基于分形损失理论的粗糙节理岩体中应力波波速研究
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摘要
从损伤力学的基本理论出发,推导了应力波在节理岩石中传播波速的解析解,建立了节理面图像分形维数与波速间的关系。为了从数值角度探讨节理面图像维数对波速的影响规律,基于图像每一像素颜色可表示为一个三维空间矢量的基本假定,构建了节理面图像的粗糙"颜色表面"模型,计算了该"颜色表面"的分形维数,此维数即为节理面图像维数,并通过实例验证了该法的可行性。在此基础上,通过数值方法探讨了波速随图像维数的变化规律,研究显示:随着节理面图像维数增大,节理面粗糙程度的增加,应力波波速相应减小,且在不同的图像维数区间里,波速减小的速率也有所不同。
With fundamental theory of damage mechanics,analytical solution to velocity of stress wave propagating in jointed rock was derived,and the relation between the velocity and joint image fractal dimensions was established.In order to study influence rule of joint image dimensions on wave velocity,based on a hypothesis that color of every pixel can be expressed into a vector of a three-dimensional space,a model of rough color surface of joint surface image was built and the fractal dimensions of rough color surface were calculated.This dimension number was considered to be the image dimension number.Also,the feasibility of the theory was validated with some examples.Then,the rule of the wave velocity with the change of image dimension number was studied with numerical methods.It was indicated that with increase in joint image dimension number,joint surface roughness increases,stress wave velocity correspondingly decreases and the decreasing rate of wave velocity is distinct in different dimension ranges.
With fundamental theory of damage mechanics,analytical solution to velocity of stress wave propagating in jointed rock was derived,and the relation between the velocity and joint image fractal dimensions was established.In order to study influence rule of joint image dimensions on wave velocity,based on a hypothesis that color of every pixel can be expressed into a vector of a three-dimensional space,a model of rough color surface of joint surface image was built and the fractal dimensions of rough color surface were calculated.This dimension number was considered to be the image dimension number.Also,the feasibility of the theory was validated with some examples.Then,the rule of the wave velocity with the change of image dimension number was studied with numerical methods.It was indicated that with increase in joint image dimension number,joint surface roughness increases,stress wave velocity correspondingly decreases and the decreasing rate of wave velocity is distinct in different dimension ranges.
引文
[1]Gurevich B,Lopatnikov S L.Velocity and attenuation ofelastic waves in finely layered porous rocks[J].GeophysicalJournal International,1995,121(3):933-947.
[2]Wright T W.Elastic wave propagation through a material withvoids[J].J.Mech.Phys.Solids,1998,46(10):2033-2047.
[3]邓庆田,杨智春.导波在多损伤板结构中的散射[J].振动与冲击,2010,29(4):40-44.
[4]杨宏峰,施行觉.轴向压力下砂岩波速的实验研究[J].地球物理学进展,2004,19(2):481-485.
[5]韩嵩,蔡美峰.节理岩体物理模拟与超声波试验研究[J].岩石力学与工程学报,2007,26(5):1026-1033.
[6]Oda M.Permeability tensor for discontinuous rock masses[J].Geotechnique,1985,35(4):483-495.
[7]Oda M.A crack tensor and its relation to wave velocityanisotropy in jointed rock masses[J].International Journalof Rock Mechanics and Mining sciences and GeomechanicsAbstracts,1986,23(6):387-397.
[8]胡刚,郝传波,景海河.爆炸作用下岩石介质应力波传播规律研究[J].煤炭学报,2001,226(3):270-273.
[9]Ju Y,Sudak L,Xie H P.Study on stress wave propagation infractured rocks with fractal joint surfaces[J].InternationalJournal of Solids and Structures,2007,44(13):4 256-4 271.
[10]逯静洲,林皋,王哲.混凝土经历三向受压荷载历史后强度劣化及超声波探伤方法的研究[J].工程力学,2002,19(5):52-57.
[11]刘天云,刘光廷.拱坝地震动随机响应分析[J].工程力学,2002,17(6):20-25.
[12]朱金颖,陈龙珠,严细水.混凝土受力状态下超声波传播特性研究[J].工程力学,1998,15(3):111-117.
