Analytical Studies On Mechanical Analysis Of Shallow Buried Supported Tunnels

In recent years,the construction of underground tunnels in China has been developed significantly.When the tunnel is excavated,the original in-situ stress in the ground is released and the in-situ stress is redistributed to form a secondary stress field,resulting in stress concentration near the tunnel excavation boundary and tunnel deformation.To reduce the stress concentration along the tunnel boundary and maintain the tunnel stability,the excavated tunnel is often supported by bolts or lining.Therefore,how to calculate the stress and displacement fields in the soil mass after applying the support has become a very important problem in the field of underground tunnel engineering.Since underground tunnel engineering can effectively alleviate the tension of aboveground space,it is widely used in many fields such as transportation,water conservancy engineering,urban construction and so on.In the analytical study of subway tunnel and hydraulic tunnel problems,since such tunnels are usually buried shallow and the influence of the ground surface needs to be considered,the problem is usually simplified to a half plane problem.In addition,when the bolt support or lining support is applied to the shallow buried tunnel,the interaction between the bolt or lining and the soil mass needs to be considered.Therefore,it is difficult to study and analyze the stress field and displacement field of shallow buried tunnel with support by using analytical solution.At present,the analytical researches on such problems are also very scarce.In this paper,the complex variable method is used to study the problem of shallow buried circular tunnel with support,so as to provide preliminary design guidance and theoretical basis for engineering practice.The main innovative works are as follows:(1)Based on the power series method in the complex variable method,the analytical solution for shallow buried circular tunnel under gravity and internal water pressure are derived,taking into account the influence of soil body force.When there is no external load acting on the ground surface,the relation expression between the two analytical functions is established using the stress boundary condition along the ground surface,and this relation expression is not only applicable to the ground surface boundary,but also holds in the whole half plane.Therefore,the stress and displacement solutions of the problem can be obtained by only solving an analytical function with coefficients to be solved according to the stress boundary condition along the tunnel excavation boundary,which greatly simplified the complexity of the solving process and laid the foundation for the subsequent problems of the shallow buried circular tunnel with support.(2)Based on the analytical solution of the shallow buried circular tunnel without support,the analytical solution of the shallow buried circular tunnel reinforced by point anchored rockbolts is derived,the axial forces of the rockbolts are solved,the stress and displacement solution in the surrounding rock mass after applying point anchored rockbolts are obtained.In the solving process,due to the characteristics of the point anchored rockbolts,the actions of the bolts on the soil mass are simplified to a pair of concentrated forces of equal magnitude and opposite direction,respectively.The magnitude of the concentrated forces exerted by the bolts on the soil mass is unknown.Therefore,the analytical solution of a concentrated force acting in the half plane with a circular hole is derived,and then on the basis of the analytical solution,the linear equations are established according to the deformation coordination conditions between the soil and the bolts.The axial force on each bolt and the displacement field and stress field of the soil after bolt support can be obtained.When verifying the reliability of this analytical solution using the numerical simulation software ANSYS,the point anchored rockbolts were simplified to spring elements in order to correspond to the assumptions of the analytical solution,the axial force of both methods agreed well.The effects of the main parameters,such as the elastic modulus ratio between the soil mass and bolts,the burial depth of the tunnel,the length of bolts and the preload,on the axial force of the bolts were analyzed using this analytical solution.In addition,the effect of the installation of point anchored bolts on the stress and displacement of the soil mass is investigated by comparing the results with those of a shallow buried circular tunnel without support.(3)The analytical solutions for stresses and displacements of a lined circular tunnel at shallow depths are presented by considering two kinds of contact conditions between the soil mass and the lining——no slip contact condition and full slip contact condition.In the solving process,the lining and surrounding rock mass are mapped into two different rings by two sets of mapping functions,the interaction between the soil mass and lining is considered,the relevant equations are listed using the stress boundary conditions along the inner boundary of the lining and the stress and displacement continuity conditions along the contact surface between the lining and soil mass.In the process of establishing the linear equation system,the traditional power series method is no longer applicable,but the idea of boundary collocation method is used to establish the linear equation system.The derivation process of the new method is simpler than power series method.The influences of main parameters such as the elastic modulus ratio of the lining and soil mass and the buried depth on stress and displacement in lining and soil mass are analyzed through examples.By comparing the results of two different contact conditions,the role of lining in maintaining soil stability under two different contact conditions is studied.