Mechanical Methods For Contact Analysis Of Rock-support System In Tunnel Engineering

Tunnel engineering is a giant system composed of complex geotechnical materials and various supporting structures,which has multi-field,multi-body,and multi-scale coupling effects.In this giant system,there are different types of contact surfaces and material interfaces,such as joints,bedding,and lining-rock interfaces.These interfaces are the important media for stress and deformation transfer between the supporting structures and surrounding rock.The continuous-discontinuous mechanical behavior at the contact interfaces will cause local stress concentration and seriously affect the overall mechanical response of the tunnel system.Therefore,the accurate analysis of supportrock coupling effect is significant in the precise design and safety control of tunnel engineering.In this paper,several numerical and analytical methods are proposed to analyze the contact effect between the surrounding rock and supporting structures,based on the complex variable method and computational contact mechanics theory,respectively.Furthermore,two mechanical analysis softwares are developed using these newly established methods and frontier theories in the mechanical field.The research results can provide an effective calculation method for the interaction analysis of the lining-rock system.The major contributions of this paper can be derived as follows:(1)Contact algorithms for the interaction analysis between various support structures and surrounding rock.The supporting structures commonly used in tunnel engineering,such as the pipe roof,anchor bolt,and reinforced member of the concrete lining,are simplified into the bar,beam,or plane elements,according to their geometric characteristics.On this basis,the line-to-solid and face-to-solid contact algorithms for the coupling analysis between supporting structures and rock mass are proposed.These contact algorithms use the dual Lagrange multiplier to impose the contact/coupling constraints between supporting structures and geotechnical materials.Therefore,the additional multiplier degrees of freedom can be condensed at a very low computational cost.The resulting finite element system matrix is positive-definite and well-conditioned.In this way,the disadvantage of the conventional algorithms deteriorating the condition number of the system matrix can be avoided.Compared with the existing methods,the proposed method does not suffer from unphysical stress oscillations,and thus has higher computational accuracy and stability.Finally,the above-mentioned methods are used to analyze the advanced support mechanism of the pipe roof,the bond-slip behavior of the rock-bolt interface,and the failure characteristics of different primary linings.(2)An efficient algorithm for cross-contact problems in the blocky rock tunnel.When using conventional finite element contact algorithms to analyze the cross-contact problem of blocky rock tunnels,the nonlinear iteration is usually difficult to converge,and the calculation accuracy is also unsatisfactory.To address these problems,an efficient contact algorithm based on the patch-by-patch decomposition is proposed.In this method,the rock surfaces are split into several contact patches,and the dual Lagrange multiplier space is defined independently on each contact patch.To avoid the over-constraint problem that often occurs in the conventional contact algorithm,a submatrix condensation method is proposed to eliminate the over-constraint conditions on each contact patch.In this way,the resulting system matrix is positive-definite and wellconditioned,which can greatly improve the efficiency of solving finite element system equations.Compared with the existing methods,the additional computational cost introduced by the proposed method can be negligible.Furthermore,this method also has high computational accuracy and efficiency.These features make it very suitable for large-scale contact problems in tunnel engineering.Finally,the above method is applied to systematically analyze the mechanical response of blocky rock tunnels under the crosscontact condition.(3)An analytical method for complex nonlinear contact behavior between tunnel linings and surrounding rock.According to the literature research,the contact behavior on the lining-rock interface is classified into friction contact,local non-contact,and loose contact.Subsequently,the corresponding analytical calculation model is established,and the basic mechanical equations of boundary and contact conditions are given by using the extended complex variable method.By introducing several theories of the numerical method into the complex variable method,this paper attempts to break through the bottleneck of existing analytical methods in solving nonlinear contact problems.In this way,the complementary function of the numerical method is introduced to determine the contact state of the lining-rock interface.Then,the mixed boundary value problem caused by contact conditions is solved by the point matching method.Furthermore,an efficient iterative method is also proposed to solve the current nonlinear contact problems.Based on the above contents,a complete analytical method for analyzing the complex contact behavior of the lining-rock system is thus established.Finally,the above method is applied to systematically analyze the mechanical response caused by the friction contact,local non-contact,and loose contact on the lining-rock interface.(4)Numerical and analytical software for contact analysis between the rock mass and supporting structures.Based on the line-to-solid,face-to-solid,and crosscontact algorithms established in this paper,a finite element software is developed.This software can perform three-dimensional contact/coupling analysis between the surrounding rock and various supporting structures,such as the pipe roof,anchor bolt,and concrete lining.Based on the nonlinear friction contact method and extended complex variable method proposed in this paper,an analytical calculation software is developed.This software can perform the mechanical analysis of the interaction between concrete linings and surrounding rock.