Mechanical Model Study Of Structural Stability For A Pressure Tunnel

Tunnel is a main underground structure and widely used for transportation, water passage, mining, petroleum, geophysical engineering practice and other purposes such as electricity or communication cable installation. With the development and upgrade of infrastructures, the demand for tunnel construction is increasing all over the world and the importance of the safety and economics of tunnel construction are recognized in tunnel engineering. In general, in relation to tunnel construction, it refers to three issues, which are: (1) maintaining stability and safety during construction; (2) minimizing unfavorable impact on adjacent structures; (3) performing the intended function over the life of a project. Among the issues, the first one is directly related to the appropriate design of tunnel support system.The excavation process reduces the confining stress to zero on the boundary of the opening. Thus, tunnel excavation always causes stress relief and deformation at the tunnel boundary before the liner is installed, which is well-known. The support system of underground facilities must be designed to withstand static overburden loads as well as to accommodate the additional deformations imposed by the earthquake induced motions. It is essential to understand the interaction between the liner and the surrounding geomaterial with the construction sequence taken into consideration. The real problem is that most of the analyses in the past completely misunderstand the history of stresses on the tunnel, which are essentially a "mechanical engineering" calculation in which one imagines an initially unstressed body (tunnel and liner) and then the stresses are applied at the outer boundaries. In fact of course certain pre-existing stresses exist in the ground. The tunnel is then opened, causing stress relief at the tunnel boundary (and consequent displacements), the liner is then installed, and finally the concrete of the liner cures. The effect of this construction sequence on the stresses in and around the liner was taken no account in the past. It is normal practice in the design of tunnel liners using surrounding geomaterial-support interaction models to consider that the geo-material behaves elasto-plastically. This means that under loading the material will first behave elastically, but when (and if) the elastic limit or plastic strength of the material (liner and surrounding geomaterial) is reached, then the material will start behaving plastically. In most of the existing elasto-plastic solutions, the first principal stress in the yield range was generally assumed to be the radial stress. In addition, the interaction between the liner and the surrounding geomaterial was not appropriately considered. Although the surrounding geomaterial-liner interaction based on elastic theory has been studied by numerous researchers. Furthermore, the variations of yield radius with the internal pressure acting on the inner boundary of the liner, the liner thickness and rigidity were not adequately discussed in the past literatures. In fact, certain pre-existing stresses exist in the geomaterail before the tunnel is excavated, which causes stress relief at the tunnel boundary (and consequent displacements). The liner is then installed, and finally the concrete of the liner cures. It is essentially important to understand how the surrounding geomaterial around a tunnel deform due to changes in stresses with the construction sequence taken into account properly. Moreover, the variations of the internal pressure acting on the inner boundary of the liner, the liner thickness and rigidity may result in the variations of the yield radius, the first principal stress and the boundary condition. Such factors should be properly considered in order to have a full picture of the elasto-plastic behavior for underground engineering problems.Many tunnels, including NATM tunnels, require two types of support: primary and secondary support. The role of the primary support is to withstand the loads that may arise during excavation. The secondary support has to withstand those loads that arise from tunnel operation, deterioration of ground strength and primary support with time, or from other changes of stresses in the ground around the tunnel. An important source for such additional loads is the change of groundwater flow around the tunnel. Water ingress into tunnels may be encountered as well in the construction phase of any tunnel as in the operation phase of hydraulic tunnels. Water ingress in the construction and in the operational phases may cause severe difficulties, downtimes and environmental impact by altering the groundwater regime and causing settlements of structures on the surface. To assess the related problems, the water ingress must be somehow predicted in advance. Even though some of the effects of pore water pressure on tunnel support have been investigated, there are many aspects that require further scrutiny, in particular a reasonable design criterion for tunnel support is needed where groundwater flow conditions are included.As an important analytical method, the complex variable method has been widely used to analyze problems associated with underground construction. The advantage of the complex variable method in solving elastic tunnelling problems is that both the stresses and displacements are solved simultaneously, enabling the solution of problems for various types of boundary conditions, and that the boundary conditions for the displacements and stresses are similar. An