Analytical Stress Solution Of Deep-buried Double Non-circular Tunnels

In the construction of water conservancy projects,in order to meet the requirements of conveying water excavating hydraulic tunnel in the mountain or underground is very necessary,and sometimes for space limitations and geological conditions,there are many tunnels very close to each other.In the construction of urban rail transit,the subway is the first choice of many urban construction traffic lines and most of the time it is constructed in the form of parallel double holes In mountainous area,where tunnels are needed for traffic,due to the factors such as geological conditions and space requirement,double tunnel excavation is also very necessary.So,it is necessary to study the stress around the twin tunnels.Analytical method of stress solution of deep-buried double non-circular tunnels will be studied in this article.According to the finite element simulation of a 3D model,some conditions of the three-dimensional problem of the deep-buried tunnel transformed into the two-dimensional plane strain problem are obtained and it is concluded that the deep buried tunnel can be regarded as a two-dimensional plane strain problem.And the problem studied in this article can be seen as an infinite elastic homogeneous plane containing two non-circular holes,one is an ellipse hole and another is an approximate circle hole.An analytical solution is presented for the plane which undergoes the internal traction along the holes and uniform compression and shears at infinity.The solution uses the conformal transformation in complex functions,with the double connected region mapping onto a circular ring.The stress distribution solved for the infinite plane containing two unequal circle holes in prior literatures for example the article of Haddon(1967)and Hoang(2008),is the special case of this article.And contrast between the results of two unequal circle holes obtained by using the present analytical method and the results of Hoang is made in the article,they are in good agreement.As there is no analytical solution for two non-circular holes,the results obtained using the present analytical method are compared with the numerical results calculated by ANSYS,and they agreed with each other.Some computational examples given in this article has been analyzed to study the effect of distance between two holes ?,the ratio of stress in two directions at infinity ?_x~?/?_y~?,and the ratio of the major and minor axis b/? on the stress distribution of the hole boundary.