数字岩芯微观结构特征及其对岩石力学性能的影响研究
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摘要
岩石本质上是一种非均质材料,其力学性质受到微观孔隙结构的影响。通过计算不同岩石微米CT图像的分形维数、孔隙半径分布和孔隙形状因子分布,分析了岩石的微观孔隙结构特征。基于数字岩芯表征单元,用有限元方法开展孔隙尺度下微观变形模拟试验,研究微观孔隙结构对岩石变形的影响。结果表明:岩石孔径分布各异,骨架和孔隙都具有分形特征,浑圆孔隙占比相对较少。岩石变形模拟试验中,由于端部束缚作用强,出现了严重的端部效应,在中部了形成X形的共轭塑性剪切带,会不断发展直至岩石破坏;不规则孔隙的存在,使得岩石内部应力集中现象明显,塑性变形区域分布极不均匀。岩石轴向上具有整体平移的特点,侧向变形严重,变形带之间过渡区域位移梯度较大;X形剪切带的下部,形成位移较小的拱形弹性变形区。岩石有效弹性模量与孔隙度和孔隙分形维数具有良好的相关性。随着孔隙度的增加,有效模量几乎呈指数递减,孔隙度对岩石力学性质影响巨大。孔隙分形维数越大,有效弹性模量大体上逐渐变小。研究从孔隙尺度揭示了岩石微观结构的变形机制,对岩石宏观性质的研究具有重要的指导意义。
Rock is essentially a kind of heterogeneous material and its mechanical properties are controlled by pore microstructures.In this paper,the fractal dimensions,pore size distributions and shape factor distributions of micro-CT images of different rocks were calculated using the image morphology algorithms.With the REV of digital images,the deformation simulation experiments were performed using FEM and the effects of microstructures on rock deformation were investigated.The results show that the pore size distributions differ significantly among these rocks of which both skeletons and pores have fractal characteristics,and the round pores account for little.Due to the restraint on the two ends of rock sample under uniaxial loading,rock failure does not firstly emerge at the sample end,but at the middle of rock sample where an X-shaped conjugated plastic shear zone emerges,and it develops continuously until the rock sample is destroyed.The highly uneven distribution of plastic deformation zones and the distinctly internal stress concentration occur due to the irregular pores.Along the loading direction,rock has a distinct displacement mode with large lateral deformation,and the displacement gradients of transition regions of the deformed belts are quite large.An arc-shaped elastic deformation zone below the X-shaped shear zone is produced.The effective elastic modulus of rock has a good correlation with the porosity and fractal dimension.With the increasing of porosity,the effective modulus decreases almost exponentially,indicating that porosity has a remarkable influence on the mechanical properties of rock.The larger the pore fractal dimension is,the smaller the elastic modulus.
Rock is essentially a kind of heterogeneous material and its mechanical properties are controlled by pore microstructures.In this paper,the fractal dimensions,pore size distributions and shape factor distributions of micro-CT images of different rocks were calculated using the image morphology algorithms.With the REV of digital images,the deformation simulation experiments were performed using FEM and the effects of microstructures on rock deformation were investigated.The results show that the pore size distributions differ significantly among these rocks of which both skeletons and pores have fractal characteristics,and the round pores account for little.Due to the restraint on the two ends of rock sample under uniaxial loading,rock failure does not firstly emerge at the sample end,but at the middle of rock sample where an X-shaped conjugated plastic shear zone emerges,and it develops continuously until the rock sample is destroyed.The highly uneven distribution of plastic deformation zones and the distinctly internal stress concentration occur due to the irregular pores.Along the loading direction,rock has a distinct displacement mode with large lateral deformation,and the displacement gradients of transition regions of the deformed belts are quite large.An arc-shaped elastic deformation zone below the X-shaped shear zone is produced.The effective elastic modulus of rock has a good correlation with the porosity and fractal dimension.With the increasing of porosity,the effective modulus decreases almost exponentially,indicating that porosity has a remarkable influence on the mechanical properties of rock.The larger the pore fractal dimension is,the smaller the elastic modulus.
引文
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[23]LI B,LIU R,JIANG Y.A multiple fractal model for estimating permeability of dual-porosity media[J].Journal of Hydrology,2016,540:659–669.