important issue is to find the deterministic relations between the stress-deformation conditions and the complex potentials. The work in the present paper can be summarized in the following:1. Four important properties for the complex potentials expressed in series expansion in the plane and anti-plane elastic fields is obtained by applying the basic equations of plane and anti-plane problems, combining the theory of analytical function, and recalling the feature of stress and deformation. Firstly, the complex potentials in the plane or anti-plane elastic fields are real functions when the stress states are symmetrical with regard to the origin. In addition, the complex potentials in the plane elastic field have real coefficient when the stress states are symmetrical with regard to the x-axis. Finally, the complex potentials in the anti-plane elastic field have imaginary coefficient when the stress states are anti-symmetric with regard to the x-axis. Then, based on the conclusions of the paper, some classic solutions are rearrived at, which indicates the results derived in this paper are right and simplify the process of constructing and solving the complex potential functions. The present conclusions provide an efficient tool to discovery the solutions in the sophisticated state.2. By applying the series expansion technique in the complex variable method established by Muskhelishvili, the plane elasticity problem for the stress and displacement field around a lined circular tunnel in conjunction with the consideration of misfit and interaction between the liner and the surrounding geomaterial is dealt with. The tunnel is assumed to be driven in a homogeneous and isotropic geomaterial. The coefficients in the Laurent series expansion of the stress functions are determined. The complex potentials in the liner and the surrounding geomaterial are explicitly derived, respectively. An elastic solution is obtained under a wide class of loading conditions, the main limitation being that internal stress sources (if any) are located in the geomaterial. Loading by misfit alone, by in situ stresses, by far-field shear stresses, and by a concentrated force, are explicitly treated as special cases. As an example, the case of a lined circular tunnel located in an isotropic initial stress field but subjected to uniform internal pressure is numerically considered. Numerical results indicate that the installation of tunnel liner can reduce the influences of the tunnel excavation on the in situ displacement and stress fields. However, the relative thickness and rigidity of the liner should be in an appropriate range. In addition, the effect of the tunnel excavation upon the displacement field is more significant than that upon the stress field. As far as the stress field in the surrounding geomaterial is concerned, when the ratio between the cover depth of tunnel and the tunnel radius is larger than 5, the results for the stress field in the paper are applicable. When the ratio between the tunnel depth and the tunnel radius is larger than 20, the results are applicable for the displacement field.3. The elasto-plastic problem for the stress fields around a lined circular tunnel is investigated in this paper. An appropriate mechanical model considering the stress relief and the installation of the liner is proposed to model the tunnel construction sequence. By considering the continuity conditions for the stresses and displacements along the boundaries, the complex potentials in the liner and the surrounding geomaterial are explicitly derived, respectively. Based on the linear Mohr-Coulomb (M-C) yield criterion, for two cases that the first principal stress is the radial stress or the tangential stress, respectively, the stress solutions are given when plastic deformation occurs in the liner and/or the surrounding geomaterial. Numerical results indicate that the influences of the internal pressure, liner thickness and rigidity on the yield range are significant. The first principal stress may vary with the variations of the above parameters and is not always the radial stress. In addition, it is shown that the variations of stresses in the surrounding geomaterial intensively rely on the relative liner rigidity, thickness and distance to the tunnel axis when the ratio between the distance of these points under investigation to the tunnel axis and the outer radius of the liner ranges from 1 to 2. Classical Fenner's solution and Lame's solution can be considered as the special cases of the present solutions.4. It is assumed that all the influence factors surrounding deep-buried circle tunnel are axially symmetrical. Firstly, the solution of fluid flow field is resolved. Secondly, in conjunction with two cases of the material character of the liner, i.e., a permeable liner or an impermeable liner, analytical solutions of elastic stress and displacement are obtained by considering the seepage force in the surrounding geomaterial as a body force. The proposed solution together with the analytical solution for axi-symmetric loading of an annular ring representing a liner are used to explain the fundamental differences in support loading obtained for various hydro-mechanical conditions. These conditions involve excavating the tunnel with a permeable liner, with and without removal of water from the tunnel, excavating the tunnel with an impermeable liner, with subsequent drainage of water in the ground around the tunnel, etc. In addition, the results of the liner as a permeable material are compared with those of the liner as an impermeable material.