Experimental Investigation of the Change of Elastic Moduli of Clastic Rocks under Nonlinear Loading

Document Type : Original Article


Department of Oil and Gas Technologies, Perm National Research Polytechnic University, Russia


This paper presents an experimental investigation on the nonlinear nature of the dynamic geomechanical characteristics of a clastic rock (sandstone). Rock samples of 7.5 mm in diameter and 15.6 mm in length were prepared. Rock properties were identified. Firstly, the limits of the rock linear elasticity zone were defined during quasistatic loading and uniaxial compressive strength determination at the Tinius Hounsfield rig. Secondly, the small experimental custom-built rig was designed to study the nonlinear nature of the Young’s modulus in the zone of linear elasticity. At the rig the sample was stationary preloaded. The dynamic load was generated by a piezoelectric actuator powered with a signal generator. The displacement of rock sample surfaces was recorded by a laser sensor and an eddy current probe. The dynamic experiments were conducted at the load amplitude ranging from 50 to 250 N for each of frequencies of 25 Hz and 40 Hz. It was found that the dynamic Young’s modulus increased with amplitude for all the frequencies studied. The newly developed experimental rig allows to investigate elastic moduli dispersion of rocks at the strain up to 10-3 under vibrations with frequency up to 40 Hz.


  1. He, M., Li, N., “Experimental research on the non-linear energy characteristics of granite and sandstone”, Géotechnique Letters, Vol. 10, No. 3, (2020), 385-392. doi: 10.1680/jgele.19.00117
  2. Geranmayeh Vaneghi, R., Ferdosi, B., Okoth, A. D., Kuek, B., “Strength degradation of sandstone and granodiorite under uniaxial cyclic loading”, Journal of Rock Mechanics and Geotechnical Engineering, Vol. 10, No. 1, (2018), 114-126. doi: 10.1016/j.jrmge.2017.09.005
  3. Marandi, S. M., Rasti, A. R., “Parametric study of the covering soil of tunnels constructed in liquefiable soil”, International Journal of Engineering, Transactions A: Basics, Vol. 25, No. 4, (2012), 375-388.
  4. Xia, K., Yao, W., Wu, B., “Dynamic rock tensile strengths of Laurentian granite: Experimental observation and micromechanical model”, Journal of Rock Mechanics and Geotechnical Engineering, Vol. 9, No. 1, (2017), 116-124. doi: 10.1016/j.jrmge.2016.08.007
  5. Jiang, Y.-Z., He, K.-F., Dong, Y.-L., Yang, D.-L., Sun, W., “Influence of load weight on dynamic response of vibrating screen”, Shock and Vibration, Vol. 2019, (2019), 4232730. doi: 10.1155/2019/4232730
  6. Lv, Y., Liu, J., Xiong, Z., “One-dimensional dynamic compressive behavior of dry calcareous sand at high strain rates”, Journal of Rock Mechanics and Geotechnical Engineering, Vol. 11, No. 1, (2019), 192-201. doi: 10.1016/j.jrmge.2018.04.013
  7. LeCompte, B., Franquet, J. A., Jacobi, D., “Evaluation of Haynesville Shale vertical well completions with a mineralogy based approach to reservoir geomechanics”, in SPE Annual Technical Conference and Exhibition 2009, Vol. 3, (2009), 1417-1430. doi: 10.2118/124227-ms
  8. Behnoud far, P., Hassani, A. H., Al-Ajmi, A. M., Heydari, H., “A novel model for wellbore stability analysis during reservoir depletion”, Journal of Natural Gas Science and Engineering, Vol. 35, (2016), 935-943. doi: 10.1016/j.jngse.2016.09.051
  9. Lozovyi, S., Bauer, A., “Static and dynamic stiffness measurements with Opalinus Clay”, Geophysical Prospecting, Vol. 67, No. 4, (2018), 997-1019. doi: 10.1111/1365-2478.12720
