A Preliminary Study On The Theory Of Incompatible Deformation In Deep Rock Mass

The classical rock mechanics theory is based on the continuum theory and is applicable to the shallow rock mass.In this case,the rock mass deformation is small,so the elastic theory can be used to analyze and solve the rock mass,and the deformation meets the coordination condition.however,the occurrence environment of deep rock mass is obviously different from that of shallow rock mass.Due to the incompatible of deformation caused by defects and internal stress,the traditional continuum theory cannot correctly describe the stress of rock mass.In this thesis,nonEuclidean geometric parameters are introduced to describe the motion and deformation of rock mass,and the deformation characteristics and failure laws of deep rock mass are revealed by comprehensive application of theoretical analysis and numerical simulation,which is of great significance to the development of deep rock mechanics theory and its application in engineering practice.The paper has obtained the following innovative research results:(1)The dislocations theory of incompatible deformation in deep rock mass is established.Saint Venant's geometric coordination equation was derived from the perspective of classical elasticity.Taking deep rock mass with dislocation as the research object,the dislocation density tensor was introduced and analyze the geometric significance of dislocation,then the incompatible theory of deep rock mass was proposed.The elastoplastic deformation of a deeply buried circular cavity with dislocation under hydrostatic pressure is studied.It is concluded that for a deep circular tunnel,the incompatible tensor varies with the radius of surrounding rock under hydrostatic pressure.The stress function satisfies poisson's equation,due to the existence of the dislocation the radial stress of surrounding rock is reduced,the hoop stress increase.(2)The internal stress theory of incompatible deformation of deep rock mass is established.The motion and deformation of deep rock mass with internal stress are analyzed by introducing Riemannian manifolds with non-Euclidean geometric mathematical tools,then the displacement incompatible equation is derived.The relationship between deformation and Riemannian curvature tensor was established,and the Riemannian curvature tensor was used as an internal variable to build a thermodynamic model of deep rock mass disharmonious deformation.The analysis shows that the deformation of rock mass is incompatible due to the existence of internal stress.Part of the internal stress dissipates with the excavation of underground engineering,and the rest remains in the rock mass,which makes the stress field of deep circular tunnel show periodic fluctuation change.When the stress at the peak exceeds the strength of the rock mass,the rock mass will fail,and the zonal fracture in deep rock mass is a periodic failure.For rock mass with internal stress,with the increase of elastic modulus E of rock mass,the peak value of hoop stress of rock mass decreases.With the increase of elastic modulus E,the more internal stress dissipation of rock mass and the smaller residual internal stress under the same deformation condition.In addition,with the increase of elastic modulus E,the position of peak stress is closer to the cavity,indicating that the harder the rock mass is,the more severe the failure near the cavity surface is.With the increase of Poisson's ratio v,the hoop stress of rock mass decreases,indicating that the larger the Poisson's ratio v is,the larger the deformation of rock mass under the same confining pressure is,the more internal stress is released,and the smaller the residual internal stress is.In addition,with the increase of Poisson's ratio v,the peak stress is closer to the interior of the tunnel.(3)The plastic theory of incompatible deformation defects in deep rock mass is established.Using non-Euclidean geometric mathematical tools to analyze the elasticplastic deformation process of rock mass,and three kinds of rock mass plastic deformation configurations are proposed.The relationship between the elastic strain tensor of elastoplastic deformation and the classical elastic strain tensor and nonEuclidean parameters is derived.The plastic stress-strain expression including nonEuclidean parameters is established and the finite element expression is derived.FORTRAN language is used to write an elastoplastic finite element program to analyze the elastoplastic deformation of deep rock mass with defects.For deep circular cavity under the condition of hydrostatic pressure,the stiffness of surrounding rock is reduced due to the existence of defects.When R = 0.1?0.3,the pressure required for surrounding rock to enter plastic state decreases linearly with the increase of R.When R exceeds 0.4,the elastic-plastic stiffness of surrounding rock decreases significantly,and the surrounding rock rapidly enters the plastic state,while the deformation increases significantly.There are 28 figures,5 tables and 138 references in the dissertation.