrossRefGoogle Scholar
  30. Shin JH, Moon HG, Chae SE (2011) Effect of blast-induced vibration on existing tunnels in soft rocks. Tunn Undergr SP Tech 26(1):51–61CrossRefGoogle Scholar
  31. Song ZP, Wang JX, Jiang AN, Liu XR, Zhang XG (2014) Ultrasonic tests on schist with saturated fractures under uniaxial compression. Chin J Rock Mech Eng 33(12):2377–2383Google Scholar
  32. Song ZP, Yang TT, Jiang AN, Zhang DF, Jiang ZB (2016) Experimental investigation and numerical simulation of surrounding rock creep for deep mining tunnels. J S Afr I Min Metall 116(12):1181–1188CrossRefGoogle Scholar
  33. Sun FR, Yao YD, Li XF, Li H, Chen G, Sun Z (2017) A numerical study on the non-isothermal flow characteristics of superheated steam in ground pipelines and vertical wellbores. J Pet Sci Eng 159:68–75CrossRefGoogle Scholar
  34. Sun FR, Yao YD, Li GZ (2018a) Comments on: The flow and heat transfer characteristics of compressed air in high-pressure air injection wells. Arab J Geosci 11(20):519Google Scholar
  35. Sun FR, Yao YD, Li GZ, Li XF (2018b) Geothermal energy development by circulating CO2 in a U-shaped closed loop geothermal system. Energ Convers Manage 174:971–982CrossRefGoogle Scholar
  36. Sun FR, Yao YD, Li GZ, Li XF (2018c) Performance of geothermal energy extraction in a horizontal well by using CO2 as the working fluid. Energ Convers Manage 171:1529–1539CrossRefGoogle Scholar
  37. Sun FR, Yao YD, Li GZ, Li XF (2018d) Geothermal energy extraction in CO2 rich basin using abandoned horizontal wells. Energy 158:760–773CrossRefGoogle Scholar
  38. Sun FR, Yao YD, Li GZ, Li XF, Zhang T, Lu CG, Liu WY (2018e) An improved two-phase model for saturated steam flow in multi-point injection horizontal wells under steady-state injection condition. J Pet Sci Eng 167:844–856CrossRefGoogle Scholar
  39. Sun FR, Yao YD, Li GZ, Li XF (2018f) Numerical simulation of supercritical-water flow in concentric-dual-tubing wells. SPE J 23(6):2188–2201CrossRefGoogle Scholar
  40. Taljaard JJ, Stephenson JD (2000) State-of-art system as applied to Palabora underground mining project. J S Afr I Min Metall 100(7):427–437Google Scholar
  41. Thill RE, Bur TR, Steckley RC (1973) Velocity anisotropy in dry and saturated rock spheres and it elation to rock fabric. Int J Rock Mech Min Sci Geomech Abstracts 10(6):535–557CrossRefGoogle Scholar
  42. Wang GS, Li CH, Hu SL, Feng C, Li SH (2010) A study of time-and spatial-attenuation of stress wave amplitude in rock mass. Rock Soil Mech 31(11):3485–3492Google Scholar
  43. Wang JB, Ren ZZ, Song ZP, Huo RK, Yang TT (2019) Study of the effect of micro-pore characteristics and saturation degree on the longitudinal wave velocity of sandstone. Arab J Geosci 12:1–11. CrossRefGoogle Scholar
  44. Yan CL, Deng JG, Lianbo HZJ, Yan XJ, Lin H, Tan Q, Yu BH (2015) Brittle failure of shale under uniaxial compression. Arab J Geosci 8(5):2467–2475CrossRefGoogle Scholar
  45. Yang ZY, Hamid RP, Biswajeet P, Chen TH, Lee YH (2015) An index to describe the earthquake effect on subsequent landslides in Central Taiwan. Arab J Geosci 8(5):3139–3147CrossRefGoogle Scholar
  46. Zhang YW, Weng XL, Song ZP, Sun YF (2019) Modeling of loess soaking induced impacts on metro tunnel using water soaking system in centrifuge. Geofluids 2019, Article ID 5487952:17. CrossRefGoogle Scholar

Copyright information

© Saudi Society for Geosciences 2019

Authors and Affiliations

  1. 1.School of Civil EngineeringXi’an University of Architecture and TechnologyXi’anChina
  2. 2.Shaanxi Key Laboratory of Geotechnical and Underground Space EngineeringXi’an University of Architecture and TechnologyXi’anChina
  3. 3.School of Architectural and Surveying EngineeringJiangxi University of Science and TechnologyGanzhouChina

Personalised recommendations