  10. Lozovyi, S., Bauer, A., “From static to dynamic stiffness of shales: Frequency and stress dependence”, Rock Mechanics and Rock Engineering, Vol. 52, (2019), 5085-5098. doi: 10.1007/s00603-019-01934-1
  11. Szewczyk, D., Bauer, A., Holt, R. M., “A new laboratory apparatus for the measurement of seismic dispersion under deviatoric stress conditions”, Geophysical Prospecting, Vol. 64, No. 4, (2016), 789-798. doi: 10.1111/1365-2478.12425
  12. Pimienta, L., Fortin, J., Guéguen, Y., “Bulk modulus dispersion and attenuation in sandstones”, Geophysics, Vol. 80, No. 2, (2015), A25-A30. doi: 10.1190/geo2014-0335.1
  13. Pimienta, L., Fortin, J., Guéguen, Y., “Effect of fluids and frequencies on Poisson’s ratio of sandstone samples”, Geophysics, Vol. 81, No. 2, (2016), D183-D195. doi: 10.1190/geo2015-0310.1
  14. Tisato, N., Quintal, B., “Measurements of seismic attenuation and transient fluid pressure in partially saturated Berea sandstone: Evidence of fluid flow on the mesoscopic scale”, Geophysical Journal International,Vol. 195, (2013), 342-351. doi: 10.1093/gji/ggt259
  15. Batzle, M. L., Han, D.-H., Hofmann, R., “Fluid mobility and frequency-dependent seismic velocity - Direct measurements”, Geophysics, Vol. 71, No. 1, (2006), N1-N9. doi: 10.1190/1.2159053
  16. Tutuncu, A. N., Podio, A. L., Gregory, A. R., Sharma, M. M., “Nonlinear viscoelastic behavior of sedimentary rocks, Part I: Effect of frequency and strain amplitude”, Geophysics,Vol.63, No. 1, (1998), 184-194. doi: 10.1190/1.1444311
  17. Biot, M. A., “Theory of propagation of elastic waves in a fluid-saturated porous solid II. Higher frequency range”, The Journal of the Acoustical Society of America, Vol. 28, No. 179, (1956), 179-191. doi: 10.1121/1.1908241
  18. O’Connell, R. J., Budiansky, B., “Viscoelastic properties of fluid‐saturated cracked solids”, Journal of Geophysical Research, Vol. 82, No. 36, (1977), 5719-5735. doi: 10.1029/JB082i036p05719
  19. Mavko, G., Nur, A., “Melt squirt in the asthenosphere”, Journal of Geophysical Research, Vol. 80, No. 11, (1975), 1444-1448. doi: 10.1029/JB080i011p01444
  20. Dvorkin, J., Nur, A., “Dynamic poroelasticity: a unified model with the squirt and the Biot mechanisms”, Geophysics, Vol. 58, No. 4, (1993), 524-533. doi: 10.1190/1.1443435
  21. Müller, T. M., Gurevich, B., Lebedev, M., “Seismic wave attenuation and dispersion resulting from wave-induced flow in porous rocks: A review”, Geophysics, Vol. 75, No. 5, (2010), X75A147-75A164. doi: 10.1190/1.3463417
  22. Mikhaltsevitch, V., Lebedev, M., Gurevich, B., “A laboratory study of the elastic and anelastic properties of the sandstone flooded with supercritical CO2 at seismic frequencies”, Energy Procedia, Vol. 63, (2014), 4289-4296. doi: 10.1016/j.egypro.2014.11.464
  23. Spencer Jr, J. W., “Stress relaxations at low frequencies in fluid-saturated rocks: attenuation and modulus dispersion”, Journal of Geophysical Research, Vol. 86, No. B3, (1981), 1803-1812. doi: 10.1029/JB086iB03p01803
  24. Winkler, K. W., “Frequency dependent ultrasonic properties of high-porosity sandstones”, Journal of Geophysical Research, Vol. 88, No. B11, (1983), 9493-9499. doi: 10.1029/JB088iB11p09493
  25. Peng, K., Zhou, J., Zou, Q., Song, X., “Effect of loading frequency on the deformation behaviours of sandstones subjected to cyclic loads and its underlying mechanism”, International Journal of Fatigue,Vol. 131, (2020), 105349. doi: 10.1016/j.ijfatigue.2019.105349
  26. Khosroshahi, A. A., Sadrnejad, S. A., “Substructure model for concrete behavior simulation under cyclic multiaxial loading”, International Journal of Engineering, Transactions A: Basics, Vol. 21, No. 4, (2008), 329-346.
