Skip to main content
Log in

A review of mechanical properties and constitutive theory of rock mass anisotropy

  • Review Paper
  • Published:
Arabian Journal of Geosciences Aims and scope Submit manuscript

Abstract

Rock anisotropy is an intrinsic property of natural rock mass, and layered rock has the most significant effect on the stress distribution and deformation of a rock mass. With the development of rock mechanics theory and constitutive theory, the study of rock anisotropy has become one of the focuses and hotspots in the field of rock mechanics. Based on the rock isotropic self-consistent theory, the rock anisotropy theory of different media such as triclinic anisotropy, monoclinic anisotropy, and orthorhombic anisotropy has been greatly developed. Rock mechanical property test, not only limited to the traditional single-axis, triaxial compression test, Brazilian split test and pure bending beam tensile test, and meso-structural characteristic test (XRD, ultrasonic test, etc.), is also widely used. With the development of numerical analysis theory and computer technology, numerical analysis methods such as finite difference method, discrete element method, finite element method, boundary element method, and interface element method have played an important role in the study of rock anisotropy characteristics. According to the assumptions and reasoning methods of anisotropic failure criterion, it can be classified into two categories: continuous failure criterion and discontinuous piecewise failure criterion. Continuous medium failure criterion can also be classified into mathematical and empirical ones. Because of the complexity of rock anisotropy, the research on yield criterion and constitutive relation of rock anisotropy is still in the stage of theoretical research, and it is seldom applied in actual rock engineering. The physics model of rock has an important influence on the study of the anisotropic characteristics of rock. Therefore, the establishment of an appropriate rock physics model has a direct impact on the accurate determination of rock anisotropy parameters and P-S wave velocity. Finally, the key and difficult points of anisotropic rock research and the direction of future research are discussed and analyzed to provide a reference for engineering practice and related problems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  • Ai C, Zhang J, Li YW, Zeng J, Yang XL, Wang JG (2016) Estimation criteria for rock brittleness based on energy analysis during the rupturing process. Rock Mech Rock Eng 49(12):4681–4698

    Article  Google Scholar 

  • Almqvist BS, Mainprice D (2017) Seismic properties and anisotropy of the continental crust: predictions based on mineral texture and rock microstructure. Rev Geophys 55(2):367–433

    Article  Google Scholar 

  • Angus DA, Fisher QJ, Segura JM, Verdon JP, Kendall JM, Dutko M, Crook AJL (2016) Reservoir stress path and induced seismic anisotropy: results from linking coupled fluid-flow/geomechanical simulation with seismic modelling. Pet Sci 13(4):669–684

    Article  Google Scholar 

  • Barton N, Quadros E (2015) Anisotropy is everywhere, to see, to measure, and to model. Rock Mech Rock Eng 48(4):1323–1339

    Article  Google Scholar 

  • Biedermann AR, Pettke T, Angel RJ, Hirt AM (2016) Anisotropy of magnetic susceptibility in alkali feldspar and plagioclase. Geophysical Supplements to the Monthly Notices of the Royal Astronomical Society 205(1):479–489

    Article  Google Scholar 

  • Bo X, Zhonghao W, Gongqiang L (2016) Based on rock electrical parameters anisotropy log evaluation method in horizontal well. J Comput Theor Nanosci 13(12):10281–10285

    Article  Google Scholar 

  • Bobet A (2016) Deep tunnel in transversely anisotropic rock with groundwater flow. Rock Mech Rock Eng 49(12):4817–4832

    Article  Google Scholar 

  • Brownlee SJ, Schulte-Pelkum V, Raju A, Mahan K, Condit C, Orlandini OF (2017) Characteristics of deep crustal seismic anisotropy from a compilation of rock elasticity tensors and their expression in s. Tectonics 36(9):1835–1857

    Article  Google Scholar 

  • Chan J, Schmitt DR (2015) Elastic anisotropy of a metamorphic rock sample of the Canadian shield in northeastern Alberta. Rock Mech Rock Eng 48(4):1369–1385