[24]RABBANI A,JAMSHIDI S,SALEHI S.An automated simple algorithm for realistic pore network extraction from microtomography images[J].Journal of Petroleum Science and Engineering,2014,123:164–171.
[25]涂新斌,王思敬.图像分析的颗粒形状参数描述[J].岩土工程学报,2004,26(5):659–662.(TU Xinbin,WANG Sijing.Particle shape descriptor in digital image analysis[J].Chinese Journal of Geotechnical Engineering,2004,26(5):659–662.(in Chinese))
[26]TANG C A,THAM L G,LEE P K K,et al.Numerical studies of the influence of microstructure on rock failure in uniaxial compression—Part II:constraint,slenderness and size effect[J].International Journal of Rock Mechanics and Mining Sciences,2000,37(4):571–583.
[27]ARNS C H,KNACKSTEDT M A,PINCZEWSKI W V.Computation of linear elastic properties from microtomographic images:Methodology and agreement between theory and experiment[J].Geophysics,2002,67(5):1 396–1 405.
[28]ROBERTS A P,GARBOCZI E J.Elastic properties of model porous ceramics[J].Journal of the American Ceramic Society,2000,83(12):3 041–3 048.
[29]YI J C,LEE W J,PARK S K,et al.Effect of pore morphology on deformation behaviors in Porous Al by FEM simulations[J].Advanced Engineering Materials,2013,15(3):166–169.
[2]TABEI S A,SHEIDAEI A,BANIASSADI M,et al.Microstructure reconstruction and homogenization of porous Ni-YSZ composites for temperature dependent properties[J].Journal of Power Sources,2013,235(4):74–80.
[3]PAIBOON J,GRIFFITHS D V,HUANG J,et al.Numerical analysis of effective elastic properties of geomaterials containing voids using3D random fields and finite elements[J].International Journal of Solids and Structures,2013,50(20/21):3 233–3 241.
[4]王金波.岩石孔隙结构三维重构及微细观渗流的数值模拟研究[博士学位论文][D].北京:中国矿业大学(北京),2014.(WANG Jinbo.3D reconstruction of porous rock and numerical simulations of fluid flow at mesoscale levels[Ph.D.Thesis][D].Beijing:China University of Mining and Technology(Beijing),2014.(in Chinese))
[5]罗荣,曾亚武,曹源,等.岩石非均质度对其力学性能的影响研究[J].岩土力学,2012,33(12):3 788–3 794.(LUO Rong,ZENG Yawu,CAO Yuan,et al.Research on influence of inhomogeneity degree on mechanical parameters of inhomogeneous rock[J].Rock and Soil Mechanics,2012,33(12):3 788–3 794.(in Chinese))
[6]杨永明,鞠杨,刘红彬,等.孔隙结构特征及其对岩石力学性能的影响[J].岩石力学与工程学报,2009,28(10):2 031–2 038.(YANG Yongming,JU Yang,LIU Hongbin,et al.Influence of porous structure properties on mechanical performances of rock[J].Chinese Journal of Rock Mechanics and Engineering,2009,28(10):2 031–2 038.(in Chinese))
[7]KAZERANI T.Effect of micromechanical parameters of microstructure on compressive and tensile failure process of rock[J].International Journal of Rock Mechanics and Mining Sciences,2013,64(6):44–55.
[8]YUE Z Q,CHEN S,THAM L G.Finite element modeling of geomaterials using digital image processing[J].Computers and Geotechnics,2003,30(5):375–397.
[9]XU W J,YUE Z Q,HU R L.Study on the mesostructure and mesomechanical characteristics of the soil–rock mixture using digital image processing based finite element method[J].International Journal of Rock Mechanics and Mining Sciences,2008,45(5):749–762.
[10]CHEN S,YUE Z Q,THAM L G.Digital image-based numerical modeling method for prediction of inhomogeneous rock failure[J].International Journal of Rock Mechanics and Mining Sciences,2004,41(6):939–957.
