Influence of heterogeneity on rock strength and stiffness using discrete element method and parallel bond model
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摘要
The particulate discrete element method(DEM) can be employed to capture the response of rock,provided that appropriate bonding models are used to cement the particles to each other.Simulations of laboratory tests are important to establish the extent to which those models can capture realistic rock behaviors.Hitherto the focus in such comparison studies has either been on homogeneous specimens or use of two-dimensional(2D) models.In situ rock formations are often heterogeneous,thus exploring the ability of this type of models to capture heterogeneous material behavior is important to facilitate their use in design analysis.In situ stress states are basically three-dimensional(3D),and therefore it is important to develop 3D models for this purpose.This paper revisits an earlier experimental study on heterogeneous specimens,of which the relative proportions of weaker material(siltstone) and stronger,harder material(sandstone) were varied in a controlled manner.Using a 3D DEM model with the parallel bond model,virtual heterogeneous specimens were created.The overall responses in terms of variations in strength and stiffness with different percentages of weaker material(siltstone) were shown to agree with the experimental observations.There was also a good qualitative agreement in the failure patterns observed in the experiments and the simulations,suggesting that the DEM data enabled analysis of the initiation of localizations and micro fractures in the specimens.
The particulate discrete element method(DEM) can be employed to capture the response of rock,provided that appropriate bonding models are used to cement the particles to each other.Simulations of laboratory tests are important to establish the extent to which those models can capture realistic rock behaviors.Hitherto the focus in such comparison studies has either been on homogeneous specimens or use of two-dimensional(2D) models.In situ rock formations are often heterogeneous,thus exploring the ability of this type of models to capture heterogeneous material behavior is important to facilitate their use in design analysis.In situ stress states are basically three-dimensional(3D),and therefore it is important to develop 3D models for this purpose.This paper revisits an earlier experimental study on heterogeneous specimens,of which the relative proportions of weaker material(siltstone) and stronger,harder material(sandstone) were varied in a controlled manner.Using a 3D DEM model with the parallel bond model,virtual heterogeneous specimens were created.The overall responses in terms of variations in strength and stiffness with different percentages of weaker material(siltstone) were shown to agree with the experimental observations.There was also a good qualitative agreement in the failure patterns observed in the experiments and the simulations,suggesting that the DEM data enabled analysis of the initiation of localizations and micro fractures in the specimens.
The particulate discrete element method(DEM) can be employed to capture the response of rock,provided that appropriate bonding models are used to cement the particles to each other.Simulations of laboratory tests are important to establish the extent to which those models can capture realistic rock behaviors.Hitherto the focus in such comparison studies has either been on homogeneous specimens or use of two-dimensional(2D) models.In situ rock formations are often heterogeneous,thus exploring the ability of this type of models to capture heterogeneous material behavior is important to facilitate their use in design analysis.In situ stress states are basically three-dimensional(3D),and therefore it is important to develop 3D models for this purpose.This paper revisits an earlier experimental study on heterogeneous specimens,of which the relative proportions of weaker material(siltstone) and stronger,harder material(sandstone) were varied in a controlled manner.Using a 3D DEM model with the parallel bond model,virtual heterogeneous specimens were created.The overall responses in terms of variations in strength and stiffness with different percentages of weaker material(siltstone) were shown to agree with the experimental observations.There was also a good qualitative agreement in the failure patterns observed in the experiments and the simulations,suggesting that the DEM data enabled analysis of the initiation of localizations and micro fractures in the specimens.
引文
Abe S,Urai JL.Discrete element modeling of boudinage:insights on rock rheology,matrix flow,and evolution of geometry.Journal of Geophysical Research:Solid Earth 2012;117(B1):1-13.
Cundall PA,Strack ODL.A discrete numerical model for granular assemblies.Géotechnique 1979;29(1):47-65.
Cho N,Martin CD,Sego DC.A clumped particle model for rock.International Journal of Rock Mechanics and Mining Sciences 2007;44(7):997-1010.
Cheung LYG,O'Sullivan C,Coop MR.Discrete element method simulations of analogue reservoir sandstones.International Journal of Rock Mechanics and Mining Sciences 2013;63:93-103.
Greco OD,Ferrero A.Pella D.Behavior of laboratory specimens composed by different rocks.In:7th ISRM Congress;1991.p.241-5.
Hoek E.Brittle failure of rock.In:Rock mechanics in engineering practice.London:John Wiley and Sons;1968.p.99-124.
Hawkes I,Mellor M.Uniaxial testing in rock mechanics laboratories.Engineering Geology 1970;4(3):179-285.
Hsieh YM,Li HH,Huang TH,Jeng FS.Interpretations on how the macroscopic mechanical behavior of sandstone affected by microscopic properties-revealed by bonded-particle model.Engineering Geology 2008;99(1-2):1-10.
Jeng FS,Wang TT,Li HH.Huang TH.Influences of microscopic factors on macroscopic strength and stiffness of inter-layered rocks—revealed by a bonded particle model.Journal of Mechanics 2008;24(4):379-89.
Kwasniewski M,Li X,Takahashi M.True triaxial testing of rocks.CRC Press;2012.
Liang W,Yang C,Zhao Y,Dusseault MB,Liu J.Experimental investigation of mechanical properties of bedded salt rock.International Journal of Rock Mechanics and Mining Sciences 2007;44(3):400-11.
Lin H,Cao P.Wang Y.Numerical simulation of a layered rock under triaxial compression.International Journal of Rock Mechanics and Mining Sciences2013;60:12-8.