    Article  Google Scholar 

  • Chang L, Konietzky H, Frühwirt T (2019) Strength anisotropy of rock with crossing joints: results of physical and numerical modeling with gypsum models. Rock Mech Rock Eng:1–25

  • Chekhonin E, Popov E, Popov Y, Gabova A, Romushkevich R, Spasennykh M, Zagranovskaya D (2018) High-resolution evaluation of elastic properties and anisotropy of unconventional reservoir rocks via thermal core logging. Rock Mech Rock Eng 51(9):2747–2759

    Article  Google Scholar 

  • Chen SJ, Zhu WC, Yu QL, Liu XG (2016) Characterization of anisotropy of joint surface roughness and aperture by variogram approach based on digital image processing technique. Rock Mech Rock Eng 49(3):855–876

    Article  Google Scholar 

  • Chen J, Ye J, Du S (2017) Scale effect and anisotropy analyzed for neutrosophic numbers of rock joint roughness coefficient based on neutrosophic statistics. Symmetry 9(10):208

    Article  Google Scholar 

  • Cossette É, Audet P, Schneider D, Grasemann B (2016) Structure and anisotropy of the crust in the Cyclades, Greece, using receiver functions constrained by in situ rock textural data. Journal of Geophysical Research: Solid Earth 121(4):2661–2678

    Google Scholar 

  • Douma LANR, Primarini MIW, Houben ME, Barnhoorn A (2017) The validity of generic trends on multiple scales in rock-physical and rock-mechanical properties of the Whitby mudstone, United Kingdom. Mar Pet Geol 84:135–147

    Article  Google Scholar 

  • Duan K, Kwok CY (2016) Evolution of stress-induced borehole breakout in inherently anisotropic rock: insights from discrete element modeling. Journal of Geophysical Research: Solid Earth 121(4):2361–2381

    Google Scholar 

  • Duveau G, Shao JF, Henry JP (1998) Assessment of some failure criteria for strongly anisotropic geomaterials. Mechanics of Cohesive-frictional Materials 3(1):1–26

    Article  Google Scholar 

  • Farhadian H, Katibeh H, Huggenberger P (2016) Empirical model for estimating groundwater flow into tunnel in discontinuous rock masses. Environ Earth Sci 75(6):471

    Article  Google Scholar 

  • Freire-Lista DM, Fort R (2017) Exfoliation microcracks in building granite. Implications for anisotropy Engineering geology 220:85–93

    Article  Google Scholar 

  • Ge Y, Tang H, Eldin MME, Chen P, Wang L, Wang J (2015) A description for rock joint roughness based on terrestrial laser scanner and image analysis. Sci Rep 5:16999

    Article  Google Scholar 

  • Gehne S, Benson PM (2017) Permeability and permeability anisotropy in crab orchard sandstone: experimental insights into spatio-temporal effects. Tectonophysics 712:589–599

    Article  Google Scholar 

  • Geng Z, Chen M, Jin Y, Yang S, Yi Z, Fang X, Du X (2016) Experimental study of brittleness anisotropy of shale in triaxial compression. Journal of Natural Gas Science and Engineering 36:510–518

    Article  Google Scholar 

  • Guayacan-Carrillo LM, Ghabezloo S, Sulem J, Seyedi DM, Armand G (2017) Effect of anisotropy and hydro-mechanical couplings on pore pressure evolution during tunnel excavation in low-permeability ground. Int J Rock Mech Min Sci 97:1–14

    Article  Google Scholar 

  • Guo ZQ, Liu C, Liu XW, Dong N, Liu YW (2016) Research on anisotropy of shale oil reservoir based on rock physics model. Appl Geophys 13(2):382–392

    Article  Google Scholar 

  • Hackston A, Rutter E (2016) The Mohr–coulomb criterion for intact rock strength and friction–a re-evaluation and consideration of failure under polyaxial stresses. Solid Earth 7(2):493–508

    Article  Google Scholar 

  • Hatzor YH, Feng XT, Li S, Yagoda-Biran G, Jiang Q, Hu L (2015) Tunnel reinforcement in columnar jointed basalts: the role of rock mass anisotropy. Tunn Undergr Space Technol 46:1–11

