Analytical Method For Elastic-plastic Analysis Of Underground Tunnels

Tunnel is a very common structure that occupies an important position in underground engineering.Tunnels can be used for water diversion and transportation,passage of pedestrians and vehicles and transportation of coal and other ore resources,which have played an irreplaceable role in many super projects in China.In recent years,an important trend in the development of tunnels and underground projects is the increasing buried depth,and the number of tunnel is gradually increasing.However,the mechanical behavior of deep rocks is significantly different from that of shallow rocks.In particular,the tunnel excavated in the deep will bear high in-situ stress,which makes the stability problem of surrounding rock more prominent.When some rock masses around the tunnels yield without causing the instability of the overall structure of the tunnel,plastic zones will be generated in a certain range around the tunnels.The distribution of plastic zones can provide a reference for the stability assessment of surrounding rock and the quantitative design of tunnel support.A characteristic of rock mechanics is that theoretical research often lags behind all kinds of engineering practice,which leads to a certain blindness in construction.Therefore,the analytical study of elastoplastic analysis of underground deep-buried tunnels not only promotes the theoretical development of rock mechanics,but also may provide an effective tool to guide engineering practice.In this thesis,it is considered that the surrounding rock is a homogeneous and isotropic material and obeys the Mohr-Coulomb criterion when the surrounding rock is yielding,and the stress-strain relationship of the surrounding rock is simplified into an ideal elastic-plastic model.In most cases,the problem of underground tunnel can be simplified as a plane strain problem in an infinite domain.Using the complex variable method,the inverse problem of determining the elastic-plastic interface is transformed into the an optimization problem for finding the conformal mapping function.The general method for establishing the basic equations involving the mapping function coefficients is found,and it is found that the differential evolution(DE)algorithm with the mapping function coefficients as the design variables can be applied to obtain a solution with sufficient accuracy.Finally,the effects of various parameters on the shape and size of plastic zone are analyzed,and the correctness of the proposed analytical solution or semi-analytical solution is verified by FLAC3D finite difference software.The main research results obtained in this thesis are as follows:(1)The plastic zone that cannot completely surround an underground circular tunnel in great depth is studied when the tunnel is subjected to non-axisymmetric in-situ stresses.Using the conformal transformation tool in the complex variable method,the non-circular elastic region with complex boundary shape on the physical plane can be conformally mapped to the outer region of the unit circle with simple boundary shape on the image plane.The combinations of elastic stress can be given by two analytical functions.The nonlinear equations containing the mapping function coefficients are established by considering both the stress continuity condition along the elastoplastic interface and the stress boundary condition along the elastic part of the tunnel,and an analytical solution for determining such non-closed elastic-plastic interface is obtained.The results show that the cohesion and the internal friction angle of rock have a significant effect on the plastic zone,but the effect of the lateral pressure coefficient λ(λ<1)on the plastic zone is weak.The threshold values of λ for different parameters of rock are all greater than 1/3 when there is no tensile stress at the tunnel edge.(2)The analytical method for determining the plastic zones around twin circular tunnels of arbitrary size that are arranged horizontally and deep-buried is proposed for the first time.The premise is that the plastic zone around each tunnel can completely enclose the tunnel wall and the two plastic zones are not connected yet.It is clarified that the stress distribution in the plastic zones around twin circular tunnels is the same as that of single circular tunnel.The stress solution in the elastic zone can be obtained by mapping the elastic zone on the physical plane onto an annular region on the image plane by the conformal transformation in two steps.On the basis of the stress continuity conditions along the two elastoplastic interfaces,the nonlinear equations about the mapping function coefficients are established.The research shows that the tunnel spacing has a great effect on the shape and size of the plastic zones.When the tunnel spacing is large,the influence between the two tunnels can be ignored,but the required distance also depends on the rock parameters and the level of in-situ stress.When the tunnel spacing is small,the two plastic zones tend to connect with each other,so as to develop into a whole.(3)For a non-circular tunnel with arbitrary section shape,the plastic stress field is numerically solved by using the slip line theory.The error analysis of the numerical solution of the plastic stress and the influence of the mesh size on the calculation accuracy are carried out.The elastic stress field is also given according to the complex variable theory.According to the stress continuity condition along the elastic-plastic interface,a set of nonlinear equations for solving the mapping function coefficients is established.Using the obtained semi-analytical solution,the law of the plastic zone around the elliptical hole affected by various parameters is analyzed in detail,and the distribution law of the plastic zone around other non-circular tunnels is revealed.The results show that the thickness of the plastic zone around the harmonic tunnel obtained based on the elastic theory can not be uniform after it enters the plastic state.There is no guarantee that a harmonic tunnel will be more stable,because the plastic zone is easy to have a rapid development along the minor axis but difficult to expands along the major axis.The sizes of the plastic zone in two directions will be greatly different,especially for larger in-situ stresses.The thickness of plastic zone formed around various non-circular tunnels in the zone with larger elastic stress concentration is smaller.