Research On Analytical Method Of Stress And Displacement For Deep Buried Tunnels With Arbitrary Shaped Sections Under Non-Axisymmetric In-situ Stress Field

The analysis of stress and deformation characteristics of surrounding rock for deep-buried tunnels with arbitrary cross sections under nonaxisymmetric in-situ field is a very important problem in underground engineering.Due to the complexity of the problem,most of the existing research uses engineering analogy method and numerical simulation technology,and the theoretical analysis is usually based on ideal simplified assumptions,which make the theoretical research lag behind the actual engineering.It is mainly reflected in the following three aspects: firstly,the in-situ stress field of deepburied tunnels in practical engineering is not completely uniform hydrostatic pressure field.While in the present theoretical research,it is usually difficult to achieve analytical solutions on the elastic-plastic stress and displacement of rock mass surrounding deep-buried tunnels under non-axisymmetric in-situ stress field;Secondly,the yield failure mechanism of surrounding rock in engineering is diverse,but at present,it is relatively difficult to achieve analytical characterization for the deformation and yield mechanism of surrounding rock with various elastoplastic constitutive models under nonaxisymmetric in-situ stress field;Third,nowadays,highway(railway)tunnels are mostly built in the form of single-hole and double-hole tunnels,but there are few theoretical research at present on the theoretical calculation of elasticplastic stress and convergence displacement for deep-buried single-hole and double-hole tunnels with arbitrary cross sections in non-axisymmetric in-situ stress field.The lack and limitation of the above theoretical research may bring hidden dangers for the prediction of tunnel convergence deformation,the evaluation for plastic zone of surrounding rock,the determination of tunnel critical support pressure,the determination of safety clearance of double-hole tunnels,the design of tunnel support structure and the determination of installation time.Therefore,it is of great theoretical and practical significance to study the analytical method of stress and displacement of deep-buried tunnels with arbitrary cross sections in non-asymmetric in-situ stress field.The main research contents and achievements of this paper are summarized as follows:(1)The adaptive stress increment method for stress-displacement analysis of strain-softening surrounding rock in axisymmetric in-situ stress field under five different principal stress states of out-of-plane stress is presented;Five selfequilibrium conditions of passive anchors are reconstructed considering the distribution of neutral points and neutral length.Combining with the proposed adaptive stress increment method,an adaptive plastic iteration method for strain-softening surrounding rock,which considering the coupling and decoupling effects between the passive bolts and surrounding rock,is formed;Based on the convergence-confinement theory,the boundary conditions of the composite lining support are embedded into the developed plastic iterative model.Finally the comprehensive numerical solutions for the stress and displacement of strain-softening surrounding rock considering the influence of out-of-plane strss,the reinforcement of passive bolts and the support of composite lining is realized.(2)The stress-displacement calculation method of strain-softening surrounding rock in axisymmetric in-situ stress field are presented based on the modified GZZ criterion,considering both associated and non-associated flow rules,and hydraulic–mechanical coupling.The numerical iterative and trialerror methods are embedded in the basic stress increment method,so that the global convergence for the numerical solution can be achieved with aribrary values of rock mass strength parameters;Finally,the theoretical analysis method for water-rich strain-softening surrounding rock in axisymmetric in-situ stress field considering lining support support is proposed based on the modified 3D G-H-B criterion.(3)Considering the influence of intermediate principal stress,biaxial insitu stress conditions and non-associated flow rule,semi-analytical solutions for stress and displacement of elastic-brittle-plastic surrounding rock for deepburied circular tunnels is proposed under biaxial in-situ stress field,using perturbation method,novel numerical iteration and stress update algorithm;Based on the proposed semi-analytical solutions,a new equivalent circular method suitable for the biaxial in-situ stress field is developed to solve the problem of the equivalent prediction for plastic radius and convergence displacement of non-circular tunnels.(4)Based on M-C criterion,the arbitrary-order perturbation solutions for plastic stress analysis of brittle-plastic surrounding rock of non-circular tunnels in biaxial in-situ stress field is established for the first time.For elastic stress analysis,a new undetermined coefficient method is proposed to quickly determine the stress function and plastic radius with any order in the elastic zone.The theoretical calculation method is extended to the elastic-plastic analysis of G-H-B surrounding rock through equivalent friction angle and equivalent cohesive strength;Based on the original perturbation solution,the extended perturbation solution is proposed to further expand the applicable range of the perturbation solutions with respect to the small parameter.At the same time,a new equivalent elliptical section method is constructed,which makes the developed perturbation solutions can be applicable to aribraryshaped tunnels.(5)The determination method for contour function of arbitrary-shaped tunnels and the boundary stress conversion equation under arbitrary unloading conditions are proposed;The theoretical calculation method for solving the plastic stress of surrounding rock of arbitrary-shaped tunnels under M-C and GH-B criteria is established through slip line method,finite difference method and numerical iterative method;Based on the discrete solving results for plastic stress based on slip line theory,the interpolation functional representation method for the plastic stress around arbitrary-shaped tunnels with arbitrary unloading conditions is constructed by the three-dimensional interpolation method;The stress continuity condition on the elastoplastic interface of the elastic-brittle-plastic rock surrounding double-hole non-circular tunnels is defined.By embedding the numerical iteration calculation into the differential evolution algorithm(i.e.,DE algorithm),the stress analysis for elastic-brittleplastic surrounding rock of the double-hole tunnels is achieved.The analytical expressions for the plastic displacements of double-hole circular tunnels are presented based on non-associated flow rule in the biaxial in-situ stress field.Combined with Schwarz alternating principle,the new method for approximately determining the elastic-plastic convergence displacement of double-hole circular tunnels is proposed.There are 87 figures,3 tables and 145 references.