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Strength Anisotropy of Rock with Crossing Joints: Results of Physical and Numerical Modeling with Gypsum Models

  • Lifu ChangEmail author
  • Heinz Konietzky
  • Thomas Frühwirt
Original Paper
  • 127 Downloads

Abstract

The geometric and mechanical characteristics of multiple intersecting joints can govern the strength anisotropy behavior of a rock mass. Laboratory uniaxial compression tests with artificial rock-like material (gypsum) were conducted to investigate the strength anisotropy behavior of jointed specimens. Three special kinds of gypsum were used to ensure that the handmade joints have a user-defined-strength for all samples. Specimens with one or two crossing joints covering more than 20 angle configurations and two different property sets were prepared and tested. The strength anisotropy behaviors of specimens with constant joint angles (90°, 80°, 60°, 45°, and 30°) were investigated, and the failure mechanisms were assessed through the damage pattern of the colored gypsum. The details of the design scheme and figures of the evaluated experimental results are presented in this paper. A new equivalent continuum model, called the multi-joint model, is developed for jointed rock masses that contain up to three arbitrary persistent joint sets. The Mohr–Coulomb yield criterion is used to check failure of the intact rock and the joints. The multi-joint model is implemented into the finite difference method code FLAC and compared with the distinct element method code UDEC. The experimental results are used to verify the developed multi-joint constitutive model and to investigate the behavior of jointed specimen. Experimental observations agree well with the simulation results and analytical solutions.

Keywords

Joint interconnectivity Multi-joint sample Lab testing Numerical simulation Strength anisotropy 

List of Symbols

c, cji (i = 1,2.3)

Cohesion of the intact rock and joint cohesion, respectively

fi,i (i = 0,1, 2, 3)

Shear failure envelopes for rock matrix and joint set, respectively.

fi,i (i = 0,1, 2, 3)

Tensile failure envelopes for rock matrix and joint set, respectively

k

Slope of the line relating maximum and minimum principal stresses

β

Joint inclination angle measured from vertical

βi (i = 1, 2, 3)

Inclination angle of weak plane

ϕ, ϕʹ

Friction angle and effective friction angle of the intact rock, respectively

ϕji (i = 1, 2, 3)

Friction angle for the joint set i

θ

Inclination angle measured from horizontal

θji (i = 1, 2, 3)

