岩石断裂和破碎的分形研究
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摘要
岩石断裂与破碎的研究一直是岩石力学的前沿领域,也是采矿、能源、水利、交通、地震等众多工程领域不可或缺的理论基础。本文系统介绍了将分形理论引进到岩石断裂和破碎研究的成果,其中包括岩石微观断裂、宏观裂纹动态扩展以及岩体破碎的块度分布,旨在从一个侧面反映分形理论在岩石力学中的应用,最后还给出了一个工程应用的例子。本文的部分结果曾发表于国际杂志上。
Researches into fracture and fragmentation in rocks have been one of the leading topics of rock mechanics, and also an important theoretical base of many engineering practices such as mining, resource development, hydropower, traffic and earthquake. The catastrophes in rock engineering such as rockbursts, coal and gas bursts, roof caving, water bursts, slope failures, dam instability, ground surface subsidence and earthquakes are closely related to fracturing in rocks. As is well known, rock has a variety of complex characteristics atypical of other solids, say, metal; the complexity of mechanical behavior arises from complexity of its structures on a variety of length scales. In terms of the complex structure of rocks, there exist a large number of defects in rocks such as dislocations, crystal boundaries, secondary phases, twin crystallites, fissures, pores, inclusions and precipitates. As a result, rock appears to be discontinuous, strongly heterogeneous and anisotropic. In addition, the scale effect is also an inherent feature of rock.
The classical theory of fracture mechanics, assuming rock to be homogenous and continuous, can not describe the inherent features of rocks. Fractal geometry originally defined by Mandelbrot supplies an alternative tool to describe quantitatively the rock features. This paper discusses special challenges posed for fractal geometry by rock fracture and fragmentations and recent advances made by applications of. fractal geometry to rock fracture and fragmentations, especially the authors' contributions to the applications of fractal geometry to fracture and fragmentation in rocks, including rock fracturing at meso scale, dynamic propagation of macro rock cracks and size distribution of rock fragmentations. In addition, a case study subjected to engineering application is given in the paper. The paper also briefly sketches a selected promising area of current researches, focusing on the physical meaning of fractals and definition of mechanical variables in fractal space.
Researches into fracture and fragmentation in rocks have been one of the leading topics of rock mechanics, and also an important theoretical base of many engineering practices such as mining, resource development, hydropower, traffic and earthquake. The catastrophes in rock engineering such as rockbursts, coal and gas bursts, roof caving, water bursts, slope failures, dam instability, ground surface subsidence and earthquakes are closely related to fracturing in rocks. As is well known, rock has a variety of complex characteristics atypical of other solids, say, metal; the complexity of mechanical behavior arises from complexity of its structures on a variety of length scales. In terms of the complex structure of rocks, there exist a large number of defects in rocks such as dislocations, crystal boundaries, secondary phases, twin crystallites, fissures, pores, inclusions and precipitates. As a result, rock appears to be discontinuous, strongly heterogeneous and anisotropic. In addition, the scale effect is also an inherent feature of rock.
The classical theory of fracture mechanics, assuming rock to be homogenous and continuous, can not describe the inherent features of rocks. Fractal geometry originally defined by Mandelbrot supplies an alternative tool to describe quantitatively the rock features. This paper discusses special challenges posed for fractal geometry by rock fracture and fragmentations and recent advances made by applications of. fractal geometry to rock fracture and fragmentations, especially the authors' contributions to the applications of fractal geometry to fracture and fragmentation in rocks, including rock fracturing at meso scale, dynamic propagation of macro rock cracks and size distribution of rock fragmentations. In addition, a case study subjected to engineering application is given in the paper. The paper also briefly sketches a selected promising area of current researches, focusing on the physical meaning of fractals and definition of mechanical variables in fractal space.
