Theoretical Analysis Of The Mechanical Behavior Of Shallow-Buried Circular Tunnel And Application

In recent years,with rapid development of China’s urban infrastructure construction,city tunnels bring good social and economic benefits with its environmentally friendliness and high efficiency,and have been gradually becoming the first choice to solve traffic jams.During the construction and operation period,the analysis of stress state and ground deformation is vital for tunnel design.Since the buried depth of deep tunnels is quite large,the influence of surface boundary and ground loads can be neglected.In the existing literatures,deep tunnels are always simplified as a hole in the infinite medium.Many scholars has studied the mechanical problems concerning about deep tunnels and have yielded fruitful results of the research.However,the outstanding feature of city tunnels are shallow buried depth,with weak surrounding rock masses and bad engineering geological conditions,and dense buildings above.For shallow-buried tunnels,the existence of ground surface makes the analytical solution more complicated.Through reviewing existing researches,it can be found that the theoretical research concerning shallow-buried tunnel is insufficient.Thus,this paper devotes to studying the mechanical behavior of shallow-buried tunnels by using the complex variable functions and Fourier series transformation.The correctness of the analytical solution is validated by results of numerical simulation and field monitoring data.The main research content and conclusions are as follows:(1)Based on the complex function solution of a concentrated force in the interior of an infinite medium,the complex function solution of shallow-buried circular tunnel is divided into three parts according to the principle of the image method.The stress boundary condition in tunnel boundary caused by the initial gravity stress is firstly derived,without considering the tunnel excavation.Then the complex variable functions related to a concentrated force acting in the interior of an semi-infinite medium is obtained,and the stress boundary condition at tunnel boundary is calculated by the derived complex variable functions.Opposite forces are applied at tunnel boundary to balance stresses caused by the above two parts.The calculation method is proposed,and a Fortran code is developed to calculate stress and displacement caused by tunnel excavation.And the correctness of the analytical solution and the developed code is validated by comparing analytical solutions with numerical simulation.A rule is established to determine the number of Laurent series based on the convergence of complex functions.The effect of buried depth on calculation accuracy of horizontal displacement is investigated.According to the theory of stress release,the analytical solution for shallow-buried circular tunnel when considering stress release is put forward.(2)The periodicity of stress boundary condition cased by forces on the outside region of the tunnel is firstly discussed,since only when the stress boundary condition is period along tunnel boundary,the complex function solution can be obtained.Then the complex function solution for tunnelling nearby existing forces and ground loads are separately derived.And the complex function solution for arbitrary load can be obtained by using the superposition principle.The derived solution is used to study the effect of ground loads on stress,displacement and the scope of plastic zones when tunnelling nearby.(3)The basic principle of Schwarz alternation method is introduced briefly,then the calculating method for solving the complex function solution of double round hole shallow-buried tunnels.The theoretical calculation process when considering gravity stress and external loads are separately discussed.Coordinate translation is introduced to calculate stress boundary condition.A finite element code is employed to validate the effectiveness of the derived solution.The effect of iterations on the accuracy of analytical results is analyzed.Then the complex function solution is employed to study the effect of lateral distance and the crossing angles on ground deformation and the scope of plastic zones.(4)According to the continuity condition of lining deformation,the deformation of tunnel lining is continuous processing and expanded as Fourier series.Due to the huge difference in elastic modulus in tunnel lining and rock masses,the mechanical characteristic of them will have a significant difference.The complex function solution is firstly derived by mapping the tunnel lining into a concentric annulus,combined the stress and deformation boundary condition in the inner boundary of tunnel lining.Since the force at the interface of tunnel lining and rock masses is a pair of action and reaction,the stress boundary condition on the inner boundary of rock masses can be obtained by the complex functions corresponds to tunnel lining.Then the complex function solutions in the region of rock masses can be simplified as the problem opposite forces acting on the interior of rock masses,the complex solution can be derived according to the method provided in section 2.2.3.The distribution on internal force along tunnel lining is obtained,and the safety factor and potential failure mode is discussed.(5)The complex function solutions is used to predict the ground deformation and plastic zones in the running tunnel between Hualong station and Chongqing West station tunnel.The analytical solution of ground deformation is compared with field monitoring data,the reason of calculation error is investigated.And the effect of the surface building loads on ground deformation and the scope of plastic zones is discussed.