    Article  Google Scholar 

  • Huang N, Jiang Y, Liu R, Xia Y (2018) Size effect on the permeability and shear induced flow anisotropy of fractal rock fractures. Fractals 26(02):1840001

    Article  Google Scholar 

  • Kanitpanyacharoen W, Vasin R, Wenk HR, Dewhurst DN (2015) Linking preferred orientations to elastic anisotropy in Muderong shale, AustraliaLinking orientations to anisotropy. Geophysics 80(1):C9–C19

    Article  Google Scholar 

  • Kim KY, Zhuang L, Yang H, Kim H, Min KB (2016) Strength anisotropy of Berea sandstone: results of X-ray computed tomography, compression tests, and discrete modeling. Rock Mech Rock Eng 49(4):1201–1210

    Article  Google Scholar 

  • Kundu J, Mahanta B, Sarkar K, Singh TN (2018) The effect of lineation on anisotropy in dry and saturated Himalayan schistose rock under Brazilian test conditions. Rock Mech Rock Eng 51(1):5–21

    Article  Google Scholar 

  • Lahmira B, Lefebvre R, Aubertin M, Bussière B (2016) Effect of heterogeneity and anisotropy related to the construction method on transfer processes in waste rock piles. J Contam Hydrol 184:35–49

    Article  Google Scholar 

  • Li Z, Peng Z (2017) Stress-and structure-induced anisotropy in Southern California from two decades of shear wave splitting measurements. Geophys Res Lett 44(19):9607–9614

    Article  Google Scholar 

  • Liu Z, Park J, Rye DM (2015a) Crustal anisotropy in northeastern Tibetan plateau inferred from receiver functions: rock textures caused by metamorphic fluids and lower crust flow? Tectonophysics 661:66–80

    Article  Google Scholar 

  • Liu ZB, Xie SY, Shao JF, Conil N (2015b) Effects of deviatoric stress and structural anisotropy on compressive creep behavior of a clayey rock. Appl Clay Sci 114:491–496

    Article  Google Scholar 

  • Liu XW, Guo ZQ, Liu C, Liu YW (2017) Anisotropy rock physics model for the Longmaxi shale gas reservoir, Sichuan Basin, China. Appl Geophys 14(1):21–30

    Article  Google Scholar 

  • Lokajíček T, Svitek T (2015) Laboratory measurement of elastic anisotropy on spherical rock samples by longitudinal and transverse sounding under confining pressure. Ultrasonics 56:294–302

    Article  Google Scholar 

  • Lusakowska E, Adamiak S, Adamski P (2017) The young Modulus and microhardness anisotropy in (Pb, cd) Te solid solution crystallizing in the rock salt structure and containing 5% of cd. Acta Phys Pol A 132(2):343–346

    Article  Google Scholar 

  • Ma T, Zhang QB, Chen P, Yang C, Zhao J (2017) Fracture pressure model for inclined wells in layered formations with anisotropic rock strengths. J Pet Sci Eng 149:393–408

    Article  Google Scholar 

  • Mainprice D (2015) 2.20—Seismic anisotropy of the deep earth from a mineral and rock physics perspective. In: Treatise on Geophysics, 2nd edn. Elsevier, Oxford, pp 487–538

    Chapter  Google Scholar 

  • Mallick S, Mukherjee D, Shafer L, Campbell-Stone E (2017) Azimuthal anisotropy analysis of P-wave seismic data and estimation of the orientation of the in situ stress fields: an example from the Rock-Springs uplift, Wyoming, USA. Geophysics 82(2):B63–B77

    Article  Google Scholar 

  • Nourani MH, Moghadder MT, Safari M (2017) Classification and assessment of rock mass parameters in Choghart iron mine using P-wave velocity. J Rock Mech Geotech Eng 9(2):318–328

    Article  Google Scholar 

  • Okaya D, Vel SS, Song WJ, Johnson SE (2018) Modification of crustal seismic anisotropy by geological structures (“structural geometric anisotropy”). Geosphere 15(1):146–170

