Elastic Solutions Of The Stresses Distribution For The Circular Unsymmetrical Tunnel

China has a vast territory, and a complex and diverse topography, high-grade roads construction engineering encountered in a large number of problems in tunnels. Subject to the restrictions and effects of topography, more and more tunnels appears the problems of unsymmetrical pressure problem, the theoretical analysis of this problem still has a lot of difficulties. Based on plane elastic complex variable theory,this Article theoretically analysised the secondary stress distribution caused by topography in circular unsymmetrical tunnel. The main contents and results include:(1) In this study, the integral stress distribution is divided into three sub-distributions. The first one is the initial stress distribution in the unsymmetrical tunnels; and the second is that of a concentrates stress, which is equal to the weight of materials dug out, in a half plane excluding the field of body forces. The third is that caused by stresses weighting on the tunnel's periphery. This stress tension is used to balance the previous two segments and to adaptive the whole distribution to satisfy the initial boundary conditions.(2) Using plane elastic complex variable method and of Fourior transform, the stress distribution in round unsymmetrical tunnels is obtained at the first time. And the Mobius conformal mapping is adopted. The solution domain is represented by a circle and the three sub-distributions are obtained. The closed form is gained by summing them.(3) Using the methods this article describes, the parameters of the circular bias tunnel's stress field can be got. Writing programs and procedures to achieve the solution of the problem. The convergence of the potential function is discussed. Coefficients can be obtained under the boundary conditions, according to tunnel on the border weeks and the stress boundary conditions, combined infinite and known boundary conditions, the value of the variable k approaches infinity, the coefficient of ak value should be zero, according to the conditions of the coefficients can be solved out of iterative ak, and then obtained the boundary conditions of other factors, to derive the potential function. As the stress field must be convergence, requires the potential function must converge, the coefficient of the potential function must converge. Through coefficient is found that the potential function of the coefficient of variable k with the rapid increase of the value of convergence, in the k= 6, the coefficient of the real and imaginary parts have convergence, and the size of the near zero.(4)Last, apply the methods this article describes to analysis stress field parameters of the circular unsymmetrical tunnel. Investigate the influence of material and geometric parameters on the calculation results, which focus on analysis of Poisson's ratio, free half-plane angle and tunnel depth and some other factors. The results show that with increasing inclination, the greater the tunnel on stress, but the maximum generally appears in the top of the cave near the region on both sides; as the depth decreases, the stress get smaller infuence area in the surface; Poisson's ratio has little effect on the stress distribution of unsymmetrical tunnel.