Mechanical Analysis Of Bolts In An Elliptical Tunnel Based On Complex Variable Method

The research on tunnel excavation and support is always one of the key and hot subjects in the field of geotechnical and underground engineering.As to the tunnel support,the application of the point anchored rockbolt is used early and still widely used.Bobet firstly proposed a analytical method for mechanical analysis of the point anchored rockbolt in a circular tunnel.However,the stress and displacement solutions used in this method are not exact solutions,but approximate solutions.In this paper,we use the ccurate closed-form solution to study the mechanical analysis of anchors in an elliptical tunnel.In this paper,the conformal transformation is used to map an elliptical domain on the physical plane to the unit circle domain on the image plane,based on the complex variable method.And according to the two complex potential functions when a concentrated force is applied at any point in the infinite domain of the elliptical tunnel,the exact analytic solutions of stress and displacement are further deduced,and display expressions are given.The effect of the point anchored rockbolt on the surrounding rock is simplified to a pair of equal and opposite concentrated forces,and the display expressions of displacement subjected to multiple point anchored anchors are obtained through the superposition principle.Considering the displacement caused by the tunnel excavation,the linear equations for solving the axial forces of the point anchored rockbolts are established by the deformation coordination conditions.The axial force distribution of each bolt with pre-tightening force or not is obtained by using Fortran,and the results are compared with the calculation results of ANSYS to verify the correctness of the method.Finally,the analysis of the influences of the elliptical half-shaft ratio,lateral pressure coefficient,the stiffness,anchor length and pre-tightening forces on the axial forces are carried out,and the effect of the anchors on the stress state of the surrounding rock is analyzed.