    Article  Google Scholar 

  • Ong ON, Schmitt DR, Kofman RS, Haug K (2016) Static and dynamic pressure sensitivity anisotropy of a calcareous shale. Geophys Prospect 64(4):875–897

    Article  Google Scholar 

  • Pan X, Zhang G, Yin X (2018) Azimuthally pre-stack seismic inversion for orthorhombic anisotropy driven by rock physics. Sci China Earth Sci 61(4):425–440

    Article  Google Scholar 

  • Park B, Min KB (2015) Bonded-particle discrete element modeling of mechanical behavior of transversely isotropic rock. Int J Rock Mech Min Sci 76:243–255

    Article  Google Scholar 

  • Price DC, Angus DA, Garcia A, Fisher QJ (2017) Probabilistic analysis and comparison of stress-dependent rock physics models. Geophys J Int 210(1):196–209

    Article  Google Scholar 

  • Ramos MJ, Espinoza DN, Torres-Verdín C, Grover T (2017) Use of S-wave anisotropy to quantify the onset of stress-induced microfracturing shear anisotropy and microfracturing. Geophysics 82(6):MR201–MR212

    Article  Google Scholar 

  • Ren F, Ma G, Fu G, Zhang K (2015) Investigation of the permeability anisotropy of 2D fractured rock masses. Eng Geol 196:171–182

    Article  Google Scholar 

  • Roy DG, Singh TN, Kodikara J (2017) Influence of joint anisotropy on the fracturing behavior of a sedimentary rock. Eng Geol 228:224–237

    Article  Google Scholar 

  • Sangode SJ, Sharma R, Mahajan R (2017) Anisotropy of magnetic susceptibility and rock magnetic applications in the Deccan volcanic province based on some case studies. J Geol Soc India 89(6):631–642

    Article  Google Scholar 

  • Sesetty V, Ghassemi A (2018) Effect of rock anisotropy on wellbore stresses and hydraulic fracture propagation. Int J Rock Mech Min Sci 112:369–384

    Article  Google Scholar 

  • Song H, Jiang Y, Elsworth D, Zhao Y, Wang J, Liu B (2018) Scale effects and strength anisotropy in coal. Int J Coal Geol 195:37–46

    Article  Google Scholar 

  • Stierle E, Vavryčuk V, Kwiatek G, Charalampidou EM, Bohnhoff M (2016) Seismic moment tensors of acoustic emissions recorded during laboratory rock deformation experiments: sensitivity to attenuation and anisotropy. Geophysical Supplements to the Monthly Notices of the Royal Astronomical Society 205(1):38–50

    Article  Google Scholar 

  • Sun H, Vega S, Tao G (2017) Analysis of heterogeneity and permeability anisotropy in carbonate rock samples using digital rock physics. J Pet Sci Eng 156:419–429

    Article  Google Scholar 

  • Togashi Y, Kikumoto M, Tani K, Hosoda K, Ogawa K (2018) Detection of deformation anisotropy of tuff by a single triaxial test on a single specimen. Int J Rock Mech Min Sci 108:23–36

    Article  Google Scholar 

  • Tomac I, Sauter M (2018) A review on challenges in the assessment of geomechanical rock performance for deep geothermal reservoir development. Renew Sust Energ Rev 82:3972–3980

    Article  Google Scholar 

  • Vishnu CS, Lahiri S, Mamtani MA (2018) The relationship between magnetic anisotropy, rock-strength anisotropy and vein emplacement in gold-bearing metabasalts of Gadag (South India). Tectonophysics 722:286–298

    Article  Google Scholar 

  • Wang P, Ren F, Miao S, Cai M, Yang T (2017) Evaluation of the anisotropy and directionality of a jointed rock mass under numerical direct shear tests. Eng Geol 225:29–41

    Article  Google Scholar 

  • Wang P, Cai M, Ren F (2018) Anisotropy and directionality of tensile behaviours of a jointed rock mass subjected to numerical Brazilian tests. Tunn Undergr Space Technol 73:139–153

