Interval Analysis Of Mechanical State For Tunnel Lining Based On Affine Arithmetic

Along with the large-scale development and construction of the undergroundengineering, How to meet the safe requirement of the underground structural is acritical issue.Because of the rock formation is very complex, as well as the limited ofthe human’s cognitive, it lead to only provide a interval force of the tunnel lining.Onthe characerstics of the underground interval model is selected to analysis thestructural. However, it is inevitable exsited the range expansion.In order to limit therange expansion of the correlation result, the affine architive is introduced to suppressthe range expansion.⑴Firstly,the basic theory of the interval architive,the interval finite elementand affine architive is introduced. On the range expansion caused by the finiteelement solution process several solving interval finite element solution is briefintroduced,for example,the different orders of operation,the truncation approach andthe interval perturbation method and so on.In the end,sub-interval perturbationmethod is selected for solving interval finite element method. however,sub-intervalperturbation method exists the interval extension in the process of the integratedstiffness matrix, and affine arithmetic can inhibit interval extension. Therefore, theaffine arithmetic is introduced to integrate stiffness matrix, and it is formed thesubinterval perturbation method based on affine architive. In this paper, thecorresponding calculation program based on the finite element is written by MATLABlanguage.⑵Because the parameter range of the variation in the underground engineeringis more large than the others,In order to satisfy the convergence condition, the workof the caculation is larger than befor.So the uniform experimental design on theinterval combination design is introduced to reduce the work.The example of the sixtrusses is caculated to verify the feasibility of this method.⑶The elastic support method of the underground engineering has the advantageof wider application and simple calculation.This method is selected as the intervalfinite element calculation of the mechanical model.Then, the subinterval perturbationbased on affine architive is applcated in the underground.Take the example of crosssection of a tunnel,different methods is compared.The result show this method ismore efficient than other methods. ⑷Affine architive based on matrix form can effectively avoid the limitations ofthe affine architive itself by matrix form depicts.The response surface method canprovide structure function which is suitable for the affine form by matrix.Affinearchitive and surface method is combined, and then this paper presents an easy way tosolve the tunnel lining interval force in the application of the response surface methodfor solving the structure function.Uniform experimental design in order to obtain thesample points is introduced and the response surface method is used to fit thestructure function.Verified instance of a project,it is show though the combiniton theinterval forces can easily deal with in the underground.