基于变形功的有效应力力学机理探究
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摘要
针对Terzaghi有效应力公式在饱和多孔介质力学中的适用性问题,提出新的饱和多孔介质的体积变形功方程,基于变形功探究有效应力力学机理.当忽略固流相基质变形时,运用机械功原理证明Terzaghi有效应力公式的正确性.当考虑固流相基质变形时,根据混合物理论将固相体应变分为固相体积分数应变和固相基质体应变.通过推导和分析体积变形功守恒方程,揭示Terzaghi有效应力与固相体积分数应变之间的功共轭力学关系.在小应变条件下,当固相基质变形、固相体积分数变化和流相基质变形之间的受力机理相互独立时,Terzaghi有效应力唯一地决定饱和多孔介质的固相体积分数应变.同时采用固相基质压力和Terzaghi有效应力才能够完全确定固相体积变形.研究结果表明,Terzaghi有效应力作为影响固相体积变形的内在因素之一,其表达式无须修正.
A new volume deformation work conservation equation of saturated porous media was proposed, and the effective stress mechanics mechanism was explored based on deformation work, in view of the validity of Terzaghi effective stress formula in saturated porous media. The mechanical work principle was used to prove the validity of Terzaghi effective stress formula without taking the deformations of solid and fluid matrix into account. The volume strain of solid phase was divided into solid volume fraction strain and solid matrix volume strain based on mixture theory, considering the deformations of solid and fluid matrix. The mechanical relationship of work conjugate between Terzaghi effective stress and solid volume fraction strain was obtained through the derivation and analysis of volume deformation work conservation equation. Terzaghi effective stress can only determine the solid volume fraction strain when the stress mechanisms among solid matrix deformation, solid volume fraction change and fluid matrix deformation were mutually independent under infinitesimal strain condition. The volume deformation of solid phase can be closely determined only if both solid matrix stress and Terzaghi effective stress were used. Results show that Terzaghi effective stress, as one of the internal factors affecting the volume strain of solid phase, does not need to be corrected.
A new volume deformation work conservation equation of saturated porous media was proposed, and the effective stress mechanics mechanism was explored based on deformation work, in view of the validity of Terzaghi effective stress formula in saturated porous media. The mechanical work principle was used to prove the validity of Terzaghi effective stress formula without taking the deformations of solid and fluid matrix into account. The volume strain of solid phase was divided into solid volume fraction strain and solid matrix volume strain based on mixture theory, considering the deformations of solid and fluid matrix. The mechanical relationship of work conjugate between Terzaghi effective stress and solid volume fraction strain was obtained through the derivation and analysis of volume deformation work conservation equation. Terzaghi effective stress can only determine the solid volume fraction strain when the stress mechanisms among solid matrix deformation, solid volume fraction change and fluid matrix deformation were mutually independent under infinitesimal strain condition. The volume deformation of solid phase can be closely determined only if both solid matrix stress and Terzaghi effective stress were used. Results show that Terzaghi effective stress, as one of the internal factors affecting the volume strain of solid phase, does not need to be corrected.
引文
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[12]GEERTSMA J.The effect of fluid pressure decline on volumetric changes of porous rocks[J].Petroleum Transaction,1957,210:331-339.
[13]BORJA R I.On the mechanical energy and effective stress in saturated and unsaturated porous continua[J].International Journal of Solids and Structures,2006,43:1764-1786.
[14]朱慈勉,张伟平.结构力学[M].北京:高等教育出版社,2010:109-111.
[15]HOULSBY G T.The work input to a granular material[J].Géotechnique,1979,29(3):354-358.
[16]BOWEN R M.混合物理论[M].许慧己,译.南京:江苏科学技术出版社,1983:1-46.
[17]BUTTERFIELD R.A natural compression law for soils:an advance on e-logp[J].Géotechnique,1979,29:469-480.
[18]黄筑平.连续介质力学基础[M].2版.北京:高等教育出版社,2012:101-104.
[19]龚晓南,谢康和.土力学[M].北京:中国建筑工业出版社,2014:87.
[2]BIOT M A.General theory of three-dimensional consolidation[J].Journal of Applied Physics,1941,12(2):155-164.
[3]SKEMPTON A W.Effective stress in soils,concrete and rocks,pore pressure and suction in soils[C]//Proceedings of the International Conference of Soil Mechanics and Foundation Engineering.London:Butterworths,1961:4-25.
[4]MITCHELL J K.Foundamentals of soil behavior[M].New York:Wiley,1976.
[5]李广信.关于有效应力原理的几个问题[J].岩土工程学报,2011,33(2):316-320.LI Guang-xin.Some problems about principle of effective stress[J].Chinese Journal of Geotechnical Engineering,2011,33(2):316-320.
[6]方玉树.土的有效应力原理相关问题的分析[J].岩土工程界,2009,12(5):11-15.FANG Yu-shu.Principle related problems of effective stress analysis of soil[J].Geotechnical Engineering World,2009,12(5):11-15.
[7]邵龙潭,郭晓霞,郑国锋,等.粒间应力、土骨架应力和有效应力[J].岩土工程学报,2015,37(8):1478-1483.SHAO Long-tan,GUO Xiao-xia,ZHENG Guo-feng,et al.Intergranular stress,soil skeleton stress and effective stress[J].Chinese Journal of Geotechnical Engineering,2015,37(8):1478-1483.
[8]路德春,杜修力,许成顺,等.有效应力原理解析[J].岩土工程学报,2013,35(增1):146-151.LU De-chun,DU Xiu-li,XU Cheng-shun,et al.Analytical solutions to principle of effective stress[J].Chinese Journal of Geotechnical Engineering,2013,35(Suppl.1):146-151.
[9]陈愈炯.有效应力原理对饱和黏土的适用性[J].岩土工程学报,2011,33(6):985-988.CHEN Yu-jiong.Validity of effective stress principle in saturated clay[J].Chinese Journal of Geotechnical Engineering,2011,33(6):985-988.
[10]SCHREFLER B A.Mechanics and thermodynamics of saturated/unsaturated porous materials and quantitative solution[J].Applied Mechanics Reviews,2002,55(4):351-388.
[11]GRAY W G,SCHREFLER B A.Analysis of the solid phase stress tensor in multiphase porous media[J].International Journal for Numerical and Analytical Methods in Geomechanics,2007,31:541-581.
[12]GEERTSMA J.The effect of fluid pressure decline on volumetric changes of porous rocks[J].Petroleum Transaction,1957,210:331-339.
[13]BORJA R I.On the mechanical energy and effective stress in saturated and unsaturated porous continua[J].International Journal of Solids and Structures,2006,43:1764-1786.
[14]朱慈勉,张伟平.结构力学[M].北京:高等教育出版社,2010:109-111.
[15]HOULSBY G T.The work input to a granular material[J].Géotechnique,1979,29(3):354-358.
[16]BOWEN R M.混合物理论[M].许慧己,译.南京:江苏科学技术出版社,1983:1-46.
[17]BUTTERFIELD R.A natural compression law for soils:an advance on e-logp[J].Géotechnique,1979,29:469-480.
[18]黄筑平.连续介质力学基础[M].2版.北京:高等教育出版社,2012:101-104.
[19]龚晓南,谢康和.土力学[M].北京:中国建筑工业出版社,2014:87.