Elastic-Plastic Analytical Solutions Of The Any Common Shaped Tunnels

Tunnel engineering occupies an important position in the country’s development strategy.The stability of the surrounding rock of the tunnel and the safety of the supporting structure are the main problems.Surrounding rock is not only a component of the tunnel system,but also the main load source,and it is also the main component of the load-bearing structure.The surrounding rock undergoes secondary stress redistribution after the tunnel excavated.When the stress in some areas of the surrounding rock exceeds the strength of the rock mass,the surrounding rock will enter a state of plastic or brittle failure.Analytical solution is the most powerful and direct tool to analyze this kind of tunnel engineering problems.Therefore,from the analytical solution point of view,this paper studies the elastic and elastoplastic solutions of typical tunnel even any common shaped tunnels under the(non-)axisymmetric external loads.The main conclusions are as follows:(1)The four basic elastic solutions of the circular tunnels under the(non-)axisymmetric external loads are improved.The elastic solutions under the non-axisymmetric external loads with the different type internal loads are deduced.The direct solution and the superposition solution of circular pressure tunnel under the(non-)axisymmetric external loads are constructed.(2)The modified Fenner formula and the analytical formula of stability evaluation under the(non-)axisymmetric external loads are deduced.A variety of expressions of the MC yield criterion under the(non-)axisymmetric external loads are deduced.The classical elastoplastic solutions of the circular tunnel under the axisymmetric conditions are compared and developed.The existing plastic zone approximate solution and the plastic radius solution under the(non-)axisymmetric external loads are revised,and three new plastic zone stress solutions,one plastic radius approximate solution and two direct solutions are proposed.The elastoplastic solutions of the circular tunnel under the(non-)axisymmetric external loads with or without inner loads are derived.(3)The elastic solutions of any common shaped tunnel are deduced under the non-axisymmetric external loads.The orthogonal curvilinear coordinates direct solution method of the circular tunnel under the non-axisymmetric external loads is deduced.And the orthogonal curvilinear coordinates indirect solution method,rectangular coordinates direct solution method and the unit circle inverse solution method are proposed for the circular tunnel under the non-axisymmetric external loads.The orthogonal curvilinear coordinates direct solution method is deduced and the new ideas of unit circle inverse solution and series mapping method are proposed,for the ellipse,rectangle,and any common shaped tunnel under the non-axisymmetric external loads.(4)The elastic-plastic solutions of any common shaped tunnel are deduced under the non-axisymmetric external loads.Based on the modified Fenner formula under the(non-)axisymmetric external loads and the idea of the unit circle series inverse solution,the elastic-plastic solutions of the circular,elliptical,rectangular,gate and any common shaped tunnel are derived.And a new idea of finding the elastoplastic boundary mapping function is proposed based on the idea of parallel mapping.The above analytical solutions are verified by numerical experiments,and the two results are in good agreement.It shows that the analytical derivation has high accuracy and reliability,and it can provide accurate theoretical basis for the research,analysis and design of underground tunnel engineering.