引文
[1] Mandelbrot B. B. The fractal geometry of nature [M]. New York, W. H. Freman, 1982．
[2] Xie H. Fractals in rock mechanics [M]. Netherlands: A A Balkema Publishers, 1993．
[3] Perie P. J.. Determination of fracture mechanism by microscopic observation of crack [J]. Int. J. Rock Mech. Min. Sci. Geomech. Abstr, 1991, 28 (1) :83-84．
[4] 谢和平.大理岩微观断裂的分形(fractal)模型研究[J].科学通报,1989,34(5) :365-368．
[5] Griffith A. A. Theory of rupture [A]. Proc. Ist Int. Congress Appl. Mech. [C]. Delft, 1924． 55-63．
[6] Irwin G.. Fracture dynamics [J]. Fracturing of Metals. Am. Soc. for Met, 1948: 147-166．
[7] 谢和平.岩石蠕变损伤非线性大变形分析及微观断裂FRACTAL模型[D].中国矿业大学北京研究生部,1987．
[8] Lung C. W. Fractals and fracture of cracked metals [M]. Preprint of the Int. Center for Theoretical Physics, Trieste, Italy IC, 1985． 123．
[9] Xie H.. The fractal effect of irregularity of crack branching on fracture toughness of brittle materials [J]. Int. J. Fracture, 1989, 41 (4) : 267-274．
[10] 谢和平.岩石混凝土损伤力学[M].徐州:中国矿业大学出版社,1990．
[11] 谢和平,陈至达.岩石类材料裂纹分叉非规则性几何的分形效应[J].力学学报.1989,21(5) :613-618．
[12] Smith E. The effect of crack front irregularity on the fracture toughness of brittle materials [J]. Arch.Mechanics, 1986, 38(1--2) : 185-190．
[13] Freunel, L. B. Dynamic Fracture Mechanics [M].Cambridge University Press, Cambridge, 1990．
[14] Gao H. Surface roughening and branching instabilities in dynamic fracture [J]. J. Mech. Phys.Solids, 1993, 41(3) : 457-486．
[15] 谢和平.裂纹扩展分形运动学[J].力学学报,1994,26(6) :757-762．
[16] Xie H., Sanderson D. J. Fractal effect of crack propagation on dynamic stress intensity factors and crack velocities [J]. Int. J. Fracture, 1995, (74) :29-42．
[17] Watanabe M. Qualitative analysis of the fast brittle fracture[J]. Int. J. Fracture, 1991 (49) : 69-77．
[18] 高峰,谢和平,赵鹏.岩石块度分布的分形性质及细观结构效应[J].岩石力学与工程学报,1994,13(3) : 240-246．
[19] Nagahama H. Fracturing in the Solid earth [J].Reprinted from the Sci. Report of the Tohoku University. Sendi, Second Series (Geology), 1991,61 (2) : 103-126．
[20] Xie H. Fractal nature on damage evolution of rock materials[A]. Proc. 2nd Int. Symp. on Min [C].Sci. & Tech.. 1991． 697-704．
[21] 谢和平,陈忠辉,段法兵,等.综放顶煤爆破能量的分形研究[J].力学与实践,2000,22(1) :16． 18．
[2] Xie H. Fractals in rock mechanics [M]. Netherlands: A A Balkema Publishers, 1993．
[3] Perie P. J.. Determination of fracture mechanism by microscopic observation of crack [J]. Int. J. Rock Mech. Min. Sci. Geomech. Abstr, 1991, 28 (1) :83-84．
[4] 谢和平.大理岩微观断裂的分形(fractal)模型研究[J].科学通报,1989,34(5) :365-368．
[5] Griffith A. A. Theory of rupture [A]. Proc. Ist Int. Congress Appl. Mech. [C]. Delft, 1924． 55-63．
[6] Irwin G.. Fracture dynamics [J]. Fracturing of Metals. Am. Soc. for Met, 1948: 147-166．
[7] 谢和平.岩石蠕变损伤非线性大变形分析及微观断裂FRACTAL模型[D].中国矿业大学北京研究生部,1987．
[8] Lung C. W. Fractals and fracture of cracked metals [M]. Preprint of the Int. Center for Theoretical Physics, Trieste, Italy IC, 1985． 123．
[9] Xie H.. The fractal effect of irregularity of crack branching on fracture toughness of brittle materials [J]. Int. J. Fracture, 1989, 41 (4) : 267-274．
[10] 谢和平.岩石混凝土损伤力学[M].徐州:中国矿业大学出版社,1990．
[11] 谢和平,陈至达.岩石类材料裂纹分叉非规则性几何的分形效应[J].力学学报.1989,21(5) :613-618．
[12] Smith E. The effect of crack front irregularity on the fracture toughness of brittle materials [J]. Arch.Mechanics, 1986, 38(1--2) : 185-190．
[13] Freunel, L. B. Dynamic Fracture Mechanics [M].Cambridge University Press, Cambridge, 1990．
[14] Gao H. Surface roughening and branching instabilities in dynamic fracture [J]. J. Mech. Phys.Solids, 1993, 41(3) : 457-486．
[15] 谢和平.裂纹扩展分形运动学[J].力学学报,1994,26(6) :757-762．
[16] Xie H., Sanderson D. J. Fractal effect of crack propagation on dynamic stress intensity factors and crack velocities [J]. Int. J. Fracture, 1995, (74) :29-42．
[17] Watanabe M. Qualitative analysis of the fast brittle fracture[J]. Int. J. Fracture, 1991 (49) : 69-77．
[18] 高峰,谢和平,赵鹏.岩石块度分布的分形性质及细观结构效应[J].岩石力学与工程学报,1994,13(3) : 240-246．
[19] Nagahama H. Fracturing in the Solid earth [J].Reprinted from the Sci. Report of the Tohoku University. Sendi, Second Series (Geology), 1991,61 (2) : 103-126．
[20] Xie H. Fractal nature on damage evolution of rock materials[A]. Proc. 2nd Int. Symp. on Min [C].Sci. & Tech.. 1991． 697-704．
[21] 谢和平,陈忠辉,段法兵,等.综放顶煤爆破能量的分形研究[J].力学与实践,2000,22(1) :16． 18．
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