Mohamed Z,Mohamed K,Cho GC.Uniaxial compressive strength of composite rock material with respect to shale thickness ratio and moisture content.Electronic Journal of Geotechnical Engineering 2007;13:1-10.
O'Sullivan C,Bray JD.Li S.A new approach for calculating strain for particulate media.International Journal for Numerical and Analytical Methods in Geomechanics 2003;27(10):859-77.
Potyondy DO,Cundall PA.A bonded-particle model for rock.International Journal of Rock Mechanics and Mining Sciences 2004;41(8):1329-64.
Paterson MS,Wong T.Experimental rock deformation-the brittle field.Springer;2005.
Potyondy DO.Simulating stress corrosion with a bonded-particle model for rock.International Journal of Rock Mechanics and Mining Sciences 2007;44(5):677-91.
Park B,Min KB.Bonded-particle discrete element modeling of mechanical behavior of transversely isotropic rock.International Journal of Rock Mechanics and Mining Sciences 2015;76:243-55.
Tien YM,Kuo MC,Juang CH.An experimental investigation of the failure mechanisrn of simulated transversely isotropic rocks.International Journal of Rock Mechanics and Mining Sciences 2006;43(8):1163-81.
Tang C,Hudson JA.Rock failure mechanisms:explained and illustrated.CRC Press;2010.
Tziallas GP,Saroglou H,Tsiambaos G.Determination of mechanical properties of flysch using laboratory methods.Engineering Geology 2013;166:81-9.
Vergara MR,Kudella P,Triantafyllidis T.Large scale tests on jointed and bedded rocks under multi-stage triaxial compression and direct shear.Rock Mechanics and Rock Engineering 2015:48(1):75-92.
Zhang Q,Zhu H,Zhang L,Ding X.Study of scale effect on intact rock strength using particle flow modeling.International Journal of Rock Mechanics and Mining Sciences 2011;48(8):1320-8.
Cundall PA,Strack ODL.A discrete numerical model for granular assemblies.Géotechnique 1979;29(1):47-65.
Cho N,Martin CD,Sego DC.A clumped particle model for rock.International Journal of Rock Mechanics and Mining Sciences 2007;44(7):997-1010.
Cheung LYG,O'Sullivan C,Coop MR.Discrete element method simulations of analogue reservoir sandstones.International Journal of Rock Mechanics and Mining Sciences 2013;63:93-103.
Greco OD,Ferrero A.Pella D.Behavior of laboratory specimens composed by different rocks.In:7th ISRM Congress;1991.p.241-5.
Hoek E.Brittle failure of rock.In:Rock mechanics in engineering practice.London:John Wiley and Sons;1968.p.99-124.
Hawkes I,Mellor M.Uniaxial testing in rock mechanics laboratories.Engineering Geology 1970;4(3):179-285.
Hsieh YM,Li HH,Huang TH,Jeng FS.Interpretations on how the macroscopic mechanical behavior of sandstone affected by microscopic properties-revealed by bonded-particle model.Engineering Geology 2008;99(1-2):1-10.
Jeng FS,Wang TT,Li HH.Huang TH.Influences of microscopic factors on macroscopic strength and stiffness of inter-layered rocks—revealed by a bonded particle model.Journal of Mechanics 2008;24(4):379-89.
Kwasniewski M,Li X,Takahashi M.True triaxial testing of rocks.CRC Press;2012.
Liang W,Yang C,Zhao Y,Dusseault MB,Liu J.Experimental investigation of mechanical properties of bedded salt rock.International Journal of Rock Mechanics and Mining Sciences 2007;44(3):400-11.
Lin H,Cao P.Wang Y.Numerical simulation of a layered rock under triaxial compression.International Journal of Rock Mechanics and Mining Sciences2013;60:12-8.
Mohamed Z,Mohamed K,Cho GC.Uniaxial compressive strength of composite rock material with respect to shale thickness ratio and moisture content.Electronic Journal of Geotechnical Engineering 2007;13:1-10.
O'Sullivan C,Bray JD.Li S.A new approach for calculating strain for particulate media.International Journal for Numerical and Analytical Methods in Geomechanics 2003;27(10):859-77.
Potyondy DO,Cundall PA.A bonded-particle model for rock.International Journal of Rock Mechanics and Mining Sciences 2004;41(8):1329-64.
Paterson MS,Wong T.Experimental rock deformation-the brittle field.Springer;2005.
Potyondy DO.Simulating stress corrosion with a bonded-particle model for rock.International Journal of Rock Mechanics and Mining Sciences 2007;44(5):677-91.
Park B,Min KB.Bonded-particle discrete element modeling of mechanical behavior of transversely isotropic rock.International Journal of Rock Mechanics and Mining Sciences 2015;76:243-55.
Tien YM,Kuo MC,Juang CH.An experimental investigation of the failure mechanisrn of simulated transversely isotropic rocks.International Journal of Rock Mechanics and Mining Sciences 2006;43(8):1163-81.
Tang C,Hudson JA.Rock failure mechanisms:explained and illustrated.CRC Press;2010.
Tziallas GP,Saroglou H,Tsiambaos G.Determination of mechanical properties of flysch using laboratory methods.Engineering Geology 2013;166:81-9.
Vergara MR,Kudella P,Triantafyllidis T.Large scale tests on jointed and bedded rocks under multi-stage triaxial compression and direct shear.Rock Mechanics and Rock Engineering 2015:48(1):75-92.
Zhang Q,Zhu H,Zhang L,Ding X.Study of scale effect on intact rock strength using particle flow modeling.International Journal of Rock Mechanics and Mining Sciences 2011;48(8):1320-8.