[11]朱万成,康玉梅,杨天鸿,等.基于数字图像的岩石非均匀性表征技术在流固耦合分析中的应用[J].岩土工程学报,2006,28(12):2 087–2 091.(ZHU Wancheng,KANG Yumei,YANG Tianhong,et al.Application of digital imaged-based heterogeneity characterization in coupled hydromechanics of rock[J].Chinese Journal of Geotechnical Engineering,2006,28(12):2 087–2 091.(in Chinese))
[12]GARBOCZI E J,BERRYMAN J G.Elastic moduli of a material containing composite inclusions:effective medium theory and finite element computations[J].Mechanics of Materials,2001,33(8):455–470.
[13]ZHANG D,ZHANG R,CHEN S,et al.Pore scale study of flow in porous media:Scale dependency,REV,and statistical REV[J].Geophysical Research Letters,2000,27(8):1 195–1 198.
[14]FERNANDES,SALVIAPPOLONI J,ROBERTOFERNANDES C,et al.Determination of the representative elementary volume for the study of sandstones and siltstones by X-Ray microtomography[J].Materials Research,2012,15(4):662–670.
[15]GITMAN I M,ASKES H,SLUYS L J.Representative volume:Existence and size determination[J].Engineering Fracture Mechanics,2007,74(16):2 518–2 534.
[16]BRANKO B,RAEINI A Q.Micro-CT images of sandstone and carbonate rocks[OL].http://www.imperial.ac.uk/earth-science/research/research-groups/perm/research/pore-scale-modelling/micro-ct-imagesand-networks/,2015.
[17]DONG H.Micro-CT imaging and pore network extraction[Ph.D.Thesis][D].London:Imperial College London,2007.
[18]ANDREW M.Reservoir condition pore scale imaging of multiphase flow using X-ray microtomography[Ph.D.Thesis][D].London:Imperial College London,2014.
[19]WANG M,WANG J,PAN N,et al.Mesoscopic predictions of the effective thermal conductivity for microscale random porous media[J].Physical Review E Statistical Nonlinear and Soft Matter Physics,2007,75(2):036702.
[20]KANIT T,FOREST S,GALLIET I,et al.Determination of the size of the representative volume element for random composites:statistical and numerical approach[J].International Journal of Solids and Structures,2003,40(13):3 647–3 679.
[21]BLAIR S C,BERGE P A,BERRYMAN J G.Using two‐point correlation functions to characterize microgeometry and estimate permeabilities of sandstones and porous glass[J].Journal of Geophysical Research Solid Earth,1996,101(B9):20 359–20 375.
[22]KIRKBY M J.Fractals:form,chance,and dimension,Benoit B.Mandelbrot,W.H.Freeman and Co.1977.No.of pages:365.Price:U.S.$14.95[J].Earth Surface Processes and Landforms,1979,4(1):98–98.
[23]LI B,LIU R,JIANG Y.A multiple fractal model for estimating permeability of dual-porosity media[J].Journal of Hydrology,2016,540:659–669.
[24]RABBANI A,JAMSHIDI S,SALEHI S.An automated simple algorithm for realistic pore network extraction from microtomography images[J].Journal of Petroleum Science and Engineering,2014,123:164–171.
[25]涂新斌,王思敬.图像分析的颗粒形状参数描述[J].岩土工程学报,2004,26(5):659–662.(TU Xinbin,WANG Sijing.Particle shape descriptor in digital image analysis[J].Chinese Journal of Geotechnical Engineering,2004,26(5):659–662.(in Chinese))
[26]TANG C A,THAM L G,LEE P K K,et al.Numerical studies of the influence of microstructure on rock failure in uniaxial compression—Part II:constraint,slenderness and size effect[J].International Journal of Rock Mechanics and Mining Sciences,2000,37(4):571–583.
[27]ARNS C H,KNACKSTEDT M A,PINCZEWSKI W V.Computation of linear elastic properties from microtomographic images:Methodology and agreement between theory and experiment[J].Geophysics,2002,67(5):1 396–1 405.
[28]ROBERTS A P,GARBOCZI E J.Elastic properties of model porous ceramics[J].Journal of the American Ceramic Society,2000,83(12):3 041–3 048.
[29]YI J C,LEE W J,PARK S K,et al.Effect of pore morphology on deformation behaviors in Porous Al by FEM simulations[J].Advanced Engineering Materials,2013,15(3):166–169.