A non-Archimedean number system to characterize the structurally inhomogeneous rock behavior nearby a tunnel  

作　　者：S.V.Lavrikov O.A.Mikenina A.F.Revuzhenko 

机构地区：[1]Institute of Mining,Siberian Branch,Russian Academy of Sciences,Novosibirsk,Russia

出　　处：《Journal of Rock Mechanics and Geotechnical Engineering》2011年第2期153-160,共8页岩石力学与岩土工程学报（英文版）

基　　金：Supported by the Russian Foundation for Basic Research (10-05-91002);the Integration Project of the Siberian Branch,Russian Academy of Sciences (69)

摘　　要：The development of mathematical models of structurally inhomogeneous media leads to the necessity to consider structure of space itself where deformation occurs, i.e. change of mathematical apparatus itself. The space, whose coordinate axes are non-Archimedean straight lines, has been considered. Refusing the fulfillment of Archimedes’s law allows to describe multi-scaling of the space, and so to consider deformation processes on different scale levels. The construction of two-scale mathematical model of rock masses has been considered as an example. The constitutive equations have been formulated on micro-and macro-levels and interaction condition between different levels as well. On micro-level, the elastic behavior of grains and plastic sliding between grains with possible softening are taken into account. On macro-level, the model represents a nonlinear system of equations describing the anisotropic rock mass behavior. On the basis of model, the numerical algorithm and code have been carried out to solve the plane boundary value problems. Examples of numerical simulations of stress-strain state of structural rock masses nearby a tunnel opening are presented. The deformation contours and isolines of stresses are plotted.The development of mathematical models of structurally inhomogeneous media leads to the necessity to consider structure of space itself where deformation occurs, i.e. change of mathematical apparatus itself. The space, whose coordinate axes are non-Archimedean straight lines, has been considered. Refusing the fulfillment of Archimedes’s law allows to describe multi-scaling of the space, and so to consider deformation processes on different scale levels. The construction of two-scale mathematical model of rock masses has been considered as an example. The constitutive equations have been formulated on micro-and macro-levels and interaction condition between different levels as well. On micro-level, the elastic behavior of grains and plastic sliding between grains with possible softening are taken into account. On macro-level, the model represents a nonlinear system of equations describing the anisotropic rock mass behavior. On the basis of model, the numerical algorithm and code have been carried out to solve the plane boundary value problems. Examples of numerical simulations of stress-strain state of structural rock masses nearby a tunnel opening are presented. The deformation contours and isolines of stresses are plotted.

关 键 词：rock mass INHOMOGENEITY mathematical model non-Archimedean analysis constitutive equations 

分 类 号：U452.12[建筑科学—桥梁与隧道工程]