The convergence-confinement method is one approach to the analysis of ground-support interaction. The conventional plane strain convergence curve cannot consider the 3-D arching effect occurring ahead of the face and the fast stress reduction in the unsupported section. The final equilibrium stresses and displacements on the liner from the 3-D analyses are compared with those obtained from the 2-D analyses. The difference between the final radial stresses from the 2-D analyses with the confinement curve and that from the 3-D could be large depending on construction procedures of the tunnel.


The current concepts for the design of tunnel supports recognize the behavior of any system as a complex function of the ground-liner interaction rather than as a function of assumed loading diagrams. The convergence-confinement method (CCM) is one approach to the analysis of ground-liner interaction. The convergence curve for the ground shows the radial stress vs, radial displacement in response to the insertion of the excavated stress-free boundary in the original in-situ stress field. The confinement curve for the support represents the response of the liner installed to control these deformations which results in pressure build up within the liner until an equilibrium point is reached. Therefore, the convergence-confinement method requires an understanding of the behavior of the ground to determine the soil convergence related to the applied confining pressure and the liner behavior to find the confining pressure acting on the lining in terms of deformation. The validation and limitation of convergence-confinement method are investigated in this study using the convergence- confinement curves obtained from 2-D and 3-D finite clement analyses.


An Experimental tunnel was chosen for the present analyses because of the availability of considerable field measurements of tunnel performance as well as soil parameters. SIGMA/W, developed by GEO-SLOPE International Ltd., was used for the two dimensional finite element analysis. SIGMA\V is a finite element program that can be used to conduct two-dimensional or axisymmetric stress and deformation analyses of earth structures. The finite element meshes used for the analyses are shown in Figure 1. Eight-noded elements were used with a total number of 122 elements and 411 nodes. The elements in the tunnel section were deactivated in one step to simulate the excavation. The internal forces, which are equal to in-situ stresses but opposite direction, were applied to the nodes along the excavated tunnel boundary to prevent any soil movement due to excavation. The internal forces were reduced to zero in 11 different steps with a 10% deduction of forces for each step. Three-dimensional finite element analyses were performed using the program SAGE developed by Chan (1985) at the University of Alberta, Canada. A linear elastic model was used for the analyses with an uniform in-situ stress ratio. An elastic modulus of 30,000 KPa with Poisson's ratio of 0.4 were used based on the results of a pressuremeter test obtained by Thomson et al. (1982). The use of an elastic model has been considered as oversimplification of soil behavior.

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