Complex Function Solution For Stress And Deformation Of Shallow Rectangular Pipe Jacking Tunnel

In recent years,with the rapid development of China’s infrastructure construction,the use of urban land resources gradually tends to saturation.More and more cities have launched the development and utilization of urban underground space,and urban tunnel construction is in full swing.As a new type of shallow tunnel excavation technology,the rectangular pipe jacking method is more and more widely used in practical engineering due to its advantages of higher space utilization and less impact on the surrounding environment.Rectangular pipe jacking tunnel is usually shallow tunnel.The rectangular pipe jacking machine will cause ground loss in the process of construction and excavation,and after the excavation of the face of the rectangular pipe segment and soil will be grouting operation.Ground loss and grouting pressure will have a greater impact on the tunnel surrounding rock stress and deformation.Because shallow rectangular pipe jacking tunnel is a complex hole problem in semi-infinite space,it is difficult to analyze and study the stress and deformation of surrounding rock by analytical method.At present,the theoretical research on shallow buried rectangular pipe jacking tunnel is still lacking.In this paper,the mechanical problem of shallow rectangular pipe jacking tunnel under the action of ground loss and grouting pressure is studied based on the method of complex variable function of elasticity.The main research contents and achievements include:(a)By using the conformal mapping principle of complex variable function,a rectangular hole in a semi-infinite space is mapped to a unit concentric ring.All the coefficients of the conformal mapping function are obtained based on the least square method and the dichotomy method.The contour of the mapping rectangle that meets the accuracy requirements is obtained.Furthermore,the influence of conformal mapping function series term and geometric parameters of shallow buried rectangular pipe jacking tunnel on mapping accuracy is analyzed.(b)Two theoretical calculation models for ground loss and grouting pressure during tunnel excavation are established.In the calculation model of ground loss,rectangular radial displacement boundary condition was set at the edge of the hole,and in the grouting pressure calculation model,uniform internal pressure was set at the edge of the hole,without considering the action of surface load.The boundary condition equations of the surface and the edge of the hole are obtained.By using the analytic property of the complex function in the ring domain,the stress function is expanded into Laurent series.At the same time,by using the Fourier series transformation of the complicated function,the analytical solutions of the complex function of the two kinds of calculation models are derived by using series method.The correctness of the theoretical solution is verified by comparing the results of finite element numerical simulation.Finally,the effects of Poisson’s ratio of soil,tunnel height-width ratio and tunnel depth on the stress and displacement fields of soil in the two calculation models are analyzed.(c)Based on two kinds of theoretical calculation models of shallow rectangular pipe jacking tunnel established according to ground loss and grouting pressure,the influence of ground loss and grouting pressure on the soil distribution conforming to the Tresca yield criterion in the theoretical solution is analyzed.and on this basis,the finite element software Abaqus is used to establish the corresponding finite element elastoplastic model by setting up soil for Tresca elastic-plastic material.The analysis of the shallow rectangular pipe jacking tunnel of the plastic zone of soil changing with the loss of soil and grouting pressure.