When the amount of field measurement data is not enough to describe the whole behaviour of rocks around a tunnel, computer analysis can be used to complement that information. For basic procedure of numerical analysis using BEM, vertical displacements of the roof of large disc-shaped opening were analyzed. Analytical solutions for displacements around the disc-shaped opening were compared with numerical BEM solutions, especially the displacement discontinuity method. This paper presents an example which introduces the calculation method for the relaxed zone in rocks, with the above numerical analysis using data from field measurements. Taking into account the in-situ condition of rocks in the BEM analysis, an empirical failure criterion for rock was used. After determination of the relaxed zone by measurement at certain locations, it is shown that the calculated relaxed zone coincides with the above result. Accordingly, the complete relaxed area of rocks around a tunnel can be determined.
The main purpose of field measurements in rock mechanics is to determine behaviour of rocks around openings. Of various measuring techniques developed, monitoring of displacements has proven to be a simple and useful method to estimate the stability of a tunnel and the relaxed boundary in rocks. The latter becomes an especially important parameter for designing the support system.
After estimation of the relaxed zone from measurements at certain locations around a tunnel, the relaxed state in rocks can be established by computer analysis using the finite element method (FEM) or the boundary element method (BEM).
Improvements to FEM and BEM have been de- Veloping (Banerjee and Butterfield, 1979; Brebbia, 1978; Crouch and Starfield, 1983). Particularly, the displacement discontinuity method of BEM requires a much smaller system Of equations to be solved than the system needed to solve the same boundary value problem by FEM. The numerical solution analyzed by BEM is based on the analytical solutions that have already been obtained for simple singular problems in such a way as to Satisfy, approximately, the specified bOUndary conditions at each element on the boundary line. The analysis of rock behavior requires data from in-situ measurements, adequate selection for input data, and modelling of the numerical analysis.
For the investigation, analytical solutions of the vertical displacement of the roof of a large disc-shaped opening with much smaller a vertical than horizontal dimension were evaluated for various ratios of the vertical dimension to the horizontal dimension. Analytical solutions of the above opening were developed with those of the numerical BEM solutions and the applicability of BEM was examined.
Finally in this paper, an example introducing the combined techniques of field measurements with computer analysis for the relaxed zone in rocks is presented.
In monitoring the displacement and convergence of the rock surrounding a tunnel, a single point rod extensometer and a tape extensometer as shown in figure 1, both of which are commercially available instruments, were used.
