Research On The Back Analysis Theory Of Rock Mass Displacement Based On Kelvin Mode

On the one hand,the rheological phenomena of rock masses are widely present in nature,and the in-depth study of viscoelastic media is closer to reality than traditional elastic media,and the solid rheological characteristics of Kelvin model can describe the small deformation of rock masses well and has a wide range of application.On the other hand,the mechanical parameters of rock masses are the basis for numerical analysis and theoretical inversion,but as complex bodies that have evolved over a long period of time,the parameters of rock masses are not easy to obtain,and the inverse analysis method provides a feasible way to determine the parameters of rock masses.Based on this,this paper investigates the theory of inverse analysis of viscoelastic rock displacement in accordance with the Kelvin model,in order to break the blockage of "accurate and fast determination of viscoelastic rock parameters".The research covers the following topics:Firstly,based on the theory of complex functions,the analytical solution of displacement of viscoelastic rock masses conforming to the Kelvin model is derived by using the creep flexure method and the tools of angle-preserving transformation and Laplace transformation.Then,the uniqueness of the inverse analysis of the displacements of viscoelastic rock masses conforming to the Kelvin model in circular and non-circular tunnels is investigated according to the criterion of parameter identification.The results show that the factors affecting the uniqueness of the displacement inverse analysis include the ground stress,the parameters to be inverted,the shape of the roadway section and the spatial location of the measurement points,etc.Based on the principle of maximum displacement,the optimal arrangement of the displacement measurement points for viscoelastic rock masses conforming to the Kelvin model is investigated using the angle of the measurement line,the depth of the measurement points and the lateral pressure coefficient as variables.The results show that the displacement of the surrounding rock will follow the direction of the large principal stress,but the maximum displacement does not always occur at the cave wall,but also at the extreme value of the analytical solution of the displacement.Finally,an engineering example analysis of the optimised arrangement of measurement points and displacement inverse analysis of a circular tunnel is carried out to prove the correctness of the theoretical derivation and provide a reference for engineering practice.