Analytical Method For Mechanical Analysis For Surrounding Rock And Lining Of Tunnels Under Frictional Slip Contact Conditions

Tunnel and underground engineering have made great progress since modern times.Especially,after entering the 20th century,with the progress of design and construction technology and the need of social development,more attention has paid to it.Because of its geographical location and the particularity of its building structure,it has outstanding advantages such as convenience,safety,environmental protection,energy saving and so on,thus it is widely used in transportation,mining,energy,hydropower engineering,urban construction and national defense construction and other fields.The surrounding rock stability problem in underground structures is one of the central topics in tunnel rock mechanics.The initial stress in the rock mass is released after the excavation of tunnels and the stress in the rock is redistributed,when the stress in the surrounding rock reaches or exceeds the strength of the rock mass,the rock mass will be unstable.At this time,it is usually necessary to set up lining support around the tunnel to further ensure the stability of surrounding rock.The complex variable method is a fundamental method for solving tunnel and underground engineering problems due to the accuracy of the analytical solution and the convenience of the solution process.In order to solve the problem of lining tunnels with complex shape,it is necessary to apply the conformal transformation method in complex variable method to transform the complex supporting section on the physical plane into the ring region on the image plane.In practical engineering,the contact problem between lining and surrounding rock is more complicated,in order to simplify the problem to obtain its basic law,the contact problem between them is simplified to the contact problem of two elastic bodies on the boundary.Frictional slip contact,as one of the contact conditions of elastic bodies,is most in line with the actual working conditions,while perfect bonding and full-slip contacts are its two limit cases.In this paper,based on the solution of two limit contact conditions,the Coulomb friction model is skillfully introduced into the solution process of frictional slip contact,and combined with the optimization method,its general solution is obtained.The main research contents include:(1)Considering full-slip contact,one of the limit cases of frictional slip contact,under the action of uniformly distributed internal water pressure,the analytical solutions of stress and displacement for deep-buried lining tunnel with arbitrary hole are derived by plane elastic complex variable method,the results are verified by the numerical software ANSYS.In the process of solution,the effect of in-situ stress and mechanical process of support delay are considered.Use the power series solution method to solve the basic equations consisting of the stress boundary conditions and the continuous conditions of stress and normal displacement,and then calculate the stress and displacement in the surrounding rock and lining through the obtained analytic function.Taking inverted U-shaped and horseshoe shaped tunnels as examples,the tangential stress and the normal stress distribution around the borders are analysed.The distributions of stress in the surrounding rock and lining are discussed under the condition of different displacement release coefficient,lateral pressure coefficient and internal water pressure.It is found that the tangential stress is larger at the inner boundary of lining and the excavation boundary of surrounding rock,and the maximum stress concentration appears at the corner of tunnel.(2)In order to describe the contact problem between the surrounding rock and the lining more accurately,the real working state of the lining is defined to minimize the relative sliding on the contact surface,the frictional slip contact condition based on Coulomb friction model is introduced introduced to simulate the contact between the surrounding rock and the lining.On the premise of considering the mechanical process of the support delay,combining the plane elastic complex function method and the optimization theory,a general frictional slip contact solution method is established.Taking a circular hydraulic tunnel as an example,an analytical solution for the stress of surrounding rock and lining under this contact condition is obtained and the analytic solutions are verified by finite element software ANSYS.Finally,a calculation example is used to analyse the influence of different fr and λ on the distributions of the stresses along every boundary and the tangential displacement discontinuity value along the interface.(3)Aiming at the shortcomings of the frictional slip contact solution of tunnel surrounding rock and lining,the optimization model is greatly simplified by reducing the number of design variables in the optimization process.A more ideal optimization theoretical model is obtained for solving the problem of deep-buried tunnel with arbitrary hole under the condition of frictional slip contact,and the calculation accuracy and speed are improved.The method can also accurately obtain the threshold value of the friction coefficient satisfying the perfect bonding contact.Through the parameter analysis of the elastic modulus ratio,displacement release coefficient,lining thickness and lateral pressure coefficient of deep-buried circular lining tunnel,it provides a theoretical basis for judging the contact mode between surrounding rock and lining.