Theoretical Analysis And Finite Difference Solution On Pipeline Deformation Due To Traversing Excavation

With ever-growing development and utilization of urban underground space,more and more complicated tunnel projects traversing underground pipelines will surelycome into existence.Tunnel excavation changes status of surrounding strata,affecting the stress state of underground pipelines and inducing its deformation.Excessive pipeline deformation will cause damage,thereby jeopardizing city's production and residents'daily lives.Reducing the risk of pipeline damage is considerately important.The key point of it is to calculate the deformation and internal forces of pipeline induced by deformation of soil.However in the present theoretical study of pipe-soil interaction,it was assumed that the pipe-soil is always in contact.The discontinuity in rigidity and rotation angle at pipeline joint was ignored,and the nonuniformity of axial stress and strain caused by vertical deformation was also neglected.These bring about limitation on the accuracy and applicability of calculation methods on pipeline deformation and internal forces.Therefore,it is of great theoretical value and practical significance to study the pipe-soil interaction theory and improve the existing calculation methods.In this paper,pipe-soil interaction was studied for continuous pipeline and jointed pipeline under the influence of tunnel excavation through theoretical analysis and finite difference method.And a corresponding calculation method was presented to improve the deficiencies of existing methods in calculating the additional pipeline deformation caused by ground displacements.The main results are as follows:(1)Based on the theory of large deformation,a governing differential equation for continuous pipelines was established.Considering the nonuniformity of pipeline's axial force,finite difference method was employed to solve differential equation.The validity of this method was verified by comparing with examples in existing literatures.The distribution of axial force was calculated,and the difference between differential solution and series solution and its causes were analyzed.The influence on the deformation and internal forces of continuous pipelines due to the nonuniformity of axial force was discussed.(2)As for a strong continuous pipeline in the shallow-buried strata,it was considered of possible separation from the soil.A step function was introduced to describe the pipeline's void.Finite difference method was used to calculate the deformation and internal forces of the pipeline.The pipe-soil interactions in different condition of pipeline's void were compared and analyzed.(3)The equivalent load was introduced to traditional differential equation of beamon elastic foundation.A boundary condition was added at the joint,so that the relative rotation angle was generated by the equivalent load which was equivalent to the joint stiffness reduction.The relationship between the equivalent loads and the second derivative of the vertical displacement of the pipeline was deduced.And the governing differential equation for jointed pipeline was establish.(4)Finite difference method was used to solve the differential equation,and the validity of this method was testified by FEM numerical simulation.Groups of calculation conditions were analyzed to explore the influence of the number of joints,the relative position between the joints and tunnel axis,and the joint's stiffness on pipeline deformation,internal force,and the relative rotation angle of the joints.It was concluded that the deformation of jointed pipeline was in the most unfavorable state when the joint was in the center of settlement trough.(5)Single factor analysis method was used to explore the influence of strata factors and pipeline parameters on the deformation of jointed pipelines.It was concluded that there was a positive correlation between strata factors and pipeline deformation.And pipeline parameters were positively correlated with the width of pipeline settlement trough,and were negatively correlated with vertical deformation and joint's relative rotation angle of the pipeline.