疏松砂岩层宏观弹性模量计算模型研究
摘要
用介观颗粒接触力学模型建立宏观弹性模量的理论规律,干颗粒堆积体宏观弹性模量和颗粒所受应力的1/3次方成正比,埋深越大,宏观弹性模量越大。颗粒直径是影响颗粒堆积体宏观弹性模量的重要因素,颗粒直径越大,宏观弹性模量越大。研究等径颗粒体的5种常见排布方式对宏观弹性模量的影响,确定调整系数,配位数和弹性模量呈大致的反比关系,但是配位数变化并不意味着巨大的弹性模量变化。颗粒堆积体的变形不符合胡克定律,并且弹性模量也存在各向异性。
Based on the mesoscopic hertzian granular contact mechanics model,a macroscopic Young's elastic modulus(MYEM) model of packing sandstone was built up.The MYEM was proportioned to the powers of 1/3 of the vertical contact force of sand particles and was inversely proportional to particle diameter.The paper calculated the vertical contact force of 5 aligning modes of the particles which affect the MYEM and adjustment coefficients be given.The coordination number is inverse proportion to MYEM but is not a sensitive parameter.The deformation of granular packing layer is not in accord with Hooke's law and the MYEM also have the nonisotropic features.
Based on the mesoscopic hertzian granular contact mechanics model,a macroscopic Young's elastic modulus(MYEM) model of packing sandstone was built up.The MYEM was proportioned to the powers of 1/3 of the vertical contact force of sand particles and was inversely proportional to particle diameter.The paper calculated the vertical contact force of 5 aligning modes of the particles which affect the MYEM and adjustment coefficients be given.The coordination number is inverse proportion to MYEM but is not a sensitive parameter.The deformation of granular packing layer is not in accord with Hooke's law and the MYEM also have the nonisotropic features.
引文
[1]刘旭.多相介质弹性参数的研究及波速计算[D].北京:中国地震局地球物理研究所,2002.
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[11]关成尧,漆家福,邱楠生,等.应力比影响下的压剪裂纹破裂角、闭锁角、摩擦系数及其耦合关系[J].岩土力学,2012,33(12):3570-3576.
[12]田嘉宁,石怀理.岩石动弹性模量与静弹性模量对比试验研究[J].西北水力发电,1988(4):21-27.
[13]安欧.构造应力场[M].北京:地震出版社,1992.
[2]夏唐代,刘瑜,吴明,等.基于颗粒接触理论的深层砂土剪切波速度[J].哈尔滨工业大学学报,2011,43(4):99-103.
[3]钟晓雄,袁建新.散粒体的细观组构与本构关系[J].岩土工程学报,1992,14(增刊):39-48.
[4]Marcial Gonzalez,Alberto M Cuitio.A Nonlocal Contact for Mulation for Confined Granular Systems[J].Journal of the Mechanics and Physics of Solids,2012,60:333-350.
[5]Zhupanska O I.Contact Problem for Elastic Spheres:Applicability of the Hertz Theory to Non-small Contact Areas[J].Int J Eng Sci,2011,49:576-588.
[6]Johnson K L.Contact Mechanics[M].London:Cambridge University Press,1985.
[7]孙其诚,厚美瑛,金峰,等.颗粒物质物理与力学[M].北京:科学出版社,2011.
[8]刘瑜.基于颗粒接触模型的砂土剪切波速研究[D].杭州:浙江大学,2010.
[9]O′Sullivan C,Bray J D,Riemer M.Examination of the Response of Regularly Packed Specimens of Spherical Partical Particles Using Physical Tests and Discrete Element Simulations[J].J Eng Mech,2004,130:1140-1150.
[10]关成尧,漆家福,邱楠生,等.裂缝三级摩擦因数及影响因素研究——以砂岩(颗粒胶结体)为例[J].应用数学和力学,2012,34(2):209-216.
[11]关成尧,漆家福,邱楠生,等.应力比影响下的压剪裂纹破裂角、闭锁角、摩擦系数及其耦合关系[J].岩土力学,2012,33(12):3570-3576.
[12]田嘉宁,石怀理.岩石动弹性模量与静弹性模量对比试验研究[J].西北水力发电,1988(4):21-27.
[13]安欧.构造应力场[M].北京:地震出版社,1992.
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