    Article  Google Scholar 

  • Watson JM, Vakili A, Jakubowski M (2015) Rock strength anisotropy in high stress conditions: a case study for application to shaft stability assessments. Studia Geotechnica et Mechanica 37(1):115–125

    Article  Google Scholar 

  • Wenning QC, Madonna C, Haller A, Burg JP (2018) Permeability and seismic velocity anisotropy across a ductile-brittle fault zone in crystalline rock. Solid Earth 9(3):683–698

    Article  Google Scholar 

  • Wu C, Chen Q, Basack S, Xu R, Shi Z (2016) Biaxial creep test study on the influence of structural anisotropy on rheological behavior of hard rock. J Mater Civ Eng 28(10):04016104

    Article  Google Scholar 

  • Xu H, Arson C (2015) Mechanistic analysis of rock damage anisotropy and rotation around circular cavities. Rock Mech Rock Eng 48(6):2283–2299

    Article  Google Scholar 

  • Yan B, Guo Q, Ren F, Cai M (2020a) Modified Nishihara model and experimental verification of deep rock mass under the water-rock interaction. Int J Rock Mech Min Sci 128:104250

    Article  Google Scholar 

  • Yan B, Ren F, Cai M, Qiao C (2020b) Bayesian model based on Markov chain Monte Carlo for identifying mine water sources in submarine gold mining. J Clean Prod 253:120008

    Article  Google Scholar 

  • Yang T, Wang P, Xu T, Yu Q, Zhang P, Shi W, Hu G (2015) Anisotropic characteristics of jointed rock mass: a case study at Shirengou iron ore mine in China. Tunn Undergr Space Technol 48:129–139

    Article  Google Scholar 

  • Zeng QD, Yao J, Shao J (2018) Numerical study of hydraulic fracture propagation accounting for rock anisotropy. J Pet Sci Eng 160:422–432

    Article  Google Scholar 

  • Zhan H, Wang J, Zhao K, Lű H, Jin K, He L, Xiao L (2016) Real-time detection of dielectric anisotropy or isotropy in unconventional oil-gas reservoir rocks supported by the oblique-incidence reflectivity difference technique. Sci Rep 6:39306

    Article  Google Scholar 

  • Zhang F (2017a) Estimation of anisotropy parameters for shales based on an improved rock physics model, part 2: case study. J Geophys Eng 14(2):238–254

    Article  Google Scholar 

  • Zhang L (2017b) Evaluation of rock mass deformability using empirical methods–a review. Underground Space 2(1):1–15

    Article  Google Scholar 

  • Zhang F (2019) A modified rock physics model of overmature organic-rich shale: application to anisotropy parameter prediction from well logs. J Geophys Eng 16(1):92–104

    Article  Google Scholar 

  • Zhang F, Li XY, Qian K (2016a) Estimation of anisotropy parameters for shale based on an improved rock physics model, part 1: theory. J Geophys Eng 14(1):143–158

    Article  Google Scholar 

  • Zhang Z, Wang E, Chen D, Li X, Li N (2016b) The observation of AE events under uniaxial compression and the quantitative relationship between the anisotropy index and the main failure plane. J Appl Geophys 134:183–190

    Article  Google Scholar 

  • Zhao Y, Song H, Liu S, Zhang C, Dou L, Cao A (2019) Mechanical anisotropy of coal with considerations of realistic microstructures and external loading directions. Int J Rock Mech Min Sci 116:111–121

    Article  Google Scholar 

Download references

Funding

This work was supported by the National Natural Science Foundation of China (Grant No. 51774022) and the National Natural Science Foundation of China (Grant No. 51604017).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Bingqian Yan.

Ethics declarations

Conflict of interest

The authors declare that they have no conflicts of interest.

Additional information

Responsible Editor: Abdullah M. Al-Amri

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yan, B., Wang, P., Ren, F. et al. A review of mechanical properties and constitutive theory of rock mass anisotropy. Arab J Geosci 13, 487 (2020). https://doi.org/10.1007/s12517-020-05536-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12517-020-05536-y

Keywords

Navigation