Joint angles measured counterclockwise from the global x-axis

ρ

Density of rock

σ, σn, σt

Tensile stress, normal stress, and intact rock tensile strength, respectively

σ1,σ3

Maximum and minimum principal stresses, respectively

σc,σu

Uniaxial compressive strength and uniaxial compression stress, respectively

τ, τ′, τji

Shear stress components in the global and local coordinates, respectively

UCS

Uniaxial compressive strength

Notes

References

  1. Bray JW (1967) A study of jointed and fractured rock. Rock Mech Eng Geol 5(2–3):117–136Google Scholar
  2. Brown ET (1970) Strength of models of rock with intermittent joints. J Soil Mech Found Div 96(SM6):1935–1949Google Scholar
  3. Brzovic A, Villaescusa E (2007) Rock mass characterization and assessment of block-forming geological discontinuities during caving of primary copper ore at the El Teniente mine, Chile. Int J Rock Mech Min Sci 44(4):565–583CrossRefGoogle Scholar
  4. Coquard P, Boistelle R (1994) Water and solvent effects on the strength of set plaster. Int J Rock Mech Min Sci Geomech Abstr Pergamon 31(5):517–524CrossRefGoogle Scholar
  5. Coquard P, Boistelle R, Amathieu L, Barriac P (1994) Hardness, elasticity modulus and flexion strength of dry set plaster. J Materials Sci 29(17):4611–4617CrossRefGoogle Scholar
  6. Clark IH (2006) Simulation of rockmass strength using ubiquitous joints. In: Hart R, Varona P (eds) Numerical modeling in geomechanics-2006. Proceedings 4th International FLAC Symposium, Paper No. 08–07, MadridGoogle Scholar
  7. Chong WL, Haque A, Gamage RP, Shahinuzzaman A (2013) Modelling of intact and jointed mudstone samples under uniaxial and triaxial compression. Arab J Geosci 6(5):1639–1646CrossRefGoogle Scholar
  8. Chang L, Konietzky H (2018) Application of the Mohr-Coulomb yield criterion for rocks with multiple joint sets using Fast Lagrangian Analysis of Continua 2D (FLAC2D) software. Energies 11(3):614.  https://doi.org/10.3390/en11030614 CrossRefGoogle Scholar
  9. Donath F (1964) Strength variation and deformational behavior in anisotropic rock. In: Judd W (ed) State of stress in the earth's crust. American Elsevier, New york, pp 281–297Google Scholar
  10. Dan Dinh Quoc (2011) Brazilian test on anisotropic rocks: laboratory experiment, numerical simulation and interpretation. PhD Thesis, TU Bergakademie Freiberg, FreibergGoogle Scholar
  11. Detournay C, Meng G, Cundall PA (2016) Development of a constitutive model for columnar basalt. In: Proceedings of the 4th Itasca symposium on applied numerical modeling. Itasca, MinneapolisGoogle Scholar
  12. Einstein HH, Hirschfeld RC, Nelson RA, Bruhn RW (1969) Model studies of jointed-rock behavior. In: The 11th US symposium on rock mechanics (USRMS). American Rock Mechanics Association, Berkeley, pp 83–103Google Scholar
  13. Esmaieli K, Hadjigeorgiou J, Grenon M (2010) Estimating geometrical and mechanical REV based on synthetic rock mass models at Brunswick Mine. Int J Rock Mech Min Sci 47(6):915–926CrossRefGoogle Scholar
  14. Ghazvinian A, Hadei MR (2012) Effect of discontinuity orientation and confinement on the strength of jointed anisotropic rocks. Int J Rock Mech Min Sci 55(10):117–124CrossRefGoogle Scholar
  15. Itasca (2012) Fast lagrangian analysis of continua, theory and background, choice of material properties, 2. Itasca Consulting Group, Inc. Minneapolis, Minnesota, pp 11–17Google Scholar
  16. Itasca (2016) FLAC user manual. Itasca Consulting Group, Inc. Minneapolis, MinnesotaGoogle Scholar
  17. Jaeger JC, Cook NG, Zimmerman R (2009) Fundamentals of rock mechanics, 4th edn. Wiley- Blackwell, MaldenGoogle Scholar
  18. Ko SC, Olgaard DL, Briegel U (1995) The transition from weakening to strengthening in dehydrating gypsum: evolution of excess pore pressures. Geophys Res Lett 22(9):1009–1012CrossRefGoogle Scholar
  19. Kulatilake PHSW, Malama B, Wang J (2001) Physical and particle flow modeling of jointed rock block behavior under uniaxial loading. Int J Rock Mech Min Sci 38(5):641–657CrossRefGoogle Scholar
  20. Kumar D, Das SK (2005) An experimental study of the parameters influencing ultimate bearing strength of weak floor strata using physical modeling. Geotech Geol Eng 23(1):1–15CrossRefGoogle Scholar
  21. Li X, Konietzky H (2014) Time to failure prediction scheme for rocks, Rock Mech Rock Eng 47(4):1493–1503CrossRefGoogle Scholar
  22. Min KB, Jing L (2003) Numerical determination of the equivalent elastic compliance tensor for fractured rock masses using the distinct element method. Int J Rock Mech Min Sci 40(6):795–816CrossRefGoogle Scholar
  23. Ramamurthy T (1993) Strength and modulus responses of anisotropic rocks. Compr Rock Eng 1(13):313–329Google Scholar
  24. Shen B, Stephansson O, Einstein HH, Ghahreman B (1995) Coalescence of fractures under shear stresses in experiments. J Geophys Res Atmos 100(B4):5975–5990CrossRefGoogle Scholar
  25. Singh RK, Dev C (1988) Strength and modulus tests on jointed specimens of plaster of Paris. M. Tech Thesis, IIT-Delhi, IndiaGoogle Scholar
  26. Singh M, Rao KS, Ramamurthy T (2002) Strength and deformational behaviour of a jointed rock mass. Rock Mech Rock Eng 35(1):45–64CrossRefGoogle Scholar
  27. Sainsbury B, Pierce M, Mas Ivars D (2008) Simulation of rock mass strength anisotropy and scale effects using a Ubiquitous Joint Rock Mass (UJRM) model. In: Hart RD, Detournay C, Cundall P (eds) Continuum and Distinct Element Numerical Modeling in Geo-Engineering—2008, Paper 01–04. Itasca Consulting Group Inc.,MinneapolisGoogle Scholar
  28. Tien YM, Tsao PF (2000) Preparation and mechanical properties of artificial transversely isotropic rock. Int J Rock Mech Min Sci 37(6):1001–1012CrossRefGoogle Scholar
  29. Tiwari RP, Rao KS (2004) Physical modeling of a rock mass under a true triaxial stress state. Int J Rock Mech Min Sci 41:396–401CrossRefGoogle Scholar
  30. Wang TT, Huang TH (2009) A constitutive model for the deformation of a rock mass containing sets of ubiquitous joints. Int J Rock Mech Min Sci 46(3):521–530CrossRefGoogle Scholar
  31. Wang TT, Huang TH (2014) Anisotropic deformation of a circular tunnel excavated in a rock mass containing sets of ubiquitous joints: theory analysis and numerical modeling. Rock Mech Rock Eng 47(2):643–657CrossRefGoogle Scholar
  32. Wasantha PLP, Ranjith PG, Viete DR (2016) Hydro-mechanical behavior of sandstone with interconnected joints under undrained conditions. Eng Geol 207:66–77CrossRefGoogle Scholar
  33. Xiao W, Deng R, Fu X (2014) Model experiments on deformation and strength anisotropy of columnar jointed rock masses under uniaxial compression. Chin J Rock Mechan Eng 33(5):957–963Google Scholar
  34. Yang ZY, Chen JM, Huang TH (1998) Effect of joint sets on the strength and deformation of rock mass models. Int J Rock Mech Min Sci 35(1):75–84CrossRefGoogle Scholar
  35. Wong NY (2008) Crack coalescence in molded gypsum and carrara marble. Dissertation, MITGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Civil Engineering and ArchitectureZhejiang Sci-Tech UniversityHangzhouChina
  2. 2.Geotechnical Institute TU Bergakademie FreibergFreibergGermany

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