The Stress Analysis Method Of Double Tunnels And The Shape Optimization Of A New Tunnel Near The Existing Tunnel

With the development of economy and the needs of production and life,the tunnel,a basic facility,has been widely used in many fields such as transportation,water conservancy and mining.However,stress concentration will inevitably occur on the hole boundary of the tunnel under load,which poses a threat to the safe use of the tunnel.The tunnel form with adjacent double holes is the most common in the project.Due to the small distance between the tunnels,the interaction is more obvious,which brings difficulties to accurately solve the stress distribution on the tunnel boundary.According to the engineering practice experience,the boundary shape of the tunnel has a great influence on the stress field distribution around the hole.A suitable tunnel shape can significantly reduce the stress concentration around the tunnel,give full play to the performance of the material,and greatly improve the safety and economy of the project.However,most of the existing studies focus on a single circular or elliptical tunnel,and there are relatively few studies on other shapes of double tunnels or multiple tunnels.Therefore,it is of great significance to study the stress analysis method and hole shape optimization problem of double tunnels to improve the economy and safety of tunnels.In the case that the buried depth of the tunnel is much larger than the aperture,the problem can be simplified to an infinite domain problem.Based on the theory of complex variable function,this paper studies the stress analysis method and the hole shape optimization problem of two arbitrary shape tunnels under deep buried conditions.The main research contents are as follows :(1)The general form of the mapping function which can map the conformal mapping of two arbitrary shape tunnels in the infinite domain to the annular domain on the imaging plane and the general form of the mapping function which can map a circular tunnel with a common symmetry axis and an arbitrary shape tunnel in the infinite domain to a concentric ring are found.Based on the correspondence between the boundary points of the hole before and after mapping,the coordinates of the midpoint of the image plane are used as design variables,and the mapping function coefficients corresponding to the actual problem are solved by using the hybrid penalty function optimization method.The applicability of the mapping function proposed in this paper to the problem of infinite biconnected domains is verified by two examples.(2)The stress analytical solutions of two adjacent tunnels are obtained.Based on the plane elastic complex variable function method,the stress boundary conditions of two arbitrary tunnels in the infinite plane are established.The two analytical functions are transformed into Laurent series respectively,and the power series method is used to solve the Laurent series to obtain the stress analytical solution of the problem.Taking two dislocation horseshoe-shaped tunnels as an example,the analytical solution and ANSYS numerical solution are compared,which proves that the stress solution method in this paper is feasible.Taking two deep-buried adjacent horseshoe tunnels as an example,the influence of load and two-hole spacing on the stress distribution around the hole is studied.It is found that when the horizontal load is applied,the increase of the horizontal spacing between the two holes has little effect on the stress of the hole edge,and the increase of the vertical spacing increases the tensile stress at the position where the two holes are close to each other.Under the action of vertical uniform load,the increase of horizontal spacing significantly reduces the compressive stress at the position where the two holes are close to each other,and the increase of vertical spacing has little effect.When the far-field shear stress is applied,the maximum tensile stress and compressive stress at the hole edge increase with the increase of horizontal spacing,and the maximum compressive stress at the hole edge decreases with the increase of vertical spacing.(3)The hole shape optimization problem of new tunnel adjacent to existing tunnel is studied.Using the mapping function that can map a circular tunnel and an arbitrary shape tunnel in an infinite domain into a concentric ring,the mapping function coefficient is used as the design variable of the hole shape optimization problem.Based on two optimization criteria,the differential evolution algorithm is used to study the optimal hole shape and the distribution of shear stress at the hole edge of the new tunnel under different hole spacing,different hole pressure and different lateral pressure.It is found that the hole spacing and lateral pressure have a great influence on the optimal shape of the tunnel,and the pressure in the hole has a relatively small influence on the optimal hole shape,while the hole spacing,pressure in the hole and lateral stress have a great influence on the stress distribution on the tunnel boundary.