最大有效力矩准则及相关地质构造
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摘要
摩尔-库伦准则广泛用以说明断裂构造的形成,然而却不能解释自然界广泛分布的大变形。最近提出的岩石变形新理论——最大有效力矩准则,其数学表达式为Meff=0.5(σ1-σ3)L.sin2α.sinα。式中,σ1-σ3代表变形岩石的屈服强度,L为单位长度,α为σ1与变形带间的角度。该准则证明最大有效力矩出现在σ1轴左右54.7°方向,55°±10°区间力矩无显著变化,天然和实验的全部观测值全部位于该区间内。相关地质构造包括:膝褶带、伸展褶劈理、膏盐层中的屈服带、低角正断层、高角逆断层、结晶基底中的菱网状剪切带、地震反射剖面中的鳄鱼嘴构造和前陆盆地中的拆离褶皱等。据该准则可确定有关构造形成时的应力状态和运动学涡度,并扩展说明深俯冲超高压岩石的折返-出露机制。
The Mohr-Coulomb criterion has been widely used to explain the formation of fractures. However, it fails to explain large strain deformation that widely occurs in nature. There is presently a new theory, the MEMC, which is mathematically expressed as Meff=0.5 (σ1-σ3) L·sin 2α·sin α, where σ1-σ3 represents the yield strength of the related rock, L is a unit length and α is the angle between σ1 and deformation bands. This criterion demonstrates that the maximum value appears at angles of ±54.7° to σ1 and there is little difference in the moment in the range of 55°±10°. This range covers all observations available from both nature and experiments. Geological structures that can be related to this criterion include: kink-bands and extensional crenulated cleavages, yield zones in evaporites, low-angle normal faults and high-angle reverse faults, lozenge ductile shear zones in basement terranes, some “crocodile” structures in seismic profiles and detachment folds in foreland basins. The method can be used to determine the stress state when the related deformation features formed and provides a new approach to determine the Wk of the related ductile shear zone. It can also be extended to explain the relationship between orogenic and late-orogenic extension events, uplift and exhumation of ultrahigh pressure rocks that experienced deep subduction.
The Mohr-Coulomb criterion has been widely used to explain the formation of fractures. However, it fails to explain large strain deformation that widely occurs in nature. There is presently a new theory, the MEMC, which is mathematically expressed as Meff=0.5 (σ1-σ3) L·sin 2α·sin α, where σ1-σ3 represents the yield strength of the related rock, L is a unit length and α is the angle between σ1 and deformation bands. This criterion demonstrates that the maximum value appears at angles of ±54.7° to σ1 and there is little difference in the moment in the range of 55°±10°. This range covers all observations available from both nature and experiments. Geological structures that can be related to this criterion include: kink-bands and extensional crenulated cleavages, yield zones in evaporites, low-angle normal faults and high-angle reverse faults, lozenge ductile shear zones in basement terranes, some “crocodile” structures in seismic profiles and detachment folds in foreland basins. The method can be used to determine the stress state when the related deformation features formed and provides a new approach to determine the Wk of the related ductile shear zone. It can also be extended to explain the relationship between orogenic and late-orogenic extension events, uplift and exhumation of ultrahigh pressure rocks that experienced deep subduction.
引文
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[12]Watterson J.The future of failure:stress or strain[J].Jour Struct Geol,1999,21:939-148.
[13]Zhang Z F,Eckert J.Unified tensile fracture criterion[J].Physical Review Letters,2005,94:1-4.
[14]Zheng Yadong,Du Siqing.A quantitative analysis of the an-gle between conjugate kink bands[C]∥Scientific paper on ge-ology for international exchange2.Beijing:Geological Pub-lishing House,1985:175-180(in Chinese).
[15]Zheng Y.Aquantitative analysis of the angle between conju-gate sets of extensional crenulation cleavages:an explanation of the low-angle normal fault development[C]∥Abstracts of29th IGC,Kyoto,1992,3(1):131.
[16]Zheng Y,Wang T,Ma M,et al.Maxi mumeffective moment criterion and the origin of low-angle normal faults[J].Jour Struct Geol,2004,26:271-285.
[17]Weiss L E.Flexural slip folding of foliated model materials[C]∥Baer A J,Norris D K.Proceedings conference on re-searchin tectonics.Ottawa:Canada Geological Survey,1968:68-52.
[18]Gay N S,Weiss L E.The relationship between principal stress direction and the geometry of kinks in foliated rocks[J].Tectonophysics,1974,21:287-300.
[19]Price N J,Cosgrove J W.Analysis of geological structure[M].Cambridge,England:Cambridge University Press,1990:1-502.
[20]Anderson T B.Kink-bands and related geological structures[J].Nature,1964,202:272-274.
[21]Anderson T B.The relationship between kink-bands and shear fractures in the experi mental deformation of slate[J].Jour Geol Soc Lond,1974,130:367-382.
[22]Hobbs B E,Means WD,Williams P F.An outline of struc-tural geology[M].New York:John Willey&Sons,1976.
[23]Johnson A M.Styles of folding:mechanics and mechanisms of folding of natural elastic materials[M].New York:Elsevi-er Scientific Pub.Co.,1977:406.
[24]Friedman M,Logan J M.Luders bands in experi mentally deformed sandstone and li mestone[J].Geol Soc Am Bull,1973,84:1465-1476.
[25]Hu Xiao,Niu Shuyin,Zhang Yingtao.Structural deforma-tion of the Mid-Upper Proterozoic Suberathemat the north-ern margin of the North China Platform[J].Journal of Hebei College of Geology,1987,10(4):335-348(in Chinese).
[26]Niu Shuyin,Hu Xiao,Xu Chuanshi.Characteristics of folds in the Chaertai areas,Inner Mongolia[J].Geology of Inner Mongolia,1990,72(2):1-14(in Chinese).
[27]Cosgrove J W.The formation of crenulation cleavage[J].Jour Geol Soc Lond,1976,132:155-178.
[28]Park R G.Shear-zone deformation and bulk strainin granite-greenstone terrain of the Western Superior Province[J].Can-ada:Precambrian Research,1981,14:31-47.
[29]Harris L B,Cobbold P R.Development of conjugate shear bands during bulk si mple shearing[J].Journal of Structural Geology,1985,7:37-44.
[30]White S H.Large strain deformation:report on a Tectonic Studied Group discussion meeting held at I mperial College,London on14November1979[J].Jour Struct Geol,1979,1:333-339.
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