[13]Kahraman S.The effects of fracture roughness on P-wavevelocity[J].Engineering Geology,2002,63(3):347-350.
[14]Mandelbrot B B.How long is the coastline of Britain?Statistical self-similarity and fractal dimension[J].Science,1967,155(4):636-638.
[15]Clarke K C.Computation of the fractal dimension oftopographic surfaces using the triangular prism surface areamethod[J].Computers&Geoscience,1986,12(5):713-722.
[16]Xie H P,Wang J A.Direct fractal measurement of fracturesurfaces[J].International Journal of Solids and Structures,1999,36(20):3073-3084.
[17]Zhou H W,Xie H P.Direct estimation of the fractaldimensions of a fracture surface of rock[J].Surface Reviewand Letters,2003,10(5):751-762.
[18]张亚衡,周宏伟,谢和平.粗糙表面分形维数估算的改进立方体覆盖法[J].岩石力学与工程学报,2005,24(17):3192-3196.
[19]彭瑞东,谢和平,鞠杨.二维数字图像分形维数的计算方法[J].中国矿业大学学报,2004,33(1):19-24.
[20]Pentland A P.Fractal—based description of nature scenes[J].IEEE Transactions on PAMI,1984,6(6):315-326.
[2]Wright T W.Elastic wave propagation through a material withvoids[J].J.Mech.Phys.Solids,1998,46(10):2033-2047.
[3]邓庆田,杨智春.导波在多损伤板结构中的散射[J].振动与冲击,2010,29(4):40-44.
[4]杨宏峰,施行觉.轴向压力下砂岩波速的实验研究[J].地球物理学进展,2004,19(2):481-485.
[5]韩嵩,蔡美峰.节理岩体物理模拟与超声波试验研究[J].岩石力学与工程学报,2007,26(5):1026-1033.
[6]Oda M.Permeability tensor for discontinuous rock masses[J].Geotechnique,1985,35(4):483-495.
[7]Oda M.A crack tensor and its relation to wave velocityanisotropy in jointed rock masses[J].International Journalof Rock Mechanics and Mining sciences and GeomechanicsAbstracts,1986,23(6):387-397.
[8]胡刚,郝传波,景海河.爆炸作用下岩石介质应力波传播规律研究[J].煤炭学报,2001,226(3):270-273.
[9]Ju Y,Sudak L,Xie H P.Study on stress wave propagation infractured rocks with fractal joint surfaces[J].InternationalJournal of Solids and Structures,2007,44(13):4 256-4 271.
[10]逯静洲,林皋,王哲.混凝土经历三向受压荷载历史后强度劣化及超声波探伤方法的研究[J].工程力学,2002,19(5):52-57.
[11]刘天云,刘光廷.拱坝地震动随机响应分析[J].工程力学,2002,17(6):20-25.
[12]朱金颖,陈龙珠,严细水.混凝土受力状态下超声波传播特性研究[J].工程力学,1998,15(3):111-117.
[13]Kahraman S.The effects of fracture roughness on P-wavevelocity[J].Engineering Geology,2002,63(3):347-350.
[14]Mandelbrot B B.How long is the coastline of Britain?Statistical self-similarity and fractal dimension[J].Science,1967,155(4):636-638.
[15]Clarke K C.Computation of the fractal dimension oftopographic surfaces using the triangular prism surface areamethod[J].Computers&Geoscience,1986,12(5):713-722.
[16]Xie H P,Wang J A.Direct fractal measurement of fracturesurfaces[J].International Journal of Solids and Structures,1999,36(20):3073-3084.
[17]Zhou H W,Xie H P.Direct estimation of the fractaldimensions of a fracture surface of rock[J].Surface Reviewand Letters,2003,10(5):751-762.
[18]张亚衡,周宏伟,谢和平.粗糙表面分形维数估算的改进立方体覆盖法[J].岩石力学与工程学报,2005,24(17):3192-3196.
[19]彭瑞东,谢和平,鞠杨.二维数字图像分形维数的计算方法[J].中国矿业大学学报,2004,33(1):19-24.
[20]Pentland A P.Fractal—based description of nature scenes[J].IEEE Transactions on PAMI,1984,6(6):315-326.
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