  27. Zhang, Q. B., Zhao, J., “A review of dynamic experimental techniques and mechanical behaviour of rock materials”, Rock Mechanics and Rock Engineering,Vol. 47, (2014), 1411-1478. doi: 10.1007/s00603-013-0463-y
  28. Zheng, Q., Liu, E., Sun, P., Liu, M., Yu, D., “Dynamic and damage properties of artificial jointed rock samples subjected to cyclic triaxial loading at various frequencies”, International Journal of Rock Mechanics and Mining Sciences,Vol. 128, (2020), 104243. doi: 10.1016/j.ijrmms.2020.104243
  29. Subramaniyan, S., Quintal, B., Tisato, N., Saenger, E. H., Madonna, C., “An overview of laboratory apparatuses to measure seismic attenuation in reservoir rocks”, Geophysical Prospecting, Vol. 62, (2014), 1211-1223. doi: 10.1111/1365-2478.12171
  30. Szewczyk, D., Holt, R. M., Bauer, A., “The impact of saturation on seismic dispersion in shales - laboratory measurements”, Geophysics, Vol. 83, No. 1, (2018), 15-34. doi 10.1190/geo20 17-0169.1
  31. Tisato, N., Madonna, C., “Attenuation at low seismic frequencies in partially saturated rocks: Measurements and description of a new apparatus”, Journal of Applied Geophysics, Vol. 86, (2012), 44-53. doi: 10.1016/j.jappgeo.2012.07.008
  32. Szewczyk, D., Bauer, A., Holt, R. M., “A new laboratory apparatus for the measurement of seismic dispersion under deviatoric stress conditions”, Geophysical Prospecting, 64, (2016), 789-798. doi: 10.1111/1365-2478.12425
  33. Borgomano, J. V. M., Gallagher, A., Sun, C., Fortin, J., “An apparatus to measure elastic dispersion and attenuation using hydrostatic- and axial-stress oscillations under undrained conditions”, Review of Scientific Instruments, Vol. 91, No. 3, (2020), 034502. doi: 10.1063/1.5136329
  34. Riabokon, E., Turbakov, M., Kozhevnikov, E., Poplygin, V., Wiercigroch, M., “Rock Fracture During Oil Well Perforation”, Lecture Notes in Mechanical Engineering, (2020), 185-192. doi: 10.1007/978-3-030-49882-5_18
  35. Yan, Z., Dai, F., Liu, Y., Du, H., “Experimental investigations of the dynamic mechanical properties and fracturing behavior of cracked rocks under dynamic loading”, Bulletin of Engineering Geology and the Environment, Vol. 79, No. 10, (2020), 5535-5552. doi: 10.1007/s10064-020-01914-8
  36. Li, X. B., Lok, T. S., Zhao, J., “Dynamic characteristics of granite subjected to intermediate loading rate”, Rock Mechanics and Rock Engineering, Vol. 38, No. 1, (2005), 21-39. doi: 10.1007/s00603-004-0030-7
  37. ASTM (2001). ASTM D4543: Standard practices for preparing rock core specimens and determining dimensional and shape tolerances. West Conshohocken, PA, USA: ASTM International.
  38. Brown E. T. Suggested Methods for Determining the Uniaxial Compressive Strength and Deformability of Rock Materials. ISRM. Brown E. T., editor. Oxford: Pergamon Press; 1981.
  39. Jaeger, J. C., Cook, N. G. W., Zimmerman, R. W. Laboratory testing of rocks. In Fundamentals of Rock Mechanics, 4th ed.; Blackwell Publishing: Malden, MA, USA, 2007, 145-167.